以血管树形态模型以及单根血管的轴向温度变化规律为基础,对传统Pennes方程进行了改进,建立了一种新型的生物传热模型,并将其模拟结果与传统Pennes方程的模拟结果进行了比较。首先采用分形L系统的方法构建了血管树模型,然后解析求解了单根血管传热问题,得到了血管轴向温度的变化规律,最后对传统Pennes方程的血液灌注项进行了改进,使其表示血管与组织间的局部挟热量。以含有简单形态血管树的二维生物组织区域为例,分别采用改进Pennes方程和传统Pennes方程对其进行了传热求解,计算结果表明改进Pennes方程可以描述血管树对于组织温度分布的局部影响,而传统Pennes方程反映的是组织区域内均匀形式的温度分布。
Based on the simulated vascular trees, a bioheat transfer model was presented. The vascular tree models were developed using fractal methods to provide the parameters of blood vessels and blood flows for the thermal calculation. Through mathematic analysis of heat exchange between a single blood vessel and the coaxial tissue cylinder, the blood temperature variations along the blood vessel were established. The blood perfusion term in Pennes' bioheat equation was modified to represent the local heat exchange between the blood and the tissue. The approach of independently meshed grids in the tissue and the blood vessel regions was adopted to simplify the numerical calculation. The temperature distribution in biological tissues containing simple vascular tree was simulated respectively, and the results retained by solving the traditional Pennes' equation and the modified Pennes' equation were compared and analyzed.