Research Papers

An Effective Finite Difference Method for Simulation of Bioheat Transfer in Irregular Tissues

[+] Author and Article Information
Zhi Zhu He

e-mail: zzhe@mail.ipc.ac.cn

Xu Xue

e-mail: xuexu6666@yahoo.cn
Beijing Key Laboratory of Cryo-Biomedical
Engineering and Key Laboratory of Cryogenics,
Technical Institute of Physics and Chemistry,
Chinese Academy of Sciences,
Beijing 100190, China

Jing Liu

Beijing Key Laboratory of Cryo-Biomedical Engineering and Key Laboratory of Cryogenics,
Technical Institute of Physics and Chemistry Chinese Academy of Sciences,
Beijing 100190, China;
Department of Biomedical Engineering,
School of Medicine,
Tsinghua University,
Beijing 100084, China

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 9, 2011; final manuscript received March 11, 2013; published online June 21, 2013. Assoc. Editor: Franz-Josef Kahlen.

J. Heat Transfer 135(7), 071003 (Jun 21, 2013) (8 pages) Paper No: HT-11-1555; doi: 10.1115/1.4024064 History: Received December 09, 2011; Revised March 11, 2013

A three-dimensional (3D) simulation of bioheat transfer is crucial to analyze the physiological processes and evaluate many therapeutic/diagnostic practices spanning from high to low temperature medicine. In this paper we develop an efficient numerical scheme for solving 3D transient bioheat transfer equations based on the alternating direction implicit finite-difference method (ADI-FDM). An algorithm is proposed to deal with the boundary condition for irregular domain which could capture accurately the complex boundary and reduce considerably the staircase effects. Furthermore, the local adaptive mesh technology is introduced to improve the computational accuracy for irregular boundary and the domains with large temperature gradient. The detailed modification to ADI-FDM is given to accommodate such special grid structure, in particular. Combination of adaptive-mesh technology and ADI-FDM could significantly improve the computational accuracy and decrease the computational cost. Extensive results of numerical experiments demonstrate that the algorithm developed in the current work is very effective to predict the temperature distribution during hyperthermia and cryosurgery. This work may play an important role in developing a computational planning tool for hyperthermia and cryosurgery in the near future.

Copyright © 2013 by ASME
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Grahic Jump Location
Fig. 1

Illustration of irregular domains map with rectangular mesh in Cartesian coordinate system: (a) • denotes inner grid, ○ is boundary grid, and ▪ is auxiliary grid; (b) illustration of L, ΔS, and ΔV for a boundary grid

Grahic Jump Location
Fig. 2

Illustration of local adaptive mesh

Grahic Jump Location
Fig. 3

The base solution is depicted by solid line and symbol • denotes the numerical results (Δl = 5×10-3m) based on irregular boundary algorithms. The right is isosurface of T = 26°C.

Grahic Jump Location
Fig. 4

The base solution is depicted by solid line and symbols • (Δl = 5×10-3m) and ▪ (Δl = 2.5×10-3m) denoting the numerical results based on irregular boundary algorithms. The right is surface fields of the solutions (T = 75°C) for Δl = 2.5×10-3 m.

Grahic Jump Location
Fig. 5

The base solution is depicted by solid line and symbols • (Δl=5×10-3 m) and ▪ (Δl=2.5×10-3 m) denoting the numerical results based on irregular boundary algorithms. The right is surface fields of the solutions (T=26°C) for Δl=2.5×10-3 m.

Grahic Jump Location
Fig. 6

The base solution is depicted by solid line, symbol • is for boundary grid volume correction, and ▪ for no volume correction

Grahic Jump Location
Fig. 7

The base solution is depicted by solid line (Δl5 = 5×10-4m), symbol • denotes coarse grids (Δl0 = 2.5×10-3m), and ▪ is corresponding to adaptive grids (Δl0,Δl5)

Grahic Jump Location
Fig. 8

Schematic illustration of computational domain and probes location

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Fig. 9

Temperature distributions at cross section z = 4.8×10-2m and x = 7.5×10-2m at t = 1440 s

Grahic Jump Location
Fig. 10

Iceball and its view along x at t = 1440 s



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