Keywords: cryosurgery, thermal stress, modeling, finite element method, kidney, RCC

ASME Journal of Biomechanical Engineering; in press

The results from this work were presented in ASME IMECE 2004, Anaheim, CA

Cryosurgical ablation of renal tumors has been investigated in both animal models (Rupp et al. 2002, Chosy et al. 1998, Nakada et al. 1998a & 1998b Campbell et al. 1998, Stephenson et al. 1996 and Onik et al. 1993) and human patients (Pantuck et al. 2002, Delworth et al. 1996, Rukstalis et al. 2001, Rodriguez et al. 2000, Gill et al. 1998, 1999 & 2000, Zegel et al. 1998, Savage and Gill 2000, and Shingleton and Sewell 2001) with promising results. However, a common problem encountered by almost all of the above studies is significant post-operative bleeding, which has been attributed to renal capsular and parenchymal fractures (or macrocrack formation) especially during thawing, although such hemorrhage was reported to be reduced when using 1.5mm ultra-thin cryoprobes (Pantuck et al. 2002). Since it is very difficult to monitor macrocrack formation during cryosurgery (Najimi and Rubinsky 1997), accurate prediction before the surgery and hence avoiding macrocrack formation during freezing and thawing are very important for successful renal cryosurgery.

Since crack formation is associated with enormous stress, prediction of crack formation during cryosurgery requires knowledge of thermal stress distribution. The first step to obtain this knowledge is to determine the mechanical properties of biomaterials and most importantly the stress-strain relationship. Rabin et al. (1996) experimentally studied the mechanical response of several biological tissues at cryogenic temperature including rabbit liver, kidney and brain. An initial, roughly linear elastic followed by a saw-tooth-like stress-strain relationship was observed for all the above-mentioned tissues under their experimental conditions. The saw-tooth-like response was attributed to the accumulation of microcracks and the average response resembles a perfectly plastic deformation. This material behavior was further speculated to be due to the heterogeneous nature of frozen biological tissue (blood vessels, bile ducts in liver, and renal tubules in kidney), which can both initiate microcrack formation and arrest the propagation of microcracks to form macrocracks (Rabin et al. 1997). However, the frozen tissue will collapse when the total (plastic plus elastic) strain is about ten times the maximum elastic strain (Rabin et al. 1997), which probably represents macrocrack/fracture formation. Other phenomenological studies found that the fracture/macrocrack formation is dependent on the experimental protocol including cooling rate, end temperature and thawing rate (Pegg et al. 1997, Song et al. 1995 and Hunt et al. 1994).

Only very limited studies have been published to model the thermal stress distribution during freezing and/or thawing. Rubinsky (1980 & 1982) analyzed the thermal stresses when inward freezing of a 1-D spherical and planar freezing of a 1-D slab-like biological tissue initially at phase change temperature. The elastic model with an analytical solution from Boley and Weiner (1960) was used. The thermal stress distribution surrounding a makeup1-D spherical cryosurgical probe was studied using both elastic (Rabin and Steif 1996) and elastic-perfectly plastic-like (Rabin and Steif 2000) analytical models. However, in the above studies, the phase change was assumed to occur at a constant temperature in order to solve the governing equations analytically. Furthermore, the volumetric expansion associated with the phase change from water to ice was ignored, although this volumetric expansion has been shown to result in far higher thermal stress than thermal expansion in single phase (Shi et al. 1998 and Rabin and Steif 1998). Lin et al. (1990) studied the thermal stress when inward freezing of water initially at phase change temperature in a 1D cylinder assuming the elastic model followed by ice crushing at a threshold stress (Michel 1978 & 1980). The volumetric expansion due to phase change was taken as the initial stress in the ice. However, the stress-strain relationship may not be true for frozen biological tissues, which will experience plastic deformation first and then crushing (Rabin et al. 1996).

In this study, we will investigate the thermal stress distribution during cryosurgery using: (1) clinically used cryoprobes of different diameters and full 3D kidney geometry; (2) both elastic and elastic-perfectly plastic material model; and (3) temperature dependent thermal properties and thermal expansion coefficient accounting for the volumetric expansion due to phase change from water to ice. This study is aimed to explain: (1) why macrocrack formation is more likely to happen during thawing rather than freezing; (2) why using probes of small diameter can reduce the macrocrack formation and (3) how to reduce the macrocrack formation by changing the design of cryoprobes.