Future Work
Previous DT-MRI studies have found that infarcted myocardium exhibits an increase in the
magnitude of water diffusivity. 17,35 Future work will use DT-MRI-based models to account for
regions of tissue damage to predict electrical propagation imbalance. Such models will be used
to analyze various infarction scenarios and determine possible implications in the mechanical
functioning of the heart.
The developed models may also be used to understand the implications of large external
electrical fields on myocardial conduction. To implement this approach one may start modeling a
magnetostatic case. When modeling electric behavior of biological tissue at very low
frequencies, a quasistatic approximation is valid. The induced electric field can be written in
terms of the magnetic vector potential A and the electric scalar potential q0 as 36
OA
E =-- V0. (5-1)
at
The tissue volume is assumed a conductive medium following the general form of Ohm's Law
J = o-E (5-2)
where J is the current density and c is the spatially varying conductivity tensor obtained from
DTI data. In a quasistatic approximation, the divergence of the current density Jis zero, so we
have
-V-(oVP)= 0. (5-3)
Combining equations (5-1)-(5-3), we obtain
-V --A7 V -.(oV) = 0 (5-4)
Also, the constitutive equation for magnetic fields needs to be included. For biological tissues,
the relative permeability is approximately 1, therefore