Page 97 - Cardiac Electrophysiology | A Modeling and Imaging Approach

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It is clear from the above simulation that the spatial inhomogeneity (asymmetry of

excitability) was introduced by a propagating action potential. It is not an intrinsic property of the
tissue and the inhomogeneity is functional, rather than structural, in nature. Figure 3.17 depicts
the distribution of excitability properties in the vicinity of the vulnerable window. Top panel shows
the membrane potential along the fiber (V ). The second panel is the spatial distribution of
m
sodium current conductance (channel availability, g ). The bottom two panels are the sodium
Na
current activation gate, m, and inactivation gate, h, computed at the time of peak g (all these
Na
variables are plotted as solid lines in the figure).
The asymmetry of excitability was quantified

by the first spatial derivatives of these variables
(curves plotted with square symbols in each
panel of the figure). dV /dx is approximately
m
proportional to – dg /dx and – dh /dx in the
Na
vicinity of the vulnerable window. Thus dV /dx
m
provides a measure of the spatial heterogeneity
of membrane excitability. This functional hetero-
geneity results mostly from the heterogeneity in

the state of sodium channel inactivation (h);
recovery from inactivation is the major
determinant of membrane refractoriness during
action potential propagation. Unlike h, m is fully

recovered in the vicinity of the window and does
not display spatial heterogeneity (dm/dx = 0) in
this region.

The width of the vulnerable window has
important implications to arrhythmogenesis; it
provides a measure of the vulnerability to the
development of unidirectional block and reentry.

In the time domain, a wide TW implies that the
probability of a premature stimulus hitting the
window is high. In contrast, very precise timing is
required to induce unidirectional block in a small

TW. In normal cardiac tissue TW is very small Figure 3.17. Spatial distribution of mem-
(<1ms), making the inducibility of unidirectional brane excitability in the neighborhood of
block and reentry negligible. 222,224 However, many the vulnerable window during the refractory
period. Solid curves represent parameters;
pathological changes in electrophysiological
squares represent first spatial derivatives.
properties of the tissue (e.g. remodeling of ion m and h are I activation and inactivation
Na
channels, reduced intercellular coupling) act to gates, respectively. From Quan and Rudy
[222], with permission from Wolters Kluwer
widen the vulnerable window, rendering the
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