U.S. patent application number 09/320270 was filed with the patent office on 2002-03-21 for pharmacokinetic-based drug design tool and method.
Invention is credited to GRASS, GEORGE M., LEESMAN, GLEN D., NORRIS, DANIEL A., SINKO, PATRICK J., WEHRLI, JOHN E..
Application Number | 20020035459 09/320270 |
Document ID | / |
Family ID | 27536966 |
Filed Date | 2002-03-21 |
United States Patent
Application |
20020035459 |
Kind Code |
A1 |
GRASS, GEORGE M. ; et
al. |
March 21, 2002 |
PHARMACOKINETIC-BASED DRUG DESIGN TOOL AND METHOD
Abstract
The present invention relates to a pharmacokinetic-based design
and selection tool (PK tool) and methods for predicting absorption
of an administered compound of interest. The methods utilize the
tool, and optionally a separately operable component or subsystem
thereof. The PK tool includes as computer-readable components: (1)
input/output system; (2) physiologic-based simulation model of one
or more segments of a mammalian system of interest having one or
more physiological barriers to absorption that is based on the
selected route of administration; and (3) simulation engine having
a differential equation solver. The invention also provides methods
for optimizing as well as enabling minimal input requirements a
physiologic-based simulation model for predicting in vivo
absorption, and optionally one or more additional properties, from
either in vitro or in vivo data. The PK tool of the invention may
be provided as a computer system, as an article of manufacture in
the form of a computer-readable medium, or a computer program
product and the like. Subsystems and individual components of the
PK tool also can be utilized and adapted in a variety of disparate
applications for predicting the fate of an administered compound.
The PK tool and methods of the invention can be used to screen and
design compound libraries, select and design drugs, as well as
predict drug efficacy in mammals from in vitro and/or in vivo data
of one or more compounds of interest. The PK tool and methods of
the invention also finds use in selecting, designing, and preparing
drug compounds, and multi-compound drugs and drug formulations
(i.e., drug delivery system) for preparation of medicaments for use
in treating mammalian disorders.
Inventors: |
GRASS, GEORGE M.; (TAHOE
CITY, CA) ; LEESMAN, GLEN D.; (HAMILTON, MT) ;
NORRIS, DANIEL A.; (SAN DIEGO, CA) ; SINKO, PATRICK
J.; (LEBANON, NJ) ; WEHRLI, JOHN E.; (MOUNTIN
VIEW, CA) |
Correspondence
Address: |
ARENT FOX KINTNER PLOTKIN & KAHN
1050 CONNECTICUT AVENUE, N.W.
SUITE 600
WASHINGTON
DC
20036
US
|
Family ID: |
27536966 |
Appl. No.: |
09/320270 |
Filed: |
May 26, 1999 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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60100224 |
Sep 14, 1998 |
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60109234 |
Nov 18, 1998 |
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60100290 |
Sep 14, 1998 |
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60109232 |
Nov 18, 1998 |
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Current U.S.
Class: |
703/11 ; 514/1.2;
514/44R; 702/19 |
Current CPC
Class: |
G16C 20/62 20190201;
Y02A 90/10 20180101; A61P 31/12 20180101; G16C 20/60 20190201; G16B
35/00 20190201 |
Class at
Publication: |
703/11 ; 702/19;
514/2; 514/44 |
International
Class: |
G01N 033/48; A01N
043/04; A01N 037/18; A01N 061/00 |
Claims
What is claimed is:
1. A computer system for simulating absorption of a compound in a
mammal, said system having as computer-implemented components an
input/output system, simulation engine, and simulation model of one
or more segments of a selected mammalian system having one or more
physiological barriers to absorption based on a selected route of
administration, said simulation model comprising as operably linked
components: (i) differential equations for one or more of fluid
transit, fluid absorption, mass transit, mass dissolution, mass
solubility, and mass absorption for one or more segments of said
mammalian system; (ii) initial parameter values for said
differential equations corresponding to physiological parameters
and selectively optimized adjustment parameters, and optionally
regional correlation parameters, for one or more segments of said
mammalian system; and (iii) control statement rules for one or more
of transit, absorption, permeability, solubility, dissolution, and
concentration for one or more segments of said mammalian system;
said input/output system, said simulation engine, and said
simulation model being capable of working together to carry out the
steps of: a. receiving as input data through said input/output
system, dose, permeability and solubility data for said compound
for one or more segments of said mammalian system; and b. applying
said simulation engine and said simulation model to simulate
absorption of said compound relative to one or more segments of
said mammalian system.
2. A computer system for simulating a pharmacokinetic property of a
compound in a mammalian system of interest, said computer system
comprising as operably linked computer-implemented components an
input/output system, a simulation engine, and a physiologic
pharmacokinetic simulation model of one or more anatomical segments
of said mammalian system of interest, said simulation model
comprising differential equations for calculating as a function of
time the change in (i) a physiological parameter of one or more of
said segments and (ii) a pharmacokinetic property comprising an
absorption parameter of a compound relative to a selected route of
administration, barrier to absorption and sampling site of one or
more of said segments, wherein one or more of said differential
equations is modified by a selectively optimized adjustment
parameter; said input/output system, said simulation engine, and
said physiologic pharmacokinetic simulation model being capable of
working together to carry out the steps of: a. receiving through
said computer readable input/output system input data comprising
dose, permeability and solubility data for said compound for one or
more segments of said mammalian system of interest; and b. applying
said simulation engine and said physiologic pharmacokinetic
simulation model to simulate a pharmacokinetic property of said
compound relative to one or more segments of said mammalian system
of interest.
3. The computer system of claim 2, wherein said differential
equations are for one or more of fluid transit, fluid absorption,
mass transit, mass dissolution, mass solubility, and mass
absorption for one or more segments of said mammalian system.
4. The computer system of claim 2, wherein said differential
equations comprise initial parameter values corresponding to said
physiological parameter and said selectively optimized adjustment
parameter for one or more segments of said mammalian system.
5. The computer system of claim 2, wherein said physiologic
pharmacokinetic simulation model comprises control statement rules
for one or more of transit, absorption, permeability, solubility,
dissolution, and concentration for one or more segments of said
mammalian system.
6. The computer system of claim 5, wherein said control statement
rules are IF . . . THEN production rules.
7. The computer system of claim 2, wherein said input/output system
comprises a user interface.
8. The computer system of claim 2, wherein said simulation engine
comprises a differential equation solver.
9. The computer system of claim 2, wherein said pharmacokinetic
property is selected from the group consisting of absorption,
distribution, metabolism, elimination and toxicity.
10. The computer system of claim 2, wherein said absorption
parameter is selected from the group consisting of concentration,
permeability, solubility, dissolution rate, transport mechanism,
and formulation release rate.
11. The article of manufacture of claim 2, wherein said
physiological parameter is selected from the group consisting of
pH, fluid volume, fluid volume transfer rate, fluid absorption,
surface area, and transit time.
12. The computer system of claim 2, wherein said mammalian system
of interest is human.
13. The computer system of claim 2, wherein said mammalian system
of interest is selected from the group consisting of
gastrointestinal tract, liver, heart, kidney, eye, nose, lung, skin
and brain.
14. The computer system of claim 13, wherein said mammalian system
of interest is gastrointestinal tract and said segments are
selected from the group consisting of stomach, duodenum, jejunum,
ileum and colon.
15. The computer system of claim 2, wherein said input data
includes data selected from the group consisting of dissolution
rate, transport mechanism and formulation release rate.
16. The computer system of claim 2, wherein said differential
equations comprise one or more input variables corresponding to
said input data for calculating as one or more output variables
said change in said physiological parameter.
17. The computer system of claim 2, wherein said differential
equations comprise one or more input variables corresponding to
said input data for calculating as one or more output variables
said change in said absorption parameter.
18. The computer system of claim 2, wherein said selectively
optimized adjustment parameter correlates said input data to output
data comprising said pharmacokinetic property of said compound.
19. The computer system of claim 18, wherein said input data
comprises in vitro data and said selectively optimized adjustment
parameter comprises a best fit value obtained by (i) assigning an
initial value to a selected adjustment parameter of said simulation
model, (ii) fitting a combination of in vitro data and in vivo data
for different compounds of a compound test set with said simulation
model, (iii) selecting a best fit value for said selected
adjustment parameter that, when assigned as an initial value to
said selected adjustment parameter, permits said simulation model
to predict said pharmacokinetic property of said compound when said
input data comprises said in vitro data, and (iv) assigning said
best fit value as a constant to said selected adjustment parameter
so as to generate said selectively optimized adjustment parameter
that modifies one or more of said differential equations.
20. The computer system of claim 19, wherein said in vitro data is
obtained from testing of a compound in one or more assays that
generate data selected from the group consisting of cell, tissue,
structure-activity relationship (SAR), and quantitative
structure-activity relationship (QSAR) data.
21. The computer system of claim 19, wherein said different
compounds of a compound test set comprise compounds having diverse
pharmacokinetic properties in said mammalian system of
interest.
22. The computer system of claim 18, wherein said input data
comprises in vivo data from a first species of mammal and said
mammalian system of interest comprises a second species of mammal,
and wherein said selectively optimized adjustment parameter
comprises a best fit value obtained by (i) assigning an initial
value to a selected adjustment parameter of said simulation model,
(ii) fitting a combination of in vivo data with said simulation
model, said combination of in vivo data derived from testing of
different compounds of a compound test set in said first species of
mammal and said second species of mammal, (iii) selecting a best
fit value for said selected adjustment parameter that, when
assigned as an initial value to said selected adjustment parameter,
permits said simulation model to predict said pharmacokinetic
property of said compound when said input data comprises said in
vitro data from said first species of mammal, and (iv) assigning
said best fit value as a constant to said selected adjustment
parameter so as to generate said selectively optimized adjustment
parameter that modifies one or more of said differential
equations.
23. The computer system of claim 22, wherein said different
compounds of a compound test set comprise compounds having diverse
pharmacokinetic properties in said mammalian system of
interest.
24. The computer system of claim 2, wherein said selectively
optimized adjustment parameter is for one or more of fluid
absorption, flux, permeability, transport mechanism, transfer rate,
and segment surface area.
25. The computer system of claim 23, wherein said physiologic
pharmacokinetic simulation model comprises at least two of said
anatomical segments and a logic function module comprising a
regional correlation estimation function and a control statement
for initiating said function, wherein said estimation function when
initiated is capable of generating an estimated value for a
selected pharmacokinetic property of said compound in a first
anatomical segment when supplied with an input value corresponding
to said selected pharmacokinetic property in a second anatomical
segment and with a regional correlation coefficient for said
selected pharmacokinetic property of said first and second
anatomical segments.
26. A computer system for simulating a pharmacokinetic property of
a compound in a mammal of interest utilizing regional correlation
parameter estimation, said computer system comprising as operably
linked computer-implemented components an input/output system, a
simulation engine, and a physiologic pharmacokinetic simulation
model of at least two segments of a selected mammalian system of
interest, said physiologic pharmacokinetic simulation model
comprising (i) differential equations for calculating the change in
one or more physiological parameters of first and second segments
of said mammalian system of interest and the movement and
disposition of said compound in said first and second segments as a
function of time, and (ii) a logic function module having a
regional correlation parameter estimation function and a control
statement for initiating said function, wherein said estimation
function when initiated is capable of generating an estimated value
for a selected pharmacokinetic property comprising an absorption
parameter of said compound in said first segment when supplied with
an input value corresponding to said selected pharmacokinetic
property of said compound in said second segment and with a
regional correlation coefficient for said selected pharmacokinetic
parameter of said first and second segments; said input/output
system, said simulation engine, and said physiologic
pharmacokinetic simulation model being capable of working together
to carry out the steps of: a. receiving through said input/output
system input data comprising a pharmacokinetic property of said
compound in said second segment of said mammalian system of
interest; and b. applying said simulation engine and said
physiologic pharmacokinetic simulation model to initiate said
estimation function to estimate said pharmacokinetic property of
said compound in said first segment of said mammalian system of
interest.
27. The computer system of claim 26, wherein said regional
correlation estimation function comprises a function/transformation
algorithm.
28. The computer system of claim 27, wherein said
function/transformation algorithm is selected from the group
consisting of a polynomial, exponential, and logarithm.
29. The computer system of claim 26, wherein said regional
correlation coefficient comprises a best fit value that transforms
said input data comprising said pharmacokinetic property of said
compound in said second segment to an estimated pharmacokinetic
property of said compound in said first segment.
30. The computer system of claim 26, wherein said pharmacokinetic
property is selected from the group consisting of absorption,
distribution, metabolism, elimination and toxicity.
31. The computer system of claim 26, wherein said pharmacokinetic
parameter is selected from the group consisting of permeability,
solubility, dissolution rate and transport mechanism.
32. The computer system of claim 26, wherein said differential
equations are selected from the group consisting of equations for
fluid transit, fluid absorption, mass transit, mass dissolution,
mass solubility, and mass absorption.
33. The computer system of claim 26, wherein said mammalian system
of interest is selected from the group consisting of
gastrointestinal tract, liver, heart, kidney, eye, nose, lung, skin
and brain.
34. The computer system of claim 26, wherein said mammalian system
of interest is human.
35. The computer system of claim 26, wherein said input data
comprises in vitro data.
36. The computer system of claim 35, wherein said in vitro data is
derived from testing of said compound in an assay that generates
data selected from the group consisting of cell, tissue,
physicochemical, structure-activity relationship (SAR) SAR, and
quantitative structure-activity relationship (QSAR) QSAR data.
37. The computer system of claim 26, wherein said computer system
comprises a data processor, a memory and a display.
38. The computer system of claim 26, wherein said input/output
system comprises a user interface.
39. The computer system of claim 26, wherein said simulation engine
comprises a differential equation solver.
40. The computer system of claim 26, wherein said physiologic
pharmacokinetic simulation model comprises a subsystem of said
computer system.
41. The computer system of claim 26, wherein one or more of said
differential equations is modified by a selectively optimized
adjustment parameter.
42. A subsystem for use in a computer system for simulating oral
absorption of a compound in a mammal, said subsystem comprising:
(i) a computer-implemented simulation model of one or more segments
of the gastrointestinal (GI) track of a mammal comprising
differential equations for one or more of fluid transit, fluid
absorption, mass transit, mass dissolution, mass solubility, and
mass absorption for one or more segments of the GI tract of said
mammal; and (ii) a computer-implemented database comprising initial
parameter values for said differential equations corresponding to
physiological parameters and selectively optimized adjustment
parameters, and optionally regional correlation parameters, for one
or more segments of the GI tract of said mammal.
43. A computer-implemented database according to claim 42 having a
compartment-flow model data structure.
44. A subsystem for use in a computer system for simulating oral
absorption of a compound in a mammal, said subsystem comprising:
(i) a computer-implemented simulation model of one or more segments
of the gastrointestinal (GI) track of a mammal comprising
differential equations for one or more of fluid transit, fluid
absorption, mass transit, mass dissolution, mass solubility, and
mass absorption for one or more segments of the GI tract of said
mammal; and (ii) a computer-implemented database comprising initial
parameter values for said differential equations corresponding to
physiological parameters and regional correlation parameters for
one or more segments of the GI tract of said mammal.
45. A computer-implemented database according to claim 44 having a
compartment-flow model data structure.
46. The subsystem of any one of claims 42 and 44, wherein said
computer-implemented database comprises computer-implemented
control statement rules for one or more of transit, absorption,
permeability, solubility, dissolution, and concentration for one or
more segments of the GI tract of said mammal.
47. A computer-implemented database for use in a computer system
for simulating absorption of a compound in a mammal, said
computer-implemented database comprising: a computer-implemented
physiologic-based simulation model of one or more segments of
selected mammalian system of interest comprising (i) differential
equations for one or more of fluid transit time, fluid absorption,
mass transit time, mass dissolution, mass solubility, and mass
absorption for one or more segments of said mammalian system; (ii)
initial parameter values for said differential equations
corresponding to physiological parameters and adjustment
parameters, and optionally one or more regional correlation
parameters, for one or more segments of said mammalian system; and
(iii) control statement rules for one or more of transit time,
absorption, permeability, dissolution, concentration, and
mathematical error correction for one or more segments of said
mammalian system; wherein said computer-implemented
physiologic-based simulation model comprises a compartment-flow
data structure for calculating time-dependent rate of absorption,
extent of absorption, and concentration of a compound at a sampling
site across a physiological barrier of one or more segments of said
mammalian system when applied in a simulation engine having a
differential equation solver and a control statement module.
48. The computer-implemented database of claim 47, wherein said
adjustment parameters are selected from the group consisting of
regional fluid absorption, permeability, flux, active transport,
carrier mediated transport, compound efflux, transfer rate, and
surface area.
49. The computer-implemented database of claim 47, wherein said
physiological parameters are selected from the group consisting of
soluble mass transfer rate constant, permeability, solubility,
dissolution rate, transport mechanism, pH, initial volume, surface
area, transit time, fluid volume transfer rate, and fluid
absorption rate.
50. The computer-implemented database of claim 47, wherein said
regional correlation parameters are for permeability.
51. A computer-implemented physiological simulation model of the
gastrointestinal (GI) track of a mammal for simulating oral
absorption of a compound in said mammal, said physiological
simulation model corresponding to a compartment-flow model
comprising: compartments characterized by fluid volume, fluid
absorption, insoluble mass, soluble mass, and mass absorption for
one or more of segments of the GI track of a mammal, wherein said
compartments are operably linked through flow regulators and
converters, wherein said flow regulators regulate flow among
compartments and said converters modify said flow regulators, and
wherein said flow regulators are characterized by fluid absorption
rate, fluid transit rate, insoluble mass transit rate, insoluble
mass dissolution rate, soluble mass transit rate, and soluble mass
absorption rate.
52. The computer-implemented physiological simulation model of
claim 51, wherein said converters are characterized by fluid
volume, fluid volume absorption rate constant, fluid volume transit
rate constant, insoluble mass, insoluble mass transit rate
constant, dissolution rate constant, soluble mass, soluble mass
transit rate constant, surface area, dissolved mass concentration
and permeability.
53. The computer-implemented physiological simulation model of
claim 51, which further comprises compartments characterized by
formulation and flow regulators characterized by formulation
transit rate and formulation release rate.
54. A computer-implemented gastrointestinal (GI) transit simulation
model for simulating mass and fluid loss in the GI track of a
mammal, said GI transit simulation model corresponding to a
compartment-flow model comprising: compartments characterized by
fluid volume and fluid volume absorption for stomach, duodenum,
jejunum, ileum and colon that are operably linked through flow
regulators and one or more converters that modify one or more of
said flow regulators, wherein said flow regulators are
characterized by fluid volume absorption rate and fluid volume
transit rate, and wherein said converters are characterized by
selectively optimized adjustment parameter values for one or more
of fluid absorption rate constant and fluid volume transit rate
constant.
55. A computer-implemented solubility simulation model for
simulating pH dependent solubility and dissolution of a compound in
the gastrointestinal (GI) track of a mammal, said solubility
simulation model corresponding to a compartment-flow model
comprising: compartments characterized by insoluble mass and
soluble mass for stomach, duodenum, jejunum, ileum and colon that
are operably linked through flow regulators and one or more
converters that modify one or more of said flow regulators, wherein
said flow regulators are characterized by insoluble mass transit
rate, insoluble mass dissolution rate, and soluble mass transit
rate, wherein said converters are characterized by insoluble mass,
insoluble mass transit rate constant, insoluble mass dissolution
rate constant, soluble mass, and soluble mass transit rate
constant, and wherein one or more of said converters are
characterized by selectively optimized adjustment parameters.
56. A computer-implemented absorption simulation model for
simulating absorption of a compound in the gastrointestinal (GI)
track of a mammal to at least the portal vein, said absorption
simulation model corresponding to a compartment-flow model
comprising: compartments characterized by soluble mass and soluble
mass absorption for stomach, duodenum, jejunum, ileum and colon
that are operably linked through flow regulators and one or more
converters that modify said flow regulators, where said flow
regulators are characterized by insoluble mass transit rate,
insoluble mass dissolution rate, soluble mass transit rate, soluble
mass absorption rate, where said converters are characterized by
insoluble mass, insoluble mass dissolution rate constant, soluble
mass transit rate constant, surface area, dissolved mass
concentration, and permeability, and wherein one or more of said
converters are characterized by selectively optimized adjustment
parameters.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application is related to the following U.S.
Provisional Applications Serial Nos.: 60/100,224 (Attorney Docket
No. NAVI-010/00US), filed Sep. 14, 1998; 60,109,234 (Attorney
Docket No. NAVI-010/01US) filed Nov. 18, 1998, 60/100,290 (Attorney
Docket No. NAVI-009/00US), filed Sep. 14, 1998; and 60,109,232
(Attorney Docket No. NAVI-009/01US), filed Nov. 18, 1998.
INTRODUCTION
TECHNICAL FIELD
[0002] The present invention relates to computer-implemented
pharmacokinetic simulation models and drug design.
BACKGROUND
[0003] A. Pharmacokinetic Modeling
[0004] Pharmacodynamics refers to the study of fundamental or
molecular interactions between drug and body constituents, which
through a subsequent series of events results in a pharmacological
response. For most drugs the magnitude of a pharmacological effect
depends on time-dependent concentration of drug at the site of
action (e.g., target receptor-ligand/drug interaction). Factors
that influence rates of delivery and disappearance of drug to or
from the site of action over time include absorption, distribution,
metabolism, and elimination. The study of factors that influence
how drug concentration varies with time is the subject of
pharmacokinetics.
[0005] In nearly all cases the site of drug action is located on
the other side of a membrane from the site of drug administration.
For example, an orally administered drug must be absorbed across a
membrane barrier at some point or points along the gastrointestinal
(GI) tract. Once the drug is absorbed, and thus passes a membrane
barrier of the GI tract, it is transported through the portal vein
to the liver and then eventually into systemic circulation (i.e.,
blood and lymph) for delivery to other body parts and tissues by
blood flow. Thus how well a drug crosses membranes is of key
importance in assessing the rate and extent of absorption and
distribution of the drug throughout different body compartments and
tissues. In essence, if an otherwise highly potent drug is
administered extravascularly (e.g., oral) but is poorly absorbed
(e.g., GI tract), a majority of the drug will be excreted or
eliminated and thus cannot be distributed to the site of
action.
[0006] The principle routes by which drugs disappear from the body
are by elimination of unchanged drug or by metabolism of the drug
to a pharmacologically active or inactive form(s) (i.e.,
metabolites). The metabolites in turn may be subject to further
elimination or metabolism. Elimination of drugs occurs mainly via
renal mechanisms into the urine and to some extent via mixing with
bile salts for solubilization followed by excretion through the GI
tract, exhaled through the lungs, or secreted through sweat or
salivary glands etc. Metabolism for most drugs occurs primarily in
the liver.
[0007] Each step of drug absorption, distribution, metabolism, and
elimination can be described mathematically as a rate process. Most
of these biochemical processes involve first order or pseudo-first
order rate processes. In other words, the rate of reaction is
proportional to drug concentration. For instance, pharmacokinetic
data analysis is based on empirical observations after
administering a known dose of drug and fitting of the data by
either descriptive equations or mathematical (compartmental)
models. This permits summarization of the experimental measures
(plasma/blood level-time profile) and prediction under many
experimental conditions. For example after rapid intravenous
administration, drug levels often decline mono-exponentially
(first-order elimination) with respect to time as described in
Equation 1, where Cp(t) is drug concentration as a function of
time, Cp(0) is initial drug concentration, and k is the associated
rate constant that represents a combination of all factors that
influence the drug decay process (e.g., absorption, distribution,
metabolism, elimination).
Cp(t)=Cp(0)e.sup.-kt (Eq. 1)
[0008] This example assumes the body is a single "well-mixed"
compartment into which drug is administered and from which it also
is eliminated (one-compartment open model). If equilibrium between
drug in a central (blood) compartment and a (peripheral) tissue
compartment(s) is not rapid, then more complex profiles
(multi-exponential) and models (two- and three-compartment) are
used. Mathematically, these "multi-compartment" models are
described as the sum of equations, such as the sum of rate
processes each calculated according to Equation 1 (i.e., linear
pharmacokinetics).
[0009] Experimentally, Equation 1 is applied by first collecting
time-concentration data from a subject that has been given a
particular dose of a drug followed by plotting the data points on a
logarithmic graph of time versus drug concentration to generate one
type of time-concentration curve. The slope (k) and the y-intercept
(CO) of the plotted "best-fit" curve is obtained and subsequently
incorporated into Equation 1 (or sum of equations) to describe the
drug's time course for additional subjects and dosing regimes.
[0010] When drug concentration throughout the body or a particular
location is very high, saturation or nonlinear pharmacokinetics may
be applicable. In this situation the capacity of a biochemical
and/or physiological process to reduce drug concentration is
saturated. Conventional Michaelis-Menten type equations are
employed to describe the nonlinear nature of the system, which
involve mixtures of zero-order (i.e., saturation:concentration
independent) and first-order (i.e., non-saturation:concentration
dependent) kinetics. Experimentally, data collection and plotting
are similar to that of standard compartment models, with a notable
exception being that the data curves are nonlinear. Using a time
versus concentration graph to illustrate this point, at very high
drug concentration the data line is linear because the drug is
being eliminated at a maximal constant rate (i.e., zero-order
process). The data line then begins to curve in an asymptotic
fashion with time until the drug concentration drops to a point
where the rate process becomes proportional to drug concentration
(i.e., first-order process). For many drugs, nonlinear
pharmacokinetics applies to events such as dissolution of the
therapeutic ingredient from a drug formulation, as well as
metabolism and elimination. Nonlinear pharmacokinetics also can be
applied to toxicological events related to threshold dosing.
[0011] Classical one, two and three compartment models used in
pharmacokinetics require in vivo blood data to describe
time-concentration effects related to the drug decay process, i.e.,
blood data is relied on to provide values for equation parameters.
For instance, while a model may work to describe the decay process
for one drug, it is likely to work poorly for others unless blood
profile data and associated rate process limitations are generated
for each drug in question. Thus, such models are very poor for
predicting the in vivo fate of diverse drug sets in the absence of
blood data and the like derived from animal and/or human
testing.
[0012] In contrast to the standard compartment models,
physiological-based pharmacokinetic models are designed to
integrate basic physiology and anatomy with drug distribution and
disposition. Although a compartment approach also is used for
physiological models, the compartments correspond to anatomic
entities such as the GI tract, liver, lung etc., which are
connected by blood flow. Physiological modeling also differs from
standard compartment modeling in that a large body of physiological
and physicochemical data usually is employed that is not
drug-specific. However, as with standard compartment models the
conventional physiological models lump rate processes together.
Also, conventional physiological models typically fail to
incorporate individual kinetic, mechanistic and physiological
processes that control drug distribution and disposition in a
particular anatomical entity, even though multiple rate processes
are represented in vivo. Physiological models that ignore these and
other important model parameters contain an underlying bias
resulting in poor correlation and predictability across diverse
data sets. Such deficiencies inevitably result in unacceptable
levels of error when the model is used to describe or predict drug
fate in animals or humans. The problem is amplified when the models
are employed to extrapolate animal data to humans, and worse, when
in vitro data is relied on for prediction in animals or humans.
[0013] For instance, the process of drug reaching the systemic
circulation for most orally administered drugs can be broken down
into two general steps: dissolution and absorption. Since
endocytotic processes in the GI tract typically are not of high
enough capacity to deliver therapeutic amounts of most drugs, the
drugs must be solubilized prior to absorption. The process of
dissolution is fairly well understood. However, the absorption
process is treated as a "black box." Indeed, although
bioavailability data is widely available for many drugs in multiple
animal species and in humans, in vitro and or in vivo data
generated from animal, tissue or cell culture permeability
experiments cannot allow a direct prediction of drug absorption in
humans, although such correlations are commonly used.
[0014] B. Computer Systems and Pharmacokinetic Modeling
[0015] Computers have been used in pharmacokinetics to bring about
easy solutions to complex pharmacokinetic equations and modeling of
pharmacokinetic processes. Other computer applications in
pharmacokinetics include development of experimental study designs,
statistical data treatment, data manipulation, graphical
representation of data, projection of drug action, as well as
preparation of written reports or documents.
[0016] Since pharmacokinetic models are described by systems of
differential equations, virtually all computer systems and
programming languages that enable development and implementation of
mathematical models have been utilized to construct and run them.
Graphics-oriented model development computer programs, due to their
simplicity and ease of use, are typically used for designing
multi-compartment linear and non-linear pharmacokinetic models. In
essence, they allow a user to interactively draw compartments and
then link and modify them with other iconic elements to develop
integrated flow pathways using pre-defined symbols. The user
assigns certain parameters and equations relating the parameters to
the compartments and flow pathways, and then the model development
program generates the differential equations and interpretable code
to reflect the integrated system in a computer-readable format. The
resulting model, when provided with input values for parameters
corresponding to the underlying equations of the model, such as
drug dose and the like can then be used to simulate the system
under investigation.
[0017] While tools to develop and implement pharmacokinetic models
exist and the scientific literature is replete with examples,
pharmacokinetic models and computer systems developed to date have
not permitted sufficient predictability of the pharmacokinetic fate
of extravascularly administered drugs in a mammal from in vitro
cell, tissue or compound structure-activity relationship (SAR/QSAR)
data. A similar problem exists when attempting to predict
absorption of a compound in one mammal (e.g., human) from data
derived from a second mammal (e.g., dog). For example, existing
pharmacokinetic models of oral absorption use several different
approaches to predict oral absorption and fraction dose absorbed
(Amidon et al., Pharm. Res., (1988) 5:651-654; Chiou, W. L., Int.
J. Clin. Pharmacol. Ther., (1994) 32:474-482; Chiou, W. L.,
Biopharm.Drug Dispos., (1995) 16:71-75; Dressman et al., J. Pharm.
Sci., (1985) 74:588-589; Lennemas et al., J Pharm. Pharmacol,
(1997) 49:682-686; Levet-Trafit et al., Life Sciences., (1996)
58:PL359-63; Sinko et al., Pharm. Res., (1991) 8:979-988; and Soria
et al.,. Biopharm. Drug Dispos., (1996) 17:817-818). Unfortunately,
these models are flawed as they make mathematical assumptions that
limit prediction to particular compounds, and the correlation
function is sigmoidal in shape (i.e., high/steep slope). Therefore
the predictive power of such models for compounds outside a
relatively small group is very limited. This is particularly true
for collections of compounds possessing variable ranges of dosing
requirements and of permeability, solubility, dissolution rates and
transport mechanism properties. Other drawbacks include use of
drug-specific parameters and values in pharmacokinetic models from
the outset of model development, which essentially limits the
models to drug-specific predictions. These and other deficiencies
also impair generation of rules that universally apply to drug
disposition in a complex physiological system such as the GI
tract.
[0018] Extravascular administration of drugs is the preferred route
for physicians, patients, and drug developers alike due to lower
product price, increased patient compliance, ease of
administration. Current assessment of the bioavailability of
extravascularly administered drugs and lead drug compounds, as well
as bioavailability of intravascularly administered compounds
relative to specialized barriers to absorption such as the blood
brain barrier, is limited in large part to animal and human
testing. The economic and medical consequences of problems with
drug absorption and variable bioavailability are immense. Failing
to identify promising or potentially problematic drug candidates
during the discovery and pre-clinical stages of drug development is
one of the most significant consequences of problems with drug
bioavailability. Accordingly, there is a need to develop a
comprehensive, physiologically-based pharmacokinetic model and
computer system capable of predicting drug bioavailability and
variability in humans that utilizes relatively straightforward
input parameters. Furthermore, considering the urgent need to
provide the medical community with new therapeutic alternatives and
the current use of high throughput drug screening for selecting
lead drug candidates, a comprehensive biopharmaceutical
computer-based tool that employs a modeling approach for predicting
bioavailability of compounds and compound formulations is
needed.
[0019] Relevant Literature
[0020] Various publications review gastrointestinal anatomy and
physiology including motility, secretion, absorption, and
digestion, as well as gastrointestinal pharmacology and physiology
in gastrointestinal diseased individuals (See, e.g., L. Johnson
ed., Physiology of the Gastrointestinal Tract, Second edition, Vol.
2, Ravind Press (1987); Kutchai, Gastrointestinal System, Part IV.,
Principles of Physiology, Mosby Press (1996); and Sleisenger,
Gastrointestinal Disease, 3rd edition, Saunders (1983)). Sharget et
al. (Physiological Factors Related to Drug Absorption, Applied
Biopharmaceutics and Pharmacokinetics (1993)) review
pharmacokinetics and compartment modeling. Various pharmacokinetic
models of oral drug absorption are disclosed in Grass, G. (Advanced
Drug Delivery Reviews (1997) 23:199-219); Amidon et al., (Pharm.
Res. (1988) 5:651-654); Chiou, W. L., (Int. J Clin. Pharmacol.
Ther., (1994) 32:474-482); Chiou, W. L., (Biopharm. Drug Dispos.,
(1995) 16:71-75); Dressman et al., (J. Pharm. Sci., (1985)
74:588-589); Lennernas et al., (J Pharm. Pharmacol., (1997)
49:682-686); Levet-Trafit et al., (Life Sciences., (1996)
58:PL359-63); Sinko et al., (Pharm. Res., (1991) 8:979-988); and
Soria et al.,. (Biopharm. Drug Dispos., (1996) 17:817-818)).
SUMMARY OF THE INVENTION
[0021] The present invention relates to a pharmacokinetic-based
design and selection tool (PK tool) and methods for predicting
absorption of a compound in a mammalian system of interest. The
methods utilize the tool, and optionally a separately operable
component or subsystem thereof.
[0022] The PK tool comprises as computer-readable components: (1)
input/output system; (2) physiologic-based simulation model of one
or more segments of a mammalian system of interest having one or
more physiological barriers to absorption that is based on the
selected route of administration; and (3) simulation engine having
a differential equation solver, and optionally, a control statement
module. The physiologic-based simulation model of the PK tool of
the invention is a multi-compartment mathematical model comprising
as operably linked components: (i) differential equations for one
or more of fluid transit, fluid absorption, mass transit, mass
dissolution, mass solubility, and mass absorption for one or more
segments of the mammalian system of interest; and (ii) initial
parameter values for the differential equations corresponding to
physiological parameters and selectively optimized adjustment
parameters, and optionally regional correlation parameters, for one
or more segments of the mammalian system of interest; and,
optionally, (iii) control statement rules for one or more of
transit, absorption, permeability, solubility, dissolution,
concentration, and mathematical error correction for one or more
segments of the mammalian system of interest.
[0023] The computer-readable input/output system, physiologic-based
simulation model, and simulation engine of the PK tool are capable
of working together to carrying out the steps of: (1) receiving
through the input/output system data comprising dose, permeability
and solubility data of a compound of interest for one or more
segments of the mammalian system of interest; and (2) applying the
physiologic-based simulation model and simulation engine to
generate an absorption profile for the compound characterized by
one or more of concentration, rate of absorption, and extent of
absorption relative to a selected sampling site that is across a
physiological barrier for one or more segments of the mammalian
system of interest.
[0024] The present invention also provides a database for
utilization in the PK tool and method of the invention. The
database includes one or more physiologic-based simulation models
of the invention. Additional databases are provided for simulation
model parameters, and may be integrated or separate from a database
having a simulation model of the invention. The database(s)
includes one or more of (i) differential equations for one or more
of fluid transit, fluid absorption, mass transit, mass dissolution,
mass solubility, and mass absorption for one or more segments of
the mammalian system of interest; (ii) initial parameter values for
the differential equations corresponding to physiological
parameters and selectively optimized adjustment parameters, and
optionally regional correlation parameters, for one or more
segments of the mammalian system of interest; and (iii) control
statement rules for one or more of transit, absorption,
permeability, solubility, dissolution, concentration, and
mathematical error correction for one or more segments of the
mammalian system of interest. The database(s) have a
compartment-flow data structure that is portable into and readable
by a simulation engine for calculating time-dependent rate of
absorption, extent of absorption, and concentration of a compound
at a sampling site across a physiological barrier of one or more
segments of the mammalian system of interest.
[0025] The invention also includes a method for selectively
optimizing a pharmacokinetic-based simulation model for use in the
PK tool of the invention. This method permits the PK tool of the
invention to accurately predict one or more in vivo pharmacokinetic
properties of a compound in a mammalian system of interest from
input data derived from a selected in vitro or in vivo data source.
The method includes the steps of (i) generating initial adjustment
parameter values for one or more independent parameters of the
simulation model by utilizing a curve-fitting algorithm to
simultaneously fit to the model one or more input variables
corresponding to a pharmacokinetic property of a compound test set
derived from (a) a first data source corresponding to the mammalian
system of interest, and (b) a second data source corresponding to a
system other than the mammalian system of interest; (ii) selecting
adjustment parameter values that permit correlation of one or more
of the input variables from the first data source to one or more
input variables from the second data source; (iii) repeating steps
(i) and (ii) one or more times for one or more additional
independent parameters of the simulation model until deviation of
the correlation is minimized; and (iv) utilizing the selected
adjustment parameters as constants for the independent parameters
in the simulation model.
[0026] The present invention further includes a method for
producing a pharmacokinetic-based simulation model for use in the
PK tool that facilitates estimation of a selected parameter value
in a first segment of mammalian system of interest utilizing input
data for the selected parameter that corresponds to a second
segment of the mammalian system of interest. The method involves
(i) providing a logic function module in the simulation model that
includes a set of regional correlation parameter values for at
least first and second segments of the mammalian system of interest
that facilitates estimation of a selected parameter value in the
first segment of the mammalian system of interest utilizing input
data for the selected parameter that corresponds to the second
segment of the mammalian system of interest; and (ii) providing a
control statement in the simulation model which initiates the
regional correlation estimation function of the logic function
module when a value for the first segment is not supplied as input
into the model.
[0027] The present invention also provides a method for generating
formulation profiles for a compound of interest utilizing the PK
tool of the invention.
[0028] The PK tool of the invention may be provided as a computer
system, as an article of manufacture in the form of a
computer-readable medium, or a computer program product and the
like. Subsystems and individual components of the PK tool also can
be utilized and adapted in a variety of disparate applications for
predicting the fate of an administered compound. The PK tool and
methods of the invention can be used to screen and design compound
libraries, select and design drugs, as well as predict drug
efficacy in mammals from in vitro and/or in vivo data of one or
more compounds of interest. The PK tool and methods of the
invention also finds use in selecting, designing, and preparing
drug compounds, and multi-compound drugs and drug formulations
(i.e., drug delivery system) for preparation of medicaments for use
in treating mammalian disorders.
DEFINITIONS
[0029] Absorption: Transfer of a compound across a physiological
barrier as a function of time and initial concentration. Amount or
concentration of the compound on the external and/or internal side
of the barrier is a function of transfer rate and extent, and may
range from zero to unity.
[0030] Bioavailability: Fraction of an administered dose of a
compound that reaches the sampling site and/or site of action. May
range from zero to unity. Can be assessed as a function of
time.
[0031] Compound: Chemical entity.
[0032] Computer Readable Medium: Medium for storing, retrieving
and/or manipulating information using a computer. Includes optical,
digital, magnetic mediums and the like; examples include portable
computer diskette, CD-ROMs, hard drive on computer etc. Includes
remote access mediums; examples include internet or intranet
systems. Permits temporary or permanent data storage, access and
manipulation.
[0033] Data: Experimentally collected and/or predicted variables.
May include dependent and independent variables.
[0034] Dissolution: Process by which a compound becomes dissolved
in a solvent.
[0035] Input/Output System: Provides a user interface between the
user and a computer system.
[0036] Permeability: Ability of a physiological barrier to permit
passage of a substance. Refers to the concentration-dependent or
concentration-independent rate of transport (flux), and
collectively reflects the effects of characteristics such as
molecular size, charge, partition coefficient and stability of a
compound on transport. Permeability is substance and barrier
specific.
[0037] Physiologic Pharmacokinetic Model: Mathematical model
describing movement and disposition of a compound in the body or an
anatomical part of the body based on pharmacokinetics and
physiology.
[0038] Production Rule: Combines known facts to produce ("infer")
new facts. Includes production rules of the "IF . . . THEN"
type.
[0039] Simulation Engine: Computer-implemented instrument that
simulates behavior of a system using an approximate mathematical
model of the system. Combines mathematical model with user input
variables to simulate or predict how the system behaves. May
include system control components such as control statements (e.g.,
logic components and discrete objects).
[0040] Solubility: Property of being soluble; relative capability
of being dissolved.
[0041] Transport Mechanism: The mechanism by which a compound
passes a physiological barrier of tissue or cells. Includes four
basic categories of transport: passive paracellular, passive
transcellular, carrier-mediated influx, and carrier-mediated
efflux.
BRIEF DESCRIPTION OF DRAWINGS
[0042] FIG. 1 shows schematic of method to generate input data for
selected route of administration, mammalian system, and at least
one primary barrier to absorption.
[0043] FIG. 2 shows schematic of method for selecting sampling site
relative to administration site and barrier to absorption.
[0044] FIG. 3 is a high level INPUT/PROCESS/OUTPUT diagram of the
PK tool of the invention.
[0045] FIG. 4 is a high level flow chart and structure chart of the
PK tool and method of the invention.
[0046] FIG. 5 is a graphical diagram illustrating generic
compartment-flow simulation model and exemplary symbolic
relationships among compartments, flow regulators, converters and
input links.
[0047] FIG. 6 is a key for FIG. 5.
[0048] FIG. 7 is a graphical diagram illustrating generic
pharmacokinetic first-order two-compartment open plasma model for
intravenous injection. D is total drug, V is apparent volume of
distribution, and C is drug concentration for either plasma (p) or
tissue (t). k12 and k21 represent first-order rate transfer
constants for movement of drug from compartment 1 to compartment 2
(k12) and from compartment 2 to compartment 1 (k21). k10 represents
first-order rate transfer constant for movement (elimination) of
drug from compartment 1 to compartment 0.
[0049] FIG. 8 is a graphical compartment-flow diagram illustrating
the plasma simulation model of FIG. 7 and exemplary relationships
among compartments, flow regulators, converters and input
links.
[0050] FIG. 9 shows schematic of a method of the invention for
development of an initial physiologic-based simulation model for PK
tool and method of the invention.
[0051] FIG. 10 shows schematic of a method of the invention for
development of a physiologic-based simulation model having
selectively optimized adjustment parameters.
[0052] FIG. 11 shows graphical compartment-flow diagram
illustrating the mass-volume GI tract simulation model of the
invention linked to a training/validation plasma model.
[0053] FIG. 12 illustrates compartment, flow regulator and
converter components of the mass-volume GI tract simulation model
of the invention.
[0054] FIG. 13 illustrates structural relationship among
compartment and flow regulator components for the mass-volume GI
tract simulation model of the invention.
[0055] FIG. 14 illustrates structural relationship among flow
regulator and converter components for the mass-volume GI tract
simulation model of the invention.
[0056] FIG. 15 illustrates converter components for the mass-volume
GI tract simulation model of the invention.
[0057] FIG. 16 compares plasma concentration profiles derived from
clinical studies of gancyclovir and simulation using volume GI
tract simulation model of the invention.
[0058] FIG. 17 compares plasma concentration profiles derived from
clinical studies of gancyclovir and simulation using mass-volume GI
tract simulation model of the invention.
[0059] FIG. 18 shows graphical compartment-flow diagram
illustrating the in vivo data analysis-processing IV/PO PK model
(intravenous/oral administration) of the invention.
[0060] FIG. 19 shows schematic of method for development of initial
integrated physiologic-based GI tract simulation model of PK tool
and method of the invention.
[0061] FIG. 20 shows graphical compartment-flow diagram
illustrating the GI tract fluid transit model component of the PK
tool and method of the invention.
[0062] FIG. 21 shows graphical compartment-flow diagram
illustrating the GI tract solubility-dissolution model component of
the PK tool and method of the invention.
[0063] FIG. 22 shows graphical compartment-flow diagram
illustrating the GI tract absorption model component of the PK tool
and method of the invention.
[0064] FIG. 23 shows graphical compartment-flow diagram
illustrating integration of the GI tract fluid transit model,
solubility-dissolution model, and absorption model components for
one GI segment of the PK tool and method of the invention.
[0065] FIG. 24 shows graphical compartment-flow diagram
illustrating integrated GI tract simulation model components
(without converters or input link connectors) of the PK tool and
method of the invention.
[0066] FIG. 25 shows graphical compartment-flow diagram
illustrating integrated GI tract simulation model components (with
converters and input link connectors) of the PK tool and method of
the invention.
[0067] FIG. 26 shows schematic of method for development of
selectively optimized adjustment parameters and for optimization of
the integrated physiologic-based GI tract simulation model of PK
tool and method of the invention.
[0068] FIG. 27 shows schematic of method for selection of model
parameters for utilization in a given physiologic-based GI tract
simulation model of PK tool and method of the invention.
[0069] FIG. 28 shows schematic of method for regional (segmental)
calculation/estimation of permeability from one or more user input
values for permeability of a given GI tract region/segment.
Regional permeability (Pe) correlation based on input of Pe value
for duodenum is illustrated.
[0070] FIG. 29 shows graphical converter diagram illustrating
volume, surface area, dose, time and pH parameters and calculations
for integrated GI tract simulation model components of the PK tool
and method of the invention.
[0071] FIG. 30 shows graphical converter diagram illustrating GI
tract transit time parameters and calculations for integrated GI
tract simulation model components of the PK tool and method of the
invention.
[0072] FIG. 31 shows graphical converter diagram illustrating GI
tract permeability parameters and calculations for integrated GI
tract simulation model components of the PK tool and method of the
invention.
[0073] FIG. 32 shows graphical converter diagram illustrating GI
tract solubility parameters and calculations for integrated GI
tract simulation model components of the PK tool and method of the
invention.
[0074] FIG. 33 shows graphical converter diagram illustrating GI
tract control release formulation parameters and calculations for
integrated GI tract simulation model components of the PK tool and
method of the invention.
[0075] FIG. 34 shows graphical compartment-converter diagram
illustrating GI tract concentration parameters and calculations for
integrated GI tract simulation model components of the PK tool and
method of the invention.
[0076] FIG. 35 shows graphical compartment-converter diagram
illustrating GI tract dissolution parameters and calculations for
integrated GI tract simulation model components of the PK tool and
method of the invention.
[0077] FIG. 36 shows graphical compartment-converter diagram
illustrating GI tract output calculations for absorption for
integrated GI tract simulation model components of the PK tool and
method of the invention.
[0078] FIG. 37 shows graphical converter diagram illustrating GI
tract output calculations for soluble mass absorption rate (flux)
for integrated GI tract simulation model components of the PK tool
and method of the invention.
[0079] FIG. 38 shows graphical compartment-flow-converter diagram
illustrating GI tract output calculations for cumulative
dissolution rate and amount for integrated GI tract simulation
model components of the PK tool and method of the invention.
[0080] FIG. 39 shows graphical compartment-flow-converter diagram
illustrating GI tract output calculations for cumulative control
release formulation rate and amount for integrated GI tract
simulation model components of the PK tool and method of the
invention.
[0081] FIG. 40 illustrates database and rulebase compartment, flow
regulator and converter components for the integrated
physiologic-based GI tract simulation model of the invention.
[0082] FIG. 41 illustrates structural relationship among
compartment and flow regulator components for the integrated
physiologic-based GI tract simulation model of the invention.
[0083] FIG. 42 illustrates structural relationship among flow
regulator and converter components for the integrated
physiologic-based GI tract simulation model of the invention.
[0084] FIG. 43 illustrates structural relationship among converter
components for the integrated physiologic-based GI tract simulation
model of the invention.
[0085] FIG. 44 is a high level INPUT/PROCESS/OUTPUT diagram of the
PK tool of the invention as presented to a user of the carrying out
a method of the invention, with inputs provided by the user and
outputs provided by the PK tool.
[0086] FIG. 45 illustrates a flow chart and structure chart of a
subsystem of the PK tool and method of the invention for selection
of a physiological GI tract model from a model database and a
parameter database.
[0087] FIG. 46 is a flow chart and structure chart of the system of
the PK tool and method of the invention.
[0088] FIG. 47 is a flow chart and structure chart of a menu of the
system of the PK tool and method of the invention.
[0089] FIG. 48 illustrates correlation of extent of absorption for
fraction of the dose absorbed in portal vein (FDp), as predicted
using physiologic-based GI tract simulation model and PK tool of
the invention, to FDp derived from human clinical data for 12
compounds.
[0090] FIG. 49 illustrates correlation of rate of absorption for
fraction of the dose absorbed in portal vein (FDp), as predicted
using integrated physiologic-based GI tract simulation model and PK
tool of the invention, to FDp derived from human clinical data for
12 compounds.
[0091] FIG. 50 compares plasma levels as predicted using integrated
physiologic-based GI tract simulation model and PK tool of the
invention, to plasma levels derived from human clinical data for a
test compound.
[0092] FIG. 51 compares plasma levels as predicted using integrated
physiologic-based GI tract simulation model and PK tool of the
invention, to plasma levels derived from human clinical data for a
test compound.
[0093] FIG. 52 compares plasma levels as predicted using integrated
physiologic-based GI tract simulation model and PK tool of the
invention, to plasma levels derived from human clinical data for a
test compound.
[0094] FIG. 53 shows high level INPUT/PROCESS/OUTPUT diagram of the
PK tool of the invention for SAR/QSAR and CAD/CAE compound design
and synthesis.
[0095] FIG. 54 shows high level flow and structure chart for
screening method of the invention utilizing the PK tool and method
of the invention.
DESCRIPTION OF SPECIFIC EMBODIMENTS
[0096] A pharmacokinetic tool (PK tool) and method is provided for
predicting absorption of a compound relative to a physiological
barrier of a mammalian system of interest, including
extravascularly administered compounds. This includes, but is not
limited to, prediction of rate, extent and/or concentration of a
compound. The mammal is a human or a non-human animal. The method
utilizes the PK tool, and optionally separately operable subsystems
or components thereof. The PK tool and method of the invention also
facilitates prediction of the fate of a compound in a mammal based
on absorption and one or more additional bioavailability parameters
including distribution, metabolism, elimination, and optionally
toxicity.
[0097] The PK tool includes as computer-readable components, an
input/output system, a physiologic-based simulation model of a
mammalian system of interest, and a simulation engine. The
input/output system may be any suitable interface between user and
computer system, for input and output of data and other
information, and for operable interaction with a simulation engine
and a simulation model.
[0098] Input data into the PK tool and method of the invention is
dose, permeability and solubility data for a test compound of
interest, and optionally one or more of dissolution rate, transport
mechanism, transit time, pH, delivery system rate such as
controlled release rate or formulation release rate (delivery
system referred to herein as "formulation"), dosing schedule, and
simulation run time. The input data may be derived from in vitro or
in vivo sources. In vitro data includes tissue and cell and natural
and artificial preparations thereof, physicochemical, molecular
structure and molecular structure-activity relationship (SAR) and
quantitative-SAR (QSAR) data. In vivo data includes mammal data.
The input data corresponds to one or more given physiological
segments/regions of the mammalian system of interest.
[0099] The simulation output includes an absorption profile
characterized by one or more of rate of absorption, extent of
absorption, and concentration of the compound relative to a
selected sampling site of interest located across a physiological
barrier of the mammalian system of interest, i.e., rate and/or
extent of transfer of a test sample from an external site (e.g.,
apical) across a physiological barrier (e.g., epithelium) to an
internal site (e.g., basolateral) of that barrier. This can include
prediction of rate, extent and/or concentration of a compound at
the site of action when the selected sampling site is the site of
action. Transfer rate and/or extent are generated utilizing initial
dose data for the test compound and in vitro and/or in vivo derived
data including permeability and solubility data, and optionally
dissolution rate and transport mechanism data (i.e., passive
paracellular, passive transcellular, carrier-mediated influx,
carrier-mediated efflux) for the test compound. Solubility and
dissolution rate are interrelated and effect the ability of the
compound to be solubilized at a rate sufficient for absorption to
occur across a particular membrane. Permeability refers to the
concentration-dependent or concentration-independent rate of
transport (flux), and collectively reflects the effect of molecular
size, charge, partition coefficient and stability of a compound on
absorption for a particular physiological barrier, where the
physiological barrier(s) depends on the selected route of
administration. Molecular size, charge and partition coefficient
determines in large part whether a compound is transported via a
paracellular or transcellular mechanism. Stability is a general
feature that relates to whether the compound remains intact long
enough to be absorbed. Together, dose, solubility and permeability
data, and optionally dissolution rate and transport mechanism data,
are primary bioavailability factors utilized by the PK tool and
method of the invention to generate an absorption profile for a
test compound of interest.
[0100] An absorption profile generated by the PK tool and method of
the invention can be uni- or multi-dimensional output that reflects
one or more simulated parameters of the mammalian system of
interest relative to the sampling site. The sampling site, for
example, portal vein, plasma, tissue, organ and the like, is chosen
depending on the intended end use of the PK tool and method of the
invention. Output of the method and PK tool can be utilized to
profile or rank the compound by a selected absorption parameter,
and optionally, absorption and one or more additional
bioavailability parameters and toxicity.
[0101] The simulation engine comprises a differential equation
solver and, optionally, a system control statement module. This
includes various computer-readable algorithms for numerical
iteration of mathematical- equations over interval dt and for
processing rules, scenarios and the like that direct a
simulation.
[0102] The simulation model corresponds to a physiologic-based
multi-compartment model of a mammalian system of interest, where
the mammalian system represents a physiological barrier to
absorption that is based on a selected route of administration,
i.e., the location at which the compound is introduced to a mammal.
More particularly, the physiologic-based simulation model of the PK
tool and method of the invention is a mathematical model comprising
as operably linked components: (i) differential equations for
calculating one or more of fluid transit, fluid absorption, mass
transit, mass dissolution, mass solubility, and mass absorption of
a test compound for one or more physiological segments of the
mammal system of interest; and (ii) initial parameter values for
the differential equations corresponding to physiological
parameters and selectively optimized adjustment parameters, and
optionally one or more regional correlation parameters, for one or
more physiological segments of the mammal system of interest; and
optionally (iii) control statement rules for one or more of
absorption, permeability, solubility, dissolution, concentration,
and mathematical error correction, for one or more physiological
segments of the mammal system of interest. The simulation model
also may include one or more smoothing functions that facilitate
calculation of transitional parameter values occurring between one
or more of the physiological segments.
[0103] The differential equations of a selected simulation model of
a mammalian system of interest describe the rate processes of
absorption, and optionally other events, of that model, which in
turn describe compound concentrations in the system as a function
of time. (See, e.g., Shargel et al., Applied Biopharmaceutics and
Pharmacokinetics, Appelton & Lange, East Norwalk, Conn., 1993).
Thus, the differential equations are selected for a particular
model.
[0104] The initial physiological parameter values of a given
simulation model can be generated de novo or obtained from existing
sources including the literature. The selectively optimized
adjustment parameter values of a given simulation model of the
invention represent regression or stochastic analysis derived
values that are used as constants for one or more independent
parameters of the model. In particular, the selectively optimized
adjustment parameter values are obtainable by using a stepwise
fitting and selection process that employs regression- or
stochastic-based curve-fitting algorithms to simultaneously
estimate the change required in a value assigned to an initial
absorption parameter of the model in order to change an output
variable. The input variables utilized for fitting include a
combination of in vitro data (e.g., permeability, solubility) and
in vivo pharmacokinetic data (e.g., fraction of dose absorbed,
plasma levels) for a compound test set having compounds exhibiting
a diverse range of in vivo absorption properties. Thus, the input
variables used for regression- or stochastic-based fitting are
derived from (a) a first data source corresponding to the mammalian
system of interest (e.g., in vivo pharmacokinetic data from human
for the compound test set), and (b) a second data source
corresponding to a system other than the mammalian system of
interest (e.g., in vitro solubility data and in vitro permeability
data from rabbit tissue for the compound test set). A fitted
adjustment parameter value for a given independent parameter is
then selected that, when supplied as a constant in the model,
permits correlation of one or more of the input variables from the
first data source to one or more input variables from the second
data source. The process is repeated one or more times for one or
more additional independent parameters of the simulation model
until deviation of the correlation is minimized. These "selectively
optimized" adjustment parameters are then provided to a given
simulation model as constants or ranges of constants or functions
that modify the underlying equations of the model. The selectively
optimized adjustment parameters facilitate accurate correlation of
in vitro data derived from a particular type of assay corresponding
to the second data source (e.g., Caco-2 cells, segment-specific
rabbit intestinal tissue sections etc.) to in vivo absorption for a
mammalian system of interest corresponding to the first data source
(e.g., segment-specific portions of the human GI tract) for diverse
test sample data sets. Selectively optimized adjustment parameters
also can be utilized to facilitate accurate correlation of in vivo
data derived from a first species of mammal (e.g., rabbit) to a
second species of mammal (e.g., human).
[0105] For a simulation model representing two or more anatomical
segments of a given mammalian system, the model will preferably
include regional correlation parameters. The regional correlation
parameters permit estimation of a selected parameter value for a
first segment of the mammalian system from correlation using a
value of the selected parameter for a second segment of the
mammalian system. The regional correlation parameters represent a
collection of empirically derived values or selectively optimized
adjustment parameter values for various segments of the mammalian
system of interest, for example, permeability values. The regional
(i.e., segmental) correlation is performed by logic function of the
model, which when activated utilizes a function/transformation
algorithm to estimate the parameter value for the second segment
from (1) the corresponding regional correlation parameters, and (2)
a user provided input value for the same parameter, but for a
different segment. The regional correlation logic function of the
model is activated when a user does not supply an input value for a
particular parameter. For example, when a user of the PK tool
supplies a single permeability value as input into a GI tract
simulation model of the invention, such as a permeability value
derived from Caco-2 cells that corresponds to colon, then regional
permeability correlation is performed by the PK tool to estimate
permeability in the other GI tract segments, such as duodenum,
jejunum, and ileum.
[0106] The control statement rules include various logic elements
utilized for providing guidance as to how a given simulation is to
proceed. For instance, a control statement rule would include "IF .
. . THEN" production rules. An example of a production rule would
be "IF solubility of compound is zero THEN absorption is zero." The
production rules are based on rules of thumb (heuristics) and the
like, and may be generated by correlation of parameters and
simulation runs. Rules can be added, modified or removed to change
how a simulation model responds to incoming data.
[0107] The input/output system, simulation engine and simulation
model of the PK tool are capable of working together to carry out
the steps of (1) receiving as input data, the initial dose of a
test compound at the site of administration and permeability and
solubility, and optionally dissolution rate and transfer mechanism
data; and (2) applying the simulation engine and the simulation
model to generate as output data a simulated in vivo absorption
profile for the test compound that reflects rate, extent and/or
concentration of the test sample at a given sampling site for a
selected route of administration in a mammalian system of interest.
This includes uni- and multi-dimensional output profiles that
collectively reflect parameters of absorption, which can be
directly or indirectly utilized for characterizing in vivo
absorption, as well as one or more additional bioavailability
parameters including distribution, metabolism, elimination, and
optionally toxicity.
[0108] The selected routes of administration include enteral (e.g.,
buccal or sublingual, oral (PO), rectal (PR)), parenteral (e.g.,
intravascular, intravenous bolus, intravenous infusion,
intramuscular, subcutaneous injection), inhalation and transdermal
(percutaneous). The preferred route of administration according to
the method of the invention is oral administration. The selected
route of administration determines the type and/or source of assay
or structure-property parameters employed for obtaining a set of
input data utilized for generating a simulated in vivo absorption
profile. That is, artificial, cell or tissue preparations and the
like derived from or representative of a physiological barrier to
absorption for a selected route of administration are chosen to
generate the relevant input data for use as input into the PK tool.
For instance, input data for simulating fate of a test sample
following oral administration can be based on cell culture and/or
tissue assays that employ biological preparations derived from or
representative of the gastrointestinal tract of a mammal of
interest, e.g., gastrointestinal epithelial cell preparations for
permeability and transfer mechanism data, and
physiological/anatomical fluid and admixing conditions
corresponding to the relevant portions of the gastrointestinal
tract for solubility and dissolution rate assays. Assays for
collecting input data for specialized physiological barriers such
as the blood brain barrier may initially assume intravascular
delivery and thus instantaneous absorption as a first step. In this
situation an assay is selected to generate input data relative to
the blood brain barrier, which include for instance cell culture
and/or tissue assays that employ biological preparations derived
from or representative of the interface between systemic blood and
the endothelial cells of the microvessels of the brain for a mammal
of interest, e.g., blood-brain-barrier microvessel endothelial cell
preparations for permeability and transfer mechanism data, and
physiological/anatomical fluid and admixing conditions
corresponding to the relevant portions of the blood membrane
barrier for solubility and dissolution rate assays. A series of
assays may be employed to collect input data for two or more
barriers to absorption. As an example, oral, hepatic, systemic and
blood brain barrier assays may be utilized to obtain input data for
screening compound libraries for orally delivered compounds that
target brain tissue.
[0109] The sampling site relates to the point at which absorption
parameters are evaluated for a test sample of interest. This is the
site at which rate, extent and/or concentration of a test sample is
determined relative to a selected site of administration, and is
separated from the site of administration by at least one
physiological barrier to absorption. For generating simulated
absorption profiles, the sampling site preferably is separated from
the site of administration by an individual primary barrier to
absorption, which can be utilized to evaluate additional absorption
events by secondary barriers to absorption so as to sequentially
and collectively reflect the summation of absorption events at
other sampling sites of interest. As an example, the sampling site
selected for oral delivery may be the portal vein where the primary
barrier to absorption is the gastrointestinal lumenal membrane, or
systemic blood where a secondary barrier to systemic absorption is
the liver after the test sample passes from the portal vein through
the liver to systemic circulation. Thus the type of physiological
barrier(s) residing between a site of administration and a sampling
site reflects the type of assay(s) employed for generating the
desired input data for use as input data into the PK tool of the
invention.
[0110] As the selected route of administration determines the
barrier(s) to absorption and the physiological parameters that
affect absorption events following administration, it also
determines the physiologic-based pharmacokinetic simulation model
employed in the PK tool for generation of the simulated in vivo
absorption profile. By way of example, if the proposed route of
administration is oral, then a primary barrier to absorption is the
lumenal membrane of the gastrointestinal tract, and a secondary
event affecting systemic bioavailability is first pass metabolism
by the liver. Thus, a given simulation model and its associated
parameters for simulating the fate of a compound selected for oral
delivery is chosen to represent this scenario. The model would
include therefore relevant components of the gastrointestinal tract
for administration and absorption (i.e., stomach, duodenum,
jejunum, ileum, and colon) and a primary sampling site (i.e.,
portal vein) from which to evaluate a primary absorption event. In
this instance a secondary barrier to absorption for oral delivery
is the liver and a secondary sampling site is systemic
blood/plasma. This basic approach to choosing a physiologic-based
pharmacokinetic model also applies to models employed to simulate
absorption by target organs and the like, where a physiological
barrier to absorption is the tissue and/or membrane separating
systemic blood from the target organ, such as the blood brain
barrier. In this situation if oral delivery is selected as the
preferred route of administration for a compound targeting brain
tissue, then a gastrointestinal tract model and blood brain barrier
model may be implemented separately and/or combined through a
complementary plasma component of the models for screening
purposes.
[0111] The physiological models are selected from a repository of
delivery route-specific models stored in a memory, a database, or
created de novo. Physiological models of the invention include
those corresponding to common routes of administration or barriers
to absorption, such as oral (GI tract), ocular (eye), transdermal
(skin), rectal, intravenous, rectal, subcutaneous, respiratory
(nasal, lung), blood brain barrier and the like. For constructing a
model de novo, the basic approach is to identify and isolate a
primary barrier to a specific absorption event from secondary
events so that each barrier to absorption can be tested and
validated in isolation. This involves selecting a site of
administration that is separated from a sampling site by a primary
physiological barrier to absorption and then building a
developmental physiological model that incorporates rate process
relations and limitations to describe the isolated absorption
event. If desired, the secondary events can be added sequentially
so that each additional layer of complexity to the model can be
tested and validated in isolation from other components of the
initial model.
[0112] The invention also relates to a method and PK tool for
designing compounds based on absorption. This aspect of the
invention utilizes output of the method and PK tool as the input to
a structure-activity relationship (SAR) or quantitative SAR (QSAR)
design/selection process, e.g., a SAR and/or QSAR computer-assisted
design/engineering/selection (CAD/CAE (collectively "CAD"))
process. Output of the CAD process is then optionally used as input
for the method and PK tool of the invention. SAR and QSAR
information may then be incorporated into a database for subsequent
iterative design and selection in the CAD process. For instance,
compounds designed using a CAD process may be tested in vitro
and/or in vivo for absorption parameters such as permeability,
solubility, dissolution, and transport mechanism, and optionally
one or more additional bioavailability parameters, and the data
employed as input into the PK tool and method of the invention
(i.e., iterative design). Alternatively, the parameters can be
predicted from SAR or QSAR information and utilized as input for
the method and PK tool of the invention. In this aspect of the
invention, the user also is allowed to vary input parameters for
"What if" analysis.
[0113] In the forward mode of operation, the user can predict
absorption, individual parameters of absorption, as well as one or
more other bioavailability parameters of a compound from relatively
few input variables including dose, permeability and solubility.
Additionally, the user can evaluate alternatives by changing any of
the parameters and constants of the system, and observe the ripple
effect of the change in one or more parameters on all other
parameters. For instance, the user can evaluate alternative
absorption profiles using "What if" analysis with any parameter of
the system.
[0114] In the backward mode of operation, the user specifies one or
more objective absorption parameters of a formulation of interest
and the PK tool and method of the invention generates alternatives
to satisfy the objective. In this aspect of the invention,
well-defined properties of the compound (and the formulation base
minus the compound) are utilized by the PK tool and method to
evaluate alternative dosing and formulation profiles for a given
compound. The user also is allowed to vary input dosing and
formulation parameters for "What if" analysis. Simulated absorption
profiles can then be utilized for preparing suitable formulations
and/or dosing regimes. Solubility, permeability, doses and the like
also may be estimated in the backward mode of operation.
[0115] The PK tool and method of the invention is exemplified by
physiologic-based simulation model for predicting oral absorption
of a compound in one or more segments of the GI tract of a mammal.
The segments include the stomach, duodenum, jejunum, ileum, and
colon. The simulation model includes differential equations for
calculating one or more of fluid transit, fluid absorption, mass
transit, mass dissolution, mass solubility, and mass absorption for
one or more segments of the GI tract of a mammal of interest. It
also includes initial parameter values for the differential
equations that correspond to physiological parameters and
selectively optimized adjustment parameters for one or more
segments of the GI tract of the mammal of interest. The initial
parameter values of simulation model also include one or more
regional correlation parameter values, which are optional, but
preferred for inclusion. The simulation model of the GI tract also
includes control statement rules for one or more of transit,
absorption, permeability, solubility, dissolution, concentration,
and mathematical error correction for one or more segments of the
GI tract of the mammal of interest.
[0116] The physiologic-based simulation model of the GI tract
corresponds to a compartment-flow simulation model of the GI tract
of a mammal characterized by one or more of fluid volume, fluid
absorption, insoluble mass, soluble mass, and soluble mass
absorption compartments. The compartments of the compartment-flow
simulation model are operably linked by one or more flow regulators
characterized by fluid absorption rate, fluid volume transit rate,
insoluble mass transit rate, insoluble mass dissolution rate,
soluble mass transit rate, and soluble mass absorption rate. The
flow regulators of the compartment-flow simulation model are
modified by one or more converters characterized by fluid volume,
fluid volume absorption rate constant, fluid volume transit rate
constant, insoluble mass, insoluble mass transit rate constant,
dissolution rate constant, soluble mass, soluble mass transit rate
constant, surface area, dissolved mass concentration and
permeability.
[0117] The PK tool and method of this invention accelerate
selection and design of compounds for treatment of mammalian
disorders, allowing same day response time. The invention optimizes
the drug development process in terms of bioavailability
parameters, and uses simple in vitro parameters for predicting the
in vivo fate of an administered compound. The PK tool and method of
the invention also permits utilization of in vivo data from one
type of mammal (e.g. rabbit) to predict absorption in a different
type of mammal (e.g. human). The invention also is particularly
well suited for iterative selection and design of compounds based
on structure-bioavailability relationships using a SAR/QSAR
approach. This reduces total drug development time, and optimizes
the drug design and selection process for animal studies and human
clinical trials. Moreover, the PK tool and method of the invention
allows separate or concurrent consideration of bioavailability
parameters and/or biological drug-receptor activity early in the
drug development process. The invention also permits a broad range
of in vitro to interspecies correlation, thereby facilitating
optimal selection of an animal model for drug development.
[0118] PK Tool and System:
[0119] The PK tool of the invention is utilized to generate a
simulated in vivo absorption profile from dose, solubility and
permeability data, and optionally in vitro dissolution rate and
transport mechanism data for a test compound. The PK tool includes
as computer-readable components, an input/output system suitable
for data input and data output, a simulation engine having a
differential equation solver, and a physiologic-based simulation
model comprising a pharmacokinetic model of the mammalian system to
be simulated. In vitro or in vivo data for the test compound is
provided through the input/output system, and then the simulation
engine and simulation model are applied to facilitate a simulation
run so as to generate a user selected in vivo absorption profile
for the test sample. Together, the simulation engine and simulation
model are employed to simulate the fate of a test sample in the
system under investigation.
[0120] The PK tool is based on a compartment-flow simulation model
system. The compartment-flow model employs compartments, flow
regulators, and converters that collectively regulate flow among
the compartments. The model components are represented by a series
of differential equations which when run through the simulation
engine are solved at each time increment dt based on the initial
underlying values of the equations, the input values supplied by
the user, and calculations performed by various subsystems of the
model when activated in a particular scenario.
[0121] The PK tool optionally comprises a repository of different
pharmacokinetic models and initial parameter values for a given
model. The repository preferably resides in a database of the PK
tool, and/or is accessible through an acquisition module. The PK
tool also may include one or more curve-fitting algorithms for
generation of absorption parameters and constants for correlation
of in vitro data to in vivo data, or in vivo data from one species
of a mammal to in vivo data of a second species of mammal based on
a selected route of administration. The curve-fitting algorithms
include regression-based and stochastic-based algorithms.
[0122] 1. Input/Output System
[0123] With regard to the components of the PK tool, the
input/output system provides a user interface between the user and
the PK tool of the invention. The input/output system may be any
suitable interface between user and computer system, for input and
output of data and other information, and for operable interaction
with a simulation engine and a simulation model. For instance, the
input/output system may provide direct input form measuring
equipment. The input/output system preferably provides an interface
for a standalone computer or integrated multi-component computer
system having a data processor, a memory, and a display. Input into
the method and PK tool of the invention is in vitro or in vivo data
derived from an assay corresponding to a selected route of
administration and mammalian system of interest. For example, the
user enters the initial parameter values for a test compound, e.g.,
dose, permeability, and solubility derived from the assay, and then
optionally indicates the transport mechanism, e.g., passive
transcellular, passive paracellular, carrier-mediated influx, or
carrier-mediated efflux. When transport mechanism is not indicated,
the PK tool can be designed to employ a default transport
mechanism, such as passive transcellular. When set to the
paracellular mechanism, the absorption of the compound is adjusted
to compensate for the lower surface area available for absorption
via the paracellular pathway. The model also may incorporate an
operation by which the mechanism of absorption can be predicted
using the permeability, solubility, molecular structure or other
information. This allows the model to automatically compensate for
paracellular and/or other absorption mechanisms without requiring
prior input and knowledge from the user. Depending on the
objective, the user also may specify the pH, delivery system rate
such as controlled release rate or formulation release rate
(delivery system referred to herein as "formulation"), dosing
schedule, and simulation run time, as well as physiologic system
specific parameters such as GI transit time when a GI tract model
is employed. If values for these parameters are not entered, the PK
tool provides default values.
[0124] Data may be entered numerically, as a mathematical
expression or as a graph that represents a physiological or
pharmacokinetic parameter, or alpha such as transcellular,
paracellular, passive, active, etc. An advantage of entering data
as a graph is that it removes any requirement to define the
mathematical relationship between a dependent and an independent
variable. The interface output displays and/or compares parameters
related to absorption, such as graphs or tables corresponding to
rate of absorption, extent of absorption, and concentration
profiles, and the like.
[0125] The absorption parameters include concentration, rate and/or
extent of absorption of a test sample. As can be appreciated,
absorption parameters can be represented in multiple different ways
that relate time, mass, volume, concentration variables, fraction
of the dose absorbed and the like. Examples include rate "dD/dt"
and "dc/dt" (e.g., mass/time-mg/hr;
concentration/time-.mu.g/ml/hr), concentration "C" (e.g.,
mass/volume-.mu.g/ml), area under the curve "AUC" (e.g.,
concentration .cndot. time, .mu.g .cndot. hr/ml), and
extent/fraction of the dose absorbed "F" (e.g., no units, 0 to 1).
Other examples include the maximum concentration (C.sub.max), which
is the maximum concentration reached during the residence of a
compound at a selected sampling site; time to maximum concentration
(T.sub.max), which is the time after administration when the
maximum concentration is reached; and half-life (t.sub.1/2), e.g.,
the time where the concentration reaches 1/2 its maximum at a
selected sampling site. Other examples of output include individual
simulated parameters such as permeability, solubility, dissolution,
and the like for individual segments, as well as cumulative values
for these and/or other parameters.
[0126] 2. Simulation Engine
[0127] The simulation engine comprises a differential equation
solver that uses a numerical scheme to evaluate the differential
equations of a given physiologic-based simulation model of the
invention. The simulation engine also may include a system control
statement module when control statement rules such as IF . . . THEN
type production rules are employed. The differential equation
solver uses standard numerical methods to solve the system of
equations that comprise a given simulation model. These include
algorithms such as Euler's and Runge-Kutta methods. Such simulation
algorithms and simulation approaches are well known (See, e.g.,
Acton, F. S., Numerical Methods that Work, New York, Harper &
Row (1970); Burden et al., Numerical Analysis, Boston, Mass.,
Prindle, Weber & Schmidt (1981); Gerald et al., Applied
Numerical Analysis, Reading, Mass., Addison-Wesley Publishing Co.,
(1984); McCormick et al., Numerical Methods in Fortran, Englewood
Cliffs, N.J., Prentice Hall, (1964); and Benku, T., The Runge-Kutta
Methods, BYTE Magazine, April 1986, pp. 191-210).
[0128] Many different numerical schemes exist for the evaluation of
the differential equations. There are literally 100's of schemes
that currently exist, including those incorporated into public
commercially available computer applications, private industrial
computer applications, private individually owned and written
computer applications, manual hand-calculated procedures, and
published procedures. With the use of computers as tools to
evaluate the differential equations, new schemes are developed
annually. The majority of the numerical schemes are incorporated
into computer applications to allow quick evaluation of the
differential equations.
[0129] Computer application or programs described as simulation
engines or differential equation solver programs can be either
interpretive or compiled. A compiled program is one that has been
converted and written in computer language (such as C++, or the
like) and are comprehendible only to computers. The components of
an interpretive program are written in characters and a language
that can be read and understood by people. Both types of programs
require a numerical scheme to evaluate the differential equations
of the model. Speed and run time are the main advantages of using a
compiled rather than a interpretive program.
[0130] A preferred simulation engine permits concurrent model
building and simulation. An example is the STELLA.RTM. program
(High Performance Systems, Inc.). STELLA.RTM. is an interpretive
program that can use three different numerical schemes to evaluate
the differential equations: Euler's method, Runge-Kutta 2, or
Runge-Kutta 4. The program KINETICA.TM. (InnaPhase, Inc.) is
another differential equation solving program that can evaluate the
equations of the model. By translating the model from a STELLA.RTM.
readable format to a KINETICA.TM. readable format, physiological
simulations can be constructed using KINETICA.TM., which has
various fitting algorithms. This procedure can be utilized when the
adjustment parameters are being optimized in a stepwise
fashion.
[0131] 3. Simulation Model
[0132] The simulation model is a mathematical model of a
multi-compartment physiological model of a mammalian system (e.g.,
GI tract) that corresponds to the selected route of administration
(e.g., oral). A given physiological model is represented by series
of differential equations that describe rate process interactions
among anatomical segments for the physiological system under
investigation. The individual segments or compartments are
represented mathematically as a one, two and/or three compartment
kinetic system. The segments are linked in a stepwise fashion so as
to form an integrated physiological model describing absorption of
a compound relative to the anatomical segments and at least one
sampling site for assessing an absorption event in isolation. For a
model simulating oral delivery, anatomical segments of the GI tract
are provided, which can include the stomach, duodenum, jejunum,
ileum and colon. A sampling site for the GI tract may be the portal
vein and/or plasma. The rectum and colon would be applicable for
modeling a rectal route of delivery. Segments and sampling site for
buccal or sublingual delivery routes can include the mouth,
cheek/tongue tissue and plasma. For ocular routes, this can include
aqueous humor, conjunctival sac, tear duct, nasal cavity and
plasma. For the lung routes, this can include respiratory
bronchioles zone and plasma. For delivery via the nose, this can
include nasal cavity and plasma. For the topical and transdermal
routes, this can include epidermal, dermal, subcutaneous tissue,
muscle and plasma. Other systems adhere to these basic designs.
[0133] Of course compartments representing a particular anatomical
segment can be added or removed depending on the model's intended
end use, such as when an isolated segment is examined, or when it
is desired to account for parameters affecting bioavailability at
additional sampling sites. For example, compartments can be added
to account for both pre- or post-absorptive protein binding or
complex formation to account for reversible association of a
compound to the proteins (albumin and al-acid glycoprotein) of
blood, or more usually plasma. Other compartments that may be added
would include those that account for phase I and/or phase II
hepatic metabolism. Formulation compartments that account for
variable compound formulations also can be added, such as
time-release, extended release or otherwise controlled release
formulations. Another example is inclusion of kidney compartments
to account for renal clearance.
[0134] The compartments can be modified by factors that influence
absorption such as mass, volume, surface area, concentration,
permeability, solubility, fluid secretion/absorption, fluid
transit, mass transit and the like, depending on the physiological
system under investigation. As a rule of thumb, compartment
modifiers relate to input variables. For instance, where transport
mechanism and dissolution rate are variables considered for
generating an absorption profile, then the physiological model will
include compartments and parameters that account for these
variables.
[0135] When represented as a compartment-flow simulation model, the
anatomical segments of a physiological model typically include one
or more central and peripheral compartments that reversibly
communicate through a flow regulator. A central compartment
represents the interior or mucosal side of an anatomical segment. A
peripheral compartment represents the blood side of the segment.
The central and peripheral compartments are connected by a flow
regulator representing a physiological barrier through which
material from the central compartment "flows" or is transferred to
the peripheral compartment at some empirically defined or
calculated transfer rate "k12" applied by a converter, which allows
calculation of parameters using compartment values. Transfers
("flows") between compartments can be zero order, first order,
second order and/or mixed order processes. As an example, a first
order transfer from central compartment 1 to peripheral compartment
2 can be defined by a finite difference equation connecting inputs
(e.g., rate constant k12 and amount of compound in central
compartment=amount+dt*(-el- imination-k12+k21)) to the flow
controller between the compartments (e.g., k12) and setting it as
the product of the two variables. Thus the underlying equations of
the model are utilized to calculate the amount of a compound in
each compartment, and standard differential equations interrelate
the system of compartments and their equations. This permits the
model to simulate movement of a compound through each compartment
according to the calculated rates at each time increment (dt).
Since all movement between compartments is in units of mass, the
blood side and transferred test compound concentration is
calculated from the amount of compound in the blood side
(peripheral compartment) and volume of the mucosal side (central
compartment). A model cycle is entered through the input/output
user interface as incremental pulses (to simulate ramp, plug
flow/lag times) or as a fixed time range to initiate and effectuate
cycling of a test compound of interest.
[0136] The basic structure of a physiological model and
mathematical representation of its interrelated anatomical segments
can be constructed using any number of techniques. The preferred
techniques employ graphical-oriented compartment-flow model
development computer programs such as STELLA.RTM., Kinetica.TM. and
the like. Many such programs are available, and most employ
graphical user interfaces for model building and manipulation. In
essence, symbols used by the programs for elements of the model are
arranged by the user to assemble a diagram of the system or process
to be modeled. Each factor in the model may be programmed as a
numerical constant, a linear or non-linear relationship between two
parameters or as a logic statement. The model development program
then generates the differential equations corresponding to the user
constructed model. For example, STELLA.RTM. employs five basic
graphic tools that are linked to create the basic structure of a
model: (1) stocks; (2) flows; (3) converters; (4) input links; and
(5) infinite stocks (See, e.g., Peterson et al., STELLA.RTM. II,
Technical Documentation, High Performance Systems, Inc., (1993)).
Stock are boxes that represent a reservoir or compartment. Flows or
flow regulators control variables capable of altering the state of
compartment variables, and can be both uni- and bi-directional in
terms of flow regulation. Thus, the flow/flow regulators regulate
movement into and out of compartments. Converters modify flow
regulators or other converters. Converters function to hold or
calculate parameter variable values that can be used as constants
or variables which describe equations, inputs and/or outputs.
Converters allow calculation of parameters using compartment
values. Input links serve as the internal communication or
connective "wiring" for the model. The input links direct action
between compartments, flow regulators, and converters. In calculus
parlance, flows represent time derivatives; stocks are the
integrals (or accumulations) of flows over time; and converters
contain the micro-logic of flows. The stocks are represented as
finite difference equations having the following form:
Stock(t)=Stock(t-dt)+(Flow)*dt. Rewriting this equation with
timescripts and substituting t for dt:
Stock.sub.t=Stock.sub.t-.DELTA.t+.DELTA.t*(Flow). Re-arranging
terms: (Stock.sub.t-Stock.sub.t-3.DELTA.t)/.DELTA.t=Flow, where
"Flow" is the change in the variable "Stock" over the time interval
"t." In the limit as .DELTA.t goes to zero, the difference equation
becomes the differential equation: d(Stock)/dt=Flow. Expressing
this in integral notation: Stock=.intg.Flow dt. For higher-order
equations, the higher-order differentials are expressed as a series
of first-order equations. Thus, computer programs such as
STELLA.RTM. can be utilized to generate physiologic-based
multi-compartment models as compartment-flow models using graphical
tools and supplying the relevant differential equations of
pharmacokinetics for the given physiologic system under
investigation. An example of iconic tools and description, as well
as graphically depicted compartment-flow models generated using
STELLA.RTM. and their relation to a conventional pharmacokinetic IV
model is illustrated in FIGS. 5-8.
[0137] The model components may include variable descriptors.
Variable descriptors for STELLA.RTM., for example, include a broad
assortment of mathematical, statistical, and built in logic
functions such as boolean and time functions, as well as
user-defined constants or graphical relationships. This includes
control statements, e.g., AND, OR, IF . . . THEN . . . ELSE, delay
and pulsing, that allow for development of a set of production
rules that the program uses to control the model. Variable
descriptors are inserted into the "converters" and connected using
"input links." This makes it is possible to develop complex rule
sets to control flow through the model. The amount of time required
to complete one model cycle is accomplished by inputting a total
run time and a time increment (dt). The STELLA.RTM. program then
calculates the value of every parameter in the model at each
successive time increment using Runge-Kutta or Euler's simulation
techniques. The preferred simulation technique is Runge-Kutta. Once
a model is built, it can be modified and further refined, or
adapted or reconstructed by other methods, including manually, by
compiling, or translated to other computer languages and the like
depending on its intended end use.
[0138] A preferred method of the invention for constructing a
physiological model for in vivo prediction from in vitro input data
is depicted in FIG. 9. This method employs a two-pronged approach
that utilizes a training set of standards and test compounds having
a wide range of dosing requirements and a wide range of
permeability, solubility, transport mechanisms and dissolution
rates to refine the rate process relations and generate the initial
values for the underlying equations of the model. The first prong
employs the training/validation set of compounds to generate in
vivo pharmacokinetic data (e.g., human plasma profiles). The second
prong utilizes the training/validation set of compounds to generate
in vitro permeability, solubility, transport mechanism and
dissolution rate data that is employed to perform a simulation with
the developmental physiological model. The in vivo pharmacokinetic
data is then compared to the simulated in vivo data to determine
how well a developmental model can predict the actual in vivo
values from in vitro data. The developmental model is adjusted
until it is capable of predicting in vivo absorption for the
training set from in vitro data input. Then the model can then be
validated using the same basic approach and to assess model
performance.
[0139] In particular, three primary sets of data are generated from
the training set for the comparison. The first set of data is
empirically derived in vivo plasma data from animals or humans. The
second set of data is obtained from conversion of the in vivo
plasma data to a form corresponding to the primary sampling site of
the developmental physiological model. The third set of data is
empirically derived in vitro data including permeability,
solubility, dissolution rate and transport mechanism data. The raw
data points are preferably collected and statistically analyzed to
provide the best fit data. The best fit data may be obtained by any
number of curve-fitting approaches, including standard regression
techniques.
[0140] The in vivo plasma data is utilized to judge how well a
developmental simulation model is able to predict absorption of the
training set of compounds relative to the empirically derived in
vivo plasma values. Plasma data also is utilized to calculate
absorption at the relevant primary sampling site of the
developmental physiological model. For instance, in order to use in
vivo plasma data in a developmental physiological model, the plasma
data must first be converted to data corresponding to the primary
sampling site of the model. If plasma is the primary sampling site
then no conversion is needed. However, if plasma is not the primary
sampling site, then a pharmacokinetic training/validation model
relating the primary sampling site and the in vivo plasma data is
utilized. For example, when the developmental model is of the
gastrointestinal tract, the portal vein can be selected as a
primary sampling site and plasma selected as a secondary sampling
site. Thus in this instance the in vivo plasma data is converted to
portal vein data so that the parameters affecting secondary
bioavailability events are separated from the primary absorption
event resulting from passage of the test sample across the
gastrointestinal lumen. This is accomplished by adding a
plasma-portal vein conversion/validation model that relates in vivo
plasma data to portal vein data. This plasma-portal vein
conversion/validation model can be separate or integrated with the
developmental model. In most cases, the plasma-portal vein model is
based on a standard central-peripheral pharmacokinetic compartment
approach for data conversion. The third set of data, the in vitro
derived data, is utilized to run the developmental model, and the
simulated absorption profile from this data set is compared to the
in vivo derived plasma and simulated sampling site data. The
developmental physiological model is modified until the simulated
absorption profiles are in agreement with the in vivo derived
plasma and simulated sampling site data.
[0141] As the number of parameters for evaluation increase it
becomes more important to isolate and test each component of the
model building process by validation using a standard validation
set of compounds. The validation set of compounds should contain a
diverse set of compounds that represent a broad range of absorption
profiles for which both in vitro permeability, solubility,
dissolution rate, and transport mechanism data, and in vivo plasma
data is available. Statistical criteria such as sum of squares of
the deviations between experimental data and calculated values
obtained from the developmental physiological model are used to
determine how well the model fits the data. If the developmental
physiological model does not predict a good fit for the data, then
the model is adjusted by isolating or including additional rate
processes by an iterative approach.
[0142] Parameter values utilized in the underlying equations of a
given physiological model may be provided in a database for ready
access and manipulation by the PK tool of the invention, or
provided with a model. The parameter values may include values for
physiological parameters, such as rate constants and various other
values employed in the PK tool. The rate constants correspond to
time-dependent (or time-independent) numerical constants describing
rate processes (e.g., k12 and k21). The physiological parameters
include rate constants, permeability, solubility, transport
mechanism and dissolution rate variables, and the like, as well as
pH, volume, surface area, transit times, transit rates, and the
like, that are based on the physiology of a given anatomical
segment represented in a selected physiological model.
[0143] To account for differences between in vitro and in vivo
conditions, as well as differences between in vivo conditions of
different type of mammals, adjustment parameters that modify one or
more of the underlying equations of given simulation model can be
utilized to significantly improve predictability. The adjustment
parameters include constants or ranges of constants that are
utilized to correlate in vitro input parameter values derived from
a particular in vitro assay system (e.g., rabbit intestinal tissue,
Caco-2 cells) to a corresponding in vivo parameter value employed
in the underlying equations of a selected physiological model
(e.g., human GI tract). The adjustment parameters are used to build
the correlation between the in vitro and in vivo situations, and in
vivo (species 1) to in vivo (species 2). These parameters make
adjustments to the equations governing the flow of drug and/or
calculation of parameters. Generally, the parameters are geometric
scaling parameters, as exemplified by the general equations
described below for a GI tract simulation model of the invention.
This aspect of the invention permits modification of existing
physiologic-based pharmacokinetic models as well as development of
new ones so as to enable their application for diverse compound
data sets.
[0144] The adjustment parameters of the PK tool and method of the
invention are obtainable from iterative rounds of simulation and
simultaneous "adjustment" of one or more empirically derived
absorption parameters (e.g., physiological parameters for different
anatomical segments) until the in vitro data from a given type of
assay (e.g., Caco-2 cell data) can be used in the model to
accurately predict in vivo absorption in the system of interest
(e.g., human GI). In particular, the adjustment parameters are
obtained by a stepwise selective optimization process that employs
a curve-fitting algorithm that estimates the change required in a
value assigned to an initial absorption parameter of a
developmental physiological model in order to change an output
variable corresponding to the simulated rate, extent and/or
concentration of a test sample at a selected site of administration
for a mammalian system of interest. The curve-fitting algorithm can
be regression- or stochastic-based. For example, linear or
non-linear regression may be employed for curve fitting, where
non-linear regression is preferred. Stepwise optimization of
adjustment parameters preferably utilizes a concurrent approach in
which a combination of in vivo pharmacokinetic data and in vitro
data for a diverse set of compounds are utilized simultaneously for
fitting with the model. A few parameters of the developmental
physiological model are adjusted at a time in a stepwise or
sequential selection approach until the simulated absorption
profiles generated by the physiological model for each of the
training/validation compounds provides a good fit to empirically
derived in vivo data. An example of this approach is depicted in
FIGS. 10 and 26. Utilization of adjustment parameters permits
predictability of diverse data sets, where predictability ranges
from a regression coefficient (r.sup.2) of greater than 0.40, 0.45,
0.50, 0.55, 0.60, 0.65, 0.60, 0.65, 0.70, or 0.75 for 80% of
compounds in a compound test set having a diverse range of dose
requirements and a diverse range of permeability, solubility and
transport mechanisms. The preferred predictability ranges from a
regression coefficient (r.sup.2) of greater than 0.60, with a
regression coefficient (r.sup.2) of greater than 0.75 being more
preferred, and greater than 0.80 being most preferred. Adjustment
parameters utilized for in vivo to in vitro prediction (e.g. dog to
human) employs the same basic approach.
[0145] The regional correlation parameters of the PK tool include
constants or ranges of constants that are utilized to estimate a
selected parameter value of a first segment of the mammalian system
under investigation when that value is not supplied by the user.
The model performs this estimation by utilizing a
function/transformation algorithm (e.g., utilizing polynomial,
exponential, logarithm, or any other variety of transformation
approaches) in which (1) regional correlation parameter values, and
(2) one or more values for the parameter that is supplied by the
user for a second segment of the mammalian system, are utilized to
estimate the value for the first segment. The regional correlation
parameters may be empirically derived values or adjustment
parameter values for various segments of the mammalian system of
interest such as for permeability. A preferred regional correlation
approach employs a polynomial-based correlation. The polynomial is
based on the particular parameter to be estimated. The regional
correlation is performed by logic function of the model, which when
activated utilizes the function/transformation algorithm to perform
the estimation. The regional correlation logic function of the
model is activated when a value is missing for the selected
parameter. The estimated value(s) are then utilized as input
variables for the particular parameter in question. The model then
proceeds by employing the estimated value for subsequent
simulation. Various regional correlation parameters can be used,
such as permeability, solubility, dissolution rate, transport
mechanism and the like. The preferred correlation parameters are
for permeability. This permits the PK tool of the invention to
predict absorption of a test sample from minimal input permeability
values, such as when the simulation model is a GI tract simulation
model and when cell-based assays are employed to provide
permeability data corresponding to a given GI segment (e.g., Caco-2
cells and colon).
[0146] The above described methodology for in vivo prediction from
in vitro input also is followed for in vivo prediction for a first
species of mammal from in vivo input data derived from a second
species of mammal.
[0147] Since the parameter values are specific for a given
physiological model (e.g., GI model-parameters, Ocular
model-parameters, Blood-Brain-Barrier-parameters, etc.), parameter
values are chosen accordingly. These values are obtainable de novo
from experiments or from the literature, and adjustment parameters
and regional correlation parameters derivable therefrom. The
preferred values are based on a diverse collection of
training/validation compounds for which in vivo pharmacokinetic
data is available.
[0148] The various physiological models also may reside in a
database, in part or in whole, and may be provided in the database
with or without the initial parameter values. The database will
preferably provide the differential equations of the model in a
compartment-flow data structure that is readily portable as well as
executable by the simulation engine.
[0149] An integrated physiological model corresponding to the GI
tract of a mammal constructed using STELLA.RTM. and the
above-described methodology is illustrated in FIGS. 24-25, and
29-39. An example of information provided by the database is
illustrated in Appendix 4 for the gastrointestinal model depicted
in FIGS. 24-25 and 29-39.
[0150] A physiologic-based simulation model of the PK tool and
method of the invention may optionally include a
training/validation model. This aspect of the invention can be used
for determining whether the model is specific and accurate with
respect to compounds of known membrane transport mechanism (e.g.,
passive transcellular, passive paracellular, transporter involved
for absorption and secretion) and/or with respect to known drug
solubility/dissolution rate limitations.
[0151] A validation model can be linked to the physiological model
of the invention as illustrated in FIG. 11. The linked system is
then run to access the specificity and accuracy computed values for
rate and extent of absorption. These values are then compared to
empirically measured plasma values. If computed values fall outside
of an acceptable range the model can be reevaluated for these
compounds and adjustments made to the model.
[0152] Data Acquisition:
[0153] Input data utilized to generate an absorption profile for a
test sample include permeability and solubility parameters, and
optionally transport mechanism and dissolution parameters. Input
data can be generated de novo following any number of techniques,
or obtained from public or existing sources where available. The
input data can be derived from chemical, and/or biological assays
as well as theoretical predictions. By way of example, the in vitro
assays may employ artificial (synthetic) or naturally occurring
biological preparations. This includes chemical, cell and/or tissue
preparations. Assays for generating input data involve screening a
plurality of test samples containing isolated compounds and/or
isolated mixtures of compounds per test sample in an assay
characterized by measurement of (1) permeability and optionally
transport mechanism for a test sample; and (2) solubility and
optionally dissolution for a test sample. Methods and materials for
performing the assays are based on the selected route of
administration, the associated barrier(s) to absorption and
proposed sampling site(s). For instance, if oral delivery is
proposed for simulation and an initial sampling site is selected to
be the portal vein (so as to isolate gastrointestinal absorption
events from hepatic metabolism) then the input data is collected
from an in vitro assay that best approximates the luminal barrier
and segmental physiology of the gastrointestinal tract.
[0154] Examples of some common cell and tissue sources for
permeability and transport mechanism assays for a selected route of
administration are provided below in Table 1.
1TABLE 1 Permeability and Transport Mechanism. Route/Tissue Cell
Culture Oral/Intestinal Caco-2 cells HT-29 cells T84 cells
Intestinal epithelial cells (IEC) SV40 T Immortalized cells Organ
culture/co-culture Primary culture Inhalation/Nasal SV40 T
immortalized cells Primary culture Ocular/Corneal RCE1 cells
Primary cultures SV40 T immortalized cells Oral-Buccal/Cheek
Primary cultures Topical/Transdermal HaCat cells
Primary/co-cultures IV/Hepatic Hepatic carcinoma cell lines Primary
cultures Co-cultures SV40 T immortalized cells IV/Blood Brain
Barrier Primary culture SV40 immortalized cells
[0155] Examples of some common parameters for solubility and
dissolution assays for a given route of administration are provided
below in Table 2.
2TABLE 2 Solubility and Dissolution Parameters.
Route/Anatomy/Physiology In vitro Parameters Oral Gastrointestinal
(GI) pH tract Temperature Stomach Concentration of test sample
Duodenum Volume Jejunum Osmotic pressure Ileum Admixing conditions
Colon Physiologic Fluid/Buffer/solvent system Buccal/Sublingual
Mouth Excipients Cheek Other Additives Tongue Test chamber
composition Rectal Lower GI tract Colon Rectum Parenteral Skin
Muscles Veins Aerosol Respiratory system Nose Lungs Mouth
Transdermal Skin Topical Ear
[0156] In vitro and in vivo techniques for collecting permeability
and transport mechanism data using cell- and/or tissue-based
preparation assays are well known in the art (Stewart et al.,
Pharm. Res. (1995) 12:693-699; Andus et al., Pharm. Res. (1990)
435-451; Minth et al., Eur. J. Cell. Biol. (1992) 57:132-137; Chan
et al., DDT 1(11):461-473). For instance, in vitro assays
characterizing permeability and transport mechanisms include in
vitro cell-based diffusion experiments and immobilized membrane
assays, as well as in situ perfusion assays, intestinal ring
assays, intubation assays in rodents, rabbits, dogs, non-human
primates and the like, assays of brush border membrane vesicles,
and everted intestinal sacs or tissue section assays. In vivo
assays for collecting permeability and transport mechanism data
typically are conducted in animal models such as mouse, rat,
rabbit, hamster, dog, and monkey to characterize bioavailability of
a compound of interest, including distribution, metabolism,
elimination and toxicity. For high-throughput screening, cell
culture-based in vitro assays are preferred. For high-resolution
screening and validation, tissue-based in vitro and/or mammal-based
in vivo data are preferred.
[0157] Cell culture models are preferred for high-throughput
screening, as they allow experiments to be conducted with
relatively small amounts of a test sample while maximizing surface
area and can be utilized to perform large numbers of experiments on
multiple samples simultaneously. Cell models also require fewer
experiments since there is no animal variability. An array of
different cell lines also can be used to systematically collect
complementary input data related to a series of transport barriers
(passive paracellular, active paracellular, carrier-mediated
influx, carrier-mediated efflux) and metabolic barriers (protease,
esterase, cytochrome P450, conjugation enzymes).
[0158] Cells and tissue preparations employed in the assays can be
obtained from repositories, or from any higher eukaryote, such as
rabbit, mouse, rat, dog, cat, monkey, bovine, ovine, porcine,
equine, humans and the like. A tissue sample can be derived from
any region of the body, taking into consideration ethical issues.
The tissue sample can then be adapted or attached to various
support devices depending on the intended assay. Alternatively,
cells can be cultivated from tissue. This generally involves
obtaining a biopsy sample from a target tissue followed by
culturing of cells from the biopsy. Cells and tissue also may be
derived from sources that have been genetically manipulated, such
as by recombinant DNA techniques, that express a desired protein or
combination of proteins relevant to a given screening assay.
Artificially engineered tissues also can be employed, such as those
made using artificial scaffolds/matrices and tissue growth
regulators to direct three-dimensional growth and development of
cells used to inoculate the scaffolds/matrices.
[0159] Epithelial and endothelial cells and tissues that comprise
them are employed to assess barriers related to internal and
external surfaces of the body. For example, epithelial cells can be
obtained for the intestine, lungs, cornea, esophagus, gonads, nasal
cavity and the like. Endothelial cells can be obtained from layers
that line the blood brain barrier, as well as cavities of the heart
and of the blood and lymph vessels, and the serious cavities of the
body, originating from the mesoderm.
[0160] One of ordinary skill in the art will recognize that cells
and tissues can be obtained de novo from a sample of interest, or
from existing sources. Public sources include cell and cell line
repositories such as the American Type Culture Collection (ATCC),
the Belgian Culture Collections of Microorganisms (BCCM), or the
German Collection of Microorganisms and Cell Cultures (DSM), among
many others. The cells can be cultivated by standard techniques
known in the art.
[0161] Preferred assays for collecting permeability data utilize
devices and methods that measure change in resistance or
conductivity of a membrane system by ion flux. Any device suitable
for such studies can be employed. These include voltage-clamp type
devices and methods that employ either cell cultures or precision
tissue slices. Diffusion chamber systems utilizing cultured cells
grown on permeable supports to measure permeability are preferred.
More preferred devices are readily adapted for high-throughput and
automated screening. Examples of such devices are known and
exemplified in U.S. Pat. No. 5,599,688; WO 96/13721; and WO
97/16717. These devices also can be adapted for examining transport
mechanisms. As can be appreciated, however, measurement of
resistance, conductivity and/or ion flux is not required to
determine permeability of compounds. Many other techniques are
available and can be employed in the invention. For instance,
permeability data also may be predicted using theoretical models to
approximate this parameter, for example, from SAR/QSAR (e.g., log
P, molecular weight, H-bonding, surface properties).
[0162] Transport mechanism of a test sample of interest can be
determined using cell cultures and/or tissue sections following
standard techniques. These assays typically involve contacting
cells or tissue with a compound of interest and measuring uptake
into the cells, or competing for uptake, compared to a known
transport-specific substrate. These experiments can be performed at
short incubation times, so that kinetic parameters can be measured
that will accurately characterize the transporter systems, and
minimize the effects of non-saturating passive functions. (Bailey
et al., Advanced Drug Delivery Reviews (1996) 22:85-103); Hidalgo
et al., Advanced Drug Delivery Reviews (1996) 22:53-66; Andus et
al., Pharm. Res. (1990) 7(5):435-451). For high-throughput
analyses, cell suspensions can be employed utilizing an automated
method that measures gain or loss of radioactivity or fluorescence
and the like such as described in WO 97/49987.
[0163] In a preferred embodiment, transport mechanism is determined
using high-throughout transporter screening cell lines and assays.
In this aspect of the invention a cell line is selected and/or
manipulated to over-express one or more transporter proteins,
and/or enzymes. The cells are then used to rapidly identify the
mechanism(s) by which a compound is transported across the
physiological barrier of interest. Transporters of interest
represent the basic categories of transport including uptake and
efflux transporters. These transporters aid in the movement of
materials in biological systems, into and out of cells and across
cellular layers. Natural combination(s) of enzyme(s) and
transporter(s) also can provide the basis of a high-throughput
transport mechanism screening assay. For instance, certain enzymes
or transporters require secondary enzymes or transporters to
function in a normal physiological mode, i.e., cytochrome P4503A is
co-regulated with P-glycoprotein. These proteins share the same
substrate and their genes are co-regulated. Thus multiple
artificial combination(s) of transporter(s) and enzyme(s) can be
employed for characterizing transport mechanism of a test sample of
interest. Examples of possible combinations of a transporter and/or
enzyme in a host cell of interest include cell-transporter-enzyme,
cell-transporter, cell-enzyme, cell-enzyme-enzyme, and
cell-transporter-transporter. Examples of transporters that can be
used to transfect the host cell of interest include peptide
transporters (PepT1), amino acid transporters, organic cation
transporters (OCT1), organic anion transporters, nucleotide
transporters (N1, N2, N3, ES, EI), glucose transporters (SGLT1,
GLUT 1 through GLUT 7), monocarboxylate transporters (MCT1), and
multi-drug transporters (LRP, MDR, MRP, PGP). Examples of enzymes
that can be used to transfect the host cell are Phase I and II
enzymes, cytochrome P450, 3A, 2D and the like.
[0164] Nucleic acid and/or amino acid sequences for
transporters/enzymes can be identified in various genomic and
protein related databases. Examples of publicly accessible
databases include GenBank (Benson et al., Nucleic Acids Res
(1998)26(l):1-7; USA National Center for Biotechnology Information,
National Library of Medicine, National Institutes of Health,
Bethesda, Md., USA), TIGR Database (The Institute for Genomic
Research, Rockville, Md., USA), Protein Data Bank (Brookhaven
National Laboratory, USA), and the ExPASy and Swiss-Protein
database (Swiss Institute of Bioinformatics, Genve,
Switzerland).
[0165] Any number of known techniques can be used to prepare
nucleic acid encoding a transporter(s) and/or enzyme(s) of
interest. To express a target protein in a host cell the nucleotide
sequence coding for the polypeptide is inserted into an appropriate
expression vector, i.e., a vector that contains the necessary
elements for the transcription and translation of the inserted
coding sequence. The host cell line can be stably or transiently
transfected by methods known in the art. Examples of transient
transfection methods include calcium phosphate, electroploration,
lipofectamine, and DEAE dextran. A cell line can be stably
transfected using methods known in the art such as calcium
phosphate. In addition, the host cell can be infected with a
retrovirus containing a target protein of interest, resulting in
stable expression of the desired target protein. Host cells that
express the target gene product can be identified by standard
techniques. These include, but are not limited to, detection of the
protein as measured by immunoprecipitation and Western blot
analysis or by measuring a specific biological response.
[0166] For synthesis in a cell, a target transporter/enzyme protein
can be generated by standard techniques. Cells that naturally
express a target protein can be employed. Transfection and
transformation of a host cell with DNA encoding a protein of
interest also can be used. For example, a polymerase chain reaction
(PCR) based strategy may be used to clone a target DNA sequence
encoding all or part of a target membrane polypeptide of interest.
(See, e.g., "PCR Cloning Protocols: From Molecular Cloning to
Genetic Engineering," B. A. White, ed., Humana Press, Methods in
Molecular Biology, Vol. 67, 1997). For example, PCR can be used for
cloning through differential and subtractive approaches to cDNA
analysis, performing and optimizing long-distance PCR, cloning
unknown neighboring DNA, and using PCR to create and screen
libraries. PCR also can be used to introduce site-specific and
random mutations into DNA encoding a target protein of
interest.
[0167] For general cloning purposes, complementary and/or
degenerate oligonucleotides corresponding to conserved motifs of
the target membrane polypeptide may be designed to serve as primers
in a cDNA and/or PCR reaction. Templates for primer design can be
obtained from any number of sources. For example, sequences,
including expressed sequence tags (ESTs) can be obtained from
various databases, such as GenBank, TIGR, ExPASy and Swiss-Protein
databanks. Homology comparisons performed using any one of a number
of alignment readily available programs that employ search engines
to find the best primers in a sequence based on various algorithms.
Any number of commercially available sequence analysis packages,
such as Lasergene, GeneWorks, DNASIS, Gene Jockey II, Gene
Construction Kit, MacPlasmap, Plasmid ARTIST, Protein Predictor,
DNA/RNA Builder, and Quanta. (See, e.g., "Sequence Data Analysis
Guidebook," Simon R. Swindell, ed., Humana Press, 1996). The
information can be used to design degenerate primers,
nested/multiplex primers, site-directed mutagenesis, restriction
enzyme sites etc. Primers can be designed from homology
information, and computer programs can be used for primer design as
well. Examples include "Primer Premier 4.0" for automatic primer
selection (CloneTech, Inc.). The amplified cDNA and/or PCR fragment
may be used to isolate full-length clones by radioactive or
non-radioactive labeling of the amplified fragment and screening a
library.
[0168] Alternatively, transporter/enzyme DNA cloned from one source
may be utilized to obtain a corresponding DNA sequence from other
sources. Specifically, a genomic and/or cDNA library constructed
from DNA and/or RNA prepared from a cell known or expected to
express the target transporter/enzyme may be used to transform a
eukaryotic or prokaryotic host cell that is deficient in the
putative gene. Transformation of a recombinant plasmid coding for
the protein into a deficient host cell would be expected to provide
the cell with a complement product corresponding to the protein of
interest. In some cases, a host cell can be selected to express a
particular phenotype associated with the target polypeptide and
thus may be selected by this property. For a review of cloning
strategies which may be used, see e.g., Sambrook et al., 1989,
Molecular Cloning, A Laboratory Manual, Cold Springs Harbor Press,
New York; and Ausubel et al., 1989, Current Protocols in Molecular
Biology, Green Publishing Associates and Wiley Interscience, New
York.
[0169] To express a target transporter/enzyme in a host cell the
nucleotide sequence coding for the protein, or a functional
equivalent for modular assembly as described above, is inserted
into an appropriate expression vector, i.e., a vector which
contains the necessary elements for the transcription and
translation of the inserted coding sequence. Host cells containing
the coding sequence and that express the target gene product may be
identified by standard techniques. For example, these include but
are not limited to DNA-DNA or DNA-RNA hybridization; the presence
or absence of "marker" gene functions; assessing the level of
transcription as measured by the expression of mRNA transcripts in
the host cell; and detection of the gene product as measured by
immunoassay or by its biological activity.
[0170] Once a clone producing the target transporter/enzyme is
identified, the clone may be expanded and used to over express the
protein(s). If desired, the proteins may be purified using
techniques well-known in the art including, but not limited to
immunoaffinity purification, chromatographic methods including high
performance liquid chromatography or cation exchange
chromatography, affinity chromatography based on affinity of the
polypeptide for a particular ligand, immunoaffinity purification
using antibodies and the like. The purified proteins can then be
bound to an artificial membrane matrix and utilized for assessing
interaction of compounds to the transporter/enzyme of interest.
[0171] Some commonly used host cell systems for expression of
transport proteins and enzymes include E. coli, Xenopus oocytes,
baculovirus, vaccinia, and yeast, as well as many higher eukaryotes
including transgenic cells in culture and in whole animals and
plants. (See, e.g., G. W. Gould, "Membrane Protein Expression
Systems: A User's Guide," Portland Press, 1994, Rocky S. Tuan, ed.;
and "Recombinant Gene Expression Protocols," Humana Press, 1996).
For example, yeast expression systems are well known and can be
used to express and recover target transporter/enzyme systems of
interest following standard protocols. (See, e.g., Nekrasova et al,
Eur. J Biochem. (1996) 238:28-37; Gene Expression Technology
Methods in Enzymology 185: (1990); Molecular Biology and Genetic
Engineering of Yeasts CRC Press, Inc. (1992); Herescovics et al.,
FASEB (1993) 7:540-550; Larriba, G. Yeast (1993) 9:441-463;
Buckholz, R. G., Curr Opinion Biotech (1993) 4:538-542; Mackett, M,
"Expression of Membrane Proteins in Yeast Membrane Protein
Expression Systems: A Users Guide," pp. 177-218, Portland Press,
(1995).
[0172] For high-resolution screening and validation, tissue-based
assays may be employed to characterize transport mechanisms. For
example, of the cytochrome P450 superfamily, CYP3A enzymes
represent the most abundant isoforms in the liver and they are
responsible for the metabolism of compounds of diverse chemical
structure. The uptake of a compound into hepatocytes can be
mediated by passive or carrier processes. Once in the parenchymal
cell of the liver, the drug can be metabolized or bind to
intracellular proteins. The drug or its metabolite(s) may return to
the circulation or exit from the hepatocyte into the bile
canaliculus, again by passive or carrier-mediated transport, before
secretion in bile. Experimental systems have been devised to study
these processes in isolation. Examples of such systems include
isolated perfused rat liver (IPRL), and bile duct cannulated (BDC)
rat models. (Chan et al., DDT (1996) 1:461-473).
[0173] Tissue from transgenic animals designed to express
particular transport properties in one or more particular tissues
also may be utilized to characterize transport mechanisms. In this
aspect of the invention, an animal can be genetically manipulated
to express or not express one or more specific proteins in a tissue
of interest, e.g. transporter protein in duodenum tissue. Tissue
from the genetically engineered animal can then be used to examine
transport mechanisms in a tissue-based assay. Transgenic animal
methodologies are well known (Gordon et al., Hum. Cell (1993)
6(3):161-169; and Jaenisch, R., Science (1998) 240:1468-1474).
[0174] Artificially engineered tissue also can be used for
permeability assays, such as tissues generated ex vivo for use as
skin grafts, transplants, and the like. Such tissues can be
obtained using standard techniques. See, for example, U.S. Pat.
Nos. 5,759,830; 5,770,193; and 5,770,417.
[0175] Solubility and dissolution data can be obtained in an in
vitro assay by testing each sample of interest in an appropriate
physiologic fluid/buffer system that best approximates the
particular physiological system selected as the barrier to
absorption. A solubility profile is a plot of solubility of a test
sample at various physiological conditions. As an example, the
natural pH environment of the gastrointestinal tract varies from
acidic in the stomach to slightly alkaline in the small intestine
and fluid composition for each segment may vary as well. The
solubility profile provides an estimation of the completeness of
dissolution of a test sample in a particular physiological
compartment or anatomical entity. In this instance, a panel of test
wells each having different pHs and physiological fluid composition
can be employed to generate a solubility profile for each test
sample. Solubility and dissolution data can also be predicted using
theoretical models to approximate these values, for example, from
SAR/QSAR information.
[0176] In vitro dissolution assays measure the rate and extent of
dissolution of a test sample in an aqueous solution. Various
parameters are considered when performing a dissolution assay and
are well known in the art. These parameters include size of the
experimental vessel, amount of agitation and nature of the stirrer,
temperature and nature of the dissolution medium, pH, viscosity,
and design of the dissolution apparatus. Standard methods known in
the art for measuring dissolution include rotating basket, paddle,
rotating bottle, flow-through dissolution, intrinsic dissolution,
and peristalsis methods. These methods can be adapted and used as a
guide for high-throughput solubility and dissolution testing.
[0177] For high-throughput collection of solubility and dissolution
data, automated methods of solid and liquid handling are employed.
This method involves addition of samples to a multi-well or
multi-tube/plate system. The data associated with these
tubes/plates, such as physiologic fluid/buffer system, volume,
concentration, pH and tube/plate maps, is transferred into an
inventory system. The inventory system generates codes containing
updated information pertaining to the aliquoting, diluting, or
pooling methods applied to the original tubes/plates. Tasks created
in the database are then carried out physically in coded
tubes/plates. Aliquots are then distributed to designated screen
sites. After testing, the solubility profiles are generated and
ported to a database for access and analysis.
[0178] Properties in addition to absorption that can be utilized as
input into the PK tool and method of the invention when adapted
with the appropriate compartments include metabolism, distribution,
and elimination, and optionally toxicity. As with absorption,
assays to characterize the relevant data are based on the selected
route of administration. Metabolism or biotransformation refers to
the biochemical transformation of a compound to another chemical
form. The biotransformation process typically results in a
metabolite that is more polar (water-soluble) than the original
parent molecule.
[0179] Most tissues have some metabolizing capacity but the liver
is by far the most important organ, on the basis of size if not
always concentration of target compound metabolizing enzyme. Phase
I reactions are defined as those that introduce a functional group
to the molecule and phase II reactions are those that conjugate
those function groups with endogenous moieties.
[0180] Since metabolism is a drug clearance process, metabolism of
a compound contributes to elimination of the compound. Thus,
compounds can be tested for metabolism in order to generate input
data that considers disposition of a test compound after or
concurrent with administration using standard techniques known in
the art. (See, e.g., Sakuma & Kamataki, Drug metabolism
research in the development of innovative drugs, In: Drug News
& Perspectives (1994) 7 (2):82-86).
[0181] Metabolism assays for high-throughput screening preferably
are cell-based (cells and cellular preparations), whereas high
resolution screening can employ both cell and tissue-based assays.
In particular, test samples from compound libraries can be screened
in cell and tissue preparations derived from various species and
organs. Although liver is the most frequently used source of cells
and tissue, other human and non-human organs, including kidney,
skin, intestines, lung, and blood, are available and can be used to
assess extra-hepatic metabolism. Examples of cell and tissue
preparations include subcellular fractions (e.g., liver S9 and
microsomes), hepatocytes (e.g., collagenase perfusion, suspended,
cultured), renal proximal tubules and papillary cells, re-aggregate
brain cells, bone marrow cell cultures, blood cells,
cardiomyocytes, and established cell lines as well as precision-cut
tissue slices.
[0182] Examples of in vitro metabolism assays suitable for
high-throughput screening include assays characterized by
cytochrome P450 form-specific metabolism. These involve assaying a
test compound by P450 induction and/or competition studies with
form-specific competing substrates (e.g., P450 inhibitors), such as
P450 enzymes CYP1A, 3A, 2A6, 2C9, 2C19, 2D6, and 2E1. Cells
expressing single or combinations of these or other metabolizing
enzymes also may be used alone or in combination with cell-based
permeability assays. A high-throughput cell-based metabolism assay
can include cytochrome P450 induction screens, other metabolism
marker enzymes and the like, such as with measurement of DNA or
protein levels. Suitable cells for metabolism assays include
hepatocytes in primary culture. Computer-implemented systems for
predicting metabolism also may be employed.
[0183] For distribution and elimination data, in vitro assays can
be performed to assess protein binding to a test compound, since
protein binding can affect compound distribution and elimination.
In general, it is free compound that diffuses into cells and
tissues. Binding can be classified as restrictive or permissive
with regard to elimination, or quantitatively defined in terms of
affinity. Affinity of the binding is defined as low or high when
reversible, or more unusually when irreversible binding occurs. The
biological half-life of a test compound will increase due to its
interaction with a protein. Usually, the higher the affinity the
lower the elimination that may be observed. Albumin is by far the
most frequent contributors to plasma protein binding since it
comprises about one half of the total plasma proteins. The al-Acid
glycoprotein also plays an important role in the protein binding of
a compound since it has an affinity for bases (many drugs are weak
bases). It is an acute phase reactant and its concentration rises
in inflammatory processes, malignant disease and stress.
Lipoproteins (HDL, LDL or VLDL) bind drugs that are highly
liposoluble and a fairly specific ligand-protein interaction occurs
between certain steroids and gamma globulins. Thus, in vitro
protein binding assays that employ one or more of albumin, al-acid
glycoprotein, lipoprotein, steroid and gamma globulins may be
utilized to collect distribution and elimination data that can be
utilized for further data collection.
[0184] Similarly, toxicity of a test compound may also be assayed
and used to generate relevant toxicity data for a test compund. Any
number of techniques in the art may be employed for this purpose.
Preferred methods are in vitro. Examples include determination of
toxicity mechanisms, determination of cytotoxic potentials in cell
and tissues of target organs, estimation of therapeutic indices
from in vitro data, cytotoxicity screening of closely related drug
compounds in cells from the same mammal or from different species,
detection and quantification of peroxisome proliferation, screening
of agents to prevent or reverse cytotoxicity, and specialized
studies on target cells using co-incubation systems, e.g., red
blood cells and hepatocytes.
[0185] Toxicity assays may utilize any technique that provides a
toxicity parameter as an endpoint. For high-throughput screening,
cell based assays are preferred. This includes gene expression
(e.g., protein or nucleic acid based) enzymatic activity, and
morphology screens and the like. Examples of cell-based assays
include in vitro peroxisome proliferation studies, which can be
used to assay palmitoyl CoA-oxidation in primary hepatocyte
culture, with or without concurrent measurement of DNA or protein
levels. Cytotoxicity assays in primary cultures also can be
utilized, and include screening for cytotoxicity in hepatocytes or
renal proximal tubules, enzyme release (lactate dehydrogenase), and
MTT conversion (mitochondrial function) following standard
techniques. Computer-implemented SAR/QSAR models for predicting
toxicity also may be employed, such as when structural information
is available.
[0186] PK Tool and System Structure:
[0187] The PK tool and system of the invention has the structure
shown in FIG. 4. The I/O system provides the user's inputs to the
simulation model of the mammalian system of interest. The
simulation engine in turn computes one or more of the
bioavailability parameters of the compound in the context of one or
more physiologic-based segments of the mammalian system under
investigation. The output of the simulation engine is then provided
to the I/O system.
[0188] Operations of the PK tool and system are exemplified in
FIGS. 3 and 44-46. After start, the first block is the I/O block
(1), where the user enters the inputs and outputs to the system.
The I/O system includes I/O panels, for example graphical user
interfaces. This may include sub-panels depending on the selected
model (see, e.g. FIG. 47). The I/O system may optionally include
one or more databases of simulation models and/or parameters for a
given simulation model that the user may access as illustrated in
FIG. 45. The PK tool and system starts with the user inputs and
then computes and displays the results in the output space. The
input and output space can be selected, e.g., by toggling, or by a
menu. It is to be understood that on-line helps also are available
to give a user information, and to guide the user through the PK
tool and system user interface.
[0189] For input, the Menu function presents various choices to the
user. These choices include dose, permeability, and solubility
among others. The user then enters the relevant values
corresponding to a given physiological segment of the selected
mammalian system in question. Depending on the simulation model
that the user chooses, the Menu function will provide options for
data input, such as pH, transit time, run time, and formulation
release rate.
[0190] The Menu function also presents various choices to the user
after the results for a simulation have been obtained. The choices
open to the user include one or more of the functions "Rate of
Absorption," "Extent of Absorption," "Concentration," "Print
Graph," "Print Table," and "Quit" among others.
[0191] For predicting absorption parameters, input of the data is
the first operation that the PK tool and system of the invention
performs when activated. In this operation, the user enters the
appropriate value of each input variable into the input panel in a
form readable or convertible by the system to a readable form and
obtains complete results in the output panel. Alternatively, the PK
tool and system can be adapted to receive structural information
that the system, or a separate interfaced system converts to the
relevant input parameter values. For this function the user inputs
the compound structure in a form readable or convertible by the
system to a readable form. This includes standard chemical
formulas, chemical names, SMILE strings, as well as two-dimensional
and/or three-dimensional structures.
[0192] After the user inputs the initial data, the Start Simulation
function is selected. In the simulation function, the simulation
engine is activated. The user may then choose to invoke the Stop
Simulation function, to terminate the simulation, or allow the
simulation engine to proceed with until a user specified or system
default time point is reached. The user may then view, print, save
and/or export then results using output functions, including
printing of the I/O panel. This includes numerical, tabular, and
graphical formats. These options are selected by the user through
the Menu function.
[0193] The Quit function exits the PK tool and system. One aspect
of the output functions and the Quit function is to save the
generated information in a format that allows them to be an input
to other programs, such as the SAR or QSAR CAD program.
[0194] Forward Mode Operation of the PK Tool:
[0195] In the forward mode operation mode, the user enters the
input data, and the PK tool reacts as described above. In one
embodiment, the PK tool displays a numerical representation or
graphic of the test compound or selected PK profile thereof. Also
displayed are parameters that can effect fate of the compound in
one or more compartments of the mammal, e.g., the dose,
formulation, pH, fluid volume, fluid absorption (fluid secretion),
dissolution rate, cumulative dissolution, transit, pH-dependent
solubility and dissolution and the like. Other variables may also
be available, e.g., through a data box.
[0196] The forward mode operation of the simulation engine displays
the resulting PK parameters, such as absorption. Changing any
parameter causes recalculation of the PK quantities, invoking the
the simulation engine and its associated simulation model. The
forward mode operation provides either, or both, a display or a
printout of the PK parameters for a test compound.
[0197] Backward Mode Operation of the PK Tool:
[0198] In backward mode operation of the PK tool, the user is
allowed to assess formulations for a compound. In this aspect of
the invention, the user specifies the required absorption profile,
or absorption parameter for a compound. The tool then generates the
formulation release rates for the compound that meets the
requirements. The user can then compare the solution set, against
previously qualified compounds and formulation designs drawn from a
database and new, unqualified designs created by the tool and
method of the invention.
[0199] Predictability:
[0200] The PK tool and method of the invention permit a high level
of accuracy in predicting bioavailability of molecules from the
following four classes of compounds: a) passive transcellular; b)
passive paracellular; c) transcellular transporter involved; d)
apically recycled. The evaluation is based on the difference
between bioavailability values predicted by the model and known
bioavailability values. For example, conformation of predictability
for human GI absorption values for passive transcellular molecules
is evaluated with dissolution rate limitations and solubility
limitations. If the computed values fall outside of an acceptable
range (r.sup.2>0.75 predictability), the PK model is reevaluated
for these compounds and adjustments made to the model. Similarly,
absorption measures that deviate from known values are reevaluated
and appropriate modifications made to the model (e.g. iterative
process).
[0201] The PK model can be used to predict bioavailability in a
mammal using dose (actual or estimated) and various input data.
Examples include (1) permeability data alone; (2) permeability data
together with solubility and dissolution data; (3) permeability
data together with animal data; and/or (4) permeability, animal and
human clinical data. Validation of the model is defined as follows,
where greater than 80% of the compounds tested will fall within the
following prediction criteria.
[0202] 1. Predictability of the PK tool using permeability data
alone with limits for dose and elimination rate (r.sup.2>0.75
predictability).
[0203] 2. Predictability of the PK tool using permeability and
solubility data along with limits for dose and elimination rate
(r.sup.2>0.75 predictability).
[0204] 3. Predictability of the PK tool using permeability data
together with animal data for pharmacokinetics together with limits
for dose (r.sup.2>0.85 predictability).
[0205] 4. Predictability of the PK tool using permeability and
animal or human IV data to predict absorption values for molecules
with solubility limitations (r.sup.2>0.85 predictability).
[0206] The correlation coefficient can be calculated using data
from the predicted line from pharmacokinetic fitting as the
observed data points and as the predicted fit, and the output of
physiologic-based simulation model coupled to the systemic kinetics
for that compound. The prediction power of a given physiological
simulation model can be demonstrated by simulating the plasma
levels in compounds. Other methods can be utilized to assess the
predictive power of the model to achieve the same end result (i.e.,
evaluation of model performance).
[0207] The method and PK tool of the invention allows the drug
developer to go from a set of user inputs, to predicting the fate
of the compound in a mammalian system of interest, to selection of
a compound design input to a SAR or QSAR CAD tool, and to chemical
synthesis development, validation and high level drug development.
The PK tool and system may advantageously be interfaced with other
databases and/or systems. For example, the system may be built
around an expert system-database manager path. The menu can invoke
the on-line documentation, the database, and any member of the
expert system-database system.
[0208] The PK tool and method of the invention can be used to
predict the rate and extent of absorption of compounds as well as
regional concentrations relative to one or more selected sampling
sites across a physiological barrier of a mammalian system of
interest. The PK tool and method of the invention also can be used
in combination with prediction of additional bioavailability
parameters such as distribution, metabolism and elimination, as
well as toxicity. Thus this information can be used to supplement
and significantly reduce animal testing during pre-clinical
testing. The PK tool and method of the invention also are
particularly useful for screening compounds earlier in the drug
discovery process. For instance, the PK tool and method may be
employed in the screening and ranking of compounds before, during
and/or after receptor activity testing, thus increasing the odds of
selecting a lead compound that will survive clinical studies,
resulting in decreased development costs, faster approval time, and
consequent lower drug prices. This permits selection and ranking of
lead compounds that not only have optimal receptor activity, but
also exhibit optimal bioavailability.
[0209] The following Examples are intended to illustrate various
aspects of the invention and are not intended to limit the scope of
the invention.
EXAMPLES
Example 1
Introduction to Model Design and Development
[0210] A physiologic-based simulation model for predicting oral
absorption of a compound in a mammal from in vitro (e.g., tissue,
cell and SAR/QSAR) and in vivo data (e.g., human) was constructed
in two primary stages. The first stage involved development of a
mass-based multi-compartment simulation model (mass model), a
volume-based multi-compartment simulation model (volume model) and
an integrated mass-volume multi-compartment simulation model
(mass-volume model). These models were individually tested and
validated for five segments of the GI tract: the stomach, the
duodenum, the jejunum, the ileum, and the colon. The second stage
involved development of an integrated multi-compartment
physiological model of the GI tract (GI model). The models were
developed using a combination of in vitro data and in vivo
data.
[0211] A computer-based mathematical model development tool with a
graphical user interface was employed to design and construct the
initial simulation models. The computer program STELLA.RTM. was
selected as suitable for this purpose since it permitted
compartment model building and mathematical equation modification
and at each stage of the build, as well as calculation of flow
between compartments at user-specified time intervals (dt) with
user-specified input functions and values. An example of iconic
tools and description, as well as graphically depicted
compartment-flow models generated using STELLA.RTM. and their
relation to a conventional pharmacokinetic IV model is illustrated
in FIGS. 5-8.
Example 2
Compound Data Sets
[0212] Compound data sets for development, and thus building,
testing, training and validation of the models were obtained from
various sources including the literature and cell, tissue, animal
and human tests as described herein. The data sets included
relevant physiological parameters related to absorption of a
compound including GI tract related parameters (e.g., pH, initial
volumes, surface area, average transit time, volume transfer rates,
new water absorption etc.) and physicochemical compound related
parameters (e.g., dissolution, permeability, solubility etc.).
[0213] Data sets were selected for compounds that permitted
development and isolated testing and validation for each stage of
the build. Compounds suitable for this purpose were chosen as
follows. For the mass, volume and integrated mass-volume simulation
models, a candidate compound was chosen based on the premise that
the best candidate compound for model development would not be a
drug that is highly correlated pharmacokinetically between cell,
tissue, animal and humans, but one that is poorly correlated. That
is, a compound predicted to have high total absorption in humans
based on pre-clinical studies, but ultimately exhibited poor
absorption in humans when tested in clinical trials was chosen.
Additionally, a compound was selected that is not subject to
pre-absorptive or hepatic metabolism so as to isolate absorption
components of the models from pre-absorptive and metabolic factors.
Gancyclovir (9-(1,3-dihydroxy-2-propoxymethyl)guanine, monosodium
salt (DHPG) or Cytovene) was suitable for this purpose. Also,
significant animal and human clinical data was publicly available
for Gancyclovir (Jacobson et al., Antimicrobial Agents and
Chemotherapy, Vol. 31, No. 8, p. 1251-1254 (1987); New Drug
Application for Gancyclovir Sodium (Syntex, Inc. USA), obtained
from the Food & Drug Administration; Drew et al., New England
Journal of Medicine, (1995) 333:615-610; and Anderson et al.,
Clinical Therapeutics, (1995)17:425-432 (1995)).
[0214] For development and testing of the integrated GI model, a
set of training and testing lead drug compounds in various stages
of human clinical testing were selected. This test set included
compounds having diverse dosage requirements and ranges of
permeability, solubility, dissolution and transport mechanisms, as
shown below in Table 3.
3TABLE 3 Compound Test Set Mechanism of Compound Permeability
Solubility Dose Absorption .alpha.1 ++++ ++++ +++++ active .alpha.2
++ +++ +++++ paracellular .alpha.3 + + ++++ unclassified .alpha.4 +
++++ ++ transcellular .alpha.5 + +++ ++++ paracellular .alpha.6
++++ ++ ++++ transcellular .alpha.10 ++++ +++++ + transcellular
.beta.1 +++++ +++++ + transcellular .beta.2 ++++ ++ ++
transcellular .beta.3 + + +++ paracellular .beta.5 ++++ ++ +++
unclassified .beta.6 + +++++ +++ unclassified +++++ = greatest
value & + = lowest value
Example 3
Experimental Data Collection and Processing
[0215] Experimentally derived in vivo and in vitro data was
obtained as follows. To ensure quality data was used for training
and validation, experimental conditions were specific enough to
ensure proper data collection techniques, but flexible to allow
minor and insignificant variations in individual protocols. Data
sets used for model development included individual data points,
i.e., raw data, that was analyzed and processed by stepwise
regression analysis using a least squares minimization technique or
similar fitting tool. In particular, data processing for
permeability involved separation of compounds by absorption
mechanism and into training and validation sets. pH dependent
solubility profiles were interpolated to obtain complete profiles.
For dissolution, data points were fit to determine dissolution
rates. For human clinical data, data analysis and processing
employed a pharmacokinetic IV/PO model and weighted least-squares
regression analysis (See FIG. 18). The IV/PO model includes a
central compartment in equilibrium with a peripheral compartment, a
pre-systemic compartment re-circulated with the central compartment
and for input PO doses (error function input), a hepatic
compartment, as well as an IV dose and first-order elimination
compartment. The plasma sample is taken from the central
compartment, and the FDp sample from the hepatic compartment.
[0216] A. Human In vivo Data--Oral (PO)
[0217] Plasma levels following oral administration (PO) in humans
were used to determine the amount of compound input to the hepatic
vein (FDp) as a function of time. Plasma levels of drug in humans
following oral administration of drug solution or suspension after
an overnight fast were used as a data set. If no solutions or
suspensions were administered, formulated dosage form data were
used. The PO profiles included individual data points for each
patient enrolled in the study from the time of administration
through 24 hours to 32 hours after administration, along with
dosage. If multiple dose regimens were administered, plasma
profiles for all doses were used.
[0218] B. Human In vivo Data--Intravenous Administration (IV)
[0219] Plasma levels following intravenous administration (IV) in
humans were used to determine the amount of drug input to the
hepatic vein (FDp) as a function of time. IV profiles included
individual data points for each patient enrolled in the study from
the time of administration through 24 hours to 32 hours after
administration, along with the dose. If multiple dosage regimens
were administered, plasma profiles for all doses were used.
[0220] C. In vitro Permeability Data
[0221] In vitro permeability data was used to calculate drug fluxes
across various regions of the intestinal mucosa. This included
rabbit intestinal tissue from one or more of duodenum, jejunum,
ileum and colon, and Caco-2 cells. The mechanism of transport, such
as passive transcellular or paracellular, carrier-mediated
absorption, carrier-mediated secretion, or mixed mechanism, was
determined for several test compounds and permeabilities for each
mechanism and assessed as listed in Table 4. Protocols for
permeability assays are described in Example 4.
4TABLE 4 Transport mechanism permeabilities and parameters for each
GI region. Mechanism Permeabilities Parameters Passive
transcellular Apical to basolateral P.sub.e (AP to BL) Passive
paracellular AP to BL P.sub.e Carrier-mediated AP to BL without
K.sub.M, P.sub.c, and P.sub.m, absoption inhibition or P.sub.e at
entire concentration range Carrier-mediated AP to BL and BL to AP
P.sub.m, P.sub.c, and P.sub.m, secretion without inhibition or
P.sub.e at entire concentration range
[0222] D. Solubility Data
[0223] Solubilities of test compounds as a function of pH were
determined from pH 1.5 to 8.2 in increments of 0.1 pH units.
Protocols describing conditions for solubility determination are
found in Example 4. Alternatively, solubility at each pH unit from
1.5 to 8.0 was used, with a minimum of 5 data points at pH 1.5,
6.0, 6.5, 7.0, and 7.5. These solubilities were used to calculate
the amount of soluble compound available for absorption across the
intestinal mucosal barrier.
[0224] E. Dissolution Data
[0225] The dissolution of test compounds as a function of pH were
determined at pH 1.5, 6.0, 6.5, 7.0, and 7.5. Protocols describing
conditions for dissolution determination are found Example 4. The
dissolution of powdered compound, and alternatively,
dissolution/disintegration data for the formulated dosage form used
to collect oral plasma profiles were used. The dissolution data
were used with solubility data to calculate the amount of drug
available for absorption across the intestinal mucous within each
region of the intestine.
Example 4
Protocols for Data Collection
[0226] Provided below are detailed protocols utilized for
collecting and calculating data described in Example 3. These
protocols were employed to ensure the quality of the data provided
for development of the simulation models.
[0227] A. In vitro Permeability Protocols
[0228] 1. Diffusion Chambers
[0229] Permeability data is determined using intestinal tissue in
vertical diffusion chambers similar in design to NaviCyte 8X24 mm,
9 mm Low-volume, or 9 mm round tissue diffusion chambers. The
chamber system used maintains the tissue as well as the donor and
receiver buffers at 37.degree. C. Both the donor and receiver
buffers within the chamber are continuously mixed throughout the
experiment.
[0230] 2. Mathematical Calculations
[0231] Effective permeability (Pe) is calculated using Equation 2.
1 P e = V A C 0 C t ( Eq . 2 )
[0232] where V is the volume of the receiver chamber (ml), A is the
surface area available for diffusion (1.78 cm2 for 8X24 mm
chambers, 0.64 cm2 for 9 mm round and Low-volume chambers), C.sub.0
is the donor concentration, and dC/dt is calculated as the slope of
the regression line of the corrected receiver concentration (see
Sampling) v. time plot. Two conditions must be satisfied for this
equation to apply: (1) sink conditions in the receiver chamber,
i.e. the accumulated concentration, must be virtually zero when
compared to the donor concentration; and (2) the donor
concentration must be constant (C.sub.0) throughout the
experiment.
[0233] The parameters for carrier-mediated absorption and secretion
are calculated using Equation 3. 2 P e = P c 1 + C 0 K m + P m ( Eq
. 3 )
[0234] where Pc is the carrier-mediated permeability, Pm is the
passive permeability, Km is the affinity of the drug for the
carrier, and C.sub.0 is the donor concentration. Pc, Pm, and Km are
calculated using non-linear regression, Pe is calculated using
Equation 2, and C.sub.0 is given as part of the experimental
conditions. To obtain valid parameter values, Pe is determined for
a sufficient number of C.sub.0's to determine Km using Equation 3
(a minimum of 6 C.sub.0's is recommended ranging between the
analytical limit and the solubility limit). If Pe values are
provided, the variability of the mean as well as the number of
experiments performed for each concentration are provided to allow
accurate regression analysis.
[0235] 3. Experimental Conditions
[0236] a. Buffers
[0237] Experiments are performed in appropriate, non-cytotoxic,
physiological saline iso-osmotic buffers at pH 7.4
(basolateral/serosal side) or pH 6.5 (apical/mucosal side).
Preferred buffers are Ringer's buffer (pH 7.4), Ringer's with
glucose (pH 7.4), MES ringer's buffers (pH 6.5), or MES Ringer's
with glucose (pH 6.5) (Table 5).
5TABLE 5 Formulas for Ringer's buffer and Ringer's with glucose
buffer. MES Ringer's Ringer's buffer Ringer's with MES Ringer's
With glucose Chemical (mM) glucose (mM) Buffer (mM) (mM) KCI 5 5 5
5 Na.sub.2HPO.sub.4 1.15 1.15 -- -- Na.sub.2HPO.sub.4 0.3 0.3 -- --
NaHCO.sub.3 25 25 -- -- MgSO.sub.4 1.1 1.1 1.1 1.1 CaSO.sub.4 1.25
1.25 1.25 1.25 NaCI qs iso-osmotic qs iso-osmotic qs iso-osmotic qs
iso-osmotic MES -- -- 25 25 Glucose -- 25 -- 25 pH adjusted with 1
N HCI or 1 N NaOH
[0238] b. Sampling
[0239] Samples are collected from the receiver chamber beginning
once steady state has been achieved and continuing for at least 90
minutes. Four to six (preferred) samples are collected to allow
accurate determination of dC/dt (Equation 2). The volume removed
from the receiver chamber at each time point is replaced with
buffer containing no drug to maintain constant volume in the
receiver chamber. The dilution of the receiver concentration due to
the addition of buffer is corrected during data analysis and Pe
calculation. The concentration may be corrected by: (1) adding the
mass removed at each sampling time to the mass removed from the
receiver chamber at all prior sampling times, by summing calculated
mass absorbed and adding to mass for sample calculation; and (2)
using Equation 4 (preferred). 3 1 X = - n k ( - 1 ) n ( S ) n - 1 n
( V ) ( Eq . 4 )
[0240] where the corrected receiver chamber concentration is
obtained by dividing the collected sample concentration by Equation
4 (1/X), S is the volume of sample withdrawn, V is the receiver
chamber volume, k is the sequential sample number, i.e., k=1 for
the first sample time, k=2 for the second sample time, k-3 for the
third sample time, etc., and .beta. is the corresponding number
from Pascal's triangle (Table 6).
6TABLE 6 Pascal's Triangle for determining .beta. coefficients.
Sample 1.sup.st term 2.sup.nd term 3.sup.rd term 4.sup.th term
5.sup.th term 6.sup.th term 1 1 2 1 1 3 1 2 1 4 1 3 3 1 5 1 4 6 4 1
6 1 5 10 10 5 1
[0241] Donor concentration (C.sub.0) is determined by sampling the
donor buffer containing the test compound with subsequent analysis
directly from the donor chamber, or from a stock solution of donor
buffer provided binding and absorption to the interior of the
chambers does not occur.
[0242] c. Intestinal Tissue
[0243] Rabbit intestinal tissue is used for permeability
experiments. During mounting of tissue onto chambers, intestinal
muscles are stripped off the mucosa and discarded. Care should be
taken to ensure integrity of the tissue. A minimum of three
chambers are used to determine P.sub.e values for each region,
concentration and compound. The mean P.sub.e and Standard Error of
the Mean are provided for each study.
[0244] d. Cell monolayers
[0245] Caco-2 cell monolayer Pe is determined in diffusion chambers
similar to NaviCyte Snapwell.TM. diffusion chambers and follow all
procedures described above except the recommended buffers are
Ringer's with glucose or MES Ringer's with glucose as listed in
Table 6.
[0246] Caco-2 cells are grown using DMEM media supplemented with
10% FBS, 5% PCN-STEP, and 1% NEAA under 95-100% humidity and 5%
CO.sub.2 at 37.degree. C. Cells are grown in flasks and the culture
split at 85-95% confluence. Snapwells.TM. are seeded at 65,000
cell/cm.sup.2 and used in the permeability experiment within 21-28
days post seeding to allow for differentiation.
[0247] 4. Determination of absorption mechanism
[0248] Absorption mechanism for a compound is determined by one of
the following methods. Determination of P.sub.e in both the
apical-basal (AB) to basal-lateral (BL) and BL to AB directions
using Equation 2, or determination of P.sub.e in the AB to BL
direction at concentrations, (a) close to the analytical limit, and
(b) close to the solubility limit.
[0249] Similar P.sub.e values in both the AB to BL and BL to AB
indicate a passively absorbed compound and no further studies are
required. AB to BL P.sub.e greater than BL to AB indicates
carrier-mediated absorption and P.sub.e must be determined for 5
additional C.sub.0 in the AB to BL direction. BL to AB P.sub.e
greater than AB to BL indicates carrier mediated secretion and
P.sub.e determined for 5 additional C.sub.0's in the BL to AB
direction.
[0250] Similar P.sub.e values at low and high concentrations
indicate a passively absorbed compound, and no further studies are
required. Low concentration P.sub.e higher than high concentration
P.sub.e indicates carrier-mediated absorption and Pe is determined
for 5 additional C.sub.0's in the AB to BL direction. High
concentration P.sub.e higher than low concentration P.sub.e may
indicate carrier-mediated secretion. BL to AB P.sub.e is then
determined at the low concentration and the mechanism determined as
described above.
[0251] B. Solubility determination
[0252] Solubility of a compound is determined using an accurate and
scientifically sound method similar to the Phase Rule and
Phase-solubility analysis as described in Remington's: The Science
and Practice of Pharmacy, 19.sup.th edition, Chapter 16.
[0253] The solubility is determined at pH 1.5 using Simulated
Gastric Fluid (USP XXII) minus pepsin. Solubility at pH 6.0, 6.5,
7.0, and 7.5 is determined in Simulated Intestinal Fluid (USB XXII)
minus pancreatin. Parameters are for data collection are carefully
monitored by ensuring purity of the test compound and accuracy of
the Simulated Gastrointestinal fluids. A temperature of 37.degree.
C. is maintained accurately during the course of the determination.
Complete saturation and accurate analysis of saturated solutions
are employed.
[0254] C. Dissolution determination
[0255] The dissolution rates are determined using the equipment,
apparatus, and methods described in USP XXII, <711>
dissolution. The dissolution rate at pH 1.5 is determined in
Simulated Gastric Fluid (USP XXII) minus pancreatin. Concentrations
are collected and analyzed for drug compound from the vessel for a
sufficient time (6 hours, preferable) to allow the initial slope of
the concentration v. time curve to be determined. The slope
(dissolution rate) is determined using the initial linear portion
of the concentration v. time plot if non-sink conditions exist.
Under sink conditions, the entire plot are used to calculate the
slope. The slope is reported as the dissolution rate. Explanations
of the dissolution rate, sink and non-sink conditions, and
equations for calculation are given in Remington's: the Science and
Practice of Pharmacy, 19th edition, Chapter 34.
[0256] If a formulated dosage form is used for dissolution testing,
the dissolution protocols described are used to determine the
dissolution rate for drug compound from the formulated dosage
form.
Example 5
Standards and Protocols for Evaluating Permeability Data
Collection
[0257] This example provides detailed protocols for controlling the
quality of permeability data collection described in Examples 3 and
4. Compounds listed in Table 7 are used as standards for monitoring
permeability data collection and quality. The compounds were chosen
to represent each intestinal transport mechanism (passive
transcellular, passive paracellular, carrier-mediate influx, or
carrier-mediated efflux).
7TABLE 7 Permeability Standards Transport mechanism Compounds
Passive Paracellular mannitol Passive Transcellular hydrocortisone
Carrier-mediated Influx D-glucose Carrier-mediated Efflux
etoposide
[0258] Mannitol, hydrocortisone, D-glucose, and etoposide also were
chosen since they are widely used as markers for intestinal
transport across rabbit tissue and other systems with well
characterized Pe values. These compounds also are available
commercially as either 3H-labeled or 14C-labeled.
[0259] Permeability data for standards is compared to the values
for rabbit listed in Table 8 (or other standard values) using basic
statistical analyses. If the data is significantly different
(p-value>0.05) for any of the standard compounds, data
collection is repeated.
8TABLE 8 Transport Characteristics of Permeability Standards*
Compound Pe (cm/s) (donor concentration) Duodenum Jejunum Ileum
Colon mannitol (1 mM)5 1.73 .times. 10.sup.-6 3.54 .times.
10.sup.-6 4.02 .times. 10.sup.-6 5.53 .times. 10.sup.-6
hydrocortisone (0.01 .mu.M)5 3.00 .times. 10.sup.-7 1.31 .times.
10.sup.-6 2.91 .times. 10.sup.-6 3.85 .times. 10.sup.-6 D-glucose
(10 mM)5 4.55 .times. 10.sup.-6 1.02 .times. 10.sup.-5 1.45 .times.
10.sup.-5 9.28 .times. 10.sup.-6 etoposide (100 .mu.M) *Note:
permeability values are representative of ranges. Other values or
extended ranges may be used.
[0260] A. Experimental Conditions
[0261] Protocols, conditions and calculations for permeability
evaluation of standards are as described in Example 4, with the
following modifications.
[0262] Permeability experiments are performed using Ringer's buffer
at pH 7.4 on both the apical/mucosal and basolateral/serosal sides.
Ringer's buffer is as described above excepting that glucose is
substituted with mannitol when Pe values for glucose are being
measured.
[0263] Samples are collected from the receiver chamber beginning 30
minutes after experiment initiation and continuing every 15 minutes
until 6 samples have been collected (105 minutes). One-half ml is
removed from each receiver chamber at each time point and compound
concentration determined. The volume removed from the receiver
chamber is replaced with buffer containing no drug to maintain
constant volume in the receiver chamber. The dilution of the
receiver concentration due to the addition of buffer should be
corrected during data analysis and Pe calculation. The
concentration is corrected by using Equation 5. 4 1 X = n = 1 k ( -
1 ) n - 1 k + 1 ( S V ) n - 1 ( Eq . 5 )
[0264] Where the corrected receiver chamber concentration is
obtained by dividing the collected sample concentration by Equation
5 (1/X), S is the volume of sample withdrawn, V is the receiver
chamber volume, k is the sequential sample number, i.e. k=1 for the
first sample time, k=2 for the second sample time, k=3 for the
third sample time, etc., and .beta. is the corresponding number
from the modified Pascal's triangle below (Table 9). Note: Since
the sample intervals are not even (i.e. the 1st interval is 30
minutes, all others 15 minutes) Equation 5 as well as the .beta.
coefficients are modified from those listed in Example 4.
9TABLE 9 Modified Pascal's Triangle for determining .beta.
coefficients Sample 1st term 2nd term 3rd term 4th term 5th term
6th term 1 2 2 3 2 3 4 5 2 4 5 9 7 2 5 6 14 16 9 2 6 7 20 30 27 11
2
[0265] The donor concentration C.sub.0 is determined by sampling
0.02 ml of the donor buffer containing drug (with subsequent
analysis) directly from the donor chamber. Potential binding of
drugs to the chambers also is monitored. Donor samples (0.02 ml)
are taken at experiment initiation and at experiment conclusion. If
a significant decrease in drug concentration has occurred (>10%)
the experiment is repeated using procedures which compensate for
the drug loss in the donor chamber. It is recommended that the
donor chamber solution be removed and replaced with fresh donor
buffer containing drug at appropriate intervals. The intervals and
volumes to be used are determined using sound scientific judgment.
Adequate data is collected to show the donor drug concentration has
remained constant throughout the experiment.
[0266] For tissue-based permeability assays, during mounting of
tissue onto chambers, intestinal muscles should be stripped off the
mucosa and discarded. Care should be taken to ensure integrity of
the tissue.
[0267] Animals donating tissue are euthanized immediately prior to
experiment initiation. The small intestine is excised from the
animal and kept in ice cold Ringer's buffer pH 7.4 until mounted in
diffusion chambers. As soon as possible after excision, the tissue
is cut into an appropriately sized piece and placed over the
diffusion chamber pins with the mucosal side down. The muscle
layers are carefully stripped away using forceps. After the tissue
is mounted the two half chambers are placed together and the donor
and receiver sides filled with the appropriate pre-warmed
(37.degree. C.) buffer. If NaviCyte chambers are used, the gas lift
system is connected with 95% O.sub.2/5% CO.sub.2 flowing at
.about.5-15 ml/min (depending upon chamber volume) into each half
chamber to maintain pH and mixing. Sampling begins 30 minutes after
connection of the gas lift system.
[0268] The mean Pe and Standard Error of the Mean are determined
for each study. Permeabilities from at least 6 chambers from 3
different animals are used in calculating the mean and Standard
Error of the Mean.
[0269] In addition, the Pe of radiolabeled mannitol is determined
simultaneously with the standard compound as a marker of intestinal
integrity. Mannitol Pe values may be determined by concurrent
diffusion using a donor buffer containing mannitol and the standard
drug compound, or by continuing the experiment for 60 minutes after
the last standard compound sample is collected using donor buffer
containing mannitol and fresh receiver buffer containing no
compounds.
[0270] Special experimental conditions are followed for certain
standard compounds. This includes such conditions as a proton
gradient, a sodium gradient, presence of glucose, etc. These
conditions are listed in Table 10 and are substituted or added to
the general conditions listed above.
10TABLE 10 Experimental Conditions Donor Standard Compound
Concentration Special Conditions mannitol 1 mM D-glucose 10 mM
hydrocortisone 0.01 .mu.M etoposide 100 .mu.M drug dissolved in
DMSO, DMSO concentration in buffer < 0.1%
Example 6
Physiologic-Based Mass Simulation Model
[0271] A. Design
[0272] A multi-compartment physiologic-based mass simulation model
(the "mass model") was designed to integrate mass-flow
relationships among GI compartments representing the stomach,
duodenum, jejunum, ileum, and colon, and thus throughout the GI
tract, and to characterize drug movement in units of mass into
peripheral compartments. Converters that interrelated transfer
rates and associated rate constants (k), which in turn were
modified by various factors including pH, solubility profiles,
compartment surface area and drug permeability were incorporated to
account for drug movement among compartments. A plasma kinetics
model also was included for validation purposes and for correlating
clinical plasma data to the mass model. Converters also were used
for unit conversion.
[0273] Gancyclovir was chosen to develop and test the mass model.
Gancyclovir exhibits no in vivo biotransformation and is poorly
absorbed. Thus, the mass model assumes no metabolism or protein
binding. Additionally, dissolution rate and delivery system were
not used in the mass model as modifying parameters of drug
absorption, i.e., drug assumed to be completely dissolved in the
stomach and solubilized according to its solubility profile.
[0274] Surface area values for each compartment of the mass model
represented a "functional surface area," as opposed to an absolute
value. A functional surface area was utilized since (1) fluids
entering the gastrointestinal compartments do not cover the
surfaces of the compartment instantaneously, but rather over a time
course; and (2) solubilized drug within the fluid is not ideally
presented to all absorptive areas. Functional surface areas for
each compartment were calculated by solving Equation 6 for the area
using various data inputs from the literature.
P.multidot.A.multidot.S.sub.p=.differential.M/.differential.t (Eq.
6)
[0275] Where P is the permeability coefficient, A is the surface
area of the membrane, S.sub.p is the solubility of the drug in the
relevant segment of the intestine, and
.differential.M/.differential.t is drug flux, where flux
.differential.m/.differential.t is determined from the permeability
of the drug in the particular intestinal compartment, the surface
area covered by drug solution and the solubility of at the pH of
the intestinal compartment.
[0276] For example, several studies have been conducted comparing
permeability of various compounds (Rubas et al., Pharmaceutical
Research, Vol. 10, No. 1 (1993)). Mannitol, which has similar
physicochemical properties to Gancyclovir, also has similar
permeability characteristics and a bioavailability of approximately
10% in humans when it is orally administered. For mannitol,
permeability is well characterized. Thus, data obtained from the
literature related to permeability in each compartment,
pH-dependent solubility and mass concentration relationships was
used to solve Equation (6) for area. Thus, it was this area, and
not the theoretical total surface area of each compartment, that
was used as the functional area of a compartment, which represented
a good approximation of in vivo surface area relationships for
initial model building.
[0277] Permeability values were obtained from published in vitro
cell diffusion experiments and were accounted for by converters
that modified luminal and peripheral flow (K12) for each
compartment. For solubility, a solubility curve was used based on
experimental data available in the literature. pH was then isolated
in a separate converter to modify the solubility curve for the
particular compartment. In contrast, for validation purposes, an
absolute solubility value was used and pH was entered as 1 to
isolate that converter from the validation model.
[0278] Absorption "transfer" rates among each two compartment
sub-system were collected into a separate flow representing total
absorption rate, which in turn was collected into a compartment
representing the total amount of drug absorbed for each GI tract
compartment, namely, stomach, duodenum, jejunum, ileum, and colon.
Absorption rates among stomach, duodenum, jejunum, ileum, and colon
modules were connected by flows modified by the associated rate
constants between each GI segment.
[0279] For validation purposes, a plasma kinetics model was
integrated with the mass-flow compartments by linking the total
absorption rate to a flow representing the absorption rate
constant, which in turn fed into the central plasma compartment. A
standard two-compartment plasma kinetics model (Ramsay, European
Journal of Pharmaceutics and Biopharmaceitucs, Vol. 37, No. 3
(1991)) was used for this purpose. (See FIGS. 5 and 6) The plasma
kinetics model incorporated first order transfers between the blood
compartment and peripheral compartment. Two flows were used and set
up as first order systems and thus different rate constants were
applied in each direction. Compartment values were represented as
mass units. Blood volume was input in a converter, which modified a
converter for concentration along with the mass compartment. An
elimination rate constant was also obtained form the literature in
a first order process. In addition, while most drugs are given in
milligram doses, plasma concentrations are reported in microgram or
nanogram per milliliter. This is done since -compounds are
distributed rapidly into a large volume after entering the blood
resulting in a concentration of drug in systemic circulation that
is quite low with respect to the concentration at the site of
administration. Accordingly, an additional converter was added to
convert milligram units to nanogram or microgram units expected for
concentrations of the test compound based on human bioavailability
data. A compartment also was added to collect elimination data.
[0280] B. Mass Model Parameters
[0281] Parameters and associated values of the mass model include
pH, solubility, permeability, and intestinal transit, and are
illustrated in Table 11.
11TABLE 11 Mass Model Parameters/Values Parameter Value Dose 1000
mg dt 0.125 Run Time 24 hrs ka assumed (mass transit) 2.8 or 3
Stomach Area 50 cm.sup.2 Solubility 31 mg/ml Permeability 1.1
.times. 10.sup.-6 cm/sec Duodenum Area 125 cm.sup.2 Solubility 3.65
mg/ml Permeability 1.1 .times. 10.sup.-6 cm/sec Jejunum Area 182
cm.sup.2 Solubility 3.65 mg/ml Permeability 2.17 .times. 10.sup.-6
cm/sec Ileum Area 102 cm.sup.2 Solubility 3.65 mg/ml Permeability
4.06 .times. 10.sup.-6 cm/sec Colon Area 138 cm.sup.2 Solubility
3.65 mg/ml Permeability 3.80 10.sup.-6 cm/sec Plasma Kinetics
k.sub.12 0.839 k.sub.21 0.670 k.sub.elim 0.161 Fluid Volume 76,800
ml
[0282] The mass model also was tested by inputting values derived
from the literature (Gibaldi et al., Pharmacokinetics, pp. 284-288,
Marcell Dekker (1975)) into the plasma kinetics model. These values
are shown in Table 12.
12TABLE 12 Values for Plasma Kinetic Module Dose 1 g 1505a 2.718
h.sup.-1 1505b 0.254 h.sup.-1 k.sub.21 0.3737 h.sup.-1 k.sub.12
0.7509 h.sup.-1 k.sub.10 1.3474 h.sup.-1 V.sub.p 20.1241
Example 7
Testing and Validation Mass Model
[0283] The mass model was tested using parameters shown in Table 11
with an initial dose of 1000 mg over a time course of 24 hours.
AUC, C.sub.max, T.sub.max, and T.sub.1/2 were simulated using
various doses (New Drug Application for Gancyclovir Sodium, Syntex
(USA), (obtained from the FDA under the Freedom of Information Act
(FIA)) and compared to human clinical data obtained for
Gancyclovir. Bioavailability simulated by the mass model for
Gancyclovir was approximately 6%. Compared to human clinical data,
obtained for two Phase I clinical studies (designated here as ICM
1505 and 1505b), bioavailability of fasted patients in clinical
trials typically ranged from 3-20%. The mass model also was tested
using a plasma kinetics validation model illustrated in FIG. 8.
[0284] FIG. 16 shows the area under the concentration time curve
for a 1000 mg dose of Gancyclovir, Tmax=1.4 hrs, Cmax=0.51 ng/ml.,
using the mass model, as compared to clinical study data of ICM
1505 and 1505b. The results demonstrate that the mass model
underestimated plasma concentration during the post-absorptive
period. Table 13 shows comparison of some values between clinical
studies and those predicted by the mass model. The clinical studies
also used a 70 Kg body weight for normalization of
concentrations.
13TABLE 13 Comparison of Mass Model to Clinical data Parameter Mass
Model Clinical 1505a Clinical 1505b Cmax (mcg/ml) 0.51 0.55 0.59
Tmax (hrs) 1.40 1.43 1.43
Example 8
Physiologic-Based Volume Simulation Model
[0285] A. Design
[0286] A physiologic-based simulation model for incorporating fluid
volume flux and GI transit (the "volume model") was developed for
integration with the mass model to account for changes in
absorption resulting from fluid absorption/secretion and transit,
and thus apparent drug concentration. The volume model was
constructed so that fluid enters a compartment and was absorbed by
a first order process based on an absorption rate for that fluid.
Movement of fluid between compartments was dependent on a zero or
first order fluid transit rate.
[0287] B. Volume Model Parameters
[0288] As a starting point for the volume model, values were
obtained from literature that described in general terms absorption
and secretion of fluid throughout the body (Change et al.,
Gastrointestinal, Hepatobiliary and Nutritional Physiology, Chapter
5, p. 92, Lippincott-Raven (1996)). Values representing total
intake of fluid per day and total secretion of fluid per day were
modeled into the system normalized linearly to increments of dt for
the model. To permit for changes in dt for the model, the values
were entered as pulses. Values used in the volume model are shown
in Table 14.
14TABLE 14 Volume Model Parameters/Values Source ml/24 hrs ml/0.1
hrs Intake/Secretion Stomach 6500 27.08 Orally 2000 8.33 Salivary
1500 6.25 Glands Stomach 2500 10.42 Duodenum 2000 8.33 Bile 500
2.08 Pancreas 1500 6.25 Jejunum/Ileum 1000 4.17 Jejunum 641 2.67
Ileum 359 1.50 Colon 0 0 Total 9000 337.57.5 Absorption Duodenum
2598 10.82 Jejunum 3783 15.76 Ileum 2120 8.83 Colon 400 1.67 Total
8900 37.09 Note: Values for compartments based on % total
intestinal area
[0289] Where data was only available for a series of compartments,
values were assigned to each compartment based on the percentage of
the total area for that series (e.g. secretions for jejunum and
ileum and absorption for parts of the small intestine). The model
was set as two flows between the blood (serosal) side of the
compartment and the compartment itself. Each flow represented the
rate constant for secretion and fluid absorption.
[0290] For development purposes, absorption and stomach secretion
were assumed to be zero order when using values from Table 14 for
both flows. Also, daily volume for fluid entry into the stomach was
entered as a pulse according to the dt values shown in Table 14.
Thus, total intake and secretions of fluid was modeled as a pulse
occurring every 6 minutes throughout a 24 hour period. Initial
volume in the stomach also was set up as a pulse of the total oral
intake, salivary excretion, and stomach secretion over each dt
increment.
Example 9
Testing and Validation of Volume Model
[0291] To test movement of fluid between compartments the volume
model was modified to approximate zero order fluid transit or
emptying and isolated from the mass component of the model. Initial
values of 1000 ml and 250 ml were used for testing.
Example 10
Physiologic-Based Mass-Volume Simulation Model
[0292] A. Design
[0293] A physiologic-based simulation model integrating the mass
and volume models (the "mass-volume model") was constructed to
integrate complex mass and fluid flow relationships. The integrated
mass-volume model also included compartments to characterize drug
movement into peripheral compartments. A plasma kinetics model for
training/validation purposes also was included. The basic design
for the integrated mass-volume model, linked to the plasma kinetics
model shown in FIG. 8, is illustrated in FIG. 11.
[0294] Volume for a compartment was added as a product to obtain
the amount of drug solubilized at a time increment volume.
Additionally, an "IF . . . THEN . . . ELSE" control statement was
added to prevent the equation from indicating that more drug was
solubilized than dosed. Thus, the integrated mass-volume model
shows the mass of drug in the stomach connected to the absorption
rate constant as well as the volume compartment.
[0295] Mass and fluid transit rate constants of 2.8 and 3 for the
stomach were calculated from values obtained from the literature
for Gancyclovir (Syntex, Clinical Studies ICM 1653 and 1774, FDA
NDA available data and Bachrach et al., Functional and Diagnostic
Aspects of the Upper Digestive Tract, Digestive System, Part I,
Upper Digestive Tract, Netter (1989)), and determined for each of
the remaining compartments to approximate mass and fluid
movement.
[0296] B. Mass-Volume Model Parameters
[0297] Parameters and associated values and equations were
systematically varied or as described above for individual mass and
volume models; an example of the equations and parameters employed
in the mass-volume model are shown in Appendix 1. Dissolution rate
and delivery system (controlled release device/formulation) were
excluded from in the mass-volume model, and thus the model assumes
a test compound is immediately in solution in the stomach.
Example 11
Testing and Validation of Mass-Volume Model
[0298] The mass-volume model was tested using the equations and
parameters shown in Appendix 1. These parameters included the
pulsed estimate of fluid absorption and gastrointestinal
secretions, and rate constants extracted from the literature.
Alternate sets of parameters for fluid absorption and secretions
also were tested. For example, simple zero and first order rate
constants of 1 or a sequential integer and various doses were
evaluated for comparison to human clinical data.
[0299] FIG. 17 shows the area under the concentration time curve
for a 1000 mg dose of Gancyclovir, Tmax=1.1875 hrs, Cmax=0.54
mcg/ml., using the mass-volume model of FIG. 11 with the estimated
absorption and secretion rates, relationships, and values of
Appendix 1, as compared to clinical study data of ICM 1505 and
1505b. The data is now less favorable for Tmax but more favorable
for AUC compared to the mass model. These results demonstrate that
the mass model underestimated plasma concentration during the
post-absorptive period, while the combined mass-volume model
appeared to overestimate it.
[0300] The mass-volume model was modified to incorporate simple
zero and first order absorption and secretion. This model was then
run using an initial volume of 250 ml and also 4 administrations of
250 ml water as done during clinical studies. Results were similar
to the results shown in FIG. 17, but with slightly higher
absorption.
[0301] The mass-volume model also was run using the following
combinations of data input: (1) doses of 500 mg, 750 mg, 1000 mg at
qid, bid, and tid dosing; (2) initial volumes of 250 ml, 500 ml,
1000 ml; (3) varying absorption and secretion rates based on
differing assumptions for daily secretion and fluid intake; (4)
varying pH values in the various compartments; and (5) simulation
of food intake and fasting conditions. Correlation was very good
with some clinical data and less than optimal with others.
Correlation with theoretical estimations also varied from very good
to poor.
[0302] Collectively, the mass-volume model represented an
improvement over the individual mass and volume models in that it
provided a better approximation of in vivo conditions. While the
simpler mass-model correlated better with clinical data, the
integrated mass-volume model was more sensitive to changes in the
various input parameters, physiological conditions and underlying
constants, and thus a more rigorous model of the GI tract.
Example 12
Physiologic-Based GI tract Simulation Model
[0303] A. Design
[0304] The mass-volume model was selectively improved in a stepwise
fashion to create an integrated physiologic-based simulation model
of the GI tract of a mammal (the "GI model") capable of
compound-independent prediction of oral absorption with a high
level of accuracy. The model was developed to be flexible. That is,
it was designed so that additional physiological factors that
influence oral absorption could be identified and incorporated into
the model as needed to improve the quality of the prediction for a
diverse set of test compounds. Additionally, the GI model was
developed to minimize input data requirements.
[0305] The basic approach involved generation, testing and
integration of a GI transit model (FIG. 20), a pH-dependent
solubility and dissolution model (FIG. 21), and an absorption model
(FIG. 22), as well as underlying equations and parameters,
constants, calculated parameters, and rules by which a given
simulation is to proceed. A controlled release device and
formulation compartment also was included. A graphical
compartment-flow model of the integrated GI model is illustrated in
FIG. 24 (without converters, ghost or connectors) and FIG. 25 (with
converters, ghost and connectors). Parameter inputs, calculations
and outputs are illustrated in FIGS. 29-39. An abbreviation key for
the GI model is provided as Appendix 3.
[0306] The GI model also incorporated additional features to
improve the predictive power and versatility of the simulation
model. One feature was the development and incorporation of
regression analysis derived adjustment parameters based on analysis
and processing of human clinical data and in vitro data for a
diverse set of compounds. The adjustment parameters Were utilized
as constants in the GI model, and thus modify underlying equations
of the model. A second feature was development and incorporation of
regional permeability correlation parameters and equations that
permitted estimation of values for segments of the model that were
missing user provided input values for corresponding parameters.
This facilitates prediction of oral drug absorption when
permeability values or other parameter for a given compound are
provided for a limited number of GI segments, for example, when
cell-based input data, such permeability data derived from Caco-2
cells is used to provide permeability input data of colon. Another
feature was development and incorporation of parameters and
calculations to account for transport mechanism and thus
transport-specific variations in compound absorption. Another
feature was incorporation of the ability to isolate and evaluate
specific regional absorption events related to dissolution and mass
transit. Also, the GI model was developed to separate absorption
into the portal vein (FDp) from hepatic metabolism, so as to
account for individual primary barriers to absorption.
[0307] B. GI Model Equations, Rules and Parameters
[0308] 1. General Equations For GI Model:
[0309] Various differential equations and rules utilized for the GI
tract model are provided below. For the equations, adjustment
parameters are designated by the letter Z.
[0310] Transit time:
[0311] First order transit process 5 A t = k TT [ A ] ( Eq . 7
)
[0312] dA/dt=rate of transit (or absorption), k.sub.TT=rate of
constant, A=amount (compound or water) in proximal compartment.
[0313] Rate constant calculation 6 k TT = ln 10 T T ADJ ( Eq . 8
)
[0314] TT.sub.ADJ=adjusted transit time
TT.sub.ADJ=(TT.sub.p.multidot.Z.sub.TT.multidot.User.sub.TT) (Eq.
9)
[0315] TT.sub.p=physiological transit time, Z.sub.TT=transit time
adjustment parameter, User.sub.TT=User controlled adjustment to
transit time.
[0316] K.sub.TT is a regionally dependent parameter, i.e. different
rate constants are used for each region of the GI tract.
[0317] Fluid volume absorption/resorption: 7 A t = k VA [ A ] ( Eq
. 10 )
[0318] dA/dt=rate of absortpion, k.sub.VA=rate constant, A=amount
of fluid (water) in the compartment
k.sub.VAZ=k.sub.emp.multidot.Z.sub.VA (Eq. 11)
[0319] Z.sub.VA=volume absorption adjustment parameter, k.sub.emp
is determined emperically to match human fluid absorption in
vivo.
[0320] Dissolution and Solubility:
[0321] Dissolution rate (regionally dependent) 8 ( A ) t = k D Z D
Mass ( S ADJ - C ) ( Eq . 12 )
[0322] A=Amount dissolved, k.sub.D=User supplied dissolution rate
constant, Z.sub.D=Dissolution rate adjustment parameter,
S.sub.ADJ=solubility, C=concentration
[0323] Solubility (regionally dependent) 9 S ADJ = ( s N - s n - 1
) ( pH n - pH n - 1 ) ( pH - pH n - 1 ) + S n - 1 ( Eq . 13 )
[0324] S.sub.ADJ=Solubility, S.sub.n=user supplied solubility
{S.sub.1 . . . S.sub.5}, pH.sub.n=user supplied pH values {pH.sub.1
. . . pH.sub.5} corresponding to user supplied solubilities, pH=pH
value appropriate to region of the system, such as GI tract. n is
selected such that pH.sub.n>pH, and pH.sub.n-1<pH. If any of
pH.sub.1 . . . pH.sub.5 are equal to pH, the corresponding S.sub.n
is used as the solubility.
[0325] Concentration (regionally dependent) 10 C = S ADJ V ( Eq .
14 )
[0326] C=concentration of soluble drug, V=volume of fluid
[0327] Flux/Absorption:
J=P.sub.ADJ.multidot.SA.sub.ADJ.multidot.C (Eq. 15)
[0328] J=flux, P.sub.ADJ=Adjusted permeability, SA.sub.ADJ=Adjusted
surface area available for absorption, C=concentration 11 P ADJ = (
2 1 + Z EFF ) P m Z F 3600 + Z ACT P c 3600 1 + C K m (Eq.16)
[0329] Z.sub.EFF=Efflux transport adjustment parameter,
P.sub.m=passive membrane permeability, Z.sub.F=passive permeability
or flux adjustment parameter, Z.sub.ACT=active permeability
adjustment parameter, P.sub.c=active carrier permeability,
C=concentration, K.sub.m=Michaelis-Menten kinetic parameter.
[0330] Regional Permeability Correlation
[0331] Any regional permeability, P.sub.m, can be calculated using
any number of other provided permeabilities. 12 ln P a = C + A ln 1
P b + B ln ( 1 P b ) 2 (Eq.17)
[0332] P.sub.a=permeability calculated using the regional
correlation, P.sub.b=permeability provided by the user, and A, B,
and C=correlation coefficients fitted to determine correlation.
[0333] By way of example, rules utilized for a GI tract model of
the PK tool and method of the invention include the following
general processes.
[0334] 2. General Processes For Rule Generation:
[0335] 1. GI transit. The transit of drug compound and fluid volume
are somewhat controlled and the transit of formulations and/or
controlled release devices is much more strictly controlled.
[0336] 2. Controlled Drug Release. The release of drug from the
dosage form must be controlled such that drug is released into the
correct intestinal region at the appropriate time.
[0337] 3. Dissolution. A comparison between the concentration and
the solubility must be made to determine if additional insoluble
compound will dissolve, or if compound already dissolved must
precipitate to insoluble drug due to solubility limitations.
[0338] 4. Absorption. Mathematically, absorption may occur when
physiologically it is impossible, e.g. when the volume in the colon
becomes low enough that any dissolved drug will be within fluid
contained in other solid waste also present in the colon and
therefore unavailable for absorption. IF . . . THEN production
rules control these situations.
[0339] 5. Permeability calculations. To estimate unprovided
permeability values from provided permeability values logical
evaluations must be made to determine the correct equations
necessary to make the correlations.
[0340] 6. Concentration calculations. The concentration in the
intestine cannot exceed the solubility for that particular region.
If it does, an incorrect flux will be calculated. IF . . . THEN
production rules are used to ensure the correct concentration is
used in the flux calculation.
[0341] 7. Mathematical anomalies. At certain times during the
simulation (especially early and late in the simulation) some
compartments, flow regulators, or converters used in other
calculations may have a value of 0 which will result in a
computational error, e.g. division by 0. Production of rules are
used to identify these situations and avoid the errors.
[0342] The following table lists the specific processes,
conditions, results that control statement rules, e.g., IF . . .
THEN production rules, are used to control. Generally, separate
rules used for each region of the GI tract and are combined into
one line in the table.
15TABLE 15 Rules for Physiologic-Based GI tract Simulation Model
Process Condition Result in True Result if False Comments GI
Transit of drug Time < 4 hours No transit to waste Transit to
waste by Applies to GI compound or fluid first order process
regions using volume different values for the condition. GI Transit
of Time, cumulative no transit to next Immediate transit to The
rate constant for formulations or physiol. transit time compartment
next compartment first order transit is controlled release set
exceedingly large devices to provide near instantaneous transit.
Controlled release Time to reach GI Drug is released No drug
release into Drug is released region < Time < from dosage
form to that GI region according to user Time to exit GI GI region
provided release region profile. Dissolution Soluble drug/volume
Drug moves from Drug moves from Precipitation rate is
(concentration) < insoluble to soluble soluble to insoluble set
to provide near Solubility compartment compartment instantaneous
according to according to precipitation without dissolution rate
precipitation rate causing "overshoot". Absorption Volume < 1
.times. 10.sup.-6 No absorption, i.e. Absorption by flux ml AND
Mass < 1 .times. concentration = 0 equation 10.sup.-8 mg
Permeability Duodenum, Use provided Estimate unprovided 1 or 2
permeabilities Calculations Jejunum, and Ileum Permeabilities
permeabilities from can be used to Permeabilities all provided
calculate unprovided provided permeabilities permeabilities
Concentration Concentration < Concentration used Solubility used
in Calculation Solubility in flux equation flux equation
Mathematical Volume = 0 Dissolution rate = 0 Dissolution rate
Dissolution given as anomalies calculated by Noyes- an example.
Similar Whitney equation condications are provided for
concentration calculations and other processes.
[0343] Exemplary equations, rules, parameters and initial values
for the graphical compartment-flow model and various sub-models of
the integrated GI model illustrated in FIGS. 20-25 and 29-39 are
provided in Appendix 4, as related to the abbreviation key provided
as Appendix 3. Various aspects of the physiological, adjustment and
regional correlation parameters employed in the GI model and their
development are described in further detail below.
[0344] 1. Physiological Parameters
[0345] Physiological parameters of the GI model included
physiological ranges reported in the literature (Table 17) as well
as specific values utilized in the model and compiled for each of
five regions of the gastrointestinal tract (stomach, duodenum,
jejunum, ileum and colon)(Table 16). These included values related
to pH, transit time, surface area, and volume parameters.
16TABLE 16 Physiological Parameters Employed In GI Model New Water
Initial Surface Average Absorption Volumes Area Transit time Volume
Transfer Rates* pH.sup.a (ml) (cm.sup.2).sup.b (hr).sup.c Rates
(t.sub.90)(hr.sup.-1).sup- .c (hr.sup.1).sup.d Stomach 1.5 100 NA
0.5 4.6 0 Duodenum 6.0 0 150 0.225 10.8 0 Jejunum 6.5 0 1000 1.5
1.54 1.75 Ileum 7.0 0 1000 1.5 1.54 1.75 Colon 6.5 0 850 24 0.094
0.1 *Water absorption rate parameters were set so that cumulative
water absorption from each region using the GI model were in
agreement with values listed in Table 17.
[0346]
17TABLE 17 Physiological Parameters Employed In GI Model New Water
Initial Surface Average Absorption Volumes Area Transit time Volume
Transfer Rates pH.sup.a (ml) (cm.sup.2).sup.b (hr).sup.c Rates
(t.sub.90)(hr.sup.-1).sup.c (hr.sup.1).sup.d Stomach 1.0-2.5 100 NA
0.5-3.0 0.8-4.6 0 Duodenum 4.0-6.4 0 147-168 0.20-0.25 9.2-11.5 0
Jejunum 4.4-6.4 0 913.5-1044 1.0-2.0 1.15-2.3 4.0-4.5 Ileum 6.8-7.4
0 913.5-1044 1.2-1.5 1.54-1.9 2.4-2.7 Colon 5.5-7.0 0 763-872 18-36
0.064-0.13 1.4-1.6
[0347] a) Lui et al. J Pharm Sci 1986;75(3):271-4; Youngberg et al.
Dig Dis Sci 1987;32(5):472-80; Charman et al. J Pharm Sci
1997;86(3):269-82; Langguth et al. Biopharm Drug Dispos
1994;15(9):719-46; Kararli T T. Biopharm Drug Dispos
1995;16(5):351-80;
[0348] b) Wagner J G. J Pharm Sci 1961;50(5):59-87; Ho N F, Park J
Y, Ni P F, et al.
[0349] Crouthamel W, Sarapu A C, editors. Animal Models For Oral
Drug Delivery In Man: In Situ And In vivo Approaches. Washington,
D.C. American Pharmaceutical Association, 1983; 2, Advancing
quantitative and mechanistic approaches in interfacing
gastrointestinal drug absorption studies in animals and humans. p.
27-106;
[0350] c) Ho et al. Crouthamel W, Sarapu A C, editors. Animal
Models For Oral Drug Delivery In Man: In Situ And In vivo
Approaches. Washington, D.C. American Pharmaceutical Association,
1983; 2, Advancing quantitative and mechanistic approaches in
interfacing gastrointestinal drug absorption studies in animals and
humans. p. 27-106; Oberle et al. Journal of Pharmacokinetics &
Biopharmaceutics 1987;15:529-44; Davis S S. S T P Pharma
1986;22:1015-22; Davis et al. Gut 1986;27:886-92;
[0351] d) Turnberg L A. Digestion (1973) 9:357-81.
[0352] 2. Adjustment Parameters
[0353] Differences between in vitro and in vivo conditions, as well
as differences between in vivo conditions for one species of mammal
and a second hamper accurate prediction of absorption using a
simulation approach. For example, in vitro dissolution rate may or
may not be comparable to dissolution rates existing in vivo, or,
the permeability in rabbits may or may not be comparable to the
permeability in humans.
[0354] To compensate for such differences, a set of selectively
optimized adjustment parameters were developed. These parameters
were designed to be utilized as constants that modify the
underlying equations of specific compartments of the GI model to
permit automatic correlation of input data to output data as well
as facilitate accurate prediction of oral absorption for a diverse
set of compounds. For example, the differential equation utilized
to calculate fluid volume absorption/resorption employs a rate
constant obtained from an equation that is modified by a volume
absorption adjustment parameter Z.sub.VA (see Eq. 11) Listed below
(Table 18) are examples of parameters that can be used to adjust
parameters and equations as well as those which can be added or
removed to a given model if necessary.
18TABLE 18 Adjustment Parameters Compartment Segment Regional fluid
absorption stomach duodenum jejunum ileum colon Flux/Permeability
duodenum jejunum ileum colon Active/Carrier mediated duodenum
Transport (absorption) jejunum ileum colon Compound Efflux
(secretion) duodenum jejunum ileum colon Transfer rates stomach to
duodenum duodenum to jejunum jejunum to ileum ileum to colon colon
to waste Surface Area duodenum jejunum ileum colon
[0355] The adjustment parameters were developed and optimized using
a stepwise selective optimization process. Initial adjustment
parameters were developed for correlation between humans and rabbit
as follows. Two primary sets of data were used: 1) FDp and best fit
plasma profiles from in vivo clinical pharmacokinetic (PK) data,
and 2) simulated FDp and plasma profiles generated from the GI
model. The FDp and best fit plasma profiles from in vivo PK data
was obtained by analyzing and processing IV and PO data from humans
for the test set of compounds described in Example 2 using a
regression-based curve fitting algorithm to determine the best fit
curve that matched the actual clinical plasma profiles. The second
set of data was generated using a developmental GI model.
[0356] In vitro data (permeability, solubility, dissolution rate,
and dose) were used as inputs into the GI model with the adjustment
parameters set to some initial value previously determined to
provide reasonably predictable values for FDp. The GI model was
used to provide FDp data for each test compound. The FDp data
generated from the GI model also was used as input data into an
IV/PO PK model, such as the one shown in FIG. 18, to determine
plasma profiles.
[0357] The PO input to the IV/PO PK model of FIG. 18 used for
fitting clinical data is an error function and shown in Equation
18. 13 F = D FDp 2 1 - erf 1 - t t 50 2 1 P e t t 50 (Eq.18)
[0358] Where D is the dose of drug delivered to the intestine, t is
time in minutes, t50 is the time for 50% of the drug to be
absorbed, and Pe is a parameter (Peclet number) related to the
slope of the linear portion of the absorption curve.
[0359] When fitting the data, all available in vivo PK data
(multiple intravenous (IV) dosing and multiple oral (PO) dosing)
was analyzed simultaneously using the IV/PO PK model of FIG. 18.
The data were weighted by 1/Standard Error of the Mean (SEM) or by
1/Concentration.sup.2.
[0360] The initial adjustment parameter values were determined
empirically. Using a limited set of compounds and corresponding in
vitro data from rabbit tissue, the adjustment parameters were
manually varied to obtain FDp values that were reasonably
consistent with the actual PK data. After the initial values were
determined, the GI model developed using STELLA.RTM. was converted
to a program file readable by a program having fitting algorithm,
such as KINETICA.TM.. The initial adjustment parameters were then
simultaneously fit using non-linear regression analysis in a
stepwise manner to determine optimized values (i.e., best fit
values) for the adjustment parameters. Within each step, a few
parameters were selected for optimization by simultaneous fitting.
The fitting was approached using an iterative process, where
selected adjustment parameters were varied systematically such that
the deviation of the GI model determined absorption from the actual
PK determined absorption was minimized. Once the deviation was
reduced to a satisfactory level, few more parameters were then
selected and optimized. The process was continued until all
parameters were successfully optimized. The new parameters were
then placed into the GI model and the FDp determined for each
compound which is compared to the PK FDp to establish the goodness
of fit. This process was repeated until an acceptable goodness of
fit was established. Using this approach, adjustment parameters
were developed to correlate, for example, in vitro solubility,
dissolution, dose and permeability in rabbits to in vivo human
absorption. Although FDp was employed as the reference for
deviation, the actual measurement of absorption can be evaluated
using any number of parameters, such as plasma levels, absorption
constants, or others. Moreover, it will be appreciated that many
sets of adjustment parameters may be developed and established. For
instance, other sets of adjustment parameters may be established to
correlate dog, rat, monkey or other species permeability data to
human, dog, rat, rabbit, monkey, or other animal in vivo
absorption.
[0361] 3. Regional Permeability Correlation Parameters
[0362] Since Pe in all intestinal regions may not be available, for
instance when cell monolayer data is employed to determine Pe in
colon, a correlation was developed that provides a reasonable
prediction of unknown Pe values in the other intestinal
regions.
[0363] An objective was to establish a correlation between regional
permeabilities that allowed prediction of permeability in the
duodenum, jejunum or ileum using known permeabilities in one or two
of the other regions.
[0364] Correlation development involved obtention of regional
permeability values in intestinal tissue from the literature and
experimentally using methods consistent with the experimental
protocols as described in Examples 4-5.
[0365] The regional correlation parameters were estimated using a
polynomial equation developed for this purpose (Equation 17). Any
regional permeability, P.sub.m, can be calculated using any number
of other provided permeabilities.
[0366] The regional correlation parameter function was incorporated
into the GI model using a logic function module. A control
statement was utilized to regulate activation of the regional
correlation parameter estimation function when a user provides less
than the total number of permeability values for the segments of
the GI tract.
[0367] The following (Table 19) shows correlations that were
established along with the corresponding correlation coefficient.
Correlations were accomplished by data transformation and fitting
to a non-linear function.
19TABLE 19 Results of Regional Correlation Variable Dependent
Independent Correlation Coefficient Duodenum Jejunum 0.870 Duodenum
Ileum 0.906 Jejunum Duodenum 0.858 Jejunum Ileum 0.914 Ileum
Duodenum 0.855 Ileum Jejunum 0.894
[0368] As an example of the capability of the correlation, two of
the above correlations were evaluated by estimating the
permeability in the duodenum and jejunum using ileum Pe values. The
compounds chosen were those for which complete Pe values were
available.
[0369] The error and % error for the permeability calculations were
determined by comparing predicted values to the known
permeabilities (Table 20).
20TABLE 20 Evaluation of Regional Correlations Intestinal Region
Duodenum Jejunum Compound Error % Error Error % Error Compound
.alpha.1 -4.64E-07 -46.36 2.42E-07 35.03 Compound .alpha.2 6.37E-08
5.79 -1.11E-07 -5.14 Compound .alpha.3 3.10E-07 114.91 -8.38E-07
-45.28 Compound .alpha.4 1.18E-05 196.00 -5.40E-06 -16.38
[0370] The above results demonstrate that the regional correlation
parameter function of the GI model was able to accurately predict
Pe values for compounds within the initial data set (i.e., high
r.sup.2).
Example 13
Validation and Testing of GI Model
[0371] To demonstrate that the physiological parameters of the
model were operating in a logical manner consistent with expected
behavior in vivo, the parameters were varied and the effect on
output monitored. For example, a decrease in the surface area
available for absorption should result in a decrease in the amount
of compound absorbed. Thus, the physiological parameters of the
model were varied by increasing and/or decreasing their values. The
effect of these variations on the rate, as measured by T50 (time
for 50% absorption), and extent, as measured by FDp, were
simulated. Table 21 shows the physiological parameters that were
varied and the expected effect on FDp and T50.
21TABLE 21 Physiological Parameter Variations* Parameter Range
evaluated Expected effect Surface Area 0.05 to 10 X Normal*
Increase in: Increase FDp or Surface Area or Permeability 1 .times.
10.sup.-7 to 1s10.sup.-5 cm/s Permeability Decrease T50 GI Transit
0.05 to 10 X Normal* Increase in: Increase FDp Time GI Transit Time
Increase T50 Dissolution 0.05 to 10 X Normal* Increase in: Increase
FDp Rate Dissolution Rate Decreased T50 Solubility 1 to 100 mg/ml
Increase in: Increase FDp Solubility Decrease T50 *Normal values
used in the model are listed in Example 12. In each case, only the
parameter chosen was varied, all other parameters were held
constant.
[0372] All effects on FDp and T50 were as expected with the changes
in the physiological parameters. While not all of the ranges were
in the physiological range, the lower part of the range was
included to assure that the model would limit to zero FDp as the
various parameters approached zero.
[0373] The basic structure of the GI model also was assessed by
comparing its ability to predict, from dose and in vitro solubility
and rabbit tissue permeability data, the rate and extent of oral
drug absorption in humans and dogs for several drugs, including
atenolol, ganciclovir, verapamil, and naproxin. These compounds
were chosen for their well known and diverse in vivo absorption
properties and interspecies absorption variability. By changing the
physiological parameter values of the simulation model so that they
corresponded to the species under investigation, but not changing
the model structure, i.e., compartment, flow regulator, converter
relationships, efficacy of the model structure could be evaluated.
Initial parameter values for dog and human were derived from the
literature. Adjustment parameters were used to build the
correlation between the in vitro data and in vivo absorption. For
all four drugs, the GI model accurately predicted FDp for both dog
and human.
[0374] To assess the basic power of the GI model for predicting
oral drug absorption, the model was tested by simulating FDp as a
function of time so as to separate absorption across intestinal
tissue from first pass metabolism and drug concentration in
systemic circulation. Accordingly, methods were developed and used
to determine FDp from clinical plasma data so that transport across
the intestinal tissue could be determined. This was accomplished by
simultaneously fitting clinical pharmacokinetic data (PO and IV) to
the two compartment open IV/PO PK model illustrated as a
compartment-flow model in FIG. 18. Elimination was from the central
compartment. Input from oral doses was into a pre-systemic
compartment (for metabolism) which was in equilibrium with the
central compartment. FDp was determined simultaneously for each
oral dose. Clinical pharmacokinetic data fitted to the IV/PO PK
model demonstrated the ability of the model to accurately determine
blood levels in the central compartment.
[0375] The fitted clinical FDp data for a test set of compounds was
then compared to FDp predicted by the GI model using both
experimental in vitro values for permeability as input as well as
estimated permeability values calculated by the model using the
regional permeability correlation function. The permeability source
of the test compounds are shown in Table 22 below.
22TABLE 22 Permeability Source of Test Compounds Permeability
Compound source* .varies.1 experimental .varies.2 experimental
.varies.3 experimental .varies.4 experimental .varies.5 estimation
.varies.6 experimental .varies.10 estimation .beta.1 estimation
.beta.2 estimation .beta.3 estimation .beta.5 estimation .beta.6
estimation *Experimental - permeability values for all intestinal
segments were submitted. Estimation - permeability values were
calculated using regional permeability correlation parameters.
[0376] FIGS. 48-52 are illustrative of the results of these tests.
The physiological model was found to accurately predict FDp for the
test set of compounds. The accuracy of the prediction is based on
both rate and extent of absorption. Correlation of FDp extent
between the clinical data and as predicted by the model for the
test set of compounds yielded a collective regression coefficient
(r.sup.2) of greater than 0.92.
Example 14
Smoothing Functions for GI Model
[0377] In the in vivo physiological situation, permeability and pH
do not change at distinct points or places within the GI tract
(with the exception of the gastro-duodenal junction). For example,
permeability of a drug in the duodenum may be measured at
1.5.times.10.sup.-6 cm/s and 2.5.times.10.sup.-6 cm/s in the
jejunum, but there is no distinct point in the intestine where such
an abrupt change exist. Since the GI model simulates five regions
or segments of the GI tract, and each segment utilizes its own set
of initial permeability and pH values, an abrupt change, as opposed
to an incremental transition, is simulated for a dosage form or
dissolved drug as it passes distally through the segmented GI
tract.
[0378] To account for this phenomenon, and to generate a GI model
that is as physiologically accurate as possible, smoothing
functions were incorporated into the model. Pairs of exponential
functions were used to adjust the permeability and pH values in
each segment of the intestine. The functions were developed to be
time/position dependent using the mean cumulative transit time as
cues for adjustment. For example, prior to the cumulative transit
time to reach the ileum (C.sub.TTI), the ileum permeability will be
equal to the user provided or regional correlation estimated
jejunum permeability. As time approaches C.sub.TTI, the ileum
permeability will correspond to the exact average of the jejunum
and ileum permeability at that point. Immediately after C.sub.TTI,
the ileum permeability continues to gradually decrease/increase
exponentially until it reaches the user provided, or estimated,
ileum permeability.
[0379] Two exponential functions were used in combination to
effectively smooth the permeability and pH values. The GI model was
adapted to employ Equation 19 as the time approaches a mean
cumulative transit time (C.sub.TT), and Equation 20 immediately
after C.sub.TT.
P=A-ke.sup.(.alpha.t) (Eq. 19)
P=B+ke.sup.-.alpha.(t-TT) (Eq. 20)
[0380] Where A=permeability or pH in the previous intestinal region
or segment, B=permeability or pH in the latter region, k is defined
in Equation 21, .alpha.=a constant used to determine the steepness
of the transition between regions and is inversely proportional to
the transit time of the region, t=time, and TT=cumulative transit
time to exit the previous region.
k=0.5(A-B)/e.sup..alpha.TT (Eq. 21)
[0381] These smoothing functions were utilized to adjust
permeability and pH at junctions of the stomach/duodenum,
duodenum/jejunum, jejunum/ileum, and ileum/colon.
[0382] All publications and patent applications mentioned in this
specification are herein incorporated by reference to the same
extent as if each individual publication or patent application was
specifically and individually indicated to be incorporated by
reference.
[0383] The invention now being fully described, it will be apparent
to one of ordinary skill in the art that many changes and
modifications can be made thereto without departing from the spirit
or scope of the appended claims.
* * * * *