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TECHNICAL PAPERS: Fluids/Heat/Transport

# Analysis of Thermal Stress in Cryosurgery of Kidneys

[+] Author and Article Information
Xiaoming He1

Department of Mechanical Engineering,  University of Minnesota, Minneapolis, MN 55455

John C. Bischof2

Departments of Mechanical Engineering, Urologic Surgery, and Biomedical Engineering,  University of Minnesota, Minneapolis, MN 55455bischof@tc.umn.edu

$σν={12[(σ1−σ2)2+(σ2−σ3)2+(σ1−σ3)2]}0.5$, $σ1$, $σ2$, and $σ3$ are principal stresses

1

Current address: Center for Engineering in Medicine, Massachusetts General Hospital, Harvard Medical School, 51 Blossom Street, Boston, MA 02114.

2

Corresponding author.

J Biomech Eng 127(4), 656-661 (Jan 24, 2005) (6 pages) doi:10.1115/1.1934021 History: Received August 14, 2004; Revised January 24, 2005

## Abstract

In this study, the thermal stress distribution in cryosurgery of kidney was investigated using a multiphysics finite element model developed in ANSYS (V8.1). The thermal portion of the model was verified using experimental data and the mechanics portion of the model (elastic) was verified using classic analytical solutions. Temperature dependent thermal and mechanical properties were used in the model. Moreover, the model accounts for thermal expansion due to both thermal expansion in single phase and volumetric expansion associated with phase change of tissue water to ice. For a clinical cylindrical cryoprobe inserted into the renal cortex from the top–middle renal capsule, it was found that the thermal stress distributions along the radial position are very different at different depths from the top renal capsule. The thermal stress is much higher at both ends than in the middle of the cryoprobe surface. It was found that there might be more tissue next to the top renal capsule than other region undergoing microcrack formation or plastic deformation. Furthermore, it was found that macrocrack formation is more likely to occur in tissue adjacent to the cryoprobe surface (especially on the sharp point tip) and during the thawing phase of cryosurgery. It was further found that the volumetric expansion associated with phase change induced much higher thermal stress than thermal expansion in a single phase and might therefore be the main cause of the frequently observed crack formation shortly after initiation of thawing in cryosurgery. Because the thermal stress adjacent to the cryoprobe is much higher than the yield stress of frozen renal tissue, a plastic stress model is required for better modeling of the thermal stress distribution in cryosurgery of kidney in future. However the computational effort will then be drastically increased due to the strong nonlinear nature of the plastic model and more experimental studies are indispensable for better understanding of the mechanical behavior of frozen tissue in cryosurgery.

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## Figures

Figure 1

A sketch of the axisymmetric renal tissue domain: the stress distribution vs radial location at the three depths named Top, Middle, and Bottom from the top renal capsule were reported and compared later

Figure 2

Verification of the thermal and stress model: (A) comparisons between experimental (symbols) and predicted thermal histories (lines), (B) comparisons between the predicted thermal stress distributions (symbols) and those from analytical stress solution (lines)

Figure 3

The deformed tissue domain after 900s freezing due to the combined effect of thermal expansion due to tissue temperature change and volumetric expansion associated with tissue water phase transition

Figure 4

Plots of the radial (A), axial (B), and circumferential (C) stress distribution when freezing the tissue for 15min at three different axial location (z direction, see Fig. 1): top (i.e., the top renal capsule), Middle (i.e., 7.5mm below), and Bottom (i.e., 15mm below). The dotted line in each figure represents the zero stress line and dotted–dashed lines in each figure represent the negative and positive yield stress of frozen renal tissue (i.e., 132MPa(32)).

Figure 5

Plots of the von Mises equivalent stress and temperature distributions when freezing the tissue for 15min at the three different axial locations (z direction, see Fig. 1): Top (i.e., the top renal capsule), Middle (i.e., 7.5mm below), and Bottom (i.e., 15mm below). The dashed–dotted line represents the yield stress of frozen renal tissue (i.e., 132MPa(32)).

Figure 6

Plots of von Mises equivalent stress distributions at different time along the radial direction at the insertion depth of 7.5mm (i.e., middle). The dash-dotted line represents the yield stress of frozen renal tissue (i.e., 132MPa(32)).

Figure 7

Plots of von Mises equivalent stress distributions at different time along the radial direction at the insertion depth of 7.5mm (i.e., middle) assuming no volumetric expansion of tissue water during phase change in the model. The dashed–dotted line represents the yield stress of frozen renal tissue (i.e., 132MPa(32)).

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