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TECHNICAL PAPERS: Fluids/Heat/Transport

Experimental Validation of an Inverse Heat Transfer Algorithm for Optimizing Hyperthermia Treatments

[+] Author and Article Information
F. Scott Gayzik

Virginia Tech—Wake Forest University School of Biomedical Engineering and Sciences, Wake Forest School of Medicine, Medical Center Blvd., Winston-Salem, NC 27157sgayzik@wfubmc.edu

Elaine P. Scott

Virginia Tech—Wake Forest University School of Biomedical Engineering and Sciences, Department of Mechanical Engineering, Virginia Tech, 114-OPP Randolph Hall, Blacksburg, VA 24061

Tahar Loulou

 Univerite de Bretagne-Sud, Rue de Saint Maude, B.P. 92116, F-56321 Lorient, France

J Biomech Eng 128(4), 505-515 (Feb 03, 2006) (11 pages) doi:10.1115/1.2205375 History: Received January 27, 2005; Revised February 03, 2006

Hyperthermia is a cancer treatment modality in which body tissue is exposed to elevated temperatures to destroy cancerous cells. Hyperthermia treatment planning refers to the use of computational models to optimize the heating protocol with the goal of isolating thermal damage to predetermined treatment areas. This paper presents an algorithm to optimize a hyperthermia treatment protocol using the conjugate gradient method with the adjoint problem. The output of the minimization algorithm is a heating protocol that will cause a desired amount of thermal damage. The transient temperature distribution in a cylindrical region is simulated using the bioheat transfer equation. Temperature and time are integrated to calculate the extent of thermal damage in the region via a first-order rate process based on the Arrhenius equation. Several validation experiments are carried out by applying the results of the minimization algorithm to an albumen tissue phantom. Comparisons of metrics describing the damage region (the height and radius of the volume of thermally ablated phantom) show good agreement between the desired extent of damage and the measured extent of damage. The sensitivity of the bioheat transfer model and the Arrhenius damage model to their constituent parameters is calculated to create a tolerable range of error between the desired and measured extent of damage. The measured height and radius of the ablated region fit well within the tolerable range of error found in the sensitivity analysis.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Cylindrical coordinate system shown over schematic of the test setup. Also shown: an isolated control volume, and the heater and thermocouple locations. The axial (r) and radial (y) axes of symmetry are shown by the dotted lines.

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Figure 2

Physical representation of metrics used to quantity thermal damage

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Figure 3

Heating protocols for tests 1–3. Test 2 and 3 were output from the minimization algorithm, test 1 was applied to calibrate Sic(T).

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Figure 4

Magnitude of empirically determined internal convection coefficient Sic(T) versus temperature

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Figure 5

Temperature histories versus time for simulated and measured results. Simulated results without including internal convection effects are also shown.

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Figure 6

Ratio of natural convection at heater surface to heat flux from heater (qconv″∕qcond″×100%) for various values of ΔTic found during the base line experiment

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Figure 7

Desired damage profile used in validation experiments, Ωd, shown with predicted extent of thermal ablation in axial (Hab) and radial (Dab) directions

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Figure 8

Simulated (FD) and experimentally measured (Exp) temperature rise versus time at thermocouple locations; test 2

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Figure 9

Magnitude of sensitivity coefficients, Xi+ along radial axis (y=0)

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Figure 10

Sensitivity analysis results for radial extent of damage, Dab. The acceptable range of values is denoted by the bars.

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Figure 11

Sensitivity analysis results for axial extent of damage, Hab. The acceptable range of values is denoted by the bars.

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Figure 12

Simulated axial damage profiles, tests 1–3. The upper set of curves shows the radial extent of ablation, the lower set shows the axial extent of ablation.

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