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PHYSIOLOGY 20: 316–325, 2005; 10.1152/physiol.00022.2005
A Strategy for Integrative Computational
Physiology
Peter Hunter and Poul Nielsen
Bioengineering Institute, University of Auckland,
Auckland, New Zealand
[email protected]
Organ function (the heart beat for example) can only be understood through
knowledge of molecular and cellular processes within the constraints of structurefunction relations at the tissue level. A quantitative modeling framework that can
deal with these multiscale issues is described here under the banner of the
International Union of Physiological Sciences Physiome Project.
The wealth of data now available from 50 years of
research in molecular and cellular biology, coupled
with recent developments in computational modeling, presents a wonderful opportunity to understand
the physiology of the human body across the relevant 109 (from nanometers to meters) range of spatial
scales and 1015 (from microseconds to a human lifetime) range of temporal scales. The challenge is to
develop mathematical models of structure-function
relations appropriate to each (limited) spatial and
temporal domain and then to link the parameters of
a model at one scale to a more detailed description of
structure and function at the level below. To span
from molecules to organ systems requires databases
of models at many spatial and temporal levels and
software tools for authoring, visualizing, and running
models based on widely adopted modeling standards. It also requires the development of ontologies
dealing with anatomy, physiology, and molecular
and cellular biology to uniquely identify and link
model components. In this review, we outline a
framework for computational physiology being
developed under the auspices of the Physiome and
Bioengineering Committee (co-chaired by P. Hunter
and A. Popel) of the International Union of
Physiological Sciences (IUPS). We give examples of
its application to several organs and organ systems,
particularly the heart, and highlight the challenges
for this so-called Physiome Project (1, 3, 10, 11, 19,
20). Note that the focus on computational physiology is the distinguishing feature of the Physiome
Project but that it also encompasses the area traditionally known as systems biology, which has arisen
out of molecular and cellular biology and which typically deals with subcellular signaling cascades,
metabolic pathways, and gene-regulation networks.
Lessons from Physics and
Engineering: Continuum Fields and
Constitutive Laws
One of the most important concepts of mathemat316
ical analysis in the physical and engineering sciences is that of a “field,” which, together with
appropriate mathematical operations on fields, is
used to express the physical conservation laws of
nature, such as conservation of mass, momentum,
charge, etc. Fields were first introduced by the great
19th-century British scientist Michael Faraday to
represent the intensity and direction of the force
experienced by a small charged particle in the presence of magnetic dipoles and electric charges
throughout a three-dimensional space. The greatest success of 19th- and early 20th-century physics
was the discovery that most observable phenomena could be described by differential equations
operating on these fields: Maxwell’s field equations
for electricity and magnetism, Einstein’s field equation for gravity, the Yang-Mills field equations for
subatomic particles, and the field equations of continuum mechanics were derived from Newton’s
laws of conservation of mass and conservation of
momentum.
There is an interesting analogy with molecular
biology here: just as the classical field theory world
of physics was overshadowed in the early 20th century by quantum theory and particle physics, the
integrative systems-level physiology of the first half
of the 20th century gave way to the reductionist
molecular biology of the second half. In both
cases the challenge now is to reconcile the continuum/systems view with the particle/molecular
view. For physicists, this may be achievable by
describing their equations in a higher-dimensional
space via superstring theory. For mathematical
biologists, it is likely to be achieved via multiscale
modeling.
Many of the great accomplishments of electrical
and mechanical engineering, respectively, in the
20th century were built (for the former), on the
sound theoretical basis of Maxwell’s field theory
and quantum mechanics and (for the latter) on
continuum mechanics. In both cases, however, the
theoretical field theory models had to be supplemented with empirical descriptions of material
behavior that hide molecular or atomic detail
behind approximate “constitutive laws.” For elec-
1548-9213/05 8.00 ©2005 Int. Union Physiol. Sci./Am. Physiol. Soc.
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The Need for a Multiscale Modeling
Framework
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Human Genome Project recognized, the outcome
will be much more than the sum of the parts: an
anatomically and biophysically based model of the
human body will reveal characteristics and interactions that could not be predicted by focusing on
only a single spatial scale, time scale, or region of
the body.
Organ-Level Modeling
Computational modeling based on the above physical principles must be applied at many levels (see
Table 1): at the scale of whole organs, in which the
overall geometry and structure is modeled and
used to solve the coupled systems of field equations (see FIGURE 1); at the tissue level, typically
dealing with millimeter-sized blocks of tissue in
which structures are defined at the micrometer
level; at the cell level, typically dealing with a resolution of 0.1 ␮m; and even at the protein level.
Good progress is being made on modeling the
anatomy and biophysics of the heart (FIGURE 1A),
the lungs (FIGURE 1B), the digestive system
(FIGURE 1C), and the musculoskeletal system
(FIGURE 1D). In each case the field equations are a
little different (the lungs, for example, do not
require the electrical field equations), and, despite
very different anatomy and material properties
(expressed via the constitutive laws), the numerical
modeling framework required to solve these field
equations is the same for all. At the current rate of
progress, models of all 12 organ systems should be
available within a few years, at least for physiologically normal human anatomy. Linking the organ
and organ systems together to yield models that
can predict and interpret multiorgan physiological
behavior is the focus of systems physiology. To
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trical engineering, for example, Ohm’s law gives a
linear relationship between voltage gradient and
current flow (analogous to Fick’s law giving solute
flux from concentration gradient via a coefficient of
diffusion). The proportionality constant (electrical
“resistance”) can be measured directly and used in
the solution of the governing Maxwell’s field equation (which reduces to Kirchoff’s current law in this
simple example) without dealing with the underlying structure of the material. An implementation of
multiscale modeling would be to derive the constitutive relation (Ohm’s law) from field equations
applied to the detailed material structure. For
mechanical engineering, the equivalent is the
empirically derived relationship between stress
and strain (or strain rate for a fluid), although in
this case these two measures of force and deformation, respectively, require the use of tensors, each
with six components (three components represent
forces or deformations acting normally to the three
orthogonal faces of a cube, and three represent the
shearing forces or deformations). The development
of stress and strain tensors as the appropriate
quantities to represent the mechanical state of the
material at a point was a major intellectual
achievement that, together with an understanding
of how to simplify these tensors and their relationships for various solids (beams, plates, shells, etc.)
and liquids (e.g., Newtonian fluids) led to an ability
to design complex engineering structures.
The application of continuum field concepts and
constitutive laws, whose parameters are derived
from separate, finer-scale models, is the key to linking molecular systems biology (with its characterization of molecular processes and pathways) to
larger-scale systems physiology (with its characterization of the integrated function of the body’s
organ systems). The appropriate name for this
application of physical and engineering principles
to physiology is computational physiology. The
term systems biology, currently inappropriately
limited to the molecular scale, needs to be associated with all spatial scales.
Two principles guiding the development of all
mathematical models are 1) “Occam’s razor”—the
simpler the better, consistent with the level of
experimental data available (which, as Einstein
noted, also implies not too simple!), and 2) that
every model must be validated against experimental measurement. This journal’s space limitations
mean that both of these issues are delegated to the
references for the models we discuss. Similarly, the
physiological insights achieved by these models are
left to the references, because the focus here is on
presenting a strategy for integrative multiscale
modeling.
There is also a third guiding principle for
Physiome Project models: just as the leaders of the
“The appropriate name for this
application of physical and
engineering principles to physiology
is computational physiology.”
examine the behavior of these systems over long
time intervals, the models are often lumpedparameter models in which system-identification
techniques are applied to the detailed field-equation models illustrated in FIGURE 1. This approach
allows the parameters of the lumped-parameter
models to be linked to the more biophysically
based organ models (see the cardiac example
below).
The organ-level models shown in FIGURE 1 are
based on finite-element models of the anatomic
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Table 1. The multiscale modeling hierarchy
Physiological Level
Organ systems
Cardiovascular, respiratory, musculoskeletal,
digestive, skin, urinary, nervous, endocrine,
lymphatic, male reproductive, female
reproductive, special sense organs
Types of Model, etc.
Imaging Technologies
Systems theory
Lumped-parameter
models
Software
JSIM
MRI, CT, PET
3-D Ultrasound
1 mm or 10–3 m
BioPSE
Organs
226 bones
850 muscles
2817 arteries, arterioles, and capillary beds
…
Continuity
Tissues
Epithelial
Connective
Muscle
Nerve
Cells
Approximately 200 cell types
Organelles
Cell membrane, mitochondria, nucleus, endoplasmic
reticulum, ribosomes, Golgi apparatus, centrioles,
lysosomes, peroxisomes
Cell function
Membrane receptors
Membrane ion channels
Signaling pathways
Metabolic pathways
Transport
Motility
Maintenance
Conservation equations
Passive flux equations
Carrier-mediated transport
Electroneutrality constraints
Continuum models
Lattice-Boltzmann equations
Stochastic models
Markov models
Hodgkin-Huxley models
Network models
Numerical methods
Finite-element method
Boundary-element method
Finite-difference method
MicroCT, Optical
coherence tomography
10 ␮m or 10–5 m
Serial sections
1 ␮m or 10–6 m
Confocal microscopy
1 ␮m or 10–6 m
2-photon microscopy
100 nm or 10–7 m
Electron tomography
1 nm or 10–9 m
Cell cycle
Proteins, carbohydrates, and lipids
Quantum mechanics
Molecular dynamics
Poisson-Boltzmann eqs.
Coarse-grained models
Software
AMBER
X-ray diffraction, NMR
1 Å or 10–10 m
CHARMM
Posttranslational modifications
Protein folding
Translation
Posttranscriptional modifications
Gene regulation
Transcription
Genes
20,000 genes
Stochastic models
Boolean network models
Microarrays
2-D gel electrophoresis
Mass spectrometry
Nucleic acid
sequencing
URLs for the software packages mentioned above are as follows: JSim, http://nsr.bioeng.washington.edu/PLN/Software; BioPSE,
http://software.sci.utah.edu; CMISS, http://www.cmiss.org; Continuity, http://www.continuity.ucsd.edu; Virtual Cell, http://www.ibiblio.org/virtualcell; Gepasi, http://www.gepasi.org; AMBER, http://amber.scripps.edu; CHARMM, http://www.charmm.org.
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Continuum theory
Conservation of mass
Conservation of momentum
Conservation of charge
Software
CMISS
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A
D
B
FIGURE 1. Organ-level models
A: geometry and microstructure of ventricular myocardium shown in a 3-D finite-element model of the heart. Left: finite-element surfaces fitted to
measurements from the left and right ventricles of the pig heart. Middle: 2 layers of streamlines (one on the epicardial surface and one midway
through the wall) are used to visualize the epicardial and midwall fiber directions. Right: coronary arteries modeled from pig heart data (52). B: models of the lung (6, 54). Left: airways. Right: pulmonary arteries. C: models of the digestive system, including the esophagus, stomach, intestines, and
colon (4). Middle: diaphragm. Right: stomach and large intestines. D: models of the musculoskeletal system (14). Left: human skeleton with all bones
modeled and also showing muscles in the left leg as well as heart, lungs, and digestive system. Right: muscles of the left arm.
fields (geometry and tissue structure) encoded in a
markup language called FieldML (http://
www.physiome.org.nz/fieldml/pages). In all of
these models, the anatomic description is designed
to facilitate the efficient solution of the field equations representing organ function. The dependent
variables used in these field equations (such as the
deformed geometry, membrane potential, oxygen
concentration, etc.) can also be exported from
computational codes in FieldML-formatted files.
The use of FieldML as a standard for encoding field
information allows the models and their solution
fields to be read by a range of simulation and visualization codes (see Table 1). The spatially varying
physical properties of the tissues are also described
with FieldML files. Note that an important difference between engineering materials and biological
tissues is that the latter are almost always
anisotropic (e.g., material properties are different
in orthogonal material directions), inhomogeneous (properties vary with position in the materi-
al), and nonlinear. This makes the characterization
of biological tissue properties much more difficult
than it is for engineering materials and also reinforces the need to derive the material parameters
of the constitutive laws used in organ models from
more detailed models of the underlying tissue
structure (13).
Cell-Level Models: CellML,
Associated Tools, and Databases
A framework for modeling cell function has been
developed over the past five years by the
Bioengineering Institute at the University of
Auckland. The key elements are: 1) the development of a markup language called CellML to standardize the mathematical description and metadata (information about the model) of cell models
(12, 15, 30); 2) application programming interfaces
(APIs) to define the way that information is passed
between the CellML model files and computer pro-
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at http://www.cellml.org/examples/repository includes ~300 models in the following categories:
Signal transduction pathway models
Metabolic pathway models
Cardiac electrophysiological models
Calcium dynamics models
Immunology models
Cell cycle models
Simplified electrophysiological models
Other cell type electrophysiological models
Smooth and skeletal muscle models
Mechanical models and constitutive laws
For each model, the information on the website
describes which biological processes are represented, references the associated publication, and links
to the CellML model file itself. Although the use of
CellML can never replace the need for a peerreviewed publication of a model, it can enhance
the availability of the model and ease the burden of
implementation validity checking by the model
users. A model-publishing workflow is being developed to allow reviewers of submitted papers to
access and test the models and also to allow updating of models if errors or omissions are found after
publication. Note that another XML-based standard called systems biology markup language
(SBML; see http://www.sbml.org) has been developed for describing models of biochemical reaction networks (18).
Multiscale User Interfaces and
Ontologies
To facilitate access to the anatomically based
FIGURE 2. MozCellML simulation tool for models
from the CellML database
The CellML file, in this case describing the cardiac cell
ion channels that generate the membrane action potential, is read and transformed into code, which is complied and linked on the fly. The resulting executable program integrates the differential equations to yield the
time course of the (typically 10–50) dependent variables
in the model. The computed action potential is seen in
the graphical output window. Another set of windows
(not shown here) is designed for creating CellML models.
Executable and source code versions of MozCellML are
available for several different operating systems from
http://cellml.sourceforge.net.
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grams written in languages such as C, C++, Fortran,
Java, Perl, Python, or Matlab (see http://
www.cellml.org/private/api); 3) the development
of authoring tools to facilitate the creation of the
computational model from the mathematical
description; 4) the creation of a simulation code
that reads the chosen CellML files, generates the
source code, and compiles and links this into an
executable that can then be run for a specified time
interval to generate model results (see FIGURE 2);
and 5) the development, in collaboration with
other groups, of ontologies to represent human
anatomy and physiological processes (9, 41). Note
that the CellML language is designed to represent
mathematical models of any biological system and
achieves the following goals: it is machine readable
because it is based on extensible markup language
(XML); it represents concepts from mathematical
modeling (model, variables, units, and mathematics); and it uses structures in common with objectoriented programming (abstraction, interfaces,
encapsulation, containment, and importing).
Where appropriate, the language builds upon
existing XML standards, such as MathML
(http://www.w3.org/Math) for the specification of
mathematical equations and the resource description framework (http://www.w3.org/RDF) for the
encapsulation of metadata. Other tools have been
written to check, for example, the consistency of
units in the CellML model descriptions. All of these
software tools are freely available, for both academic and commercial use, at http://cellml.sourceforge.net. The goal is to make all published models
of cellular function available in CellML format and
to encourage the authors of these models (or others) to ensure that the model parameters and initial
conditions available on the CellML site are consistent with the model results published in the paper.
The repository of models currently available
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FIGURE 3. A generic framework for generating
graphical user interfaces for FieldML and CellML
files
The example here is a user interface designed to teach
the principles of EKG to medical students. The window
on the left includes 3-D anatomically based models of
the heart and torso that can be rotated and zoomed.
EKG leads are shown at the standard positions on the
torso, but these can be moved. An activation sequence
is shown on the heart (hidden in this view) and torso.
Moving current dipole vectors are also computed and
displayed. Potential maps are shown on the torso surface
as a color map, and the time course of EKG leads is
shown on the right. Image courtesy of Carey Stevens
(Bioengineering Institute, Auckland, New Zealand).
An Example: Computational
Physiology of the Heart
The development of the Auckland-Oxford-UCSD
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organ-level models and their links downward to tissue properties and cell-level processes, we are
developing browser-based graphical user interfaces that exploit the open-source software framework provided by the Mozilla community
(http://www.mozilla.org). These use an XML-based
description of the user interfaces, called XUL,
which allows problem-specific interfaces to be easily created, as illustrated in FIGURE 3.
Providing a set of unique names for the components of a biological model (a “controlled vocabulary”), together with the relationships between the
components, allows the application of reasoning
algorithms and access to the growing number of
protein databases that give, for example, data on
protein-protein interactions. We are working with a
number of groups who are developing domainspecific ontologies such as the Gene Ontology
project (http://www.geneontology.org) and the
Foundational Model of Anatomy (http://sig.
biostr.washington.edu/projects/fm/AboutFM.htm
l) (41). A web interface based on these ontologies is
being developed for accessing models (http://
n2.bioeng5.bioeng. auckland.ac.nz/ontology). The
specific biological information that is relevant to
each model in the CellML model repository is represented in the metadata associated with a model
and is bound directly to parts of the ontology. The
CellML metadata editor will be extended to use the
ontologies, supplying modelers with a system of
biological entities and relations that they can associate with their modeling structures.
heart model is used here as an example of multiscale physiome modeling. The long-term goal is to
be able to predict the effect of a channel mutation
or drug-binding event on arrhythmogenesis at the
whole-heart level, together with its clinically
observable effect on the body surface. Although
there are still many gaps, this example will serve to
illustrate what has been achieved with the physiome approach and where further research is needed. All models described here are encoded in
CellML and FieldML and are available from the
IUPS Physiome Project databases. The various levels referred to here are illustrated in FIGURE 4.
Atomistic models
Molecular dynamics (MD) models of the atomic
structure of ion channels, pumps, exchangers, etc.
are needed that can predict the open-channel permeation of the channels, the voltage dependence
of the channel permeability, and the time- and
voltage-dependent gating behavior. These models
describe the atomic mass and bonded (covalent)
and nonbonded (electrostatic, van der Waals)
forces operating on all (or a sizable subset of)
atoms in the protein and then solve Newton’s laws
of motion. The covalent forces can be computed as
a function of bond length, bond angle, and dihedral
angle from quantum-mechanical calculations.
Water is usually included in discrete molecular
form or, for greater distances, as a bipolar continuum field. These models require the protein’s atomic structure to be known from X-ray diffraction or
NMR, and this has proved very difficult for membrane-bound proteins. Ideally of course this structure would come from protein-folding computations, but this is some way off. Structures are currently known for a few bacterial potassium chan-
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1
Atomic
3
Subcellular pathways
IKATP IK1
K+
2
IKto IKr1 IKr2
K+
K+
K+
K+
IKs
INa
Calcium buffering
TropC
Calmodulin
Ca2+
Ca2+
Vleak
K+
Magnesium buffering
MgATP
MgADP
Mg2+
MgPi
3MgADP + 3Pi
H2+
Protein
TT
Vtr
2+
Ca
Vrel
Glycogenesis
3MgATP
2Lac
IbNa IpNa
Na+ Na+ Na+
JSR
Ca2+
IbCa
Vup
NSR
MgATP+
2K+
Ca2+
MgATP
3H+
Ca2+
Contraction
ADP
MgADP
ImKATP
H2PO4–
H+
AK
K+
MgADP + Pi + H
OxPhos
AMP
PCr
Ca2+
MgATP
Lac
4
3-D cell
5
Na+
H+
LAT
Tissue
ATP
Na+ HCO3–
H+
H2PO4–
NPE
NHE
6
Intrinsic
buffers
CK
Cr
2Na+
MgATP
ADP + H+
VCO2transport
NBC
Whole heart
Cl–
Cl–
OH–
CHE
3Na+
HCO3–
CBE
7
Ca2+
NCE
Torso
FIGURE 4. An illustration of the hierarchy of spatial scales
used in the IUPS Heart Physiome Project
The levels are 1) atomic, shown here by the atomic coordinates for the
sarco(endo)plasmic reticulum calcium ATPase (SERCA) from the PDB database (note the 2 bound calcium atoms in white); 2) protein A, demonstrating a coarser-grained model of structure for the same protein; 3) subcellular pathways, which include the cell electrophysiology, calcium transport,
proton transport, myofilament mechanics, metabolic pathways, and some cell-signaling pathways; 4) 3-D cell, in this case cardiac muscle cell from
electron micrograph; 5) tissue organization, shown here with collagen fibers in a transmural tissue block from a rat heart; 6) whole heart (The
Auckland Textured Virtual Heart); and 7) torso (the Auckland Human Torso Model).
nels such as KcsA, KirBac, and KvAP, which have
close homology (at least in the pore region) to
mammalian potassium channels (43). MD calculations, based on ~100,000 atoms in current models,
are very expensive and are typically run for periods
of only 10 ns (7). Sometimes homology modeling is
used in combination with MD simulation to generate, test, and refine models of mammalian potassium channels based on bacterial templates (8). The
structures of sodium and calcium channels are also
on the horizon, as well as those of key pumps and
exchangers.
Protein models
A major challenge now is to develop coarse-grained
models of these ion channels and other proteins
with parameters calculated from the MD models.
This will allow the models to include transient gating behavior for time intervals up to ~100 ms.
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Models of channel kinetics based on whole-cell
voltage-clamp data—the now classic HodgkinHuxley equations (16)—were developed over 50
years ago for sodium, potassium, and chloride
channels in giant squid axons and over 40 years ago
by Denis Noble for cardiac ion channels (36). The
subsequent development of the single-channel
patch clamp led to refinement of these models with
Markov-state variable models (53). One of the challenges now for the Heart Physiome Project is to
derive the parameters of the Hodgkin-Huxley or
Markov models from the MD models via coarsegrained intermediate models as the molecular
structures of these proteins become available.
Subcellular pathways
Lumped-parameter models (i.e., without diffusion
modeling) of various processes within cardiac
myocytes are now well advanced. The composite
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+
CO2
3Na+
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cell models encompass all of the ion channels,
ATPase pumps, and exchangers known to support
the cardiac action potential (34), together with
equations governing calcium transport (47), proton
exchange (55, 56), myofilament mechanics (21),
metabolic pathways (2), and signal-transduction
pathways that modulate the phosphorylation state
of intracellular proteins (44, 45, 46). All of these
models are available in the CellML repository.
3-D cell models
Tissue models
Cardiac cells (myocytes and fibroblasts) are organized into layers three or four cells thick (27, 28, 29)
that ensure high-conductivity gap-junction-mediated connections within sheets to ensure rapid
activation of the myocardium but allow mechanical shearing to occur between sheets to allow the
wall thickening that ensures a high ejection fraction for the ventricles. This tissue structure has
been modeled mechanically and electrically to
bridge the gap between cell-level and tissue-level
models (23, 31, 33). For example, computing the
propagation of an activation wavefront through a
tissue block with a detailed model of tissue structure allows the continuum orthotropic conductivity parameters, which are then used in the wholeheart models, to be evaluated in different regions of
the myocardium (17).
Whole-heart models
Models at the whole-heart level can now deal with
the large deformation mechanics of the ventricles
by using orthotropic constitutive properties based
on the fiber-sheet orientations (29, 35) and with the
activation wavefront propagation computed from
bidomain field equations (23) by using a conductivity tensor based on the fiber-sheet orientations
and the ion-channel cell models referred to above.
The coupling between the mechanical and electrical models is also achieved with calcium released
from ryanodine receptors binding to troponin-C to
initiate cross-bridge interaction (21) and mechanoelectric feedback mechanisms such as stretch-activated channels (25). A model of the coronary tree
Torso models
A model of the torso has been developed that
includes the heart and lungs within the thoracic
cavity and the layers of skin, fat, and muscles on
the chest to compute the current flow out of the
heart that gives rise to the measured EKG or more
detailed body surface maps of skin potentials (5).
One goal of this work is to solve the inverse problem of electrocardiology: how to compute activation patterns in the heart from measured potential
maps on the body surface (40).
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The next stage of development of cell models will
need to take account of the spatial distribution of
proteins within a cell and subcellular compartments, where second messengers (Ca2+, IP3, cAMP,
etc.) are localized (47). The spatial distribution of
the transverse-tubular system in cardiac myocytes
has been measured with two-photon microscopy
(51), and the spatial modeling of proton transport
and buffering in the myocyte is also well advanced
(55). Developing 3-D models at the cellular level
will help to fill the large gap in spatial scales
between proteins and intact cells.
has also been developed (49, 50) and coupled with
the ventricular mechanics model to examine
regional energy demand/supply relations (48).
Current work is linking myocardial mechanics to
the fluid mechanics of blood flow in the ventricles
and to the function of the heart valves. Future work
will need to include models of the Purkinje network
and the autonomic nervous system (39).
Summary, Goals, and Future
Directions
Anatomically and biophysically based models of 4
of the 12 organ systems in the human body are now
quite well developed at the organ and tissue levels
(the cardiovascular, respiratory, digestive, and
musculoskeletal systems). Others (the lymphatic
system, the kidney and urinary system, the skin,
the female reproductive system, and the special
sense organs) are at an early stage of development,
and the remainder (the endocrine, male reproductive, and brain and nervous systems) will be
addressed over the next few years. Software to visualize anatomically based models and solve the coupled biophysical field equations on these models is
available (see Table 1). All of the models can be
readily adapted to an individual patient if appropriate clinical imaging data are available (14, 57).
Many of the tools required to author, visualize,
and run models at the cell level are either available
now or soon will be (22, 24, 26, 32). In the near
future these tools will become more integrated and
more easily able to link through ontologies to
bioinformatic databases (19, 20, 37). This will facilitate international collaboration between groups
working in complementary areas—with the multiscale models acting as the glue to connect and integrate information (38, 42).
Much of the framework for dealing with cell
function is in place, and a substantial repository
from published models has been created
(http://www.cellml.org). An important future
development of the CellML framework is to use the
importing feature to assemble models from their
individually described components. For example, a
cardiac cell model may contain mathematical
PHYSIOLOGY • Volume 20 • October 2005 • www.physiologyonline.org
323
REVIEWS
We are grateful to many of our colleagues in the
Bioengineering Institute at the University of Auckland,
whose research work we have drawn on, and in particular
to Shane Blackett, Matt Halstead, Catherine Lloyd,
Andrew Miller, David Nickerson, Greg Sands, and Carey
Stevens for contributions to the cmgui graphics library,
ontologies, CellML model database, MozCellML code,
CellML APIs, tissue image processing, and Mozilla/XUL
user interfaces, respectively. We also gratefully acknowledge Professors Denis Noble, David Paterson, and Peter
Kohl at Oxford University, and Professor Andrew
McCulloch at the University of California, San Diego, all of
whom are contributing to the Wellcome Trust Heart
Physiome Project.
Some of the work reported here has been funded by the
New Zealand Government Tertiary Education Commission
(TEC) through a Centre of Research Excellence grant to
the Centre of Molecular Biodiscovery; the Wellcome Trust,
through a grant on the Heart Physiome Project; the Health
Research Council of New Zealand and the Royal Society
(New Zealand) Marsden fund.
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