Biomedical Engineering Reference
In-Depth Information
geodesic curves running on surfaces as demonstrated by quantitative polarized light
microscopy in the whole left ventricle [
432
].
82
The Clairaut number indeed remains
invariant on the geodesic of the revolution surface.
Sheets of geodesic fibers between 2 left ventricle slices have been reconstructed.
An anatomical model of toroidal surfaces, fitted into each other inside the ventricular
wall, over which run the myocardial fibers with a spiral pattern has also been
proposed [
433
].
Spatial distribution of ventricular wall stresses is sensitive to the orientation of the
muscular fibers [
434
]. The structure of the left ventricle is designed for maximum
homogeneity of fiber strain during ejection [
435
]. Cardiomyocyte orientation may
result from an optimization process (minimization of muscular tension for a given
pressure).
Transmural difference in myofiber orientation equals to about 20 degrees per mm
in human heart [
436
]. Therefore, transmural discretization of wall computational
models must be small enough to compute strains and stresses.
Arrangement of cardiac myofibers takes the form of a special minimal surface,
the
generalized helicoid
, a minimal surface maintained during the cardiac cy-
cle, hence minimizing myofiber length and optimizing ventricular ejection vol-
ume [
437
]. The arrangement of myofibers in generalized helicoids characterizes
their orientation in the entire cardiac wall.
5.10
Ion Carriers
The main involved Na
+
,K
+
,andCa
2
+
ion channels span the sarcolemma and
membranes of cell organelles, especially the sarcoplasmic reticulum (Table
5.9
and Fig.
5.16
)[
438
]. Their permeability depends on the protein conformation. Sar-
colemmal Na
+
-K
+
ATPase slightly contributes to the resting membrane potential
by admitting 2 K
+
into the cell and expelling 3 Na
+
from it to the extracellular fluid
for every ATP consumed. To avoid local acidosis, H
+
is expelled from the cell by
Na
+
-H
+
exchanger.
82
Each cardiac slice is discretized into 130
×
130
m squares over which 2 square-averaged angles
are measured: (1) an elevation angle γ
e
between the fiber and slice plane and (2) an azimuth angle
γ
a
between the fiber projection in the slice and the east-west direction. The fiber direction
f
is then
given by:
f
x
=
cos γ
e
cos γ
a
,
f
y
=
cos γ
e
sin γ
a
,and
f
z
=
sin γ
e
. Angles close to degree 0 and greater
than 75 degrees cannot be accurately measured. The measurement error is estimated to be equal to
1 degree.
Search WWH ::
Custom Search