Optimal Control Problems in Hyperthermia
Hyperthermia is an effective method for the treatment of cancer.The objective of hyperthermia is to raise the temperature of diseased tissue (tumour) to a therapeutic value by avoiding the damage of surrounding healthy tissues.Heat is generated at the tumour site due to microwave induced heating power applying on the skin surface or by inserting a small microwave antenna into the tumour through hypodermic needles.In this book we consider one-dimensional Pennes bio-heat equation with constant thermal parameters which is a good approximation when heat mainly propagates in the direction perpendicular to the skin surface.The desired temperature of the tumour is attained by controlling both time dependent heating power induced by microwave and surface cooling temperature.Two methodologies ‘Conjugate gradient method’ and ‘Hamiltonian method’ have been adopted for optimum control of the parameters. The book provides a basic concept on optimal control problems in hyperthermia. The book may be helpful to the Post-graduate students and researchers of Bio-mathematics and Bio-medical engineering with an interest in applied mathematics.