Biomedical Engineering Reference
In-Depth Information
showed how low or high influx through either channel leads to the dominance of
Ca
2
+
and/or electrical coupling, and to the loss of oscillatory activity. For the case
of a single cell model, the effects of variations in the control parameters
A
and
E
Ca
were investigated by nullcline analysis in [
19
].
3 Integrated Approach
The modelling framework presented here can be used in realistic scenarios, to gain
insights into the fundamental physiology of inter-cellular coupling, by analysing the
emergence of synchronization and macroscopic wave propagation. The theoretical
consequences of local neighbour interactions through electrical and/or chemical cou-
pling via inter-cellular diffusion of
Ca
2
+
ions have only been briefly explored, and
can be further compared using the Nernst-Planck equation. This approach may also
identify key dynamical features, by exploring stability characteristics and critical
scaling phenomena near the onset of synchronization, as described for Kuramoto-
type phase synchronization of oscillators [
54
], and the mode locking observed in
nonlinear systems [
55
].
Additional components will include the coupling between the SM and the
endothelium, especially with a view to provide a robust basis for the study of vari-
ous patho-physiological scenarios. Further manifestations of blood-wall and arterial
dynamics coupling could then be investigated, by manipulation of a number of poten-
tial mechanisms underlying flow-endothelium interactions. Such mechanisms may
include wall shear stress, which can modulate calcium responses in SMCs indi-
rectly, via mass transfer of agonist and receptor-ligand interactions, as described in
Sect.
1.2.3
, and directly through wall shear stress operated channels. In this context,
ATP and its derived products can be considered. Potential mechanisms of action may
include: (i) ATP as a mediator of
Ca
2
+
extrusion ATPase, (ii) the sodium-potassium
exchanger Na
+
/K
+
-ATPase involved in maintaining the cell membrane potential,
and (iii) ATP-sensitive potassium (K
AT P
) channels in the endothelium. Such an
integrated approach will enable the active coupling between blood flow and arterial
wall dynamics, and provide a uniquely global view of cardiovascular physiology that
has not been achieved before in computational fluid flow studies.
References
1. Halcox, J.P.J., Donald, A.E., Ellins, E.: Endothelial function predicts progression of carotid
intima-media thickness. Circ.
119
, 1005-1012 (2009)
2. Halcox, J.P.J., Schenke, W.H., Zalos, G.: Prognostic value of coronary vascular endothelial
dysfunction. Circ.
106
, 653-658 (2002)
3. Schachinger, V., Britten, M.B., Zeiher, A.M.: Prognostic impact of coronary vasodilator dys-
function on adverse long-term outcome of coronary heart disease. Circ.
101
, 1899-1906 (2000)
