COMPUTATIONAL MODELING AND SIMULATION AS ENABLERS FOR BIOLOGICAL DISCOVERY 171
- The underlying anatomical descriptions are based on finite element techniques, and orthotropic
constitutive laws based on the measured fiber-sheet structure of myocardial tissue drive the dynamics
of the large deformation soft-tissue mechanics involved. - Patterns of electrical current flow in the heart are computed using reaction-diffusion equations
on a grid of deforming material points which access systems of ordinary differential equations repre-
senting the cellular processes underlying the cardiac action potential; these result in representations of
the activation wavefronts that spread around the heart and initiate contraction. - Coronary blood flow is computed based on the Navier-Stokes equations in a system of branching
blood vessels embedded in the deforming myocardium and the delivery of oxygen and metabolites is
coupled to the energy-dependent cellular processes.
These models of different cardiac phenomena have been been implemented with “horizontal”
integration of mechanics, electrical activation and metabolism, together with “vertical” integration from
cell to tissue to organ. Thus, these models can be said to deconstruct an organ into a set of (submodels
for) constituent functions, with explicit feedback and connection between them represented in the
overall model of the whole organ.
Results from Integrated Modeling (Examples 2 and 3)
In the clinical arrhythmogenic disorder long-QT syndrome, a mutation in a gene coding for a cardiomyocyte
sodium or potassium-selective ion channel alters its gating kinetics. This small change at the molecular level
affects the dynamics and fluxes of ions across the cell membrane and thus affects the morphology of the
recorded electrocardiogram (prolonging the QT interval and increasing the vulnerability to life-threatening
cardiac arrhythmia). Such an understanding could not be derived by considering only the single gene, chan-
nel, or cell; it is an integrated response across scales of organization. A hierarchical integrative simulation
could be used to analyze the mechanism by which this genetic defect can lead to sudden cardiac death, for
example, by exploring the effects of altered repolarization on the inducibility and stability of reentrant activa-
tion patterns in the whole heart. A recent study made excellent progress in spanning some of these scales by
incorporating a Markov model of altered channel gating, based on the structural consequences of the genetic
defect in the cardiac sodium channel, into a whole-cell kinetic model of the cardiac action potential that
included all the major ionic currents.... [It] is becoming clearer that mutations in specific proteins of the cardiac muscle contractile filament system
lead to structural and developmental abnormalities of muscle cells, impairment of tissue contractile function,
and the eventual pathological growth (hypertrophy) of the whole heart as a compensatory response. In this
case, the precise physical mechanisms at each level remain speculative, although much detail has been
elucidated recently, so an integrative model will be useful for testing various hypotheses regarding the mech-
anisms. The modeling approach could be based on the same integrative paradigm commonly used by exper-
imental biologists, in which the integrated effect of a specific molecular defect or structure can be analysed
using techniques such as in vivo gene targeting.
SOURCE: R.L. Winslow, D.F. Scollan, A. Holmes, C.K. Yung, J. Zhang, and M.S. Jafri, “Electrophysiological Modeling of Cardiac
Ventricular Function: From Cell to Organ,” Annual Review of Biomedical Engineering 2:119-156, 2000. Adapted by permission from Annual
Review of Biomedical Engineering. (References and citations omitted.)