Page 66 - Artificial Intelligence for Computational Modeling of the Heart

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

Domain Ω can change substantially over the heart cycle, re-
sulting in volume variations in the order of 50% of the maximum
value in normal physiological conditions [137]. In an average male
subject, the resulting aortic flow rate is in the order of 5 l/min, and
with most of the ejection happening during the systolic phase, this
leads to peak flow rate values in the order of 500 ml/s. Peak ve-
locity values measured in the ascending aorta can reach as high
as 9 m/s [178] in systole, while being negligible in diastole. The
fast, pulsatile dynamics of blood flow can induce flow instabilities
and transient turbulence effects [101,179], which need to be ac-
counted for when designing the discretization approach. Flow sta-
bility is often characterized with a single parameter, the Reynolds
number, representing the ratio of intertial forces to viscous forces.
The Reynolds number is proportional to the mean flow velocity
and to the characteristic length of the domain, and inversely pro-
portional to the fluid viscosity. Large values of the Reynolds num-
ber identify scenarios in which inertial forces are dominant over
viscous forces, and vice versa. Typical values in the human car-
diovascular system range from few thousands (in bigger arteries
such as aorta, iliac arteries, brachial arteries and in bigger veins)
to less than 1000 in medium-size vessels (such as carotid arteries,
the main coronary arteries and medium-size veins) and even less
than 1 (arterioles, capillaries, venules). At Reynolds number values
around 2300, a steady flow could become turbulent; pulsatility in
blood flow however causes the transition to turbulence to appear
at higher values of the Reynolds number, to then disappear after
the deceleration phase. The critical Reynolds number depends in
general on the rate of change of velocity, as well as on the geom-
etry of the domain [101]. Turbulence in blood flow is associated
with oscillating pressure and increased wall shear stresses on the
boundary of the domain. These effects are particularly relevant
when studying non-physiological situations that can increase the
likelihood of flow instabilities, as in the case of valvular disease
[180] or the presence of devices such as artificial valves [181]or
ventricular assist devices [182], and in which an altered hemody-
namics environment could promote disease progression.
1.4.2.2 Fluid-structure interaction
A fluid-structure interaction cardiac computation system in-
tegrates the electrophysiology-controlled biomechanical compo-
nents with 3D computations of intra-ventricular flow dynamics,
as well as valve kinematics or dynamics. The FSI problem can be
solved with a monolithic approach or a partitioned approach. In
a monolithic approach, the equations governing the fluid dynam-
ics and the elastodynamics are solved simultaneously, therefore