Page 171 - Artificial Intelligence for Computational Modeling of the Heart

Chapter 4 Data-driven reduction of cardiac models 143

4.2.1.4 Application to tissue-level cardiac EP modeling
The monodomain model described in section 1.2.2 describes
the temporal and spatial distribution of the transmembrane po-
tential v(t) in cardiac tissue. In particular, when coupled with the
CRN cell model, the mono-domain equations describe the electri-
cal activation of human atrial tissue. The disadvantages of using
full-order cellular models are the computational complexity asso-
ciated to the numerical solution of the underlying ordinary differ-
ential equations, and the challenges of estimating an often large
number of patient-specific model parameters. A reduced order,
data driven model of the action potential time profile allows for
both a significant gain in computational efficiency, by removing
the need to solve the model equations, and simplifies the param-
eter estimation problem, by enabling fast model evaluation, and
therefore a more efficient optimization procedure.
A large database of sample transmembrane potential pro-
files can be generated on the reference anatomical model of the
human atria, with varying values of the CRN model parame-
ters θ, by numerically solving the monodomain equation. For
each sampled set of CRN model parameters, the computed ionic
current J ion (t) is recorded at a pre-defined measurement site in
the computational domain. For the sake of simplicity, we hereby
consider periodic electrical activity and focus on a single heart
beat. The database used for regression is then built by collect-
i 0
ing observations of the action potential defined as v(t ) = v(t ) +
j=1 ion (t )dt. The regression approach described in the previ-
i i
J
ous section allows for the definition of an action potential profile
model as a function of the cellular model parameters. In the fol-
lowing, we refer to the estimated action potential profile as v ref ;
and to the corresponding ionic current as J ref .
The estimated action potential profile can then be used in
combination with a numerical solver of the monodomain equa-
tion, to compute the electrical activation of the target cardiac tis-
sue for a new set of model parameters. To achieve this, the ionic
current term in Eq. (1.5) is replaced by the estimated J ref ,after the
action potential is triggered, and for each time frame in which the
monodomain equation is solved.
To identify the time at which the action potential is generated
at each location in the computational model, Eikonal models can
be used as a very efficient option. However, as discussed in sec-
tion 1.2.2, Eikonal model do not allow modeling pathological phe-
nomena like arrhythmias. Alternatively, phenomenological mod-
els can be used to simulate the temporal and spatial evolution of
the transmembrane potential in the cardiac tissue. One option is
to use the monodomain model based on the Mitchell–Schaeffer