U.S. patent application number 11/390250 was filed with the patent office on 2006-07-27 for system and methods for optimized drug delivery and progression of diseased and normal cells.
This patent application is currently assigned to OPTIMATA. Invention is credited to Zvia Agur, Sarel Fleishmann, Kirill Skomorovski, Moshe Vardi.
Application Number | 20060167637 11/390250 |
Document ID | / |
Family ID | 24774975 |
Filed Date | 2006-07-27 |
United States Patent
Application |
20060167637 |
Kind Code |
A1 |
Agur; Zvia ; et al. |
July 27, 2006 |
System and methods for optimized drug delivery and progression of
diseased and normal cells
Abstract
Systems for recommending an optimal treatment protocol for a
specific individual are disclosed. The systems comprise generally a
system model, a plurality of treatment protocols, a system model
modifier, wherein said system model is modified by the system model
modifier based on parameters specific to the individual; and a
selector to select an optimal treatment protocol from said
plurality of treatment protocols based on the modified system
model. Systems embodying the above techniques but for a general
patient are also disclosed. Systems for a general patient and an
individual for various specific diseases are disclosed. Methods and
computer program products embodying the above techniques are also
disclosed.
Inventors: |
Agur; Zvia; (Tel Aviv,
IL) ; Fleishmann; Sarel; (Nes-Ziona, IL) ;
Skomorovski; Kirill; (Rehovot, IL) ; Vardi;
Moshe; (Rehovot, IL) |
Correspondence
Address: |
SUGHRUE MION, PLLC
2100 PENNSYLVANIA AVENUE, N.W.
SUITE 800
WASHINGTON
DC
20037
US
|
Assignee: |
OPTIMATA
|
Family ID: |
24774975 |
Appl. No.: |
11/390250 |
Filed: |
March 28, 2006 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10192001 |
Jul 10, 2002 |
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11390250 |
Mar 28, 2006 |
|
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09691053 |
Oct 19, 2000 |
6871171 |
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10192001 |
Jul 10, 2002 |
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Current U.S.
Class: |
702/19 ; 128/898;
703/11 |
Current CPC
Class: |
A61P 43/00 20180101;
G16H 20/10 20180101; G16H 50/50 20180101 |
Class at
Publication: |
702/019 ;
128/898; 703/011 |
International
Class: |
G06G 7/48 20060101
G06G007/48; G06F 19/00 20060101 G06F019/00; A61B 19/00 20060101
A61B019/00 |
Claims
1. A computer system for recommending an optimal treatment protocol
for an individual, said system interfacing with the computer and
said system further comprising: a system model; a treatment
protocol generator adapted to generate a plurality of treatment
protocols; a system model modifier, wherein said system model
modifier is adapted to modify said system model based on parameters
specific to the individual; and a selector adapted to select an
optimal treatment protocol from said plurality of treatment
protocols based on the modified system model.
2. The system of claim 1 wherein the system model further
comprises: a biological process model; and a treatment model that
is adapted to model effects of a treatment on said biological
process.
3. The system of claim 2, wherein said biological process model
comprises mathematical models for biological processes affecting
healthy cell populations and biological processes affecting
diseased cell populations with at least one disease.
4. The system of claim 3 wherein said healthy cell populations
include bone-marrow cells and host tissue cells that are affected
by said treatment model.
5. The system of claim 3 wherein said diseased cell populations is
one of cancer cells, and diseased bone-marrow cells.
6. The system of claim 2, wherein said treatment model comprises
treatment specific processes that affect cell populations.
7. The system of claim 6 wherein said treatment specific process
comprises interactions and associated biological processes
involving one of a group consisting of pharmacokinetic interactions
and processes, pharmacodynamic interactions and processes,
cytostatic interactions and processes, cytotoxic interactions and
processes, and methods of affecting cell biology and causing cell
death.
8. The system of claim 1 wherein, said parameters specific to the
individual includes one selected from a group consisting of
parameters related to biological process dynamics, patient specific
drug pharmacokinetics, pharmacodynamics, and dynamics of
dose-limiting host tissues.
9. The method of claim 8, wherein said parameters related to
biological process' dynamics comprise age, weight, gender, blood
picture, desired length of treatment protocol, previous reaction to
treatment, molecular markers, genetic markers, pathologic specifics
and cytologic specifics.
10. The system of claim 1, wherein the selector is adapted to
incorporate user-specific parameters in performing selection.
11. The system of claim 10 wherein said selector is adapted to
incorporate user-specific parameters by using a fitness
function.
12. The system of claim 11 wherein said fitness function adapted to
incorporate at least one parameter selected from a group consisting
of patient survival, time to death, time to reach a specified
disease stage, tumor load, pathogen load, cytotoxicity, side
effects, quality of life, cost of treatment, and pain.
13. The system of claim 12, wherein the system is adapted to
receive user input for specific coefficients for said at least one
parameter and the system is further adapted to adjust the fitness
function to satisfy the user's goals.
14. The system of claim 10, wherein the user-specific parameters
are based on a user, said user being a medical doctor.
15. The system of claim 10, wherein the user-specific parameters
are based on a user, said user being a scientist.
16. The system of claim 10, wherein the user-specific parameters
are based on a user, said user being a drug developer.
17. The system of claim 1 wherein said system is adapted to
consider cytotoxic effects during selection of treatment
protocols.
18. The system of claim 1 wherein said system is adapted to
consider drug efficacy during selection of treatment protocols.
19. The system of claim 1, wherein the selector is adapted to use
operation research methods for the selection.
20. The system of claim 1, wherein the selector further comprises
heuristics, said selector being adapted to use the heuristics for
searching and selection.
21. The system of claim 20 wherein, said heuristics comprise
computational feasibility.
22. The system of claim 1 wherein said recommendation comprises a
combination of disease and treatment strategy, wherein said
treatment strategy includes at least one of types of treatment,
device, drug combination, treatment schedule and dosage.
23. The system of claim 1, wherein, said system is adapted to be
implemented over a distributed computing system.
24. The system of claim 23, wherein the distributed computing
system is the Internet.
25. The system of claim 23, wherein the system is adapted to be
used remotely by a user.
26. A computer system for recommending an optimal treatment
protocol for a general patient, said system interfacing with the
computer and said system further comprising: a system model; a
treatment protocol generator adapted to generate a plurality of
treatment protocols; and a selector to select an optimal treatment
protocol from said plurality of treatment protocols based on the
system model.
27. The system of claim 26 wherein the system model further
comprises: a biological process model; and a treatment model that
is adapted to model the effects of a treatment on said biological
process.
28. The system of claim 27, wherein said biological process model
comprises mathematical models for biological processes affecting
healthy cell populations and biological processes affecting
diseased cell populations with at least one disease.
29. The system of claim 28 wherein said healthy cell populations
include bone-marrow cells and host tissue cells that are affected
by said treatment model.
30. The system of claim 28 wherein said diseased cell populations
is one of cancer cells, and diseased bone-marrow cells.
31. The system of claim 27, wherein said treatment model comprises
treatment specific processes that affect cell populations.
32. The system of claim 31 wherein said treatment specific process
comprises interactions and associated biological processes
involving one of a group consisting of pharmacokinetic interactions
and processes, pharmacodynamic interactions and processes,
cytostatic interactions and processes, cytotoxic interactions and
processes, and methods of affecting cell biology and causing cell
death.
33. The system of claim 26, wherein the selector is adapted to
incorporate user-specific parameters in performing selection.
34. The system of claim 33 wherein said selector is adapted to
incorporate user-specific parameters by using a fitness
function.
35. The system of claim 34 wherein said fitness function is a
function of at least one parameter selected from a group consisting
of patient survival, time to death, time to reach a specified
disease stage, tumor load, pathogen load, cytotoxicity, side
effects, quality of life, cost of treatment and pain.
36. The system of claim 35, wherein the system is adapted to
receive user input for specific coefficients for said at least one
parameter and the system is further adapted to adjust the fitness
function to satisfy the user's goals.
37. The system of claim 33, wherein the user-specific parameters
are based on a user, said user being a medical doctor.
38. The system of claim 33, wherein the user-specific parameters
are based on a user, said user being a scientist.
39. The system of claim 33, wherein the user-specific parameters
are based on a user, said user being a drug developer.
40. The system of claim 26 wherein said system is adapted to
consider cytotoxic effects during selection of treatment
protocols.
41. The system of claim 26 wherein said system is adapted to
consider drug efficacy during selection of treatment protocols.
42. The system of claim 26, wherein the selector is adapted to use
operation research methods for the selection.
43. The system of claim 26, wherein the selector further comprises
heuristics, said selector being adapted to use the heuristics for
searching and selection.
44. The system of claim 43 wherein, said heuristics comprise
computational feasibility.
45. The system of claim 26 wherein said recommendation is a
combination of disease and treatment strategy, wherein said
treatment strategy includes at least one of types of treatment,
device, drug combination, treatment schedule and dosage.
46. The system of claim 26, wherein, said system is adapted to be
implemented over a distributed computing system.
47. The system of claim 46, wherein the distributed computing
system is the Internet.
48. The system of claim 46, wherein the system is adapted to be
used remotely by a user.
49. The system of claim 48, wherein the remote system is a
telephone
50. A computer-implemented method of recommending an optimal
treatment protocol for an individual comprising: creating a system
model; enumerating a plurality of treatment protocols; modifying
the system model based on parameters specific to the individual;
selecting an optimal treatment protocol from said plurality of
treatment protocols based on the modified system model and
recommending said optimal treatment.
51. The method of claim 50 wherein the step of creating the system
model further comprises: modelling a biological process; and
modelling effects of a treatment on said biological process.
52. The method of claim 51, wherein said modelling of biological
processes is done by mathematically modelling biological processes
affecting healthy cell populations and mathematically modelling
biological processes affecting diseased cell populations with at
least one disease.
53. The method of claim 52 wherein said healthy cell populations
include bone-marrow cells and host tissue cells that are affected
by said treatment model.
54. The method of claim 52 wherein said diseased cell populations
is one of cancer cells, and diseased bone-marrow cells.
55. The method of claim 51, wherein said treatment models comprise
treatment specific processes that affect cell populations.
56. The method of claim 55 wherein said treatment specific process
is interactions and associated biological processes involving one
of a group consisting of pharmacokinetic interactions and
processes, pharmacodynamic interactions and processes, cytostatic
interactions and processes, cytotoxic interactions and processes,
and methods of affecting cell biology and causing cell death.
57. The method of claim 50 wherein, said parameters specific to the
individual include one or more selected from a group consisting of
parameters related to biological process dynamics, patient specific
drug pharmacokinetics, pharmacodynamics and dynamics of
dose-limiting host tissues.
58. The method of claim 57, wherein said parameters related to
biological process' dynamics comprise age, weight, gender, blood
picture, desired length of treatment protocol, previous reaction to
treatment, molecular markers, genetic markers, pathologic specifics
and cytologic specifics.
59. The method of claim 50, wherein user-specific parameters are
used in selecting the optimal treatment.
60. The method of claim 59 wherein a fitness function is used to
perform the selection.
61. The method of claim 60 wherein said fitness function
incorporates at least one parameter selected from a group
consisting patient survival, time to death, time to reach a
specified disease stage, tumor load, pathogen load, cytotoxicity,
side effects, quality of life, cost of treatment and pain.
62. The method of claim 61, wherein a user can input specific
coefficients for said at least one parameter to adjust the fitness
function to satisfy the user's goals.
63. The method of claim 59, wherein the user-specific parameters
are based on a user, said user being a medical doctor.
64. The method of claim 59, wherein the user-specific parameters
are based on a user, said user being a scientist.
65. The method of claim 59, wherein the user-specific parameters
are based on a user, said user being a drug developer.
66. The method of claim 50 wherein said system is adapted to
consider cytotoxic effects during selection of treatment
protocols.
67. The method of claim 50 wherein said system is adapted to
consider drug efficacy during selection of treatment protocols.
68. The method of claim 50, wherein operation research techniques
are used in performing the selection.
69. The method of claim 50, wherein heuristics are used to perform
searching and selection.
70. The method of claim 69 wherein, said heuristics comprise
computational feasibility.
71. The method of claim 50 wherein said recommendation is a
combination of disease and treatment strategy, wherein said
treatment strategy includes at least one of types of treatment,
device, drug combination, treatment schedule and dosage.
72. A computer-implemented method of recommending an optimal
treatment protocol for a general patient comprising: creating a
system model; enumerating a plurality of treatment protocols;
selecting an optimal treatment protocol from said plurality of
treatment protocols based on the modified system model; and
recommending said optimal treatment.
73. The method of claim 72 wherein the step of creating the system
model further comprises: modelling a biological process; and
modelling effects of a treatment on said biological process.
74. The method of claim 73, wherein said modelling of biological
processes is done by mathematically modelling biological processes
affecting healthy cell populations and mathematically modelling
biological processes affecting diseased cell populations with at
least one disease.
75. The method of claim 74 wherein said healthy cell populations
include bone-marrow cells and host tissue cells that are affected
by said treatment model.
76. The method of claim 74 wherein said diseased cell populations
with at least one disease is one of cancer cells, and diseased
bone-marrow cells.
77. The method of claim 73, wherein said treatment models comprise
treatment specific processes that affect cell populations.
78. The method of claim 77 wherein said treatment specific process
is interactions and associated biological processes involving one
of a group consisting of pharmacokinetic interactions and
processes, pharmacodynamic interactions and processes, cytostatic
interactions and processes, cytotoxic interactions and processes,
and methods of affecting cell biology and causing cell death.
79. The method of claim 72, wherein user-specific parameters are
used in selecting the optimal treatment.
80. The method of claim 79 wherein a fitness function is used to
perform the selection.
81. The method of claim 80 wherein said fitness function
incorporates at least one parameter selected from a group
consisting of patient survival, time to death, time to reach a
specified disease stage, tumor load, pathogen load, cytotoxicity,
side effects, quality of life, cost of treatment and pain.
82. The method of claim 81, wherein a user can input specific
coefficients for said at least one parameter to adjust the fitness
function to satisfy the user's goals.
83. The method of claim 79, wherein the user-specific parameters
are based on a user, said user being a medical doctor.
84. The method of claim 79, wherein the user-specific parameters
are based on a user, said user being a scientist.
85. The method of claim 79, wherein the user-specific parameters
are based on a user, said user being a drug developer.
86. The method of claim 72 wherein said system is adapted to
consider cytotoxic effects during selection of treatment
protocols.
87. The method of claim 72 wherein said system is adapted to
consider drug efficacy during selection of treatment protocols.
88. The method of claim 72, wherein operation research techniques
are used in performing the selection.
89. The method of claim 72, wherein heuristics are used to perform
searching and selection.
90. The method of claim 89 wherein, said heuristics comprise
computational feasibility.
91. The method of claim 72 wherein said recommendation is a
combination of disease and treatment strategy, wherein said
treatment strategy includes at least one of types of treatment,
device, drug combination, treatment schedule and dosage.
92. A computer program product, including a computer readable
medium, said program product comprising a set of instruction to
enable a computer system to aid in recommending an optimal
treatment protocol for an individual comprising: a system model
code; treatment protocol generator code for generating a plurality
of treatment protocols; a system model modifier code, wherein said
system model code is adapted to modify the system model based on
parameters specific to the individual to generate a modified system
model code; and a selector code to select an optimal treatment
protocol from said plurality of treatment protocols based on the
modified system model.
93. The computer program product of claim 92 wherein the system
model code further comprises: a biological process model code; and
a treatment model code that enables a computer to model the effects
of a treatment on the biological process.
94. A computer program product, including a computer readable
medium, said program product comprising a set of instructions to
enable a computer system to aid in recommending an optimal
treatment protocol for a general patient comprising: a system model
code; treatment protocol generator code for a generating a
plurality of treatment protocols; and a selector code to select an
optimal treatment protocol from said plurality of treatment
protocols.
95. The computer program product of claim 94 wherein the system
model code further comprises: a biological process model code; and
a treatment model code that enables a computer to model the effects
of a treatment on the biological process.
Description
I. DESCRIPTION OF THE INVENTION
[0001] I.A. Field of the Invention
[0002] The present invention relates generally to prediction of a
progression of healthy and diseased cells in patients with/without
treatment effect incorporated therein. The present invention is
embodied in systems, methods and computer program products for
predicting the progression of a biological system, and for
prediction and optimization of treatment of disease. These systems,
methods and computer program products can be used to simulate a
general patient for the use in certain stages in drug development
and trials as well as for an individual patient.
[0003] I.B. Background of the Invention
[0004] It is well known that when drugs are administered to combat
diseases, they do not differentiate between healthy and diseased
cells. The drugs are often toxic to healthy cells as well.
Therefore, in prescribing a specific treatment protocol, it is
necessary to consider the effect of the treatment protocol on both
healthy cells as well as diseased cells.
[0005] Mathematical models that model biological systems are well
known in the art. A wide variety of models are known including
those that use ordinary differential equations, partial
differential equations and the like. More specifically, these
mathematical models can simulate cell lines, tumor growth, etc.
Conventionally, these models have been used for prediction of
treatment results. However, such conventional predictive models
generally employ an analytical approach, in which generalizations
about the effect of the treatment protocols on a disease must be
made. This approach, while providing useful general information,
cannot be used to predict results of treatment in realistic
circumstances. Thus, techniques that include more complex and
detailed scenarios are needed.
II. SUMMARY OF THE INVENTION
[0006] It is an objective of the present invention to provide
techniques for recommending optimal treatments for a general
patient and a specific individual patient.
[0007] It is another objective of the invention to provide
techniques for predicting the progress of biological processes in a
general patient and a specific individual patient under a variety
of treatment protocols as well as under no treatment.
[0008] It is yet another objective of the present invention to
provide techniques for modelling various specific biological
processes for a general patient and a specific individual patient
under a plurality of treatment protocols including no
treatment.
[0009] To meet the objectives of the present invention, there is
provided a system for recommending an optimal treatment protocol
for an individual comprising a system model, a plurality of
treatment protocols, a system model modifier. The system model is
modified by the system model modifier based on parameters specific
to the individual. The system further comprises a selector to
select an optimal treatment protocol from the plurality of
treatment protocols based on the modified system model.
[0010] Preferably the system model further comprises a realistic
biological process model and a realistic treatment model that
models the effects of a treatment on the biological process.
[0011] Still preferably, the biological process model comprises
mathematical models for biological processes affecting healthy cell
populations and biological processes affecting cell populations
with at least one disease.
[0012] Still preferably the healthy cell populations include
bone-marrow cells and host tissue cells that are affected by the
treatment model.
[0013] Still preferably the cell populations with at least one
disease is one of cancer cells, and diseased bone-marrow cells
including diseased Neutrophil cells and diseased Thrompocyte
cells.
[0014] Preferably, the treatment models comprise treatment specific
processes that affect cell population.
[0015] Still preferably the treatment specific process is
interactions involving one of a group comprising pharmacokinetic,
pharmacodynamic, cytostatic, cytotoxic, and methods of affecting
cell biology and causing cell death, with associated biological
processes.
[0016] Preferably the parameters specific to the individual include
one or more selected from a group consisting of parameters related
to the biological process dynamics, patient specific drug PK, PD
and dynamics of dose-limiting host tissues.
[0017] Still preferably the parameters related to biological
process' dynamics comprise age, weight, gender, blood picture,
desired length of treatment protocol, previous reaction to
treatment, molecular markers, genetic markers, pathologic specifics
and cytologic specifics.
[0018] Preferably the selector incorporates user-specific
parameters in performing selection.
[0019] Still preferably the incorporation is done by using a
fitness function.
[0020] Still preferably the fitness function incorporates at least
one parameter selected from a group comprising patient survival,
time to death, time to reach a specified disease stage (including
cure), tumor load, pathogen load, cytotoxicity, side effects,
quality of life, cost of treatment, and pain.
[0021] Still preferably a user can input specific coefficients for
said at least one parameter to adjust the fitness function to
satisfy the user's goals.
[0022] Still preferably the user-specific parameters are based on a
user, said user being a medical doctor.
[0023] Still preferably the user-specific parameters are based on a
user, said user being a scientist.
[0024] Still preferably the user-specific parameters are based on a
user, said user being a drug developer.
[0025] Preferably the selection of treatment protocols incorporate
cytotoxic effects.
[0026] Preferably the selection of treatment protocols incorporate
drug efficacy.
[0027] Preferably the selector performs the selection using
operation research methods.
[0028] Preferably the selector further comprises heuristics, said
heuristics being used to perform searching and selection.
[0029] Still preferably said heuristics comprise computational
feasibility.
[0030] Preferably, the recommendation is a combination of disease
and treatment strategy, including types of treatment, e.g.
chemotherapy, radiotherapy, surgery, immunotherapy, etc, device,
drug or drug combination and treatment schedule and dosage.
[0031] Preferably the system is implemented over a distributed
computing system.
[0032] Still preferably the distributed computing system is the
Internet.
[0033] Still preferably a user uses the system remotely.
[0034] Another aspect of the present invention is a system for
recommending an optimal treatment protocol for a general patient
comprising a system model, a plurality of treatment protocols and a
selector to select an optimal treatment protocol from said
plurality of treatment protocols based on the system model.
[0035] Preferably the system model further comprises a realistic
biological process model and a realistic treatment model that
models the effects of a treatment on said biological process.
[0036] Still preferably, the biological process model comprises
mathematical models for biological processes affecting healthy cell
populations and biological processes affecting cell populations
with at least one disease.
[0037] Still preferably, the healthy cell populations include
bone-marrow cells and host tissue cells that are affected by said
treatment model.
[0038] Still preferably, the cell populations with at least one
disease is one of cancer cells, and diseased bone-marrow cells
including diseased Neutrophil cells and diseased Thrompocyte
cells.
[0039] Still preferably, the treatment models comprise treatment
specific processes that affect cell populations.
[0040] Still preferably, the treatment specific process is
interactions involving one of a group comprising pharmacokinetic,
pharmacodynamic, cytostatic, cytotoxic, and methods of affecting
cell biology and causing cell death, with associated biological
processes.
[0041] Preferably the selector incorporates user-specific
parameters in performing selection.
[0042] Still preferably, the incorporation is done by using a
fitness function.
[0043] Still preferably, the fitness function incorporates at least
one parameter selected from a group comprising patient survival,
time to death, time to reach a specified disease stage and cure,
tumor load, pathogen load, cytotoxicity, side effects, quality of
life, cost of treatment and pain.
[0044] Still preferably, a user can input specific coefficients for
said at least one parameter to adjust the fitness function to
satisfy the user's goals.
[0045] Still preferably, the user-specific parameters are based on
a user, said user being a medical doctor.
[0046] Still preferably, the user-specific parameters are based on
a user, said user being a scientist.
[0047] Still preferably, the user-specific parameters are based on
a user, said user being a drug developer.
[0048] Preferably, the selection of treatment protocols incorporate
cytotoxic effects.
[0049] Preferably, the selection of treatment protocols incorporate
drug efficacy.
[0050] Preferably, the selector performs the selection using
operation research methods.
[0051] Preferably, the selector further comprises heuristics, said
heuristics being used to perform searching and selection.
[0052] Still preferably, the heuristics comprise computational
feasibility.
[0053] Preferably, the recommendation is a combination of disease
and treatment strategy, including types of treatment, e.g.
chemotherapy, radiotherapy, surgery, immunotherapy, etc, device,
drug or drug combination and treatment schedule and dosage.
[0054] Preferably, the system is implemented over a distributed
computing system.
[0055] Still preferably, the distributed computing system is the
Internet.
[0056] Still preferably, a user uses the system remotely.
[0057] Still preferably, the remote system is a telephone.
[0058] Yet another aspect of the present invention is a system for
predicting progression of a biological process in an individual
patient under a plurality of treatment protocols, wherein said
biological process could be related to healthy or diseased
processes, said plurality of protocols including no treatment. The
system comprises a system model, a plurality of treatment protocols
and a system model modifier. The system model is modified by the
system model modifier based on parameters specific to the
individual. The system further comprises a predictor to predict the
progression of at least one of the disease and the natural
biological process under said plurality of treatment protocols
based on the modified system model.
[0059] Preferably, the system model further comprises a realistic
biological process model and a realistic treatment model that
models the effects of a treatment on said biological process.
[0060] Still preferably, the biological process model comprises
mathematical models for biological processes affecting healthy cell
populations and biological processes affecting cell populations
with at least one disease.
[0061] Still preferably, the healthy cell populations include
bone-marrow cells and host tissue cells that are affected by said
treatment model.
[0062] Still preferably, the cell populations with at least one
disease is one of cancer cells, and diseased bone-marrow cells
including diseased at least one of Neutrophil cells and diseased
Thrombocyte cells.
[0063] Still preferably, the treatment models comprise treatment
specific processes that affect cell population.
[0064] Still preferably the treatment specific process is
interactions involving one of a group comprising PK, PD,
cytostatic, cytotoxic, and methods of affecting cell biology and
causing cell death, with associated biological processes.
[0065] Preferably the parameters specific to the individual include
one or more selected from a group consisting of parameters related
to the biological process' dynamics, patient specific drug PK, PD
and dynamics of dose-limiting host tissues.
[0066] Still preferably, the parameters related to biological
process' dynamics comprise age, weight, gender, blood picture,
desired length of treatment protocol, previous reaction to
treatment, molecular markers, genetic markers, pathologic specifics
and cytologic specifics.
[0067] Yet another aspect of the present invention is a system for
predicting progression of a biological process in a general patient
under a plurality of treatment protocols, wherein said biological
process could be healthy or diseased processes, said plurality of
protocols including no treatment. The system comprises a system
model, a plurality of treatment protocols and a predictor to
predict the progression of the disease or the natural biological
process under said plurality of treatment protocols.
[0068] Preferably, the system model further comprises a realistic
biological process model and a realistic treatment model that
models the effects of a treatment on said biological process.
[0069] Still preferably, the biological process model comprises
mathematical models for biological processes affecting healthy cell
populations and biological processes affecting cell populations
with at least one disease.
[0070] Still preferably, the healthy cell populations include
bone-marrow cells as well as other host tissue cells that are
affected by said treatment model.
[0071] Still preferably, the cell populations with at least one
disease is one of cancer cells, and diseased bone-marrow cells
including diseased Neutrophil cells and diseased Thrombocyte
cells.
[0072] Still preferably, the treatment models comprise treatment
specific processes that affect cell population.
[0073] Still preferably, the treatment specific process is
interactions involving one of a group comprising PK, PD, drug
cytostatics, drug cytotoxics, and methods of affecting cell biology
and causing cell death, with associated biological processes.
[0074] Yet another aspect of the present invention is a system for
modelling Thrombopietic lineage in an individual, said system
comprising a Thrombopoiesis system model including a realistic
process progression model, for cells involved in Thrombopoiesis,
said progression model including multiplication and differentiation
and a system model modifier, wherein said Thrombopoiesis system
model is modified by the system model modifier based on parameters
specific to the individual.
[0075] Preferably, the system model incorporates a realistic
progression of cells involved in diseased Thrombopoiesis.
[0076] Still preferably, the diseased Thrombopoiesis includes
Thrombocytopenia.
[0077] Still preferably, the system model incorporates effects of
at least one drug in the realistic progression of cells involved in
Thrombopoiesis.
[0078] Still preferably, said at least one drug is Thrombopoietin
(TPO).
[0079] Still preferably, the process model imitates a course of the
individual's bone marrow progression, peripheral platelet counts
and TPO concentration changes.
[0080] Still preferably, said process model incorporates
cell-suppressive treatment effects and administration of TPO to the
patient.
[0081] Still preferably, said cell-suppressive treatment can be
chemotherapy.
[0082] Still preferably, the process model further comprises a
plurality of compartments.
[0083] Still preferably, the compartments include:
[0084] a stem cell (SC) compartment that comprises bone marrow
haemopoietic progenitors that have an ability to differentiate into
more than one cell line wherein cells in the stem cell compartment
proliferate and differentiate into one of megakaryocyte;
[0085] a colony forming units--megakaryocytes (CFU-Meg)
compartment, wherein the megakaryocyte progenitors get committed as
a megakaryocyte line and spend some time multiplying and
maturing;
[0086] a megakaryoblast (MKB) compartment, which receives the cells
from CFU-Meg, wherein the cells in the MKB compartment have lost
their ability to proliferate but are not mature to release
platelets;
[0087] a MK16 compartment, which receives cell from the MKB
compartment, wherein a subset of cells in the MK16 compartment
release platelets at a constant rate until they exhaust their
capacity and are disintegrated and a second subset of cells do not
release platelets but continue with endomitosis;
[0088] a MK32 compartment that receives cells from the MK16
compartment, wherein a subset of cells in this compartment release
platelets and a second subset of cells do not release platelets but
continue with endomitosis;
[0089] a MK64 compartment that receives cells from the MK32
compartment wherein a subset of cells in this compartment release
platelets and a second subset of cells do not release platelets but
continue with endomitosis;
[0090] a MK128 compartment that receives cells from the MK64
compartment wherein a subset of cells in this compartment release
platelets; and
[0091] a platelets (PL) compartment.
[0092] Still preferably, an effect of apoptosis is included with an
overall effect of cell proliferation in giving rise to an
amplification of cell numbers in a corresponding compartment.
[0093] Still preferably, the process model further incorporates the
effects of TPO on the SC, CFU-Meg and MKB compartments.
[0094] Still preferably, the effects are expressed in terms of
effects of TPO concentration on amplification rate, rate of cell
maturation and a fraction of cells that undergo endomitosis.
[0095] Still preferably, when the TPO concentration is above a
predetermined threshold level, the amplification rate of cells in
the SC compartment are affected and below the threshold the
amplification rate is dependent only on a current number of
cells.
[0096] Still preferably, in the CFU-Meg compartment the cells are
sensitive to TPO concentration regardless of the concentration of
TPO.
[0097] Still preferably the transit time is same in all platelet
releasing compartments and the transit time of the SC, CFU-Meg and
MKB compartments are functions of micro-environmental
conditions.
[0098] Still preferably, the SC compartment when the TPO
concentration is above the threshold, the transit time is shortened
based the dose.
[0099] Still preferably, in the CFU-Meg and MKB, the transit time
is solely based on TPO concentration.
[0100] Still preferably, a fraction of cells in the SC compartment
that commits to megakaryocytic lineage is constant and dependent on
TPO.
[0101] Still preferably in the CFU-Meg and MKB compartments, every
mature cell passes on to the next compartment.
[0102] Still preferably, in the MK16, MK32 and MK64 compartments, a
fraction of cells pass on to the next compartment, said fraction
being dependent on the TPO concentration.
[0103] Still preferably, cells from MK128 compartment do not flow
into any other compartment.
[0104] Still preferably, each of said compartments is further
divided into sub-compartments, each of said sub-compartments
containing cells of a specific age in hours.
[0105] Still preferably, cells that spend all their corresponding
transit time in a given compartment pass on to the next
compartment, wherein cells that have left a corresponding
compartment each hour fill the first sub-compartment of the next
compartment.
[0106] Still preferably, the platelet releasing cells contribute
platelets to the first sub-compartment of the PL compartment.
[0107] Preferably the model is used for recommending an optimal
treatment protocol, wherein said system further comprises a
plurality of treatment protocols and a selector to select an
optimal treatment protocol from said plurality of treatment
protocols based on the modified system model.
[0108] Yet another aspect of the present invention is a system for
modelling Thrombopietic lineage in a general patient, said system
comprising a Thrombopoiesis system model including a realistic
process model for cells involved in Thrombopoiesis.
[0109] Preferably, the system model incoporates a realistic
progression of cells involved in diseased Thrombopoiesis.
[0110] Still preferably, the diseased Thrombopoiesis includes
Thrombocytopenia.
[0111] Still preferably, the system model incorporates effects of
at least one drug in the realistic progression of cells involved in
Thrombopoiesis.
[0112] Still preferably, said at least one drug is Thrombopoietin
(TPO).
[0113] Still preferably, the process model imitates a course of the
patient's bone marrow progression, peripheral platelet counts and
TPO concentration changes.
[0114] Still preferably, the process model incorporates
cell-suppressive treatment effects and administration of TPO to the
patient.
[0115] Still preferably, the cell-suppressive treatment is
chemotherapy.
[0116] Still preferably, the process model further comprises a
plurality of compartments.
[0117] Still preferably, the compartments include:
[0118] a stem cell (SC) compartment that comprises bone marrow
haemopoietic progenitors that have an ability to differentiate into
more than one cell line wherein cells in the stem cell compartment
proliferate and differentiate into one of megakaryocyte;
[0119] a colony forming units--megakaryocytes (CFU-Meg)
compartment, wherein the megakaryocyte progenitors get committed as
a megakaryocyte line and spend some time multiplying and
maturing;
[0120] a megakaryoblast (MKB) compartment, which receives the cells
from CFU-Meg, wherein the cells in the MKB compartment have lost
their ability to proliferate but are not mature to release
platelets;
[0121] a MK16 compartment, which receives cell from the MKB
compartment, wherein a subset of cells in the MK16 compartment
release platelets at a constant rate until they exhaust their
capacity and are disintegrated and a second subset of cells do not
release platelets but continue with endomitosis;
[0122] a MK32 compartment that receives cells from the MK16
compartment, wherein a subset of cells in this compartment release
platelets and a second subset of cells do not release platelets but
continue with endomitosis;
[0123] a MK64 compartment that receives cells from the MK32
compartment wherein a subset of cells in this compartment release
platelets and a second subset of cells do not release platelets but
continue with endomitosis;
[0124] a MK128 compartment that receives cells from the MK64
compartment wherein a subset of cells in this compartment release
platelets; and
[0125] a platelets (PL) compartment.
[0126] Still preferably, an effect of apoptosis are included with
an overall effect of cell proliferation in giving rise to an
amplification of cell numbers in a corresponding compartment.
[0127] Still preferably, the process model further incorporates the
effects of TPO on the SC, CFU-Meg and MKB compartments.
[0128] Still preferably, the effects are expressed in terms of
effects of TPO concentration on amplification rate, rate of cell
maturation and a fraction of cells that undergo endomitosis.
[0129] Still preferably, when the TPO concentration is above a
predetermined threshold level, the amplification rate of cells in
the SC compartment are affected and below the threshold the
amplification rate is dependent only on a current number of
cells.
[0130] Still preferably, the CFU-Meg compartment the cells are
sensitive to TPO concentration regardless of the concentration of
TPO.
[0131] Still preferably, the transit time is same in all platelet
releasing compartments and the transit time of the SC, CFU-Meg and
MKB compartments are functions of micro-environmental
conditions.
[0132] Still preferably, in the SC compartment when the TPO
concentration is above the threshold, the transit time is shortened
based the dose.
[0133] Still preferably, in the CFU-Meg and MKB, the transit time
is solely based on TPO concentration.
[0134] Still preferably, a fraction of cells in the SC compartment
that commits to megakaryocytic lineage is constant and dependent on
TPO.
[0135] Still preferably, in the CFU-Meg and MKB compartments, every
mature cell passes on to the next compartment.
[0136] Still preferably, in the MK16, MK32 and MK64 compartments, a
fraction of cells pass on to the next compartment, said fraction
being dependent on the TPO concentration.
[0137] Still preferably, cells from MK128 compartment do not flow
into any other compartment.
[0138] Still preferably, each of said compartments is further
divided into sub-compartments, each of said sub-compartments
containing cells of a specific age in hours.
[0139] Still preferably, cells that spend all their corresponding
transit time in a given compartment pass on to the next
compartment, wherein cells that have left a corresponding
compartment each hour fill the first sub-compartment of the next
compartment.
[0140] Still preferably, the platelet releasing cells contribute
platelets to the first sub-compartment of the PL compartment.
[0141] Preferably, said model is used for recommending an optimal
treatment protocol, wherein said system further comprises a
plurality of treatment protocols; and a selector to select an
optimal treatment protocol from said plurality of treatment
protocols based on the modified system model.
[0142] Yet another aspect of the present invention is a system for
predicting progression of Thrombopoiesis and a model of
Thrombocytopenia for an individual under a plurality of treatment
protocols, said plurality of protocols including no treatment, said
system comprising a Thrombopoiesis and a Thrombocytopenia system
model, a plurality of treatment protocols for affecting
Thrombopoiesis and treating Thrombocytopenia using at least one
drug, a system model modifier. The Thrombopoiesis and
Thrombocytopenia system models are modified by the system model
modifier based on parameters specific to the individual. The system
further comprises a predictor to predict the progression of the
disease or the natural biological process under said plurality of
treatment protocols based on the modified system model.
[0143] Preferably, the system model incoporates a realistic
progression of cells involved in diseased Thrombopoisis.
[0144] Still preferably, diseased Thrombopoiesis includes
Thrombocytopenia.
[0145] Still preferably, the system model incorporates effects of
at least one drug on the realistic progression of cells involved in
Thrombocytopenia.
[0146] Still preferably, said at least one drug is Thrombopoietin
(TPO).
[0147] Still preferably, said process model imitates a course of
the individual's bone marrow progression, peripheral platelet
counts and TPO concentration changes.
[0148] Still preferably, said process model incorporates
cell-suppressive treatment effects and administration of TPO to the
patient.
[0149] Still preferably, said cell-suppressive treatment is
chemotherapy.
[0150] Still preferably, said process model further comprises a
plurality of compartments.
[0151] Still preferably, said compartments include:
[0152] a stem cell (SC) compartment that comprises bone marrow
haemopoietic progenitors that have an ability to differentiate into
more than one cell line wherein cells in the stem cell compartment
proliferate and differentiate into one of megakaryocyte;
[0153] a colony forming units--megakaryocytes (CFU-Meg)
compartment, wherein the megakaryocyte progenitors get committed as
a megakaryocyte line and spend some time multiplying and
maturing;
[0154] a megakaryoblast (MKB) compartment, which receives the cells
from CFU-Meg, wherein the cells in the MKB compartment have lost
their ability to proliferate but are not mature to release
platelets;
[0155] a MK16 compartment, which receives cell from the MKB
compartment, wherein a subset of cells in the MK16 compartment
release platelets at a constant rate until they exhaust their
capacity and are disintegrated and a second subset of cells do not
release platelets but continue with endomitosis;
[0156] a MK32 compartment that receives cells from the MK16
compartment, wherein a subset of cells in this compartment release
platelets and a second subset of cells do not release platelets but
continue with endomitosis;
[0157] a MK64 compartment that receives cells from the MK32
compartment wherein a subset of cells in this compartment release
platelets and a second subset of cells do not release platelets but
continue with endomitosis;
[0158] a MK128 compartment that receives cells from the MK64
compartment wherein a subset of cells in this compartment release
platelets; and
[0159] a platelets (PL) compartment.
[0160] Still preferably, an effect of apoptosis are included with
an overall effect of cell proliferation in giving rise to an
amplification of cell numbers in a corresponding compartment.
[0161] Still preferably, the process model further incorporates the
effects of TPO on the SC, CFU-Meg and MKB compartments.
[0162] Still preferably, the effects are expressed in terms of
effects of TPO concentration on amplification rate, rate of cell
maturation and a fraction of cells that undergo endomotisis.
[0163] Still preferably, the TPO concentration is above a
predetermined threshold level, the amplification rate of cells in
the SC compartment are affected and below the threshold the
amplification rate is dependent only on a current number of
cells.
[0164] Still preferably, in the CFU-Meg compartment the cells are
sensitive to TPO concentration regardless of the concentration of
TPO.
[0165] Still preferably, the transit time is same in all platelet
releasing compartments and the transit time of the SC, CFU-Meg and
MKB compartments are functions of micro-environmental
conditions.
[0166] Still preferably, in the SC compartment when the TPO
concentration is above the threshold, the transit time is shortened
based the dose.
[0167] Still preferably, in the CFU-Meg and MKB, the transit time
is solely based on TPO concentration.
[0168] Still preferably, a fraction of cells in the SC compartment
that commits to megakaryocytic lineage is constant and dependent on
TPO.
[0169] Still preferably, in the CFU-Meg and MKB compartments, every
mature cell passes on to the next compartment.
[0170] Still preferably, in the MK16, MK32 and MK64 compartments, a
fraction of cells pass on to the next compartment, said fraction
being dependent on the TPO concentration.
[0171] Still preferably, cells from MK128 compartment do not flow
into any other compartment.
[0172] Still preferably, each of said compartments is further
divided into sub-compartments, each of said sub-compartments
containing cells of a specific age in hours.
[0173] Still preferably, cells that spend all their corresponding
transit time in a given compartment pass on to the next
compartment, wherein cells that have left a corresponding
compartment each hour fill the first sub-compartment of the next
compartment.
[0174] Still preferably, the platelet releasing cells contribute
platelets to the first sub-compartment of the PL compartment.
[0175] Yet another aspect of the present invention is a system for
predicting progression of Thrombopoiesis and a model of
Thrombocytopenia for a general patient under a plurality of
treatment protocols, said plurality of protocols including no
treatment. The system comprises a Thrombopoiesis and a
Thrombocytopenia system model, a plurality of treatment protocols
for affecting Thrombopoiesis and treating Thrombocytopenia using at
least one drug; and a predictor to predict the progression of the
disease or the natural biological process under said plurality of
treatment protocols based on the modified system model.
[0176] Preferably the system model incorporates a realistic
progression of cells involved in diseased Thrombopoiesis Still
preferably, diseased Thrombopoiesis includes Thrombocytopenia.
[0177] Still preferably, the system model incorporates effects of
at least one drug in the realistic progression of cells involved in
Thrombocytopenia.
[0178] Still preferably, said at least one drug is Thrombopoietin
(TPO).
[0179] Still preferably, said process model imitates a course of
the individual's bone marrow progression, peripheral platelet
counts and TPO concentration changes.
[0180] Still preferably, said process model incorporates
cell-suppressive treatment effects and administration of TPO to the
patient.
[0181] Still preferably, said cell-suppressive treatment is
chemotherapy.
[0182] Still preferably, said process model further comprises a
plurality of compartments.
[0183] Still preferably, said compartments include:
[0184] a stem cell (SC) compartment that comprises bone marrow
haemopoietic progenitors that have an ability to differentiate into
more than one cell line wherein cells in the stem cell compartment
proliferate and differentiate into one of megakaryocyte;
[0185] a colony forming units--megakaryocytes (CFU-Meg)
compartment, wherein the megakaryocyte progenitors get committed as
a megakaryocyte line and spend some time multiplying and
maturing;
[0186] a megakaryoblast (MKB) compartment, which receives the cells
from CFU-Meg, wherein the cells in the MKB compartment have lost
their ability to proliferate but are not mature to release
platelets;
[0187] a MK16 compartment, which receives cell from the MKB
compartment, wherein a subset of cells in the MK16 compartment
release platelets at a constant rate until they exhaust their
capacity and are disintegrated and a second subset of cells do not
release platelets but continue with endomitosis;
[0188] a MK32 compartment that receives cells from the MK16
compartment, wherein a subset of cells in this compartment release
platelets and a second subset of cells do not release platelets but
continue with endomitosis;
[0189] a MK64 compartment that receives cells from the MK32
compartment wherein a subset of cells in this compartment release
platelets and a second subset of cells do not release platelets but
continue with endomitosis;
[0190] a MK128 compartment that receives cells from the MK64
compartment wherein a subset of cells in this compartment release
platelets; and
[0191] a platelets (PL) compartment.
[0192] Still preferably, an effect of apoptosis are included with
an overall effect of cell proliferation in giving rise to an
amplification of cell numbers in a corresponding compartment.
[0193] Still preferably, the process model further incorporates the
effects of TPO on the SC, CFU-Meg and MKB compartments.
[0194] Still preferably, the effects are expressed in terms of
effects of TPO concentration on amplification rate, rate of cell
maturation and a fraction of cells that undergo endomotisis.
[0195] Still preferably, when the TPO concentration is above a
predetermined threshold level, the amplification rate of cells in
the SC compartment are affected and below the threshold the
amplification rate is dependent only on a current number of
cells.
[0196] Still preferably, in the CFU-Meg compartment the cells are
sensitive to TPO concentration regardless of the concentration of
TPO.
[0197] Still preferably, the transit time is same in all platelet
releasing compartments and the transit time of the SC, CFU-Meg and
MKB compartments are functions of micro-environmental
conditions.
[0198] Still preferably, in the SC compartment when the TPO
concentration is above the threshold, the transit time is shortened
based the dose.
[0199] Still preferably, in the CFU-Meg and MKB, the transit time
is solely based on TPO concentration.
[0200] Still preferably, a fraction of cells in the SC compartment
that commits to megakaryocytic lineage is constant and dependent on
TPO.
[0201] Still preferably, in the CFU-Meg and MKB compartments, every
mature cell passes on to the next compartment.
[0202] Still preferably, in the MK16, MK32 and MK64 compartments, a
fraction of cells pass on to the next compartment, said fraction
being dependent on the TPO concentration.
[0203] Still preferably, cells from MK128 compartment do not flow
into any other compartment.
[0204] Still preferably, each of said compartments is further
divided into sub-compartments, each of said sub-compartments
containing cells of a specific age in hours.
[0205] Still preferably, cells that spend all their corresponding
transit time in a given compartment pass on to the next
compartment, wherein cells that have left a corresponding
compartment each hour fill the first sub-compartment of the next
compartment.
[0206] Still preferably, wherein the platelet releasing cells
contribute platelets to the first sub-compartment of the PL
compartment.
[0207] Another aspect of the present invention is a system for
modelling Neutrophil lineage for an individual, said system
comprising a Neutrophil system model including a realistic process
model for cells involved in Granulopoiesis and a system model
modifier. The Neutrophil system model is modified by the system
model modifier based on parameters specific to the individual.
[0208] Preferably, the system model incorporates a realistic
progression of cells involved in Granulopoietic disorders,
including Neutropenia.
[0209] Still preferably, the system incorporates effects of at
least one drug in the realistic progression of cells involved in
Granulopoiesis and Neutropenia.
[0210] Still preferably, said at least one drug is Granulocyte
Colony Stimulating Factor (G-CSF);
[0211] Still preferably, said model comprises at least three
stages, a first stage related to an administered amount of
cytokine;
[0212] a second stage representing a pharmacokinetic behavior of
G-CSF; and
[0213] a third stage representing a phrmacodynamic effect of G-CSF
on kinetic parameters of the system.
[0214] Still preferably, said model comprises a mitotic
compartment, and a post mitotic compartment, said mitotic
compartment being divided into subcompartments wherein a kth
sub-compartment contains cells of age between k-1and k hours
relative to a time of entry into the mitotic compartment.
[0215] Still preferably, effects of toxic drugs, including
chemotherapy are incorporated by mapping various cell-cycle phases
to the sub-compartments and formulating a function of cytotoxic
effects of toxic drugs, including chemotherapy on the cell-cycle
phases.
[0216] Still preferably, the effects of G-CSF on the mitotic
compartment are modeled as an increase in a rate of cells entering
the myeloblasts compartment from an uncommitted stem cell pool.
[0217] Still preferably, the post-mitotic compartment is modeled as
a single pool of cells wherein cells in a last sub-compartment of
the mitotic compartment enters the post-mitotic compartment and a
proportion of cells within the post-mitotic compartment enters the
mature Neutrophil pool every hour.
[0218] Still preferably, effects of G-CSF on the Neutrophil lineage
are modeled as a decrease in the cells in the post-mitotic
compartment which is subsequently compensated by an increased
production in the mitotic compartment, said compensation sustaining
an increase in Neutrophil count.
[0219] Still preferably, an elimination of Neutrophils in the
post-mitotic compartment is represented by a Poisson
distribution.
[0220] Still preferably, the cytotoxic effects of toxic drugs,
including chemotherapy in the post-mitotic compartment is modeled
as an effect on a single pool of cells.
[0221] Still preferably, kinetic of G-CSF is modeled as an
exponential distribution.
[0222] Still preferably, a selection of an optimal treatment uses
an objective function that aims at minimizing G-CSF administration
and returning Neutrophil lineage to normal levels.
[0223] Still preferably, said selection is performed using linear
programming.
[0224] Still preferably, phrmacokinetics and pharmacodynamics of
G-CSF are defined using piecewise linear functions.
[0225] Preferably, said model is used for recommending an optimal
treatment protocol, wherein said system further comprises a
plurality of treatment protocols; and a selector to select an
optimal treatment protocol from said plurality of treatment
protocols based on the modified system model.
[0226] Yet another aspect of the present invention is system for
modelling Neutrophil lineage for a general patient, said system
comprising a Granulopoiesis system model including a realistic
process model for cells involved in Neutrophil production.
[0227] Preferably, the system model incorporates a realistic
progression of cells involved in Granulopoiesis disorders including
Neutropenia.
[0228] Still preferably, the system incorporates effects of at
least one drug in the realistic progression of cells involved in
Granulopoiesis disorders including Neutropenia.
[0229] Still preferably, said at least one drug is Granulocyte
Colony Stimulating Factor (G-CSF)
[0230] Still preferably, said model comprises at least three
stages, a first stage related to an administered amount of
cytokine;
[0231] a second stage representing a pharmacokinetic behavior of
G-CSF; and
[0232] a third stage representing a phrmacodynamic effect of G-CSF
on kinetic parameters.
[0233] Preferably, said model comprises a mitotic compartment, and
a post mitotic compartment, said mitotic compartment being divided
into subcompartments wherein a kth sub-compartment contains cells
of age between k-1 and k hours relative to a time of entry into the
mitotic compartment.
[0234] Still preferably, effects of toxic drugs, including
chemotherapy are incorporated by mapping various cell-cycle phases
to the sub-compartments and formulating a function of cytotoxic
effects of toxic drugs, including chemotherapy on the cell-cycle
phases.
[0235] Still preferably, the effects of G-CSF on the mitotic
compartment are modeled as an increase in a rate of cells entering
the myeloblasts compartment from an uncommitted stem cell pool.
[0236] Still preferably, the post-mitotic compartment is modeled as
a single pool of cells wherein cells in a last sub-compartment of
the mitotic compartment enters the post-mitotic compartment and a
proportion of cells within the post-mitotic compartment enters the
mature Neutrophil pool every hour.
[0237] Still preferably, effects of G-CSF on the Neutrophil lineage
are modeled as a decrease in the cells in the post-mitotic
compartment which is subsequently compensated by an increased
production in the mitotic compartment, said compensation sustaining
an increase in Neutrophil count.
[0238] Still preferably, an elimination of Neutrophils in the
post-mitotic compartment is represented by a Poisson
distribution.
[0239] Still preferably, the cytotoxic effects of toxic drugs,
including chemotherapy in the post-mitotic compartment is modeled
as an effect on a single pool of cells.
[0240] Still preferably, kinetic of G-CSF is modeled as an
exponential distribution.
[0241] Preferably, a selection of an optimal treatment uses an
objective function that aims at minimizing G-CSF administration and
returning Neutrophil lineage to normal levels.
[0242] Still preferably, said selection is performed using linear
programming.
[0243] Still preferably, phrmacokinetics and pharmacodynamics of
G-CSF are defined using piecewise linear functions.
[0244] Preferably, said model is used for recommending an optimal
treatment protocol, wherein said system further comprises: a
plurality of treatment protocols; and a selector to select an
optimal treatment protocol from said plurality of treatment
protocols based on the modified system model.
[0245] Yet another aspect of the present invention is a system for
predicting progression of Granulopoiesis for an individual under a
plurality of treatment protocols, said plurality of protocols
including no treatment, said system comprising a Granulopoiesis
system model including a realistic process model for cells involved
in Neutrophil production; a plurality of treatment protocols;
and
[0246] a system model modifier. The Neutrophil production system
model is modified by the system model modifier based on parameters
specific to the individual. The system further comprises a
predictor that predicts the progression under the plurality of
treatment protocols based on the modified system model.
[0247] Preferably, the system model incorporates a realistic
progression of cells involoved in Granulopoietic disorders,
including Neutropenia.
[0248] Still preferably, the system incorporates effects of at
least one drug in the realistic progression of cells involved in
Granulopoiesis and Neutropenia.
[0249] Still preferably, said at least one drug is Granulocyte
Colony Stimulating Factor (G-CSF).
[0250] Still preferably, said model comprises at least three
stages, a first stage related to an administered amount of
cytokine;
[0251] a second stage representing a pharmacokinetic behavior of
G-CSF; and
[0252] a third stage representing a phrmacodynamic effect of G-CSF
on kinetic parameters.
[0253] Still preferably, said model comprises a mitotic
compartment, and a post mitotic compartment, said mitotic
compartment being divided into subcompartments wherein a kth
sub-compartment contains cells of age between k-1 and k hours
relative to a time of entry into the mitotic compartment.
[0254] Still preferably, effects of toxic drugs, including
chemotherapy are incorporated by mapping various cell-cycle phases
to the sub-compartments and formulating a function of cytotoxic
effects of toxic drugs, including chemotherapy on the cell-cycle
phases.
[0255] Still preferably, the effects of G-CSF on the mitotic
compartment are modeled as an increase in a rate of cells entering
the myeloblasts compartment from an uncommitted stem cell pool.
[0256] Still preferably, the post-mitotic compartment is modeled as
a single pool of cells wherein cells in a last sub-compartment of
the mitotic compartment enters the post-mitotic compartment and a
proportion of cells within the post-mitotic compartment enters the
mature Neutrophil pool every hour.
[0257] Still preferably, effects of G-CSF on the Neutrophil lineage
are modeled as a decrease in the cells in the post-mitotic
compartment which is subsequently compensated by an increased
production in the mitotic compartment, said compensation sustaining
an increase in Neutrophil count.
[0258] Still preferably, an elimination of Neutrophils in the
post-mitotic compartment is represented by a Poisson
distribution.
[0259] Still preferably, the cytotoxic effects of toxic drugs,
including chemotherapy in the post-mitotic compartment is modeled
as an effect on a single pool of cells.
[0260] Still preferably, kinetic of G-CSF is modeled as an
exponential distribution.
[0261] Still preferably, a selection of an optimal treatment-uses
an objective function that aims at minimizing G-CSF administration
and returning Neutrophil lineage to normal levels.
[0262] Still preferably, said selection is performed using linear
programming.
[0263] Still preferably, phrmacokinetics and pharmacodynamics of
G-CSF are defined using piecewise linear functions.
[0264] Yet another aspect of the present invention is a system for
predicting progression of Granulopoiesis for a general patient
under a plurality of treatment protocols, said plurality of
protocols including no treatment, said system comprising a
Neutrophil system model including a realistic process model for
cells involved in Neutrophil production a plurality of treatment
protocols; and a predictor that predicts the progression under the
plurality of treatment protocols based on the modified system
model.
[0265] Still preferably, the system model incorporates a realistic
progression of cells involved in Granulopoietic disorders,
including Neutropenia.
[0266] Still preferably, the system incorporates effects of at
least one drug in the realistic progression of cells involved in
Granulopoiesis and Neutropenia.
[0267] Still preferably, said at least one drug is Granulocyte
Colony Stimulating Factor (G-CSF).
[0268] Still preferably, said model comprises at least three
stages, a first stage related to an administered amount of
cytokine;
[0269] a second stage representing a pharmacokinetic behavior of
G-CSF; and
[0270] a third stage representing a phrmacodynamic effect of G-CSF
on kinetic parameters.
[0271] Still preferably, said model comprises a mitotic
compartment, and a post mitotic compartment, said mitotic
compartment being divided into subcompartments wherein a kth
sub-compartment contains cells of age between k-1 and k hours
relative to a time of entry into the mitotic compartment.
[0272] Still preferably, effects of toxic drugs, including
chemotherapy are incorporated by mapping various cell-cycle phases
to the sub-compartments and formulating a function of cytotoxic
effects of toxic drugs, including chemotherapy on the cell-cycle
phases.
[0273] Still preferably, the effects of G-CSF on the mitotic
compartment are modeled as an increase in a rate of cells entering
the myeloblasts compartment from an uncommitted stem cell pool.
[0274] Still preferably, the post-mitotic compartment is modeled as
a single pool of cells wherein cells in a last sub-compartment of
the mitotic compartment enters the post-mitotic compartment and a
proportion of cells within the post-mitotic compartment enters the
mature Neutrophil pool every hour.
[0275] Still preferably, effects of G-CSF on the Neutrophil lineage
are modeled as a decrease in the cells in the post-mitotic
compartment which is subsequently compensated by an increased
production in the mitotic compartment, said compensation sustaining
an increase in Neutrophil count.
[0276] Still preferably, an elimination of Neutrophils in the
post-mitotic compartment is represented by a Poisson
distribution.
[0277] Still preferably, the cytotoxic effects of toxic drugs,
including chemotherapy in the post-mitotic compartment is modeled
as an effect on a single pool of cells.
[0278] Still preferably, kinetic of G-CSF is modeled as an
exponential distribution.
[0279] Still preferably, a selection of an optimal treatment uses
an objective function that aims at minimizing G-CSF administration
and returning Neutrophil lineage to normal levels.
[0280] Still preferably, said selection is performed using linear
programming.
[0281] Still preferably, phrmacokinetics and pharmacodynamics of
G-CSF are defined using piecewise linear functions.
[0282] Yet another aspect of the present invention is a system for
recommending an optimal treatment protocol for treating cancer
using drugs, including chemotherapy, for an individual, said system
comprising a cancer system model a plurality of treatment protocols
for treating cancer using chemotherapy, a system model modifier.
The cancer system model is modified by the system model modifier
based on parameters specific to the individual. The system further
comprises a selector to select an optimal treatment protocol from
said plurality of treatment protocols based on the modified system
model.
[0283] Preferably, the system model further comprises a realistic
process model of cancer development; and a realistic treatment
model that models the effects of treating cancer with drugs,
including chemotherapy.
[0284] Still preferably, said process model incorporates a
distribution of cycling cells and quiescent cells.
[0285] Still preferably, a tumor cell cycle is divided into at
least four compartments G1, S, G2 and M and a quiescent stage is
denoted by G0, wherein each of said four compartments is further
subdivided into sub-compartments and an ith sub-compartment
representing cells of age I in the corresponding compartment,
wherein cells entering a compartment always enter a first
sub-compartment of the compartment.
[0286] Still preferably, the model traces development of cancer
cells using a predetermined set of parameters by calculating a
number of cells in each subcompartment using stepwise
equations.
[0287] Still preferably, a probability vector is used to determine
a fraction of cells that leaves any subcompartment in a compartment
to move to a first subcompartment of the next compartment.
[0288] Still preferably, a set control functions uniquely determine
an outcome of every single step, wherein said control functions
depend on age of cells, state of a current population and
associated environment.
[0289] Still preferably, a tumor is modelled as a combination of a
plurality of homogeneous group of cells, each of said homogeneous
group of cells representing a similarly behaving group of cells
distributed between all the cell-cycle compartments.
[0290] Still preferably, in each step, a number of cells in each
sub-compartment of each compartment of each group is calculated
according to factors including a previous state, parameters of
tumor, tumor current microenvironment and drug concentration.
[0291] Still preferably, spatial structure of the tumor is included
in the model.
[0292] Still preferably, PK and PD, cytostatic effects, cytotoxic
effects , and other effects on cell disintegration of anticancer
drugs are incorporated into the model.
[0293] Still preferably, a dose-limiting toxicity is incorporated
into the model.
[0294] Still preferably, said parameters specific to the individual
comprise parameters related to tumor dynamics, patient specific
drug PK, and dynamics of dose-limiting host tissues.
[0295] Still preferably, said parameters related to tumor dynamics
comprise age, weight, gender, percentage of limiting healthy cells,
desired length of treatment protocol, previous reaction to
treatment, molecular markers, genetic markers, pathologic specifics
and cytologic specifics.
[0296] Yet another aspect of the present invention is a system for
predicting the a progression of cancer in individual patients
comprisin a cancer system model, a plurality of treatment protocols
for treating cancer using drugs, including chemotherapy a system
model modifier. The cancer system model is modified by the system
model modifier based on parameters specific to the individual. The
system further comprises a predictor to predict the progression of
cancer under the plurality of treatment protocols based on the
modified system model.
[0297] Still preferably, the system model further comprises:
[0298] a realistic process model of cancer development; and
[0299] a realistic treatment model that models the effects of
treating cancer with drugs, including chemotherapy.
[0300] Still preferably, said process model incorporates a
distribution of cycling cells and quiescent cells.
[0301] Still preferably, a tumor cell cycle is divided into at
least four compartments G1, S, G2 and M and a quiescent stage is
denoted by G0, wherein each of said four compartments is further
subdivided into sub-compartments and an ith sub-compartment
representing cells of age i in the corresponding compartment,
wherein cells entering a compartment always enter a first
sub-compartment of the compartment.
[0302] Still preferably, the model traces development of cancer
cells using a predetermined set of parameters by calculating a
number of cells in each subcompartment using stepwise
equations.
[0303] Still preferably, a probability vector is used to determine
a fraction of cells that leaves any subcompartment in a compartment
to move to a first subcompartment of the next compartment.
[0304] Still preferably, where a set control functions uniquely
determine an outcome of every single step, wherein said control
functions depend on age of cells, state of a current population and
associated environment.
[0305] Still preferably, a tumor is modelled as a combination of a
plurality of homogeneous group of cells, each of said homogeneous
group of cells representing a similarly behaving group of cells
distributed between all the cell-cycle compartments.
[0306] Still preferably, in each step, a number of cells in each
sub-compartment of each compartment of each group is calculated
according to factors including a previous state, parameters of
tumor, tumor current microenvironment and drug concentration.
[0307] Still preferably, spatial structure of the tumor is included
in the model.
[0308] Still preferably, PK and PD, cytotoxic effects and
cytostatic effects of anticancer drugs are incorporated into the
model.
[0309] Still preferably, a dose-limiting toxicity is incorporated
into the model.
[0310] Still preferably, said parameters specific to the individual
comprise parameters related to tumor dynamics, patient specific
drug PK, and dynamics of dose-limiting host tissues.
[0311] Still preferably, said parameters related to tumor dynamics
comprise age, weight, gender, percentage of limiting healthy cells,
desired length of treatment protocol, previous reaction to
treatment, molecular markers, genetic markers, pathologic specifics
and cytologic specifics.
[0312] Yet another aspect of the present invention is a system for
predicting the a progression of cancer in a general patients
comprising a cancer system model, a plurality of treatment
protocols for treating cancer using drugs, including chemotherapy;
and a predictor to predict the progression of cancer under the
plurality of treatment protocols based on the modified system
model.
[0313] Preferably, the system model further comprises a realistic
process model of cancer development; and a realistic treatment
model that models the effects of treating cancer with drugs,
including chemotherapy.
[0314] Still preferably, said process model incorporates a
distribution of cycling cells and quiescent cells.
[0315] Still preferably, where a tumor cell cycle is divided into
at least four compartments G1, S, G2 and M and a quiescent stage is
denoted by G0, wherein each of said four compartments is further
subdivided into sub-compartments and an ith sub-compartment
representing cells of age I in the corresponding compartment,
wherein cells entering a compartment always enter a first
sub-compartment of the compartment.
[0316] Still preferably, the model traces development of cancer
cells using a predetermined set of parameters by calculating a
number of cells in each subcompartment using stepwise
equations.
[0317] Still preferably, a probability vector is used to determine
a fraction of cells that leaves any subcompartment in a compartment
to move to a first subcompartment of the next compartment.
[0318] Still preferably, a set control functions uniquely determine
an outcome of every single step, wherein said control functions
depend on age of cells, state of a current population and
associated environment.
[0319] Still preferably, a tumor is modelled as a combination of a
plurality of homogeneous group of cells, each of said homogeneous
group of cells representing a similarly behaving group of cells
distributed between all the cell-cycle compartments.
[0320] Still preferably, in each step, a number of cells in each
sub-compartment of each compartment of each group is calculated
according to factors including a previous state, parameters of
tumor, tumor current microenvironment and drug concentration.
[0321] Still preferably, spatial structure of the tumor is included
in the model.
[0322] Still preferably, PK and PD, cytotoxic effects and
cytostatic effects of anticancer drugs are incorporated into the
model.
[0323] Still preferably, a dose-limiting toxicity is incorporated
into the model.
[0324] Yet another aspect of the present invention is a method of
recommending an optimal treatment protocol for an individual
comprising: creating a system model; enumerating a plurality of
treatment protocols; modifying the system model based on parameters
specific to the individual; and selecting an optimal treatment
protocol from said plurality of treatment protocols based on the
modified system model.
[0325] Preferably, the step of creating the system model further
comprises: modelling a biological process; and realistically
modelling effects of a treatment on said biological process.
[0326] Still preferably, said modelling of biological processes is
done by mathematical modelling biological processes affecting
healthy cell populations and mathematically modelling biological
processes affecting cell populations with at least one disease.
[0327] Still preferably, said healthy cell populations include
bone-marrow cells and host tissue cells that are affected by said
treatment model.
[0328] Still preferably, said cell populations with at least one
disease is one of cancer cells, and diseased bone-marrow cells
including diseased Neutrophil cells and diseased Thrompocyte
cells.
[0329] Still preferably, said treatment models comprise treatment
specific processes that affect cell population.
[0330] Still preferably, said treatment specific process is
interactions involving at least one of a group comprising
pharmacokinetic (PK), pharmacodynamic (PD), cytostatic, cytotoxic,
and methods of affecting cell biology and causing cell death, with
associated biological processes.
[0331] Still preferably, said parameters specific to the individual
include one or more selected from a group consisting of parameters
related to the biological process' dynamics, patient specific drug
PK, PD and dynamics of dose-limiting host tissues
[0332] Still preferably, said parameters related to biological
process' dynamics comprise age, weight, gender, blood picture,
desired length of treatment protocol, previous reaction to
treatment, molecular markers, genetic markers, pathologic specifics
and cytologic specifics.
[0333] Still preferably, user-specific parameters are used in
selecting the optimal treatment.
[0334] Still preferably, a fitness function is used to perform the
selection.
[0335] Still preferably, said fitness function incorporates at
least one parameter selected from a group consisting patient
survival, time to death, time to reach a specified disease stage
and cure, tumor load, pathogen load, cytotoxicity, side effects,
quality of life, cost of treatment and pain.
[0336] Still preferably, a user can input specific coefficients for
said at least one parameter to adjust the fitness function to
satisfy the user's goals.
[0337] Still preferably, the user-specific parameters are based on
a user, said user being a medical doctor.
[0338] Still preferably, the user-specific parameters are based on
a user, said user being a scientist.
[0339] Still preferably, the user-specific parameters are based on
a user, said user being a drug developer.
[0340] Preferably, said selection of treatment protocols
incorporate cytotoxic effects.
[0341] Still preferably, said selection of treatment protocols
incorporate drug efficacy.
[0342] Still preferably, operation research techniques are used in
performing the selection.
[0343] Still preferably, heuristics are used to perform searching
and selection.
[0344] Still preferably, said heuristics comprise computational
feasibility.
[0345] Still preferably, said recommendation is a combination of
disease and treatment strategy, including type of treatment,
device, drug or drug combination, raditherapy, surgery and
treatment schedule and dosage. Yet another aspect of the present
invention is a method of recommending an optimal treatment protocol
for a general patient comprising: creating a system model;
enumerating a plurality of treatment protocols; and selecting an
optimal treatment protocol from said plurality of treatment
protocols based on the modified system model.
[0346] Still preferably, the step of creating the system model
further comprises: mathematical modelling a biological process; and
realistically modelling effects of a treatment on said biological
process;
[0347] Still preferably, said modelling of biological processes is
done by mathematical modelling biological processes affecting
healthy cell populations and mathematically modelling biological
processes affecting cell populations with at least one disease.
[0348] Still preferably, said healthy cell populations include
bone-marrow cells and host tissue cells that are affected by said
treatment model.
[0349] Still preferably, said cell populations with at least one
disease is one of cancer cells, and diseased bone-marrow cells
including diseased Neutrophil cells and diseased Thrompocyte
cells.
[0350] Still preferably, said treatment models comprise treatment
specific processes that affect cell population.
[0351] Still preferably, said treatment specific process is
interactions involving one of a group comprising pharmacokinetic,
pharmacodynamic, cytostatic, cytotoxic, or any other method of
affecting cell biology and causing cell death, with associated
biological processes.
[0352] Still preferably, user-specific parameters are used in
selecting the optimal treatment.
[0353] Still preferably, a fitness function is used to perform the
selection.
[0354] Still preferably, said fitness function incorporates at
least one parameter selected from a group comprising patient
survival, time to death, time to reach a specified disease stage
(including cure)e, tumor load, pathogen load, cytotoxicity, side
effects, quality of life, cost of treatment and pain.
[0355] Still preferably, a user can input specific coefficients for
said at least one parameter to adjust the fitness function to
satisfy the user's goals.
[0356] Still preferably, the user-specific parameters are based on
a user, said user being a medical doctor.
[0357] Still preferably, the user-specific parameters are based on
a user, said user being a scientist.
[0358] Still preferably, the user-specific parameters are based on
a user, said user being a drug developer.
[0359] Still preferably, said selection of treatment protocols
incorporate cytotoxic effects.
[0360] Still preferably, said selection of treatment protocols
incorporate drug efficacy.
[0361] Still preferably, operation research techniques are used in
performing the selection.
[0362] Still preferably, heuristics are used to perform searching
and selection.
[0363] Still preferably, said heuristics comprise computational
feasibility.
[0364] Still preferably, said recommendation is a combination of
disease and treatment strategy, including type of treatment,
device, drug, drug combination, radiotherapy, surgery and treatment
schedule and dosage.
[0365] Yet another aspect of the present invention is a method of
predicting progression of a biological process in an individual
patient under a plurality of treatment protocols, wherein said
biological process could be related to healthy or diseased
processes, said plurality of protocols including no treatment, said
method comprising creating a system model, enumerating a plurality
of treatment protocols; modifying the system model based on
parameters specific to the individual, and selecting an optimal
treatment protocol from said plurality of treatment protocols based
on the modified system model.
[0366] Preferably, the step of creating a system model further
comprises:
[0367] realistically modelling a biological process; and
realistically modelling the effects of the treatment on said
biological process.
[0368] Still preferably, said step of modelling a biological
process comprises creating a mathematical model for biological
processes affecting healthy cell populations and creating a
biological processes affecting cell populations with at least one
disease.
[0369] Still preferably, said healthy cell populations include
bone-marrow cells and host tissue cells that are affected by said
treatment model.
[0370] Still preferably, said cell populations with at least one
disease is one of cancer cells, and diseased bone-marrow cells
including diseased Neutrophil cells and diseased Thrombocyte
cells.
[0371] Still preferably, said treatment models comprise treatment
specific processes that affect cell population.
[0372] Still preferably, said treatment specific process is
interactions involving one of a group comprising PK, PD,
cytostatic, cytotoxic, or any other method of affecting cell
biology and causing cell death, with associated biological
processes.
[0373] Still preferably, said parameters specific to the individual
include one or more selected from a group consisting of parameters
related to the biological process' dynamics, patient specific drug
PK, PD and dynamics of dose-limiting host tissues.
[0374] Still preferably, said parameters related to biological
process' dynamics comprise age, weight, gender, blood picture,
desired length of treatment protocol, previous reaction to
treatment, molecular markers, genetic markers, pathologic specifics
and cytologic specifics.
[0375] Yet another aspect of the present invention is a method of
predicting progression of a biological process in a general patient
under a plurality of treatment protocols, wherein said biological
process could be related to healthy or diseased, said plurality of
protocols including no treatment, said method comprising creating a
system model; enumerating a plurality of treatment protocols; and
selecting an optimal treatment protocol from said plurality of
treatment protocols based on the modified system model.
[0376] Preferably, the step of creating a system model further
comprises realistically modelling a biological process; and
realistically modelling the and the effects of the treatment on
said biological process.
[0377] Still preferably, said step of modelling a biological
process comprises creating a mathematical model for biological
processes affecting healthy cell populations and creating a
biological processes affecting cell populations with at least one
disease.
[0378] Still preferably, said healthy cell populations include
bone-marrow cells and host tissue cells that are affected by said
treatment model.
[0379] Still preferably, said cell populations with at least one
disease is one of cancer cells, and diseased bone-marrow cells
including at least one of diseased Neutrophil cells and diseased
Thrombocyte cells.
[0380] Still preferably, said treatment models comprise treatment
specific processes that affect cell population.
[0381] Still preferably, said treatment specific process is
interactions involving one of a group comprising PK, PD, drug
cytostatics, drug cytotoxics, and methods of affecting cell biology
and causing cell death, with associated biological processes.
[0382] Yet another aspect of the present invention is a method for
modelling Thrombopietic lineage in an individual, said method
comprising: realistically modelling a process to create a process
model for cells involved in Thrombopoiesis; and modifying the
process model based on parameters specific to the individual.
[0383] Preferably, a realistic progression of cells involved in
diseased Thrombopoiesis is incorporated in the process model.
[0384] Still preferably, diseased Thrombopoiesis includes
Thrombocytopenia.
[0385] Still preferably, effects of at least one drug in the
realistic progression of cells involved in Thrombopoiesis is
incorporated.
[0386] Still preferably, said at least one drug is Thrombopoietin
(TPO).
[0387] Still preferably, said process model imitates a course of
the individual's bone marrow progression, peripheral platelet
counts and TPO concentration changes.
[0388] Still preferably, said process model incorporates
cell-suppressive treatment effects and administration of TPO to the
patient.
[0389] Still preferably, said cell-suppressive treatment is
chemotherapy.
[0390] Preferably, said method is used for recommending an optimum
treatment protocol, and wherein said method further comprises:
enumerating a plurality of treatment protocols; and selecting an
optimal treatment protocol from said plurality of treatment
protocols based on the modified system model.
[0391] Yet another aspect of the present invention is a method for
modelling Thrombopietic lineage in a general patient, said method
comprising: realistically modelling a process to create a process
model for cells involved in Thrombopoiesis.
[0392] Preferably, a realistic progression of cells involved
indiseased throbmopoiesis is incorporated in the process model.
[0393] Still preferably, diseased Thrombopoiesis includes
Thrombocytopenia.
[0394] Still preferably, effects of at least one drug in the
realistic progression of cells involved in Thrombopoiesis is
incorporated.
[0395] Still preferably, said at least one drug is Thrombopoietin
(TPO).
[0396] Still preferably, said process model imitates a course of
the individual's bone marrow progression, peripheral platelet
counts and TPO concentration changes.
[0397] Still preferably, said process model incorporates
cell-suppressive treatment effects and administration of TPO to the
patient.
[0398] Still preferably, said cell-suppressive treatment is
chemotherapy.
[0399] Preferably, said method is used for recommending an optimum
treatment protocol, and wherein said method further comprises:
enumerating a plurality of treatment protocols; and selecting an
optimal treatment protocol from said plurality of treatment
protocols based on the modified system model.
[0400] Yet another aspect of the present invention is a method for
predicting progression of Thrombopoiesis and Thrombocytopenia for
an individual under a plurality of treatment protocols, said
plurality of protocols including no treatment, said method
comprising: creating a realistic model of Thrombopoiesis and
Thrombocytopenia; generating a plurality of treatment protocols for
affecting Thrombopoiesis and treating Thrombocytopenia using at
least one drug;
[0401] modifying the model based on parameters specific to the
individual; and
[0402] predicting the progression of the disease or the natural
biological process under said plurality of treatment protocols
based on the modified system model.
[0403] Preferably, the model incorporates a realistic progression
of cells involved indiseased Thrombopoiesis.
[0404] Still preferably, diseased Thrombopoiesis includes
Thrombocytopenia.
[0405] Still preferably, the model incorporates effects of at least
one drug in the realistic progression of cells involved in
Thrombocytopenia.
[0406] Still preferably, said at least one drug is Thrombopoietin
(TPO).
[0407] Still preferably, the model imitates a course of the
individual's bone marrow progression, peripheral platelet counts
and TPO concentration changes.
[0408] Still preferably, the model incorporates cell-suppressive
treatment effects and administration of TPO to the patient.
[0409] Still preferably, said cell-suppressive treatment is
chemotherapy.
[0410] Still preferably, said process model further comprises a
plurality of compartments.
[0411] Still preferably, said compartments include:
[0412] a stem cell (SC) compartment that comprises bone marrow
haemopoietic progenitors that have an ability to differentiate into
more than one cell line wherein cells in the stem cell compartment
proliferate and differentiate into one of megakaryocyte;
[0413] a colony forming units--megakaryocytes (CFU-Meg)
compartment, wherein the megakaryocyte progenitors get committed as
a megakaryocyte line and spend some time multiplying and
maturing;
[0414] a megakaryoblast (MKB) compartment, which receives the cells
from CFU-Meg, wherein the cells in the MKB compartment have lost
their ability to proliferate but are not mature to release
platelets;
[0415] a MK16 compartment, which receives cell from the MKB
compartment, wherein a subset of cells in the MK16 compartment
release platelets at a constant rate until they exhaust their
capacity and are disintegrated and a second subset of cells do not
release platelets but continue with endomitosis;
[0416] a MK32 compartment that receives cells from the MK16
compartment, wherein a subset of cells in this compartment release
platelets and a second subset of cells do not release platelets but
continue with endomitosis;
[0417] a MK64 compartment that receives cells from the MK32
compartment wherein a subset of cells in this compartment release
platelets and a second subset of cells do not release platelets but
continue with endomitosis;
[0418] a MK128 compartment that receives cells from the MK64
compartment wherein a subset of cells in this compartment release
platelets; and
[0419] a platelets (PL) compartment.
[0420] Still preferably, an effect of apoptosis are included with
an overall effect of cell proliferation in giving rise to an
amplification of cell numbers in a corresponding compartment.
[0421] Still preferably, the model further incorporates the effects
of TPO on the SC, CFU-Meg and MKB compartments.
[0422] Still preferably, the effects are expressed in terms of
effects of TPO concentration on amplification rate, rate of cell
maturation and a fraction of cells that undergo endomotisis.
[0423] Still preferably, when the TPO concentration is above a
predetermined threshold level, the amplification rate of cells in
the SC compartment are affected and below the threshold the
amplification rate is dependent only on a current number of
cells.
[0424] Still preferably, in the CFU-Meg compartment the cells are
sensitive to TPO concentration regardless of the concentration of
TPO.
[0425] Still preferably, the transit time is same in all platelet
releasing compartments and the transit time of the SC, CFU-Meg and
MKB compartments are functions of micro-environmental
conditions.
[0426] Still preferably, in the SC compartment when the TPO
concentration is above the threshold, the transit time is shortened
based the dose.
[0427] Still preferably, in the CFU-Meg and MKB, the transit time
is solely based on TPO concentration.
[0428] Still preferably, a fraction of cells in the SC compartment
that commits to megakaryocytic lineage is constant and dependent on
TPO.
[0429] Still preferably, in the CFU-Meg and MKB compartments, every
mature cell passes on to the next compartment.
[0430] Still preferably, in the MK16, MK32 and MK64 compartments, a
fraction of cells pass on to the next compartment, said fraction
being dependent on the TPO concentration.
[0431] Still preferably, cells from MK128 compartment do not flow
into any other compartment.
[0432] Still preferably, each of said compartments is further
divided into sub-compartments, each of said sub-compartments
containing cells of a specific age in hours.
[0433] Still preferably, cells that spend all their corresponding
transit time in a given compartment pass on to the next
compartment, wherein cells that have left a corresponding
compartment each hour fill the first sub-compartment of the next
compartment.
[0434] Still preferably, the platelet releasing cells contribute
platelets to the first sub-compartment of the PL compartment.
[0435] Yet another aspect of the present invention is a method for
predicting progression of Thrombopoiesis and Thrombocytopenia for a
general patient under a plurality of treatment protocols, said
plurality of protocols including no treatment, said method
comprising: creating a realistic model Thrombopoiesis and
Thrombocytopenia; generating a plurality of treatment protocols for
affecting Thrombopoiesis and treating Thrombocytopenia using at
least one drug; and predicting the progression of the disease or
the natural biological process under said plurality of treatment
protocols based on the modified system model.
[0436] Preferably, the model incorporates a realistic progression
of cells involved in diseased Thrombopoiesis.
[0437] Still preferably, diseased Thrombopoiesis includes
Thrombocytopenia.
[0438] Still preferably, the model incorporates effects of at least
one drug in the realistic progression of cells involved in
Thrombocytopenia.
[0439] Still preferably, said at least one drug is Thrombopoietin
(TPO).
[0440] Still preferably, the model imitates a course of the
individual's bone marrow progression, peripheral platelet counts
and TPO concentration changes.
[0441] Still preferably, the model incorporates cell-suppressive
treatment effects and administration of TPO to the patient.
[0442] Still preferably, said cell-suppressive treatment is
chemotherapy.
[0443] Still preferably, said process model further comprises a
plurality of compartments.
[0444] Still preferably, said compartments include:
[0445] a stem cell (SC) compartment that comprises bone marrow
haemopoietic progenitors that have an ability to differentiate into
more than one cell line wherein cells in the stem cell compartment
proliferate and differentiate into one of megakaryocyte;
[0446] a colony forming units--megakaryocytes (CFU-Meg)
compartment, wherein the megakaryocyte progenitors get committed as
a megakaryocyte line and spend some time multiplying and
maturing;
[0447] a megakaryoblast (MKB) compartment, which receives the cells
from CFU-Meg, wherein the cells in the MKB compartment have lost
their ability to proliferate but are not mature to release
platelets;
[0448] a MK16 compartment, which receives cell from the MKB
compartment, wherein a subset of cells in the MK16 compartment
release platelets at a constant rate until they exhaust their
capacity and are disintegrated and a second subset of cells do not
release platelets but continue with endomitosis;
[0449] a MK32 compartment that receives cells from the MK16
compartment, wherein a subset of cells in this compartment release
platelets and a second subset of cells do not release platelets but
continue with endomitosis;
[0450] a MK64 compartment that receives cells from the MK32
compartment wherein a subset of cells in this compartment release
platelets and a second subset of cells do not release platelets but
continue with endomitosis;
[0451] a MK128 compartment that receives cells from the MK64
compartment wherein a subset of cells in this compartment release
platelets; and
[0452] a platelets (PL) compartment.
[0453] Still preferably, an effect of apoptosis are included with
an overall effect of cell proliferation in giving rise to an
amplification of cell numbers in a corresponding compartment.
[0454] Still preferably, the model further incorporates the effects
of TPO on the SC, CFU-Meg and MKB compartments.
[0455] Still preferably, the effects are expressed in terms of
effects of TPO concentration on amplification rate, rate of cell
maturation and a fraction of cells that undergo endomotisis.
[0456] Still preferably, when the TPO concentration is above a
predetermined threshold level, the amplification rate of cells in
the SC compartment are affected and below the threshold the
amplification rate is dependent only on a current number of
cells.
[0457] Still preferably, in the CFU-Meg compartment the cells are
sensitive to TPO concentration regardless of the concentration of
TPO.
[0458] Still preferably, the transit time is same in all platelet
releasing compartments and the transit time of the SC, CFU-Meg and
MKB compartments are functions of micro-environmental
conditions.
[0459] Still preferably, in the SC compartment when the TPO
concentration is above the threshold, the transit time is shortened
based the dose.
[0460] Still preferably, in the CFU-Meg and MKB, the transit time
is solely based on TPO concentration.
[0461] Still preferably, a fraction of cells in the SC compartment
that commits to megakaryocytic lineage is constant and dependent on
TPO.
[0462] Still preferably, in the CFU-Meg and MKB compartments, every
mature cell passes on to the next compartment.
[0463] Still preferably, in the MK16, MK32 and MK64 compartments, a
fraction of cells pass on to the next compartment, said fraction
being dependent on the TPO concentration.
[0464] Still preferably, cells from MK128 compartment do not flow
into any other compartment.
[0465] Still preferably, each of said compartments is further
divided into sub-compartments, each of said sub-compartments
containing cells of a specific age in hours.
[0466] Still preferably, cells that spend all their corresponding
transit time in a given compartment pass on to the next
compartment, wherein cells that have left a corresponding
compartment each hour fill the first sub-compartment of the next
compartment.
[0467] Still preferably, the platelet releasing cells contribute
platelets to the first sub-compartment of the PL compartment.
[0468] Yet another aspect of the present invention is a method for
modelling Neutrophil lineage for an individual, said method
comprising: creating a realistic a Neutrophil system model
including a realistic process model for cells involved in
Neutrophil lineage; and modifying the system model based on
parameters specific to the individual.
[0469] Preferably, the system model incorporates a realistic
progression of cells involved in Granulopoietic disorders,
including Neutropenia.
[0470] Still preferably, the system model incorporates effects of
at least one drug in the realistic progression of cells involved in
Granulopoiesis and Neutropenia.
[0471] Still preferably, said at least one drug is Granulocyte
Colony Stimulating Factor (G-CSF).
[0472] Still preferably, said system model comprises at least three
stages, a first stage related to an administered amount of
cytokine;
[0473] a second stage representing a pharmacokinetic behavior of
G-CSF; and
[0474] a third stage representing a phrmacodynamic effect of G-CSF
on kinetic parameters of the system.
[0475] Still preferably, said model comprises a mitotic
compartment, and a post mitotic compartment, said mitotic
compartment being divided into subcompartments wherein a kth
sub-compartment contains cells of age between k-1 and k hours
relative to a time of entry into the mitotic compartment.
[0476] Still preferably, effects of toxic drugs, including
chemotherapy are incorporated by mapping various cell-cycle phases
to the sub-compartments and formulating a function of cytotoxic
effects of toxic drugs, including chemotherapy on the cell-cycle
phases.
[0477] Still preferably, the effects of G-CSF on the mitotic
compartment are modeled as an increase in a rate of cells entering
the myeloblasts compartment from an uncommitted stem cell pool.
[0478] Still preferably, the post-mitotic compartment is modeled as
a single pool of cells wherein cells in a last sub-compartment of
the mitotic compartment enters the post-mitotic compartment and a
proportion of cells within the post-mitotic compartment enters the
mature Neutrophil pool every hour.
[0479] Still preferably, effects of G-CSF on the Neutrophil lineage
are modeled as a decrease in the cells in the post-mitotic
compartment which is subsequently compensated by an increased
production in the mitotic compartment, said compensation sustaining
an increase in Neutrophil count.
[0480] Still preferably, an elimination of Neutrophils in the
post-mitotic compartment is represented by a Poisson
distribution.
[0481] Still preferably, the cytotoxic effects of toxic drugs,
including chemotherapy in the post-mitotic compartment is modeled
as an effect on a single pool of cells.
[0482] Still preferably, kinetic of G-CSF is modeled as an
exponential distribution.
[0483] Still preferably, a selection of an optimal treatment uses
an objective function that aims at minimizing G-CSF administration
and returning Neutrophil lineage to normal levels.
[0484] Still preferably, selection is performed using linear
programming.
[0485] Still preferably, phrmacokinetics and pharmacodynamics of
G-CSF are defined using piecewise linear functions.
[0486] Preferably, said method is used for recommending an optimum
treatment protocol, and wherein said method further comprises:
enumerating a plurality of treatment protocols; and selecting an
optimal treatment protocol from said plurality of treatment
protocols based on the modified system model.
[0487] Yet another aspect of the present invention is a method for
modelling Neutrophil lineage for a general patient, said method
comprising: creating a realistic a Granulopoiesis system model
including a realistic process model for cells involved in
Granulopoiesis lineage.
[0488] Preferably the system model incorporates a realistic
progression of cells involved in Granulopoietic disorders,
including Neutropenia.
[0489] Still preferably, the system model incorporates effects of
at least one drug in the realistic progression of cells involved
Granulopoiesis and in Neutropenia.
[0490] Still preferably, said at least one drug is Granulocyte
Colony Stimulating Factor (G-CSF).
[0491] Still preferably, said system model comprises at least three
stages, a first stage related to an administered amount of
cytokine;
[0492] a second stage representing a pharmacokinetic behavior of
G-CSF; and
[0493] a third stage representing a phrmacodynamic effect of G-CSF
on kinetic parameters.
[0494] Preferably, wherein said model comprises a mitotic
compartment, and a post mitotic compartment, said mitotic
compartment being divided into subcompartments wherein a kth
sub-compartment contains cells of age between k-1 and k hours
relative to a time of entry into the mitotic compartment.
[0495] Still preferably, effects of toxic drugs, including
chemotherapy are incorporated by mapping various cell-cycle phases
to the sub-compartments and formulating a function of cytotoxic
effects of toxic drugs, including chemotherapy on the cell-cycle
phases.
[0496] Still preferably, the effects of G-CSF on the mitotic
compartment are modeled as an increase in a rate of cells entering
the myeloblasts compartment from an uncommitted stem cell pool.
[0497] Still preferably, the post-mitotic compartment is modeled as
a single pool of cells wherein cells in a last sub-compartment of
the mitotic compartment enters the post-mitotic compartment and a
proportion of cells within the post-mitotic compartment enters the
mature Neutrophil pool every hour.
[0498] Still preferably, effects of G-CSF on the Neutrophil lineage
are modeled as a decrease in the cells in the post-mitotic
compartment which is subsequently compensated by an increased
production in the mitotic compartment, said compensation sustaining
an increase in Neutrophil count.
[0499] Still preferably, an elimination of Neutrophils in the
post-mitotic compartment is represented by a Poisson
distribution.
[0500] Still preferably, the cytotoxic effects of toxic drugs,
including chemotherapy in the post-mitotic compartment is modeled
as an effect on a single pool of cells.
[0501] Still preferably, kinetic of G-CSF is modeled as an
exponential distribution.
[0502] Still preferably, a selection of an optimal treatment uses
an objective function that aims at minimizing G-CSF administration
and returning Neutrophil lineage to normal levels.
[0503] Still preferably, said selection is performed using linear
programming.
[0504] Still preferably, phrmacokinetics and pharmacodynamics of
G-CSF are defined using piecewise linear functions.
[0505] Still preferably, said method is used for recommending an
optimum treatment protocol, and wherein said method further
comprises: enumerating a plurality of treatment protocols; and
selecting an optimal treatment protocol from said plurality of
treatment protocols based on the modified system model.
[0506] Yet another aspect of the present invention is a method for
predicting progression of Granulopoiesis for an individual under a
plurality of treatment protocols, said plurality of protocols
including no treatment, said system comprising: creating a
Neutrophil system model including a realistic process model for
cells involved in Neutrophil production; generating a plurality of
treatment protocols; modifying the system model modifier, wherein
said Neutrophil system model is modified by the system model
modifier based on parameters specific to the individual; and
predicting the progression under the plurality of treatment
protocols based on the modified system model.
[0507] Preferably, the system model incorporates a realistic
progression of cells involved in Granulopoietic disorders,
including Neutropenia.
[0508] Still preferably, the system incorporates effects of at
least one drug in the realistic progression of cells involved in
Granulopoiesis and Neutropenia.
[0509] Still preferably, said at least one drug is Granulocyte
Colony Stimulating Factor (G-CSF).
[0510] Still preferably, said model comprises at least three
stages, a first stage related to an administered amount of
cytokine;
[0511] a second stage representing a pharmacokinetic behavior of
G-CSF; and
[0512] a third stage representing a phrmacodynamic effect of G-CSF
on kinetic parameters.
[0513] Still preferably, said model comprises a mitotic
compartment, and a post mitotic compartment, said mitotic
compartment being divided into subcompartments wherein a kth
sub-compartment contains cells of age between k-1 and k hours
relative to a time of entry into the mitotic compartment.
[0514] Still preferably, effects of toxic drugs, including
chemotherapy are incorporated by mapping various cell-cycle phases
to the sub-compartments and formulating a function of cytotoxic
effects of toxic drugs, including chemotherapy on the cell-cycle
phases.
[0515] Still preferably, the effects of G-CSF on the mitotic
compartment are modeled as an increase in a rate of cells entering
the myeloblasts compartment from an uncommitted stem cell pool.
[0516] Still preferably, the post-mitotic compartment is modeled as
a single pool of cells wherein cells in a last sub-compartment of
the mitotic compartment enters the post-mitotic compartment and a
proportion of cells within the post-mitotic compartment enters the
mature Neutrophil pool every hour.
[0517] Still preferably, effects of G-CSF on the Neutrophil lineage
are modeled as a decrease in the cells in the post-mitotic
compartment which is subsequently compensated by an increased
production in the mitotic compartment, said compensation sustaining
an increase in Neutrophil count.
[0518] Still preferably, an elimination of Neutrophils in the
post-mitotic compartment is represented by a Poisson
distribution.
[0519] Still preferably, the cytotoxic effects of toxic drugs,
including chemotherapy in the post-mitotic compartment is modeled
as an effect on a single pool of cells.
[0520] Still preferably, kinetic of G-CSF is modeled as an
exponential distribution.
[0521] Preferably, a selection of an optimal treatment uses an
objective function that aims at minimizing G-CSF administration and
returning Neutrophil lineage to normal levels.
[0522] Still preferably, said selection is performed using linear
programming.
[0523] Still preferably, phrmacokinetics and pharmacodynamics of
G-CSF are defined using piecewise linear functions.
[0524] Yet another aspect of the present invention is a method for
predicting progression of Granulopoiesis for a general patient
under a plurality of treatment protocols, said plurality of
protocols including no treatment, said system comprising: creating
a Neutrophil system model including a realistic process model for
cells involved in Neutrophil production; generating a plurality of
treatment protocols; and predicting the progression under the
plurality of treatment protocols based on the modified system
model.
[0525] Still preferably, the system model incorporates a realistic
progression of cells involved in Granulopoietic disorders,
including Neutropenia.
[0526] Still preferably, the system incorporates effects of at
least one drug in the realistic progression of cells involved in
Granulopoiesis and Neutropenia.
[0527] Still preferably, said at least one drug is Granulocyte
Colony Stimulating Factor (G-CSF).
[0528] Still preferably, said model comprises at least three
stages, a first stage related to an administered amount of
cytokine;
[0529] a second stage representing a pharmacokinetic behavior of
G-CSF; and
[0530] a third stage representing a phrmacodynamic effect of G-CSF
on kinetic parameters.
[0531] Still preferably, said model comprises a mitotic
compartment, and a post mitotic compartment, said mitotic
compartment being divided into subcompartments wherein a kth
sub-compartment contains cells of age between k-1 and k hours
relative to a time of entry into the mitotic compartment.
[0532] Still preferably, effects of toxic drugs, including
chemotherapy are incorporated by mapping various cell-cycle phases
to the sub-compartments and formulating a function of cytotoxic
effects of toxic drugs, including chemotherapy on the cell-cycle
phases.
[0533] Still preferably, the effects of G-CSF on the mitotic
compartment are modeled as an increase in a rate of cells entering
the myeloblasts compartment from an uncommitted stem cell pool.
[0534] Still preferably, the post-mitotic compartment is modeled as
a single pool of cells wherein cells in a last sub-compartment of
the mitotic compartment enters the post-mitotic compartment and a
proportion of cells within the post-mitotic compartment enters the
mature Neutrophil pool every hour.
[0535] Still preferably, effects of G-CSF on the Neutrophil lineage
are modeled as a decrease in the cells in the post-mitotic
compartment which is subsequently compensated by an increased
production in the mitotic compartment, said compensation sustaining
an increase in Neutrophil count.
[0536] Still preferably, an elimination of Neutrophils in the
post-mitotic compartment is represented by a Poisson
distribution.
[0537] Still preferably, the cytotoxic effects of toxic drugs,
including chemotherapy in the post-mitotic compartment is modeled
as an effect on a single pool of cells.
[0538] Still preferably, kinetic of G-CSF is modeled as an
exponential distribution.
[0539] Still preferably, a selection of an optimal treatment uses
an objective function that aims at minimizing G-CSF administration
and returning Neutrophil lineage to normal levels.
[0540] Still preferably, said selection is performed using linear
programming.
[0541] Still preferably, pharmacokinetics and pharmacodynamics of
G-CSF are defined using piecewise linear functions.
[0542] Yet another aspect of the present invention a method for
recommending an optimal treatment protocol for treating cancer
using drugs, including chemotherapy, for an individual, said method
comprising: creating a cancer system model; enumerating a plurality
of treatment protocols for treating cancer using drugs, including
chemotherapy; modifying the system model based on parameters
specific to the individual; and selecting an optimal treatment
protocol from said plurality of treatment protocols based on the
modified system model.
[0543] Preferably, the system model further comprises: a realistic
process model of cancer development; and a realistic treatment
model that models the effects of treating cancer with drugs,
including chemotherapy.
[0544] Still preferably, said process model incorporates a
distribution of cycling cells and quiescent cells.
[0545] Still preferably, where a tumor cell cycle is divided into
at least four compartments G1, S, G2 and M and a quiescent stage is
denoted by G0, wherein each of said four compartments is further
subdivided into sub-compartments and an ith sub-compartment
representing cells of age I in the corresponding compartment,
wherein cells entering a compartment always enter a first
sub-compartment of the compartment.
[0546] Still preferably, the model traces development of cancer
cells using a predetermined set of parameters by calculating a
number of cells in each subcompartment using stepwise
equations.
[0547] Still preferably, a probability vector is used to determine
a fraction of cells that leaves any subcompartment in a compartment
to move to a first subcompartment of the next compartment.
[0548] Still preferably, a set of control functions uniquely
determine an outcome of every single step, wherein said control
functions depend on age of cells, state of a current population and
associated environment.
[0549] Still preferably, a tumor is modelled as a combination of a
plurality of homogeneous group of cells, each of said homogeneous
group of cells representing a similarly behaving group of cells
distributed between all the cell-cycle compartments.
[0550] Still preferably, in each step, a number of cells in each
sub-compartment of each compartment of each group is calculated
according to factors including a previous state, parameters of
tumor, tumor current microenvironment and drug concentration.
[0551] Still preferably, spatial structure of the tumor is included
in the model.
[0552] Still preferably, PK and PD, cytotoxic effects,cytostatic
effects and other effects on cell disintegration of anticancer
drugs are incorporated into the model.
[0553] Still preferably, a dose-limiting toxicity is incorporated
into the model.
[0554] Still preferably, said parameters specific to the individual
comprise parameters related to tumor dynamics, patient specific
drug PK, and dynamics of dose-limiting host tissues.
[0555] Still preferably, said parameters related to tumor dynamics
comprise age, weight, gender, percentage of limiting healthy cells,
desired length of treatment protocol, previous reaction to
treatment, molecular markers, genetic markers, pathologic specifics
and cytologic specifics.
[0556] Yet another aspect of the present invention is a method of
predicting a progression of cancer in an individual, said method
comprising: creating a cancer system model; enumerating a plurality
of treatment protocols for treating cancer using drugs, including
chemotherapy; modifying the system model based on parameters
specific to the individual; and selecting an optimal treatment
protocol from said plurality of treatment protocols based on the
modified system model.
[0557] Preferably, the system model further comprises: a realistic
process model of cancer development; and a realistic treatment
model that models the effects of treating cancer with drugs,
including chemotherapy.
[0558] Still preferably, said process model incorporates a
distribution of cycling cells and quiescent cells.
[0559] Still preferably, a tumor cell cycle is divided into at
least four compartments G1, S, G2 and M and a quiescent stage is
denoted by G0, wherein each of said four compartments is further
subdivided into sub-compartments and an ith sub-compartment
representing cells of age I in the corresponding compartment,
wherein cells entering a compartment always enter a first
sub-compartment of the compartment.
[0560] Still preferably, the model traces development of cancer
cells using a predetermined set of parameters by calculating a
number of cells in each subcompartment using stepwise
equations.
[0561] Still preferably, a probability vector is used to determine
a fraction of cells that leaves any subcompartment in a compartment
to move to a first subcompartment of the next compartment.
[0562] Still preferably, a set control functions uniquely determine
an outcome of every single step, wherein said control functions
depend on age of cells, state of a current population and
associated environment.
[0563] Still preferably, a tumor is modelled as a combination of a
plurality of homogeneous group of cells, each of said homogeneous
group of cells representing a similarly behaving group of cells
distributed between all the cell-cycle compartments.
[0564] Still preferably, in each step, a number of cells in each
sub-compartment of each compartment of each group is calculated
according to factors including a previous state, parameters of
tumor, tumor current microenvironment and drug concentration.
[0565] Still preferably, spatial structure of the tumor is included
in the model.
[0566] Still preferably, PK and PD, cytotoxic and other cell
disintegration effects, and cytostatic effects of anticancer drugs
are incorporated into the model.
[0567] Still preferably, a dose-limiting toxicity is incorporated
into the model.
[0568] Still preferably, said parameters specific to the individual
comprise parameters related to tumor dynamics, patient specific
drug PK, and dynamics of dose-limiting host tissues.
[0569] Still preferably, said parameters related to tumor dynamics
comprise age, weight, gender, percentage of limiting healthy cells,
desired length of treatment protocol, previous reaction to
treatment, molecular markers, genetic markers, pathologic specifics
and cytologic specifics.
[0570] Yet another aspect of the present invention is a method of
predicting a progression of cancer in a general patient, said
method comprising: creating a cancer system model; enumerating a
plurality of treatment protocols for treating cancer using drugs,
including chemotherapy; and selecting an optimal treatment protocol
from said plurality of treatment protocols based on the modified
system model.
[0571] Still preferably, the system model further comprises: a
realistic process model of cancer development; and a realistic
treatment model that models the effects of treating cancer with
drugs, including chemotherapy.
[0572] Still preferably, said process model incorporates a
distribution of cycling cells and quiescent cells.
[0573] Still preferably, a tumor cell cycle is divided into at
least four compartments G1, S, G2 and M and a quiescent stage is
denoted by G0, wherein each of said four compartments is further
subdivided into sub-compartments and an ith sub-compartment
representing cells of age I in the corresponding compartment,
wherein cells entering a compartment always enter a first
sub-compartment of the compartment.
[0574] Still preferably, the model traces development of cancer
cells using a predetermined set of parameters by calculating a
number of cells in each subcompartment using stepwise
equations.
[0575] Still preferably, a probability vector is used to determine
a fraction of cells that leaves any subcompartment in a compartment
to move to a first subcompartment of the next compartment.
[0576] Still preferably, a set control functions uniquely determine
an outcome of every single step, wherein said control functions
depend on age of cells, state of a current population and
associated environment.
[0577] Still preferably, a tumor is modelled as a combination of a
plurality of homogeneous group of cells, each of said homogeneous
group of cells representing a similarly behaving group of cells
distributed between all the cell-cycle compartments.
[0578] Still preferably, in each step, a number of cells in each
sub-compartment of each compartment of each group is calculated
according to factors including a previous state, parameters of
tumor, tumor current microenvironment and drug concentration.
[0579] Still preferably, spatial structure of the tumor is included
in the model.
[0580] Still preferably, PK and PD, cytotoxic effects and
cytostatic effects of anticancer drugs are incorporated into the
model.
[0581] Still preferably, a dose-limiting toxicity is incorporated
into the model.
[0582] Yet another aspect of the present invention is a computer
program product, including a computer readable medium, said program
product comprising a set of instruction to enable a computer system
to aid in recommending an optimal treatment protocol for an
individual comprising:
[0583] a system model code; treatment protocol code for a plurality
of treatment protocols;
[0584] a system model modifier code , wherein said system model is
modified by the system model modifier based on parameters specific
to the individual; and
[0585] a selector code to select an optimal treatment protocol from
said plurality of treatment protocols based on the modified system
model.
[0586] Preferably, the system model code further comprises: a
realistic biological process model code; and a realistic treatment
model code that enables a computer to model the effects of a
treatment on the biological process.
[0587] Yet another aspect of the present invention is a computer
program product, including a computer readable medium, said program
product comprising a set of instructions to enable a computer
system to aid in recommending an optimal treatment protocol for a
general patient comprising: a system model code; treatment protocol
code for a plurality of treatment protocols; and a selector code to
select an optimal treatment protocol from said plurality of
treatment protocols based on the modified system model.
[0588] Preferably, the system model code further comprises: a
realistic biological process model code; and
[0589] a realistic treatment model code that enables a computer to
model the effects of a treatment on the biological process.
III. BRIEF DESCRIPTION OF THE DRAWINGS
[0590] The present invention will be understood and appreciated
more fully from the following detailed description taken in
conjunction with the appended drawings in which:
[0591] FIG. 1 is a schematic illustration of the basis of the
present invention;
[0592] FIG. 2 is a flow chart illustration of steps of the
invention, useful in understanding FIG. 1; FIG. 2a further
illustrates a protocol space;
[0593] FIG. 3 is a schematic illustration of a biological model, in
accordance with one embodiment of the present invention;
[0594] FIG. 4 is a chart illustration of the biological model of
FIG. 3;
[0595] FIG. 5 is a graphical illustration of the chart of FIG.
4;
[0596] FIG. 6 is a chart illustration of the biological model of
FIG. 3 in a different format;
[0597] FIG. 7 is a graphical illustration of the chart of FIG.
6;
[0598] FIGS. 8A and 8B are graphical illustrations of the output of
the model of FIG. 3;
[0599] FIGS. 9A and 9B are graphical illustrations of experimental
data as compared to the output shown in FIGS. 8A and 8B;
[0600] FIG. 10 is a schematic illustration of a biological model,
in accordance with a further embodiment of the present
invention;
[0601] FIG. 11 is a graphical illustration of results of the
simulation of the model shown in FIG. 10;
[0602] FIGS. 12A and 12B are graphical illustrations of the effects
of two doses of G-CSF on the Neutrophil line, according to the
model of FIG. 10;
[0603] FIG. 13 is a schematic illustration of a biological model,
in accordance with a further embodiment of the present
invention;
[0604] FIGS. 14 and 15 show a comparison of Neutrophil production
according to the described model and experimental data in the
literature.
IV. DETAILED DESCRIPTION OF THE PRESENT INVENTION
[0605] Systems and methods have been disclosed for identifying
optimal treatment strategies for a general patient and a specific
individual patient, and for predicting progression of a biological
process and treatment, using selected parameters. The techniques
are based on biological and clinical knowledge, mathematical
models, computer simulations, and optimization methods. The
optimization techniques could be any available mathematical
techniques including, but not limited to, linear programming and
heuristic search. The disclosed heuristic search techniques use
heuristic (or rules of thumb) determinations.
[0606] Such a use of heuristics search enables the user to find
near optimal solutions even for complex mathematical descriptions
of a combination of relevant biological, clinical, pharmacological
scenarios. These complex mathematical descriptions are contemplated
to be realistic simulations of actual scenarios. It is contemplated
that this holds both for the general case ("optimal generic
treatment"), as well as at the level of an individual patient.
[0607] The general case is intended for several purposes including
use by pharmaceutical companies and by researches who are more
concerned with designing systems and recommending treatment for a
general patient as opposed to recommending treatment for a specific
patient in a clinical setting. It is also contemplated that the
general case can be used for a better understanding of the
underlying processes for any other use. Likewise, the individual
case is intended for several purposes including, for example, the
use by a doctor to understand the progress of a treatment protocol
or the progression of a disease, and to optimize the treatment for
a specific. individual patient. These indicated uses are not
intended to be restrictive. It should be clear to the skilled
practitioner that the techniques disclosed can be put to several
other uses.
[0608] FIG. 1 illustrates the general concept behind the disclosed
technique. Detailed parameters are input to a protocol space. The
protocol space comprises a plurality of treatment protocols. From
this protocol space an optimal treatment protocol is selected by
performing a heuristic search.
[0609] FIG. 2 shows a diagram chart that depicts an illustration of
an embodiment of the disclosed techniques for optimization. The
Figure generally depicts the basic concept. The disclosed
techniques are used to optimize a drug delivery protocol after
consideration of a plurality of possible protocols. The plurality
of protocols together form a protocol space 2.5. Determination of
an optimal protocol is partially based on specific parameters input
by a user. The user may be a physician, a drug developer, a
scientist, or anyone else who may need to determine a treatment
strategy, including drug protocols. The specific parameters may
include several categories and needs of a specific user and other
particulars such as patient survival, efficacy, time to death, time
to reach a specified disease stage (including cure), tumor load,
pathogen load, cytotoxicity, side effects, quality of life, cost of
treatment, and pain. maximum length of treatment, confidence level,
etc. In case of the disclosed techniques for the individual
patient, general characteristic parameters which determine the
system's behaviour, are altered according to individual patient
characteristics and/or medical history of the patient.
[0610] Initially, system models are created. These included models
to simulate all the relevant biological, clinical and
pharmaceutical process 2.1. These models include mathematical
models for processes that affect healthy cells as well as
mathematical models for processes that affect cell populations with
one or more diseases. In addition, a model of treatment effects 2.3
on each of these processes is created. The treatment effects
include processes that are specific to individual treatment. Such a
treatment may be based on the effects of a drug's process that
affects the relevant cell population. Examples of these effects
include interactions invovlving pharmacokinetic (PK),
pharmacodynamics (PD), cytotoxic and cytostatics, or any other
method of affecting cell biology and causing cell death, with
associated biological processes.
[0611] The combination of these models provides a detailed
mathematical model of the overall bio-clinical scenario in a
general sense or for a specific patient, together with the specific
effects of a particular treatment. Once the comprehensive model is
constructed, the characteristic parameters are incorporated in it.
The characteristic parameters could be either population averaged
or patient specific. In case of the general case, average patient
parameters are incorporated. The average patient parameters include
parameters related to biological process dynamics, average drug PK,
average drug PD and dynamics of does-limiting host tissues. In this
way a "virtual general patient" in the form of a complete detailed
model 2.4 is generated. In case of the individual case, patient
specific parameters 2.2 are incorporated. The patient specific
parameters include parameters related to biological process
dynamics, patient specific drug PK, patient specific drug PD and
dynamics of does-limiting host tissues. The parameters related to
biological process dynamics include, age, gender, weight, blood
picture, desired length of the treatment protocol, previous
reactions to treatment, molecular markers, genetic markers,
pathologic specifics and cytologic specifics or clinical
indications. In this way a "virtual individual patient" in the form
of a complete detailed model 2.4 is generated.
[0612] Then a protocol space 2.5 is generated. To do this, possible
permutations of certain parameters such as drug doses, dosing
intervals, etc. are considered. Thus, a number of possible
treatment protocols is generated. This number could be very large
because of the number of permutations possible. The amount of
possibilities depends on the number and ranges of parameters
considered.
[0613] A fitness function 2.6 is then constructed by mathematically
considering different possible factors which may be influenced by
the treatment. These may include patient survival, time to death,
time to reach a specified disease stage (including cure), tumor
load, pathogen load, cytotoxicity to normal or diseased tissues,
other side effects, quality of life, cost of treatment, pain, etc.
The user can alter certain specific parameters in the fitness
function so as to adjust this function to the user's specific
goals. The user can be anybody, including a medical doctor, a
scientist or a drug developer. Based on the selected parameters,
the fitness function is applied. This results in the calculation of
a fitness score for each and every protocol in the protocol space.
Finally, the optimization step is carried out 2.7, either by search
heuristics or by analytical methods, in order to select the optimal
treatment protocol 2.8 from all the scored possibilities. The
analytical methods include the use of Operations Research
techniques. In selecting the optimal treatment protocol cytotoxic
effects as well as treatment efficacy are incorporated, as well as
other objectives of the said fitness function. The heuristics, or
rules of thumb employed include computational facility. The optimal
treatment protocol is a combination of disease and treatment
strategy, including type of treatment, device, drug or drug
combination, radiotherapy, surgery and treatment schedule.
[0614] In this way, a disease specific, patient specific, situation
specific, treatment type specific (e.g. drug therapy, operation,
radiotherapy), drug specific, or an objective specific treatment
protocol may be obtained. The actual time it takes once the
parameters are entered may be negligibly short or up to hours,
depending on the length of the simulated treatment period and the
power of the specific search heuristics and the computational
tools, making this a very feasible tool.
[0615] Systems and methods embodying the above disclosed technique
for a general patient as well as for an individual patient are
within the scope of the present invention.
[0616] The system can be implemented remotely over a distributed
computing system with the user remotely dialing in. It can also be
implemented over the internet. The computer could be a PC,
mainframe, a workstation or a remote computer on a network.
[0617] Another aspect of the disclosed technique is a computer
program code. The computer program product includes a computer
readable medium. It should be noted that the computer readable
medium includes any fixed media including, but not limited to,
floppy disk, hard disk, CD, chips, tapes, cartridges with Ics, etc.
The computer readable media also includes instructions transmitted
through a network or downloaded from the internet. The computer
program product includes instructions for enabling a computer to
aid in selecting a treatment protocol. The instructions include a
system model code. A treatment protocol code is provided for a
plurality of treatment protocols. In case of the disclosed
technique for an individual patient, a system model modifier code
is provided that enables the computer to modify the system model
based on parameters specific to the individual. A selector code
enables a computer to select an optimal treatment protocol from the
plurality of treatment protocols based on the modified system
model.
[0618] Construction of detailed mathematical models for biological
processes and treatments are discussed herein in relation to
various other embodiments of the disclosed technique. Techniques
involving a model of platelets production and related diseases,
including Thrombocytopenia, with treatment by TPO, a model of
Neutrophil production and related diseases, including Neutropenia,
and treatment by G-CSF, and a model of cancer growth and cancer
treatment, including chemotherapy, are disclosed herein. An
embodiment for specific optimization (by linear programming) is
implemented for the system involving the Neutrophil model. An
embodiment that uses a general heuristic optimization method is
disclosed as well.
IV.A. Thrombopoiesis and Thrombopoietin (TPO)
[0619] An embodiment of the present invention involves the
disclosed techniques for modeling the Thrombopietic lineage,
diseased Thrombopoiesis such as Thrombocytopenia and treatment with
Thrombopoietin. Thrombocytopenia is a common hazardous blood
condition, which may appear in different clinical situations,
including cancer chemotherapy. Recently, a
Thrombopoiesis-controlling cytokine, Thrombopoietin (TPO), was
isolated and its human recombinant analog became available. A
mathematical model is disclosed herein that simulated dynamics of a
Thrombopoietic lineage in the bone marrow, of platelet counts in
the periphery, and effects of TPO administration on the lineage and
platelet counts.
[0620] TPO is a cytokine, glycoprotein of about 350 amino acids,
that resembles erythropoiesis-stimulating hormone, erythropoietin.
Its synthetic analogs, recombinant human Thrombopoietin (rHuTPO)
and recombinant human megakaryocyte growth and development factor
(rHuMGDF), are available as well and are undergoing clinical
trials.
[0621] For further details see Alexander WS: Thrombopoietin. Growth
Factors. 1999; 17(1); pp. 13-24.; Kaushansky K: Thrombopoietin: the
primary regulator of platelet production. Blood. July 1995; Vol.
86(2); pp. 419-431; Vadhan_Raj-Raj S: Recombinant human
Thrombopoietin: clinical experience and in vivo biology. Seminars
Hem. July 1998; Vol. 35(3); pp. 261-268.; Harker L A: Physiology
and clinical applications of platelet growth factors. Current
Opinion Haematol. 1999; Vol. 6; pp. 127-134; and Neelis K J,
Hartong S C, Egeland T, Thomas G R, Eaton D L, Wagemaker G: The
efficacy of single-dose administration of Thrombopoietin with
coadministration of either Granulocyte/macrophage or Granulocyte
colony-stimulating factor in myelosuppressed rhesus monkeys. Blood.
October 1997; Vol. 90(7); pp. 2565-2573.
[0622] These compounds have been shown to have the same biological
activity as TPO has, so the term TPO will be used without
distinguishing between its different forms and analogs. Is TPO is a
primary growth factor of the Thrombopoietic cell line both in vivo
and in vitro. Aside from this, TPO may be potent in stimulation and
co-stimulation of other haemopoietic lineages (e.g., Granulopoietic
or erythropoietic).
IV.A.1. Model of the Biological System
[0623] a) Background of Thrombopoiesis
[0624] Like all other haemopoietic lines, the Thrombopoietic line
originates from poorly differentiated, multipotential cells, that
are capable of some division and self-reconstitution. For more
background details, see Swinburne J L, Mackey M C: Cyclical
Thrombocytopenia: characterization by spectral analysis and a
review. J Theor Medicine. 2000; Vol. 2; pp. 81-91.; and Beutler E,
Lichtman M A, Coller B S, Kipps T J : Williams HAEMATOLOGY.
5.sup.th edition McGraw-Hill, Inc. 1995; Chapter 118; pp.
1149-1161.Such bone marrow cell compartments as pluripotential
haemopoietic stem cells and common myeloid progenitor cells
(CFU-GEMM) have more or less these characteristics. For more
background details, see Beutler E, Lichtman M A, Coller B S, Kipps
T J: Williams HAEMATOLOGY. 5.sup.th edition McGraw-Hill, Inc. 1995;
Chapter 118; pp. 1149-1161.
[0625] Gradually, the cells become more and more differentiated and
thus committed to the Thrombopoietic line. At this stage they
proliferate extensively. Colony-forming Units--megakaryocytes
(CFU-Meg) is an example of such compartment. Sometimes
burst-forming units--megakaryocyte (BFU-Meg), promegakaryoblasts or
megakaryoblasts are considered as having the similar properties.
For more background details, see Swinburne J L, Mackey M C:
Cyclical Thrombocytopenia: characterization by spectral analysis
and a review. J Theor Medicine. 2000; Vol. 2; pp. 81-91.; and
Beutler E, Lichtman M A, Coller B S, Kipps T J: Williams
HAEMATOLOGY. 5.sup.th edition McGraw-Hill, Inc. 1995; Chapter 118;
pp. 1149-1161.
[0626] The committed megakaryocytopoietic cells, megakaryocyte
precursors, go through several stages of maturation. However,
megakaryocyte maturation is somewhat different from that of other
haemopoietic lines. Here, along with cytoplasmic maturation, cell
nuclei undergo mitotic events. However, although the DNA material
of these cells doubles, cell division does not happen. Such
incomplete mitosis is termed endomitosis or endoreduplication.
Consequently, the cell becomes poliploid with 2N, 4N, 8N, etc.,
amount of DNA. Some authors call the cells with 2N to 4N chromosome
number promegakaryoblasts, others call them megakaryoblasts or
immature megakaryocytes. For more background details, see Swinburne
J L, Mackey M C: Cyclical Thrombocytopenia: characterization by
spectral analysis and a review. J Theor Medicine. 2000; Vol. 2; pp.
81-91.; and Beutler E, Lichtman M A, Coller B S, Kipps T J:
Williams HAEMATOLOGY. 5.sup.th edition McGraw-Hill, Inc. 1995;
Chapter 118; pp. 1149-1161.
[0627] Usually, megakaryocytes do not start to release platelets
until they reach 8N to 16N state. For more background details, see
Gordon AS : Regulation of haematopoiesis. N.-Y. 1970 Vol. 2,
Section IX (textbook); and Beutler E, Lichtman M A, Coller B S,
Kipps T J: Williams HAEMATOLOGY. 5.sup.th edition McGraw-Hill, Inc.
1995; Chapter 118; pp. 1149-1161.
[0628] Then they begin to create demarcation membranes that envelop
cytoplasm fragments generating platelets. The platelets are
released into the blood stream. A small fraction of the
megakaryocytes do not cease their endoreduplication at the
16N-stage, but rather continue with one or more additional
endomitoses and get thus a ploidy of 32N or more. For background
details, see Swinburne J L, Mackey M C: Cyclical Thrombocytopenia:
characterization by spectral analysis and a review. J Theor
Medicine. 2000; Vol. 2; pp. 81-91.
[0629] The amounts of cytoplasm, cell volume and the ability to
release platelets increase proportionally to the cell ploidy. For
background details, see Harker L A, Finch C A: Thrombokinetics in
man. J Clin Invest. 1969; Vol. 48; pp. 963-974; and Harker L A:
Thrombokinetics in idiopathic Thrombocytopenic purpura. Br J
Haematol. 1970; Vol. 19; pp. 95-104.
[0630] b) B. Mathematical Model
[0631] Reference is now made to FIG. 3, which is a detailed
illustration of a model predicting Thrombopoiesis. As shown in FIG.
3, the Thrombopoietic lineage is divided into eight compartments.
The first compartment, called Stem Cells (SC) and labeled 30,
refers to all bone marrow haemopoietic progenitors that have an
ability to differentiate into more than one line (e.g.,
pluripotential stem cells, CFU-GEMM, and others). Cells of SC
compartment 30 proliferate, giving rise to "new" stem cells, or
mature, and subsequently differentiate into megakaryocytes or other
precursors. Although the consideration of the former process, i.e.
the renewal of the stem cells by "new" ones, is not completely
understood biologically, our simple description may serve as an
acceptable assumption since the characteristics of this population
are not elaborated in details. For background details, see,
Schofield R, Lord B I et al: Self-maintenance capacity of CFU-S. J
Cellular Phisiol. 1980; Vol. 103: 355-362; and Rosendaal M, Hodgson
G S, Bradley T R: Organization of haemopoietic stem cells: the
generation-age hypothesis. Cell Tissue Kinetics. 1979; Vol. 12:
17-29.
[0632] Cell death through apoptosis may have a significant effect
on cell number within proliferating compartments. For background
details, see, Swinburne J L, Mackey M C: Cyclical Thrombocytopenia:
characterization by spectral analysis and a review. J Theor
Medicine. 2000; Vol. 2; pp. 81-91.
[0633] However, the effect of apoptosis is combined with the effect
of cell proliferation into a total amplification of cell number in
a given compartment (for example .alpha..sub.SC). An assumption is
made that no apoptosis occurs in non-proliferating megakaryocytic
compartments, due to lack of evidence to the contrary. However, an
assumption of apoptotic non-proliferating megakaryocytes can be
incorporated in the mathematical model.
[0634] Biologically, rates of proliferation and maturation, the
ability to reconstitute, and other characteristics differ between
particular cell types within a primitive progenitor population.
However, in this model there is no distinction between them; all
progenitor cells are considered to be one population with common
properties.
[0635] It has been shown conventionally that probabilities of stem
cell differentiation into one or another haemopoietic lineage are
constant in time. Thus, it is assumed here that a flow of stem
cells into the megakaryocyte lineage is fixed (for example
.PHI..sub.SC). For background details, see Mayani H, Dragowska W,
Lansdorp P M: Lineage commitment in human hemopoiesis involves
asymmetric cell division of multipotent progenitors and does not
appear to be influenced by cytokines. J Cellular Physiol. 1993;
Vol. 157; pp. 579-580; Golde D W: The Stem Cell. Medicine. December
1991; Morrison S J, Uchida N, Weissman I L: The biology of
haematopoietic stem cells. Annu Rev Cell Dev Biol. 1995; Vol. 11;
pp. 35-71; and von Schulthess G K, Gessner U : Oscillating platelet
counts in healthy individuals: experimental investigation and
quantitative evaluation of Thrombopoietic feedback control. Scand J
Haematol. 1986; Vol. 36; pp. 473-479.
[0636] The same was assumed about the stem cell self-renewal. Thus,
after the cells spend a defined transit time, for example
.tau..sub.SC, in SC compartment 30, a certain constant fraction of
the cells return to their "young state", i.e. start their passage
through SC compartment 30 again, as shown in line 31. Another
constant fraction (.PHI..sub.SC, for example) of cells pass into
the next compartment named Colony-Forming Units (CFU-Meg), labeled
40. It is presumed that remaining stem cells differentiate into
haematopoietic lineages other than megakaryocytic.
[0637] CFU-Meg refers to all cells that are already committed to
the megakaryocyte line but are still capable of proliferation.
Cells of CFU-Meg compartment 40, like those of SC compartment 30,
spend some time multiplying at an amplification rate of about
.alpha..sub.SFU, for example, and maturing before losing their
proliferative abilities and passing on to the next compartment 50,
called megakaryoblasts (MKB). For background details see, Eller J,
Gyori I et al: Modelling Thrombopoiesis regulation--I: model
description and simulation results. Comput Math Applic. 1987; Vol.
14 (9-12); pp. 841-848.
[0638] The time they spent in CFU-Meg compartment is
.tau..sub.CFU.
[0639] MKB compartment 50 includes all the cells that have lost the
ability to proliferate, but are not yet sufficiently mature to
release platelets. For the purposes of the model, the assumption is
made that megakaryocytes do not start to release platelets until
they reach the 16N-ploidy phase. For background details, see Gordon
AS : Regulation of haematopoiesis. N.-Y. 1970 Vol. 2, Section IX
(textbook).
[0640] Hence, MKB refers to 2N, 4N and 8N cells of megakaryocyte
lineage that cannot divide, at all stages of cytoplasmic maturity.
After these cells spend the designated transit time .tau..sub.MKB,
for example, in MKB compartment 50, they move to the next
compartment 60, which is a MK16 bone marrow compartment.
[0641] The cells of MK16 compartment 60 are megakaryocytes of
16N-ploidy class that release platelets at a constant uniform rate
(.gamma..sub.MK16) until they exhaust their capacity (C.sub.MK16,
for example), and then are disintegrated. For background details,
see, Harker L A, Finch C A: Thrombokinetics in man. J Clin Invest.
1969; Vol.48; pp. 963-974; and Eller J, Gyori I et al: Modelling
Thrombopoiesis regulation--I: model description and simulation
results. Comput Math Applic. 1987; Vol. 14 (9-12); pp. 841-848.
[0642] Cell volume has a linear relationship with megakaryocyte
ploidy. Hence, it is assumed that all 16N-megakaryocytes have the
same volume and, thus, the same platelet-releasing capacity. For
background details, see, Harker L A, Finch C A: Thrombokinetics in
man. J Clin Invest. 1969; Vol. 48; pp. 963-974.
[0643] Therefore all platelet-releasing 16N-megakaryocytes are in
transit for the same amount of time (.tau..sub.MK16, for example)
until they are exhausted and disintegrated.
[0644] However, some 16N-megakaryocytes do not participate in
platelet release, but rather continue with another endomitosis over
a 48-hour time period, and become 32N-megakaryocytes. These
constitute a new and distinct MK32 compartment 70. Thus, after time
.mu. in MK16 compartment 60, a certain fraction of the cells leave
MK16 compartment 60 and go on to MK32 compartment 70.
[0645] 32N-megakaryocytes release platelets as well. The rate of
platelet release is constant for every compartment and proportional
to the ploidy state of megakaryocytes in it. For background
details, see, Harker L A, Finch C A: Thrombokinetics in man. J Clin
Invest. 1969; Vol. 48; pp. 963-974; and Harker L A: Thrombokinetics
in idiopathic Thrombocytopenic purpura. Br J Haematol. 1970; Vol.
19; pp. 95-104.
[0646] Thus, every 16N-megakaryocyte releases, for example,
.gamma..sub.MK16 platelets per hour and every 32N-megakaryocyte ,
for example, releases .gamma..sub.MK32 platelets per hour (twice as
much). However, 32N-megakaryocytes are not exhausted more quickly
than 16N-megakaryocytes, since they have 2 times greater volume and
platelet-releasing capacity. Consequently, all platelet-releasing
megakaryocyte compartments have the same transit time.
[0647] Once again, some fraction of cells, for example
.PHI..sub.MK32, are not engaged in platelet formation, and continue
to the 64N-stage. Additional endomitosis in MK32 compartment 70
takes the same amount of time .mu. as in MK16 compartment 60. The
64N-megakaryocytes continue the process in a new MK64 compartment
80, and .PHI..sub.MK64 of them become 128N-cells in yet another
MK128 compartment 90. Additional endomitosis in MK64 compartment 80
takes the same amount of time .mu. as before. Megakaryocytes of
greater ploidy classes have not been known to be encountered in
humans.
[0648] Finally, there is a platelet (PL) compartment 100. This is
not a bone marrow compartment, but rather the platelet pool in the
peripheral blood Platelets released from megakaryocytes of 16N-,
32N-, 64N-, and 128N-ploidy classes enter platelet compartment 100.
There are two mechanisms of platelet elimination from circulation:
By age-dependent destruction and by the normal utilization in order
to maintain the integrity of blood vessels. For background detials,
see, Harker L A, Roskos L K, Marzec U M, Carter R A, Cherry J K,
Sundell B, Cheung E N, Terry D, Sheridan W: Effects of
megakaryocyte growth and development factor on platelet production,
platelet life span, and platelet function in healthy human
volunteers. Blood. 2000 April; Vol. 95(8); pp. 2514-2522; and von
Schulthess G K, Gessner U: Oscillating platelet counts in healthy
individuals: experimental investigation and quantitative evaluation
of Thrombopoietic feedback control. Scand J Haematol. 1986; Vol.
36; pp. 473-479.
[0649] The first mechanism is reflected as platelet disappearance
after they spend their designated transit time, for example , in
the PL compartment. The second one is rather age-independent and it
is reflected as constant platelet efflux (d) throughout all
platelet age-stages.
IV.A.2. Model of Treatment Effects
[0650] a) A. Background of TPO
[0651] The major sites of TPO production are the liver and kidney.
TPO is also produced in the spleen and bone marrow, but the
production rate in these organs is 5 times lower than in the liver
and kidneyFor background details, see, Alexander W S:
Thrombopoietin. Growth Factors. 1999; 17(1); pp. 13-24; Sungaran R,
Markovic B, Chong B H: Localization and regulation of
Thrombopoietin mRNA expression in human kidney, liver, bone marrow,
and spleen using in situ hybridization. Blood. January 1997; Vol.
89(1); pp. 101-107; Nagata Y, Shozaki Y, Nagahisa H, Nagasawa T,
Abe T, Todokoro K: Serum Thrombopoietin level is not regulated by
transcription but by the total counts of both megakaryocytes and
platelets during Thrombocytopenia and Thrombocytosis. Thromb
Haemost. 1997; Vol. 77; pp. 808-814; Nagahisa H, Nagata Y, Ohnuki
T, Osada M, Nagasawa T, Abe T, Todokoro K: Bone marrow stromal
cells produce Thrombopoietin and stimulate megakaryocyte growth and
maturation but suppress proplatelet formation. Blood. February
1996; Vol. 87(4); pp. 1309-1316; and Rasko J E J, Begley C G:
Molecules in focus: The Thrombopoietic factor, Mpl-ligand. Int J
Bioch Cell Biol. 1998; Vol. 30: 657-660.
[0652] Some low TPO production has also been found in many other
sites in the body. For background details, see Nagata Y, Shozaki Y,
Nagahisa H, Nagasawa T, Abe T, Todokoro K: Serum Thrombopoietin
level is not regulated by transcription but by the total counts of
both megakaryocytes and platelets during Thrombocytopenia and
Thrombocytosis. Thromb Haemost. 1997; Vol. 77; pp. 808-814; and
Wichmann H E, Gerhardts M D, Spechtmeyer H, Gross R: A mathematical
model of Thrombopoiesis in rats. Cell Tissue Kinet. 1979; Vol. 12;
pp. 551-567.
[0653] Rates of liver and kidney TPO production are constant under
Thrombocytopenia and Thrombocytosis of varying degrees of severity.
For background details, see, Alexander W S: Thrombopoietin. Growth
Factors. 1999; 17(1); pp. 13-24; Sungaran R, Markovic B, Chong B H:
Localization and regulation of Thrombopoietin mRNA expression in
human kidney, liver, bone marrow, and spleen using in situ
hybridization. Blood. January 1997; Vol. 89(1); pp. 101-107; and
Nagahisa H, Nagata Y, Ohnuki T, Osada M, Nagasawa T, Abe T,
Todokoro K: Bone marrow stromal cells produce Thrombopoietin and
stimulate megakaryocyte growth and maturation but suppress
proplatelet formation. Blood. February 1996; Vol. 87(4); pp.
1309-1316.
[0654] TPO production in the spleen and bone marrow is inversely
related to the megakaryocyte mass, but the actual contribution is
negligible with regard to total TPO production. For background
details, see, Alexander W S: Thrombopoietin. Growth Factors. 1999;
17(1); pp. 13-24; and Sungaran R, Markovic B, Chong B H:
Localization and regulation of Thrombopoietin mRNA expression in
human kidney, liver, bone marrow, and spleen using in situ
hybridization. Blood. January 1997; Vol. 89(1); pp. 101-107.
[0655] Another mechanism of TPO concentration regulation is
receptor-mediated TPO uptake, since TPO-receptors on the platelet
and megakaryocyte surfaces are the main TPO-clearance mechanism.
Thus, TPO concentration is inversely related to the total platelet
and megakaryocyte mass. For background details, see, Alexander W S:
Thrombopoietin. Growth Factors. 1999; 17(1); pp. 13-24; Harker L A:
Physiology and clinical applications of platelet growth factors.
Current Opinion Haematol. 1999; Vol. 6; pp. 127-134; Hsu H C, Tsai
W H, Jiang M L, Ho C H, Hsu M L, Ho C K, Wang S Y: Circulating
levels of Thrombopoietic and inflammatory cytokines in patients
with clonal and reactive Thrombocytosis. J Lab Clin Med. 1999; Vol.
134(4); pp. 392-397; Stoffel R, Wiestner A, Skoda R C:
Thrombopoietin in Thrombocytopenic mice: evidence against
regulation at the mRNA level and for a direct regulation role of
platelets. Blood. January 1996; Vol. 87(2); pp. 567-573; Alexander
W S: Thrombopoietin and the c-Mpl receptor: insights from gene
targeting. Int J Biochem Cell Biol. 1999 October; Vol. 31(10); pp.
1027-1035. [ABSTRACT]; Miyazaki M, Fujiwara Y, Isobe T, Yamakido M,
Kato T, Miyazaki H: The relationship between carboplatin AUC and
serum Thrombopoietin kinetics in patients with lung cancer.
Anticancer Research. 1999; Vol. 19; pp. 667-670; and Rasko J E J,
Begley C G: Molecules in focus: The Thrombopoietic factor,
Mpl-ligand. Int J Bioch Cell Biol. 1998; Vol. 30: 657-660.
[0656] The effects of TPO on the Thrombopoietic line may be divided
into three types: (i) stimulation of proliferation of megakaryocyte
progenitors that have an ability to proliferate; (ii) stimulation
of maturation of all megakaryocyte progenitors; (iii) induction of
additional endomitosis of already mature megakaryocytes, which
leads to an increase in the modal megakaryocyte ploidy. For
background details, see, Kaushansky K: Thrombopoietin: the primary
regulator of platelet production. Blood. July 1995; Vol. 86(2), pp.
419-431; Somlo G, Sniecinski I, ter Veer A, Longmate J, Knutson G,
Vuk-Paviovic S, Bhatia R, Chow W, Leong L, Morgan R, Margolin K,
Raschko J, Shibata S, Tetef M, Yen Y, Forman S, Jones D, Ashby M,
Fyfe G, Hellmann S, Doroshow J H: Recombinant Human Thrombopoietin
in combination with Granulocyte colony-stimulating factor enhances
mobilization of peripheral blood progenitor cells, increases
peripheral blood platelet concentration, and accelerates
haematopoietic recovery following high-dose chemotherapy. Blood.
May 1999; Vol. 93(9); pp. 2798-2806; Murray L J, Luens K M, Estrada
M F, Bruno E, Hoffman R, Cohen R L, Ashby M A, Vadhan-Raj S:
Thrombopoietin mobilizes CD34.sup.+ cell subsets into peripheral
blood and expand multilineage progenitors in bone marrow of cancer
patients with normal haematopoiesis. Exp Hem. 1998; Vol. 26; pp.
207-216; Vadhan-Raj S, Murray U, Bueso-Ramos C, Patel S, Reddy S P,
Hoots W K, Johnston T, Papadopolous N E, Hittelman W N, Johnston D
A, Yang T A, Paton V E, Cohen R L, Hellmann S D, Benjamin R S,
Broxmeyer H E: Stimulation of megakaryocyte and platelet production
by a single dose of recombinant human Thrombopoietin in patients
with cancer. Ann Intern Med. May 1997; Vol. 126(9); pp. 673-681;
Wichmann H E, Gerhardts M D, Spechtmeyer H, Gross R: A mathematical
model of Thrombopoiesis in rats. Cell Tissue Kinet. 1979; Vol. 12;
pp. 551-567; Harker L A, Roskos L K, Marzec U M, Carter R A, Cherry
J K, Sundell B, Cheung E N, Terry D, Sheridan W: Effects of
megakaryocyte growth and development factor on platelet production,
platelet life span, and platelet function in healthy human
volunteers. Blood. 2000 April; Vol. 95(8); pp. 2514-2522; Swinburne
J L, Mackey M C: Cyclical Thrombocytopenia: characterization by
spectral analysis and a review. J Theor Medicine. 2000; Vol. 2; pp.
81-91; Rasko J E J, Begley C G: Molecules in focus: The
Thrombopoietic factor, Mpl-ligand. IntJ Bioch Cell Biol. 1998; Vol.
30: 657-660; and De Sauvage F J, Carver-Moore K, Luoh S-M, Ryan A,
Dowd M, Eaton D L, Moore M W: Physiological regulation of early and
late stages of megakaryocytopoiesis by Thrombopoietin. J Esp Med.
1996 February; Vol. 183: 651-656.
[0657] b) Mathematical Model of TPO Effects
[0658] TPO concentration effects on the Thrombopoiesis line is now
considered. As discussed above, three things depend on TPO
concentration: (i) amplification rate (amp), (ii) the rate of cell
maturation or, alternatively, transit time through a given
compartment (transit), and (iii) the fraction of megakaryocytes of
given ploidy that undergo additional endomitosis and pass on to the
next ploidy class.
[0659] (1) TPO Concentration
[0660] Recombinant human full-length TPO and its truncated form
rHuMGDF are fully active biologically. Therefore, in our model we
add exogenously administered recombinant protein to endogenously
produced TPO in order to calculate actual TPO concentration
(c).
[0661] As mentioned above, the rate of TPO production in the main
TPO production sites, i.e. liver and kidney, is constant under
Thrombocytopenia or Thrombocytosis. For background details, see,
Alexander W S: Thrombopoietin. Growth Factors. 1999; 17(1); pp.
13-24; Sungaran R, Markovic B, Chong B H: Localization and
regulation of Thrombopoietin mRNA expression in human kidney,
liver, bone marrow, and spleen using in situ hybridization. Blood.
January 1997; Vol. 89(1); pp. 101-107; and Nagata Y, Shozaki Y,
Nagahisa H, Nagasawa T, Abe T, Todokoro K: Serum Thrombopoietin
level is not regulated by transcription but by the total counts of
both megakaryocytes and platelets during Thrombocytopenia and
Thrombocytosis. Thromb Haemost. 1997; Vol. 77; pp. 808-814.
[0662] The level of TPO mRNA in sites like the bone marrow and
spleen, where it is produced in a 5-fold lower rate than in the
liver and kidney, is not significantly different from the TPO level
in peripheral blood. For background details, see Hsu H C, Tsai W H,
Jiang M L, Ho C H, Hsu M L, Ho C K, Wang S Y: Circulating levels of
Thrombopoietic and inflammatory cytokines in patients with clonal
and reactive Thrombocytosis. J Lab Clin Med. 1999; Vol. 134(4); pp.
392-397.
[0663] Therefore, the assumption is made that the bone marrow and
spleen contributions to the total TPO concentration are
insignificant. Endogenously produced TPO is assumed to have a
constant rate of production p. However, this number can change.
[0664] The main mechanism that controls TPO concentration in the
blood is receptor-mediated TPO uptake (u). For background details,
see, Alexander W S: Thrombopoietin. Growth Factors. 1999; 17(1);
pp. 13-24; Harker L A: Physiology and clinical applications of
platelet growth factors. Current Opinion Haematol. 1999; Vol. 6;
pp. 127-134; Hsu H C, Tsai W H, Jiang M L, Ho C H, Hsu M L, Ho C K,
Wang S Y: Circulating levels of Thrombopoietic and inflammatory
cytokines in patients with clonal and reactive Thrombocytosis. J
Lab Clin Med. 1999; Vol. 134(4); pp. 392-397; Stoffel R, Wiestner
A, Skoda R C: Thrombopoietin in Thrombocytopenic mice: evidence
against regulation at the mRNA level and for a direct regulation
role of platelets. Blood. January 1996; Vol. 87(2); pp. 567-573;
Alexander W S: Thrombopoietin and the c-Mpl receptor: insights from
gene targeting. Int J Biochem Cell Biol. 1999 October; Vol. 31(10);
pp. 1027-1035. [ABSTRACT].
[0665] Another mechanism of TPO removal from the blood is
non-specific TPO-receptor-independent clearance (l). This mechanism
is rather insignificant in the normal state, when receptor-mediated
TPO binding, endocytosis, and degradation remove most of the TPO.
Thus, the formula that calculates TPO concentration hourly is given
in Equation 1 as follows:
C*.sub.i+1=C.sub.i+p+x.sub.i-u.sub.i-l.sub.ip,x.sub.i,u.sub.i,l-
.sub.i.gtoreq.0C.sub.i>0 (1) where Ci is TPO concentration at
the current hour (i); C*i+1 is approximation of the TPO
concentration at the next hour (detailed below); p is TPO
concentration produced per hour endogenously; xi is the addition to
TPO concentration due to exogenous TPO administration; ui is TPO
concentration removed from the blood by receptor-mediated binding;
li is TPO concentration cleared from circulation by non-specific
mechanisms.
[0666] It is assume that receptor-mediated TPO clearance depends on
the total number of TPO receptors (n) and on the ability of each
receptor to uptake TPO (a): u.sub.i=n.sub.ia n.sub.i,a.gtoreq.0 (2)
where n.sub.i represents the receptor pool and a is TPO-clearing
ability of the receptors, i.e. amount of TPO that each receptor
removes per hour. Both, megakaryocyte and platelet mass contribute
to the total receptor number (n) and, thus, to the rate of TPO
clearance (u).15 We assume that every platelet bears the same
number of TPO receptors (mPL). The receptor number on
megakaryocytes, however, changes. Thus, the receptor pool (n) is: n
i = comp = 1 4 .times. ( j = 1 [ .tau. comp ] .times. ( q comp , j
, i m comp , j ) ) + q PLi m PL q comp , j , i , q PL , i , m comp
, j , m PL .gtoreq. 0 ( 3 ) ##EQU1## where comp (1 to 4) is one of
the platelet releasing megakaryocyte compartments (MK16, MK32,
MK64, MK128, respectively); j is the period (in hours) that a given
megakaryocyte already spent in the specific compartment; [.tau.]
denotes .tau. rounded to an integer; q.sub.comp,j,i is the quantity
of the megakaryocytes of the specific compartment (comp), which
spent a given period (j) in it; m.sub.comp,j, is the receptor
number on given megakaryocyte; q.sub.PL i is the platelet number;
m.sub.PL is the receptor number per platelet.
[0667] It is assumed that the number of TPO receptors on each
megakaryocyte (m.sub.comp,j) equals the number of platelets that
the megakaryocyte is capable of releasing (c.sub.comp) times the
average number of receptors per every potential platelet (b).
m.sub.comp,j=(c.sub.comp-r.sub.compj)b
c.sub.comp,r.sub.comp,j,b.gtoreq.0 (4) where ccomp is the number of
platelets that the megakaryocyte of the specific compartment comp
can release during its entire life-span (.tau..sub.comp); rcomp is
the rate of platelet release by the megakaryocyte; j is the period
that this megakaryocyte already spent in this compartment; b is the
number of receptor on the megakaryocyte per potential platelet.
[0668] It is also assumed that the non-specific TPO clearance
(l.sub.i) is exponential, i.e. every hour some fraction (f) of a
current amount of TPO (c.sub.i) is removed from circulation:
l.sub.i=fC.sub.if.gtoreq.0 (5) where f is the coefficient of
non-specific TPO clearance and c.sub.i is the current TPO
concentration. Other modes of non-specific TPO removal can be
assumed as well. Exogenous TPO is included in the model as a linear
relation of the initial maximum TPO blood concentration (x.sub.i)
to the administered intravenous (IV) dose (s) (the relation
coefficient is 0.0167) 21: x.sub.i=0.0167s.sub.i, s.sub.i.gtoreq.0
(6) The state when TPO completely disappears from the blood seems
very unlikely based on biological logic, so we restricted the lower
limit of possible TPO concentration to certain minimum .epsilon.
(positive). Thus, the equation (1) is modified to receive the full
TPO concentration equation:
C.sub.i+1=max((C.sub.i+p+x.sub.i-an.sub.i-fC.sub.i),.epsilon.).epsilon.&g-
t;0 (7) In steady state, the TPO concentration (C) is constant.
[0669] (2) TPO Effects on Amplification Rate
[0670] In the disclosed model, there are only two compartments, SC
compartment 30 and CFU-Meg compartment 40, whose cells are capable
of dividing. These compartments differ significantly from each
other, thus, we shall discuss them separately. Cells of other model
compartments do not proliferate, and so their amplification rate
equals 1 under all circumstances.
[0671] SC Compartment 30:
[0672] Since TPO is primarily a Thrombopoiesis-stimulating
cytokine, we assume that the cells, which are not committed to
Thrombopoietic line yet (the SC compartment in our model), are
relatively insensitive to TPO, compared to committed megakaryocytic
cells. In the disclosed model this is considered as a threshold
(.theta.) in TPO concentration. Only above this threshold (.theta.)
TPO affects stem cells. As long as TPO remains below the threshold
(.theta.), stem cells in the model are regulated by intrinsic
TPO-independent mechanism that keeps the size of their population
almost constant.
[0673] Thus, below the threshold (.theta.), SC amplification rate
(.alpha..sub.SC) is determined hourly depending on the current
number of cells in the SC compartment. It is biologically
reasonable that the dependence equation is a sigmoidal function
where .alpha..sub.SC changes from 1 (i.e., no amplification, the
cell number remains the same) when the cell number approaches
infinity, up to the maximal value .alpha..sub.SCw when the cell
number approaches zero. The increase in amplification rate
(.alpha..sub.SC) is relatively gradual as long as the cell number
(q.sub.SCi) exceeds certain critical value (we assumed it to be a
fraction (v) of the normal cell number (q.sub.SCnorm)). However,
when the cell number falls bellow this threshold, .alpha..sub.SC
begins to increase rapidly in order to restore the SC compartment
as soon as possible. It is assumed that at normal cell numbers
(q.sub.SCnorm), .alpha..sub.SCi should be a fraction (y) of its
maximal value .alpha..sub.SCw. Following is an example of such
equation: .alpha. SC , i + 1 * .function. ( q SC , i , C i ) C i
.ltoreq. .theta. = { ( .alpha. SC .times. .times. w - 1 ) 1 ( 1 y -
1 ) ( q SC , i q SC .times. .times. norm ) S 1 + 1 + 1 , q SC , i
.gtoreq. v q SC .times. .times. norm .alpha. SC .times. .times. w -
( .alpha. SC .times. .times. w - .alpha. SC ~ ) ( q SC , i v q SC
.times. .times. norm ) S 2 , q SC , i < v q SC .times. .times.
norm .times. .times. .alpha. SC ~ = ( .alpha. SC .times. .times. w
- 1 ) 1 ( 1 y - 1 ) v S 1 + 1 + 1 .times. q SC , S 1 , 2 , .theta.
.gtoreq. 0 .alpha. SC .times. .times. w .gtoreq. 1 0 < y , v
.ltoreq. 1 ( 8 ) ##EQU2## where .alpha.*.sub.SC,i+1 is the
amplification rate calculated based solely on the cell number;
.alpha..sub.SCw is the maximal possible rate of cell amplification
in the SC compartment when TPO concentration (C.sub.i) is below the
threshold; q.sub.SC,i is a quantity of cells in the SC compartment;
q.sub.SC norm is the normal quantity of cells there. S1 and S2 are
the sensitivity coefficients in the regions of q.sub.SC,i higher or
lower than the critical value (vq.sub.SCnorm), respectively. These
values determine the sensitivity of the mechanism that links the
amplification rate (.alpha..sub.SC) with the cell number
(q.sub.SC,i). In other words, they determine the steepness of the
dependence curve in the corresponding regions. High S1 or S2 mean
that asc changes significantly due to slight changes of q.sub.SC,
and low S1 or S2 mean that asc remains relatively constant whatever
the changes of q.sub.SC are. Distinguishing between S1 and S2
allows us to force the amplification rate (.alpha..sub.SC) to grow
rapidly as the cell number (q.sub.SCi) falls below the critical
value, thereby increasing the resistance of the system to further
cell number (q.sub.SC,i) decay. Although the symbols S1 and S2
appear in several equations, their values are specific for every
equation.
[0674] It is suggested that TPO concentration (C) increase above
the threshold should occur in severe platelet and/or megakaryocyte
deficiency, or when TPO is administered exogenously. It is assumed
that at these circumstances, TPO further increases the rate of cell
amplification in the "Stem Cell" compartment (.alpha..sub.SC). It
is also assumed that the increase is proportional to the difference
between actual TPO concentration (C.sub.i) and the threshold. Thus,
TPO effects appear gradually from the zero increase, when TPO
concentration (C.sub.i) equals the threshold. Saturation of the
mechanisms of TPO effect is reflected in the concavity of the
effect function.
[0675] The following is an example of such a function: .alpha. SC ,
i + 1 .function. ( q SC , i , C i ) C i > .theta. = .alpha. SC ,
i + 1 * .function. ( q SC , i , C i ) + t ln .function. ( C i -
.theta. + 1 ) t , .theta. .gtoreq. 0 ( 9 ) ##EQU3## where
.alpha.*.sub.SC,i+1 is the same expression as in equation (8), i.e.
amplification calculated based on a TPO-independent mechanism, and
the second operand is the TPO-related contribution to the
amplification rate (.alpha..sub.SC,i+1). t determines the steepness
of the dependence curve (t is non-negative). Although the symbol t
appears in several equations, its value is specific for every
equation. One is added to the ln argument in order to ensure
positivity of the In result.
[0676] CFU-Meg compartment 40:
[0677] In contrast to the cells of the SC compartment, we assume
that cells of this compartment are fully sensitive to TPO and
respond to the absolute TPO concentration. (C.sub.i), not to its
difference with a threshold (C.sub.i-.theta.). In the disclosed
model, there is no TPO-independent proliferative mechanism, and
CFU-Meg cease to proliferate when deprived of TPO. On the other
hand, when TPO concentration (C.sub.i) in the system increases,
.alpha..sub.CFU does not rise to infinity, but rather gradually
reaches saturation, which also seems reasonable biologically. At
normal TPO concentrations (C.sub.norm), we assume .alpha..sub.CFU
to be a fraction (h) of its maximal value (.alpha..sub.CFUmax).
Thus an equation that describes the relation of the amplification
rate of CFU-Meg cells (.alpha..sub.CFU) to TPO concentration
(C.sub.i) represents a sigmoidal function with .alpha..sub.CFU
equaling 1 when TPO concentration (C.sub.i) is zero, passing
through h times .alpha..sub.CFUmax when TPO concentration is normal
(C.sub.i), and approaching an asymptote in .alpha..sub.CFUmax when
TPO concentration (C.sub.i) approaches infinity. In addition, in
order to enable the system to be sensitive both to the regulation
by endogenously produced TPO and to the effect of the exogenously
administered drug, it was assumed that the function changes
relatively rapidly in the region of normal TPO concentration
(C.sub.norm) and with a much smaller rate when a TPO concentration
(C.sub.i) is somewhat higher than normal (C.sub.norm). The
following is an example of such a function: .alpha. CFU , i + 1
.function. ( C i ) = ( .alpha. CFU .times. .times. max - 1 ) ( 1 -
1 1 1 h - 1 ( C i C norm ) t + 1 ) + 1 .times. C norm > 0 t
.gtoreq. 0 0 < h .ltoreq. 1 ( 10 ) ##EQU4## where
.alpha..sub.CFU,i+1 is an amplification rate of the CFU
compartment; .alpha..sub.CFUmax is a maximal value of amplification
rate there; C.sub.norm is normal TPO concentration; t is the
parameter that determines the steepness of the dependence
curve.
[0678] (3) TPO Effects on Transit Time
[0679] For the reason noted earlier, it is assumed that all
platelet-releasing megakaryocyte compartments have the same transit
time (.tau..sub.MK). It is also assumed that neither the relation
of megakaryocyte volume (and thus, its platelet releasing capacity
C.sub.comp) nor of its rate of platelet release rcomp to
megakaryocyte ploidy, is affected by TPO. Therefore, the transit
time (.tau..sub.MK) through the noted compartments is constant.
Platelets also spend in average a constant time in the circulation
(.tau..sub.PL), which is not affected by TPO concentration
(C.sub.i).
[0680] In contrast, the transit times of the SC, CFU-Meg, and MKB
compartments (.tau..sub.SC, .tau..sub.CFU, .tau..sub.MKB,
respectively) are functions of the micro-environmental conditions.
Since cells that are far from maturation are not expected
biologically to undergo a sudden shift to maturation, it seems that
these functions determine the value the transit time should
approach, rather than the actual transit time. The actual transit
time changes gradually: every hour it changes by 1-2 hours towards
the function-determined value. Thus, the mean of the value is
determined, that transit time approaches rather than the transit
time itself when speaking about transit time (.tau.) calculations
below.
[0681] a. SC Compartment:
[0682] It is assumed that regarding transit time (.tau..sub.SC),
the SC compartment differs from others in the same way as regarding
amplification rate (.alpha..sub.SC). It means that the cells of
this compartment respond to TPO only when its concentration
(C.sub.i) rises above a threshold (.theta.). This threshold is the
same as for the amplification rate (.alpha..sub.SC). Below the
threshold SC transit time is assumed to be regulated by a
TPO-unrelated mechanism dependent on the current cell number
(q.sub.SCi) only. The function of this dependence changes the
transit time from its minimal value (.tau..sub.SCu) when the cell
numbers (q.sub.SCi) approach infinity, through the normal value
that is greater than the minimal one by factor g, up to the highest
value ((.tau..sub.SCmax) determined solely by biological reasons.
This means that when the cell number in SC compartment (q.sub.SCi)
is relatively large, the cells will pass relatively rapidly to the
next compartment, thus reducing the SC one; and they will remain
longer in the SC compartment when their number (q.sub.SCi) is low,
thus repopulating it. This manner of regulation seems reasonable
biologically.
[0683] It is suggested that similar to the amplification rate
(.alpha..sub.Sc), the transit time (.tau..sub.SC) in the range of
very low cell numbers (q.sub.SCi) (lower than a certain fraction
(v) of the normal (q.sub.SCnorm)), is very sensitive to further
cell number decrease, and grows rapidly, thereby resisting
compartment exhaustion. This fraction (v) is the same as for the SC
amplification rate.
[0684] Following is an example of such a function: .tau. SC , i + 1
* .function. ( q SC , i , C i ) C i .ltoreq. .theta. = { .tau. SC
.times. .times. u ( 1 + ( g - 1 ) ( q SC .times. .times. norm q SC
, i ) S 1 ) , q SC , i .gtoreq. v q SC .times. .times. norm .tau.
SC .times. .times. max - ( .tau. SC .times. .times. max - .tau. SC
~ ) ( q SC , i v q SC .times. .times. norm ) S 2 , q SC , i < v
q SC .times. .times. norm .times. .times. .tau. ~ SC = .tau. SC
.times. .times. u ( 1 + ( g - 1 ) 1 v S 1 ) .times. S 1 , 2
.gtoreq. 0 .tau. SC .times. .times. u > 0 g .gtoreq. 1 0 < v
.ltoreq. 1 ( 11 ) ##EQU5## where .tau.*.sub.SC,i+1 is the transit
time calculated based on cell numbers (q.sub.SC,i) only, i.e. when
TPO concentration (Ci) remains below the threshold; .tau..sub.SCu
is the minimal possible transit time through SC compartment in
these circumstances; v is the fraction of normal cell number
(q.sub.SCnorm), below which the dependence of the transit time
(.tau.*.sub.SC,i+1) on the cell number (q.sub.SCi) changes; S1 and
S2 are the sensitivity coefficients in the regions of q.sub.SC,i
lower and higher than vqSCnorm, respectively.
[0685] If TPO concentration (Ci) in the model rises above the
threshold, the transit time (.tau..sub.SC) is assumed to shorten in
a dose dependent manner. As for the amplification rate
(.alpha..sub.SC), its decrease is presumed to be proportional to
the difference between actual TPO concentration (C.sub.i) and the
threshold. However, a shortening of the transit time down to zero
by TPO is biologically illogical , so we assume that the transit
time (.tau..sub.SC) approaches some minimal value as TPO
concentration (C.sub.i) increases. In our model this minimum
represents a fraction (k) of the transit time calculated on the
basis of cell numbers (.tau.*.sub.SC,i+1) as described earlier
(equation (11)).
[0686] Following is an example of such an equation: .tau. SC , i +
1 .function. ( q SC , i , C i ) C i > .theta. = .tau. SC , i + 1
* .function. ( q SC , i , C i ) k ( 1 t ( C i - .theta. C * -
.theta. ) t + k 1 - k + 1 ) 0 < k .ltoreq. 1 t .gtoreq. 0 ( 12 )
##EQU6##
[0687] where r.sub.SC,i+1 is the transit time when TPO
concentration (C.sub.i) is higher than the threshold;
.tau.*.sub.SC,i+1 is the transit time calculated on the basis of
cell numbers as described in equation (11); k is the fraction of
.tau.*.sub.SCi+1 that gives the minimum transit time approaches as
TPO concentration (C.sub.i) increases; C* determines the point of
TPO concentration (C.sub.i), around which the transit time
(.tau..sub.SC) is the most sensitive to concentration (C) change; t
determines the steepness of the dependence curve (t is
non-negative). Multiplication by t enables to regulate the
sensitivity to C.sub.i with t<1 in the same manner as when
t>1.
[0688] b. CFU-Meg and MKB Compartments: [0689] It is assumed that
the transit time parameters of these two compartments
(.tau..sub.CFU, .tau..sub.MKB, respectively) are dependent solely
on TPO and respond to the absolute TPO concentration (C.sub.i),
rather than to its difference with a threshold (C.sub.i-.theta.).
As TPO level (C.sub.i) drops, the cell passage through these
compartments slows, i.e. transit time (.tau..sub.comp) increases up
to the values limited solely by biological reasons
(.tau..sub.comp,max) (it is assumed that the cells cannot stay in
these compartments for an infinite period of time). On the other
hand, when the TPO concentration (C.sub.i) in the system increases,
.tau..sub.comp does not shorten to zero, but rather asymptotically
reaches .tau..sub.comp,min, thus bounding the function from below.
This also seems biologically reasonable, as the cells cannot move
through the compartment in one instant. At normal TPO
concentrations (Cnorm), we set .tau..sub.comp to equal its normal
value (.tau..sub.comp,norm). In addition, in order to enable the
system to be sensitive both to the regulation by endogenously
produced TPO and to the effect of the exogenously administered
drug, it was assumed that the function changes relatively rapidly
in the region of TPO concentrations (C.sub.i) lower than normal
(C.sub.norm) and with a smaller rate when a TPO concentration
(C.sub.i) is higher than normal (C.sub.norm). The following is an
example of such a function: .tau. comp , i + 1 = { .tau. comp , max
- ( .tau. comp , max - .tau. comp , norm ) ( C i C norm ) t 1 , C i
.ltoreq. C norm ( .tau. comp , norm - .tau. comp , min ) 2 ( C i C
norm ) t 2 + 1 + .tau. comp , min , C i > C norm .times. .times.
0 < .tau. comp , min .ltoreq. .tau. comp , norm .ltoreq. .tau.
comp , max t 1 , 2 .gtoreq. 0 ( 13 ) ##EQU7## where comp is one of
the aforementioned compartments (CFU-Meg or MKB);
.tau..sub.comp,i+1 represents the transit times through these
compartments; .tau..sub.comp,min, .tau..sub.comp,norm, and
.tau..sub.comp,max are the minimal, normal and maximal transit
times when TPO concentration is normal; t1 and t2 determine the
steepness of the dependence curve in the regions of C.sub.i lower
and higher than Cnorm, respectively.
[0690] (4) TPO Effects on the Fraction of Cells that Flow from One
Compartment to the Next
[0691] The discussed parameter is the proportion of cells that
passes to the next compartment at any given moment (.phi.). As was
noted earlier, it is assumed that the fraction of the SC that
commits to the megakaryocytic lineage (.phi..sub.SC) is constant
and TPO-independent. TPO in our model does not affect the two
subsequent compartments, CFU-Meg and MKB.
[0692] In contrast, the fractions of MK16-, MK32-, and
MK64-megakaryocytes that undergo additional endomitoses and flow to
the next compartment (.phi..sub.comp) are assumed to be in the
range of 0 to 1 depending on TPO concentration (C.sub.i). Because
there is no compartment with ploidy greater than 128N, the
megakaryocytes of the MK128 compartment do not flow to any other
compartment.
[0693] The dependence of MK16, MK32, and MK64 .phi. parameters on
TPO concentration assumed to be delayed with .phi. calculated based
on TPO concentration prior to last endomitosis (C.sub.i-.mu.).
[0694] In the model, this dependence is expressed by a sigmoidal
function with .phi. set to 0 when TPO concentration (C.sub.i) is 0,
equaling the normal value (.phi..sub.norm) when TPO concentration
is normal (C.sub.norm), and approaching 1 asymptotically. .phi.
comp , i + 1 .function. ( C i - .mu. ) = 1 - C norm t ( 1 .phi.
comp , norm - 1 ) C i - .mu. t + C norm t ( 1 .phi. comp , norm - 1
) 0 .ltoreq. .phi. comp , norm .ltoreq. 1 t , .mu. .gtoreq. 0 ( 14
) ##EQU8## where comp is one of the discussed compartments (MK16,
MK32, or MK64); .phi..sub.comp,i+1 is a .phi. parameter of these
compartments; .mu. is the time needed for one additional
endomitosis; .phi..sub.comp,norm is the value of .phi..sub.comp
under normal TPO concentration (C.sub.norm); t determines the
steepness of the dependence function (t is non-negative).
[0695] The time needed for an additional endomitosis (.mu.) assumed
to be the same in the three relevant compartments (MK16, MK32, and
MK64).
IV.A.3. Complete Detailed Model
[0696] The complete model was built as an imitation of what happens
in real bone marrow. Each compartment is subdivided into small
sections that contain the cells of a specific age with a resolution
of one hour. For example, the fifth age-section of MKB compartment
50 contains cells within MKB compartment 50 that have been within
that compartment for 5 hours. Every hour, all the cells in the
"bone marrow" pass to the next age-section in the same
compartment.
[0697] When the cell has spent all the transit time predetermined
for it in a given compartment, it passes to the next compartment to
the zero age-section. Thus, every hour the cells that leave one
compartment fill the zero age-section of the next one. The cells
that leave MK128 compartment 90 die. The zero age-section of SC
compartment 30 is filled by a certain fraction of the cells that
leave SC compartment 30.
[0698] The cells that release platelets add a certain platelet
number to the zero age-section of PL compartment 100 every hour.
Reference is now made to FIG. 4, which is an illustration of the
implementation of the model. The model is implemented as a chart of
8 rows and 360 columns. The 8 rows relate to 8 cell compartments,
and the columns relate to the age sections, with the assumption
that transit time does not exceed 360 hours. This chart is updated
hourly according to the rules described above.
[0699] Reference is now made to FIG. 5, which shows a graphical
representation of the chart of FIG. 4. Within the compartments
where proliferation occurs (SC and CFU-Meg), the number of
proliferating cells increases from the first to the last
age-section. In contrast, the cell number in the compartments that
have no proliferating ability remains constant (MKB, MK128, PL), or
decreases when cells that have undergone additional endomitosis
leave the compartment for the next one (MK16, MK32, MK64).
[0700] Reference is now made to FIG. 6, which is an illustration of
another representation of the model, based on the time courses of
different compartments. The rows in the chart represent cell
compartments and the columns represent time of simulation course.
At every time-step of the simulation (one hour of "patient's
life"), the number of cells in all age-sections is summarized for
each compartment and the next column in time-course chart (FIG. 6)
is filled. Thus, every cell in the chart represents the total
number of cells in a given compartment at a given time point.
[0701] There is an additional row in the time-course chart that
relates to the TPO concentration in the blood. TPO concentration is
monitored and out-put every time-step concurrently with the cell
numbers.
[0702] Reference is now made to FIG. 7, which is a graphical
representation of the chart of FIG. 6, and is the most useful model
output The implementation of the described model results in a
computer simulator that describes the changes that occur in the
human Thrombopoietic system (platelet counts, bone marrow precursor
numbers, and TPO concentration) over a time span that may last
several years. The resolution of the simulator output is one
hour.
[0703] Time units and periods that will mentioned hereafter relate
to the simulated patient's life, rather to the running time of the
program.
IV.A.4. Parameter-Specific Adaptation of Model
[0704] This model may be fit to patients with diverse blood and
bone marrow parameters. People differ in their baseline platelet
counts and numbers of bone marrow precursors, in the sensitivity of
their stem cell "intrinsic" regulation mechanism, in their minimum
and normal transit times and maximal amplification rates, rates of
platelet release by megakaryocytes, fractions that each
megakaryocyte ploidy class contribute for additional endocytosis,
and the time needed for endomitosis (.mu.). Furthermore, the
baseline TPO level, the rate of TPO production, receptor- and
non-receptor-mediated TPO clearance, the threshold of TPO effect on
the SC compartment, and the sensitivity of different cell
parameters to TPO also differ between patients.
[0705] To obtain an ideal fitness of the model to each patient, the
patient-related parameters should be given individually for each
patient. However, practically, it would be extremely difficult to
predetermine many of these parameters for every patient. Therefore,
certain average parameters have been calculated based on published
data, and are shown in Table 1 below. These averaged parameters are
used as a framework into which known individual characteristics are
included. Thus, before a particular simulation is begun, relevant
known information about the individual may be included, sometimes
replacing certain parameters of the model. TABLE-US-00001 TABLE
COMMON PARAMETERS Compartment Parameter SC CFU-Meg MKB MK16 MK32
MK64 MK128 PL q.sub.norm 480 650 5959 3900 1380 15 3 17,857,000
(.times.1000/kg body weight) .tau..sub.min (.tau..sub.u in SC) 12
30 143 -- -- -- -- -- (hours) .tau..sub.norm -- 60 186 250 250 250
250 240 (hours) .tau..sub.max 350 360 360 -- -- -- -- -- (hours)
.phi..sub.norm 0.2846 1 1 0.2682 0.0128 0.1685 -- -- (/hour) c --
-- -- 4000 8000 16000 32000 -- (platelets) r -- -- -- 11.19 22.38
44.76 89.52 -- (platelet/hr) STEEPNESSES (t) OF THE TPO-SENSITIVITY
CURVES a.sub.SC a.sub.CFU .tau..sub.SC .tau..sub.CFU (t.sub.1)
.tau..sub.CFU (t.sub.2) .tau..sub.MKB (t.sub.1) .tau..sub.MKB
(t.sub.2) .phi..sub.MK16 .phi..sub.MK32 .phi..sub.MK64 0.02 0.1 0
10.sup.-10 1 1 1 2 2 4 SC-RELATED PARAMETERS S.sub.1 for S.sub.2
for S.sub.2 for .nu. a.sub.SC a.sub.SC S.sub.1 for .tau..sub.SC
.tau..sub.SC k a.sub.w y g 0.01 0.5 0.5 1 0 0.5 1.116 0.25 5
TPO-RELATED PARAMETERS a (pg/ml/hr/ p .theta. f receptor C.sub.norm
.epsilon. C* (pg/ml) (pg/ml) (/hr) molecule) (pg/ml) (pg/ml)
(pg/ml) 48 10,000 0.1 38 100 0.01 .theta. + 50 OTHER PARAMETERS d
(fraction from each age- .mu. section per (hours) m.sub.PL b
a.sub.CFUmax b hour) 16 220 220 1.204 0.125 2.59 .times.
10.sup.-4
[0706] Usually, the known patient-related data are not parameters
in the form defined by our model, but rather measurements obtained
in the clinic (e.g., day s and value of post-chemotherapy
Thrombocytopenia nadir, day and value of platelet peak after TPO
administration, change in megakaryocyte modal ploidy following some
perturbation, etc.). In these cases, the available data is
converted into a model-compatible format.
[0707] Sometimes, the only available patient-related data are the
graphic representation of the patient's platelet course following
some perturbation (e.g., cell-suppressive therapy or TPO
administration). The data may also be a picture of the platelet
course without any external disturbance (e.g., cyclic
Thrombocytopenia). In these cases the model parameters are changed
by trial-and-error until a good compliance of the model graphic
output and the patient's graphs is achieved. It should be noted,
however, that even in the case of trial and error, the choices of
parameter sets are not random but rather are also based on some
analysis.
[0708] Specifically, the following tools are available for
providing maximum flexibility: [0709] 1) The user can set the
baseline values and all other known patient-specific Thrombopoietic
parameters before starting the simulation. [0710] 2) The user
(e.g., physician) can determine how long of a time period to
simulate, from a number of hours up to several years. [0711] 3) The
user can determine the frequency of showing the course of a patient
counts up to the moment. The frequency can change from as much as
every 12 hours to once during the overall period of simulation.
[0712] 4) The user can determine the resolution of the output
graph, from the hourly representation of the patient's state down
to any other resolution. [0713] 5) The user can choose to view the
graphical representation of the age distribution through the
compartments at any moment of the simulation. [0714] 6) The user
can simulate a cell-suppressive therapy at any moment while running
the simulation by reducing one or several of the compartments by
any value. [0715] 7) The user can simulate exogenous TPO
administration at any moment while running the simulation by
controlling dose height, number of dosings or frequency of
dosings.
[0716] The simulation tool has been carefully tested with respect
to the published experimental results, and has proved to be well
calibrated for average human data. Parameters may be modified
relatively quickly for efficient use of the system. The following
model parameters are important for individualized adjustment of the
model: [0717] baseline number of: SC, CFU-Meg, MKB, MK16, MK32,
platelets. [0718] amplification rate of: SC, CFU-Meg. [0719]
transit time of: MKB, MK16, MK32, MK64. [0720] fraction undergoing
additional endomitosis in: MK16, MK32, MK64. [0721] rate of
platelet release of: MK16, MK32, MK64, MK128. [0722] Time needed
for additional endomitosis. [0723] Rate of endogenous TPO
production. [0724] Ratio of receptor- and non-receptor-mediated TPO
clearance. [0725] Steepness of the sensitivity curve of: CFU-Meg
amplification rate; MKB transit time; MK16, MK32, and MK64 fraction
undergoing additional endomitosis. Reference is now made to FIGS.
8A, 8B, 9A and 9B, which show a comparison between experimentally
obtained data and the simulated model. Experimentally obtained in
vivo platelet counts following TPO administration are shown in FIG.
8A and chemotherapy without TPO is shown in FIG. 9A. FIGS. 8B and
9B show simulations of the same. By using a TPO schedule designed
by the described model, one can obtain platelet profiles that are
similar to those obtained clinically (FIG. 8B) or even more
effective (FIG. 9B). In this case, these results are achieved by
administering a pre-calculated TPO protocol whose total dose
amounts to 25% of the original total dose.
[0726] The complete model simulates cell and platelet counts in the
steady state, as well as after perturbations to the haematopoietic
system, e.g., cell-suppressive therapy, recombinant Thrombopoietin
administration for uses such as platelets harvesting, etc. It is
possible to simulate any protocol of drug administration and any
haematological state of a patient, regarding his/her platelet count
and number of bone marrow megakaryocytes and their precursors. The
model can be adapted to many categories of patients, or healthy
platelet donors. It can also be modified to fit species other than
human. By providing specific parameters one can adjust the model so
as to yield particular predictions about the Thrombopoietic profile
of an individual patient. Other platelet disorders, such as cyclic
Thrombocytopenia, may also be simulated.
IV.B. Neutrophil Production in the Bone Marrow and its
Concentration in the Peripheral Blood Compartment Alone or Under
the Effects of Growth-Factors and Treatment with Granulocyte Colony
Stimulating Factor (G-CSF)
[0727] Another embodiment of the present invention involves the
disclosed techniques for Neutrophil lineage, Granulopoietic
disorders, including Neutropenia and its treatment with GCS-F. The
Neutrophil lineage originates in pluripotent stem cells that
proliferate and become committed to the Neutrophil lineage. These
cells then undergo gradual maturation accompanied with furhter
proliferation. The present model uses the state-of-the-art discrete
compartmentalization of this continuous maturation-proliferation
process, but is not restricted to it and can easily accomodate
other modes of describing this continuous process using.
[0728] It is customary to divide the neutrophil maturation process
in the bone marrow into three morphologically distinguishable
mitotic compartments: Myeloblasts, promyelocytes and
myelocytes.
[0729] The myelocytes then mature and lose their capacity to
proliferate, and thus enter the post mitotic compartment. In the
post-mitotic compartment the cells continue their gradual
maturation, which is not accompanied with proliferation through the
three morphologically distinguishable sub-compartments:
Metamyelocyte, band and segmented-Neutrophils. Cells exit the
various sub-compartments in the post-mitotic compartment and enter
the blood as Neutrophils. They then migrate from the blood to the
tissues.
[0730] The Granulocyte-Colony Stimulating Factor (G-CSF) generates
an increase in blood Neutrophil levels primarily by increasing
production in the mitotic compartment and shortening the transit
time of the post-mitotic compartment.
[0731] Thus, the first compartment of the mitotic pool (myeloblast)
receives an inflow of cells from stem-cell precursors. Inflow for
each of the other compartments is from outflow of the previous one,
subject to multiplication factors due to cell replication in the
mitotic stages.
[0732] Models regarding Granulopoiesis in normal humans and in
humans with pathologies of the bone marrow were suggested
previously in order to give a coherent description of the kinetics
of Granulocytes from experimental data. For background details,
see, Cartwright G E, Athens J W, Wintrobe M M. 1964. The kinetics
of Granulopoiesis in normal man. Blood. 24(6): 780-803;
[0733] In recent years Schmitz et al. developed a kinetic
simulation model for the effects of G-CSF on Granulopoiesis (for
further details, see Schmitz, S., Franke, H., Brusis, J., Wichmann,
H. E. 1993. Quantification of the Cell Kinetic Effects of G-CSF
Using a Model of Human Granulopoiesis. Experimental Haematology.
21:755-760), and used it for the analysis of administration of
G-CSF to patients suffering from cyclic Neutropenia (for further
details, see Schmitz, S., Franke, H., Wichmann, H. E., Diehl, V.
1995. The Effect of Continuous G-CSF Application in Human Cyclic
Neutropenia: A Model Analysis. British Journal of Haematology.
90:41-47.). However, the data Schmitz rests upon for his model has
been more accurately assessed in recent years by Price et al. and
Chatta et al. For further details, see Price T H, Chatta G S, Dale
D C. 1996. Effect of Recombinant Granulocyte Colony-Stimulating
Factor on Neutrophil Kinetics in Normal Young and Elderly Humans.
Blood. 88(1): 335-40; and Chatta G S, Price T H, Allen R C, Dale D
C. 1994. Effects of in vivo Recombinant Methionyl Human Granulocyte
Colony-Stimulating Factor on the Neutrophil Response and Peripheral
Blood Colony-Forming Cells in Healthy Young and Elderly Adult
Volunteers. Blood. 84(9): 2923-9. Actual empirical data regarding
compartment sizes and their transit times was not incorporated into
their model despite the importance of these data (For further
details, see Dancey J T, Deubelbeiss K A, Harker L A, Finch C A.
1976. Neutrophil Kinetics in Man. J Clin Invest. 58(3):
705-15).
IV.B.1. Model of Neutrophil Lineage And Effects of G-CSF
[0734] a) G-CSF The effects of G-CSF on the Neutrophil lineage are
relayed in the model in three stages. The first is the administered
amount of cytokine given at time t, which is marked:
G.sub.dm.sup.t
[0735] The Gadm vector serves as the control variable for
optimization of G-CSF administration.
[0736] The second stage represents the pharmacokinetic behavior of
G-CSF in circulation. It incorporates, for instance, the half-life
of G-CSF, and could in the future be modified to express more of
the effects of time on G-CSF activity. This level is marked:
G.sub.blood.sup.t
[0737] G-CSF is eliminated from the blood in a Poissonic manner
according to the following equation, as stated by Stute N, Furman W
L, Schell M and Evans W E in "Pharmocokinetics of recombinant human
Granulocyte-macrophage colony stimulating factor in children after
intravenous and subcutaneous administration"" Journal of
Pharmaceutical Science, 84(7): 824-828, 1995: G blood t + 1 = G
blood t .function. ( 1 - ln .times. .times. 2 t ~ 1 / 2 ) + G adm t
+ 1 ( 14 ) ##EQU9## where {tilde over (t)}.sub.1/2 the half-life of
G-CSF in the blood, and G.sub.blood.sup.1=G.sub.adm.sup.1.
[0738] Recent data by Terashi K, Oka M, Ohdo S, Furudubo T, Ideda
C, Fukuda M, Soda H, Higuchi S and Kohno S, in "Close association
between clearance of recombinant human Granulocyte colony
stimulating factor (G-CSF) and G-CSF receptor on Neutrophils in
cancer patients", Antimicrobial Agents and Chemotherapy, 43(1):
21-24, 1999, points to the dependence of the half-life of G-CSF on
Neutrophil counts. In the absence of exact kinetics of G-CSF
effects on the Neutrophil lineage, the half-life is considered as a
constant, though this could be modified should more exact
information emerge.
[0739] Only exogenously produced G-CSF is considered to affect the
kinetic parameters, and endogenously produced G-CSF levels and
effects are set to zero. If more empirical data regarding the
production of endogenous G-CSF is made available, it could be
incorporated into the equation as well.
[0740] The third and final stage models the pharmacodynamic effects
of G-CSF on the kinetic parameters. As will be elaborated
subsequently, the dependence of the various kinetic parameters of
the Neutrophil lineage on the level of G-CSF in the blood is
assumed to be through either non-decreasing concave or
non-increasing convex functions. This reproduces the effects of
saturation that are seen in clinical studies on the effects of
G-CSF, such as the study by Duhrsen U, Villeval J L, Boyd J
Kannourakis G, Morstyn G and Metcalf D in "Effects of recombinant
human Granulocyte colony-stimulating factor on haematopoietic
progenitor cells in cancer patients", Blood, 72(6): 2074-2081,
1988. That is, addition of G-CSF carries a lesser effect when its
level in circulation is already high.
[0741] b) Biological Mode
(1) Mitotic Compartment
[0742] Long-term effects of G-CSF administration take place in the
mitotic compartment. Although the major contributor to heightened
blood Neutrophil counts in the short term is the post mitotic
compartment's shortening of transit time due to G-CSF
administration, this high level cannot be maintained over the long
term without increased production in the mitotic compartment.
[0743] The mitotic compartment is divided into subcompartments. The
kth subcompartment contains all cells of chronological age between
k-1 and k hours, relative to the time of entry into the mitotic
compartment. The number of cells in subcompartment k at time t is
marked as m.sub.k.sup.t. k.epsilon.{1 . . . .tau.}
m.sub.1.sup.t=l.sub.1.sup.t(G.sub.blood.sup.t) (15) where .tau. is
the transit time of the entire mitotic compartment, and is assumed
to be the same and constant for all cells entering the mitotic
compartment, and l.sub.1 is a vector reflecting the flow of newly
committed cells into the mitotic compartment. The biological
grounds for this definition is the existence of a myeloid stem cell
reservoir, which is known to supply new committed cells to the
mitotic compartment. However, the reservoir's actual kinetics are
not very well explored empirically. Therefore l.sub.1 is fixed to
levels such that the overall size of the mitotic compartment as
well as the kinetics of the Neutrophils in circulation would match
those obtained empirically.
[0744] Any new biological data that emerges may help define the
kinetics more accurately within the framework of this model,
although results of this model indicate that the assumption of a
constant rate of stem cells flowing into the mitotic compartment in
the absence of G-CSF is plausible. For every n.epsilon.{1. . . }
and for every t, amplification occurs at the exit from
m.sub.n.sup.t, according to Equation 15 as follows:
m.sub.n+1.sup.t+1=m.sub.n.sup.t.alpha..sub.n(G.sub.blood.sup.t)
(16) where: ps .alpha..sub.n is a non-decreasing concave function
of G-CSF levels in the blood, which determines the factor of
amplification in the hourly subcompartment n. If, for instance, no
amplification occurs at subcompartment n.sub.0 at time t then
.alpha..sub.n.sub.0.sup.20=1
.A-inverted.n,G.sub.blood.sup.t1.ltoreq..alpha..sub.n(G.sub.blood.sup.t).-
ltoreq.2 (17)The size of the morphological sub-compartments in the
mitotic compartment at time t is determined as:(18) n = n 0 n 1
.times. m n t ##EQU10## Where n.sub.0 is the first hourly
sub-compartment of a morphological sub-compartment and n.sub.1 is
its last hourly sub-compartment. The division into the
morphological sub-compartments is used only for fine-tuning of the
kinetic parameters with the use of experimental data.
[0745] The mitotic compartment was modeled with an intention to
facilitate the specific cell-cycle cytotoxic effects of
chemotherapy. Therefore, cohorts of one hour are modeled as
undergoing a process of maturation and amplification culminating in
their entry into the post-mitotic as described below. Effects of
chemotherapy may be incorporated into the model by mapping the
various cell-cycle phases (G1, S, G2, M) to the hourly cohorts
modeled and formulating a function of the cytotoxic effects of
chemotherapy on these phases.
[0746] The experimental literature shows wide agreement regarding
the steady state normal amounts of circulating Neutrohpils, size of
the post-mitotic compartment and the three morphologically distinct
sub-compartments of the mitotic compartment, and post-mitotic
transit time and amplification rates in the mitotic
sub-compartments (see, for example, Dancey J T, Deubelbeiss K A,
Harker L A and Finch C A, in "Neutrophil kinetics" in Man. Journal
of Clinical Investigation, 58(3): 705-715, 1976; Price T H, Chatta
G S and Dale D C, "Effect of recombinant Granulocytee
colony-stimulating factor on Neutrophil kinetics in normal young
and elderly humans", Blood 88(1): 335-340, 1996; and Dresch Mary in
"Growth fraction of myelocytes in normal human Granulopoiesis",
Cell Tissue Kinetics 19: 11-22, 1986). To determine other relevant
kinetic parameters, which were either not available in the
literature or were given a wide range by experimentalists, steady
state kinetics was assumed and an iterative process was employed.
These parameters include the inflow of stem cells to the myeloblast
compartment and the transit times of the mitotic
sub-compartments.
[0747] The half life of blood Neutrophils and the steady state
number of Neutrophils were taken as 7.6 h and 0.4.times.10.sup.9
cells/kg body weight, respectively (taken from Dancey J T,
Deubelbeiss K A, Harker L A, Finch C A. 1976. Neutrophil Kinetics
in Man. J Clin Invest. 58(3): 705-15 ). Similarly, the same
calculation may be made for each patient that is to be modeled.
This would allow the dynamics of every patient to be described by
the simulation. The average size of the post-mitotic compartment
(5.84.times.10.sup.9 cells/kg body weight--Dancey J T, Deubelbeiss
K A, Harker L A, Finch C A. 1976. Neutrophil Kinetics in Man. J
Clin Invest. 58(3): 705-15) and the transit time of the compartment
(160 h--Dancey J T, Deubelbeiss K A, Harker L A, Finch C A. 1976.
Neutrophil Kinetics in Man. J Clin Invest. 58(3): 705-15; Dresch,
Mary. 1986. Growth Fraction of Myelocytes in Normal Human
Granulopoiesis. Cell Tissue Kin. 19: 11-22; Price T H, Chatta G S,
Dale D C. 1996. Effect of Recombinant Granulocyte
Colony-Stimulating Factor on Neutrophil Kinetics in Normal Young
and Elderly Humans. Blood. 88(1): 335-40) are compatible with the
size and half-life of the circulating Neutrophil compartment
reported by Dancey, thus supporting the steady state analysis.
[0748] In order to determine the amount of cells in the hourly
sub-compartments in the mitotic compartment, all compartments in
the lineage were modeled using a steady state assumption. The
number of cells exiting the circulating Neutrophil pool equals the
number of cells exiting the post mitotic compartment, which in turn
equals the hourly production of cells in the mitotic compartment.
Thus, the number of cells in the last hourly cohort of the mitotic
compartment can be determined from the Neutrophil decay rate, which
is available in the literature. However, this calculation is based
on assumptions that there is no apoptosis in the post-mitotic
compartment. Direct experimental data by Thiele J, Zirbes T K,
Lorenzen J, Kvasnicka H M, Scholz S, Erdmann A, Flucke U, Diehl V
and Fischer R, in "Haematopoietic turnover index in reactive and
neoplastic bone marrow lesions: Quantification by apoptosis and
PCNA labeling," Annals of Haematology 75(1-2): 33-39, 1997,
suggests that apoptosis is not a significant phenomenon in normal
human bone marrow. The size calculated for the mitotic compartment
is close to that experimentally obtained by Dancey and Price, thus
supporting the notion that apoptosis is not a significant kinetic
factor in the lineage. Values for the production of cells in the
mitotic compartment can later be modified in light of new
evidence.
[0749] Regarding the transit time of the mitotic compartment there
is little agreement in the literature, with a range of 90-160 hours
given by most experimentalists (see Dresch Mary in "Growth fraction
of myelocytes in normal hman Granulopoiesis," Cell Tissue Kinetics
19: 11-22, 1986). In order to determine the transit times of the
mitotic morphological sub-compartments, as in Equation 18, the
following constraints were considered: [0750] 1. The sizes of the
theoretically obtained morphological sub-compartments must fit
those reported experimentally in normal human haematopoiesis
(Dancey J T, Deubelbeiss K A, Harker L A, Finch C A. 1976.
Neutrophil Kinetics in Man. J Clin Invest. 58(3): 705-15) and under
the effects of G-CSF (Price T H, Chatta G S, Dale D C. 1996. Effect
of Recombinant Granulocyte Colony-Stimulating Factor on Neutrophil
Kinetics in Normal Young and Elderly Humans. Blood. 88(1): 335-40);
[0751] 2. At least 24 hours, the typical cell cycle, must separate
amplification points; [0752] 3. The size of the last hourly
sub-compartment must equal the hourly production of the mitotic
compartment (calculated with the aforementioned iterative process
assuming steady state kinetics); [0753] 4. Amplification inside the
compartment is set at the levels determined by Mary, J. Y. 1984.
Normal Human Granulopoiesis Revisited I. Blood data, II. Bone
Marrow Data. Biomedicine & Pharmacotherapy. 38: 33-43, 66-67;
and [0754] 5. The total transit time of the mitotic compartment
must be within the 90-160 hour range. By using the values shown in
Table x, an excellent fit was obtained within the above-mentioned
constraints.
[0755] It should be noted that when other alternatives with shorter
transit times were attempted, results could not be obtained that
agreed with the literature regarding the size of the mitotic pool
or its production. Furthermore, a fit between our simulation
model's results regarding Polymorphonuclear (PMN) cell counts in
peripheral blood with empirical data could not be achieved without
speculating extensively on the nature of G-CSF effects on
non-committed stem cells. It should be noted, that little empirical
quantitative data is available regarding stem cells.
[0756] The effects of G-CSF on this compartment are modeled as an
increase in the rate of cells entering the myeloblasts from the
uncommitted stem cell pool, increases in the rates of mitosis, and
introduction of new points of amplification as shown in Equation
15, 16. Since little data is available regarding the increases in
amplification due to G-CSF, an initial assumption was made that
amplification reaches full potential at points that under normal
conditions undergo an amplification of below a factor of 2.
Additionally, it was assumed that the transit time in all mitotic
sub-compartments and the typical cell cycle duration are not
affected by G-CSF, based on lack of evidence to the contrary.
[0757] Reference is now made to FIGS. 14 and 25 which show a
comparison of Neutrophil production according to the described
model and experimental data in the literature. Increased Neutrophil
production is in accordance with the Neutrophil counts reported by
Price et al. In addition, these increases are in accordance with
Price's data about Neutrophil bone marrow pool sizes.
[0758] Reproduction of the effect of G-CSF on Neutrophil counts and
the mitotic compartment sizes beyond day 5 of administration was
accomplished by assuming an increase (15% with the highest dose of
G-CSF) in the rate of cells entering the myeloblast compartment.
Alternatively, G-CSF may change the behavior of the myeloblast
compartment such that some of the cells there undergo self-renewal
instead of moving on to the promyelocyte compartment. However, no
empirical data to support this is available. The model can be
modified in light of new experimental data in the future.
[0759] (2) Post-Mitotic Compartment
[0760] The different post mitotic compartments seem
indistinguishable in insensitivy to cytotoxic chemotherapy.
Therefore, it is biologically acceptable and computationally
sensible to model this compartment as a single pool of cells, such
that the last hourly cohort of the mitotic compartment enters the
compartment, and a proportion of the cells within the compartment
enter the Neutrophil pool every hour.
[0761] The post mitotic compartment at time t is a single quantity
of cells pt, such that:
p.sup.t+1=l.sub.3(G.sub.blood.sup.t)p.sup.t+m.sub..tau..sup.t (19)
where l.sub.3 is a convex, non-increasing function of G-CSF levels
in the blood, which takes values in the range of [0-1]. This
definition entails p.sup.t>0. We shall mark as ot the outflow
from the post mitotic compartment:
o.sup.t=m.sub..tau..sup.t+p.sup.t-p.sup.t+1 (20) The number of
Neutrophils in the circulating blood compartment at time t is
marked nt and is modeled as a single quantity of cells, such that:
n t + 1 = o t + n t .function. ( 1 - ln .times. .times. 2 t 1 2
.times. ) ( 21 ) ##EQU11## where t1/2 is the half-life of
Neutrophils in the blood, as defined in the biological literature.
t1/2 is assumed to be held constant regardless of G-CSF levels
(Lord B. I, Bronchud, M. H., Owens, S., Chang, J., Howell, A.,
Souza, L., Dexter, T. M. 1989. The Kinetics of Human Granulopoiesis
Following Treatment with Granulocyte Colony-Stimulating Factor in
vivo. Proc. Natl. Sci. USA. 86: 9499-9503), though this could be
easily modified. The kinetics of Neutrophils in the tissues are not
modeled in this work.
[0762] This model will be incorporated into an optimization scheme
that will have as its objective function both the aims of
minimizing G-CSF administration and returning the Neutrophil
lineage to its normal levels. At G.sub.blood.sup.t=0, p.sup.t=.PI.,
m.sub..tau..sup.t at the normal healthy level we have the following
obvious relationship: .PI. T = m .tau. t = o t = n t t .times. 1 2
.times. ln .times. .times. 2 ( 21 ) ##EQU12## Which reflects the
stability of the steady state.
[0763] G-CSF affects the post-mitotic compartment by shortening its
transit time (i. e. decreasing l.sub.3). Price notes that the
number of cells in the post mitotic compartment is not
significantly changed following administration of G-CSF. This
determination is based on counts made on day 5 after G-CSF
administration. Thus, it can be safely assumed that any increased
production of the mitotic compartment flowing into the post mitotic
compartment is translated over the long-term to an increase in the
flow of cells from the post mitotic compartment to the Neutrophil
pool. This increased flow is compensated by increased production in
the mitotic compartment only at a later stage. Therefore, an upper
limit to the number of cells in the post mitotic compartment was
set, which is at the values given as steady state counts
(.PI.).
[0764] In brief, the effects of G-CSF on the Neutrophil lineage are
modeled during the first few days primarily as a decrease in the
counts of the post-mitotic compartment, which is then compensated
by an increased production in the mitotic pool. This compensation
sustains the increase in Neutrophil counts in peripheral blood.
[0765] Reference is now made to FIG. 11, which is a graphical
illustration of a simulation of the model. Though no empirical data
is available on this point, simulations of the model predict that
the number of cells in the post-mitotic compartment decreases
substantially during the first two days of G-CSF administration,
and then replenishes, so that on the sixth day the counts return
almost to their normal levels. This replenishment lags behind that
of Price et al report by a few hours. A testable hypothesis can
thus be formulated, i.e., whether using the same G-CSF protocol
Price et al used, there is indeed a nadir on day 3 of the
treatment. TABLE-US-00002 TABLE 1 Simulated kinetics after 15 days
of subcutaneous administration of 300 .mu.g G-CSF/kg weight. Day 0
values are the mean values Dancey et al (1976) use. Day 0 (no
G-CSF) Day 15 of G- Relative (.times.10.sup.9 CSF treatment
increase in cells/ (.times.10.sup.9 cells/ compartment kg. Body kg.
body size due to G- Compartment weight) weight) CSF Myeloblasts
0.140 0.153 1.09 Promyelocytes 0.582 0.898 1.54 Myelocytes 1.373
3.564 2.60 Mitotic Total = 2.10 4.615 2.20 Circulating 0.4 2.35
5.88 Neutrophils
IV.B.2. Neutrophils and G-CSF in the Circulating Blood
[0766] The elimination of Neutrophils from peripheral blood follows
a Poisson distribution, and can therefore be described as an
exponential function, as shown by Cartwright G E, Athens J W,
Wintrobe M M. 1964. The kinetics of Granulopoiesis in normal man.
Blood. 24(6): 780-803. Therefore the rate of cells leaving this
compartment is based on half-life determinations available in the
literature. Since no direct cytotoxic effects of chemotherapy have
been described for this compartment it is also modeled as a single
pool of cells.
[0767] The kinetics of G-CSF is also modeled as an exponential
distribution with a half-life of 3.5 hours (Eq. 14).
[0768] The effects of G-CSF on the kinetics of the Neutrophil
lineage appear not to be a linear function of G-CSF administration
levels. Since data provided in the literature (Chatta G S, Price T
H, Allen R C, Dale D C. 1994. Effects of in vivo Recombinant
Methionyl Human Granulocyte Colony-Stimulating Factor on the
Neutrophil Response and Peripheral Blood Colony-Forming Cells in
Healthy Young and Elderly Adult Volunteers. Blood. 84(9): 2923-9)
only refers to two doses (30 and 300pgram/kg body weight) we can
only speculate on the effects of other levels of G-CSF. After trial
and error analysis, it was found that assuming that the effects of
the 300-.mu.gram dose are the maximal, at the 30-.mu.gram its
effects are about 30% of the maximum.
[0769] Reference is now made to FIGS. 12A and 12B, which are
graphical illustrations of the effects of G-CSF at the two doses.
The effects as a function of G-CSF level are connected piece-wise
linearly. This way, the Neutrophil levels observed clinically under
both the 300 and the 30-.mu.gram protocols are obtained.
IV.C. Linear Implementation of the Model
[0770] Another embodiment of the present invention is the
implementation of the above model by incorporating it into an
optimization scheme that has as its objective function both the
aims of minimizing G-CSF administration and returning the
Neutrophil lineage to its normal levels.
[0771] Although the above-outlined model may be implemented in any
number of optimization methods, the disclosed embodiment using
linear programming was chosen because of its inherent advantages
compared with some other techniques, i.e. its ability to provide an
optimal solution using partially analytical methods, and therefore
being more computationally tractable (Gill 1991). On the other
hand, implementation of this model in linear programming carries
with it the disadvantage that certain computations must be
approximated linearly since they cannot be performed directly using
linear methods. Thus, we shall compare the `closeness` of the
solution obtained through linear programming with that obtained
through another, non-linear method of optimization.
[0772] The significant parts of the model that must be modified due
to the linear programming implementation are the sections in which
multiplication of two {(x.sub.min, y.sub.min, x.sub.miny.sub.min),
(x.sub.min, y.sub.max, x.sub.miny.sub.max), (x.sub.max, y.sub.min,
x.sub.maxy.sub.min), (x.sub.max, y.sub.max, x.sub.maxy.sub.max)}
variables is defined, since this operator is not itself linear.
Therefore, multiplication is defined as an approximated value
constrained within piecewise linear constraints that most closely
bound the product within a four-faced polyhedron in 3-dimensional
space whose vertices are Where x.sub.min, x.sub.max, y.sub.min,
y.sub.max are the constant biologically defined minima and maxima
of x and y. M .function. ( x , y ) .times. { .gtoreq. y min .times.
x + x min .times. y - x min .times. y min .gtoreq. y max .times. x
+ x max .times. y - x max .times. y max .ltoreq. y min .times. x +
x max .times. y - x max .times. y min .ltoreq. y max .times. x + x
min .times. y - x min .times. y max ( 22 ) ##EQU13##
[0773] Multiplication may also be approximated with variations on
the linear least squares method, by finding one plane that's
closest to the four vertices defined.
[0774] The other functions that need to be defined linearly are
those concerning the pharmacodynamics of G-CSF. Due to the nature
of these functions (either non-increasing convex or non-decreasing
concave), these effects are implemented as piece-wise linear
functions whose breakpoints are the doses for which actual
experimental data is available (Chatta G S, Price T H, Allen R C,
Dale D C. 1994. Effects of in vivo Recombinant Methionyl Human
Granulocyte Colony-Stimulating Factor on the Neutrophil Response
and Peripheral Blood Colony-Forming Cells in Healthy Young and
Elderly Adult Volunteers. Blood. 84(9): 2923-9). Note that the
effects of G-CSF on each of the kinetic parameters have not been
determined in a detailed manner by experimentalists. Rather its
effects over a few dose levels on the Neutrophil blood counts and
the size of the morphologically different mitotic compartments and
the post mitotic compartment have been determined. From these data,
the effects of G-CSF on the actual kinetic parameters (probability
of mitosis, transit time and inflow of cells into the myeloblast
compartment from stem cell progenitors) has been reconstructed at
the dose levels available in the literature. These points are then
connected linearly to obtain piecewise linear functions relating
G-CSF levels to their effect on those parameters. Further
experimental data in the future could be used to produce more
accurate functions.
[0775] At the amplification points within the mitotic compartment,
the linearly approximated multiplication operator (Eq 22) is used
instead of the product defined in Eq. 16.
[0776] At points where no amplification occurs the quantity from
one compartment is simply transferred to the next according to the
following Equation: m n + 1 t + 1 = m n t ##EQU14## m n 0
##EQU14.2## Values are set according to the steady state values of
the mitotic compartment, or are depleted according to the kill
function of the chemotherapy.
[0777] The flow out of the post mitotic compartment (Eq. 20) is
similarly defined as a linear approximation of a product.
IV.C.1. Formulation of the Model as an Optimization Problem for
Linear Programming
[0778] The simulation spans a finite number of discrete time steps
denoted by T. We define as the control variable the vector that
represents G-CSF administration at every given hour t:
G.sub.adm.sup.t,t .epsilon.{1 . . . T} The objective function is
defined as maximization of the following expression: t = 1 T
.times. .times. ( .beta. t p t - G adm t ) ( Eq . .times. 24 )
##EQU15## where p.sup.t is the number of cells in the post mitotic
compartment at time t, and .beta. is a scalar weighting
coefficient. The logic for formulating the objective function this
way is that the ability to maintain the post mitotic compartment's
steady state size for a prolonged period of time is sufficient for
rehabilitation of the Neutrophil lineage as a whole. Also, our goal
is to minimize the total administered quantity of G-CSF. .beta. is
introduced to allow us to factor in both these goals in one
objective. Also, this would allow a different weight to be given
for certain times, e.g. were it determined (by clinicians) that the
later states of the post-mitotic compartment should be weighted
more than the first ones. Obviously this is only one of the
possible formulations of the objective function as defined in the
previous section.
[0779] The pharmacokinetics and pharmacodynamics of G-CSF that were
defined generally in the mathematical model are defined piecewise
linearly. Some of the considerations that was put into formulating
these functions were based directly on experimental evidence
(elaborated in the main body of text). It is noted however, that
actual experimental data regarding the direct effects of G-CSF on
the kinetic parameters in which this model is interested is rather
scant. Therefore, some formulations were conducted through partly
analytic and partly trial-and-error methods.
[0780] The formulation of the model in piecewise linear terms will
allow use of this model as a clinical tool in three ways. First,
the model will determine the effectiveness of various protocols
suggested by clinicians prior to their actual use on human
patients. Second, the model allows computation of the optimal
protocol in a given situation of Neutrophil counts, so that the
e.g., Neutropenic period following chemotherapy is either shortened
or completely avoided at a minimal cost and exposure to G-CSF.
Third, the model serves as a constituent in a broader framework of
clinical tools that will compute the most optimal treatment plan
for chemotherapy and growth factors. These uses should help
clinicians administer more rational treatment to their patients
minimizing both suffering and medical costs. TABLE-US-00003 TABLE 1
Kinetics under steady state conditions in healthy humans. Size
(10.sup.6 Amplification Mean transit cells/kg at the exit time
(hours) weight) Compartment 2.sup.+ 24.sup.- 0.139* Myeloblasts
2.sup.+ 48.sup.- 0.558* Promyelocytes 1.5.sup.+ 48.sup.- 1.4*
Myelocytes 1 160* 5.84* Post mitotic 0 10.96* 0.4* Neutrophils
*Dancey, 1976. .sup.+Dresch, 1986. .sup.-Calculated based on the
steady state assumption as elaborated in the main text.
IV.D. Cancer and Treatment with Cytotoxic Drug Delivery
[0781] IV.D.1. Introduction
[0782] Still another embodiment of the present invention deals with
cancer and its treatment using chemotherapy. Cancer is the second
leading cause of mortality in the US, resulting in approximately
550,000 deaths a year. There has been a significant overall rise in
cancer cases in recent years, attributable to the aging of the
population.
[0783] Another contributing factor to the rise in the verifiable
number of cases is the wider use of screening tests, such as
mammography and elevated levels of prostate specific antigen (PSA)
in the blood.
[0784] Neither better detection nor the natural phenomenon of
aging, however, can entirely explain the increase in new cases of
tumors. Meanwhile, other cancers, like brain tumors and
non-Hodgkin's lymphoma, are becoming more common. Their increase
could reflect changes in exposures to as yet unidentified
carcinogens. Current trends suggest that cancer may overtake heart
disease as the nation's no. 1 killer in the foreseeable future. As
gene therapy still faces significant hurdles before it becomes an
established therapeutic strategy, present control of cancer depends
entirely on chemotherapeutic methods.
[0785] Chemotherapy is treatment with drugs to destroy cancer
cells. There are more than 50 drugs that are now used to delay or
stop the growth of cancer. More than a dozen cancers that formerly
were fatal are now treatable, prolonging patients' lives with
chemotherapy.
[0786] Treatment is performed using agents that are widely
non-cancer-specific, killing cells that have a high proliferation
rate. Therefore, in addition to the malignant cells, most
chemotherapeutic agents also cause severe side-effects because of
the damage inflicted on normal body cells. Many patients develop
severe nausea and vomiting, become very tired, and lose their hair
temporarily. Special drugs are given to alleviate some of these
symptoms, particularly the nausea and vomiting. Chemotherapeutic
drugs are usually given in combination with one another or in a
particular sequence for a relatively short time.
[0787] Chemotherapy is a problem involving many interactive
nonlinear processes which operate on different organizational
levels of the biological system. It usually involves genomic
dynamics, namely, point mutations, gene amplification or other
changes on the genomic level, which may result in increasing
virulence of the neoplasia, or in the emergence of drug resistance.
Chemotherapy may affect many events on the cellular level, such as
cell-cycle arrest at different checkpoints, cell transition in and
out of the proliferation cycle, etc. Chemotherapy may also
interfere with the function of entire organs, most notably, with
bone marrow blood production. In recent years molecular biology and
genetics has made an important step forward in documenting many of
these processes. Yet, for assessing the contribution of specific
molecular elements to the great variety of disease profiles,
experimental biology must be provided with tools that allow a
formal and systematic analysis of the intricate interaction between
the genomic, cellular and cell populationsprocesses in the host and
in the disease agent. This system is so complex that there is no
intuitive way to know how small changes in the drug protocol will
affect prognosis. But in spite of this intricacy, attempts to
improve chemotherapy have been carried out by "trial and error"
alone, with no formal theory underlying the application of specific
drug schedules. Such an approach "is apt to result in no
improvement, only discouragement and little useful information for
future planning" (Skipper, 1986).
[0788] The treatment of cancer by cytotoxic drug (or drug
combination) delivery is addressed. In the current model, two
generic types of cells are considered: the limiting (i.e. the most
drug-sensitive) host cells and the target cells. Target cells are,
in fact, the tumor. Both types of cells may be damaged while
exposed to chemotherapy. The aim is to obtain the most suitable
treatment protocol according to specified conditions and
limitations. It is assumed that the cell dynamics are deterministic
and known, and that both types of cells are sensitive to
chemotherapeutic agents in certain known period (fraction of the
cell-cycle time ranging from 0 to 1) of the cell-cycle (denoted
critical phase). If a cell is exposed to chemotherapy during part
of its critical phase, there is a chance that it will be
eliminated, blocked or affected in any other known way. The
description of the dynamics of the delivered drugs is assumed to be
known as well.
[0789] In order to achieve the goal optimization process is applied
to the model. The optimization module uses the model predictions in
order to search for the suitable solution to posted optimization
problem. Precise defining of optimization objectives as well as the
relevant parameters adjustment is done according to the settings
defined by user/operator for every special case. The method can be
applied in general cases as well as in specific ones.
IV.D.2. Model of Biological System
[0790] The basic layer of the model incorporates a description of
age distribution of cycling cells and number of resting (quiescent)
cells. The term "age of the cell" here refers to chronological age
starting from the conventional beginning point of mitotic
cycle.
[0791] Reference is now made to FIG. 13, which is a schematic
illustration of the tumor cell cycle layer. The whole cycle is
divided into 4 compartments, or stages (G.sub.1, S, G.sub.2 and M).
Each compartment is divided into equal subcompartments, where
i.sub.th subcompartment in each stage represents cells of age i in
the particular stage (i.e. they have spent i time-steps in this
stage). The quiescent stage is denoted G.sub.0. The cell cycle
follows a direction as shown by arrows (#). Thus, cells enter each
stage starting with the first subcompartment, denoted G.sub.1.
[0792] The model can be described mathematically as follows: Let
T.sub.k denote the maximum duration of k.sup.th stage in the cycle.
Let .DELTA.t the symbol is showing up as a rectangle] denote the
time resolution of the model in discrete time steps.
X.sub.k.sup.i(t) is a function, which represents the number of
cells in stage k in the I.sup.th sub-compartment, at time t to
t+.DELTA.t. Both time and age are measured in the same unit, in
this case, hours. Let Q(t) represent the number of resting cells at
time t to t+.DELTA.t. Trans(k,i,t) represents the probability that
a cell of age i in the stage k will move to the next (k+1)
compartment. Cells entering the new stage always start from the
first subcompartment, i.e. from i=1. This probability may change
with time, representing the influence of conditions on cycle length
distribution.
[0793] By definition, the cell cannot remain more than T.sub.k
timesteps in the k.sup.th compartment, as described in the
following equation. .A-inverted.k: Trans (k, T.sub.k)=1
[0794] The restriction point (R-point) represents a cell's
commitment to complete the mitotic cycle. Let T.sub.R denote the
age at which the cell passes through the restriction point in G1.
Only cells in G.sub.1 with I<T.sub.R can the cycle (in the
absence of a drug).
[0795] The total number of proliferating cells P(t) can be
calculated as follows: P .function. ( t ) = k = G .times. .times. 1
, S , G .times. .times. 2 , M .times. .times. ( i = 1 T k .times.
.times. x k i .function. ( t ) ) ##EQU16##
[0796] In every time interval, quiescent cells may return to the
proliferation pool. Alternatively, proliferating cells may change
their state to become quiescent if and only if they are in the G1
stage and at age i, where T.sub.R.gtoreq.i.gtoreq.0. To describe
this process we introduce the function G.sub.1.quadrature.0(i,t)
which describes the number of G1 cells in age i which become
quiescent during time interval [t, t+.DELTA.t]. This function may
receive negative values, accounting for cells that return from
resting to proliferation.
[0797] As it is assumed that the exit to quiescence can occur only
prior to the R-point (even in cancer cells), and that a resting
cell that returns to proliferation enters the cycle at T.sub.0, it
can be stated: .A-inverted.i>T.sub.R, .A-inverted.t:
G.sub.1.fwdarw.0(i,t)=0 It must be noted that this function is not
dependent on i and t solely. Its value is determined according to
current cell distribution and all the general parameters that
characterize the described cells group. The same should be said
about the values of Trans vector that can change during the history
of given population.
[0798] The model traces the development of described group of
cancer cells using given parameters, by calculating the number of
cells in each and every subcompartment according to the following
stepwise equations: x k i .function. ( t ) = { x k i - 1 .function.
( t - 1 ) [ 1 - Trans .times. .times. ( k , i - 1 , t - 1 ) ] , 1
< i .ltoreq. T k j = 1 T k - 1 .times. .times. [ x k - 1 j
.function. ( t - 1 ) Trans .times. .times. ( k - 1 , j , t - 1 ) ]
, i = 1 .times. .times. x s i .function. ( t ) = { x s i - 1
.function. ( t - 1 ) [ 1 - Trans .function. ( S , i - 1 , t - 1 ) ]
, 1 < i .ltoreq. T G .times. .times. 1 j = 1 T G .times. .times.
1 .times. .times. [ x G .times. .times. 1 j .function. ( t - 1 )
Trans .times. .times. ( G .times. .times. 1 , j , t - 1 ) ] [ 1 - G
1 .fwdarw. 0 .function. ( i - 1 , t - 1 ) , i = 1 .times. .times.
for .times. .times. k = G 2 , M , k - 1 .times. .times. returns
.times. .times. the .times. .times. previous .times. .times. stage
.times. .times. ( e . g . .times. G 2 - 1 = S ) . ##EQU17##
[0799] These equations make it possible to calculate the number of
cells in each subcompartment at every time interval [t, .DELTA.t]
starting from initial distribution (e.g. at time t=0). Since in
this model cell ages are measured in absolute time units, these
measurements refer to the chronological age of the cell, and not
the biological age, whose units are relative to a maturation rate
that differs from cell to cell. Consequently, in this model no cell
can remain in the same age subcompartment after every time step. On
the other hand, a fraction of the cells that leaves any
subcompartment may be transferred to the first subcompartment of
the next stage, according to probability vector Trans(k,i,t). This
vector provides the ability to account for variability of cycle
lengths while retaining a deterministic approach.
[0800] The behavior of the cell populations in this model is
completely controlled by two components: Trans vector, and
G1.fwdarw.G0 function. These two functions determine uniquely the
outcome of every single time step, and, consequently the result
over long periods. Thus, they are referred to as "control
functions". The values of these functions may be dependent not only
on time and age of cells, but also on the current population state
(or, generally, on the whole history of the population) as well as
on the environment associated with a given cell group. However,
those parameters are similar for all the cells in the group,
implying that the model presented here is suitable for describing
highly homogenous group of cells. Therefore, the basic layer of the
model should give a realistic description for a uniform group of
cancer cells for which environmental conditions and relevant
biological properties are defined, in a way that will allow the
construction of the control functions for the group.
IV.D.3. The General Tumor Model
[0801] In the general approach the whole model is viewed as
constructed from similar components, each of them derived from the
basic structure described in the previous paragraph. Each component
represents cells that are subjected to the same environmental
conditions and, therefore behaves similarly (to be denoted
homogenous group). The whole tumor is modeled as a union of many
different homogenous groups of cells, where the development of each
group can be accurately predicted (when local conditions are
known).
[0802] This general model simulates progress of the tumor in
discrete steps of time. At each step the number of cells in each
subcompartment of each group is calculated according to the
previous state, parameters of tumor, drug concentration, etc. The
parameters of the tumor must include all the information that is
relevant to prognosis. Some of these parameters are defined
locally, e.g., those relating to the tumor's geometry. For this
reason the representation of the spatial structure will be
included.
[0803] The cells will be able to pass between the groups during the
development of the tumor. This allows the representation of the
changes in the local conditions during the tumor evolution (e.g.
forming of necrotic core, improvement in "living conditions" in
vascularized regions, etc.). In addition, all the parameters of the
tumor may change in accordance with the dynamics of the cancer.
[0804] The calculation of the tumor development over time will be
done by stepwise execution of the described simulation and can be
used to predict the outcome of the treatment or in fitness function
for search algorithms.
IV.D.4. From General to Individual Tumor Model
[0805] When the general theoretical description of the model is
accomplished, the model is fitted to represent the actual tumors.
It is rendered patient-specific by adjusting all the parameters
that determine the behavior of the modeled tumor to those of the
real cancer in the patient's body. In order to accomplish this task
we will establish the connections between mathematical parameters
(most of them will have direct biological implication) and every
kind of data that is practically obtainable in the clinic. These
connections may be defined through research on statistic
correlation between different parameters (including
genotype-phenotype correlation), or using advanced biochemical
research showing the relationships between a given bio-marker and
its effects on the reaction rates described by our model.
[0806] Thus defined, the model will be able to give realistic
predictions for treatment outcomes either for specific patient or
for a broad range profiles of patients and diseases. This tool can
serve to perform the prognosis of either an untreated cancer
patient, or as a basis for treatment modeling as is described
below.
IV.D.5. Introducing Pharmacology
[0807] In order to simulate cancer treatment pharmacologic
component is added to the above model. Pharmacokinetics as well as
pharmacodynamics for specific anticancer drugs are modelled.
Cell-cycle specific drugs and cell-cycle unspecific drugs are taken
account of by our model.
[0808] The distribution of the drug in and around the tumor as well
as in the blood (the drug kinetics) are modelled. For this purpose,
a suitable model is used, defining it precisely for every certain
type of the drug. The concentrations of drug in the body are
calculated at every time step in accordance with the drug
administration specified by the protocol, and different processes
that define drug kinetics in the body.
[0809] The dynamics of the drug are represented through the direct
influence of the drug on tumor cells. The effects on the
proliferating cells are mostly blocking the cycle in different
stages (which can be modeled as cell arrest) and cell death
(immediate or some time after the block). Cell-cycle specific drugs
are believed to have no direct influence on quiescent cells, but
can affect them indirectly by killing proliferative cells and
therefore changing local conditions. Where additional types of
drugs added to the model, their effect on any kind of cells is
modeled as killing certain fraction of cells (which is
dose-dependent) or changing the behavior of the cells.
[0810] Additional phenomena that may prove significant in drug
kinetics and dynamics (e.g. rate of absorption by the cells,
development of tumor resistance to specific drug, angiogenesis
etc.) can be introduced into the model to make it as realistic as
needed.
[0811] The description of the drug in the model is done in terms of
quantitative functions, which enable to calculate the drug amounts
at certain locations and the tumor response to it at every time
step. In the general case, these functions include parameters that
depend on the specific data (drug type, body parameters,
characteristic of the tumor, etc.) and can be determined in given
situation (patient/case).
[0812] The combination of cancer model with the limiting normal
tissue (see below), and the drug model described above makes it
possible to predict the outcome of the treatment, given the
relevant parameters for the drug, the cancer and the patient.
Again, the prognosis may be made for specified cases as well as for
broad profiles of patients or disease. This simulation also serves
to build the fitness function used for the optimization
objectives.
IV.D.6. Combining with minimizing host toxicity.
[0813] Although an accurate predictive tool, the model that
represents chemotherapy of tumor alone hardly suffice for
optimization of drug protocols. Actually, this model implies using
as much drug as possible until the final elimination of the tumor;
while in the living system the toxicity of the drug is the most
important constraint limiting the treatment. In most cases of
anticancer chemotherapy the dose-limiting toxicity is bone marrow
suppression, the two most sensitive bone marrow lineages being
Granulopoiesis and Thrombopoiesis. Accordingly, those two were
chosen as an example and are modeled separately and in a similar
way to predict the negative effect of the chemotherapy on them.
These models reconstruct the damage caused by the chemotherapy to
the bone marrow cells and the recovery of these lineages (treated
by specific growth factors).
[0814] Thus, the whole system is capable of predicting the result
of chemotherapy treatment for the tumor as well as for bone marrow
cells, allowing the use of the protocols that combine anticancer
drugs and growth factors for healthy cells.
[0815] Chemotherapy toxicity to any other normal host cell
populations can be similarly taken into account, if it is defined
as relevant for dose and schedule optimization.
IV.D.7. Individualization of the Models
[0816] Due to a great degree of heterogeneity between malignant
tumors (even among similar tissue types) and between patients, it
would be advantageous to adjust the treatment protocol to the
individual case. This individualization procedure includes three
aspects: [0817] 1) individual parameters of tumor dynamics. [0818]
2) individual parameters of patient-specific drug pharmacokinetics
and interaction. [0819] 3) individual parameters of the dynamics of
dose-limiting normal host tissues.
[0820] Relevant data concerning individual cases can be obtained by
research on statistic correlation between different parameters
(including genotype-phenotype correlation), or using advanced
biochemical research (which may establish quantitative relations).
In the general model, important dynamic parameters are estimated
from experimental studies conducted in certain patient populations.
Any of these parameters, when available on the per patient basis,
can be individualized, while those that are unavailable can be left
as a population-based figure. This approach allows continuous
increase in the degree of individualization of the treatment
protocols with progress in the technology of parameter evaluation
(e.g., oncochips).
[0821] All different parameters may then be adjusted, which will
result in an adjusted array of models to be simulated. Parameters
may include many different factors, which are adjustable according
to the needs of a researcher or a pharmaceutical company for
general use of the treatment, or may even be individualized for use
by a specific clinician for a particular individual. Examples of
parameters may include, but are not limited to age, weight, gender,
previous reaction to treatment, desired percentage of healthy body
cells, desired length of treatment protocol, pathologic or
cytologic specifics, molecular markers, genetic markers etc.
[0822] In order for the system to be user-friendly, all possible
parameters are termed in ways that are easy for the user to
understand.
[0823] Once all the parameters are set, an array of solutions is
produced based on the input parameters. A number of possible
protocols can be set (is thus generated by the computer). a fitness
function is applied, which results in scores for each of the
proposed solutions.
IV.D.8. Generation of Protocol Space
[0824] Referring back to FIG. 2, this model makes it possible to
check any given treatment protocol and to choose a very good one
according to user's criteria. The user may be a physician, a drug
developer, a scientist, or anyone else who may need to determine a
treatment protocol for a drug. The specific parameters may include
several categories, such as individual patient characteristics
and/or medical history, needs of a specific user (research,
efficacy, treatment, etc.), and other particulars (such as maximum
length of treatment, confidence level, etc.).
[0825] That is, an array of possible treatment protocols is created
from which the optimal treatment protocol can then be chosen. It
should be noted that the method does not imply the fitness
estimation for all possible protocols. The use of operation
research allows a much more sophisticated, yet resource saving
procedure.
[0826] An example of this procedure will be described as it relates
to cancer treatment by chemotherapy, as described in
above-disclosed embodiment of the invention. However, it should be
noted that a similar procedure may be performed in any of the
embodiments.
[0827] The procedure implements cell growth and cell death
procedures, as defined in the detailed model above. There are
certain pre-defined parameters, including the lengths of the host
and target life-cycles, the lengths of their critical phases, and a
resolution factor, that determines the length of a single time
unit. The user is asked to define an action (treatment or
non-treatment). Simulation of cell growth and death is then
performed for the single time unit. This procedure is repeated
until the end of the total simulation. Alternatively, the choice of
treatment or non-treatment is made by the processor, with many
possible permutations considered. In that case, the protocol space
would be very large, and the resolution would depend on the
(selected) length of the time unit (and computer capacity)
[0828] There are two procedures: one for growth simulation during
treatment and one without. The array in which the numbers of cells
are kept is updated once per time unit, whether with or without
treatment present at that time.
IV.D.9. Defining the Fitness Function
[0829] The fitness function is an important tool in Operation
Research. In this case of protocol optimization, it allows the
comparison between a number of different protocols each one of them
scoring differently with respect to various objectives that can be
set by the developers or by the users and identifying the protocol
for which the highest weighted score is predicted. The fitness
function calculates for any given protocol its relative efficacy
("score" or "fitness"), thus enabling a definite decision of the
best protocol from a given set of protocols.
[0830] In different cases, different objectives can be formulated.
There are several settings in which such a model can be used,
including but not limited to: [0831] One) clinical practice--where
objectives can change depending on type of disease, condition of
the patient, purpose of treatment, etc. [0832] Two) pharmaceutical
company--where objectives can be aimed at finding the therapeutic
window and an optimal schedule. [0833] Three) scientific
setting--research oriented objectives can be aimed at.
[0834] In each case, a particular fitness function can be
formulated, reflecting all given requirements. Thus, in any
particular case one can compare between different protocols and
obtain the most suitable to his/her special purposes and needs.
[0835] Examples for some alternative objectives are given: [0836]
1. The smallest number of drug dosings required for achieving any
given aim. [0837] 2. The lowest total drug dose required for
achieving any given aim. [0838] 3. The minimal total amount of drug
needed for rehabilitation. [0839] 4. The smallest deviation from
the baseline at normal cell populations count (e.g., platlet nadir)
after chemotherapy or another cell-suppressive treatment. [0840] 5.
The shortest period of disease (e. g., Thrombocytopenia).
[0841] Using the fitness function it is possible to a) estimate the
efficacy of a given protocol, b) search for the solution of an
optimization problem, i.e., predict which protocol will be best of
many potential protocols considered for curing/relieving the
patient.
IV.D.10. Solving the Optimization Problem
[0842] The optimization problem is stated using the described
models: to find the protocol for drug administration (with option
to growth factor administration) which maximizes the given fitness
function.
[0843] As explained above, the fitness function is defined
according to the user requirements. For example, the goal of the
treatment may be defined as minimizing the number of cancer cells
at the end of the treatment, minimizing the damage to the BM cells
throughout the treatment or at its end, and curing the patient
(where cure is defined precisely) as quickly as possible. Note that
the fitness function may also include goals such as maximizing life
expectancy, minimizing cost of treatment, minimizing treatment
hazards and/or discomfort etc. Generally, the aim of optimization
is to find the best protocol, i.e. the protocol that generates the
best value of fitness. Customarily, this is achieved by
mathematical analysis. However, mathematical analysis is restricted
to over simplified models, whereas, in order to accommodate
biologically realistic parameters, the described models are very
complex and, therefore, cannot be solved analytically. On the other
hand, the practical purpose of the treatment is not to find the
best possible protocol (i.e., the global optimum) but "only" one
that will suit the user's objectives, even if its fitness is not
absolutely the best (i.e., the local optimum). For this reason the
solution that can be shown to promise the pre-defined objectives is
deemed satisfactory.
[0844] Hence, the optimization problem may be reformulated as
follows: for given initial conditions, find the treatment protocol
which will fulfill the user's requirements (e.g. curing a patient
according to given definitions of cure) and subjected to given
limitations (e.g. treatment duration, drug amounts, etc.). To this
end it is not compulsory to find the global solution. It is enough,
with regards to objectives and limitations, to perform search,
using search algorithms, in certain regions of the protocols'
space, and find the local maxima of the fitness function. After
determining the locally best protocols, we can verify that they
serve one's objectives and check them numerically for
stability.
[0845] Such a strategy can be used for identifying patient-specific
treatment, as well as in the general case, where only the profile
of the disease and the drug are specified. If more patient-specific
data are supplied, the solution will be tailored more specifically.
On the other hand, the optimization program could propose general
recommendations for the protocol types for certain kinds of
disease, treated with a certain kind of medication.
[0846] It will be appreciated that the present invention is not
limited by what has been described hereinabove and that numerous
modifications, all of which fall within the scope of the present
invention, exist. For example, while the present invention has been
described with respect to certain specific cell lineages, the
concept can be extended to any other lineage and treatment protocol
which can be detailed mathematically (e.g., viral or bacterial
diseases). Furthermore, certain assumptions were necessarily used
in computing the mathematical models of the embodiments. Values and
equations based on these assumptions can be changed if new
information becomes available.
[0847] It will be appreciated by persons skilled in the art that
the present invention is not limited by what has been particularly
shown and described herein above. Rather the scope of the invention
is defined by the claims which follow.
[0848] Other modifications and variations to the invention will be
apparent to those skilled in the art from the foregoing disclosure
and teachings. Thus, while only certain embodiments of the
invention have been specifically described herein, it will be
apparent that numerous modifications may be made thereto without
departing from the spirit and scope of the invention.
* * * * *