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TECHNICAL PAPERS: Fluids/Heat/Transport

Two-Phase Computerized Planning of Cryosurgery Using Bubble-Packing and Force-Field Analogy

[+] Author and Article Information
Daigo Tanaka

Department of Biomedical Engineering, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213

Kenji Shimada

Department of Mechanical Engineering and Department of Biomedical Engineering, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213

Yoed Rabin1

Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213rabin@cmu.edu

1

Corresponding author.

J Biomech Eng 128(1), 49-58 (Sep 19, 2005) (10 pages) doi:10.1115/1.2136166 History: Received May 13, 2005; Revised September 19, 2005

Background : Cryosurgery is the destruction of undesired tissues by freezing, as in prostate cryosurgery, for example. Minimally invasive cryosurgery is currently performed by means of an array of cryoprobes, each in the shape of a long hypodermic needle. The optimal arrangement of the cryoprobes, which is known to have a dramatic effect on the quality of the cryoprocedure, remains an art held by the cryosurgeon, based on the cryosurgeon’s experience and “rules of thumb.” An automated computerized technique for cryosurgery planning is the subject matter of the current paper, in an effort to improve the quality of cryosurgery. Method of Approach : A two-phase optimization method is proposed for this purpose, based on two previous and independent developments by this research team. Phase I is based on a bubble-packing method, previously used as an efficient method for finite element meshing. Phase II is based on a force-field analogy method, which has proven to be robust at the expense of a typically long runtime. Results : As a proof-of-concept, results are demonstrated on a two-dimensional case of a prostate cross section. The major contribution of this study is to affirm that in many instances cryosurgery planning can be performed without extremely expensive simulations of bioheat transfer, achieved in Phase I. Conclusions : This new method of planning has proven to reduce planning runtime from hours to minutes, making automated planning practical in a clinical time frame.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 3

The quality of bubble-packing is measured by the extent of overlapping: (a) bubbles with too little volume, (b) nearly appropriately sized bubbles by adaptive volume control, and (c) oversized bubbles

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Figure 4

Overlap of bubbles. The ideal overlap ratio in the two-dimensional case, α=6.0. Bubbles are located too sparsely when α<6.0, and too densely when α>6.0.

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Figure 5

Schematic illustration of the idealized prostate model used in the benchmark experiment: (a) the entire region simulated by means of a finite difference method and (b) the idealized prostate model

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Figure 6

Schematic illustration of the circular placement method of cryoprobes, prior to the force-field analogy phase

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Figure 7

Schematic illustration of the cryoprobe layout resulting from bubble-packing

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Figure 8

Temperature volume histograms (TVH) of the prostate (a), and the external region (b), at the end of Phase I. Each bar represents the relative area which has temperatures of no less than the listed temperature.

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Figure 9

Ultrasound image of the prostate area. The outer contour of the prostate and the inner contour of the urethra are highlighted with dashed lines.

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Figure 10

Layout results for 14 cryoprobes at the end of Phase I (a) and II (b). The white, light, medium, and dark shades of gray correspond to areas with temperatures above 0°C, below 0°C, below −22°C, and below −45°C, respectively.

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Figure 1

The interbubble forces between adjacent bubbles are defined by a piecewise third-order polynomial function, Eq. 3

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Figure 2

Boundary conditions for bubble-packing: (a) in the current method, where bubbles are limited to the target region, and (b) in the original bubble-packing scheme (13), where bubble centers are placed on the contour of the target region; in cryosurgery, this would cause external cryoinjury

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Figure 11

Temperature volume histograms at the end of Phase I, internal (a) and external (b) to the target region, and at the end of Phase II, internal (c) and external (d) to the target region. Each bar represents the relative area which has temperatures of no less than the listed temperature. Simulated duration of cryosurgery at the end of Phase II is 4.6, 3.8, 2.8, and 2.5min for 8, 10, 12, and 14 cryoprobes, respectively.

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