Theoretical model of temperature regulation in the brain during changes in functional activity

Abstract

The balance between metabolic heat production, heat removal by blood flow, and heat conductance defines local temperature distribution in a living tissue. Disproportional local increases in blood flow as compared with oxygen consumption during functional brain activity disturb this balance, leading to temperature changes. In this article we have developed a theoretical framework that allows analysis of temperature changes during arbitrary functional brain activity. We established theoretical boundaries on temperature changes and explained how these boundaries depend on physiology (blood flow and metabolism) and external (heat exchange with the environment) experimental conditions. We show that, in regions located deep in the brain, task performance should be accompanied by temperature decreases in regions where blood flow increases (activated regions) and by temperature increases in regions where blood flow decreases (deactivated regions). The sign of temperature effect may be reversed for superficial cortex regions, where the baseline brain temperature is lower than the temperature of incoming arterial blood due to the heat exchange with the environment. Importantly, due to heat conductance, the temperature effect is not localized to the activated region but extends to a surrounding tissue at rest over the distances regulated by the temperature-shielding effect of blood flow. This temperature-shielding effect quantifies the means by which cerebral blood flow prevents "temperature perturbations" from propagating away from the perturbed regions. For small activated regions, this effect also substantially suppresses the magnitude of the temperature response, making it especially important for small animal brains.

Fig. 1.

Temperature change in the deep brain AFR. (a) The distribution of temperature change, ΔT(r) = T(r) − T_b (in °C) (r, distance from the center of AFR in millimeters) at F_i′ = 1.5·F_i, q′_i = 1.1·q_i for different R. Solid and dashed lines correspond to the following cases: (i) AFR of GM surrounded by WM and (ii) AFR of GM surrounded by nonactivated GM. (b) ΔT(0) (in °C) as a function of the ratio F_i′/F_i for q′_i = q_i for different radii of the AFR, R (numbers next to the curves are in millimeters). The default values (see Table 1) of other parameters are assumed.

Fig. 2.

The temperature change in the cortex-located AFR. (a) ΔT(z) = T(z) − T₀(z) (in °C; z in millimeters) for different thicknesses d (numbers next to the curves are in millimeters) of the AFR; F_i′ = 1.5·F_i, q′_i = 1.1·q_i and the default values of other parameters (see Table 1). (b) ΔT_s (in °C) as a function of the ratio F_i′/F_i for different values of the effective heat transfer coefficient [numbers next to the curves are in 10⁻³ W/(cm²·°C)] for OEF′_i = OEF_i (solid lines) and q′_i = q_i (dashed lines).

Fig. 3.

ΔT_s as a function of the effective heat transfer coefficient h [in 10⁻³ W/(cm²·°C)] (a) and of the ambient temperature T_ext for F_i′ = 1.5·F_i, q′_i = 1.1·q_i (b). The default values of other parameters and d = 3 mm are assumed.