Haider S A, Cetas T C, Roemer R B
Department of Radiation Oncology, University of Arizona, Tucson 85724.
IEEE Trans Biomed Eng. 1993 May;40(5):408-17. doi: 10.1109/10.243421.
An approximate analytical model based upon the bioheat transfer equation is derived and used to calculate temperatures within a perfused region implanted regularly with dielectrically coated hot source implants; for example, hot water tubes, electrically heated rods, or inductively heated ferromagnetic implants. The effect of a regular array of mutually parallel heat sources of cylindrical shape is approximated by idealizing one of the boundary conditions. The solution, as could be expected, is in terms of modified Bessel functions. In calculating the temperature of each thermoregulating source in the array, the steady state power balance is enforced. The important feature of the model is that the finite size of implant diameter and its dielectric coating can be incorporated. The effect of thickness and thermal conductivity of the coating on the source and tissue temperatures along with various other interesting features are deduced from this model. The analytically calculated implant and tissue temperatures are compared with those of a numerical 3-D finite difference model. The analytical model also is used to define a range of parameters such that minimal therapeutic temperatures will be achieved in the implanted volume without exceeding prescribed maximum temperatures. This approach leads to a simple means of selecting implant spacing and regulation temperatures of hot source methods prospectively.
基于生物热传递方程推导了一个近似解析模型，并用于计算在规则植入有介电涂层热源植入物的灌注区域内的温度，例如热水管、电加热棒或感应加热的铁磁植入物。通过理想化一个边界条件来近似圆柱形相互平行热源规则阵列的影响。不出所料，解是用修正贝塞尔函数表示的。在计算阵列中每个热调节源的温度时，强制实现稳态功率平衡。该模型的重要特点是可以纳入植入物直径的有限尺寸及其介电涂层。从该模型推导出涂层厚度和热导率对源温度和组织温度的影响以及各种其他有趣的特征。将解析计算得到的植入物温度和组织温度与数值三维有限差分模型的结果进行比较。该解析模型还用于定义一系列参数，以便在植入体积内达到最小治疗温度而不超过规定的最高温度。这种方法为前瞻性地选择植入物间距和热源方法的调节温度提供了一种简单手段。
