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Technical Brief

Finite Element Method Based Three-Dimensional Thermal Tomography for Disease Diagnosis of Human Body

[+] Author and Article Information
Chao Jin

Department of Biomedical Engineering,
School of Medicine,
Tsinghua University,
Beijing 100084, China;
Department of Diagnostic Radiology,
The First Affiliated Hospital of Xi'an Jiaotong University,
Xi'an 710061, China

Zhi-Zhu He

Beijing Key Lab of Cryo-Biomedical Engineering and Key
Lab of Cryogenics,
Technical Institute of Physics and Chemistry,
Chinese Academy of Sciences,
Beijing 100190, China
e-mail: zzhe@mail.ipc.ac.cn

Jing Liu

Department of Biomedical Engineering,
School of Medicine,
Tsinghua University,
Beijing 100084, China;
Beijing Key Lab of Cryo-Biomedical Engineering
and Key Lab of Cryogenics,
Technical Institute of Physics and Chemistry,
Chinese Academy of Sciences,
Beijing 100190, China
e-mail: jliubme@tsinghua.edu.cn

1Corresponding authors.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 30, 2014; final manuscript received May 3, 2016; published online June 7, 2016. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 138(10), 104501 (Jun 07, 2016) (6 pages) Paper No: HT-14-1839; doi: 10.1115/1.4033612 History: Received December 30, 2014; Revised May 03, 2016

A finite element method (FEM)-based thermal approach to reconstruct the disease-associated heat source distribution has been developed. The congruent relationship between the heat sources and the observed temperature is established from the FEM solution matrix. The regularization method based parameter iteration algorithm is further developed to solve the inverse bioheat transfer problems. Typical simulations on sphere model and real digital human head have been performed to validate the feasibility and efficacy of the current method. In addition, the regularization parameter is optimized to speed up the reconstruction process and reduce the thermal noises. All the results indicate that both the heat source distribution and three-dimensional (3D) temperature field within the biological body were successfully reconstructed with acceptable accuracy.

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Figures

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Fig. 1

The schematic diagram of the biological body (including two domains Ω1 and Ω2) and its boundary conditions

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Fig. 2

The geometrical model of digital head and mesh generation: (a) the geometrical model of human head, (b) the mesh results of head tissue section, (c) the geometrical model of gray matter, (d) the mesh results of gray matter section, and (e) the mesh density distribution near the interface between the head tissue and gray matter

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Fig. 3

The calculated results of the initial solving condition and the reconstructed target: (a) the normal 3D temperature distribution, (c) the preset heat source induced 3D temperature distribution within the sphere biological body, and (b) and (d) represent the numerical results on the yOz section for cases (a) and (c), respectively

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Fig. 4

The reconstructed results of the heat source distribution within the spherical biological body: (a) the view of the reconstructed 3D temperature field's slice images and (b) the monitoring results of residual curve during the iterative process for solving the inverse problem

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Fig. 5

The accuracy analysis of the reconstructed 3D temperature field: (a) the reconstructed 3D temperature distribution within the sphere biological body, (c) the deviation distribution between the reconstructed target and reconstructed result, and (b) and (d) represent the numerical results on the yOz section for cases (a) and (c), respectively

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Fig. 6

The quantitative analysis for the reconstructed accuracy and efficiency with the regularization parameter. (a) The deviation distribution between the reconstructed target and reconstructed result at (a) λ = 10−2, (c) λ = 10−4, and (e) λ = 10−6; the residual error curve during the iterative process at(b) λ = 10−2 (computational time = 850.5 s), (d) λ = 10−4 (computational time = 197.7 s), and (f) λ = 10−6 (computational time = 180.3 s).

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Fig. 7

The calculated results of the initial solving condition and reconstructed target: (a) the normal 3D temperature distribution and (b) the preset heat source induced 3D temperature distribution within the human head

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Fig. 8

The reconstructed results and accuracy analysis of the heat source distribution within the human head: (a) the view of the reconstructed 3D temperature field's slice images, (b) the reconstructed 3D temperature distribution within the human head, (c) the deviation distribution between the reconstructed target and the original result, and (d) the monitoring results of residual curve during the iterative process for solving the inverse problem

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