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The development of improved numerical methods and physical models of thermal ablation is necessary for reducing uncertainties in the prediction of Thermal Protection System (TPS) performance and hence the reduction of TPS weight and the maximization of aerospace vehicle payloads. Models simulating ablation must address significantly disparate temporal and spatial scales, including molecular scale chemical physics of resin pyrolysis and macroscale resin and fiber ablation. Numerical methods must also be able to account for solid erosion effects and the resulting geometry evolution. This research has developed the first discrete nonholonomic Hamiltonian approach for the multiscale modeling of thermal ablation. The model incorporates three scales of interest, including a reacting molecular dynamics model at the nanoscale and hybrid particle element models at the meso and macro scales. Unlike all previous works in literature, the disparate temporal and spatial scales of the ablation problem are addressed, in part, by incorporating a fully coupled chemical-thermomechanical ablation model at the mesoscale. The research builds on previous work on the hybrid particle element method by the addition of variable mass particles at the meso and macro scales, as well as a description of the resin and fiber composite architecture in the macroscale model. Solid erosion effects and the resulting surface recession are accounted for explicitly in the particle-element kinematics. The presented methodology improves on existing macroscale models in three main respects: first, the solid dynamics is modeled explicitly with full chemical-thermomechanical coupling at the mesoscale and thermomechanical coupling at the macroscale, second mass and energy is rigorously conserved in the formulation of the state space equations, and third a general method of accounting for solid erosion effects and geometry evolution is included. The formulation is validated by comparison with published ablation experiments on fiber reinforced phenolic and cyanate ester composites.

Focal therapies (FT), including cryosurgery, thermal ablation and irreversible electroporation (IRE) have been widely used in the treatment of cancer and other diseases, with the aim to expose cells to extreme physical conditions, leading to cell death. The use of FT has increased recently due to advantages such as being minimally invasive and having lower costs, shorter recovery periods, and lower morbidity. The advent of imaging tools has also helped FT gain more attention among surgeons. However, limited understanding of the energy field around the FT probes might cause undertreatments, which would lead to recurrence of the disease, or overtreatment, which would lead to damages to the surrounding sensitive organs such as nerves and create severe side effects. Moreover, choosing the most suitable FT modality for treating a special organ target is essential.Our first objective for a successful focal therapy treatment is to have a clear understanding of the energy field distribution around the probes, both in clinical and preclinical applications. In preclinical cancer research, syngeneic tumors and xenograft tumors in rodent models are often used to define pre-clinical thresholds and outcomes for focal therapy modalities alone and with adjuvant approaches. Nevertheless, application of clinical-sized focal therapy probes in rodent tumor models can be difficult to control or characterize for this purpose. This, in turn, affects our understanding of the energy dose necessary to destroy diseased tissue. The fact that tumors in small animals come in different sizes and shapes and have thermal properties raises the need for a computational model capable of visualizing the temperature and electric field distribution within the tumor during the process of focal ablation. Understanding the interaction between the energy field and the tissue affects our understanding of the actual role of those ablation modalities in creating the tissue damage and enables us to predict and optimize the outcome of the procedure. Our second objective for a successful focal therapy treatment is to propose methods for preventing the damage to the surrounding organs, especially neural targets that are in close proximity to the treated area. In this work, we focus on preventing neural damage during prostate cancer cryosurgery. One major complication associated with prostate cancer cryosurgery is erectile dysfunction, caused by cryoinjury to the cavernous nerve in the neurovascular bundle, which is in close proximity to the prostate and is therefore directly exposed to freezing temperatures during cryosurgery. The use of cryoprotective agents (CPAs) to protect nerves against freezing temperatures is a method that has been used in nerve cryopreservation. While existing literature has established the idea of using CPAs to prevent nerve damage, there is still a lack of experimental data and quantitative models to study the effect of CPAs in preventing nerve cryoinjury during prostate cryosurgery. Moreover, no comprehensive study has assessed both the toxicity and the cryoprotective effectiveness of CPA exposure to the nerve within a repeatable and relevant biological model. Choosing a suitable FT modality is also crucial for a successful FT treatment. Certain modalities have better outcomes for specific organ targets than others. In this work, we propose a novel approach for renal denervation using Iron-oxide nanoparticle heating for treating hypertension. The most common ablation technique currently used in clinic for renal denervation is radiofrequency. However, this approach suffers from several disadvantages due to heating from inside of the renal artery which would result in damage to the artery wall, limited nerve ablation depth and inconsistent and unpredictable denervation. The use of iron-oxide nanoparticles, however, will alleviate some of the disadvantages mentioned by providing a repeatable treatment that can be used in combination with alcohol or other neurolytic agents as well. Using iron-oxide nanoparticles can also benefit from image guidance. This work will advance the application of FT by helping to better understand the energy field around the probe and helping to prevent unwanted damage to surrounding organs such as nerves.

Liver cancer, including hepatocellular carcinoma and colorectal metastases, is the second greatest cause of cancer-related death worldwide. Liver transplantation is considered the gold standard for hepatic cancer treatment. However, it is limited by the availability of liver donors and by cost. Hepatic resection is another treatment option that offers a high long-term survival rate. However, the overall resectability rate is low due to chronic liver disease and tumor location. Thermal ablation, including radiofrequency ablation as well as microwave and ultrasound ablation, has become an important alternative to liver resection and transplantation. To avoid incomplete treatments and cancer recurrence while reducing morbidity, a real-time monitoring and control approach, capable of providing consistent thermal ablation in minimal time, is needed. Echo decorrelation imaging has been successfully employed to monitor ultrasound ablation and radiofrequency ablation both ex vivo and in vivo. In this dissertation, its utility for real-time control of ultrasound ablation was assessed in ex vivo bovine liver and in vivo rabbit liver with VX2 tumor. Ultrasound exposures and echo decorrelation imaging were performed using 5 MHz linear image-ablate array. Sonications were automatically ceased when the minimum or average cumulative echo decorrelation within a control region of interest (ROI) exceeded a predetermined threshold, corresponding to high specificity for prediction of local tissue ablation or complete ROI ablation. Ablation outcomes, treatment time and prediction performance were statistically compared between controlled and uncontrolled groups.For controlling ex vivo focused ultrasound treatments, a small control ROI was placed at the focal zone and the selected control threshold corresponded to 90% specificity of local ablation prediction for preliminary ex vivo experiments. Controlled trials were compared to uncontrolled trials employing 2, 5 or 9 therapy cycles. For controlling ex vivo unfocused ultrasound treatments, an optimization approach was developed to determine stopping criteria for two series of controlled experiments using different echo decorrelation imaging feedback parameters and sonication sequences. Controlled trials were compared with uncontrolled trials employing 9 or 18 therapy cycles of matching sonication sequences. For controlling in vivo focused and unfocused ultrasound treatments, the selected control threshold corresponded to 90% specificity for tumor ablation prediction in previous in vivo experiments. Controlled trials were compared with a previous series of uncontrolled in vivo experiments employing focused and unfocused ultrasound ablation in rabbit liver and VX2 tumor. In general, controlled trials resulted in higher ablation rate, smaller lesion dimensions and treatment time compared to uncontrolled trials with longer duration. However, controlled trials showed equivalent lesion dimensions and treatment time, but higher ablation rate compared to uncontrolled trials with shorter duration. Better echo decorrelation prediction capability was observed for controlled trials compared to uncontrolled trials with shorter duration, but equivalent prediction performance was observed when compared to uncontrolled trials with longer duration. For most controlled trials, integrated backscatter imaging showed similar behavior to echo decorrelation for local ablation prediction. These results indicate that control using echo decorrelation imaging may improve the reliability and duration of ultrasound-guided focused and unfocused ultrasound ablation treatments.

The goals of this work are to investigate the feasibility of endoluminal ultrasound for delivering thermal ablation and hyperthermia to pancreatic tumors, and to perform a comprehensive design analysis of both practical and more intricate ultrasound applicator configurations suitable for endoluminal thermal therapy. A platform for modeling the 3D acoustic, temperature, and thermal dose distributions generated from endoluminal ultrasound applicators and applied to pancreatic tumors and surrounding anatomy was developed. Performance ranges of practical endoluminal applicator designs were determined through comprehensive parametric analyses of applicator design and expected tissue parameters. Modeling studies in patient specific anatomies highlighted the capability of endoluminal ultrasound applicators positioned in the duodenum or stomach to deliver conformal and volumetric ablation or hyperthermia of pancreatic tumors with boundaries within 3-4 cm of the luminal wall while mitigating thermal damage to surrounding sensitive tissues.A family of MR-compatible endoluminal ultrasound applicators, with distinct transducer configurations (~3 MHz, planar or curvilinear-focused) were designed, fabricated, and acoustically-characterized using bench-top methods. The capability of these applicators to be endogastrically delivered within the GI tract and to generate ablative temperature distributions in pancreatic tissue was evaluated in ex vivo and in vivo porcine studies, performed under MR navigation guidance and real-time treatment monitoring using MR temperature imaging. Preliminary acute studies in four in vivo pigs demonstrated the capabilities of the applicators to generate ablative temperature elevations of ~20-30 °C in pancreatic tissue at ~2-3 cm depths from the applicator, resulting in histologically-verified localized thermal lesions.Novel endoluminal ultrasound applicator configurations that integrate deployable balloon-based acoustic reflector and fluid lens components were introduced and analyzed using theoretical modeling analysis and preliminary experimental validation. These applicators would be endoluminally delivered in a small profile, then expanded at the target luminal site to enhance the effective therapeutic aperture. A modeling framework, incorporating wave refraction and reflection at material interfaces was developed and used to perform comprehensive parametric studies for “end-firing” and “side-firing” design alternatives. Simulation studies illustrated the capability of these designs to achieve more localized thermal lesion formation and deeper penetration (up to 8-10 cm) as compared to conventional endoluminal ultrasound applicator designs.

Thermal ablation, which uses localized heating by external energy sour-ces to destroy abnormal tissues, has been increasingly used as a treatment modality for cancers. Its efficacy hinges on the ability to control temperature and induce sufficient thermal damage in the targeted tissue regions. However, it is difficult for clinicians to decide what treatment settings should be applied to obtain the best treatment outcome while minimizing adverse effects. Help from numerical simulations in the treatment planning process would therefore be highly valuable, if the predictions are realistic, reliable and accurate. The complexity of tissue structures and the coupling of heat transfer with other biophysical phenomena such as blood perfusion, tissue damage and thermoregulation make it a challenge to predict temperature fields and thermal damage in living tissues. Approximate models with uncertain parameters are then used in the simulations. The important question is, which features are necessary to include in a model for plausible predictions to guide clinical treatment? Furthermore, what can be done to improve prediction accuracy? To address these issues a series of numerical simulations of radiofrequency (RF) ablation were performed that include the following effects: 1) the thermal effects of micro vascular perfusion, 2) the impact of tissue damage on that perfusion, and 3) the thermal effects of discrete blood vessels. In addition two distinct models of the thermal effects of perfusion, with very different underlying assumptions were used: Penne's bioheat transfer model, and a porous media model. The former is expected to be valid at large scales (e.g.,~the scale of a whole organ), while the latter is expected to be valid at small scales (e.g.,~the scale of a capillary bed). It is not clear what perfusion model is most appropriate at the intermediate scale of thermal ablation. The results of these simulations were analyzed to identify the most important factors to consider in treatment planning for RF ablation. By far the most important uncertainty in predicting the tissue damaged by RF ablation therapy was due to the difference between the two ablation models studied, resulting in a factor of two difference in the predicted volume of damaged tissue. Also important were the effective porosity of the tissue and the perfusion rate, especially in the case of the Pennes' perfusion model, and the presence of blood vessels larger than 0.5 mm in diameter and closer than 20 mm from the applicator. Of particular interest is the finding that it is very difficult to damage all tissue very close to a blood vessel larger than 3 mm in diameter, because of the cooling it provides. These observations suggest improved perfusion modeling, reliable determination of effective porosity and perfusion rate, and the mapping of large vessels in the treatment area would all improve the ability to predict the response to RF thermal ablation for treatment planning.

Hepatocellular carcinoma (HCC) and colorectal metastases (CRC) are common tumors worldwide with an increasing incidence in the United States. Thermal ablation techniques such as radiofrequency ablation (RFA), high intensity focused ultrasound (HIFU), microwave and laser ablation techniques have shown potential to treat unresectable tumors. Still lacking is a treatment monitoring technique that can accurately predict ablation. Echo decorrelation imaging is a novel pulse-echo ultrasound imaging method that quantifies and maps changes in echo signals occurring over millisecond time scales during thermal ablation. In this dissertation, the utility of echo decorrelation imaging as a treatment monitoring tool was assessed during in vivo and in vitro thermal ablation. To test the utility of echo decorrelation imaging for the prediction of ablation, RFA was performed on ex vivo bovine liver (N = 9). Echo decorrelation was computed from the Hilbert transformed pulse-echo data acquired during RFA treatments. For comparison, integrated backscatter was also computed from the same data. Pixel-by-pixel comparison between the echo decorrelation and integrated backscatter maps and the ablated region from gross tissue histology was performed using receiver operating characteristic (ROC) curves. Echo decorrelation and integrated backscatter were then quantitatively evaluated as predictors of ablation. The area under the ROC curves (AUROC) was determined for both echo decorrelation and integrated backscatter imaging methods. Ablation was predicted more accurately with echo decorrelation (AUROC = 0.820) than with integrated backscatter (AUROC = 0.668). To test the utility of echo decorrelation imaging for the prediction of ablation during in vivo thermal ablation, RFA was performed on normal swine liver (N = 5) and ultrasound ablation using image-ablate arrays was performed on rabbit liver implanted with VX2 tumors (N = 2). Consistent with the in vitro studies, ablation was predicted more accurately with echo decorrelation (AUROC = 0.833 and 0.776 for RFA and ultrasound ablation, respectively) than with integrated backscatter (AUROC = 0.733 and 0.494). Mean cumulative echo decorrelation was greater in the ablated tissue regions compared to the unablated regions for both in vitro (t = 6.808, p = 6.10-6, N = 9) and in vivo (t = 3.498, p = 0.036, N = 5 ) RFA treatments, indicating the ability of echo decorrelation to delineate between the ablated and unablated regions. For in vivo RFA, motion gating reduced the mean echo decorrelation in both ablated (t = 3.526, p = 0.036, N = 5) and unablated (t = 5.173, p = 0.013, N = 5) regions. However, with or without motion gating, the mean cumulative echo decorrelation was significantly greater in the ablated region than in the unablated region (t = 3.883, p = 0.008, N = 5).The effect of tissue temperature on echo decorrelation was assessed during in vitro RFA. RFA experiments (N = 15) were performed on ex vivo bovine liver tissue. Temperature maps were simulated by a finite element method, with tissue parameters determined using an unscented Kalman filter to best match measured ablation results. Significantly higher AUROC values (p = 0.019, p ≤ 10-14, p ≤ 10-14) were obtained for the prediction of tissue temperatures greater than 40, 60, and 80 °C with echo decorrelation (AUROC = 0.871, 0.948, and 0.966) when compared to integrated backscatter (AUROC = 0.865, 0.877, and 0.832). Overall, the results presented in this dissertation show potential for the utility of echo decorrelation imaging as a treatment monitoring tool.

Echo decorrelation imaging, a pulse–echo method that maps heat-induced changes in ultrasound echoes, was investigated for in vivo monitoring of thermal ablation in a liver cancer model. In open surgical procedures, rabbit liver with implanted VX2 tumor were imaged by image-ablate arrays and treated with bulk ultrasound (unfocused) ablation (N=10) or high-intensity focused ultrasound (HIFU) (N=13). Echo decorrelation and integrated backscatter (IBS) images were formed from pulse-echo images recorded during rest periods following each sonication pulse. Echo decorrelation images were corrected for motion- and noise-induced artifacts using measured echo decorrelation from corresponding sham trials. Sectioned ablated tissue was vitally stained with triphenyl tetrazolium chloride (TTC) and binary images were constructed based on local TTC staining. Analysis was performed for the focused exposures, unfocused exposures and for all exposures combined. Motion correction significantly reduced echo decorrelation in non-ablated liver regions. The reduction was significant in non-ablated VX2 tumor regions for focused exposures and all exposures combined. The reduction was not significant in ablated VX2 tumor regions for unfocused exposures. Echo decorrelation reduction was marginally significant in ablated regions for focused and unfocused exposures and was significant for all exposures combined.Prediction of ablation by echo decorrelation and IBS imaging was assessed using receiver operating characteristic (ROC) curves. Areas under the ROC curve (AUC) were significantly greater than chance for ablated liver prediction by corrected echo decorrelation and IBS. Echo decorrelation did not predict ablated VX2 tumor significantly better than chance for focused exposures. IBS did not predict ablated VX2 tumor better than chance for focused exposures and unfocused exposures. Corrected echo decorrelation predicted ablated liver significantly better than IBS for the focused exposures and all exposures combined. AUC differences between corrected echo decorrelation and IBS were not significant for all exposure groups in ablated VX2 tumor, for which echo decorrelation was marginally higher. At the optimal threshold, defined as the threshold corresponding to the point nearest to the top left-hand corner of the ROC plot, echo decorrelation had a better sensitivity than specificity for the focused and unfocused exposures in normal liver and VX2 tumor. To assess tissue motion effects due to large inter-frame times, echo decorrelation and IBS was computed for inter-frame times up to 847.5 ms. Uncorrected and corrected echo decorrelation prediction performance was marginally affected by large inter-frame times; however, corrected decorrelation was less affected. IBS prediction performance was nearly constant by comparison for large inter-frame times. Over the range of inter-frame times investigated, IBS predicted overall better than echo decorrelation for the unfocused group while echo decorrelation predicted overall better than IBS for the focused group. These results indicate echo decorrelation imaging is a successful predictor of local ablation, with potential for successful clinical implementation.

Cancer is one of the main killers of mankind. There are more than one million people in the U.S. alone are diagnosed with cancer each year. There have been millions of dollars invested into finding a cure. Equally important is the pursuit of new ways to treat cancer. Current treatment methods lack specificity and cause a great deal of collateral damage to patients. The goal of this study is not to find a cure, but rather to find a means of treatment that is at least equally as effective to current treatment methods and less damaging to the patient’s unaffected cells. At present, one option is the use of nanomaterials, which is a developing area of research. These nanomaterials have various usages from drug delivery to cancer diagnostics and therapy. Carbon nanotubes (CNTs) have shown to have a reduced toxicity, in comparison to other nanomaterials and, like its counterparts, possess the ability to absorb and redistribute heat very well resulting in localized heating while minimizing detrimental effects on surrounding tissues. The use of antibodies or other chemical compounds is imperative for their increased affinity for particular cells lines in order to localize this heating to cancer cells. This project used the conjugation of carbon nanotubes to anti-CD44 to target cancer cells and induce thermal ablation via novel microwave radiation. By coupling the power of microwaves with the ability of the CNTs to efficiently absorb heat, antibody-functionalized CNTs (Ab-CNTs) should be able to localize, amplify, and redistribute that heat to cancer cells that they are associated with through antibody binding to surface receptors. Optimal concentrations of CNTs and microwave power were found at 0.025-0.01 mg/ml and 900 W, respectively. These parameters showed significant cell death occurring in vitro when Ab-CNTs were used, compared to controls. These findings are supported in vivo using zebrafish embryos and via confocal imaging. Future directions for this project should include finding more suitable antibodies for various forms of cancer, as well as, moving trials into higher-level animal models.

The goals of this work are to investigate the feasibility of interstitial ultrasound ablation of tumors in and near the spine and to develop treatment guidelines. Interstitial ultrasound ablation, which allows for directional control of heat deposition, could potentially take advantage of the preferential acoustic absorption and heating that occurs along sonicated bone surfaces in order to ablate targets adjacent to vertebrae without damaging nearby critical anatomy such as the spinal cord. A platform for modeling patient-specific temperature and thermal dose distributions during catheter-cooled interstitial ultrasound ablation involving bone was developed in Comsol. The 3D, transient, finite element models developed herein considered various approximations of the complex interactions between ultrasound and bone. Experiments in phantoms, ex vivo tissues, and in vivo tissues were used to validate the numerical models and to characterize the impact of bone on ablation performance. Temperature distributions were measured using both invasive thermometry and MR-based techniques. Comprehensive parametric and patient-specific simulation studies were performed to investigate the feasibility of interstitial ultrasound ablation of paraspinal tumors and osteolytic vertebral tumors and to develop treatment guidelines. High ultrasound absorption at bone/soft tissue interfaces increased the volumes of target tissue that could be ablated and/or reduced the necessary treatment times. Models using simplified approximations produced temperature and thermal dose profiles closely matching both experimental measurements and more comprehensive models. Patient-specific and parametric simulations indicated that tumors up to 44 mm in diameter and insulated from the spinal canal by at least 4-5 mm of bone could be completely ablated within 15 min. Critical anatomy closer to the tumor could be preserved by reducing the acoustic energy aimed towards these structures and/or through gaseous insulation. Preferential bone heating and the insulating quality of bone resulted in thermal lesions closely conforming to the shapes of osteolytic targets and fast treatment times.This work demonstrates that interstitial ultrasound ablation appears feasible for treatment of paraspinal and vertebral tumors. Models and experiments indicate that preferential bone heating may provide improved localization, faster treatment times, and larger treatment zones in unossified tumors bordering bone as compared to other heating modalities.

MRI provides different types of exquisite soft tissue and functional contrast. However, depending on the desired contrast and spatial resolution properties, the acquisition time can be quite long. The long-term objective of this work is to improve methods to quickly and accurately diagnose human disease using MRI and provide resources that can be used for image-guided therapy and real-time imaging.Balanced steady state free precession (bSSFP) or True-FISP provides the highest signal-to-noise ratio efficiency of any pulse sequence. However, in bSSFP, contrast is a mixture of T1 and T2 weightings, which is often not desired clinically, and the signal from flowing blood is hyperintense, which can obscure the vessel wall and create artifacts. Also, there are obstructive saturation band artifacts at intersections of rapidly-acquired multiplanar images. The objective of this work was to modify the magnetization preparation and readout properties of the bSSFP sequence to: 1) improve methods that eliminate T1 and isolate T2 contrast, 2) suppress the signal from flowing blood, and 3) characterize and reduce the saturation banding artifacts.A new T-One insensitive Steady State Imaging (TOSSI)-bSSFP combined acquisition technique, Resolution Enhanced TOSSI (RE-TOSSI), has been developed by using a partial Fourier acquisition and eliminating the inversion pulses from TOSSI after the data around the center of k-space is acquired. Results show that TOSSI contrast is maintained, while spatial resolution degradation is reduced. Additional benefits include reduced RF power deposition and faster imaging time. Application to high-resolution, non-subtraction thermal ablation monitoring is demonstrated.An improved dark blood bSSFP pulse sequence (HEFEWEIZEN) has been developed by introducing spatial saturation in True-FISP. This method does not increase the repetition time (TR) or substantially alter stationary tissue contrast and allows for directional suppression of blood flow (e.g. arterial vs. venous). Comparison to diffusion-prepared SSFP in the common carotid artery demonstrated significantly improved vessel wall-lumen contrast-to-noise ratio efficiency (p = 0.02).Intersecting-plane saturation band artifacts were characterized in three common steady-state pulse sequences (FLASH, FISP, and bSSFP). Substantial temporal and pulse sequence dependencies were found. Reverse centric phase encoding is demonstrated to be a simple and effective way of minimizing this artifact.

This research is motivated by the need for more effective and efficient clinical application of minimally invasive thermal ablation of solid tumors. During the ablation procedure, it is important to determine the region of tissue in which the cells have been killed and to predict input changes needed to kill tumor cells with minimal damage to normal tissue. To achieve this goal, we proposed an approach that combines fast magnetic resonance image (MRI) with mathematical modeling and simulation to monitor and predict the dynamics of temperature distribution and lesion boundary. The interactive use of MRI monitoring and model prediction provides a foundation for a real-time, clinical technique. The development of this approach has been described in the following chapters. Chapter 1: Background is presented about solid cancerous tumors and methods of thermal therapy and image techniques for monitoring. Chapter 2: The combination of MRI and model simulation to monitor and predict thermal ablation dynamics is developed and validated by in vivo experiments using radio-frequency (RF) ablation in normal paraspinal muscle of rabbits. Simulations of tissue temperature distribution and cell damage dynamics are compared with data obtained from MR phase and magnitude images. Chapter 3: The validity of this approach is tested by its application to RF ablation in VX2 tumors implanted in paraspinal muscle of rabbits. Chapter 4: A model of thermal ablation with laser light as a heat source is developed. Model simulation of tissue temperature distribution dynamics is compared with MR images from in vivo experiments with laser ablation of brain tissue of rabbits. Chapter 5: The thermal model is extended to describe the effects of an internal cooled RF probe that may also allow saline leakage into tissue. Model simulations quantify the lesion-enlarging effect of this type of RF probe. Chapter 6: Cooling by a large blood vessel in tissue near the heat source is simulated to determine how it would effect thermal ablation of tissue. Chapter 7: A summary is presented of major achievements of this research, its limitations, and possible future work.