Research Papers

Mathematical Modeling of Thermal Ablation in Tissue Surrounding a Large Vessel

[+] Author and Article Information
Xin Chen, Gerald M. Saidel

Department of Biomedical Engineering, Case Western Reserve University, Cleveland, OH 44106

J Biomech Eng 131(1), 011001 (Nov 18, 2008) (5 pages) doi:10.1115/1.2965374 History: Received December 06, 2006; Revised May 28, 2008; Published November 18, 2008

Thermal ablation of a solid tumor in a tissue with radio-frequency (rf) energy can be accomplished by using a probe inserted into the tissue under the guidance of magnetic resonance imaging. The extent of the ablation can be significantly reduced by heat loss from capillary perfusion and by blood flow in a large vessel in the tissue. A mathematical model is presented of the thermal processes that occur during rf ablation of a tissue near a large blood vessel, which should not be damaged. Temperature distribution dynamics are described by the combination of a 3D bioheat transport in tissue together with a 1D model of convective-dispersive heat transport in the blood vessel. The objective was to determine how much of the tissue can be ablated without damaging the blood vessel. This was achieved by simulating the tissue temperature distribution dynamics and by determining the optimal power inputs so that a maximum temperature increase in the tissue was achieved without inducing tissue damage at the edge of the large vessel. The main contribution of this study is to provide a model analysis for pretreatment and, eventually, for intra-operative application to thermal ablation of a tumor located near a large blood vessel.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Position of the rf tip (heat source) relative to a large blood vessel in a cube of tissue: (a) parallel and (b) orthogonal. Temperature boundary conditions at the inlet and at the outlet of the large vessel are shown.

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Figure 2

Lesion boundary in tissue related to the probability PD of cell damage by heating. (a) Probability of cell damage decreases with the distance from the heat source (rf tip). Lesion boundary approximated by the average interquartile (triangle) distance ⟨Δ⟩=[Δ(25%)+Δ(75%)]∕2 from the rf tip. Distances Δ=x2+y2+z2 computed for the upper (75%) quartile (circle) and the lower (25%) quartile (square) probabilities. (b) Simulated lesion boundary (bold curve) at any time (t) computed from the interquartile average distance ⟨Δi(t)⟩ from the rf tip of subareas AM,i(t) that sum upto the total lesion area AM(t).

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Figure 3

Isothermal contours in tissue with the large vessel (4mm) orthogonal to the rf tip depending on the distance (δ) between the vessel and the tip: (a) δ=4mm and (b) δ=8mm

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Figure 4

Isothermal contours in tissue with the large vessel (4mm) parallel to the rf tip depending on the distance (δ) between the vessel and the tip: (a) δ=4mm and (b) δ=8mm

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Figure 5

Thermal model domains in a rectangular coordinate system of the tissue cube relative to the rf tip (thick line at the center). Region I: above the upper end of the rf tip and perpendicular to it. Region II: below the lower end of the rf tip and perpendicular to it. Region III: between the two planes perpendicular to the rf tip ends (excluding the rf tip). Region IV: at the rf tip. Region V: large vessel domain.



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