含肿瘤皮肤组织传热分析的广义有限差分法

李艾伦; 傅卓佳; 李柏纬; 陈文

doi:10.6052/0459-1879-18-155

含肿瘤皮肤组织传热分析的广义有限差分法

doi: 10.6052/0459-1879-18-155

河海大学力学与材料学院工程与科学数值模拟软件中心, 南京 211100

基金项目: 1)国家自然科学基金(11772119, 11572111)和中央高校基本业务费(2016B06214)资助项目.

详细信息

作者简介:
2)傅卓佳, 教授, 主要研究方向: 计算力学及工程仿真软件. E-mail: paul212063@hhu.edu.cn

通讯作者:
傅卓佳

中图分类号: O302;
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出版历程
- 收稿日期: 2018-05-09
- 刊出日期: 2018-09-18

GENERALIZED FINITE DIFFERENCE METHOD FOR BIOHEAT TRANSFER ANALYSIS ON SKIN TISSUE WITH TUMORS

Center for Numerical Simulation Software in Engineering & Sciences, College of Mechanics and Materials, Hohai University, Nanjing 211100, China

摘要

摘要: 生物传热分析在低温外科手术、肿瘤热疗、病热诊断等临床医学治疗和诊断中有着广泛的应用. 由于健康皮肤组织内肿瘤的存在使得肿瘤附近区域的温度会明显升高, 这一特性常被用于检测皮肤组织内的肿瘤生长, 因此有必要开展生物传热数值分析的研究. 本文以含肿瘤的皮肤组织为研究对象, 将一种新型区域型无网格配点法——广义有限差分法应用于能描述含肿瘤皮肤组织传热过程的Pennes方程求解. 广义有限差分法利用泰勒展开式与移动最小二乘法将计算区域内的每个离散点上的物理量导数表示成其与邻近点物理量及权重系数的线性组合, 进而构建得到仅含各离散点未知物理量的线性方程组. 该方法不仅具有无需划分网格、避免数值积分等无网格配点法的优点, 同时还克服了大多数无网格配点法中插值矩阵高度病态的问题, 为此类方法在大规模工程数值计算中的应用提供了可能性. 本文首先介绍了模拟含肿瘤皮肤组织传热过程的广义有限差分法离散模型, 随后通过不含肿瘤与含规则形状肿瘤的基准算例, 检验广义有限差分法的计算精度与收敛性; 在此基础上, 通过数值模拟研究不同肿瘤形状及肿瘤位置分布对皮肤组织内温度分布的影响.
- 广义有限差分法 /
- 配点法 /
- 移动最小二乘法 /
- 泰勒展开式 /
- Pennes生物传热方程
Abstract: Bioheat transfer analysis is widely used in clinical medical treatment and diagnosis, such as cryosurgery, tumor hyperthermia, disease diagnosis and so on. The presence of a tumor inside healthy skin tissues makes the temperature increment in the vicinity of the tumor. This characteristic is often used to detect tumor growth in skin tissue. Therefore it is necessary to do some numerical investigation on bioheat transfer analysis. Considering the skin tissue containing tumor, a novel meshless collocation method-generalized finite difference method (GFDM) is applied to Pennes bioheat equation, which can be used to describe the heat transfer process of the skin tissue containing tumors. Based on Taylor expansion and moving least squares method, the derivative of physical quantity at each discrete node can be expressed by the linear combination of physical quantities and weight coefficients at several adjacent nodes in the GFDM. Then the linear system of equations is constructed with the unknown physical quantities at discrete nodes. The proposed method not only has the advantages without mesh and numerical integration, but also overcomes the problem of highly ill-conditioned resultant matrix in most meshless collocation methods. It provides a possibility for the application of this kind of methods in large-scale engineering numerical calculation. The GFDM numerical model for simulating the bioheat transfer process in skin tissue with tumors is first introduced. Then the numerical accuracy and convergence of the GFDM are verified through some benchmark examples with/without regular-shaped tumors. Finally the effects of the arbitrary-shaped tumor including the location, geometry and size on the thermal behavior inside the skin tissue are investigated.
- generalized finite difference method /
- collocation method /
- moving least square method /
- Taylor expansion /
- Pennes bioheat equation

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参考文献(1)

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