Numerical Simulation of the Thermal Fields Occurring in the Treatment of Malignant Tumors by Local Hyperthermia

Abstract

Dual beam microwave heating is known to deposit heat at depth in a medium. Thus transient heating times may be reduced and more even heating may be obtained. Such a system has potential in the treatment of cancer by hyperthermia. A theoretical analysis of this situation is presented here. A simulation has been made of the thermal fields generated in the treatment of malignant tumors using local hyperthermia. The simulation utilizes the alternating direction implicit method which is particularly suited to the solution of the governing equations, and provides rapid convergence in multiple dimensions. The simulation is three dimensional in temperature, with variations occurring through two spatial coordinates and one time coordinate. The simulation can accommodate the transient flow of heat due to conductive heat transfer through tissues such as healthy tissue, malignant tumors, cartilage and bone, convective heat transfer through perfusion in the tissue and flow through the arteries, and heat generation from sources such as microwave beams. Small changes in the thermophysical properties of the tissue, and the blood perfusion rates are shown to exhibit only minor effects on the thermal fields, whereas the power of the heat sources, and the conductive flux are shown to have major effects on the thermal fields. The effects of adjacent physiological structures such as arteries and bones have also been determined. The temperature fields have been found to be weakly dependent on the increased perfusion rates encountered in the arteries except when the perfusion rate in the artery exceeds that in the tissue by at least one order of magnitude. A similar effect is noticed if the tumor is close to a bone. The greater thermal insulation exhibited by the bone restricts the flow of heat into it, and therefore causes the tissue to increase in temperature. Once the transient heating has been employed and the heating proceeds under steady-state conditions, the dual beam microwave applicator must be controlled to avoid overheating. The effect of on/off control and proportional + integral + derivative control is discussed.