An efficient numerical technique for bioheat simulations and its application to computerized cryosurgery planning

doi:10.1016/j.cmpb.2006.09.014

Computer Methods and Programs in Biomedicine

Volume 85, Issue 1, January 2007, Pages 41-50

https://doi.org/10.1016/j.cmpb.2006.09.014 Get rights and content

Abstract

As a part of ongoing efforts to develop computerized planning tools for cryosurgery, the current study focuses on developing an efficient numerical technique for bioheat transfer simulations. Our long-term goal is to develop a planning tool for cryosurgery that takes a 3D reconstruction of a target region, and suggests the best cryoprobe layout. Toward that goal, a planning algorithm, termed “force-field analogy,” has been recently presented, based on a sequence of bioheat transfer simulations, which are by far the most computationally expensive part of the planning method. The objective in the current study is to develop a finite difference numerical scheme for bioheat transfer simulations, which reduces the overall run time of computerized planning, thereby making it clinically relevant. While the general concept of variable grid size and time intervals is not new, its application to the phase change problem of cryosurgery is the unique contribution of the current study.

Introduction

Simulation of heat transfer problems involving phase change is of great importance in the study of thermal injury to biological systems. One of the most relevant examples is cryosurgery, which is the intentional destruction of undesired biological tissues by freezing [1]. Modern cryosurgery is frequently performed as a minimally-invasive procedure, with the application of a large number of cooling probes (cryoprobes), in the shape of long hypodermic needles, strategically located in the area to be destroyed (the target region) [2]. Here, the reconstruction of the target region, as well as monitoring of the freezing process, must be performed by means of imaging devices such as ultrasound or MRI [3], [4], [5], [6].

The clinical application of cryosurgery is not without technical difficulties, some of which are related to planning and control of a large number of cryoprobes, while others are related to the quality and limitations of imaging techniques. The long-term benefit of cryosurgery is not only affected by those technical difficulties, but also by the specific thermal history forced upon the tissue, the unique response of the tissue to low temperature exposure, and possibly the presence of drugs that sensitize that tissue to injury at low temperatures [7].

Since temperature can be measured only at discrete points in the target region, simulation of heat transfer is an extremely useful tool in developing and improving cryosurgical techniques [8], [9], [10], [11]. Here, heat transfer simulations can be calibrated with temperature measurements in the target tissue for the purpose of parametric estimation of tissue properties [12]. Heat transfer simulations can also assist in evaluating the certainty in temperature measurements, as has been demonstrated for the application of hypodermic thermocouples during cryosurgery [13]. Heat transfer simulations can also be used to augment imaging in real time, by identifying specific temperature thresholds within the frozen region [14]. However, one must bear in mind that the quality of those simulations relies on the certainty of the available values of the thermophysical properties of the tissue [15].

As a part of an ongoing project to develop an automated planning tool for cryosurgery, the current study is aimed at developing a numerical scheme which significantly reduces the heat transfer simulation run time; the duration of simulation has been identified as a critical factor in making that tool clinically relevant. Prior work on this ongoing project focused on the development of a force-field analogy technique, which executes a series of heat transfer simulations and automatically relocates cryoprobes between every two consecutive runs, until an optimum cryoprobe layout is found [16], [17]. Prior work also included the development of an algorithm to predict the best initial condition for the force-field analogy procedure (termed “bubble-packing”), in order to decrease the number of heat transfer simulations required in the force-field analogy process [18]. Finally, prior work included the development of the cryoheater, a self-controlled electrical heater, which helps to limit freezing injury to the target region [19]. Consistent with previous work, the new technique is demonstrated on a geometrical model of a prostate, where prostate cryosurgery is a common minimally-invasive procedure.

Section snippets

Mathematical formulation

Bioheat transfer in this study is modeled with the classic bioheat equation [20]: $C \frac{\partial T}{\partial t} = \nabla (k \nabla T) + {\dot{w}}_{b} C_{b} (T_{b} - T) + {\dot{q}}_{met}$ where C is the volumetric specific heat of the tissue, T the temperature, t the time, k the thermal conductivity of the tissue, ${\dot{w}}_{b}$ the blood perfusion volumetric flow rate per unit volume of tissue, C_b the volumetric specific heat of the blood, T_b the blood temperature entering the thermally treated area, and ${\dot{q}}_{met}$ is the metabolic heat generation. Numerous scientific reports have

Application to computerized planning of cryosurgery

While the numerical scheme presented above is quite general, the main objective for its development is to accelerate numerical simulations of cryosurgery, in order to make previously established planning algorithms practical [17], [18]. The objective in cryosurgery is to maximize freezing damage internal to the target region while minimizing freezing damage external to the target region. Consistent with prior work, a target region area is defined by the outer contour of the prostate, excluding

Results and discussion

The new numerical scheme has been analyzed in 1D, 2D, and 3D, to study its various characteristics. The prostate model used in the 2D and 3D cases has been reconstructed from a set of ultrasound images which were made available by the Robarts Imaging Institute, London, Ontario, Canada [25] for the purpose of the current study. The prostate images were segmented manually at our laboratory in order to reconstruct a full 3D target region. Since the ultrasound image data was not obtained during

Summary and conclusions

As a part of an ongoing project to develop an automated tool for cryosurgery planning, the current study presents a numerical scheme that significantly reduces the heat transfer simulation run time, which has been identified as a limiting factor in making this tool clinically relevant. The new numerical scheme is a modification of an early numerical scheme, in which modification is focused on variable grid and time intervals. Prior work focused on the development of a force-field analogy

Acknowledgements

This project is supported by the National Institute of Biomedical Imaging and Bioengineering (NIBIB)—NIH, grant #R01-EB003563-02,03. The authors would like to thank Dr. Aaron Fenster from the Robarts Imaging Institute, London, Ontario, Canada, for providing ultrasound images of the prostate.

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View full text

An efficient numerical technique for bioheat simulations and its application to computerized cryosurgery planning

Abstract

Introduction

Section snippets

Mathematical formulation

Application to computerized planning of cryosurgery

Results and discussion

Summary and conclusions

Acknowledgements

Cryobiology

Cryobiology

Cryobiology

Magn. Reson. Imaging

Cryobiology

Int. J. Heat Mass Transfer

Cryostatic congelation: a system for producing a limited controlled region of cooling or freezing of biological tissues

J. Nerve Mental Dis.

Cryosurgery in the treatment of cancer

Surg. Gynecol. Obstet.

Transrectal ultrasound-guided percutaneous radical cryosurgical ablation of the prostate

Cancer

Sonographic monitoring of hepatic cryosurgery in an experimental animal model

Am. J. Roentgenol.

Interventional and intraoperative MR: review and update of techniques and clinical experience

Eur. Radiol.

Modeling of bioheat transfer processes at high and low temperatures

Optimization of multiprobe cryosurgery

ASME Trans. J. Heat Transfer