Detecting ischemic regions from noninvasive (or minimally invasive) measurements is of primary importance to prevent lethal ventricular ischemic tachycardia. This is usually performed by recording the electrical activity of the heart, by means of either body surface or intracardiac measurements. Mathematical and numerical models of cardiac electrophysiology can be used to shed light on the potentialities of electrical measurements in detecting ischemia. More specifically, the goal is to combine boundary measurements of (body-surface or intracavitary) potentials and a mathematical description of the electrical activity of the heart in order to possibly identify the position, shape, and size of heart ischemias and/or infarctions. The ischemic region is a non-excitable tissue that can be modeled as an electrical insulator (cavity) and the cardiac electrical activity can be comprehensively described in terms of the monodomain model, consisting of a boundary value problem for the nonlinear reaction-diffusion monodomain system. In my talk, I will illustrate some recent results concerning the inverse problem of detecting the cavity from boundary measurements.

This talk deals with the inverse problem of identifying the real valued electric potential of the time-fractional Schrödinger equation, by boundary observation of its solution. Its main purpose is to establish that the Dirichlet-to-Neumann map computed at one fixed arbitrary time uniquely determines the time-independent potential.

The Westervelt equation is a common formulation used in nonlinear optics and several of its coefficients are meaningful as imaging parameters of physical consequence. We look at the recovery of some of these from both an analytic and a reconstruction perspective.