生物组织在冻结过程中的三维相变传热问题精确解  

Exact Analytical Solution to Three Dimensional Phase Change Heat Transfer Problems in Biological Tissues Subject to Freezing

作　　者：李方方[1] 刘静[1] 乐恺[2] 

机构地区：[1]中国科学院理化技术研究所,北京100080 [2]北京科技大学热能工程系,北京100080

出　　处：《应用数学和力学》2009年第1期64-74,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(50776097)

摘　　要：对冻结过程中的三维生物传热相变问题进行分析求解是低温生物医学中一个困难而有重要理论意义的课题.围绕离体生物材料的低温冻存过程,引入移动热源模型及Green函数法,求得几组不同边界(全对流、全定温和复合边界)条件下,生物组织瞬态温度场的三维精确解表达式;进一步地,针对低温手术中生物活体组织受单枚或多枚冷冻探针的作用问题,考虑了血液灌注率、代谢热产及探针冷源的存在,同样推导出相应边界条件下瞬态温度场的精确解.该方法对于处理复杂生物传热问题的分析求解有重要的理论参考价值.Analytically solving three dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult, however theoretically importantm. The moving heat source model and the Green function method were introduced for the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various bound- ary conditions such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces were obtained. Further, the cryosurglcal process in living tissues subject to freezing by a single or multiple cryoprobes was also analytically solved. A closed form analytical solution to the bioheat phase change process by taking account of contributions from blood peffusion heat transfer, metabolic heat generation and heat sink of cryoprobe was derived. The present method is expected to be of significant value for analytically solving complex bioheat transfer problems with phase change.

关 键 词：三维相变生物传热 低温外科 低温保存 移动热源 GREEN函数 解析解 

分 类 号：O175.21[理学—数学] TK124[理学—基础数学]