Numerical Simulation for Heat Transfer in Prostate Cancer Cryosurgery

Quantifying the unknown impact of segmentation uncertainty on image-based simulations

Image-based simulation, the use of 3D images to calculate physical quantities, relies on image segmentation for geometry creation. However, this process introduces image segmentation uncertainty because different segmentation tools (both manual and machine-learning-based) will each produce a unique and valid segmentation. First, we demonstrate that these variations propagate into the physics simulations, compromising the resulting physics quantities. Second, we propose a general framework for rapidly quantifying segmentation uncertainty. Through the creation and sampling of segmentation uncertainty probability maps, we systematically and objectively create uncertainty distributions of the physics quantities. We show that physics quantity uncertainty distributions can follow a Normal distribution, but, in more complicated physics simulations, the resulting uncertainty distribution can be surprisingly nontrivial. We establish that bounding segmentation uncertainty can fail in these nontrivial situations. While our work does not eliminate segmentation uncertainty, it improves simulation credibility by making visible the previously unrecognized segmentation uncertainty plaguing image-based simulation.

Evaluation of a numerical simulation for cryoablation - comparison with bench data, clinical kidney and lung cases

PURPOSE

The accuracy of a numerical simulation of cryoablation ice balls was evaluated in gel phantom data as well as clinical kidney and lung cases.

MATERIALS AND METHODS

To evaluate the accuracy, 64 experimental single-needle cryoablations and 12 multi-needle cryoablations in gel phantoms were re-simulated with the corresponding freeze-thaw-freeze cycles. The simulated temperatures were compared over time with the measurements of thermocouples. For single needles, temperature values were compared at each thermocouple location. For multiple needles, Euclidean distances between simulated and measured isotherms (10 °C, 0 °C, -20 °C, -40 °C) were computed. Furthermore, surface and volume of simulated 0 °C isotherms were compared to cryoablation-induced ice balls in 14 kidney and 13 lung patients. For this purpose, needle positions and relevant anatomical structures defining material parameters (kidney/lung, tumor) were reconstructed from pre-ablation CT images and fused with postablation CT images (from which ice balls were extracted by manual delineation).

RESULTS

The single-needle gel phantom cases showed less than 5 °C prediction error on average. Over all multiple needle experiments in gel, the mean and maximum isotherm distance were less than 2.3 mm and 4.1 mm, respectively. Average Dice coefficients of 0.82/0.63 (kidney/lung) and mean surface distances of 2.59/3.12 mm quantify the prediction performance of the numerical simulation. However, maximum surface distances of 10.57/10.8 mm indicate that locally larger errors have to be expected.

CONCLUSION

A very good agreement of the numerical simulations for gel experiments was measured and a satisfactory agreement of the numerical simulations with measured ice balls in patient data was shown.

Generalized solution and estimation method for cooling performance of downscaled cryoprobe

In cryosurgery, downscaling of cryoprobes is important to minimize surgical invasion. In this study, a set of analytical solutions to the freezing phenomenon around a cryoprobe in a dimensionless form is derived and the general trend is discussed to clarify the relationship between the freezing ability of a biological tissue and the cooling power of a cryoprobe. A one-dimensional axisymmetric model in the steady-state condition is considered. The relationship between the size of the frozen region, fluid temperature in the cryoprobe, and heat transfer coefficient on the wall of the cryoprobe in the dimensional form is derived under the condition mentioned above. The fluid temperature and heat transfer coefficient are eliminated from the solutions by introducing the steady-state cryoprobe surface temperature. This transformation indicates that the steady-state surface temperature directly affects the size of the frozen region and combination of fluid temperature and heat transfer coefficient occurs, which has the same cooling effect. The derived solutions are transformed into a dimensionless form using the characteristic length of bioheat transfer and normalizing the temperature distribution in an unfrozen tissue. The applicability of these analytical solutions is evaluated by comparing them with numerical simulation results from existing studies. The dimensionless solutions describe the general trend of the relationship between the frozen region and the cooling power of a cryoprobe, which is independent of the type of organ, fluid temperature, and heat transfer coefficient. Finally, the concept of freezing limit is established using the derived solutions. The freezing limit describes the minimum requirements to freeze a tissue, and it can be used as guideline to design future downscaled cryoprobes with a suitable cooling mechanism.

Numerical Simulation of the Heat Transfer in the Cryoprobe of an Innovative Apparatus for Cryosurgery

Cryosurgery is a rapidly developing discipline, alternative to conventional surgical techniques, used to destroy cancer cells by the action of low temperatures. Currently, the refrigeration is obtained via the adiabatic expansion of gases in probes used for surgeries, with the need of inherently dangerous pressurized vessels. The proposed innovative prototypal apparatus aims to reach the cryosurgical temperatures exploiting a closed-loop refrigeration system, avoiding the hazardous presence of pressurized vessels in the operating room. This study preliminarily examines the technical feasibility of the cryoablation with this machine focusing the attention on the cryoprobe design. Cryoprobe geometry and materials are assessed and the related heat transfer taking place during the cryoablation process is simulated with the aid of the computational fluid dynamics software ANSYS®Fluent. Parametric analyses are carried out varying the length of the collecting tubes and the inlet velocity of the cold carrier fluid in the cryoprobe. The values obtained for physical quantities such as the temperature reached in the treated tissue, the width of the obtained cold front, and the maximum pressure required for the cold carrier fluid are calculated and discussed in order to prove the effectiveness of the experimental apparatus and develop the machine further.

NUMERICAL ANALYSIS OF TRIPLE LAYER SKIN TISSUE FREEZING USING NON-FOURIER HEAT CONDUCTION

The classical Fourier’s law assumes that the propagation speed of thermal disturbance is infinite, which is contradictory to physical reality. The living tissues are highly non-homogeneous and need a relaxation time to accumulate enough energy to transfer to the nearest element. This study proposes hyperbolic bio-heat model to study the freezing process in triple layer skin tissue with non-ideal property of skin tissue, metabolism and blood perfusion. The enthalpy formulation and finite difference method are used to solve the hyperbolic bio-heat model for triple layer skin tissue freezing. The effects of relaxation time for heat flux on temperature profile, liquidus and solidus interfaces are studied during the freezing of skin tissue. It is observed that the different values of relaxation time for heat flux have significant effect on temperature distribution, liquidus and solidus interfaces within the skin tissue.

Patient specific modeling of palpation-based prostate cancer diagnosis: effects of pelvic cavity anatomy and intrabladder pressure

Computational modeling has become a successful tool for scientific advances including understanding the behavior of biological and biomedical systems as well as improving clinical practice. In most cases, only general models are used without taking into account patient-specific features. However, patient specificity has proven to be crucial in guiding clinical practice because of disastrous consequences that can arise should the model be inaccurate. This paper proposes a framework for the computational modeling applied to the example of the male pelvic cavity for the purpose of prostate cancer diagnostics using palpation. The effects of patient specific structural features on palpation response are studied in three selected patients with very different pathophysiological conditions whose pelvic cavities are reconstructed from MRI scans. In particular, the role of intrabladder pressure in the outcome of digital rectal examination is investigated with the objective of providing guidelines to practitioners to enhance the effectiveness of diagnosis. Furthermore, the presence of the pelvic bone in the model is assessed to determine the pathophysiological conditions in which it has to be modeled. The conclusions and suggestions of this work have potential use not only in clinical practice and also for biomechanical modeling where structural patient-specificity needs to be considered. © 2015 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons Ltd.

Automatic Segmentation of Mechanically Inhomogeneous Tissues Based on Deformation Gradient Jump

Variations in properties, active behavior, injury, scarring, and/or disease can all cause a tissue's mechanical behavior to be heterogeneous. Advances in imaging technology allow for accurate full-field displacement tracking of both in vitro and in vivo deformation from an applied load. While detailed strain fields provide some insight into tissue behavior, material properties are usually determined by fitting stress-strain behavior with a constitutive equation. However, the determination of the mechanical behavior of heterogeneous soft tissue requires a spatially varying constitutive equation (i.e., one in which the material parameters vary with position). We present an approach that computationally dissects the sample domain into many homogeneous subdomains, wherein subdomain boundaries are formed by applying a betweenness based graphical analysis to the deformation gradient field to identify locations with large discontinuities. This novel partitioning technique successfully determined the shape, size and location of regions with locally similar material properties for: (1) a series of simulated soft tissue samples prescribed with both abrupt and gradual changes in anisotropy strength, prescribed fiber alignment, stiffness, and nonlinearity, (2) tissue analogs (PDMS and collagen gels) which were tested biaxially and speckle tracked (3) and soft tissues which exhibited a natural variation in properties (cadaveric supraspinatus tendon), a pathologic variation in properties (thoracic aorta containing transmural plaque), and active behavior (contracting cardiac sheet). The routine enables the dissection of samples computationally rather than physically, allowing for the study of small tissues specimens with unknown and irregular inhomogeneity.

Methods for characterizing convective cryoprobe heat transfer in ultrasound gel phantoms

While cryosurgery has proven capable in treating of a variety of conditions, it has met with some resistance among physicians, in part due to shortcomings in the ability to predict treatment outcomes. Here we attempt to address several key issues related to predictive modeling by demonstrating methods for accurately characterizing heat transfer from cryoprobes, report temperature dependent thermal properties for ultrasound gel (a convenient tissue phantom) down to cryogenic temperatures, and demonstrate the ability of convective exchange heat transfer boundary conditions to accurately describe freezing in the case of single and multiple interacting cryoprobe(s). Temperature dependent changes in the specific heat and thermal conductivity for ultrasound gel are reported down to -150 °C for the first time here and these data were used to accurately describe freezing in ultrasound gel in subsequent modeling. Freezing around a single and two interacting cryoprobe(s) was characterized in the ultrasound gel phantom by mapping the temperature in and around the "iceball" with carefully placed thermocouple arrays. These experimental data were fit with finite-element modeling in COMSOL Multiphysics, which was used to investigate the sensitivity and effectiveness of convective boundary conditions in describing heat transfer from the cryoprobes. Heat transfer at the probe tip was described in terms of a convective coefficient and the cryogen temperature. While model accuracy depended strongly on spatial (i.e., along the exchange surface) variation in the convective coefficient, it was much less sensitive to spatial and transient variations in the cryogen temperature parameter. The optimized fit, convective exchange conditions for the single-probe case also provided close agreement with the experimental data for the case of two interacting cryoprobes, suggesting that this basic characterization and modeling approach can be extended to accurately describe more complicated, multiprobe freezing geometries. Accurately characterizing cryoprobe behavior in phantoms requires detailed knowledge of the freezing medium's properties throughout the range of expected temperatures and an appropriate description of the heat transfer across the probe's exchange surfaces. Here we demonstrate that convective exchange boundary conditions provide an accurate and versatile description of heat transfer from cryoprobes, offering potential advantages over the traditional constant surface heat flux and constant surface temperature descriptions. In addition, although this study was conducted on Joule-Thomson type cryoprobes, the general methodologies should extend to any probe that is based on convective exchange with a cryogenic fluid.

Biphasic investigation of tissue mechanical response during freezing front propagation

Cryopreservation of engineered tissue (ET) has achieved limited success due to limited understanding of freezing-induced biophysical phenomena in ETs, especially fluid-matrix interaction within ETs. To further our understanding of the freezing-induced fluid-matrix interaction, we have developed a biphasic model formulation that simulates the transient heat transfer and volumetric expansion during freezing, its resulting fluid movement in the ET, elastic deformation of the solid matrix, and the corresponding pressure redistribution within. Treated as a biphasic material, the ET consists of a porous solid matrix fully saturated with interstitial fluid. Temperature-dependent material properties were employed, and phase change was included by incorporating the latent heat of phase change into an effective specific heat term. Model-predicted temperature distribution, the location of the moving freezing front, and the ET deformation rates through the time course compare reasonably well with experiments reported previously. Results from our theoretical model show that behind the marching freezing front, the ET undergoes expansion due to phase change of its fluid contents. It compresses the region preceding the freezing front leading to its fluid expulsion and reduced regional fluid volume fractions. The expelled fluid is forced forward and upward into the region further ahead of the compression zone causing a secondary expansion zone, which then compresses the region further downstream with much reduced intensity. Overall, it forms an alternating expansion-compression pattern, which moves with the marching freezing front. The present biphasic model helps us to gain insights into some facets of the freezing process and cryopreservation treatment that could not be gleaned experimentally. Its resulting understanding will ultimately be useful to design and improve cryopreservation protocols for ETs.

An optimisation approach to multiprobe cryosurgery planning

In cryosurgery operations, tumoural cells are killed by means of a freezing procedure realised with the insertion of cryoprobes in the diseased tissue. Cryosurgery planning aims at establishing the best values for operation parameters like number and position of the probes or temperature and duration of the freezing process. Here, we present an application of ant colony optimisation (ACO) to cryosurgery planning, whereby the ACO cost function is computed by numerically solving several direct Stefan problems in biological tissues. The method is validated in the case of a 2D phantom of a prostate cross section.

Adjuvant approaches to enhance cryosurgery

Molecular adjuvants can be used to enhance the natural destructive mechanisms of freezing within tissue. This review discusses their use in the growing field of combinatorial or adjuvant enhanced cryosurgery for a variety of disease conditions. Two important motivations for adjuvant use are: (1) increased control of the local disease in the area of freezing (i.e., reduced local recurrence of disease) and (2) reduced complications due to over-freezing into adjacent tissues (i.e., reduced normal functional tissue destruction near the treatment site). This review starts with a brief overview of cryosurgical technology including probes and cryogens and major mechanisms of cellular, vascular injury and possible immunological effects due to freeze-thaw treatment in vivo. The review then focuses on adjuvants to each of these mechanisms that make the tissue more sensitive to freeze-thaw injury. Four broad classes of adjuvants are discussed including: thermophysical agents (eutectic forming salts and amino acids), chemotherapuetics, vascular agents and immunomodulators. The key issues of selection, timing, dose and delivery of these adjuvants are then elaborated. Finally, work with a particularly promising vascular adjuvant, TNF-alpha, that shows the ability to destroy all cancer within a cryosurgical iceball is highlighted.

A High-Resolution Voxel Model for Predicting Local Tissue Temperatures in Humans Subjected to Warm and Hot Environments

This work describes and presents results from a new three-dimensional whole-body model of human thermoregulation. The model has been implemented using a version of the “Brooks Man” anatomical data set, consisting of 1.3×108 cubic volume elements (voxels) measuring 0.2 cm/side. The model simulates thermoregulation through passive mechanisms (metabolism, blood flow, respiration, and transpiration) and active mechanisms (vasodilatation, vasoconstriction, sweating, and shivering). Compared with lumped or compartment models, a voxel model is capable of high spatial resolution and can capture a level of anatomical detail not achievable otherwise. A high spatial resolution model can predict detailed heating patterns from localized or nonuniform heating patterns, such as from some radio frequency sources. Exposures to warm and hot environments (ambient temperatures of 33–48°C) were simulated with the current voxel model and with a recent compartment model. Results from the two models (core temperature, skin temperature, metabolic rate, and evaporative cooling rate) were compared with published experimental results obtained under similar conditions. Under the most severe environmental conditions considered (47.8°C, 27% RH for 2 h), the voxel model predicted a rectal temperature increase of 0.56°C, compared with a core temperature increase of 0.45°C from the compartment model and an experimental mean rectal temperature increase of 0.6°C. Similar, good agreement was noted for other thermal variables and under other environmental conditions. Results suggest that the voxel model is capable of predicting temperature response (core temperature and skin temperature) to certain warm or hot environments, with accuracy comparable to that of a compartment model. In addition, the voxel model is able to predict internal tissue temperatures and surface temperatures, over time, with a level of specificity and spatial resolution not achievable with compartment models. The development of voxel models and related computational tools may be useful for thermal dosimetry applications involving mild temperature hyperthermia and for the assessment of safe exposure to certain nonionizing radiation sources.

Numerical Simulation of Local Temperature Distortions During Ice Nucleation of Cells in Suspension

Knowledge of intercellular ice formation in cells embedded in an extra-cellular suspension is essential for effective design of freezing protocols. The presence of cell membrane causes super-cooling of the intra-cellular region, which nucleates at much lower temperatures than the surrounding extra-cellular space and is accompanied by the exothermic release of the latent heat. This is a dynamic process and causes thermal distortions in and around the cell where nucleation occurs. In the present study, an attempt has been made to numerically determine the magnitude of thermal distortion (ΔT) and the time (dt) it takes for this distortion to damp out to the local temperature. A two-dimensional computational model is presented in which the maximum thermal distortions (with an assumed cell diameter of 50 μm, nucleating at -5 °C while being cooled at 5 °C/min; denoted as Scenario 1) and the lowest-possible thermal distortions (with an assumed cell diameter of 5 μm, nucleating at -20 °C while being cooled at 100 °C/min; denoted as Scenario 2) are determined. Extensive computations have been performed assuming either the presence of a single, dual, or four cells in suspension. It is expected that these representative results would serve the purpose of estimating an effective sampling rate of microscale thermocouples currently being fabricated and of other biomedical devices used to measure intracellular ice formation.

The current use and future trends of focal surgical therapy in the management of localized prostate cancer

The current treatment algorithms for management of localized prostate cancer are mainly extirpative in nature. Treatment varies from expectant management to radical prostatectomy or radiation therapy. However, the ever-increasing emphasis on achieving the best survival benefit while better preserving quality of life, coupled with the introduction of new, safer, and efficacious minimally invasive ablative technologies, has led to the increased popularity of minimally invasive treatment (MIT). MIT refers to the use of a wide range of techniques for local target ablation of the prostate gland with minimal damage to the surrounding tissue. Currently these include cryotherapy and high-intensity focused ultrasound. However, other experimental technologies such as photodynamic therapy, interstitial prostate brachytherapy, and microwave and radiofrequency interstitial tumor ablation are also currently under investigation in early clinical trials. To date, the overall interim results for these relatively new modalities of treatment appear comparable to those for surgical and radiation therapies. However, randomized, controlled studies are needed to support use of these modalities as an alternative to surgery and radiation. In this review, we will address the current rationale for and knowledge of MIT with regard to its safety and efficacy in the treatment of localized prostate cancer. In addition, we will discuss future promising tools in MIT such as photodynamic therapy and the target focal therapy approach as a new trend for the treatment of organ-confined low-volume disease.

Effect of blood flow and metabolism on multidimensional heat transfer during cryosurgery

Cryosurgery has been recently accepted as a treatment option for eradicating undesirable tissues, especially tumor tissues, due to its minimally invasive nature and low hospitalization needs. A multidimensional, finite element analysis (FEA) for the cooling, holding and rewarming processes of biological tissues during cryosurgery is presented. The tissues were treated as non-ideal materials with temperature dependent thermophysical properties. The enthalpy method has been applied to solve the non-linear problem. The influence of heating effect due to blood flow and metabolism was studied, and furthermore, the effect of pre-injecting solutions with particular thermal properties into the target tissues was also numerically studied. It was found that the heat source term due to blood flow and metabolism in the bioheat transfer equation has a significant influence on the thermal and thermal gradient histories of the target tissues, and that the method of injection of solutions with particular thermal properties into the target tissues before cryosurgery may be a possible way to optimize the treatment process. However, in vitro experiments have not fully supported this viewpoint.

Numerical Simulation of a BPH Thermal Therapy—A Case Study Involving TUMT

The use of numerical simulation as a means to predict the outcome of transurethral microwave thermotherapy (TUMT) is set forth in detail. The simulation was carried out as a case study of a specific TUMT procedure. The selection of the case study was based on the availability of extensive medical records which documented an extraordinary application of TUMT. Predictions were made of the time-varying temperature patterns within the prostate, the bladder, the sphincter, the pelvic floor, and the fat and connective tissue which envelop these organs. These temperature patterns provided the basis of maps which highlighted those locations where necrosis occurred. An injury integral was used to predict the extent of the necrotic tissue produced by the therapy. It was found that, for the specific case being considered, necrosis occurred not only within the prostate but also extended to the neck of the bladder and to the fatty tissue. A special feature of the simulation was the accounting of the liquid-to-vapor phase change of the interstitial water. The vapor generated by the phase change is believed to significantly enlarge the region of necrosis. By the same token, the vapor pressure is expected to cause motion of the high-temperature liquid to deep-tissue regions. The damage predicted by the numerical simulation was compared, in detail, with post-operative medical examinations and found to be corroborated.