Page 165 - Artificial Intelligence for Computational Modeling of the Heart

Chapter 4 Data-driven reduction of cardiac models 137

Specialized cellular models have been developed for the de-
scription of electrophysiology in different tissues in the heart, in-
cluding the behavior of ventricular and atrial myocardium, as well
as tissue belonging to the conduction system of the heart (sino-
atrial node, atrio-ventricular node, His bundle and Purkinje sys-
tem). Basic models of cellular electrophysiology stem from the
seminal work of Hodgkin and Huxley [12], and describe ionic in-
teractions across the cell membrane. More recent models include
a detailed representation of the biological phenomena control-
ling ion channels, ion interactions and underlying cell function
(see section 1.2.1). Such models are computationally demanding
due to the numerous and coupled algebraic and ordinary differen-
tial equations governing the dynamics of different ionic channels
and gating variables. As an example, the Courtemanche–Ramirez–
Nattel (CRN) atrial cell model [359] has 35 static parameters, 12
ionic channels, and 21 ordinary differential equations for gating
variables and ionic concentrations. A diagram showing the differ-
ent components of the CRN model is shown in Fig. 4.13.While the
descriptive power of the model can potentially greatly increase,
as more aspects of the cell electrophysiology are explicitly cap-
tured, additional challenges arise from the uncertainty associated
to the model parameters. Since many of the microscopic phenom-
ena described by the model cannot be directly observed by non-
invasive techniques, the parameters may have to be chosen as
representative of the average behavior of populations or groups of
persons, based for instance on extrapolation from data acquired
from animal studies or ex-vivo analysis. Even when the phenom-
ena described by the model can be observed to a certain extent (ei-
ther directly or indirectly), the joint estimation of multiple model
parameters for the definition of a patient-specific model presents
significant methodological challenges (see chapter 5).
This motivates the design of models that are computation-
ally efficient (potentially enabling real-time simulations), reliable
in capturing the main aspects of cardiac electrophysiology, and
whose parameters can easily be estimated, directly or statisti-
cally, from clinical data. Several studies proposed models with
these properties [64], generally providing the representation of
the macroscopic behavior of the cell or tissue rather than a de-
tailed description of the underlying ionic phenomena. The focus
on macro-scale dynamics allows the reduction of the number of
model parameters, which are directly related to the features of
measurable signals (e.g. the shape of the action potential or ECG
measurements). A potential disadvantage, however, is that the re-
covered dynamics may lack important features linked to the un-
derlying physics, such as distinct time scales for the depolariza-