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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.

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References

Roemer, R. B., 1999, “Engineering Aspects of Hyperthermia Therapy,” Annu. Rev. Biomed. Eng., 1, pp. 347–376. [CrossRef] [PubMed]
Rubinsky, B., 2000, “Cryosurgery,” Annu. Rev. Biomed. Eng., 2, pp. 157–187. [CrossRef] [PubMed]
Bischof, J. C., 2000, “Quantitative Measurement and Prediction of Biophysical Response During Freezing in Tissues,” Annu. Rev. Biomed. Eng., 2, pp. 257–288. [CrossRef] [PubMed]
Liu, J., Lv, Y. G., and Zhang, J., 2006, “Theoretical Evaluation of Burns to the Human Respiratory Tract Due to Inhalation of Hot Gas in the Early Stage of Fires,” Burns, 32, pp. 436–446. [CrossRef] [PubMed]
Deng, Z. S., and Liu, J., 2004, “Mathematical Modeling of Temperature Mapping Over Skin Surface and Its Implementation in Thermal Disease Diagnostics,” Comput. Biol. Med., 34, pp. 495–521. [CrossRef] [PubMed]
Zhao, J. J., Zhang, J., Kang, N., and Yang, F. Q., 2005, “A Two Level Finite Difference Scheme for One Dimensional Pennes' Bioheat Equation,” Appl. Math. Comput., 171, pp. 320–331. [CrossRef]
Karaa, S., Zhang, J., and Yang, F. Q., 2005, “A Numerical Study of a 3D Bioheat Transfer Problem With Different Spatial Heating,” Math. Comput. Simul., 68, pp. 375–388. [CrossRef]
Rossi, M. R., Tanaka, D., Shimada, K., and Rabin,Y., 2007, “An Efficient Numerical Technique for Bioheat Simulations and Its Application to Computerized Cryosurgery Planning,” Comput. Methods Programs Biomed., 85, pp. 41–50. [CrossRef] [PubMed]
Bertaccini, D., and Calvetti, D., 2007, “Fast Simulation of Solid Tumors Thermal Ablation Treatments With a 3D Reaction Diffusion Model,” Comput. Biol. Med., 37, pp. 1173–1182. [CrossRef] [PubMed]
Velez, F. F., Romanov, O. G., and Diego, J. L. A., 2009, “Efficient 3D Numerical Approach for Temperature Prediction in Laser Irradiated Biological Tissues,” Comput. Biol. Med., 39, pp. 810–817. [CrossRef] [PubMed]
Pisa, S., Cavagnaro, M., Piuzzi, E., Bernardi, P., and Lin, J. C., 2003, “Power Density and Temperature Distributions Produced by Interstitial Arrays of Sleeved-Slot Antennas for Hyperthermic Cancer Therapy,” IEEE Trans. Microwave Theory Techniques, 51, pp. 2418–2426. [CrossRef]
Belhamadiaa, A. F. Y., 2005, “Numerical Prediction of Freezing Fronts in Cryosurgery: Comparison With Experimental Results,” Comput. Methods Biomech. Biomed. Eng., 8, pp. 241–249.
Yang, B. H., Wan, R. G., Muldrew, K. B., and Donnelly, J. B., 2008, “A Finite Element Model for Cryosurgery With Coupled Phase Change and Thermal Stress Aspects,” Finite Elements Anal. Design, 44, pp. 288–297. [CrossRef]
Li, E., Liu, G. R., Tan, V., and He, Z. C., 2010, “An Efficient Algorithm for Phase Change Problem in Tumor Treatment Using Alpha FEM,” Int. J. Thermal Sci., 49, pp. 1954–1967. [CrossRef]
Haemmerich, D., Tungjitkusolmun, S., Staelin, S. T., Lee, F. T., Mahvi, D. M., and Webster, J. G., 2002, “Finite-Element Analysis of Hepatic Multiple Probe Radio-Frequency Ablation,” IEEE Trans. Biomed. Eng., 49, pp. 836–842. [CrossRef] [PubMed]
Wang, H., and Qin, Q. H., 2010, “Fe Approach With Green's Function As Internal Trial Function for Simulating Bioheat Transfer in the Human Eye,” Arch. Mech., 62, pp. 493–510.
Lu, W. Q., Liu, J., and Zeng, Y. T., 1998, “Simulation of the Thermal Wave Propagation in Biological Tissues by the Dual Reciprocity Boundary Element Method,” Eng. Anal. Boundary Elements, 22, pp. 167–174. [CrossRef]
Deng, Z. S., and Liu, J., 2004, “Modeling of Multidimensional Freezing Problem During Cryosurgery by the Dual Reciprocity Boundary Element Method,” Eng. Anal. Boundary Elements, 28, pp. 97–108. [CrossRef]
Zhou, J. H., Zhang, Y. W., and Chen, J. K., 2008, “A Dual Reciprocity Boundary Element Method for Photothermal Interactions in Laser-Induced Thermotherapy,” Int. J. Heat Mass Transfer, 51, pp. 3869–3881. [CrossRef]
Ng, E. Y. K., Tan, H. M., and Ooi, E. H., 2009, “Boundary Element Method With Bioheat Equation for Skin Burn Injury,” Burns, 35, pp. 987–997. [CrossRef] [PubMed]
Ooi, E. H., Ang, W. T., and Ng, E. Y. K., 2007, “Bioheat Transfer in the Human Eye: A Boundary Element Approach,” Eng. Anal. Boundary Elements, 31, pp. 494–500. [CrossRef]
Chan, C. K., 1992, “Boundary Element Method Analysis for the Bioheat Transfer Equation,” ASME J. Biomech. Eng., 114, pp. 358–365. [CrossRef]
Bottauscio, O., Chiampi, M., and Zilberti, L., 2011, “A Boundary Element Approach to Relate Surface Fields With the Specific Absorption Rate (SAR) Induced in 3-D Human Phantoms,” Eng. Anal. Boundary Elements, 35, pp. 657–666. [CrossRef]
Deng, Z. S., and Liu., J., 2002, “Monte Carlo Method to Solve Multidimensional Bioheat Transfer Problem,” Numer. Heat Transfer Part B, 42, pp. 543–567. [CrossRef]
Zhang, H. F., 2008, “Lattice Boltzmann Method for Solving the Bioheat Equation,” Phys. Med. Biol., 53, pp. 15–23. [CrossRef]
Bellia, S. A., Saidane, A., Hamou, A., Benzohra, M., and Saite, J. M., 2008, “Transmission Line Matrix Modelling of Thermal Injuries to Skin,” Burns, 34, pp. 688–697. [CrossRef] [PubMed]
Amri, A., Saidane, A., and Pulko, S., 2011, “Thermal Analysis of a Three-Dimensional Breast Model With Embedded Tumour Using the Transmission Line Matrix (TLM) Method,” Comput. Biol. Med., 41, pp. 76–86. [CrossRef] [PubMed]
Cao, L. L., Qin, Q. H., and Zhao, N., 2010, “An RBF-MFS Model for Analysing Thermal Behaviour of Skin Tissues,” Int. J. Heat Mass Transfer, 53, pp. 1298–1307. [CrossRef]
Dillenseger, J. L., and Esneault, S., 2010, “Fast FFT-Based Bioheat Transfer Equation Computation,” Comput. Biol. Med., 40, pp. 119–123. [CrossRef] [PubMed]
Shih, T. C., Horng, T. L., Lin, W. L., Liauh, C. T., and Shih, T. C., 2007, “Effects of Pulsatile Blood Flow in Large Vessels on Thermal Dose Distribution During Thermal Therapy,” Med. Phys., 34, pp. 1312–1320. [CrossRef] [PubMed]
Chai, J. C., and Yap, Y. F., 2008, “A Distance-Function-Based Cartesian (DIFCA) Grid Method for Irregular Geometries,” Int. J. Heat Mass Transfer, 51, pp. 1691–1706. [CrossRef]
Mittal, R., and Iaccarino, G., 2005, “Immersed Boundary Methods,” Annu, Rev, Fluid Mech., 37, pp. 239–261. [CrossRef]
Ingram, D. M., Causon, D. M., and Mingham, C. G., 2003, “Developments in Cartesian Cut Cell Methods,” Math. Comput. Simul., 61, pp. 561–572. [CrossRef]
Samaras, T., Christ, A., and Kuster, N., 2006, “Effects of Geometry Discretization Aspects on the Numerical Solution of the Bioheat Transfer Equation With the FDTD Technique,” Phys. Med. Biol., 51, pp. 221–229. [CrossRef] [PubMed]
Neufeld, E., Chavannes, N., Samaras, T., and Kuster, N., 2007, “Novel Conformal Technique to Reduce Staircasing Artifacts at Material Boundaries for FDTD Modeling of the Bioheat Equation,” Phys. Med. Biol., 52, pp. 4371–4381. [CrossRef] [PubMed]
Douglas, J. J., and Gunn, J. E., 1964, “A General Formulation of Alternating Direction Methods—Part I: Parabolic and Hyperbolic Problems,” Numer. Math., 6, pp. 428–453. [CrossRef]
Zeng, P., Deng, Z. S., and LiuJ., 2011, “Parallel Algorithms for Freezing Problems During Cryosurgery,” Int. J. Inform. Eng. Electron. Bus., 2, pp. 11–19. [CrossRef]
Gibou, F., Chen, H., and Min, C. H., 2007, “A Supra-Convergent Finite Difference Scheme for the Poisson and Heat Equations on Irregular Domains and Non-Graded Adaptive Cartesian Grids,” J. Sci. Comput., 31, pp. 19–60. [CrossRef]
Consiglieri, L., Santos, I. D., and Haemmerich, D., 2003, “Theoretical Analysis of the Heat Convection Coefficient in Large Vessels and the Significance for Thermal Ablative Therapies,” Phys. Med. Biol., 48, pp. 4125–4134. [CrossRef] [PubMed]
He, Z. Z., and Liu, J., 2011, “The Effects of Blood Flow on the Iceball Evolution During a Multiple Probe Cryosurgery,” ASME 2011 International Mechanical Engineering Congress & Exposition.

Figures

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

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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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