Page 72 - Cardiac Electrophysiology | A Modeling and Imaging Approach

P. 72
properties and does not vary as r is changed. This simplified model of continuous conduction
i
is applicable to cardiac action potential propagation only under limited special conditions,
where the tissue can be represented (to a good approximation) as a syncytium. This requires
sufficient level of coupling between cells at the microscopic scale and absence of macroscopic

discontinuities such as branching of fibers, trabeculations and presence of connective tissue
barriers. In general, action potential propagation in cardiac tissue is discontinuous in nature,
reflecting the structural discontinuities of myocardial architecture.

The Safety Factor of Conduction

It is very useful to establish a quantitative measure of the robustness of action potential
propagation in cardiac tissue. This index can help evaluate the relative importance of
173
membrane properties and tissue structural factors in determining conduction. The safety factor
(SF) for conduction provides such a measure and could be expressed mathematically as
174
dt
dt +
I c ∫ dt ∫ I out dt
A A
SF dt dt ; A/Qm>0 (3.2)
SF =
A ∫ I in in

In this equation, I is the capacitive current of a given cell and I and I are the axial current
c in out
that enters and leaves this cell, respectively. Q is the charge carried by a current during a certain
time period; it is computed by integrating the current over time. The interval of integration in
equation (3.2) is chosen as A, the time during which the net membrane charge Q is positive.
m

During action potential propagation, a depolarized cell serves as a source, providing charge

to depolarize neighboring unexcited cells. The unexcited cells that draw charge from the excited
cell constitute an electric load (sink) on this cell. The SF in equation (3.2) is formulated in terms of
the source-sink relationship during the excitation cycle of a cell in the fiber. Initially, prior to
excitation, the cell is at rest and its membrane potential is V = V . No current flows in or out of
m rest
the cell and Q , by definition, is zero. During its depolarization phase, the cell is a sink that receives
m
charge from the upstream fiber. During this phase, Q is positive and increases to a peak value.
m
It then starts to decrease when the cell switches roles, becoming a source that provides charge
to depolarize downstream cells. The sink-source cycle of the cell is completed when the cell has

returned all the charge it received and Q returns to zero. In equation (3.2) this interval is
m
A / Q > 0 . The numerator of equation (3.2) computes the sum of the charge that the cell
m.
generates for its own depolarization (Q ) and the charge it generates for depolarizing downstream

c
cells (Q ). The denominator is the charge that the cell has received from the upstream cells (Q ).
out in
For SF > 1, more charge is produced during the cell excitation cycle than the charge received by
the cell and conduction is successful. If SF < 1, the cell does not produce sufficient charge to
sustain conduction.