Abstract:

Detecting ischemic regions is crucial for preventing lethal ventricular ischemic tachycardia.
This is typically done by recording the heart’s electrical activity using either noninvasive
or minimally invasive methods, such as body surface or intracardiac measurements. Math-
ematical and numerical models of cardiac electrophysiology can provide insight into how
electrical measurements can be used to detect ischemias. The goal is to combine boundary
measurements of potentials with a mathematical model of the heart’s electrical activity
to identify the position, shape, and size of ischemias and/or infarctions. Ischemic regions
can be modeled as electrical insulators using the monodomain model, which is a semilinear
reaction-diffusion system that describes cardiac electrical activity comprehensively.
In this talk, I will focus on the case of an insulated heart without coupling to the torso. I
will first review some results related to reconstructing cavities for the stationary model, and
then present some results obtained recently in the case of the time-dependent monodomain
model.