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.

A mathematical model to study thermoregulation and heat-transfer processes in hypothermic neonates under variable physiological parameters.

All neonates, whether term or preterm, are prone to hypothermia, which is a major health issue causing many health problems to infants and sometimes even death. Thus, such subjects are imperative to study to help researchers and biologists in neonatology, for developing certain methods, procedures and devices to prevent these abnormal temperature fluctuations to save the neonates from this health threat. To this purpose, a multi-node mathematical model is developed, to provide detailed insights and its applications to study the temperature profiles, thermoregulatory and heat-transfer mechanisms in hypothermic neonates. The model is constructed using the radial form of heat equation along with appropriate boundary and initial conditions. The model solution is obtained with the aid of the variational finite element method followed by the fundamental matrix method. The model outcomes obtained show the temperature fluctuations and tissue responses in hypothermic neonates. Finally, the model outcomes are compared with the published/experimental work to prove the feasibility and validity of the proposed work. Moreover, this work generalizes the several previously published works in the related field.

Mathematical modelling of drug-diffusion from multi-layered capsules/tablets and other drug delivery devices.

In this paper, two mathematical models have been formulated by extending the basic reaction-diffusion model, along with suitable initial and boundary conditions to study the drug delivery and its diffusion in biological tissues from multi-layered capsules/tablets and other drug delivery devices (DDDs), respectively. These devices are either taken orally or through other drug-administration routes. The formulated models are solved using the variational finite element method followed by the fundamental matrix method, to study the drug delivery and its diffusion more efficiently. The main aim of this work is to provide an effective model, using optimal mathematical techniques to help researchers and biologists in medicine in decreasing the endeavours and expenses in designing DDDs. The outcomes obtained are compared with the experimental data to demonstrate the validity and the feasibility of the proposed work.

Variational finite element approach to study heat transfer in the biological tissues of premature infants.

The body temperature of newborn preterm infants depends on the heat transfer between the infant and the external environment. Factors that influence the heat exchange include the temperature and humidity of the air and the temperature of surfaces in contact with and around the infant. Neonatal thermoregulation has a different pattern as they have an immature thermoregulatory system. For this purpose, mathematical models can provide detailed insights for the heat transfer processes and its applications for clinical purposes. A new multi-compartment mathematical model of the neonatal thermoregulatory system is presented. The formulation of the model is based on the Pennes' bio-heat equation with suitable boundary and initial conditions. The variational finite element method has been employed to determine heat transfer and exchange in the biological tissues of premature infants. The results obtained in this paper have shown that premature infants are unable to maintain a constant core temperature and resemble the empirically obtained results, proving the validity and feasibility of our model. AMS (2010): SUBJECT CLASSIFICATION: 92BXX, 92CXX, 92C35, 92C50, 46N60.