Biomedical Engineering Reference
In-Depth Information
Cardiac electrophysiology is a field with an extensive history of integrative
modeling that has been coupled closely with both the design and interpretation
of experiments. The first models of the cardiac action potential (AP) were de-
veloped shortly after the Hodgkin-Huxley model of the squid AP (1,2), and were
formulated in order to explain the experimental observation that, unlike the neu-
ronal AP, cardiac APs exhibit a long-duration plateau phase. It was not long
after the formulation of these early myocyte models that initial models of elec-
trical conduction in cardiac tissue were formulated and applied to yield clini-
cally useful insights into mechanisms of arrhythmia (3). This close interplay
between experiment and integrative modeling continues today, with new model
components and applications being developed in close coordination with the
emergence of new subcellular, cellular, and whole-heart data describing cardiac
function in health and disease.
This chapter will review the current state of integrative modeling of the
heart, focusing on three topics. First, we will review the integration of experi-
mental data into the most commonly used class of ventricular myocyte mod-
els—common pool models. These models take the form of coupled systems of
ordinary differential-algebraic equations. We will examine both the successes
and failures of these common pool models. Second, we will review the formula-
tion of a new class of myocyte models known as local-control models. These
models take the form of coupled systems of stochastic differential equations,
whose properties are evolved in time using a combination of Monte Carlo simu-
lation and numerical integration. While these models are more computationally
intensive than common pool models, they are able to capture critically important
aspects of single channel behaviors that have a profound impact on myocyte
function, and which cannot be described using common pool models. Finally,
we will review how cellular models may be integrated with imaging data on
heart geometry and micro-anatomic structure to formulate computational models
of cardiac ventricular electrical conduction.
2.
CELLULAR MODELS
2.1. The Cardiac Action Potential
In order to understand the properties of modern computational models of
the cardiac myocyte, it is necessary to review the ionic mechanisms giving rise
to the cardiac AP. In this and all other sections of this chapter, we will focus
exclusively on the description and models of the properties of cardiac ventricu-
lar myocytes, as the properties of these cells figure so importantly in the genesis
of heart disease.
Figure 1A shows a schematic illustration of the large mammalian cardiac
AP. The currents mediating the AP upstroke (Phase 0) are the fast inward so-
dium (Na
+
) current (
I
Na
, for review see (4)), and to a lesser extent the L-Type
