Heat distribution and the condition of hypothermia in the multi-layered human head: A mathematical model.

The conduction, perfusion and metabolic heat generation based partial differential equation has been used to study the heat transfer in human head. The main objective of this study is to predict the temperature distribution at the multi-layered human head that results in hypothermic condition. The temperature profiles have been estimated at the interface points of brain, skull and scalp with respect to various parameters including atmospheric temperature, arterial temperature and metabolic heat generation. The variational finite element method and analytical method based on Laplace transform has been employed to establish the solution of the formulated model, and the resulting outcomes are illustrated graphically. Under cold exposure, the blood capillaries around scalp exchange core heat with the external cold environment and experience lowering in the tissue temperature of the blood in the scalp. It is reflected in the graphical view of the model that the prolonged exposure to cold transmits its effect into the deep brain capillaries, wherein the temperature gradually lowers down below the normal body temperature that results hypothermia and hence abnormal body homoeostasis.

Mathematical analysis of oxygen and carbon dioxide exchange in the human capillary and tissue system.

Human body has a great ability to maintain homeostasis and the respiratory system plays a pivotal role in physiological processes. In this paper, a mathematical model of oxygen and carbon dioxide transport in the human body through capillary and tissue system has been formulated. The model is given by four ordinary differential equations for the oxygen and carbon dioxide transport, two equations for the capillary and other two for the tissue. An analytic approach based on Taylor's series method has been presented in this paper to obtain a computable approximate solution of the differential equation to model the oxygen and carbon dioxide diffusion in a spherical tissue. The concentration profiles at the capillary and tissue regions has been estimated in relation with partial pressure as the main driving force. The results are in agreement with the literature data those arrived at by Whiteley et al. (2005). The results obtained may help bio-medical sciences to deal with hypoxia and other respiratory ailments faced by the people living at high altitudes. Moreover, facilitated diffusion due to haemoglobin has been presented.