Page 167 - Artificial Intelligence for Computational Modeling of the Heart

Chapter 4 Data-driven reduction of cardiac models 139

Motivated by recent results in meta-modeling, we explore here
a reduced model of atrial cellular electrophysiology, based on
state-of-the-art mechanistic models and data reduction tech-
niques. The reduced model allows for an efficient computation,
capturing the dynamics of the original biophysically detailed
model with less input parameters. This chapter also illustrates the
use of such reduced model based on statistical learning for mul-
tiscale modeling of cardiac electrophysiology. In the following we
first focus on the CRN atrial cell model (section 4.2.1.1). We con-
sider the dynamics of the action potential described by that model
and build a lower-dimensional manifold using manifold learn-
ing techniques such as principal component analysis (PCA), or
locally linear embedding (LLE) (section 4.2.1.2). Next, we learn a
forward regression model of the action potential dynamics, given
a set of CRN model parameters (section 4.2.1.3). Finally we in-
tegrate this reduced cellular model into tissue-level EP modeling
(section 4.2.1.4).
We show in section 4.2.2 that the dimension of the action po-
tential manifold can be reduced significantly while still reproduc-
ing the output of a non-linear system. On the other hand, this
drastically improves performance of the atrial tissue-level elec-
trophysiology modeling, by reducing computational cost by up
to two orders of magnitude. Section 4.2.3 discusses these results
and proposes future considerations. The content of this section is
based on work published in [362].

4.2.1 Methods
4.2.1.1 Atrial electrophysiology models
The Courtemanche–Ramirez–Nattel (CRN) cell model [359]
was developed based on human atrial cell data and was validated
for both tissue- [363] and organ- [364] level electrophysiology sim-
ulations. The CRN model considers 12 ionic channels with 21
variables including voltages, gating variables for the transmem-
brane currents and calcium (Ca 2+ ) ion release current, Ca 2+ con-
+
+
centrations and intracellular sodium Na and potassium (K )ion
concentrations. The governing equation is
dv
=−I ion − I stim (4.2)
dt
with

I ion = I Na + I K1 + I to + I Kur + I Kr + I Ks + I Ca,L + I p,Ca
+ I NaK + I NaCa + I b,Na + I b,Ca (4.3)