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

Abstract

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.

Keywords:

• Bio-heat equation
• variational finite element method
• hypothermia
• Laplace transform

AMS Subject Classification:

• 92-XX
• 92BXX
• 92B05

Acknowledgements

This work was supported by the SERB-DST, Government of India, under award No.-EMR/2015/002487. The authors would also like to thank Dr. Nasir N. Hurrah for their helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Science and Engineering Research Board, Department of Science and Technology, India. Award No. = EMR/2015/002487.