Computerized planning for multiprobe cryosurgery using a force-field analogy

Cryosurgery is the destruction of undesired biological tissues by freezing. For internal organs, multiple cryoprobes are inserted into the tissue with the goal of maximizing cryoinjury within a predefined target region, while minimizing cryoinjury to the surrounding tissues. The objective of this study is to develop a computerized planning tool to determine the best locations to insert the cryoprobes, based on bioheat transfer simulations. This tool is general and suitable for all available cooling techniques and hardware. The planning procedure employs a novel iterative optimization technique based on a force-field analogy. In each iteration, a single transient bioheat transfer simulation of the cryoprocedure is computed. At the end of the simulation, regions of tissue that would have undesired temperatures apply "forces" to the cryoprobes directly moving them to better locations. This method is more efficient than traditional numerical optimization techniques, because it requires significantly fewer bioheat transfer simulations for each iteration of planning. For demonstration purposes, 2D examples on cross sections typical of prostate cryosurgery are given.     

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.     

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.     

Fast inverse prediction of the freezing front in cryosurgery

Cryosurgery has become a well-established technique for the ablation of undesirable tissues such as tumors and cancers. The motivation for this study is to improve the efficacy and safety of this technique. This study presents an inverse heat transfer method for monitoring the motion of the freezing front from a cryoprobe. With the help of a thermocouple inserted into the layer of diseased tissue, the inverse heat transfer method estimates simultaneously the blood perfusion rate and the thermal conductivities of both frozen and unfrozen tissues. This information is then fed to the Pennes bioheat equation that: (1) calculates the time-varying temperature distribution inside the layer of tissue and (2) predicts the motion of the freezing front. The effect of the most influential parameters on the inverse predictions is investigated. These parameters are (1) the initial guesses for the unknown Levenberg-Marquardt polynomial parameters of the thermo-physical properties; (2) the temperature of the cryoprobe; (3) the heat transfer coefficient of the impinging jet of liquid nitrogen; and (4) the noise on the temperature data recorded by the thermocouple probe. Results show that the proposed inverse method is a promising alternative to ultrasound and Magnetic Resonance Imaging (MRI) for monitoring the motion of the freezing front during cryosurgery. For all the cryogenic scenarios simulated, the predictions of the inverse model remain accurate and stable.     

24-gauge ultrafine cryoprobe with diameter of 550 μm and its cooling performance

This paper describes the development of a novel cryoprobe with the same size as a 24-gauge injection needle and the evaluation of its cooling performance. This ultrafine cryoprobe was designed to reduce the invasiveness and extend application areas of cryosurgery. The ultrafine cryoprobe has a double-tube structure and consists of two stainless steel microtubes. The outer diameter of the cryoprobe is 550 μm, and the inner tube has a 70-μm inner diameter to depressurize the high-pressure refrigerant. By solving the bioheat transfer equation and considering freezing phenomena, the relationship between the size of the frozen region and the heat transfer coefficient of the refrigerant flow in an ultrafine cryoprobe was derived analytically. The results showed that the size of the frozen region is strongly affected by the heat transfer coefficient. A high heat transfer coefficient such as that of phase change heat transfer is required to generate a frozen region of sufficient size. In the experiment, trifluoromethane (HFC-23) was used as the refrigerant, and the cooling effects of the gas and liquid phase states at the inlet were evaluated. When the ultrafine cryoprobe was cooled using a liquid refrigerant, the surface temperature was approximately −50 °C, and the temperature distribution on the surface was uniform for a thermally insulated condition. However, for the case with vaporized refrigerant, the temperature distribution was not uniform. Therefore, it was concluded that the cooling mechanism using liquid refrigerant was suitable for ultrafine cryoprobes. Furthermore, to simulate cryosurgery, a cooling experiment using hydrogel was conducted. The results showed that the surface temperature of the ultrafine cryoprobe reached −35 °C and formed a frozen region with a radius of 4 mm in 4 min. These results indicate that the ultrafine cryoprobe can be applied in actual cryosurgeries for small affected areas.     

A new simplified bioheat equation for the effect of blood flow on local average tissue temperature

A new simplified three-dimensional bioheat equation is derived to describe the effect of blood flow on blood-tissue heat transfer. In two recent theoretical and experimental studies [1, 2] the authors have demonstrated that the so-called isotropic blood perfusion term in the existing bioheat equation is negligible because of the microvascular organization, and that the primary mechanism for blood-tissue energy exchange is incomplete countercurrent exchange in the thermally significant microvessels. The new theory to describe this basic mechanism shows that the vascularization of tissue causes it to behave as an anisotropic heat transfer medium. A remarkably simple expression is derived for the tensor conductivity of the tissue as a function of the local vascular geometry and flow velocity in the thermally significant countercurrent vessels. It is also shown that directed as opposed to isotropic blood perfusion between the countercurrent vessels can have a significant influence on heat transfer in regions where the countercurrent vessels are under 70-micron diameter. The new bioheat equation also describes this mechanism.     

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.     

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.     

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.     

Analytical study on bioheat transfer problems with spatial or transient heating on skin surface or inside biological bodies

Several closed form analytical solutions to the bioheat transfer problems with space or transient heating on skin surface or inside biological bodies were obtained using Green's function method. The solutions were applied to study several selected typical bioheat transfer processes, which are often encountered in cancer hyperthermia, laser surgery, thermal comfort analysis, and tissue thermal parameter estimation. Thus a straightforward way to quantitatively interpret the temperature behavior of living tissues subject to constant, sinusoidal, step, point or stochastic heatings etc. both in volume and on boundary were established. Further solution to the three-dimensional bioheat transfer problems was also given to illustrate the versatility of the present method. Implementations of this study to the practical problems were addressed.     

Cryosurgical nitrogen apparatus and recent results of its application in the radical treatment of certain neoplasms

In recent years a rapid development of equipment for controlled local freezing of tissues for cryosurgery has occurred. Depending on the velocity of freezing and on the technical parameters of the apparatus, diverse spreading of the ice front and tissue destruction are observed. The Research Centre of Medical Technology in Warsaw designed and produced an apparatus for cryosurgery, which was used in the Institute of Oncology in Warsaw for the radical treatment of skin, mucous membranes, and lip neoplasms. In the years 1973 to 1975 this technique was applied in 221 cases. In 167 patients radical treatment was performed (Group A); in 31 patients the treatment was paliativc (Group B); and in 23 patients non-neoplastic growths of the skin were treated (Group C). The present work concerns the results observed in Group A, where the mean duration of follow-up observations was 11 months. For the analysis of recent results of cryosurgery a subgroup was chosen from the Group A patients, i.e., those for whom the follow-up lasted at least 24 months (32 cases). The observations demonstrated that the apparatus is useful and simple to handle. In the clinical groups T₁, T₂, N₀, and M₀ the recent results of cryosurgery were similar to those observed with other types of treatment. Cryosurgical treatment is painless, is without blood loss, and is easy to perform. The period of healing is not longer than 3 weeks, and the cosmetic effect is good. General debilitation and the patient's age do not serve as counterindications to the performance of such treatment.     

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.     

Transport lattice models of heat transport in skin with spatially heterogeneous,temperature-dependent perfusion

Background  

Investigation of bioheat transfer problems requires the evaluation of temporal and spatial distributions of temperature. This class of problems has been traditionally addressed using the Pennes bioheat equation. Transport of heat by conduction, and by temperature-dependent, spatially heterogeneous blood perfusion is modeled here using a transport lattice approach.     

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.     

Conventional and newly developed bioheat transport models in vascularized tissues: A review

Heat transfer in a biological system is a complex process and its analysis is difficult. Heterogeneous vascular architecture, blood flow in the complex network of arteries and veins, varying metabolic heat generation rates and dependence of tissue properties on its physiological condition contribute to this complexity. The understanding of heat transfer in human body is important for better insight of thermoregulatory mechanism and physiological conditions. Its understanding is also important for accurate prediction of thermal transport and temperature distribution during biomedical applications. During the last three decades, many attempts have been made by researchers to model the complex thermal behavior of the human body. These models, viz., blood perfusion, countercurrent, thermal phase-lag, porous-media, perturbation, radiation, etc. have their corresponding strengths and limitations. Along with their biomedical applications, this article reviews various contextual issues associated with these models. After brief discussion of early bioheat models, the newly developed bioheat models are discussed in detail. Dependence of these models on biological properties, viz., thermophysical and optical properties are also discussed.     

Differences in planning performance,a neurocognitive endophenotype,are associated with a functional variant in PER3 gene

Performance alterations in executive function have been studied as potential endophenotypes for several neuropsychiatric diseases. Planning is an important component of executive function and has been shown to be affected in diseases such as attention deficit hyperactivity disorder, schizophrenia, obsessive–compulsive disorder and Parkinson’s disease. Several genes related to dopaminergic systems, such as COMT, have been explored as candidates for influencing planning performance. The circadian clock gene PERIOD3 (PER3) has been shown to be associated with several complex behaviors in humans and could be involved in different signaling mechanisms. In this study, we evaluated the possible association between a functional polymorphism in the PER3 gene (PER3-VNTR, rs57875989) and performance in a commonly used test of planning (Tower of London, TOL) in 229 healthy subjects from Bogotá, Colombia. PER3-VNTR genotyping was carried out with conventional PCR and all participants completed the TOL test using the computerized Psychology Experiment Building Language (PEBL) battery. A linear regression model was used for the analysis of association with the SNPStats program. We found that 4/4 genotype carriers showed a better performance and made fewer moves, in comparison to 4/5 and 5/5 genotype carriers (p?=?0.003). These results appear to be independent from effects of this polymorphism on self-reported average hours of sleep during work days in our sample. This is the first evidence of an association between PER3-VNTR and planning performance in a sample of healthy subjects and our results are consistent from previous findings for alterations in other cognitive domains. Future studies examining additional genes could lead to the identification of novel molecular underpinnings of planning in healthy subjects and in patients with neuropsychiatric disorders.     

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.     

An analytical study on the thermal effects of cryosurgery on selective cell destruction

The aim of cryosurgery is to kill cells within a closely defined region maintained at a predetermined low temperature. To effectively kill cells, it is important to be able to predict and control the cooling rate over some critical range of temperatures and freezing states in order to regulate the spatial extent of injury during any freeze-thaw protocol. The objective of manipulating the freezing parameters is to maximize the destruction of cancer cells within a defined spatial domain while minimizing cryoinjury to the surrounding healthy tissue. An analytical model has been developed to study the rate of cell destruction within a liver tumor undergoing a freeze-thaw cryosurgical process. Temperature transients in the tumor undergoing cryosurgery have been quantitatively investigated. The simulation is based on solving the transient bioheat equation using the finite volume scheme for a single or multiple-probe geometry. Simulated results show good agreement with experimental data obtained from in vivo clinical study. The calibrated model has been employed to study the effects of different freezing rates, freeze-thaw cycle(s), and multi-probe freezing on cell damage in a liver tumor. The effectiveness of each treatment protocol is estimated by generating the cell survival-volume signature and comparing the percentage of cell damaged within the ice-ball. Results from the model show that employing freeze-thaw cycles has the potential to enhance cell destruction within the cancerous tissue. Results from this study provide the basis for designing an optimized cryosurgical protocol which incorporates thermal effects and the extent of cell destruction within tumors.