This paper is an attempt to establish the mathematical models to understand the distribution of drug administration in human body through oral and intravenous routes. Three models were formulated based on diffusion process using Fick's principle and law of mass action. The rate constants governing the law of mass action were used on the basis of the drug efficacy at different interfaces. The Laplace transform and eigenvalue methods were used to obtain the solution of the ordinary differential equations concerning the rate of change of concentration in different compartments viz. blood and tissue medium. The drug concentration in the different compartments has been computed using numerical parameters. The graphs plotted illustrate the variation of drug concentration with respect to time using MATLAB software. It has been observed from the graphs that the drug concentration decreases in the first compartment and gradually increases in other compartments.

The main purpose of this study is to investigate the thermal behavior of living tissues in the presence of spatial external heat source. An effort has been made to formulate the mathematical model to study the temperature distribution in in vivo tissues of the human body. The mathematical formulation is governed by bio-heat equation together with appropriate initial, boundary and interface conditions. The solution of the model was carried out using variational finite element method and computational simulations. The model describes the exchange of heat between the internal biological tissues and other surrounding media. The effect of external heat source under different conditions of atmospheric temperature and as a local hyperthermic method provides an important information to the temperature regulation in biological tissues under normal and malignant conditions. Thermal fluctuations at the targeted regions were obtained with respect to various time-dependent heating sources and scattering coefficients. The results obtained may be helpful for clinical purposes especially in the treatment of cancerous tumors through radiotherapy and other local hyperthermic approaches.

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The severe ambient temperature always disrupts the normal thermoregulatory system of the human body. The decrease in core temperature leads to hypothermia and the development of cold injuries takes place at the exposed shells of the human body. The intensity of the cold exposure and its duration leads to various degrees of frostbites and resulting cell damage and fluid passage from the necrotic regions. In this paper, variational finite element has been employed to estimate the thermal damage due to severe cold conditions. The formulation of the model is based on Pennes’ bioheat equation and mass diffusion equation. Moreover, the fluid passage from the cold injuries at the peripheral tissues of the human body with respect to extreme cold conditions has been analyzed in relation with other parameters.

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