Analytical study on optimal distribution of heating power in hyperthermia

In this paper we have investigated analytically optimal distribution of time dependent heating power Q2(t)(W/m2) in a system, described by bio-heat equation in a multilayered tissue, consisting of skin, fat, muscle and tumor layers, so as to attain a beneficial desired temperature χ⁎ across the entire length of the tumor. The desired temperature of the tumor is achieved at the end of time of operation of the process when the surface cooling temperature is taken as constant. The spatial heating power per unit volume Q1(x,t)(W/m3) is constructed according to the well known Beer's Law [1], given by, Q1(x,t)=βe−βxQ2(t) when β is scattering coefficient. The methodology adopted here is the usual ‘Maximal Principal’ with a suitably constructed ‘Hamiltonian’ followed by the use of a variant of the finite difference method [2]. The temperature of the tissue against its length at different total times of operation of the process due to calculated distribution of heating power is numerically evaluated for investigation of the desired rise of temperature of the tumor.