Page 151 - Artificial Intelligence for Computational Modeling of the Heart

Chapter 4 Data-driven reduction of cardiac models 123

Figure 4.2. Three stage approach for generating synthetic coronary geometries:
(A) Define coronary tree skeleton, (B) Define healthy coronary anatomy, (C) Define
stenoses.

curacy of non-invasively computed FFR varied between 75% and
85% [322,328,343–347].
The hemodynamic model displayed in Fig. 4.3 is represented
by a set of partial differential equations which can be solved only
numerically. The reduced-order Navier–Stokes equations em-
ployed herein enable the computation of time-varying pressures,
flow rates and cross-sectional areas. A population-average viscos-
ity value is employed and a lumped parameter model representa-
tive for the coronary microcirculation is coupled at the outlets of
the epicardial coronary arteries [348]. The reduced-order Navier–
Stokes equations are valid as long as no abrupt radius variations
are present. To ensure that pressures are computed accurately
in the stenosis regions, the momentum conservation equation is
modified to enable a correct computation of the additional energy
losses caused by the flow turbulence. Thus, the complex shapes of
stenoses are taken into account appropriately and the pressure
loss across the stenoses are predicted correctly. The coronary tree
is coupled to a simple, population-average systemic circulation
model composed from the aorta and the distal circulation. The in-
let boundary condition of the aorta is set by a lumped parameter
model of the heart: the ventricular pressure is applied as intramy-
ocardial pressure in the lumped parameter model of the coronary