Page 56 - Artificial Intelligence for Computational Modeling of the Heart

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

• Flow-driven models: the pressure is prescribed to the biome-
chanical solver and is known at any time [45].
Pressure-driven models are more complex to solve but offer
a larger flexibility and fidelity, as they can naturally model valve
insufficiency, stenosis, and other hemodynamics diseases. Sec-
tion 2.3 presents an implementation of such a model. In brief
the ventricular hemodynamics is modeled using a homogeneous
pressure field [6]. The arterial pressure is represented using a
lumped Windkessel model, while the atrial pressure is represented
using an active elastance model [133]. Finally, the valves, which
control the blood flow through the chambers and hence the tran-
sition from one cardiac phase to the other, are represented as 0D
dynamical systems, functionally coupled with the ventricles, ar-
teries and atria through the pressure variable.

Attachment to neighboring vessels and tissue
The second type of boundary conditions model the interac-
tion of neighboring organs with the myocardium. These boundary
conditions have been found crucial for realistic simulations and
to avoid non-physiological apex motion or rocking of the ventri-
cles [134]. First, heart ventricles and atria are connected to the
vessels, which creates additional stiffness in the insertion regions.
A common way to model these effects is to add stiff springs f vessels
at the vessels insertion points [6,45,134]. Second, a pericardium
constraint has also been used by some groups to achieve more
realistic deformation [6,135,136]. The idea consists in constrain-
ing the epicardial motion either through stiff springs or by us-
ing an explicit, contact-based, friction-less pericardial force f peri ,
whose domain is derived from the epicardial surface at mid-
diastole [135]. The total boundary condition f b = f vessels + f peri is
then injected into Eq. (1.13). Implementation details are provided
in Section 2.3.

1.4 Hemodynamics modeling

The mechanical coupling between the heart and the blood cir-
culatory system is a crucial aspect of heart function. Venous return
to the atria (through the inferior and superior vena cava on the
right side and through the pulmonary veins on the left side) pro-
vides the preload conditions to the cardiac pump and determines
the stroke volume of the ventricles. Mean arterial pressure (in the
aorta on the left side and in the pulmonary artery on the right side)
represents the afterload conditions and determines the amount of
work that the heart has to exert in one heart beat. The dynamics