生物传热方程中灌注率函数的数值反演算法  

NUMERICAL METHOD FOR RECOVERING PERFUSION COEFFICIENT IN A BIOLOGICAL HEAT TRANSFER EQUATION

作　　者：曹庆发 胡彬 万殊 王泽文 CAO Qing-fa;HU Bin;WAN Shu;WANG Ze-wen(School of Science,East China University of Technology,Nanchang,Jiangxi 330013,China)

机构地区：[1]东华理工大学理学院,江西南昌330013

出　　处：《井冈山大学学报（自然科学版）》2022年第2期22-27,共6页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(11961002,11761007);江西省教育厅科技计划项目(GJJ170444);东华理工大学大学生科技创新基金项目。

摘　　要：本文研究了一类生物传热方程的灌注率函数反演问题。基于附加的非局部条件和有限差分的Crank-Nicolson方法,构造了重建灌注率函数的迭代算法;经进一步简化后,得到了反演灌注率的一个显格式。为克服计算的不稳定性,引入移动平均滤波方法对误差数据进行去噪,算例结果表明结合移动平均滤波去噪的数值反演算法是可行的,能有效反演出灌注率函数。The inversion of the perfusion coefficient function of a class of bioheat transfer equations is studied in this paper.Based on the additional non-local conditions and the Crank-Nicolson method of finite difference,an iterative algorithm for reconstructing the perfusion coefficient function is constructed;after further simplification,an explicit scheme for retrieving perfusion coefficient is obtained.In order to overcome the instability of calculation,the moving average filtering method is introduced to denoise the error data.The results of calculation examples show that numerical inversion algorithms combined with the moving average filtering denoising are feasible and effective for retrieving perfusion coefficient function.

关 键 词：生物传热方程 灌注率 反问题 有限差分 移动平均 

分 类 号：O29[理学—应用数学]