# Applications of control theory in defibrillation

## Description

The purpose of this dissertation is to merge control theory techniques with the existing mathematical models of cardiac tissue in the presence of strong electric fields. This line of research should eventually produce new enhancements in functionality, reliability and quality of defibrillators. Even though cardiac fibrillation is one of the main causes of death all over the world, development of control theory applications for the challenging problem of defibrillation has been delayed. Consequently, so far, the advancements in devices used in defibrillation therapy have resulted primarily from empirical studies, with conclusions expressed in qualitative, rather than quantitative form The possibility of expanding the model by adding a term so that it in the state-space the problem takes a form of a singularly perturbed system, has been presented. The proposed modification has been motivated by a high expectation that some so far disregarded phenomena of higher order dynamics will get captured, and the result will be a better or more accurate model. Related to it, all the advantages of the singular perturbation theory as a tool for dealing with high order and multi-scale systems have been highlighted Once the state-space version of the bidomain model was derived, it became clear that the bidomain model can be interpreted as a circuit consisting of an infinite number of simple parallel resistor-capacitor models, connected through the same input. This finding might be the missing link between two seemingly completely different class of mathematical models of defibrillation. Also, it is obvious that the so far unexplained success of simple RC circuit models can be better understood It is well known that most control designs for distributed parameter models such as the bidomain model, must be performed on some lower order models. With the established connection with the simple parallel resistor-capacitor circuit, it was natural to assume that the feedback control design should start from there. The first step specified was to develop a new model for optimal cardiac defibrillation, based on simultaneous minimization of energy consumption and defibrillation time requirements. That can be considered as a step ahead, as the only other work found in the literature about defibrillating pulse synthesis is based on mathematically strict optimization resulted from minimization of energy only. (Abstract shortened by UMI.)