Biomedical Engineering Reference
In-Depth Information
Fig. 14.2
Fiber distribution on the myocardium (
left panel
), and sketch of the geometrical domain
decomposition of the corresponding mesh into 16 subdomains (
right panel
)
stimulate the entire endocardial surface. This is done either synchronously or with
a slight delay going from apex to base. No-flux boundary conditions apply to the
electric variables, while mixed boundary data are imposed to the displacement field.
Robin conditions mimic the presence of the pericardial sac at the outer wall, while
blood pressure inside the ventricles is computed on the basis of pressure-volume
diagrams, relating the blood pressure depending to the ventricular volume.
14.4 Numerical Simulation
In what follows we present a simple numerical example illustrating the feasibility
of electromechanical active strain models. The simulations reported in the present
work are performed using the parallel finite element library LifeV (
2001
). We em-
ployed a biventricular geometry (originally from Sermesant,
2003
) where the mesh
consists of 29 504 tetrahedral elements. Myocardial fibers are distributed in the mus-
cle following an analytical description so that the orientation varies linearly from
an elevation angle (between the short axis plane and the fiber) of 65° in the epi-
cardium, to
65° in the endocardium (see Fig.
14.2
, left panel). The domain is then
partitioned into 16 subdomains (Fig.
14.2
, right panel).
Since we are interested in the myocardium activation more than the passive prop-
erties of the muscle, we consider a simple neo-Hookean material with strain-energy
function
−
μ
385 kPa, in all regions of the cardiac muscle.
Moreover, the active strain
F
o
is chosen to be transversely isotropic, so
γ
s
=
W
=
2
F
:
F
, where
μ
=
0
and therefore condition (
14.7
) is not needed. This means that the second Piola-
Kirchhoff tensor reads:
γ
n
=
2
−
γ
f
S
=
μ(
1
−
γ
f
)
I
+
μγ
f
f
0
⊗
f
0
.
(14.11)
1
−
γ
f
