Biomedical Engineering Reference
In-Depth Information
Fig. 4
Computational modelling results illustrating the emergence of propagating wave fronts for
a stronger
Ca
2
+
coupling (
g
Ca
= 50). Colour coded as in Fig.
3
2) are dominated by local dynamics, producing a
complex field of interacting and non-repetitive waveforms characterised by spiral and
scroll waves, typical of chaotic dynamics. These highly complex, yet deterministic
in nature, types of oscillatory behaviour have been often observed in syncytia of car-
diac myocytes [
53
]. For stronger
Ca
2
+
coupling (
g
Ca
=
Weakly coupled cells (
g
Ca
=
20), discrete
pacemaker nodes become prominent. These are eventually dominated by a single
pacemaker resulting in clear wave fronts propagated longitudinally along the arterial
wall, as depicted in Fig.
3
. A propagating wave is illustrated in Fig.
4
, for a stronger
value of the coupling coefficient. As the oscillatory behaviour emerges, ion move-
ments in and out of the SR are associated with successive high and low
10 and
g
Ca
=
Ca
2
+
]
SR
.
This behaviour coincides with the synchronization of intracellular
Ca
2
+
oscillations
of the arterial wall, showing that macroscopic rhythmic activity can indeed reflect
ion movements at the level of the individual cell.
[
2.2.2 Electrical Coupling
Limited degree of synchronization, mostly at short length scales, was observed under
conditions of purely electrical coupling (not shown). This is due to the present formu-
lation of themodel, which is expressing primarily the dynamics of intracellular CICR.
The inclusion of a specific ionic transport process as a further independent variable
would allow membrane potential to support oscillatory activity independently of
the CICR mechanism. This is indeed the case when the open state probability of
K
Ca
channels is employed as an independent variable in a four differential equation
model [
51
].
The interplay between extracellular
Ca
2
+
influx via NSCCs and VOCCs was also
investigated. Independently of the coupling parameters
g
,asgivenin(
3
), simulations
