Biomedical Engineering Reference
In-Depth Information
1.2.4 Link to Cardiovascular Disease
We previously demonstrated that specific dynamical transitions, associated phenom-
enologically with cardiovascular disease, can be readily effected by pharmacological
manipulation of cellular mechanisms (e.g. irregular
Ca
2
+
inflow or outflow from the
SR/ER via the SERCA and RyR pumps respectively) [
44
]. Such mechanisms can
be probed in a rigorous fashion, providing a broad range of relevant experimental
data for model development and validation. There is substantial evidence showing
that the prevalence of vasomotion can indeed be altered under specific pathological
conditions. In a large proportion of diabetic patients, for example, vasomotion is
impaired, and the amplitude of flow-motion is also reduced [
45
,
46
].
The formation of atheromatic plaque in stenosed vessels is another central area
of modelling investigation [
47
-
49
]. In addition to the effects of hæmodynamics and
transport, in early atheroma, there exists complex interactions between the arterial
wall components (SMCs and ECs), which cause inflammatory signalling that leads
to monocyte accumulation, foam cell degeneration and formation of atheromatous
plaque. Such alterations can result in significant modification of the arterial geometry.
These contributory factors can thus be incorporated in order to gain insights into
potential causes of vascular adaptation.
The role of mathematical/computational modelling in studying cardiovascular
disease as an integrated systemic dysfunction is therefore very important. Compre-
hensive studies of the mechanisms involved in the genesis of disease will require
concurrent modelling of endothelial factors, electrical coupling, calcium synchro-
nization and wave propagation as critical components. Afirst attempt in this direction
is presented here.
2Model
The intracellular oscillator (outlined previously) is modelled as CICR from the SR
via ryanodine sensitive
Ca
2
+
channels. This formulation is based on experimen-
tal evidence that CICR/IICR can be attributed to distinct store subtypes in rabbit
ear arteries [
17
,
20
]. The ryanodine-sensitive channel is modelled as a product of
two sigmoidal functions that account for
Ca
2
+
]
Ca
2
+
]
in the
SR, in agreement with experimental evidence [
50
]. There are contradictory obser-
vations that
Ca
2
+
oscillations may occur under constant elevated levels of InsP
3
,
or under fluctuating concentrations of intracellular InsP
3
. Considering the dominant
modulatory effect of ryanodine on arterial dynamics observed in rabbit ear arteries,
we assume
Ca
2
+
release from InsP
3
-sensitive stores to be a constant that increases
directly with concentrations of histamine. The effect of IICR is thus included in
the coefficient
A
, that corresponds to
Ca
2
+
uptake/release in the cytosol. Seques-
tration of
Ca
2
+
by the SERCA pump is represented by a sigmoidal function of
intracellular
[
in the cytosol and
[
Ca
2
+
]
. A passive leak from the SR is included to account for exper-
imental evidence, although it has limited effect on the oscillatory dynamics under
[
