Elsevier

Journal of Thermal Biology

Volume 29, Issues 7–8, October–December 2004, Pages 583-587
Journal of Thermal Biology

An analytical model of temperature regulation in human head

https://doi.org/10.1016/j.jtherbio.2004.08.028Get rights and content

Abstract

An analytical model of human brain temperature regulation is proposed. The model describes the distribution of brain temperature as a function of internal and external parameters, such as temperature of the incoming arterial blood, blood flow, oxygen consumption rate, ambient temperature, and heat exchange with the environment. It is shown that substantial changes in human brain temperature can be accomplished only through changes in the temperature of the incoming arterial blood or substantial suppression of blood flow. Other parameters can lead only to temperature changes near the brain surface.

Introduction

It is well accepted that temperature regulation in a human brain is accomplished through several major mechanisms. They are: blood flow, temperature of incoming arterial blood, oxygen consumption rate, and heat exchange with the environment. Several computer-simulated models of temperature distribution in a human head have been developed (e.g., Nelson and Nunneley 1998; van Leeuwen et al., 2000). While these models provide important insights into the problem, their results substantially depend on input parameters that are not always known and may vary in broad ranges. The goal of our study is to develop an analytical model describing temperature distribution in a human head. The model provides analytical expressions that allow evaluation of changes in brain temperature under the influence of measurable input parameters. It can be used to predict a brain temperature response to such conditions as extreme heat or cold, external cooling with air or water flow, extensive exercise, cardiac by-pass surgery, etc.

Section snippets

Theoretical approach

Our approach is based on a bio-heat equation originally proposed by Pennes (1948) for description of the temperature distribution in organs. We consider the head as a system consisting of cerebral tissue (brain) with overlaying layers of cerebrospinal fluid (CSF), skull and scalp. The temperature distributions in these four regions, Tj(r) (j=0,1,2,3 corresponds to the brain, CSF, skull and scalp, respectively) can be found as a solution of a set of static bio-heat equationsα02T0-ρbcbw0(T0-Ta0)+

Results and discussion

A solution of Eqs. (1) is sought in the formT0(x)=Ta0+Tm0+A0exp(κ0x),T1(x)=A1x+B1,T2(x)=A2x+B2,T3(x)=Ta3+Tm3+A3exp(κ3x)+B3exp(-κ3x),where for j = 0 and 3, κj=(ρbcbwj/αj)1/2 and Tmj=qj/ρbcbwj are metabolic temperature shifts. Note that κ0=1/Δ with Δ defined by Eq. (3). The coefficients Aj, Bj can be found by substituting Eqs. (6) into the boundary conditions (4). After some straightforward but tedious algebra, the coefficient A0 can be written in the formA0=-ρ0(h-1+ρ0+ρ1+ρ2+ρ˜3)×[(Ta0+Tm0-T˜e)+ΔT

Conclusion

A model of the temperature distribution in the human head is developed. The analysis predicts changes in the brain temperature as a function of major internal and external parameters: the temperature of incoming arterial blood, blood flow, oxygen extraction fraction, ambient temperature, and heat exchange with the environment. In particular, the model can be used for predicting a head temperature response to extreme conditions such as heavy exercise or exposure to heat or cold and for

Acknowledgements

The authors are grateful to Professors Joseph J. H. Ackerman, Marcus E. Raichle and Mark S. Conradi for discussion and helpful comments. This work was supported by NIH Grant R01 NS41519.

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