Page 47 - Artificial Intelligence for Computational Modeling of the Heart

Chapter 1 Multi-scale models of the heart for patient-specific simulations 17

This problem formulation allows to define a direct relation-
ship between the parameters of the electrophysiology models at
the cellular and tissue level and signals that can be acquired non-
invasively on the surface of the torso. Based on this, parameter
identification strategies can be designed to recover the optimal
parameterization of the electrophysiology models so that patient-
specific ECG readings can be reproduced. Examples and more ex-
tensive discussion of this application are provided in section 5.1.
Without changing the coupling framework here presented, the
different components can be modified and adapted to the require-
ment of the specific application. For instance, the torso can be
described as a non homogeneous medium, accounting for the
presence of multiple tissues with different conductive properties.
This can potentially enable higher fidelity in the modeled ECG
traces [92]. The tissue electrophysiology model can be simplified
to an extended monodomain model [99]oreventoanEikonal
model, with proper assumptions on the relationship between the
transmural and extracellular electrical potentials. One example of
coupled heart-torso model based on the monodomain model is
presented in section 2.2.4.

1.3 Biomechanics modeling
The goal of a biomechanical model of the heart is to capture
the active contraction and passive relaxation of the muscle, trig-
gered by the cardiac electrophysiology model as described in the
previous section and under the constraints determined by the
surrounding tissues. The myocardium is an active, non-linear, or-
thotropic, visco-elastic tissue, bi-directionally coupled with car-
diac electrophysiology [5,47,100]. Its constitutive law, which de-
scribes its macroscopic behavior, comprises an active component,
namely the relationship between the stress generated by the mus-
cle and the resulting contraction, and a passive component, the
underlying elasticity of the tissue due to the myocytes and extra-
cellular matrix. In practice, the active contraction is viewed as
a transient external force that makes the myocardium contract,
while the passive properties of the tissue are modeled such that
they ensure realistic motions due to the internal forces [100]. The
Hill–Maxwell framework [101,102] is traditionally used to inte-
grate the action of these forces. Fig. 1.8 shows one Hill–Maxwell
model of the myocardium [103] with three elements. The resis-
tance W e represents the passive work. τ c is the macroscopic active
stress, controlled by the electrical signal u,while E s is an addi-
tional elastic element that allows modeling of the isometric be-
havior (when active stress results in no strain). Dissipation due to