Two-phase computerized planning of cryosurgery using bubble-packing and force-field analogy

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.     

Computerized planning of prostate cryosurgery using variable cryoprobe insertion depth

The current study presents a computerized planning scheme for prostate cryosurgery using a variable insertion depth strategy. This study is a part of an ongoing effort to develop computerized tools for cryosurgery. Based on typical clinical practices, previous automated planning schemes have required that all cryoprobes be aligned at a single insertion depth. The current study investigates the benefit of removing this constraint, in comparison with results based on uniform insertion depth planning as well as the so-called “pullback procedure”. Planning is based on the so-called “bubble-packing method”, and its quality is evaluated with bioheat transfer simulations. This study is based on five 3D prostate models, reconstructed from ultrasound imaging, and cryoprobe active length in the range of 15-35 mm. The variable insertion depth technique is found to consistently provide superior results when compared to the other placement methods. Furthermore, it is shown that both the optimal active length and the optimal number of cryoprobes vary among prostate models, based on the size and shape of the target region. Due to its low computational cost, the new scheme can be used to determine the optimal cryoprobe layout for a given prostate model in real time.     

Theory on thermal probe arrays for the distinction between the convective and the perfusive modalities of heat transfer in living tissues

Recent suggestions for an improved model of heat transfer in living tissues emphasize the existence of a convective mode due to flowing blood in addition to, or even instead of, the perfusive mode, as proposed in Pennes' "classic" bioheat equation. In view of these suggestions, it might be beneficial to develop a technique that will enable one to distinguish between these two modes of bioheat transfer. To this end, a concept that utilizes a multiprobe array of thermistors in conjunction with a revised bioheat transfer equation has been derived to distinguish between, and to quantify the perfusive and convective contribution of blood to heat transfer in living tissues. The array consists of two or more temperature sensors one of which also serves to locally insert a short pulse of heat into the tissue prior to the temperature measurements. A theoretical analysis shows that such a concept is feasible. The construction of the system involves the selection of several important design parameters, i.e., the distance between the probes, the heating power, and the pulse duration. The choice of these parameters is based on computer simulations of the actual experiment.     

Key issues in bioheat transfer simulations for the application of cryosurgery planning

The bioheat transfer simulation is undoubtedly the foundation for developing computerized tools for cryosurgery planning and analysis. While a large variety of techniques for bioheat transfer simulations are available in the literature of the past several decades, it is only their integration with clinical criteria and constraints which can make computerized planning a practical reality. This brief communication outlines (in the opinion of this author) the key issues that must be addressed in the application of bioheat transfer to cryosurgery planning and analysis, while drawing attention to recent and relevant publications in other journals, with reference to the most recent publication on the topic in the Journal of Cryobiology [Z. Magalov, A. Shitzer, D. Degani, Isothermal volume contours generated in a freezing gel by embedded cryo-needles with applications to cryo-surgery, Cryobiology 55 (2) (2007) 127–137].     

Numerical simulation for heat transfer in prostate cancer cryosurgery

A comprehensive computational framework to simulate heat transfer during the freezing process in prostate cancer cryosurgery is presented. Tissues are treated as nonideal materials wherein phase transition occurs over a temperature range, thermophysical properties are temperature dependent and heating due to blood flow and metabolism are included. Boundary conditions were determined at the surfaces of the commercially available cryoprobes and urethral warmer by experimental study of temperature combined with a mathematical optimization process. For simulations, a suitable computational geometry was designed based on MRI imaging data of a real prostate. An enthalpy formulation-based numerical solution was performed for a prescribed surgical protocol to mimic a clinical freezing process. This computational framework allows for the individual planning of cryosurgical procedures and objective assessment of the effectiveness of prostate cryosurgery.     

The effects of large blood vessels on temperature distributions during simulated hyperthermia.

Several three-dimensional vascular models have been developed to study the effects of adding equations for large blood vessels to the traditional bioheat transfer equation of Pennes when simulating tissue temperature distributions. These vascular models include "transiting" vessels, "supplying" arteries, and "draining" veins, for all of which the mean temperature of the blood in the vessels is calculated along their lengths. For the supplying arteries this spatially variable temperature is then used as the arterial temperature in the bioheat transfer equation. The different vascular models produce significantly different locations for both the maximum tumor and the maximum normal tissue temperatures for a given power deposition pattern. However, all of the vascular models predict essentially the same cold regions in the same locations in tumors: one set at the tumors' corners and another around the inlets of the large blood vessels to the tumor. Several different power deposition patterns have been simulated in an attempt to eliminate these cold regions; uniform power in the tumor, annular power in the tumor, preheating of the blood in the vessels while they are traversing the normal tissue, and an "optimal" power pattern which combines the best features of the above approaches. Although the calculations indicate that optimal power deposition patterns (which improve the temperature distributions) exist for all of the vascular models, none of the heating patterns studied eliminated all of the cold regions. Vasodilation in the normal tissue is also simulated to see its effects on the temperature fields.(ABSTRACT TRUNCATED AT 250 WORDS)     

Studying the performance of bifurcate cryoprobes based on shape factor of cryoablative zones

Conventional cryosurgical process employs extremely low temperatures to kill tumor cells within a closely defined region. However, its efficacy can be markedly compromised if the same treatment method is administrated for highly irregularly shaped tumors. Inadequate controls of freezing may induce tumor recurrence or undesirable over-freezing of surrounding healthy tissue. To address the cryosurgical complexity of irregularly shaped tumors, an analytical treatment on irregularly-shaped tumors has been performed and the degree of tumor irregularities is quantified. A novel cryoprobe coined the bifurcate cryoprobe with the capability to generate irregularly shaped cryo-lesions is proposed. The bifurcate cryoprobe, incorporating shape memory alloy functionality, enables the cryoprobe to regulate its physical configuration. To evaluate the probe’s performance, a bioheat transfer model has been developed and validated with in vitro data. We compared the ablative cryo-lesions induced by different bifurcate cryoprobes with those produced by conventional cryoprobes. Key results have indicated that the proposed bifurcate cryoprobes were able to significantly promote targeted tissue destruction while catering to the shape profiles of solid tumors. This study forms an on-going framework to provide clinicians with alternative versatile devices for the treatment of complex tumors.     

Numerical analysis for determination of the presence of a tumor and estimation of its size and location in a tissue

This article deals with the numerical analysis to ascertain the presence of a tumor and to estimate its size and location in a tissue. Heat transfer in the tissue is modeled using the Pennes bioheat transfer equation, and is solved using the finite volume method. Consideration is given to 1-D brain and breast tissues. Temperature distributions in the tissues are specific to the tumor grades, its locations and sizes, and these are different than that of a normal tissue. With temperature distribution known a priori, estimations of the position and the size of a tumor are done using the inverse analysis. The proposed approach gives a correct estimation of the presence of a tumor and its location and size.     

Application of Different Variants of the BEM in Numerical Modeling of Bioheat Transfer Problems

Heat transfer processes proceeding in the living organisms are described by the different mathematical models. In particular, the typical continuous model of bioheat transfer bases on the most popular Pennes equation, but the Cattaneo-Vernotte equation and the dual phase lag equation are also used. It should be pointed out that in parallel are also examined the vascular models, and then for the large blood vessels and tissue domain the energy equations are formulated separately. In the paper the different variants of the boundary element method as a tool of numerical solution of bioheat transfer problems are discussed. For the steady state problems and the vascular models the classical BEM algorithm and also the multiple reciprocity BEM are presented. For the transient problems connected with the heating of tissue, the various tissue models are considered for which the 1st scheme of the BEM, the BEM using discretization in time and the general BEM are applied. Examples of computations illustrate the possibilities of practical applications of boundary element method in the scope of bioheat transfer problems.     

Estimates for the acoustical stimulation and heating of multiphase biotissue

Low-intensity, unfocused, ultrasound-induced diathermy can produce undesired temperature increases at the interface of adjacent tissues within the body; particularly, at the interface of soft tissue and bone. This study provides a computational framework for predicting an upper bound on the temperature profile within a multiphase system composed of gel pad (water), tissue and bone from an input of acoustic energy, at frequencies and power levels consistent with applications of therapeutic hyperthermia. The model consists of solving a (one-dimensional) spatially discretized bioheat transfer equation via finite-difference method and updating the solution in time with a forward-Euler scheme. Simulations are then compared to experimental data to determine the energy-to-heat conversion factors within each constituent material using thermocouple-embedded, tissue-mimicking phantom material, with and without bone. Viscous heating artifacts from the presence of the thermocouples in the experimental phantom tissue are accounted for via additional experimental methods similar to those described by Morris et al. (Phys Med Biol 53:4759, 2008). Finally, an example application of the model is presented via prediction of the maximum temperature at the tissue–bone interface, as well as the peak temperatures in the composite structure at the end of a prescribed 2-min sonication, of blood-perfused, human soft-tissue at 1, 2 and 3 MHz frequencies and a spatial peak temporally averaged intensity of \(1.0 \ W/cm^{2}\). The results of this simulation are then related to comparable experimental studies in the literature.     

Comparison of iceball diameter and temperature distribution achieved with 3-mm accuprobe cryoprobes in porcine and human liver tissue and human colorectal liver metastases in vitro

We aimed to assess the thermal profile and size of iceballs produced by Accuprobe cryoprobes in fresh porcine and human liver and human colorectal cancer liver metastases in vitro to allow better planning of cryosurgical treatment of liver metastases. Iceballs were produced by a 20-min single freeze cycle using 8-mm cryoprobes in pig liver in a waterbath at 37 degrees C (n = 8) and 3-mm cryoprobes in pig liver (n = 8), human liver (n = 3), and human colorectal cancer liver metastases (n = 8). The iceball diameters and the temperatures at different distances from the cryoprobe were measured. Mean iceball diameters produced by 8-mm cryoprobes in pig liver were 56.3 mm and varied from 38.7 to 39.6 mm for 3-mm cryoprobes in the different tissues used. There was no significant difference in iceball size in the different tissues. The diameter of the zone of -40 degrees C or less was approximately 44 mm using 8-mm cryoprobes in porcine liver and between 27 and 31 mm using 3-mm cryoprobes in the different tissues examined. The results may allow better preoperative planning of the cryosurgical treatment of liver metastases with Accuprobe cryoprobes.     

Theoretical analysis of thermal damage in biological tissues caused by laser irradiation

A bioheat transfer approach is proposed to study thermal damage in biological tissues caused by laser radiation. The laser light propagation in the tissue is first solved by using a robust seven-flux model in cylindrical coordinate system. The resulting spatial distribution of the absorbed laser energy is incorporated into the bioheat transfer equation for solving temperature response. Thermal damage to the tissue is assessed by the extent of denatured protein using a rate process equation. It is found that for the tissue studied, a significant protein denaturation process would take place when temperature exceeds about 53 degrees C. The effects of laser power, exposure time and beam size as well as the tissue absorption and scattering coefficients on the thermal damage process are examined and discussed. The laser conditions that cause irreversible damage to the tissue are also identified.     

Numerical analysis of dynamic temperature in response to different levels of reactive hyperaemia in a three-dimensional image-based hand model

Vascular reactivity (VR) is considered as an effective index to predict the risk of cardiovascular events. A cost-effective alternative technique used to evaluate VR called digital thermal monitoring (DTM) is based on the response of finger temperature to vessel occlusion and reperfusion. In this work, a simulation has been developed to investigate hand temperature in response to vessel occlusion and perfusion. The simulation consists of image-based mesh generation and finite element analysis of blood flow and heat transfer in tissues. In order to reconstruct a real geometric model of human hand, a computer programme including automatic image processing for sequential MR data and mesh generation based on the transfinite interpolation method is developed. In the finite element analysis part, blood flow perfused in solid tissues is considered as fluid phase through porous media. Heat transfer in tissues is described by Pennes bioheat equation and blood perfusion rate is obtained from Darcy velocities. Capillary pressure, blood perfusion and temperature distribution of hand are obtained. The results reveal that fingertip temperature is strongly dependent on larger arterial pressure. This simulation is of potential to quantify the indices used for evaluating the VR in DTM test if it is integrated with the haemodynamic model of blood circulation in upper limb.     

Experimental validation of an inverse heat transfer algorithm for optimizing hyperthermia treatments

Hyperthermia is a cancer treatment modality in which body tissue is exposed to elevated temperatures to destroy cancerous cells. Hyperthermia treatment planning refers to the use of computational models to optimize the heating protocol with the goal of isolating thermal damage to predetermined treatment areas. This paper presents an algorithm to optimize a hyperthermia treatment protocol using the conjugate gradient method with the adjoint problem. The output of the minimization algorithm is a heating protocol that will cause a desired amount of thermal damage. The transient temperature distribution in a cylindrical region is simulated using the bioheat transfer equation. Temperature and time are integrated to calculate the extent of thermal damage in the region via a first-order rate process based on the Arrhenius equation. Several validation experiments are carried out by applying the results of the minimization algorithm to an albumen tissue phantom. Comparisons of metrics describing the damage region (the height and radius of the volume of thermally ablated phantom) show good agreement between the desired extent of damage and the measured extent of damage. The sensitivity of the bioheat transfer model and the Arrhenius damage model to their constituent parameters is calculated to create a tolerable range of error between the desired and measured extent of damage. The measured height and radius of the ablated region fit well within the tolerable range of error found in the sensitivity analysis.     

Uncertainty analysis for temperature prediction of biological bodies subject to randomly spatial heating

An analytical solution to the Pennes bioheat transfer equation in three-dimensional geometry with practical hyperthermia boundary conditions and random heating was obtained in this paper. Uncertainties for the predicted temperatures of tissues due to approximate parameters were studied based on analyzing one-dimensional heat transfer in the biological bodies subject to a spatially decay heating. Contributions from each of the thermal parameters such as heat conductivity, blood perfusion rate, and metabolic rate of the tissues, the scattering coefficient and the surface power flux of the heating apparatus were compared and the uncertainty limit for temperature distribution in this case was estimated. The results are useful in a variety of clinical hyperthermia and biological thermal parameter measurement.     

Dimensionless solutions and general characteristics of bioheat transfer during thermal therapy

The derivation and application of the general characteristics of bioheat transfer for medical applications are shown in this paper. Two general bioheat transfer characteristics are derived from solutions of one-dimensional Pennes’ bioheat transfer equation: steady-state thermal penetration depth, which is the deepest depth where the heat effect reaches; and time to reach steady-state, which represents the amount of time necessary for temperature distribution to converge to a steady-state. All results are described by dimensionless form; therefore, these results provide information on temperature distribution in biological tissue for various thermal therapies by transforming to dimension form.     

Laser-induced hyperthermia of nanoshell mediated vascularized tissue – A numerical study

Laser-induced hyperthermia treatment of tumor in a 2-D axisymmetric tissue embedded with moderate size (100–150 µm) blood vessels is studied. Laser absorption is enhanced by embedding gold–silica nanoshells in the tumor. Heat transfer in the tissue is modeled using Weinbaum–Jiji bioheat transfer equation. With laser irradiation, the volumetric radiation is accounted in the governing bioheat equation. Radiative information needed in the bioheat equation is calculated using the discrete ordinate method, and the coupled bioheat-radiation equation is solved using the finite volume method. Effects of power density, laser exposure time, beam radius, diameter of blood vessel and volume fractions of nanoshells on temperature spread in the tissue are analyzed.     

传递函数在生物组织光传输问题中的应用

本文将传递函数的概念引入生物组织光传输问题,并将传递函数理论用于面光源照射下生物组织内特定深度层面上光场强度分布的理论计算。结合Monte Carlo模拟获取脉冲相应函数,我们分析了不同面光源照射下层状组织样品透射面上的光场强度分布。理论计算结果与实验测试结果的一致性较好,这充分说明了本文建立的基于Monte Carlo模拟的传递函数方法是一种处理面光源照射下生物组织内光场空间的直接而有效的手段。