Biomedical Engineering Reference
In-Depth Information
and apical basal directions, two elements in the radial direction on the LV free wall
and one element in the radial direction in both the septum and RV free wall, was
fitted using CMISS.
2
The apex was meshed with collapsed elements and was
closed. A high resolution tetrahedral mesh (average edge length 0.25 mm) was
created over the cubic Hermite mesh geometry using Tarantula
3
for simulating the
monodomain equations. The fibre orientation is derived from animal studies aug-
mented with human data [
3
]. Late-enhancement gadolinium MRI studies were used
to identify regions of myocardial scarring. The model heart was separated into two
regions: regions with scar and the remaining viable tissue.
2.2.2 Electrophysiology
Electrical activation was simulated using the monodomain equations [
4
]. The
electrophysiology mesh had ~27 million degrees of freedom and ~150 million
tetrahedral elements. The transmembrane ionic current was simulated using the
ten Tusscher 2006 human ventricular myocyte cell model [
5
]. All simulations were
performed using the CARP [
6
] software package. Simulations were performed on
UK national supercomputer resource HECToR
4
using 128-512 cpus. The tissue
was defined as viable or scar tissue. Scar tissue conduction was modeled as
isotropic with a tenfold decrease in fibre direction conduction. The conduction
parameters were fitted using EnSite
™
endocardium activation maps.
2.2.3 Mechanics
Mechanical deformation was modeled using the finite elasticity equations [
7
]in
CMISS using the Oxford Supercomputing ORAC
5
shared memory machine. Many
simulations were performed concurrently using 4 cpus. The reference geometry was
determined by unloading the end diastolic pressure from the end diastolic geometry.
As the RV end diastolic pressure was not measured it was approximated as 50% of
the LV pressure based on bi ventricular pressure measurements [
8
-
10
]. As limited
bi-ventricle pressure measurements are available in healthy and/or diseased human
hearts we have assumed this ratio remains constant for all simulations.
The passive material properties of the heart were modeled using a transversely
isotropic material law [
11
], aligned to the fibre microstructure of the myocardium.
The hyperelastic strain energy function is given by
