Page 100 - Artificial Intelligence for Computational Modeling of the Heart

70 Chapter 2 Implementation of a patient-specific cardiac model

2.3.3 Myocardial boundary conditions
Endocardial pressure
The intra-ventricular blood pressure is computed using a
lumped parameter model of blood flow coupled with the ven-
tricles through the pressure unknown p(t).Fig. 2.21 shows the
pressure-flow model used in this chapter, with coupled valve,
artery, ventricle, and atrium modules. In brief, there is a two-
way interaction between the remote (arterial and atrial) systems,
which receive flow (positive or negative, depending on the time
in the cardiac cycle) from the valve modules, and the ventricles,
which receive pressure values used as boundary conditions from
the arterial and atrial systems.

Figure 2.21. Cardiac pressure-flow system with pressure driven valves that
modulate the interactions between the ventricles, arteries and atria. The remote
pressures can be set independently to physiological values or can be connected
as part of a whole body circulation system.

The mass balance of the ventricular volume V(t) can be speci-
fied in such a way that the isovolumic stages of the cardiac cycle,
where there is no flow through valves and therefore the pressure
variable p(t) is an unknown of the coupled system, are handled by
the same equation:

dV arterial atrial dp
= φ + φ − μ (2.22)
dt dt
φ arterial and φ atrial are the bulk flow rates across the valves, ex-
pressed from the ventricle point of view. They are treated as in-
dependent variables and handled by the valve modules (Fig. 2.21),