Biomedical Engineering Reference
In-Depth Information
C
1
e
a
Q
W
¼
þ
;
C
2
E
ff
2
C
3
f
E
ss
2
E
nn
2
2
E
ns
2
2
C
4
E
fs
2
E
nf
2
Q
¼
þ
þ
þ
þ
(1)
where
W
is the strain energy,
C
i
are the material parameters,
is a scaling variable,
and
E
MN
corresponds to the Green Strains in the microstructure fibre (
f
), sheet
normal (
n
) and sheet directions (
s
). The
C
2
,
C
3
, and
C
4
parameters were fixed at 1,
0.5, and 0.25, respectively, to reflect the relative stiffness in each direction. Scar
was simulated as an isotropic region (
C
2
¼
a
C
3
¼
C
4
¼
1) with increased stiffness
modeled by increasing
and
C
1
parameters were then fit to the pressure and volume relationship during atria
contraction, when the myocardium was assumed to be quiescent.
Active contraction was simulated as a function of electrical activation time and
fibre strain. The model of activate contraction was adapted from [
12
] and reduced
to allow the parameters to be fit. The model parameters correspond to the rate
of relaxation, tension transient duration, rate of activation, length-dependent rate of
activation scalar, peak tension, minimum length of tension generation, and degree
of length dependence. The parameters were fitted to the recorded pressure transient.
and
C
1
by a factor of 5 and 2, respectively. The
a
a
2.2.4 Boundary Conditions
During isovolumetric contraction (IVC), the volume of the LV and RV cavities were
held constant. AWindkessel model provided the pressure-volume relationship for the
heart model during ejection. The parameters for the LVWindkessel model were fitted
to the recorded pressure volume relationship during ejection. The RV Windkessel
parameters were estimated based on the LV measurements. The values for systemic
compliance and resistance and pulmonary resistance in the RV were set to 4.5, 0.125,
and 0.35 times the LV values based on prior experimental data [
13
-
15
].
2.3 Model Stimulation and Lead Location
The intrinsic activation through the functioning RV Purkinje network was
approximated by stimulating the RV from the volume of earliest activation derived
from literature values [
16
]. The Purkinje network in the LV was significantly
attenuated as the patient was suffering from left branch bundle block. Intrinsic
activation of the LV through the remaining Purkinje network was approximated
by stimulating the septum at the volume of first activation derived from Ensite maps
in the absence of pacing. The difference between the start of LV endocardial
activation, as measured on the Ensite maps, and the start of the QRS was 30 ms.
This delay was used to define the difference between the intrinsic LV and RV
activation times.
