Workpackage 2

Workpackage 2 deals with open loop optimal control problems for monodomain and bidomain equations.
The bidomain equations describe the electrical activity of the heart which is influenced by ionic flow across cell membranes. These equations consist of a nonlinear reaction-diffusion system, coupled with ordinary differential equations describing the chemical reactions. The actuators are electrodes through which an extracellular stimulation current is applied to the myocardium with the goal of dampining arrhythmias in an optimal manner.
Precisely, our main aim is to investigate two open loop optimal control problems for first monodomain equations and then the bidomain equations: optimal actuator placement (realized by implantable cardioverter-defibrillator systems, for instance) with the techniques of workpackage 1 and time optimal control (with the goal of damping exitation and reentry waves in minimal time). We will use some new tools to investigate these problems: Carleman inequalities for PDE-ODE systems, moving controls, spectral inequalities, Faedo-Galerkin method and the techniques of workpackage 1.   
Finally, it is worth mentioning that any reduction of the applied current that can be achieved on the basis of control techniques to e.g. defibrillation would be of tremendous impact in medical applications.