Alya Red CCM: HPC-Based Cardiac Computational Modelling - Selected Topics of Computational and Experimental Fluid Mechanics - page 196

that the ejection fraction is not too sensitive to the kind of changes in the density and
distribution of the Purkinje system we have applied.
In Fig. 7 , we compare the ejection fraction curves for two different values of the
parameter in Eq. ( 5 ). A remarkable fact is observed, that has been already noted

by Arís et al. ( 2014 ): thanks to the complex helicoidal structure of the fiber field,
large differences in

ʳ

produce small differences in the ejection rates. Varying this
value from 0.3 to 0.2 reduces the muscular active stress by 30%. However, the peak
ejection fraction is only 8% smaller.
The ejection fraction time evolution represents an integral parameter which shows
great robustness to the selected varying input parameters, at least in the ranges we
explore here. Another aspect we analyze concern the local variations. Although
the impact in the integral parameters could be small, it is important to see how
localized transient behaviour is affected. Table 1 shows a qualitative analysis of the
wavefront at t

ʳ

45ms measured from the initial activation. At these early times,
the electromechanical wave has already reached the epicardium in all cases but the
total activation of the ventricles is not completed yet. In Table 1 , we can also observe
that different initial stimuli leads to different activation sequences of the heart. For
instance, the closest matching appears between the activation protocols which have
the same number of nodes in the activation of the right ventricle (RV), activation
protocols 5-12, 8-10 and 7-11. In the cases 10, 11 and 12, no sites are activated in
the left ventricle (LV), and so the activation is produced purely by transmission from
the RV and the contraction occurs later.
In Arís ( 2014 ) and Arís et al. ( 2014 ) we have analyzed in depth the influence
of the fiber architecture and synthetically created Purkinje systems. We studied the
propagation dynamics throughout the volume of the ventricles giving measures like
ejection fraction and rotation around the long axis.
These results show that Purkinje system variations must be very large to really
account for changes in the ventricles contractile action. On the other hand, the fiber
model has a much greater influence in contraction than the initial activation through
the Purkinje system. As a consequence, linear and cubic rule-based models predict
different displacements, especially in areas such as the base or the apex. Additionally,
thanks to the complex helicoidal fiber structure, heart contraction is very robust also
against changes in active stress intensity. Indeed, the heart is the perfect pump, created
after millions years of evolution.

=

4.2 Electro-Mechanical-Fluid Coupling in a Simplified
Ventricular Geomety

The next example shows the fully-coupled scenario. Here we present some prelimi-
nary results using simplified geometries (Fig. 8 ).
Figure 9 shows a sequence of a bar of cardiac tissue submerged in blood as it
contracts under electromechanical activation. The bar is fixed on the right, where the
electrical activation starts. The fibers are oriented longitudinally to the bar. As the