U.S. patent application number 09/353301 was filed with the patent office on 2002-01-03 for configurable bio-transport system simulator.
Invention is credited to KEANE, JOHN A..
Application Number | 20020002447 09/353301 |
Document ID | / |
Family ID | 22234095 |
Filed Date | 2002-01-03 |
United States Patent
Application |
20020002447 |
Kind Code |
A1 |
KEANE, JOHN A. |
January 3, 2002 |
CONFIGURABLE BIO-TRANSPORT SYSTEM SIMULATOR
Abstract
A method of simulating a bio-transport system comprising: (a)
characterizing one or more elements to represent a bio-transport
system of an organism or a portion thereof; (b) constructing one or
more mathematical representations that model one or more
bio-transport dynamics for each element based on the
characterization of the elements to form a configured simulation
model; (c) initializing the configured simulation model; (d)
executing the configured simulation model to obtain bio-transport
dynamics data for one or more elements; and (e) outputting
information to a user based on at least a portion of the
bio-transport dynamics data.
Inventors: |
KEANE, JOHN A.; (PRINCETON,
NJ) |
Correspondence
Address: |
STEPHEN J DRISCOLL
SYNNESTVEDT & LECHNER LLP
1101 MARKET STREET
SUITE 2600
PHILADELPHIA
PA
191072950
|
Family ID: |
22234095 |
Appl. No.: |
09/353301 |
Filed: |
July 13, 1999 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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60092608 |
Jul 13, 1998 |
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Current U.S.
Class: |
703/11 |
Current CPC
Class: |
G06N 3/002 20130101;
B82Y 10/00 20130101 |
Class at
Publication: |
703/11 |
International
Class: |
G06N 003/00 |
Claims
What is claimed is:
1. A method of simulating a bio-transport system comprising:
characterizing one or more elements to represent a bio-transport
system of an organism or a portion thereof; constructing one or
more mathematical representations that model one or more
bio-transport dynamics for each element based on the
characterization of said elements to form a configured simulation
model; initializing said configured simulation model; executing
said configured simulation model to obtain bio-transport dynamics
data for one or more elements; and outputting information to a user
based on at least a portion of said bio-transport dynamics
data.
2. The method of claim 1, wherein characterizing one or more
elements is performed using data obtained from imaging
equipment.
3. The method of claim 1, further comprising: exchanging
bio-transport dynamics data between one or more organ models.
4. The method of claim 3, wherein bio-transport dynamics data is
exchanged between two or more organ models via said configured
simulation model.
5. The method of claim 4, wherein one or more organ models are
interfaced to said configured simulation model via a
telecommunication link.
6. The method of claim 1, wherein an element is characterized as an
organ.
7. The method of claim 1, wherein said bio-transport system is a
subsystem of an organ and said configured simulation model is an
object in an organ model modeling said organ.
8. The method of claim 1, wherein said bio-transport system is a
subsystem of a cell and said simulation model is an object in a
cell simulation model modeling said cell.
9. The method of claim 1, wherein one bio-transport dynamic is the
flow of fluid within the bio-transport system.
10. The method of claim 9, wherein additional bio-transport
dynamics are selected from the group consisting of mass transport
and/or reactions of entities in the fluid; heat transport in the
fluid; external dynamical and mechanical effects on the fluid;
effects at a distance; and combinations of two or more thereof.
11. The method of claim 10, wherein effects at a distance are
simulated using a relations processing engine.
12. The method of claim 1, wherein at least one of said
user-specified characteristics is a condition of state.
13. The method of claim 1, wherein a plurality of elements are
characterized to model multilevel branching.
14. The method of claim 1, wherein initializing said simulation
model comprises entering prime mover data and/or input/output
conditions of said bio-transport system.
15. The method of claim 14, wherein prime mover data represents a
function of time and state.
16. The method of claim 15, wherein one bio-transport dynamic is
fluid flow which is a function of an element's position relative to
said prime mover and the state condition of said prime mover.
17. The method of claim 1, wherein each element is an object in
object-oriented programming environment.
18. The method of claim 1, wherein said bio-transport system is a
circulatory system
19. The method of claim 1, wherein said information is used for
diagnostic purposes.
20. The method of claim 1, wherein said information is used for
determining drug dissemination in a circulatory system as a
function of time and position within a circulatory system.
21. The method of claim 1, wherein said configured simulation model
incorporates conditions of state relationships in an overall set of
relationships to be solved during execution of the configured
simulation model.
22. The method of claim 1, wherein the mathematical relationships
of one or more bio-transport dynamics are interrelated such that
the output of one relationship is used as the input to at least
another relationship.
23. The method of claim 1, wherein said configured simulation model
comprises at least two simulation models.
24. A method of simulating a transport system comprising: providing
a constructed simulation model comprising: one or more elements
characterized to represent a bio-transport system or a portion
thereof; at least one model having one or more mathematical
representations of one or more bio-transport dynamics for each
element, said mathematical representation being constructed based
on the characterization of said elements; initializing said
constructed simulation model; executing said constructed simulation
model to obtain bio-transport dynamics data for each element; and
outputting information to a user based on at least a portion of
said bio-transport dynamics data.
25. A computer system for simulating a transport system comprising:
a processor; a user interface operatively connected to the
processor for receiving input from and conveying output to a user;
and memory operatively connected to the processor and containing
instructions for constructing and/or executing the simulation
model; wherein constructing said simulation model comprises (a)
receiving construction data characterizing one or more elements to
represent a bio-transport system or a portion thereof; (b)
constructing one or more mathematical representations that model
one or more bio-transport dynamics for each element based on the
data characterizing said elements to form a configured simulation
model; and wherein executing said simulation model comprises (a)
initialing said configured simulation model; and (b) executing said
configured simulation model to obtain bio-transport dynamic data
for each element.
26. A computer-readable medium comprising instructions for enabling
a computer-based system to construct and/or execute the simulation
model; wherein constructing said simulation model comprises (a)
receiving data characterizing one or more elements to represent a
bio-transport system or a portion thereof; (b) constructing one or
more mathematical representations that model one or more
bio-transport dynamics for each element based on the data
characterizing said elements to form a configured simulation model;
and wherein executing said simulation model comprises (a)
initialing said configured simulation model; and (b) executing said
configured simulation model to obtain bio-transport dynamic data
for each element.
27. A process for simulating on a computer system a circulatory
system, said process comprising the steps of: inputting an ordered
selection of channel elements and fluid characteristics into a
computer system; inputting data of initial and boundary conditions;
configuring a circulatory model resident within said computer
system according to said selection to form a configured circulatory
model, said configured circulatory model having at least one
mathematical representation corresponding to said selection;
applying said data to the configured circulatory model; and
displaying on a user interface of said computer the results of
applying data to said configured circulatory model.
28. A method of simulating the interaction of two or more organs
over a circulatory system, said method comprising: constructing a
matrix of one or more relationships between at least a first organ
and a second organ over a circulatory system; providing data
relating to said first organ's interaction with said circulatory
system; applying said data to said matrix and solving to generate
at least one solution corresponding to the effect of said first
organ on said second organ over said circulatory system; and
outputting said solution.
29. The method of claim 28, wherein said data is provided by at
least a first organ model modeling said first organ, and said
solution is outputted to a second model modeling said second
organ.
30. The method of claim 28, wherein said one or more solutions is
generated by a relations processing engine.
31. The method of claim 28, wherein said relationships comprise a
time delay to account for spacial separation effects between said
first and second organs.
32. The method of claim 28, wherein one of said first or second
organ is a heart.
33. The method of claim 28, wherein one of said first or second
organ is a kidney.
Description
RELATED APPLICATION
[0001] This application is based on application Ser. No.
60/092,608, filed Jul. 13, 1998 entitled "Circulatory System
Simulator."
FIELD OF INVENTION
[0002] This invention relates to a computer-based simulation model
for simulating a transport system in an organism. More
specifically, the present invention relates to a configurable
simulation model that emulates the behavior of a circulatory
system.
BACKGROUND OF THE INVENTION
[0003] Almost all organisms have systems for channeling or
otherwise controlling the movement of mass and/or energy in or
around the organism. These systems are referred to herein as
"bio-transport systems" (BTS), and include, for example,
circulatory systems, digestive (gastrointestinal) systems,
pulmonary systems, lymphatic systems, renal systems, and the
movement of chemical and biological entities within and among
tissues and cells just to name a few.
[0004] One bio-transport system of particular interest herein is
the circulatory system. The circulatory system channels blood and
other entities through vessels and among the various organs to
supply nutrients to tissues, to regulate body mechanisms, and to
facilitate the flow of materials and interactions necessary in
general to keep an organism alive. Additionally, the circulatory
system contains a medium, that is, blood, in which various
chemical, biological and physical reactions take place. Thus, the
circulatory system is a complex system having geometric, physical
and chemical/biological properties; flow behavior; internal
reactions; and interactions among blood, vessels, connected organs,
and the organism in general. The properties, configurations,
behaviors, reactions and interactions of a bio-transport system are
collectively referred to herein as "bio-transport dynamics"
[BTD].
[0005] As medicine becomes more quantitative, there is a need for
analytic tools to relate more precisely causes to effects in
organisms and to more clearly elucidate the mechanisms involved.
This requires obtaining bio-transport dynamic data. For example, in
the pharmaceutical field, there is a need to evaluate the effects
of chemicals in drug studies by computing and displaying the
concentration, at different points in the circulatory system and as
a function of time, of a chemical injected into the body at a point
in time and space, or bio-availability of an orally ingested drug
in its journey through the GI tract and the circulatory system to
its final destination at an organ or other target within the body.
Aside from pharmaceutical applications, there is a need for
analyzing bio-transport dynamics for diagnostic purposes, such as,
when assigning a quantitative measure to the degree of
atherosclerosis present in an individual's specific circulatory
system.
[0006] Despite the desire to analyze bio-transport dynamics of mass
transport systems within organisms, the dynamic nature of these
systems makes them inherently difficult to study. Conventional
approaches of studying bio-transport dynamics of the circulatory
system for example involve obtaining clinical measurements or
images of the circulatory system in humans and animals. For
example, blood pressure cuffs and direct pressure probes are used
to measure flow rates and pressures, and ultrasound and angiography
are used to image vessels of the circulatory system. These
measurements and images are compared against norms to attempt to
qualify an organism's status and to help locate anomalies. Some of
these tools are non-invasive but imprecise, such as
sphygmomanometer, while others are precise but invasive, and
potentially life threatening, such as cardiac catheterization.
[0007] Animal testing is another approach for obtaining
bio-transport dynamic data that traditionally has allowed for more
invasive measurements. Animal testing, however, is under scrutiny.
Political and social pressure against animal testing has become
very strong and is expected to increase. For example, scientists
now must seek approval from the FDA for every primate subjected to
experimentation and must account for every rat used. Animal testing
is being framed today in a broader ethical context, and is likely
to become even more circumscribed in the future.
[0008] Given the limitations presented by in-vivo testing, a
theoretical approach in analyzing bio-transport dynamics is
attractive. There are a number of practical difficulties, however,
associated with a pure theoretical analysis of bio-transport
dynamics that are not normally encountered outside living
organisms. Sir James Lighthill [Lighthill M. J. Mathematical
Biofluiddynamics" SIAM Regional Conference Series in Applied Math.
1975] lists four broad categories:
[0009] 1. Unusual vessel distensability and resultant attenuation
of wave propagation;
[0010] 2. Great range of Reynolds numbers >5000 to <100 with
small capillaries <10 microns;
[0011] 3. Atypical fluid properties; and
[0012] 4. Branching in lungs and circulatory system [20-30 forkings
leading to >100 m branches].
[0013] To this list should be added the historic difficulty of
obtaining clinical experimental data as mentioned above to compare
with theory.
[0014] Piecemeal solutions that arise from considering only part of
a problem-, or a radical simplification of the problem to obtain an
assumption-restricted solution, while useful within the stipulated
range of applicability, do not meet current and future
clinical/research needs for scope, detail, accuracy and
architecture. For example, in Guyton, et. al. "Computer Analysis of
Total Circulatory Function and of Cardiac Output Regulation", Chap.
17, Graphical, Algebraic and Computer Analyses 1973, a mathematical
representation of the circulatory system is provided based on the
system as a whole. Although such a model provides useful
information on the circulatory system in gross terms, no detailed
information with regard to spatial dependence of the system is
available. In other words, this model can only provide data on bulk
values for variables in the circulatory system and not for
different components of the system where data tend to vary as
suggested by Lighthill.
[0015] Therefore, a need exists for an approach that will enable
researchers and physicians to experiment and practice with a
bio-transport system without the attendant time constraints, risks
and difficulties of dealing with a real bio-transport system in a
living organism. The present invention fulfills this need among
others.
SUMMARY OF INVENTION
[0016] The present invention provides an approach for analyzing
bio-transport dynamics that overcomes the above-identified problems
by simulating, in silico, a bio-transport system of an organism
using a configurable simulation model. The configurable simulation
model provides a generic framework that is readily customizable to
simulate one or more bio-transport dynamics aspects of a
user-defined bio-transport system as a function of both time and
position within the system. More specifically, the present
invention applies finite-element techniques along with first
principles and empirical relationships to a bio-transport system to
construct mathematical representations of one or more bio-transport
dynamics in and around the bio-transport system based on
user-characterized elements representing the bio-transport system.
By using a finite-element approach, the bio-transport system can be
compartmentalized to manage its intricacies and provide
sophisticated bio-transport dynamic data not only as a function of
time, but also as a function of the spatial position locating each
element defined.
[0017] By combining a configurable finite element approach with
modern techniques in computer programming and current computer
architecture, the present invention creates a simulation model that
affords the flexibility and scope needed to address many of the
complexities outlined by Lighthill by offering one or more of the
following functional capabilities:
[0018] (1) Configurable to provide detailed solutions as a function
time and at least one space dimension (e.g. axial position along
the blood vessels);
[0019] (2) Configurable to account for both nonlinear effects (e.g.
vessel elasticity and/or conditions of state dependency) and
non-Newtonian fluid behavior;
[0020] (3) Configurable to represent multi-level branching;
[0021] (4) Provides a platform that is readily extendable to cover
(a) various bio-transport dynamics phenomena in a bio-transport
system such as fluid behavior, chemical, biological, thermal and
gravitational/inertial effects, (b) entities that interact with a
bio-transport system such as organs and (c) physiological
phenomena, effectuated via systems other than bio-transport systems
[e.g. the central nervous system], which influence the
bio-transport dynamics behavior of a bio-transport system;
[0022] (5) Offers an open architecture to permit concurrent,
inter=operability with complementary models (e.g. existing organ
models);
[0023] (6) Harmonizes with modern computer programming paradigms
and infrastructure (e.g. with respect to parallel processing,
object oriented programming and Imaging & Visualization);
and
[0024] (7) Extensible to approximate continuity of time and space
to any desired degree, within the constraints of computational
power and storage access available.
[0025] The simulation model of the present invention enables a user
to make decisions regarding the configuration of a bio-transport
system and to see the effects of these decisions on a system's
bio-transport dynamics, such as, for example, fluid flow rates,
pressure gradients, chemical and biological concentrations and
fluid temperatures, at various points in time and space. The
simulator may be used as an instructional tool to illustrate, for
example, the behavior of a representative circulatory system.
Additionally, it may be used with respect to a specific
bio-transport system as a planning guide to examine alternative
strategies to correct problems, or as an experimental platform to
elucidate mechanisms occurring in classes of circulatory systems
for example. Since it is only a simulator, the user can learn,
teach, plan, diagnose or experiment without risk to sentient
organisms and in ways that are not ethically and/or technically
possible with live organisms.
[0026] One aspect of the invention is a method of simulating
bio-transport dynamics of a bio-transport system using the
configurable simulation model. In practice, computer simulation of
a bio-transport system involves two basic steps: (a) constructing a
simulation model of a bio-transport system of an organism; and (b)
simulating the behavior of the bio-transport system by running the
simulation model on a computer. It should be obvious to those
skilled in the art that the simulation model must be constructed
before it can be run, and that, once constructed, it can be run
repeatedly without being "reconstructed." Consequently, these steps
may be performed jointly or individually.
[0027] In a preferred embodiment of the construction phase, a user
defines and characterizes elements and one or more transported
entities associated therewith to represent the initial state of one
of the organism's bio-transport systems or a portion thereof. A
transported entity may be, for example, fluid, energy, chemicals,
and biologicals. The term "fluid" is used broadly herein and refers
to any material capable of flowing and includes, but is not limited
to, traditional fluids such as liquids and gases, plus mixtures,
dispersions, suspensions or slurries of solid and viscoelastic
materials. Examples of fluids include blood, food, and air.
[0028] Based on the characterization of the elements, one or more
mathematical representations that model particular bio-transport
dynamics are constructed for each element. This forms a configured
bio-transport system simulation model which has a mathematical
representation for particular bio-transport dynamics phenomena at
each element of the bio-transport system being modeled. It is
especially convenient to designate an object for each element in an
object-oriented programming environment, although the present
invention is not limited to object-orientated programming
techniques.
[0029] In a preferred embodiment of the simulation phase, a
conventional simulator uploads the configured simulation model,
initial conditions are entered, and then the mathematical
representations are executed by the simulator for a desired period
of time to obtain bio-transport dynamics data at each element as a
function of time.
[0030] The degree to which one defines and characterizes the
elements representing the bio-transport system depends upon the
bio-transport dynamics and the specificity desired which may be
determined by one skilled in the art. Generally, an element is
characterized in terms of its geometry and physical characteristics
which may include, for example, shape, dimensions, orientation,
elasticity, permeability and resistance to flow, just to name a
few. The fluid associated with the element is characterized
generally in terms of physical properties such as, for example,
viscosity, heat capacity and density, just to name a few. In the
preferred embodiment, the model is adapted to handle
characteristics which are dependent on "conditions of state,"
meaning that the characteristics' values are dependent upon other
conditions existent at a particular element. For example, viscosity
may be dependent upon temperature of the element's associated
fluid, and an element's dimensions may be dependent upon the
pressure of the element's associated fluid. The term "associated
fluid" as used herein refers to the fluid contained within an
element at a particular point in time.
[0031] Rather than defining and characterizing an element only as a
flow channel component in a bio-transport system, it may be
preferable to define an element to include entities that are not
only flow channel components of the bio-transport system but also
may interact in a special way with the system, such as an organ or
a tumor. An element characterized to represent such an entity would
model it in an average or "bulk" manner such that detailed
information with regard to spatial dependence within say an organ
would not be available. Thus, for example, an organ may be modeled
as an "organ element" and characterized generally with a certain
resistance to flow and a certain volumetric capacity, which perhaps
is altered by pressure. However, in addition to normal element
properties, the organ element may have special properties, such as
volumetric pumping rates in a heart organ element, or hormone
production in the case of the hypothalamus to mention just a
few.
[0032] In a preferred embodiment, certain data characterizing
elements of a particular bio-transport system are automatically
generated by an imaging device such as magnetic resonance imaging
(MRI), Computer tomography (CT) or ultrasound. The data generated
from these devices then are inputted into the simulation model to
construct a simulation model having elements representing the
imaged bio-transport system, said configuration possibly being
manually adjusted to compensate for any limitations in a totally
automated process. The structural arrangement of the computational
code effecting this construction preferably is adapted to readily
receive the standard format of the input data from the imaging
device. Using data from imaging devices is particularly useful in
clinical circumstances where the physician/surgeon needs to analyze
the unique bio-transport system of a specific patient.
[0033] The mathematical constructs are based on known relationships
between user-specified characteristics to provide a prediction of
bio-transport dynamics. Most bio-transport dynamics are governed by
established first principles and physical relationships, for
example, conservation of mass, conservation of momentum,
conservation of energy, constitutive equations and other empirical
relationships. The simulation model uses these relationships along
with the user-specified characteristics to calculate bio-transport
dynamics aspects such as flow rates, concentrations and pressures
at different points in the configured simulation model at different
points in time. The results are dependent on how the simulator is
configured by the user, so any number of different bio-transport
systems may be modeled for different organisms or different parts
thereof. It should be understood that the formulae presented herein
are to predict behavior and interaction and are not intended to
describe or theorize bio-transport dynamics. In other words, the
invention does not depend on the theoretical merit of a particular
equation providing that it predicts conditions as accurately and
precisely as desired by at least one user. It is anticipated that
alternative equations may be used to progressively improve the
predictive ability and speed of convergence of the simulator as
desired by other users.
[0034] The particular bio-transport dynamics modeled depend upon
the user's preference although bio-transport simulations in one
form or another generally model flow behavior since most
bio-transport dynamics, such as dispersion of a chemical or
biological component, relate to the fluid flow in the bio-transport
system. In a preferred embodiment, to enhance realism and
predictability, the simulation model further comprises one or more
of the following bio-transport dynamics in addition to fluid
behavior: (a) mass transport and reactions of chemicals and other
entities, such as viruses, bacteria and clots, in the fluid; (b)
heat transport in the fluid including its effects and Transport;
(c) external dynamical and mechanical effects such as gravitational
and inertial forces, and (d) interaction of elements/organs with
other elements/organs that are effectuated by systems outside the
bio-transport system under study [for example, effects at a
distance produced by the central nervous system when the
circulatory system is under study]. This last enhancement provides
for user definition of mathematical relationships among variables
to represent physiological interactions that exist within an
organism, but are not effectuated by bio-transport mechanisms
within the bio-transport system being simulated. In addition to
modeling for these bio-transport dynamics, the simulator of the
present invention may be enhanced with other models as applications
dictate.
[0035] In a preferred embodiment, the simulation model has an open
architecture to permit concurrent, interoperability with
complementary models. Such a feature is particularly useful in
enabling organ simulators to be networked to provide for more
realistic simulations. Since organs are connected by the
circulatory system, to model the behavior of an organ in situ, an
organ simulator also should be able to simulate the circulatory
system through which it communicates chemically and biologically
with the rest of the organism and with certain extra-circulatory
functional interactions, such as the central nervous system. In
addition to providing a common platform to network organs, the
simulation model of the present invention provides an open
interface for interconnection among various organ models. This
saves developers of organ simulators the effort of individually
constructing an ancillary circulatory simulator with
extra-circulatory functional interactions for each organ model.
Additionally, groups of organ developers can leverage on one
another's modeling efforts by jointly using the interface provided
by the present invention over remote connections, such as the
Internet. Thus, the simulation model of the present invention
constitutes a global platform for collaborative research on
physiological processes of organisms.
[0036] In addition to configuring the simulation model of the
present invention as an inter-organ transport model, it may
configured as an intra-organ, intra-tissue or intra-cell transport
model. In other words, the configurability of the simulation model
of the present invention also enables it to simulate fluid flow and
transport within an organ, tissue or cell. With respect to organs,
flow and transport phenomena underlie the basic behavior of many
organs. At least one organ has already been modeled in a fashion to
approximate a time-space continuum, for example, in Winslow, R.
et.al "Simulating Cardiac Sinus and Atrial Network Dynamics on the
Connection Machine" Physica D 64 pp281-298, 1993. Likewise, with
respect to cells, Tomita, M. et.al. "E-CELL: Software Environment
for Whole Cell Simulation" Bio. Mag. Keio 1996 describes an "E-CELL
simulator" that emulates transcription, translation and other
chemical reactions occurring in the cell. Cell modeling, as
described in that paper, would be enhanced by the inclusion of
fluid flow, chemical/biological and thermal transport phenomena and
possibly dynamic effects. Instead of repeating the effort of
creating a bio-transport simulator bound to a specific organ,
tissue or cell model for each organ, tissue and cell respectively,
the simulation model of the present invention, with its ability to
be configured and its open architecture, can be used as the
bio-transport simulator component in any organ, tissue or cell
model, thereby relieving the model developer of the task of
managing the bio-transport part of the organ, tissue or cell
simulation. Thus, the bio-transport simulation model becomes a
simple "bio-transport object" in a modem object-oriented
programming environment, or its equivalent in a more-traditional
programming environment. It is anticipated that the use of this
bio-transport object will accelerate the development of new
physiological models and leverage many existing ordinary
differential equation [ODE] models of physiological processes by
reducing the effort to incorporate true spatial representations
using partial differential equations [PDE] into the models.
[0037] Another aspect of the invention involves an apparatus for
simulating a bio-transport system. In a preferred embodiment, the
apparatus comprises (a) a processor; (b) a user interface
operatively connected to the processor for receiving input from and
conveying output to a user; and (c) memory operatively connected to
the processor and containing instructions for constructing and/or
executing the simulation model as described above. Preferably, the
user interface prompts the user in a logical fashion to define and
characterize the elements to represent the transport system to the
desired precision/accuracy. Additionally, the user interface
preferably displays output in a natural fashion so that the user
can intuitively interpret results, thereby reducing errors and
increasing acceptability. To this end, it is preferable to employ a
structural arrangement of computational code that harmonizes with
the natural display of results.
[0038] Yet another aspect of the present invention is a
computer-readable medium of instructions for enabling the system
described above to construct and/or execute the simulation model as
described above.
BRIEF DESCRIPTION OF THE DRAWINGS
[0039] The invention may best be understood by reference to the
following description taken in conjunction with the accompanying
drawings, wherein like reference numerals identify like elements,
and wherein:
[0040] FIG. 1 shows a diagram of the present invention;
[0041] FIG. 2 shows overall flow chart of the invention's
operations;
[0042] FIG. 3 shows a flow chart of the configuration of the
bio-transport system model;
[0043] FIG. 4 shows a flow chart of the fluid flow model;
[0044] FIG. 5 shows a flow chart of the mass transport
chemical/biological model;
[0045] FIG. 6 shows a flow chart of the heat transport model;
[0046] FIG. 7 shows a flow chart of the dynamics and mechanics
model;
[0047] FIG. 8 shows a flow chart of the organs' interface;
[0048] FIG. 9 shows a flow chart of the user defined
extra-transport model and the relations processing engine;
[0049] FIG. 10 shows a flow chart of motion video output of the
configurable bio-transport system simulator results; and
[0050] FIG. 11 shows a flow chart of the automatic input of the
bio-transport system geometry and certain aspects of the initial
state.
DETAILED DESCRIPTION OF THE PRESENT INVENTION AND PREFERRED
EMBODIMENTS
[0051] The present invention provides for a system and method for
simulating bio-transport dynamics of a bio-transport system, using
the configurable simulation model. More specifically, the invention
may be practiced to simulate the transport of fluids, energy,
materials, chemicals and biologicals in any bio-transport system,
such as, for example, a circulatory system, a lymphatic system, a
gastro-intestinal tract, channel arrays formed by tissue such as
fluid flow channels in the kidney and heart, and nutrient intake
and protein production transport inside and among cells. The
particular bio-transport system modeled need not be confined to
humans, but may include those found in animals, insects, plants,
and bacteria or any other organism.
[0052] The present invention and preferred embodiments are
discussed below with respect to (I) the Overall System, (II) the
Overall Process, and (III) the Models. For illustrative purposes,
the human circulatory system is described in detail herein using
terminology consistent with that system such as vessels, organs and
blood. Aside from being a familiar reference, the human circulatory
system also is simplistic from the standpoint that it is a
closed-loop system which is a function of time and essentially one
spacial dimension. It should be understood, however, that the
invention should not be construed as being limited to circulatory
systems and other embodiments exist, including open-looped systems
that are functions of time and multiple spacial relationships.
I. Overall System
[0053] The system 100 consists of a central processor unit 101,
memory 102, and a user interface 103. The user interface may
comprise traditional equipment such as a monitor and printer for
displaying information for the user and a keyboard and mouse for
entering information, as well as more exotic equipment such as
scanners, voice recognition systems, touch screens, CT and MRI
imaging devices for input and constructed output for MRI, CT and 3D
graphics displays [e.g. 3D Virtuoso from Siemens]. It is
anticipated that system 100 can be configured to accommodate any
user interface both known and in the future.
[0054] The memory contains at least one model, such as a fluid flow
model 104, labeled as Fluid Flow Model [FFM] and may possibly
contain other models such as a chemicals and biologicals mass
transport and reactions model 105, labeled as "Mass Transport
Chemical/Biological Model [MTC/BM], a heat Transport model 106,
labeled as Heat Transport Model [HTM], a dynamics and mechanics
model 107, an interface 108 to detailed models of organs, and an
Extra-Bio-transport model 109 containing a Relations Processing
Engine [RPE] to process user defined relationships among
elements/organs that are effectuated outside the bio-transport
system under study. These simulator models [104. 105.106, 107 and
109] and the user input for the RPE have mathematical algorithms to
simulate a bio-transport system and extra-bio-transport system
relations.
[0055] The memory 102 also stores the resident data to enable the
CPU 101 to construct and process the mathematical algorithms. In
this disclosure, types of data are referred to, for example, as
characteristics, properties, parameters, initial conditions, and
boundary conditions. This terminology is adopted from common usage
in continuum mechanics for illustrative purposes and should not be
used to limit the scope of the invention. One skilled in the art
will recognize that data, labeled as, for example, parameters,
initial conditions and boundary conditions, could be grouped
together under the generic heading of data.
[0056] The system 100 may be configured to allow processing to
occur on more than one processor unit, and that the processing
units need not reside on a single computer, nor must the CPUs
reside at a single physical site. Once the CPU processes the
information, the memory 102 stores the results. The system 100 may
also include a data storage component 124 for storing information
associated with the aforementioned models.
II. Overall Process
[0057] The overall process of the system is shown in FIG. 2. When a
user starts the system 100, the various models are inputted
according to Block 251 and stored in memory 102 such that the
models are resident within the system 100. Alternatively, certain
models may be stored on disk or other information storage devices
if the memory cannot accommodate all the models simultaneously. In
this configuration, the CPU 101 would transfer models from the
storage 124 to memory 102 if needed and return models back to the
storage 124 when dormant. Such a function is well known in the
art.
[0058] Next, dictionary data to identify components and data, such
as the physical characteristics of the flow channel elements, the
geometric connection of flow channel elements one to the other, the
gross characteristics of organ elements, their geometries, and
characteristics of the fluid are made resident in memory by block
252. These data customize the model to a particular organism's
bio-transport system, or part thereof, rather than operating on a
preset arbitrary model. Such data may be entered by the user
contemporaneously with the program's operations, or it may be
entered into data storage 124 prior to the program's operation and
accessed as needed by the CPU 101. The data storage may be any data
storage means such as disk, hard drive, or memory. If other than
memory, the exchange of data between memory 102 and the data
storage 124 would be controlled by the CPU 101 using known
methods.
[0059] Automatic input of data from certain experimental/diagnostic
tools reduces the tedious effort of manual inputting for example
the geometry data associated with even simple Bio-Transport
systems. It is anticipated that the CB-TSS will be used to aid in
the diagnosis and correction of problems in individual
Bio-Transport systems. For this to be practical, automatic entry of
setup data for each specific Bio-Transport system is considered to
be a requirement. In a preferred version, gray scale or color
coding of, for example, image density produced by radioactive
chemical concentrations further reduces the setup of certain CB-TSS
models
[0060] Referring to FIG. 11, the clinical results of an MRI [or
other common diagnostic tool] are first stored on a storage device
1102 by the user. During the data input section of the CB-TSS, the
user selects an option 315 directing the CB-TSS to use these data,
instead of manual input, to construct the Bio-Transport system
geometry. These data are read into memory 1101 and then, using the
known format of the diagnostic tool and associated graphic
detection algorithms, converts these data to the input format for
the Bio-Transport system geometry.
[0061] The system 100 is finally initialized when data such as
initial conditions of state, boundary conditions and other data and
parameters are also made resident in memory 102 by block 253 to
customize the model to an initial state. Parameters allow the
simulator configuration to be quickly changed making it easy for
the user to conduct parametric studies. Each of the models has its
own parameters. An example of a parameter is organism size, where,
for example, all dimensions are scaled in proportion to a size
parameter. One skilled in the art will recognize that the functions
of Blocks 251, 252 and 253 can be performed in any sequence. By
initializing the simulator according to a particular set of data,
characteristics, conditions of state and parameters it becomes
customized for a particular bio-transport system in a particular
initial state, enabling the computer system 100 to generate
realistic and useful information on the behavior of that particular
system over time.
[0062] Following the initialization of the simulator by Blocks 251,
252 and 253, Block 254 determines if another time step should be
run. If not, the process ends. If another time step should be run,
then the various models are executed for another time step in Block
255, and the results of the simulation are displayed in Block
256.
[0063] The user can display snapshots of the simulator state [e.g.,
pressures, flow rates, chemical concentrations at each of the
element locations]. These displays are graphical as well as
tabular.
[0064] In a preferred embodiment, the results of state conditions
for the respective models are saved with a periodicity determined
by the user. Referring to FIG. 10, after all time steps are
processed, these data are supplied by Block 1002 to Block 1001
where they are assembled into a series of graphics images which are
sequentially presented on a displaying unit 1003 creating the
effect of an animated motion video. A number of different displays
are possible. For example, the CB-TSS geometry of the circulatory
system under study can be drawn and the concentration of a chemical
at each element location superimposed thereon, using color-coding
or a grey scale, for each time step. The result is a motion video
of the dispersion of the chemical through the circulatory system
over time. It is also possible to create a CB-TSS view from the
prospective of an observer traveling with the fluid through the
Bio-Transport system. The technology to save and assemble the data
into a graphical display is well known.
[0065] It is anticipated that the timing and other aspects of the
graphics images will be altered to enhance the effect of the
display for certain teaching purposes. This usage is termed a
stylized animation of the simulation, wherein the relation to
actual physics is distorted, compared with an unaltered view or
series of images of a simulation as described above. It is
anticipated that such animations will be constructed using computer
executed algorithms to construct the desired stylized series of
images of the physical phenomena. Although such simulations of the
Bio-Transport system, or parts thereof, may not be based on first
principles and physical laws, the result is a simulation, distorted
or otherwise of the Bio-Transport system and is therefore a B-TSS
as a subset of CB-TSS. Such imaginative constructions are
anticipated and thus covered by this teaching.
[0066] In a preferred embodiment the output of the Bio-Transport
system simulator is reformatted to serve as data input for a
variety of diagnostic and experimental tools such as MRI. For
example, instead of the display component of an MRI system using
processed signals originating in the sensing device to form a
graphic display, it would use similarly formatted data constructed
by the output component 1004 of the CB-TSS to create a disk file
1005 which is then used as input for an MRI, et. al. display. The
user of the MRI equipment would see what appears to be a MRI of the
organism's actual Bio-Transport system. This mode of output has the
advantage of familiarity to current users of these important
experimental and diagnostic tools.
III. Models
[0067] The construction/initialization of one or more models in
Blocks 251-253 is considered in greater detail in this section. The
models are described generally in the first section (1. Models
Generally), and then more specifically with respect to each model
in the second section, (2. Detailed Description of Models).
[0068] 1. Models Generally
[0069] In a preferred embodiment, the Fluid Flow Model 204 is
configured by a user. In Block 252, the user inputs a selection of
flow channel elements and organ elements, collectively referred to
as elements, together with their respective characteristics such as
initial and final diameter, length, elasticity, permeability and
convection coefficients, volume of associated interstitial space,
as well as fluid characteristics. Fluid characteristic may include,
for example, general properties, such as temperature, pressure, and
viscosity, as well as the identification, concentration and
interactions of its components, which, in the case of blood, may
include, plasma, blood cells, enzymes, hormones, proteins, amino
acids and other chemical elements and compounds, viruses, bacteria,
macrophages, t cells and other products of the immune system,
parasites, clots and other biological entities. Certain data, such
as the diameter of a flow channel element, may depend on state
conditions of the element and associated fluid, such as pressure
and concentration of certain chemicals in the associated, or may
depend on the state of external influences, such as a central
nervous system. In a preferred embodiment, the user can specify
such relationships and the model incorporates the relationships in
the overall set of algorithms to be executed.
[0070] Also associated with each element is a mathematical
relationship within the Fluid Flow Model describing the behavior of
the associated fluid. When the user selects a specific element and
specifies its characteristics, this mathematical relationship is
constructed. Hence the configured Fluid Flow Model comprises a
selection of a set of mathematical relationships representing the
fluid behavior within the Fluid Flow Model.
[0071] The driving force for fluid motion is traced back to a prime
mover, for example, the pumping action of the heart, or to boundary
conditions at "input/output" elements which may be used if the
simulator is configured to represent part of a circulatory system,
for example, a region of microcirculation. These prime mover
functions are modeled by special elements whose characteristics
allow the user to specify data that describe mathematical relations
for the pressure increment and flow as a function of time at the
special element location. In one preferred embodiment, these
relations are not explicit functions of time, but rather depend on
the state of the special element as well as time. It is anticipated
that other types of prime mover representations and other types of
special elements will be included in future embodiments of the
simulator.
[0072] Next the relationships are combined together and solved
simultaneously to determine the flow performance of the
bio-transport system. Means to solve sets of simultaneous equations
by computer are well known in the art. At the end of an incremental
time period, the user receives the results of the solution process
for that point in time 256. The information may be output through
the user interface as either a monitor display or a printout.
Optionally, the output may be omitted for certain time periods.
[0073] The basic Fluid Flow Model may be augmented with other
models to more realistically emulate the operation of an actual
bio-transport system. Like the Fluid Flow Model 204, these models
are resident in the memory 102 of the computer 100, or are brought
into memory by the processor 101 from storage 124 as needed. To
account for concentrations of chemicals and biologicals within the
bio-transport system, the Mass Transport Chemical/Biological Model
205 may be employed. This model 205 accounts for the mass transport
within the vessels and organs, flow across porous/semi-permeable
vessel and organ walls of chemical elements, compounds, including
drugs proteins and enzymes, and changes in mass brought about by
chemicals/biologicals reactions. As well, mass transport within the
vessels and organs and cross-wall movement of other entities such
as viruses and bacteria, [collectively referred to as biologicals]
and reactions thereof can be modeled. In a preferred embodiment,
chemical and biological reactions and reaction rates within the
bio-transport fluid, within organs and at element walls are
included. Like the Fluid Flow Model 204, the MTC/BM 205 requires
the user to input data regarding, for example, initial conditions
and boundary conditions. In the preferred embodiment, mathematical
descriptions of chemical and biological reactions and reaction
rates can be included as part of the data for MTC/BM 205. By
applying the flow rate results 211 of the current time step of the
Fluid Flow Model and the reaction relations to the MTC/BM
concentrations of the previous time step, the concentrations of the
current time step for MTC/BM can be computed.
[0074] Supplementing the bio-transport simulator with a Heat
Transport Model 206 adds further realism, accuracy and predictive
ability to the simulation. The HTM 206 emulates the flow of thermal
energy through mass transport, conduction, convection and
generation. Like the Fluid Flow Model 204, HTM 206 requires the
user to input data regarding the initial and boundary conditions.
Mathematical relations regarding the flow of heat involved are
applied at each element. These relations are well known to those
skilled in the art. By applying the flow rate results 212 of the
current time step for the Fluid Flow Model to the HTM temperatures
from the previous time step, the temperatures of the current time
step at each of the elements can be computed. By including the heat
generated from chemical and biological reactions 213 temperatures
at each of the elements for the time step can be computed to a
higher degree of conformance to reality.
[0075] Including a Dynamics Model 207 as part of the bio-transport
system simulator enables a user to account for certain external
effects such as gravitational attraction and acceleration resulting
from rotational and translational motion of the organism. This
increases the realism of the simulator and is especially important
in situations where a reduction or increase of pressure could be
life threatening, for example, where there is a risk of an aneurism
or where a pilot may blackout during turning and banking. The
effect of the Dynamic Model [DM] on the pressure gradients in the
flow model is applied through pressure gradient adjustments 216 for
the next time step. While chemical and biological reaction rates
are a condition of state [for example, pressure and temperature]
direct external dynamic effects on the MTC/BM model are omitted in
this embodiment, except as reflected through pressure adjustments
to the Fluid Flow Model as explained above. Heat convection can be
markedly altered by pressure [e.g. nascent boiling]. Again, as
explained above, the DM influences pressure gradients in the Fluid
Flow Model which, in turn, are applied 212 to the heat Transport
model. The unit flows and other results of the Fluid Flow Model are
made available 214 to the Dynamics Model. This enables one to
account for the changing of direction of a moving fluid. Inclusion
of a DM 207 provides the opportunity to study possible effects of
external forces on processes within the organism and perhaps
uncover new mechanisms or explain current anomalies regarding the
effect of these external forces on organisms.
[0076] The configurable bio-transport system simulator (CB-TSS) has
the internal ability to represent organs in an average, "gross" or
"lumped" manner. Organs are modeled as organ elements with, for
example, a certain resistance to flow and a certain volumetric
capacity, which may be a condition of state. Because the organ is
represented in lumped fashion, however, no detailed information
with regard to spatial dependence within the organ is
available.
[0077] To expand the realism of the CB-TSS, in a preferred
embodiment, the present invention facilitates the incorporation of
an organ model 209. There are a variety of spatially detailed
computer models of human organs that exist today [Winslow 1993] and
it is anticipated that many computer models of organs as functions
of 1-, 2-, or 3-Dimensions and time will develop in the future.
Preferably, a organ interface 208, in the form of an object, is
used for mathematically/algorithmically coupling the Configurable
Bio-Transport System Simulator to the organ model 209. The organ
interface 208 supplies the detailed organ model 209 with input
representing the current time step conditions created by the CB-TSS
at the organ/simulator interface [e.g. inlet and outlet flow ports
of the organ]. After the detailed computer organ model 209 is
processed through the current time step, the organ interface 208
converts the results of the organ detailed models into organ
element gross characteristics such as resistance to flow and
volumetric capacity based on boundary conditions between the models
at the current time step. This allows the CB-TSS to operate as if
an organ element, with certain gross characteristics, were in
place.
[0078] The technology to transmit and receive data between two
processes operating on a computer is well known. Obviously there
must be agreement between the organ model and the CB-TSS interface
with respect to, for example, format and protocol. Standard
interfaces would facilitate open interconnectiveity. In a single
CPU environment, the computational load of the various detailed
organ models may restrict the fineness of structure possible for
the Bio-Transport system simulator. However, in a parallel
processing environment, certain processors can be assigned to
various detailed organs models without appreciable loss in detail
or time required to obtain a solution for the CB-TSS. It is
anticipated that network communications speeds will increase so
that the detailed organ models will be able to reside on server
computers in remote locations. The technology to transmit and
receive data between two processes operating on separate computers
connected by a network is well known [e.g. CORBA and COM/DCOM].
While the organ interface is described in this embodiment as a
serial process to aid in learning, other, non-serial arrangements
are within the scope of the invention.
[0079] The present embodiment of the CB-TSS can be configured to
include an Input Element or an Output Element to model, for
example, the injection of a drug into the circulatory system or the
removal of a sample of matter from the interior of a circulatory
system. This feature may be employed by users to model segments of
a circulatory system, i.e. an open set of elements and organs
terminated at its ends by Input/Output Elements having specified
boundary conditions, e.g. flow rates. This leads to an obvious
extension wherein several CB-TSS are used, each to model in detail
individual components of a total Bio-Transport System, such as,
microcirculation fields, the lymphatic system, the kidneys and the
GI tract. These detailed components are in turn incorporated as
organ objects in a CB-TSS model of a complete Bio-Transport System.
In addition to being able to study a segment of a Bio-Transport
system, or an organ such as the GI tract in detail, advantages in
terms speed of convergence are anticipated by dividing a larger
simulation into a set of smaller simulations coupled at discrete
interface points.
[0080] Inclusion of an Extra-Bio-Transport Modeling [EBTM] ability
as part of the CB-TSS enables a user to specify mathematical
relations among variables that model interactions among certain
parts/components of an actual organism through mechanisms external
to the Bio-Transport System under study. The underlying mechanisms
external to the Bio-Transport System under study may be other
Bio-Transport Systems. To help illustrate the distinction between
what may be modeled in a "system under study" and in the EBTM,
consider the brain. The brain may respond to certain
chemical/biological concentrations in its neighborhood by producing
certain chemical/biological products in its neighborhood. These
products can enter the circulatory Bio-Transport System directly
and are so distributed. This can be accounted for in the system
under study. On the other hand, the brain also responds to certain
chemical/biological concentrations in its neighborhood and/or in
other remote locales by producing/receiving electrical signals to
and from these remote locales via the central nervous system [CNS].
In this way, CNS signals can effect reactions in locales remote to
the brain. These CNS signals can be said to "produce an effect at a
distance." Instead of trying to model the CNS in detail, the EBTM
makes it possible to represent this behavior as a set of functional
relations expressing how some condition in one part of the
Bio-Transport System under study affects conditions in another part
of the Bio-Transport System under study. While CNS effects
illustrate one application of this EBTM, there are many other
physiological phenomena that can be modeled in this fashion and
employment of this CNS example should not be used to limit the
scope of such a generic modeling capability or the scope of this
invention.
[0081] To accommodate representation of such phenomena, the user is
provided with an ability to specify a matrix of such "effects at a
distance" which is processed by a Relations Processing Engine RPE
of a generic type. This EBTM functionality may be used to model
interactions among organs for example, even when these interactions
are effectuated by fluid flow and/or other bio-transport dynamics.
For example, one may wish to model the human heart and simulate its
connection to the circulatory system and interactions with other
organs by using just the EBTM and its user specified input as an
expedient. In effect, the EBTM by itself would act as a CB-TSS.
Using the EBTM, spacial separation effects are represented by time
delays, yielding a faster bio-transport system simulation at the
expense of spacial detail. Methods to create an RPE to solve sets
of equations/relations with time delays and nonlinear terms are
well known, and commercial RPEs are available. Hence, the EBTM by
itself is a novel, useful simulator for modeling bio-transport
phenomena in organisms under certain circumstances.
[0082] In a preferred embodiment, the heat Transport model 206
passes temperatures back 218 to the Fluid Flow Model to permit
adjustment of temperature dependent characteristics such as fluid
viscosity for the next time step. The HTM 206 also passes
temperatures back 219 to the chemical/biological model 205 to
permit adjustment of temperature dependent data such as reaction
rates. The MTC/BM 205 passes back 220 chemical concentrations to
the Fluid Flow Model to permit adjustment of chemical concentration
dependent data such as channel wall elasticity and
porosity/permeability. The Organ Interface passes effects of organ
objects back to both the Fluid Flow Model via 217 and the MTC/BM
via 221, as does the Extra-Bio-Transport Model via 222 and 223
respectively. For one skilled in the art, it can be seen that the
order in which one chooses to compute the results of the various
models within the CB-TSS affects the results and computational
efficiency. For example, in an organism with a relatively stable
temperature profile and little in the way of external
forces/accelerations, computing the Fluid Flow Model appears to be
most appropriate. If on the other hand, the user was interested in
simulating the bio-transport system under conditions which affected
other bio-transport dynamics more than those represented by the
Fluid Flow Model, then the models representing the other
bio-transport dynamics should be a higher computational priority.
Optimal ordering for computing the various models would be
ascertainable to one of ordinary skill in the art. Additionally,
one skilled in the art would be aware that there are computational
techniques available that allow one, under a broad set of
circumstances, to iterate among models to that extent necessary to
obtain a specified degree of accuracy, reducing or eliminating the
need for considering the effect of computational order on the
results of the simulation. Computational speeds available today,
even from parallel CPU configurations, would likely limit such
iterative approaches for certain problems that require a high
degree of accuracy and a very fine mesh size. It is anticipated
these limitations will be relaxed in the future.
[0083] 2. Detailed Descriptions of the Models
[0084] The models will now be explained in detail with reference to
FIGS. 3-9. These figures show flow charts representing the process
of each model as well as the interactions among the models. In the
depicted embodiment, models' couplings are centered around the
Fluid Flow Model. This is to say the data input, programming logic
flow, data transmission and model interaction generally follow the
fluid flow. This explanatory approach is chosen to enhance the
clarity of teaching. It also makes practical sense to use such a
scheme to illustrate the CB-TSS since fluid flow is often a major
transport mechanism for many Bio-Transport system phenomena. It
should be understood, however, that other arrangements are possible
and this choice should not be construed to limit the scope of the
invention. Moreover, throughout this disclosure certain
relationships are presented in the BASIC computer language, or in
subscript notation for compactness in writing. The subscript
convention adopted herein also enables one to use a single term to
denote both, a mathematical relationship and its counterpart in a
computer program. This mapping is typically one to one onto from
physical equations to computer algorithms particularly in
"scientific" computer languages and is intended to enhance the
clarity of the teaching. Again, it should be understood that the
procedural aspects of the algorithms could be implemented in any
number of different computer languages including, but not limited
to, 4g1 languages. Furthermore, other logically equivalent computer
algorithms could be used to effect the same result.
[0085] Furthermore, one skilled in the art will realize that in
contemporary programming nomenclature elements with a set of
characteristics can be represented as objects with a set of
properties. This is the preferred implementation of the present
invention. The selection of the term "element" goes back to the
development of "finite element" approaches to set up and solve
certain classes of physical problems. As such, it would be more
familiar to those in the physical sciences than the term "object."
The terminology and methodology chosen to explain and implement the
logic on a particular machine is for illustrative purposes, like
the code, and should not be construed to limit the scope of the
invention.
[0086] In the teaching that follows, physical laws are applied to
materials such as blood which are assumed to be homogenous down to
whatever scale one chooses to impose, while still being able to
account for spatial and temporal variation using variables that are
continuous in the mathematical sense. Such a hypothesis is commonly
used as a starting point in continuum mechanics. It seems
reasonable to apply this assumption to the flow of materials in a
Bio-Transport system when a component such as blood is viewed
without magnification, but can be questioned as the magnification
is increased. It turns out that such modeling has proven to be
remarkably robust in predictive ability, even at a scale that is
obviously heterogeneous on a small scale and somewhat
discontinuous. Nevertheless, there is a point at which the behavior
of individual components creates differences between the
homogenous/continuous model predictions and reality. Accordingly,
the simulator may be expanded to include the ability to account for
certain of these realities by including, for example, monte carlo
modeling techniques to extend the usefulness of the CB-TSS into
this realm where the stochastic nature of certain biological
phenomena are important.
[0087] a. Fluid Flow Model.
[0088] FIG. 3 shows the entry of data regarding element and fluid
characteristics, initial conditions, boundary conditions, material
properties and other information, generically labeled as data in
FIG. 3, for the various models in this embodiment. In this
embodiment, an option is provided 315 to the user allowing element
data to be entered either manually 301 or automatically 316 from
the output of diagnostic equipment such as MRI machines. Data are
entered in the order the models are explained [301 for the Fluid
Flow Model to 313 for the Extra-Bio-Transport Model]. One skilled
in the art will realize that the order used for data entry is not
material.
[0089] Since the CB-TSS in this embodiment is oriented around the
fluid flow, a description of the Fluid Flow Model 400 as shown in
FIG. 4 provides a logical starting point. The CB-TSS results for
the time step n+1 are computed on the basis of the state of the
simulator at the n.sup.th time step and the mathematical relations
determined by the CB-TSS configuration at that point in time. The
first time step results are computed on the basis of initial
conditions input by the user. The initial conditions are input as
part of data by the user in Blocks 301, 303, 305, 307, 309, 311 and
313 and are stored in memory as data for the various models in 302,
304, 306, 308, 310, 312 and 314. If the user chooses to substitute
a detailed organ object for an organ element, the detailed organ
model and data relating to that organ model would be entered by the
user into the organ simulator for that organ. As well, the
interface data regarding that organ object is entered by the user
in Block 311. Again, one skilled in the art will realize that the
order of data entry in 300 is not material.
[0090] These data are combined in Block 401 and arranged in Block
402 in a manner suitable for the Fluid Flow Model equation solver
in Block 403 to determine the results for time step n=1. For
subsequent time steps [i.e. n=2,3,4 . . . ], the prior time step
state values are resident in memory 102, or can be retrieved from
storage 124, and are made accessible through blocks 405, 406, 407,
408 and 409. This permits one to compute data values that are
dependent on conditions of state. For example, a new value for
fluid viscosity in 401 at each element based on the temperature of
the fluid at that element in the prior time step can be made
available in Block 408. As used herein, the term "flow states"
refers, for example, to the pressure and flow rates of the
associated fluid at a particular time step and also the effects
this has on the element itself, e.g. drag force at the wall.
[0091] These elements and associated fluid characteristic values,
element conditions of state, and associated fluid flow states are
used to construct mathematical relations 402, based on known laws
and empirical relationships, expressing the relations among
variables at each of the elements. Different models of fluid motion
can be constructed, depending on assumptions made about the fluid
and element behavior as determined by user input.
[0092] A highly preferred embodiment accommodates three types of
dependency relating to time: (1) steady state, in which the
variables are functions of spatial location alone; (2)
quasi-steady-state, in which the fluid flow is independent or
relatively independent of time [e.g. fluid acceleration terms
negligible] but concentrations of chemicals and biologicals, for
example, can change with time at each spatial location; and (3)
transient, in which fluid flow and pressures vary to accommodate
for example pulsation of the heart. This embodiment also allows
quasi-spatial independence where major sections of the
Bio-Transport System are lumped into single elements, removing
almost all spatial detail and reducing the problem to the solution
of sets of ordinary differential equations in time. For
illustrative purposes, this embodiment covers one spatial dimension
[along the channel length], although other time and spacial
dependencies [e.g. two or three spatial dimensions] may be
accommodated.
[0093] To help clarify the process step of assigning algorithms
representing equations of flow to an element, a simple example is
used wherein at the j.sup.th element of the j.sub.max elements
[flow channel elements and organs elements], for the n.sup.th time
step:
[0094] p.sub.n,j,1 is the pressure at the inlet of the j.sup.th
element
[0095] p.sub.n,j,2 is the pressure at the outlet of the j.sup.th
element
[0096] v.sub.n,j,1 is the unit flow rate at the inlet of the
j.sup.th element
[0097] v.sub.n,j,2 is the unit flow rate at the outlet of the
j.sup.th element
[0098] A.sub.n,j,1 is the Area at the inlet of the j.sup.th
element
[0099] A.sub.n,j,2 is the Area at the outlet of the j.sup.th
element
[0100] 1.sub.j is the length of the j.sup.th element
[0101] As explained above, this subscript notation is used for
writing compactness to help in the teaching. In the BASIC language
algorithms, variables would be appear, for example, as P(N,J,1) and
a long expression might run to several lines of text. Another
convention adopted is to use the <= sign to mean "replaced by"
in equations, a common operation within computers, but
conventionally denoted by = in many computer languages, which
latter convention will be maintained for computer algorithms.
Actual equalities will be denoted by a single = equal sign.
Definitions, as listed above will be written with "is the" instead
of an = sign or double colon. In this disclosure, certain data are
presented as fixed, or dependent on position only or time only.
Element length above is an example of a characteristic presented as
a function of position only. This embodiment does, in fact, treat
many of these "constants," such as the fluid viscosity, as
functions of state by recomputing their values at each time step,
although storage may not be provided to track such values over
time. These conventions, used here and elsewhere to aid the
teaching, should not limit the scope of the invention.
[0102] For purposes of this illustration, it is assumed that:
[0103] The fluid motion is steady state and incompressible;
[0104] There is no transverse flow of the fluid, or other
materials, across the element walls;
[0105] The vessel walls are rigid;
[0106] The element network considered in this example, representing
one of the simplest types of Bio-Transport system geometry, is
non-branching;
[0107] The network is closed with a single prime mover that
supplies a constant head; and
[0108] No external gravitational or motion effects are present.
[0109] These assumptions lead to a certain set of equations [see
below]. It should be noted, however, that other equations relating
the variables for other types of flow behavior, are well known
[see, for example, Streeter & Wylie 1967; Fung, Y. C.,
"Biodynamics: Circulation", Springer Verlag, New York 1984;
McDonald, D A, "Blood Flow in Arteries", Edward Arnold, London,
1974; Milnor, W. R., "Heamodynamics", Williams & Wilkins,
Baltimore, 1982] and can be applied in an analogous manner. This
embodiment allows a user to chose, from different sets of such
equations, a set/model suitable to match operating conditions of
the Bio-Transport System under study as mentioned above. The CB-TSS
may be expanded to allow a user to chose from an even broader menu
of equation sets.
[0110] Under the conditions assumed above, the state of the n+1
incremental time step of the Fluid Flow Model is equal to the state
of the n.sup.th time step, for all n, and the mass flow is the same
in all elements of a steady state, non-branching network. For an
incompressible fluid, mass flow and volume flow are equivalent, so
conservation of fluid mass without any transverse flow across the
element wall yields:
v.sub.n,j,1A.sub.n,j,1=v.sub.n,j,2A.sub.n,j,2 for all n, for each
j. [1.1]
[0111] And by identity, the input unit flow rate of an element is
equal to the output unit flow rate of the predecessor element:
v.sub.n,j+1,1=v.sub.n,j,2 for all n, for each j. [1.2]
[0112] With each area specified as geometry by the user, every
v.sub.n,j can be expressed in terms of a single one. Combining
[1.1] and [1.2], the entrance flow rate for the j+1 element can be
computed from the entrance flow rate of the j.sup.th element for
each j:
v.sub.n,j+1,1.<=v.sub.n,j,1A.sub.n,j,1/A.sub.n,j,2 for all n,
for each j. [1.3]
[0113] Furthermore, since continuity of the vessel wall across
elements is required:
A.sub.n,j+1,1=A.sub.n,j,2. [1.4]
[0114] Thus,
v.sub.n,j+1,1<=v.sub.n,j,1A.sub.n,j,1/A.sub.n,j+1,1 for all n,
for each j. [1.5]
[0115] This expression can be compared with [Watters 1984 p5 (2.1)]
for a constant fluid density.
[0116] Expressing this relationship [1.5] in BASIC, provides an
algorithm for computing all flow rates at a given time step, N,
as:
[0117] V(N,1)=V1(N)
[0118] FOR J=1 TO NUMBER_OF_ELEMENTS
V(N, J+1)=V(N, J)*A(N, J, 1)/A(N, J+1, 1)
NEXT J [1.51]
[0119] So the entrance flow of an element can be computed from the
entrance flow of its predecessor element beginning with the first
element flow rate, which is labeled V.sub.1 [or in BASIC
nomenclature V1(N)]. Using [1.5], the entrance flow of the second
element from the entrance flow of the first element can be
computed. Applying [1.5] again, the entrance flow of the third
element can be computed. In this recursive fashion, as illustrated
in [1.51], all flow rates can be expressed in terms of one unknown,
V.sub.1.
[0120] An empirical equation relates the wall drag in an element to
the flow rate, which in turn must balance the pressure drop when
there is no fluid acceleration. For a Newtonian fluid this is of
the form as it appears in the steady state, balance of forces
equation:
p.sub.n,j,1A.sub.n,j,1-p.sub.n,j,2A.sub.n,j,2=C.sub.dn,jv.sub.n,j.sup.21.s-
ub.jPER.sub.wn,j for all n, for each j [1.6]
[0121] where:
[0122] Cdn,j is the unit surface area coefficient of channel wall
drag within the j.sup.th element in the n.sup.th time period which
is a function of the fluid's Reynold's number and the surface
roughness of element wall;
[0123] v.sub.n,j is the average flow rate within the element;
and
[0124] PER.sub.wn,j is the wetted perimeter of the j.sup.th element
in that time period.
[0125] This formulation can be compared with the Darcy-Weisbach
formula [ibid. p7, equation (2.4)].
[0126] It is then possible to compute the pressure at the exit of
an element from the entry pressure as follows:
p.sub.n,j,2=[p.sub.n,j,1A.sub.n,j,1-C.sub.dn,jv.sub.n,j.sup.21.sub.j
PER.sub.w]/A.sub.n,j,2 for all n, for each j. [1.7]
[0127] Since the pressure at the entrance of an element is equal to
the pressure at the exit of the preceding element and the elements
are continuous:
p.sub.n,j+1,1=[p.sub.n,j,1A.sub.n,j,1-C.sub.dn,jv.sub.n,j.sup.21.sub.jPER.-
sub.w]/A.sub.n,j+1,1 for all n, for each j. [1.8]
[0128] The average flow rate within the element, v.sub.n,j is
approximated as:
v.sub.n,j=[v.sub.n,j,1+v.sub.n,j,2]/2. [1.9]
[0129] Thus,
p.sub.n,j+1,1<=[p.sub.n,j,1A.sub.n,j,1-C.sub.dn,j[[v.sub.n,j,1+v.sub.n,-
j,2]/2].sup.21.sub.jPER.sub.w]/A.sub.n,j+1,1. [1.91]
[0130] Therefore, the algorithm [1.91] relates the pressure at the
entrance of an element to the following:
[0131] The pressure at the entrance of the predecessor element,
[0132] Flow rates, all of which can be expressed in terms of
V.sub.1, and
[0133] Known properties of the fluid and elements [C.sub.d,n,j,
cross-sectional areas, et. al.]
[0134] The difference between dynamic pressure and static pressure
should be discussed. In an element where the exit area is
smaller/larger than the entrance area, the fluid actually
accelerates/decelerates. Hence, part of the pressure difference
between entrance and exit is taken up with this acceleration of
fluid. Also side-wall pressure should be addressed and the possible
turning of the element [elbows] in the direction of flow. These
aspects are explained in the literature [Kenyon 1960, pp 104-108]
and, for a straight element, equate to a pressure correction
of:
p=.rho.v.sup.2.sub.n,j,1[1-[A.sub.n,j+1,1/A.sub.n,j,1].sup.2]/2
[1.10]
[0135] where .rho. is the mass density of the fluid.
[0136] This additional term illustrates the possible confusion that
can arise in teaching when the starting point is a mathematically
precise statement of the total problem..sup.*note-2 For simplicity,
an "intuitive" derivation is outlined here and a dynamic term is
included as a "correction."
[0137] The combination of these two terms can be converted to an
equivalent BASIC notation, viz:
[0138] TOTAL_P=0.0
[0139] FOR J=1 TO NUMBER_OF_ELEMENTS
[0140] VBAR=(V(N,J)+V(N,J+1))/2
[0141] P(N, J+1)=(P(N,J)*A(N,J)-CD(N,J)[[VBAR**2*L(J)*PERW(J))/A(N,
J+1)
[0142]
P(N,J+1)=P(N,J+1)-RHO*V(N,J)**2*(1-(A(N,J+1)/A(N,J))**2)/2
[0143] TOTAL_P=TOTAL_P+P(N,J+1)
NEXT J [1.92]
[0144] In a closed loop, the sum of the individual pressure drops
through each element must add up to, for example, the head provided
by a constant prime mover pump. Thus,
dp.sub.n,j=Head.sub.prime-mover,n j=1,j max for all n. [1.10]
[0145] Combining [1.5] and [1.6] and expressing all flow rates in
terms of V.sub.1 provides:
F(V.sub.1)=Head.sub.prime-mover,n [1.11]
[0146] Given that the head of the prime mover is known, and here is
only one unknown, V.sub.1, this is, under normal circumstances,
solvable in the mathematical sense of existence. To obtain a
solution using a computer requires a known value on the right side
of the = sign, and the value sought to be computed on the left
side. One approach would be to explicitly invert F() so as to
compute:
V.sub.1=F.sup.-1(Head.sub.prime-mover,n)
[0147] This task, upon looking at the algebraic equations involved,
appears formidable, but quite desirable from a computational
viewpoint.
[0148] Another approach is to assume a value for V.sub.1 and use
algorithm [1.51] to compute all subsequent V(N,J). Then the
algorithm [1.92] can be used to compute the pressure drop in each
element, the total of which must add up to the constant head pump
capacity of [1.10]. For example, assume an initial guess for the
volumetric flow, Q.sub.1=V.sub.1A.sub.1, of 50 ml/sec and a
computed total pressure drop of 0.1 atm, compared with an actual
pump pressure head of 0.11 atm. One might try the next volumetric
guess at a value of 55 ml/sec, likely leading to a computed value
somewhat in excess of the actual pump pressure. One would then
reduce the second guess in some rational way and proceed in this
fashion until the difference between the computed pressure drop
matched the actual pressure drop to the degree of accuracy desired.
Techniques to converge on an answer by a series of successive
rational adjustments are well known to one skilled in the art.
[0149] In many practical situations, the prime mover does not
deliver a specified head, but one implicitly related to the flow
rate. Accordingly the following must be solved:
F(V.sub.1)=Head(V.sub.1).
[0150] This is still one equation and one unknown and, in most
instances can also be solved in the mathematical sense of
existence, and in the algorithmic sense of convergence to a
physically correct answer. In this embodiment, both implicit and
explicit boundary conditions are handled. It should be noted here
that the heart actually consists of two, coupled pumps so what has
been outlined above needs to be modified somewhat before it is
directly applied to the human circulatory system.
[0151] Some quite practical circulatory configurations can be
approximated using a non-branching circuit by replacing parallel
element paths with one equivalent element. However, most problems
require the solution of a branching network of elements. There
exist known methods in the art to accommodate branching and joining
of elements in a network of flow channels, for example, Fox, J. A.
"Hydraulic Analysis of Unsteady Flow in Pipe Networks", John Wiley
& Son New York 1977 and Lighthill 1975, much as currents and
voltages are determined in a network of serial and parallel
resistors. Other restrictions imposed by the initial assumptions,
such as transverse flow through the vessel walls are Bergel, D. H.
"Cardiovascular Fluid Dynamics" Academic Press London & New
York 1972, an open rather than a closed network, and external
gravitational forces [see Dynamic Model in this disclosure] can be
relaxed using methods well known in the art.
[0152] In addition to providing a relatively simple illustration of
the process of assigning equations/algorithms to each of the
elements, the steady state solution for circulatory flow is quite
useful in predicting many practical results. Using perturbation
theory, transient chemical/biological and heat transport, as well
as certain effects of external dynamical and physiological
influences can be reasonably approximated using the steady-state
flow model. The modest computational demands of the steady-state
solution permit simulations with much finer mesh size to be
computed in the same time as a transient flow solution, yielding
more accurate results for the same investment in computational
resources.
[0153] It is also possible to represent slow transient changes,
where the flow and pressure values of n+1.sup.th time step differs
only slightly from the n.sup.th, in what is referred to herein as a
quasi-steady state manner. This extends further the usefulness of
the steady state circulatory model to include changes brought
about, for example, by a gradual modulation of flow and/or
pressure.
[0154] While steady state and quasi-steady state flow simulations
are very useful, they cannot account for pressure and flow pulses
created by a prime mover such as the heart in animal circulatory
systems. For this class of problems [transient flow], a true time
dimension is added to the Bio-Transport flow model.
[0155] In simple fashion, this adds a term to account for the
acceleration of the mass of fluid within the element. The effect is
to give rise to traveling pressure waves, for example, Shadwick,
Robert E. "Elasticity in Arteries", American Scientist,
November-December 1998, pp 535-541, and Lighthill 1975. The
governing equations for transient flow of compressible fluids in
elastic vessels are well known in the art see, for example,
Streeter & Wylie 1967. Streeter & Wylie also detail a
solution using the Method of Characteristics [ibid]. These
mathematical formulations can be reduced to computer algorithms in
a manner analogous to that outlined above for steady state flow by
procedures well know in the art.
[0156] While the Method of Characteristics is useful for certain
classes of problems, it can have some difficulty providing accurate
solutions to an important class of physiological configurations
that involve "Windkessel" effects [Shadwick op.cit.] where the
pressure pulse is rapidly modulated by a large/flexible vessel
section close to the prime mover pump.
[0157] An alternative to the Method of Characteristics is outlined
below by way of suggesting a more suitable approach for certain
types of bio-transport dynamic transient problems and to indicate
that alternative approaches are possible to obtain a computer-based
solution. For this example, a simplified case of transient flow is
outlined. For purposes of illustration, assume that:
[0158] The fluid is incompressible,
[0159] The vessels all have the same cross-sectional area,
[0160] The fluid is frictionless,
[0161] There is no transverse flow of the fluid or other materials
across the element walls,
[0162] The stress/strain characteristic relationships of the
vessels are piecewise linearly elastic.
[0163] The element network considered in this example, representing
one of the simplest types of circulatory system geometry, is
non-branching,
[0164] The network is closed with a single prime mover that
supplies a time varying head,
[0165] The initial state of the fluid and elements throughout the
network are known to be, for example, some steady state
condition,
[0166] No external gravitational or motion effects are present.
[0167] At the inlet of the first element after the pump [j=1], the
pressure for the n+1 time step is determined by a user-specified
pump pressure profile over time, P.sub.prime-mover, .sub.n+1,
providing the following condition at the outlet of the pump prime
mover:
p.sub.n+1,1,1=P.sub.prime-mover,n+1 [2.1]
[0168] From conservation of momentum, the change in average flow in
the first element for the n+1 time period is given as d(mv)=fdt,
providing:
v.sub.n+1,j=v.sub.n,j+[A[p.sub.n+1,j,1+p.sub.n,j,1]/2-A[p.sub.n+1,j+1,1+p.-
sub.n,j+1,1]].DELTA.t/.rho.[VOL.sub.n+,j+VOL.sub.n,j]/2 [2.2]
[0169] From conservation of mass for an incompressible fluid:
vbar.sub.n+1,j,2A=vbar.sub.n+1,j,1A-[VOL.sub.n+1,j-VOL.sub.n,j]/.DELTA.t
[2.3]
[0170] where:
[0171] vbar.sub.n+1,j,2 is outlet average flow rate during the time
period;
[0172] .DELTA.t is the time lapse between the n and n+1 time
step;
[0173] .rho. is the mass density of the fluid; and
[0174] VOL.sub.n,j is the volume of fluid in j.sup.th element at
the n.sup.th time step.
[0175] The change in volume is a result of a pressure change and
can be estimated from basic material properties of a vessel wall.
To this end, a linear relationship is used:
VOL.sub.n+1,j-VOL.sub.n,j=VOL.sub.n+1,jKp.sub.n+1,j [2.4]
[0176] where K is the experimentally determined proportionality
constant. This covers approximately the relationship in many
ordinary vessels with simple geometries. This also covers, as a
first order approximation, certain vessels of complex structure
and/or geometry whose pressure-volume relationship cannot be
reduced, even with great effort, to basic material properties.
Shadwick [ibid] provides an extended discussion and references of
the elastic behavior of blood vessels, including axial constraint
due to the Possion effect.
[0177] One skilled in the art realizes that the pressure-expansion
relationship for a tubular vessel contains the potential for
progressive failure. Thus an approximation such as [2.4] might be
inappropriate in the study of aneurisms, for example. In the
CB-TSS, there are a few options available for the user to specify
the elastic characteristics of the vessels; hence the term
"configurable". Many more options may be added in the future to
improve the realism and accuracy of the projections over a broad
range of applications.
[0178] The elasticity of the vessel walls is addressed at this
point since it is an important consideration in pulsating flow in
the human circulatory system. Wall extension affects the
attenuation of the pressure wave, in comparison with a rigid wall
model, as the wave moves away from the heart thereby reducing the
potential for wall fatigue failure.
[0179] Combining [2.3] and [2.4] and simplifying provides:
vbar.sub.n+1,j,2=vbar.sub.n+1,j,1-[Kp.sub.n+1,j]/A.DELTA.t
[2.5]
[0180] Average flow is approximated as follows:
vbar.sub.n+1,j,2=[v.sub.n,j,2+v.sub.n+1,j,2]/2, [2.6]
[0181] and average flow within the element is approximated as
follows:
v.sub.n,j=[v.sub.n,j,1+v.sub.n,j,2]/2 [2.7]
[0182] These relations suggest a computational strategy to
determine the three components v1, v2 and p2. Conservation of
momentum provides:
[0183] v=[v1+v2]/2=impulse from p1 without p2 pushback (a somewhat
high estimate).
[0184] Conservation of mass provides:
[0185] v1-v2=change in vol due to p1/2 (a somewhat lower
difference).
[0186] Conservation of energy provides an estimate of p2 based on
an integral of conservation of momentum (p1,v1,v2) less strain
energy absorbed by the vessel wall. That is, the actual momentum
integral must be reduced by p2 so enough is left for strain energy
(se), basically p2dt=se. Since the first estimate of se will be
high, the second estimate of p2 will be high. If it converges, it
probably would converge by oscillation.
[0187] Two new physical effects arise as a result of considering
transient flow conditions. In equation [2.2] an impulse is imparted
to the slug of fluid within the element as a result of the
imbalance of forces. In equation [2.3], some of this impulse "shock
wave" is "absorbed" by the flexibility of the vessel walls
[Shadwick ibid], and some passed on to create a p2, thus
providing:.
p.sub.n+1,2,1<=p.sub.n+1,1,2 [2.5]
[0188] By repeating the above process for all elements, equations
can be constructed in Block 402 at each of the elements and then
solved in Block 403 to determine the pressure and flow rate vectors
in Block 403 for the n+1 [current] time step from the past
conditions of state in this transient condition.
[0189] The resultant solution for flow rates and pressures at each
element for this current time step is assembled for output in Block
404, stored by Block 410 for later use, and is subsequently used
via Block 406 to determine characteristic values, for example wall
diameter from a known relation to fluid pressure, for the next time
step. The flow rates and pressures are stored by Block 410 and are
subsequently used in the Mass Transport Chemical/Biological Model
via Block 506 and the Heat Transport Model via Block 606, in the
Dynamics Model via 706, in the Organs Interface via 810, and in the
Extra-Bio-Transport Model via Block 906, to determine respectively
mass and thermal energy transport for the current time step.
Displays of the Fluid Flow Model-results are made available to the
user via Block 413.
[0190] It is not the intent of this disclosure to teach how to set
up and/or solve finite difference or finite element problems either
for steady state, transient or other flow conditions. The process
of setting up accurate and efficient computational procedures for
fluid flow in channels is well known [Lighthill 1975]. The
preceding simplified equations for steady state and transient flow
are included only to clarify the process step for setting up
computational procedures at each of the elements rather than to
specify computationally correct or efficient procedures. One
skilled in the art will recognize the following:
[0191] 1. There are other computational techniques to determine
pressures and flow rates for the next time step which minimize some
of the cumulative errors possibly introduced by the simplified
techniques used for illustrative purposes in the steady state and
transient procedures outlined above. Empirical relations more
complex than given in [2.4] which can be dealt with using known
techniques to approximate different relationships in different
regions of the Bio-Transport system.
[0192] 2. Blood is a common medium in circulatory systems. It
consists mainly of a fluid-like plasma, and discrete cells. This
combination does not behave as a Newtonian fluid [Bergel 1972], for
example, when the cells are of the order of the vessel diameter,
nor, when it can be so approximated, does a Newtonian fluid operate
in the laminar region below the transition Reynolds Number as it
does above the transition Reynolds Number with a dependance on the
square of the flow rate. These facts may require different
relationships than that given in [2.4], and some of these are
accommodated in the present embodiment.
[0193] 3. The conditions that exist at the outlet of a heart may
require a different type of forcing function, e.g. more like that
of a piston, than a prescribed pressure schedule as used in the
computational example above. For example, actual outlet conditions
may be better approximated by a prescribed flow schedule. Using,
Q.sub.prime-mover,n+1 as the starting point volumetric flow rate
for the next time step and the prime mover outlet, one skilled in
the art can see that a similar process to that described above for
a prescribed pressure driver could be used to determine, in an
analogous succession of operations through the elements, the
pressures and flow rates at each of the elements for the n+1 time
step. For the pump element, the ability to specify combinations of
both flow driven and pressure driven conditions as well as implicit
relationships may need to model a wide range of actual
bio-transport situations.
[0194] 4. Other embodiments of the simulator may provide more
extensive menus of conditions of flow and constitutive
relationships, covering, for example, flow of elastic-plastic and
viscoelastic materials in the digestive tract and elements capable
of emulating peristaltic effects, and the algorithms used to arrive
at solutions will be both more accurate and more efficient.
[0195] Therefore, the scope of this invention should not be limited
by the illustrated process of setting up the algorithms as outlined
above.
[0196] b. Mass Transport Chemical/Biological Model
[0197] To help illustrate the Mass Transport Chemical/Biological
Model [MTC/BM] 500 it is assumed that:
[0198] Changes in chemical concentration are primarily caused by
flow of the transporting medium, rather than by diffusion of a
chemical brought about by a concentration gradient within the
fluid;
[0199] Both flow through vessel walls and chemical/biological
reactions among the various chemical/biological components in the
circulatory system are negligible
[0200] Conservation of mass for a single chemical provides a simple
way to compute the new concentration at an element:
c.sub.n+1,j<=[c.sub.n,jVOL.sub.n,j+[c.sub.n,j,1A.sub.n+1,j,1v.sub.n+1,j-
,1-c.sub.n,j,2A.sub.n+1,j,2v.sub.n+1,j,2]t]/VOL.sub.n+1,j [3.1]
[0201] where:
[0202] c.sub.n+1,j is the concentration within the j.sup.th
element, at the n+1 time step;
[0203] c.sub.n,j,1 is the concentration at the inlet of the
j.sup.th element at the n.sup.th time step;
[0204] c.sub.n,j,2 is the concentration at the inlet of the
j.sup.th element at the n.sup.th time step;
[0205] A.sub.n+1,j,1 is the inlet area at the j.sup.th element at
the n+1.sup.th time step;
[0206] v.sub.n+1,j,1 is the unit flow rate at the j.sup.th element
inlet at the n+1.sup.th time step;
[0207] A.sub.n+1,j,2 is the outlet area at the j.sup.th element at
the n+1.sup.th time step;
[0208] v.sub.n+1,j,2 is the unit flow rate at the j.sup.th element
outlet at the n+1.sup.th time step; and
[0209] VOL.sub.n+1,j is the volume within the j.sup.th element at
the n+1.sup.th time step.
[0210] The values of A and VOL input in 505 for the current time
step [n+1] are computed using the Fluid Flow Model solution that,
in this embodiment, precedes the chemical/biological calculations
within the current time step, and is therefore available through
Block 506 for use computing characteristic values in Block 501.
These known and computed quantities are used in Block 502 to
construct the algorithms. The fluid unit flow values [v.sub.n+1,j,1
and v.sub.n+1,j,2] for the Fluid Flow Model are also for the
current time step [n+1] of the Fluid Flow Model and separately
shown as input in Block 506.
[0211] This sequencing of the solution steps so that the unit flow
values precede the other Bio-Transport system model values [MTC/BM,
Heat Transport Model, et. al.] is for illustrative purposes and
should not be used to limit the invention. Forward differences,
which permit the next state values to be computed explicitly from
previous values, as mentioned elsewhere, can cause cumulative
errors to build but are computational fast since iteration and/or
matrix inversion is avoided. Again, it is not the intent of this
disclosure to teach how to construct accurate, efficient algorithms
to solve finite difference/finite element equation. These
techniques are well known to one skilled in the art. Nowadays, use
of more accurate algorithms is possible for many practical
problems. It is anticipated that increased availability of parallel
processing computers and/or fast networks connecting server
computers will provide the computational power necessary for the
next time step in all of the models to take place in a manner that
is an improvement over simple algorithms, as outlined herein, to
solve simultaneous equations.
[0212] Noting for example that c.sub.n,j,1 can be approximated by
the following computation:
c.sub.n,j,1<=[c.sub.n,j-1+c.sub.n,j]/2. [3.2]
[0213] It is now possible to compute the concentration of a
chemical/biological constituent within each of the elements for
time step n+1 from known quantities at the previous
chemical/biological model time step and the current time step for
the Fluid Flow Model results using an algorithm that applies [3.2]
and then uses that result in [3.1]. Obtaining the solution occurs
in Block 503.
[0214] A few observations are in order:
[0215] 1. The mass balance for this chemical, as given in algorithm
[3.1], is based on flow conditions at the end of the current time
step. One skilled in the art will realize that writing the mass
balance on the basis of average flow during the time step provides
improved accuracy at the expense of computational efficiency
although the resultant complexity would obscure the teaching
herein.
[0216] 2. The linear interpolative relation [3.2] assumes that the
average concentration in the mass balance [3.1] is identical to the
concentration at the geometric center of the element. This would
require, at minimum, through mixing, such as might occur in
turbulent flow. Empirical relations describing, for example, mixing
under laminar flow conditions may be included in future embodiments
of the Bio-Transport system simulator.
[0217] 3. Even if the Fluid flow is steady state, the concentration
of a chemical [or biological] entity, initially only a function of
spatial location, can vary over time. This speaks to the utility of
a steady state or quasi steady state fluid flow option for the
rapid but reasonably accurate solutions of this class of conditions
where, for example, concentrations are low.
[0218] 4. Biologicals and other materials may consist of
undissolved particles whose densities differ from the fluid. These
particulates can travel at flow rates that differ from that of the
surrounding fluid. There are known techniques to incorporate such
effects and these effects may be included in other embodiments of
this invention.
[0219] Having initially ignored chemical/biological flow across the
wall of the elements, it will now be instructive to outline the
components of this term in the mass chemical balance stated above
in algorithm [3.1], realizing that analogous algorithms can be
constructed for biologicals. At an element with a semi-permeable
wall, the chemical flow across the element wall in a time step
t.sub.n can be approximated, for example, as a linear function of
the concentration gradient:
Q.sub.o,n,j<=H.sub.w[c.sub.n,j-C.sub.n,j]t.sub.n1.sub.jPER.sub.w
[3.3]
[0220] where:
[0221] Q.sub.o,n,j is the outflow rate of the chemical from the
volume within the element during the time step;
[0222] H.sub.w is the coefficient of chemical gradient flow across
the semi-permeable wall membrane;
[0223] C.sub.n,j is the concentration of the chemical on the
outside of the element wall; and
[0224] PER.sub.w is the wetted perimeter of the element.
[0225] Including this term in computer equation [3.1] means that
the effect of mass transport across the element wall boundary can
be incorporated to extend the usefulness of the simulator. One
skilled in the art will realize that transport relationships other
than the one chosen for this teaching can be simulated and in
particular, that osmotic processes, wherein the flow of the solvent
is involved can also be modeled. In addition, empirical relations
can be constructed for biological entities. Some simple linear
relationships are included in this embodiment. Other embodiments
may comprise a more extended menu of transport relationships both
for biological and chemical entities.
[0226] This embodiment associates a volume characteristic with an
element. The concentration, C.sub.n,j, of this volume is adjusted
in accordance with mass conservation by the amount of chemical
flowing out of or into the fluid contained within the element. This
provides an ability to account for local equilibrium conditions,
wherein the material surrounding the outside of a vessel/capillary
[e.g. the interstitial space] reaches a chemical concentration
equal to the concentration in the fluid contained within the
element. Sodium chloride levels within blood vessels versus levels
within the surrounding tissue provide an example of how such
functionality could be usefully employed. Once the tissue
associated with an element achieves equilibrium, salt in the blood
is no longer removed [or added in reverse flow] at that element
location. It may be preferable to account for the ability to
consume a chemical at a given rate in the exterior neighborhood of
an element. For example, studies then can be conducted on depletion
phenomena such as oxygen consumption in the human body.
[0227] Chemicals and biologicals react with one another within the
Bio-Transport system fluid, on vessel walls and within and in the
neighborhood of organs. These reactions affect the algorithms
constructed from balance of mass considerations. Therefore, the
algorithm for conservation of mass [3.1] for any of the chemical
and biological entities also needs to be adjusted for generation of
additional mass from the combination of reactants when that entity
is the product of the reaction, and removal of mass when that
entity is one of the reactants. This does not violate conservation
of mass but simply extends it to include, for example, reactions
and radioactive decay.
[0228] In this embodiment provision is made for the specification
by the user of reactions of the type:
N.sub.1 Reactant.sub.1+N.sub.2
Reactant.sub.2[Catalyst.sub.1+Catalyst.sub.- 2]=>M.sub.1
Product.sub.1+M.sub.2 Product.sub.2+KCAL
[0229] Where:
[0230] N.sub.1 is the number of units [e.g. moles] of the
chemical/biological Reactant.sub.1:
[0231] Reactant.sub.1 is the first entity to be combined to product
the end products;
[0232] Catalyst.sub.1 is the chemical/biological catalyst
facilitating the reaction;
[0233] M.sub.1 is the number of units [e.g. moles] of the
chemical/biological Product.sub.1 produced; and
[0234] KCAL is the amount of energy given off/absorbed by the unit
reaction [e.g./mole].
[0235] And reaction rate forms such as Michaelis-Menten:
r=R.sub.max*[c]/([c]+K.sub.m)
[0236] where:
[0237] R.sub.max is the maximum reaction rate [e.g. moles/sec];
[0238] r in the reaction rate;
[0239] c is the reactant concentration; and
[0240] K.sub.m is the Michaelis constant.
[0241] Data regarding the reactions for each of the chemical and
biological entities, their reaction rates are supplied 509 from
input originally provided by the user. Reaction rates can depend
on, among other factors, the nature of the reaction, the
thermodynamic state in the time-space neighborhood, and the
presence of catalysts such as enzymes. Biological entities can have
need for additional rules for example to account for cell division.
In this embodiment, these reactions are solved by the
chemicals/biologicals reactions engine 513 and the resultant mass
adjustments used to modify the transport results in the current
time step 514.
[0242] The MTC/BM processes these user input reaction equations at
each element to adjust the mass balances for all chemicals and
biologicals after results from the current time step of the
transport effects have been made. One knowledgeable in the art will
realize that these adjustments can be iterated to create the effect
of a parallel solution. It is anticipated that other embodiments
will include such iterative solutions.
[0243] In algorithm [3.1] the computation of the current chemical
concentration level within the element associated fluid is made
from results available from the previous time step [or in the case
of the Fluid flow results, the current time step] through Blocks
505, 506 507, 508 and 509. For the first time step, these results
are part of the initial conditions input by the user in Blocks 301,
303, 305, 307, 309, 311 and 313 and are stored in memory as model
data in Blocks 302, 304, 306, 308, 310, 312 and 314.
[0244] In a similar manner, the results of the chemical/biological
calculations for the current time step are output in Blocks 510 and
511 for use in the next time step by the Fluid flow model, or in
the current time step by the Heat Transport model and the organ
interface. Display of the chemical/biological results is made
available to the user by Block 512.
[0245] In light of this disclosure, one skilled in the art will
realize that:
[0246] 1. There are known computational techniques to reduce or
eliminate cumulative error effects. This results in increased
accuracy for a given mesh size and time increment.
[0247] 2. Entry or exit of a chemical/biological via transverse
transport through a semi-permeable element wall, or from the
reaction of chemicals/biologicals within the element volume, or via
injection from an outside may be handled more precisely and with
better accuracy than as outlined above using known techniques.
[0248] 4. The movement of particles through the Bio-Transport
system is predictable under certain conditions relating to the size
of the particles and the flow channel diameters.
[0249] 5. The movement and reproduction of cells, viruses, bacteria
and other biological entities is predictable under certain
conditions relating to size and concentration of the biological
entity and channel diameters.
[0250] 6. The effect of diffusion of chemicals on concentrations is
estimable using established techniques.
[0251] 7. Formation of deposits on the vessel walls can be
simulated approximately by changes in the inside diameter of the
affected vessel segments generically determined by
chemical/biological concentrations/reactions in the neighborhood of
the segment. The mechanisms for such deposits may be elucidated
more fully and the simulator modified to represent more
realistically the actual behavior.
[0252] The outcome of the chemical/biological model computations
may affect the conditions used to determine the flow rates in the
Bio-Transport model. For example, a change in concentration of a
chemical may affect the viscosity of the Bio-Transport fluid, or
the channel wall buildup of material deposits might change the
effective inside wall diameter as well as the drag coefficient for
various elements. The relevant MTC/BM results are fed back through
220 to the Fluid flow model. It is easy to see that in the case of
wall build-up, the diameter used to compute the n+1 flow rates will
consistently be larger than the actual element diameter, again
resulting in cumulative errors for the method and order chosen for
teaching. Here it is more obvious than in the Bio-Transport model's
difference algorithms that errors can accumulate using simple
forward differences. As mentioned elsewhere, there are known
techniques to reduce or eliminate the effect of a biased estimate
in the difference algorithms.
[0253] c. Heat Transport Model
[0254] A simple exposition of the Heat Transport Model [HTM] 600
also is built around the assumptions that:
[0255] The primary effect of changes in thermal energy
concentration, as measured by temperature, results from mass
transport of this energy by the transporting medium rather than by
thermal diffusion on a temperature gradient within the fluid.
[0256] Heat flow across the wall and heat generation from
chemical/biological reactions are neglected for the moment
[0257] Under this set of assumptions and using conservation of
thermal energy, algorithms analogous to [3.1] and [3.2] above can
be used to compute the n+1 time step temperature vector from known
quantities at time step n. These known quantities such as the
characteristic values of the elements and fluid within the elements
Block 605, unit flow values from the current time step of the Fluid
Flow Model Block 606, chemical/biological state effects Block 607,
and the prior thermal state Block 608 are input to the Heat
Transport Model. In Block 601 these known values are used to
compute thermal characteristics such as the specific heat of the
fluid contained in an element. From these known and computed
values, equations are constructed in Block 602, which includes the
flow rates input from the Fluid Flow Model 606.
[0258] These thermal equations are adjusted to account for heat
energy transport across the element wall in a manner similar to
[3.3] for chemical/biological mass migration across a
semi-permeable wall membrane, and for heat generated from chemical
and biological reactions input in Block 610. The resultant
equations are solved in Block 603 and the results assembled for
output in Block 604. The temperatures are stored by Block 611 to be
used in the next time step for the Fluid flow model, and a display
of thermal results is available to the user in Block 612.
[0259] In light of this disclosure, one skilled in the art will
realize that:
[0260] 1. There are known computational techniques to reduce or
eliminate cumulative error effects of forward differences as they
relate to time steps. This results in increased accuracy for a
given mesh size and time increment, typically at the expense of
computational simplicity.
[0261] 2. The effects of diffusion of thermal energy through the
fluid on a temperature gradient within the fluid is estimable using
established techniques.
[0262] The outcome of the HTM computations may affect the
conditions used to determine the flow rates and the chemical
concentrations. For example, temperature affects both viscosity and
chemical/biological reaction rates, and so the solution obtained
does not reflect simultaneity. While more computationally
intensive, as mentioned elsewhere, there are techniques known to
one skilled in the art, to reduce errors resulting from these
effects. Such techniques may be included in the Bio-Transport
system simulators.
[0263] d. Dynamic Model
[0264] The Dynamic Model 700 accounts for external gravitational
attraction and rotational and translational accelerations to which
the organism is subjected.
[0265] In the steady state Fluid flow model, conservation of
momentum was reduced to a static balance of pressure drop against
resistance to incompressible flow of a viscous fluid in a
one-dimensional channel. In many practical cases, both these
effects [fluid acceleration as a result of directional change and
compressibility] could be included in the model by a person skilled
in the art without need to consider a dimension other than that
along the length of the channels.
[0266] To account for gravitational attraction or acceleration from
external motions, however, each element is positioned in a 3D
space. This then establishes an angular relationship between the
external force/acceleration [dynamics] vector with the axis of
flow, allowing the dynamics vector to be resolved into an axial
component and one perpendicular to the axis of flow. The axial
component either increases or decreases the pressure gradient,
dependent on whether the axial component direction is opposite the
direction of flow or in the same direction.
[0267] The positional location of the elements in space and the
flow states within the elements are input in Block 705. Block 701
computes the geometric data needed for the dynamic equations to be
constructed in Block 702. Once the appropriate geometric equations
have been constructed, the external gravitational effects are
combined with the geometries in Block 703 to yield axial and
transverse components of the dynamic forces on the fluid within
each element. These results are output by Block 704 to store Block
709 and then supply the Fluid Flow Model--with this impact on the
pressure gradient in the next time step, for example. Output of the
geometry and external forces on each element is prepared in Block
704 and made available as a display for the user through Block
710.
[0268] e. Interface to External Organ Models
[0269] Organs are typically represented in the simulator 100 as
organ elements having gross characteristics such as an inlet area,
an outlet area, an internal volume and an overall resistance to
flow. Chemical and biological concentrations and reactions within
the organ and heat Transport are handled on a bulk organ-averaging
basis as well. This permits many useful real-life situations to be
simulated with a reasonable degree of resolution and speed.
However, there is no spatial mesh structure within an organ
element. Certain important types of simulation studies would be
ruled out if the Bio-Transport system simulator were limited to
organ elements.
[0270] To add more realism to the Bio-Transport simulation and to
permit a wider range of applicability for the CB-TSS, interfaces
are provided that communicate, using known techniques, between the
simulator 100 and external organ simulators operating either on the
same CPU or on other CPUs that are part of the same multi-CPU
computer, or as part of a network of computers. This arrangement
not only improves the usefulness of all the connected simulators,
but it forms the basis for an overall organism simulator of
considerable scope and detail. Partitioning the problem into M
inversions of matrices of dimension S.sup.3 with loose coupling, is
typically more computationally efficient compared with inversion a
single matrix of dimension [MS].sup.3.
[0271] The boundary conditions imposed by the CB-TSS at the organs
interfaces are provided to the organ interface in this embodiment
through Blocks 809, 810, 811 and 812. Block 801 maps these values
into a set of property values for each particular organ model.
Block 802 uses standard techniques, well known in the art, to pass
this information to the respective organ models [objects] residing
either on the same computer using the same CPU, on the same
computer using a parallel CPU, or on a server computer on a
network. Block 803 initiates the independent processing tasks and
initiates a local task 804 to collect the returning data from the
various independent organ models. These data are passed to Block
805 which converts the data into organ element gross values such as
average temperature and average chemicals/biologicals
concentrations. These organ gross characteristics are stored by
Block 806 for future use in the Bio-Transport system simulator. One
skilled in the art will realize that accuracy can be improved by
iterating within a time step among the organ objects simulators and
the CB-TSS. This may create unacceptable delays for certain problem
types using today's Internet response times for example. It is
anticipated that techniques will be developed to both reduce the
number of iterations within a time step and extend the time between
inter-simulator communications to several time steps, instead of
one to one, for many practical classes of problems. As mentioned
earlier, describing the Organ Interface connection in a serial
fashion should not be used to limit the scope of this
invention.
[0272] It is anticipated that the ability to interface with an
external organ model will be used by some to interface with
important transitional vessel sections of a circulatory system.
Thus, a user could create an external CB-TSS detailed model of the
transition vessel section and declare that model as an "organ".
[0273] f. Extra-Bio-Transport Model and Relations Processing
Engine
[0274] In this embodiment, the Extra-Bio-Transport Model 900, takes
the n+1 step results from the prior models/interfaces [905, 906,
907, 908] and combines them with the user specified
extra-Bio-Transport relations 909 to construct a set of
extra-Bio-Transport relations equations 901. The resultant
equations are solved by the Relations Processing Engine [RPE]902.
The solution results are made available to the user via a display
904 and saved for use in the next time step and for after
processing displays 911. In this embodiment the extra-Bio-Transport
relations can affect elements and associated fluid characteristics,
flow states, chemicals/biologicals states and thermal states. The
term "chemicals/biologicals state" refers, for example, to the
concentrations of chemicals/biologicals within the associated fluid
and the concentrations of chemicals/biologicals on the wall of the
element wall at a particular time step. Thus output 911 reflects
all these modifications.
[0275] To provide a simple example, imagine a somewhat hypothetical
situation wherein receptors in the hypothalamus at a position
(x.sub.1,t) sense the local concentration of water in plasma,
Cw(x.sub.1,t), and then regulate, r.sub.1 time steps later, the
production and thus the concentration of a hormone,
C.sub.h(x.sub.2,t+r.sub.1dt), at a different point in space,
x.sub.2. At some later time [i.e. r.sub.2 time steps], this hormone
increase, working its way through the circulatory system, would
reach the kidneys where it would have a concentration
C.sub.h(x.sub.3,t+(r.sub.1+r.sub.2)dt) and accordingly cause
elements in the kidney to permit absorption of water from the
distal tubules so that the concentration of water in the plasma at
the kidney C.sub.w(x.sub.3,t+(r.sub.1+r.sub.2)dt) now begins to
increase. In turn, the increase in water concentration at the
kidneys would eventually work its way through the circulatory
system and reach the receptors as
C.sub.w(x.sub.1,t+(r.sub.1+r.sub.2+r.sub.3)dt). Here the increased
concentration of water would begin to moderate the production of
the hormone in a fashion typical to close the feedback loop.
[0276] To represent this in a standard simulator for the
circulatory system, one can express at the receptor organ element a
relationship:
Int(x.sub.1,t)=f.sub.1(Cw(x.sub.1,t)), [4.1]
[0277] where:
[0278] Int is an intermediate standing for the link between the
water concentration at the hypothalamus organ element and the
production of the hormone; and
[0279] f.sub.1 is the functional relationship between the water
concentration and the intermediate.
[0280] This is the type of special property an organ element can
have, or that special elements can be endowed with. It relates the
production of one entity to the concentration of another chemical
entity at the same point in time/space.
[0281] And, at the kidney organ element:
C.sub.w(x.sub.3,t)=f.sub.2(C.sub.h(x.sub.3,t)) 4.2
[0282] Again, this is the type of special property an organ element
can have, or that special elements can be endowed with. It relates
the production of one chemical entity to the concentration of
another chemical entity at the same point in time/space.
[0283] The link between the Intermediate, Int, and the hormone
output is:
C.sub.h(x.sub.2,t+r.sub.1dt)=f.sub.3(Int(x.sub.1,t)) [4.3]
[0284] Combining [4.1] and [4.3] provides:
C.sub.h(x.sub.2,t+r.sub.1dt)=f.sub.3(f.sub.1(Cw(x.sub.1, t)))
[4.4]
[0285] And [4.4] would be contained in the set of reactions at a
distance relations to be processed by RPE. The relationships
between the hormone concentration at the kidneys and its
concentration at the hormone excretion site is automatically
handled by transport in the circulatory system. Likewise, the
relationship between the water concentration at the kidneys and its
concentration at the receptors is also automatically handled by
transport in the circulatory system.
[0286] Alternatively, we can express the relationship between the
hormone concentration at the kidneys and its concentration at the
hormone excretion site as:
C.sub.h(x.sub.3, t+(r.sub.1+r.sub.2)dt)=f.sub.4(C.sub.h(x.sub.2,
t+r.sub.1dt)) [4.5]
[0287] And the concentration of the water at the receptor site in
terms of its concentration at the kidneys as:
C.sub.w(x.sub.1,t+(r.sub.1+r.sub.2+r.sub.3)dt)=f.sub.5(C.sub.w(x.sub.3,t+(-
r.sub.1+r.sub.2)dt)) [4.6]
[0288] Both [4.5] and [4.6] are reactions at a distance that can be
processed by the RPE. Hence certain types of bio-transport
phenomena can be modeled as reactions at a distance. Thus the EBTM,
which is a useful component of the CB-TSS, is, in its own right, a
CB-TSS that can simulate bio-transport systems by means of
reactions at a distance.
[0289] These functional relationships at a distance [f.sub.3,
f.sub.4 and f.sub.5] can be quite complex, and non-linear,
involving functions of several other variables. So many
bio-transport systems can be simulated using the EBTM. However,
bear in mind that spacial definition is lost compared with the
principal bio-transport simulation technique [partial differential
equations representing both space and time], and physical
phenomena, which may be relatively simple to describe over a space
dimension, might be too difficult to capture in a bulk
representation to the degree of accuracy required.
[0290] In this embodiment the user defined extra-Bio-Transport
relations are not affected by any changes in state, including those
changes produced by the extra-Bio-Transport relations
themselves.
[0291] In the case of the brain, it appears intuitive that the
latest value for a concentration of a chemical/biological or other
condition within the brain itself will create signals that move
through the CNS and produce an effect in the organism at some
distance from the brain in the next time step. While this image is
useful in teaching, one skilled in the art will realize that the
computed effect might be more accurately applied to the n+rth step
instead of the n+1th to account for delay in the CNS transmission
in the case of millisecond time steps. On the other hand, the user
selected time step may be so large as to have the effect manifested
"instantaneously," causing a forward differences approach to
accumulate a significant error after a relatively small number of
time steps. There are techniques well known to those skilled in the
art to reduce the cumulative error. As noted elsewhere, the order
of application of the models in this embodiment is to aid in
teaching and is not meant to limit the scope of the invention. The
use of explicit relationships in this embodiment and use of the CNS
as an example is to facilitate the teaching and is not meant to
limit the scope of the invention. It is anticipated that users will
employ the RPE to incorporate a wide variety of physical
relationships within organisms. It is also anticipated that
extensions to the RPE will include the ability to deal with
implicit relationships and the ability to incorporate certain of
these user specified relationships into the built-in models,
thereby increasing realism and/or improving the accuracy and speed
of solutions.
[0292] The Extra-Bio-Transport Model is the last one processed
within a time step in this embodiment of the Bio-Transport system
simulator. When RPE is finished processing all the user specified
extra-Bio-Transport relationships, the process either continues at
the start of the time step loop, i.e. at the Fluid Flow Model via
Block 912 for another time step, depending on user data 907, or the
process is ended and various output displays can be selected by the
user in Motion Display.
* * * * *