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Article

Numerical Simulation for Heat Transfer in Prostate Cancer Cryosurgery

[+] Author and Article Information
Jiayao Zhang, Jayathi Y. Murthy

 School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907

George A. Sandison

 School of Health Science, Purdue University, West Lafayette, IN 47907

Lisa X. Xu1

 School of Mechanical Engineering and Department of Biomedical Engineering, Purdue University, West Lafayette, IN 47907 and  School of Life Sciences and Technology, Shanghai Jiao Tong University, Shanghai, 200030, PRClxu@ecn.purdue.edu

1

Corresponding author.

J Biomech Eng 127(2), 279-294 (Sep 18, 2004) (16 pages) doi:10.1115/1.1865193 History: Received October 29, 2003; Revised September 18, 2004

A comprehensive computational framework to simulate heat transfer during the freezing process in prostate cancer cryosurgery is presented. Tissues are treated as nonideal materials wherein phase transition occurs over a temperature range, thermophysical properties are temperature dependent and heating due to blood flow and metabolism are included. Boundary conditions were determined at the surfaces of the commercially available cryoprobes and urethral warmer by experimental study of temperature combined with a mathematical optimization process. For simulations, a suitable computational geometry was designed based on MRI imaging data of a real prostate. An enthalpy formulation-based numerical solution was performed for a prescribed surgical protocol to mimic a clinical freezing process. This computational framework allows for the individual planning of cryosurgical procedures and objective assessment of the effectiveness of prostate cryosurgery.

Copyright © 2005 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Reconstruction of the prostate with a urethra from MRI images. The prostate contours on the MRI slices were drawn manually on the Philips MxView workstation (a), and smoothed by spline curves, then saved as ICEM data. The ICEM data file was imported into GAMBIT to generate faces and a volume for the prostate (b), (c). The urethra (or urethral warmer) was constructed in the same way; it was assumed to cross the center of each prostate slice with a circular cross section and protrude 8mm toward the bladder at the base side and 16mm toward the penis at the apex side (c).

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Figure 2

Configuration of the cryoprobes. Locations of the cryoprobes can be adjusted in the graphic user interface (GUI) of GAMBIT to fulfill the clinical requirements.

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Figure 3

Locations of the planned cryoprobes in the x-y plane, shown together with the projected contour of the prostate (thick solid line) and the urethral warmer (thick dashed-dotted line). Also shown are the apex and base slices of the prostate (dashed lines) and their corresponding cross sections of the urethral warmer (dotted circles). According to the location with respect to anatomical structure of the prostate, probes 1 and 2 are called anterior probes, 3 and 4 are midline probes, and 5 and 6 are posterior probes.

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Figure 4

The computational geometry is a large tissue cylinder, subtracted by the volume of the cryoprobes and that enclosed by the urethral warmer. The cylinder has a diameter of 188mm and a height of 60mm, with one end bounded by the bladder (“Bladder Wall”) and 8mm above the prostate base, and the other end next to the penis (“Apex End”) and 16mm below the prostate apex.

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Figure 5

Meshed geometry of the tissue cylinder by nonconformal grids with the Apex End facing up (a). To obtain a good mesh, the cylinder was split into two parts by an elliptical cylinder enclosing the urethra water (b). The elliptical cylinder was discretized by tetrahedral mesh elements which conform to the irregular surface of the urethral warmer closely, and the remainder was meshed by the Cooper-type hexahedral meshes, which have excellent mesh quality. Overall, the volume was discretized into 1,209,282 mixed elements and 618,630 nodes.

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Figure 6

Typical transverse cross-sectional temperature contour at the end of the operation. The white curve is the contour of prostate. The dimensions are in meters (the same for Figs.  78).

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Figure 8

The 3D plot of the simulated critical isotherms (blue) shown together with the prostate (red), urethral warmer (yellow), and cryoprobes (cyan) at the end of the 10min operation.

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Figure 9

Time-temperature volume histogram of the treated prostate. The evolution of the prostate volume enclosed by different critical isotherms is shown. The prostate volume is 31,080mm3.

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Figure 10

Hold-time–tissue-volume histogram (HTVH) for the treated prostate at different critical isotherm values by the end of the 10min cryosurgical freeze. (Integrating the prostate volume for each hold-time for the 0°C isotherm gives 99.98%, which means almost all the prostate volume has been frozen to or below 0°C during the operation.)

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Figure 11

Time-temperature volume histogram for surrounding normal tissues subject to freezing injury under the assumptions of different critical temperatures. The volume is normalized to the prostate volume of 31,080mm3.

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Figure 12

Sensitivity analysis of the heat transfer coefficient on the average cryoprobe surface temperature along the active freezing length of a cryoprobe. This was calculated by numerical simulations with the same presumed temperature profile for argon gas. It was shown that when the heat transfer coefficient is over 5000W∕m2K, its further increase has a very small effect on the probe surface temperature.

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Figure 13

Location of thermocouples (crossed circles) in the single-probe freezing experiments. To suppress the thermal artifact caused by the more conductive thermocouple wires, the thermocouple wires (dotted lines, only three of them were shown to avoid confusion) were oriented parallel to the probe shaft, a direction with the minimum temperature gradient; and each group of thermocouples were placed side by side in a different radial plane. All the dimensions are in millimeter.

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Figure 14

Approximations of the temperature profile inside the cryoprobe used for the optimization process. Temperature profile inside the probe is approximated by two piecewise connected linear functions defined by T1,T2,T3 located at the probe tip, 10mm and 34mm up the probe, respectively. Continuously varied temperature Ti(i=2,3) (dashed curve) is approximated by constant time elements (solid line).

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Figure 15

Schematic diagram of the experimental step used in the calibration of the urethral warmer. The insert at the lower right is the cross section of urethral warmer. The dimension is in millimeters.

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