Biomedical Engineering Reference
In-Depth Information
physiological conditions [
51
]. The dominant cell
Ca
2
+
influx pathway in arterial SM
is provided by VOCCs. Voltage sensitivity of
Ca
2
+
refilling can account for large-
scale vascular contractile activity and synchronization, under conditions of electrical
cell-cell coupling [
19
]. With a reversal potential of
∼
0.1V and a sigmoidal open
state probability centred at
0.024V, VOCCs are maximally active during cellular
depolarization, a state generally associated with enhanced vascular contraction [
52
].
In spite of a central role in
Ca
2
+
transport and the generation of contractile activ-
ity, VOCCs account for only up to 10% of cellular polarization. A number of ionic
transport mechanisms that are fundamental in polarization of the arterial wall have
also been included in the quantification of SM membrane potential. These are the
Cl
−
channel, the NCX, known to be central in cardiac muscle contraction, and the
K
+
channels. With a reversal potential of
∼−
0.095V,
K
+
channels are particularly
important in vascular dynamics since they constitute the main hyperpolarizing force
in the arterial wall [
22
]. A large number of
Ca
2
+
-activated
K
+
channel subtypes
have been identified, conventionally grouped as large, intermediate and small con-
ductance channels. In the present formulation, we have grouped all
K
+
transport
activity under a single idealised channel subtype with a linear voltage dependence
and a sigmoidal
Ca
2
+
activation. Typically, ionic transport mechanisms are both
Ca
2
+
- and voltage-sensitive, as indeed reflected in the mathematical formulation of
each transport component.
∼−
2.1 Coupled Intracellular and Membrane C a
2
+
Oscillators in
Smooth Muscle Cells
Ca
2
+
]
SR
the
Ca
2
+
concentration in the sarcoplasmic reticulum and
z
the cell membrane potential.
The system described above and depicted in Fig.
1
is represented by the following
equations:
Ca
2
+
]
i
represent the cytosolic free
Ca
2
+
concentration,
y
Let
x
=[
=[
z
−
z
Ca
1
1
+
e
−
(
z
−
z
Ca
2
)/
R
Ca
VOCC influx
x
+
x
Na
/
Ca
z
−
z
Na
/
Ca
NCX
dx
dt
=
x
influx
−
E
Ca
+
E
Na
/
Ca
A
NSCC
x
n
x
p
r
y
m
r
−
B
+
C
r
+
x
b
SR uptake
+
x
p
r
y
m
r
r
x
n
y
m
r
x
p
r
+
r
RyR CICR
−
Dx
k
1
+
z
−
z
d
R
d
(1a)
+
Ly
SR leak
Ca
2
+
extrusion
x
n
x
p
r
y
m
r
dy
dt
=
B
(1b)
−
C
r
+
x
b
SR uptake
+
x
p
r
r
+
y
m
r
r
x
n
y
m
r
x
p
r
RyR CICR
