Foster K R, Lozano-Nieto A, Riu P J, Ely T S
Department of Bioengineering, University of Pennsylvania, Philadelphia 19104-6392, USA.
Bioelectromagnetics. 1998;19(7):420-8. doi: 10.1002/(sici)1521-186x(1998)19:7<420::aid-bem3>3.0.co;2-3.
We consider the thermal response times for heating of tissue subject to nonionizing (microwave or infrared) radiation. The analysis is based on a dimensionless form of the bioheat equation. The thermal response is governed by two time constants: one (tau1) pertains to heat convection by blood flow, and is of the order of 20-30 min for physiologically normal perfusion rates; the second (tau2) characterizes heat conduction and varies as the square of a distance that characterizes the spatial extent of the heating. Two idealized cases are examined. The first is a tissue block with an insulated surface, subject to irradiation with an exponentially decreasing specific absorption rate, which models a large surface area of tissue exposed to microwaves. The second is a hemispherical region of tissue exposed at a spatially uniform specific absorption rate, which models localized exposure. In both cases, the steady-state temperature increase can be written as the product of the incident power density and an effective time constant tau(eff), which is defined for each geometry as an appropriate function of tau1 and tau2. In appropriate limits of the ratio of these time constants, the local temperature rise is dominated by conductive or convective heat transport. Predictions of the block model agree well with recent data for the thresholds for perception of warmth or pain from exposure to microwave energy. Using these concepts, we developed a thermal averaging time that might be used in standards for human exposure to microwave radiation, to limit the temperature rise in tissue from radiation by pulsed sources. We compare the ANSI exposure standards for microwaves and infrared laser radiation with respect to the maximal increase in tissue temperature that would be allowed at the maximal permissible exposures. A historical appendix presents the origin of the 6-min averaging time used in the microwave standard.
我们考虑了非电离（微波或红外）辐射作用下组织加热的热响应时间。分析基于生物热方程的无量纲形式。热响应由两个时间常数控制：一个（τ1）与血流的热对流有关，对于生理正常灌注率，其量级为20 - 30分钟；第二个（τ2）表征热传导，并且随表征加热空间范围的距离的平方而变化。研究了两种理想化情况。第一种是表面绝缘的组织块，受到比吸收率呈指数下降的辐射，这模拟了暴露于微波的大面积组织。第二种是在空间上均匀比吸收率下暴露的半球形组织区域，这模拟了局部暴露。在这两种情况下，稳态温度升高都可以写成入射功率密度与有效时间常数τ(eff)的乘积，τ(eff)针对每种几何形状定义为τ1和τ2的适当函数。在这些时间常数比值的适当极限下，局部温度升高由传导或对流热传输主导。块模型的预测与最近关于暴露于微波能量时感知温暖或疼痛阈值的数据吻合良好。利用这些概念，我们开发了一个热平均时间，可用于人类暴露于微波辐射的标准中，以限制脉冲源辐射导致的组织温度升高。我们比较了微波和红外激光辐射的美国国家标准学会（ANSI）暴露标准在最大允许暴露下组织温度的最大升高情况。一个历史附录介绍了微波标准中使用的6分钟平均时间的由来。
