An analytical model of temperature regulation in human head
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) ( corresponds to the brain, CSF, skull and scalp, respectively) can be found as a solution of a set of static bio-heat equations
Results and discussion
A solution of Eqs. (1) is sought in the formwhere for j = 0 and 3, and are metabolic temperature shifts. Note that 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 form
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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