Page 107 - Cardiac Electrophysiology | A Modeling and Imaging Approach

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Figure 3.23. Different
temporal oscillatory
behavior observed
at a single site during
reentry. APD (left) and
[Ca ] i, peak (right)
2+
oscillations in three
different size rings: L=70,
61 and 60 cells (in A, B, C,
respectively).
A. Beat-to-beat alternans.
B. 5:5 periodic behavior
(pattern repeats every
5 beats). C. Quasi-period-
ic behavior. From Hund
et. al. [239]; experimental
data from Frame and
Simson [236] and Fei et.
al. [240], with permission
from Wolters Kluwers
Health, Inc.

conduction velocity is shown in Figure 3.25. An analytical expression relating velocity and
241
curvature in an excitable two-dimensional isotropic syncytium has been derived 242 : θ = θ + Dρ
p
where θ is the velocity of the curved wave, θ is planar velocity, D represents properties of the
p
tissue D =1/C S R (where C is membrane capacitance, S is cell surface-to-volume ratio, R is
m v i m v i
intracellular resistivity), and ρ (wave front curvature) is defined in terms of the radius of curvature
r as ρ = –1/r. Clearly, ρ cannot be infinite, implying that conduction cannot occur with a radius

of curvature smaller than some critical minimum value r . This property has important
m
consequences to the formation and sustenance of functional reentrant waves (called spiral
waves or rotors) that underlie many cardiac arrhythmias.