Finite element analysis of hepatic radiofrequency ablation probes using temperature-dependent electrical conductivity

Optimizing electrode placement using finite-element models in radiofrequency ablation treatment planning

Conventional radiofrequency ablation (RFA) planning methods for identifying suitable electrode placements typically use geometric shapes to model ablation outcomes. A method is presented for searching electrode placements that couples finite-element models (FEMs) of RFA together with a novel optimization strategy. The method was designed to reduce the need for model solutions per local search step. The optimization strategy was tested against scenarios requiring single and multiple ablations. In particular, for a scenario requiring multiple ablations, a domain decomposition strategy was described to minimize the complexity of simultaneously searching multiple electrode placements. The effects of nearby vasculature on optimal electrode placement were also studied. Compared with geometric planning approaches, FEMs could potentially deliver electrode placement plans that provide more physically meaningful predictions of therapeutic outcomes.

Effects of variation in perfusion rates and of perfusion models in computational models of radio frequency tumor ablation

PURPOSE

Finite element method (FEM) models are commonly used to simulate radio frequency (RF) tumor ablation. Prior FEM models of RF ablation have either ignored the temperature dependent effect of microvascular perfusion, or implemented the effect using simplified algorithms to reduce computational complexity. In this FEM modeling study, the authors compared the effect of different microvascular perfusion algorithms on ablation zone dimensions with two commercial RF electrodes in hepatic tissue. They also examine the effect of tissue type and inter-patient variation of perfusion on ablation zone dimensions.

METHODS AND MATERIALS

The authors created FEM models of an internally cooled and multi-tined expandable electrode. RF voltage was applied to both electrodes (for 12 or 15 min, respectively) such that the maximum temperature in the model was 105 degrees C. Temperature dependent microvascular perfusion was implemented using three previously reported methodologies: cessation above 60 degrees C, a standard first-order Arrhenius model with decreasing perfusion with increasing degree of vascular stasis, and an Arrhenius model that included the effects of increasing perfusion at the ablation zone boundary due to hyperemia. To examine the effects of interpatient variation, simulations were performed with base line and +/-1 standard deviation values of perfusion. The base line perfusion was also varied to simulate the difference between normal and cirrhotic liver tissue.

RESULTS

The ablation zone volumes with the cessation above 60 degrees C perfusion algorithm and with the more complex Arrhenius model were up to 70% and 25% smaller, respectively, compared to the standard Arrhenius model. Ablation zone volumes were up to 175% and approximately 100% different between the simulations where -1 and +1 standard deviation values of perfusion were used in normal and cirrhotic liver tissue, respectively.

CONCLUSIONS

The choice of microvascular perfusion algorithm has significant effects on final ablation zone dimensions in FEM models of RF ablation. The authors also found that both interpatient variation in base line tissue perfusion and the reduction in perfusion due to cirrhosis have considerable effect on ablation zone dimensions.

Finite element modeling of cooled-tip probe radiofrequency ablation processes in liver tissue

Finite element model of radiofrequency ablation (RFA) with cooled-tip probe in liver has been developed by employing COMSOL Multiphysics software. It describes coupled electric, thermal and sodium chloride solution infiltration flow phenomena taking place during ablation processes. Features of hydraulic capacity, saturation of the tissue by infiltration, and dependency of electrical conductivity on the damage integral of the tissue have been supplied to the model. RFA experiments have validated the model. Physical parameters describing hydraulic capacity and hydraulic conductivity in the tissue, as well as, the relation of electrical conductivity against the value of damage integral have been determined.

Assessment of hyperbolic heat transfer equation in theoretical modeling for radiofrequency heating techniques

Theoretical modeling is a technique widely used to study the electrical-thermal performance of different surgical procedures based on tissue heating by use of radiofrequency (RF) currents. Most models employ a parabolic heat transfer equation (PHTE) based on Fourier's theory, which assumes an infinite propagation speed of thermal energy. We recently proposed a one-dimensional model in which the electrical-thermal coupled problem was analytically solved by using a hyperbolic heat transfer equation (HHTE), i.e. by considering a non zero thermal relaxation time. In this study, we particularized this solution to three typical examples of RF heating of biological tissues: heating of the cornea for refractive surgery, cardiac ablation for eliminating arrhythmias, and hepatic ablation for destroying tumors. A comparison was made of the PHTE and HHTE solutions. The differences between their temperature profiles were found to be higher for lower times and shorter distances from the electrode surface. Our results therefore suggest that HHTE should be considered for RF heating of the cornea (which requires very small electrodes and a heating time of 0.6 s), and for rapid ablations in cardiac tissue (less than 30 s).

Deep brain stimulation electrodes used for staged lesion within the basal ganglia: experimental studies for parameter validation

Object

Deep brain stimulation (DBS) has been shown to be an effective treatment for various types of movement disorders. High-frequency stimulation is applied to specific brain targets through an implanted quadripolar lead connected to a pulse generator. These leads can be used for creating lesions in the brain. The experimental study reported here was designed to examine the electrical parameters that could be used to create reproducible therapeutic lesions in the brain.

Methods

Egg whites were used to measure the relationship between the electrical parameters (current and voltage) applied through the DBS electrode and the size of coagulum. The authors measured current spread from the electrode contact used for lesioning to the adjacent contact. Similar studies were performed in the pallidum or the thalamus of human cadavers. Modeling of the lesion size was performed with simulation of current density and temperature. The ultrastructure of the electrodes after lesioning was verified by electron microscopy.

Results

Coagulation size increased with time but reached a plateau after 30 seconds. For a given set of electrical parameters, reproducibility of the size of lesions was high. Using constant voltage, lesions were larger in egg whites than in cadaveric brains with a mean length of 5 ± 0.6 mm in egg whites at 40 V, 125 mA, impedance 233 Ω; and 4.0 ± 0.8 mm in cadavers at 40 V, 38 mA, impedance 1333 Ω. Computer modeling indicated negligible current flow to the adjacent, unused electrodes. The electrodes showed no structural alterations on scanning electron microscopy after more than 200 lesions.

Conclusions

Results of this study demonstrate that DBS electrodes can be used to generate lesions reproducibly in the brain. The choice of lesioning parameters must take into account differences in impedance between the test medium (egg whites) and the human brain parenchyma.

Temperature and SAR measurement errors in the evaluation of metallic linear structures heating during MRI using fluoroptic probes

The purpose of this work is to evaluate the error associated with temperature and SAR measurements using fluoroptic temperature probes on pacemaker (PM) leads during magnetic resonance imaging (MRI). We performed temperature measurements on pacemaker leads, excited with a 25, 64, and 128 MHz current. The PM lead tip heating was measured with a fluoroptic thermometer (Luxtron, Model 3100, USA). Different contact configurations between the pigmented portion of the temperature probe and the PM lead tip were investigated to find the contact position minimizing the temperature and SAR underestimation. A computer model was used to estimate the error made by fluoroptic probes in temperature and SAR measurement. The transversal contact of the pigmented portion of the temperature probe and the PM lead tip minimizes the underestimation for temperature and SAR. This contact position also has the lowest temperature and SAR error. For other contact positions, the maximum temperature error can be as high as -45%, whereas the maximum SAR error can be as high as -54%. MRI heating evaluations with temperature probes should use a contact position minimizing the maximum error, need to be accompanied by a thorough uncertainty budget and the temperature and SAR errors should be specified.

Modeling the interaction of electric current and tissue: importance of accounting for time varying electric properties

Time varying computer models of the interaction of electric current and tissue are very valuable in helping to understand the complexity of the human body and biological tissue. The electrical properties of tissue, permittivity and conductivity, are vital to accurately modeling the interaction of the human tissue with electric current. Past models have represented the electric properties of the tissue as constant or temperature dependent. This paper presents time dependent electric properties that change as a result of tissue damage, temperature, blood flow, blood vessels, and tissue property. Six models are compared to emphasize the importance of accounting for these different tissue properties in the computer model. In particular, incorporating the time varying nature of the electric properties of human tissue into the model leads to a significant increase in tissue damage. An important feature of the model is the feedback loop created between the electric properties, tissue damage, and temperature.

Radio-Frequency Ablation in a Realistic Reconstructed Hepatic Tissue

This study uses a reconstructed vascular geometry to evaluate the thermal response of tissue during a three-dimensional radiofrequency (rf) tumor ablation. MRI images of a sectioned liver tissue containing arterial vessels are processed and converted into a finite-element mesh. A rf heat source in the form of a spherically symmetric Gaussian distribution, fit from a previously computed profile, is employed. Convective cooling within large blood vessels is treated using direct physical modeling of the heat and momentum transfer within the vessel. Calculations of temperature rise and thermal dose are performed for transient rf procedures in cases where the tumor is located at three different locations near the bifurcation point of a reconstructed artery. Results demonstrate a significant dependence of tissue temperature profile on the reconstructed vasculature and the tumor location. Heat convection through the arteries reduced the steady-state temperature rise, relative to the no-flow case, by up to 70% in the targeted volume. Blood flow also reduced the thermal dose value, which quantifies the extent of cell damage, from ∼3600min, for the no-flow condition, to 10min for basal flow (13.8cm∕s). Reduction of thermal dose below the threshold value of 240min indicates ablation procedures that may inadequately elevate the temperature in some regions, thereby permitting possible tumor recursion. These variations are caused by vasculature tortuosity that are patient specific and can be captured only by the reconstruction of the realistic geometry.

Bio-heat transfer model of deep brain stimulation-induced temperature changes

There is a growing interest in the use of chronic deep brain stimulation (DBS) for the treatment of medically refractory movement disorders and other neurological and psychiatric conditions. Fundamental questions remain about the physiologic effects of DBS. Previous basic research studies have focused on the direct polarization of neuronal membranes by electrical stimulation. The goal of this paper is to provide information on the thermal effects of DBS using finite element models to investigate the magnitude and spatial distribution of DBS-induced temperature changes. The parameters investigated include stimulation waveform, lead selection, brain tissue electrical and thermal conductivities, blood perfusion, metabolic heat generation during the stimulation and lead thermal conductivity/heat dissipation through the electrode. Our results show that clinical DBS protocols will increase the temperature of surrounding tissue by up to 0.8 degrees C depending on stimulation/tissue parameters.

Improved perfusion system for bipolar radiofrequency ablation of liver: preliminary findings from a computer modeling study

Current systems for radiofrequency ablation of liver tumors are unable to consistently treat tumors larger than 3 cm in diameter with a single electrode in a single application. One of the strategies for enlarging coagulation zone dimensions is to infuse saline solutions into the tissue through the active electrodes. Nevertheless, the uncontrolled and undirected diffusion of boiling saline into the tissue has been associated with irregular coagulation zones and severe complications, mainly due to reflux of saline along the electrode path. In order to improve the perfusion bipolar ablation method, we hypothesized that the creation of small monopolar coagulation zones adjacent to the bipolar electrodes and previous to the saline infusion would create preferential paths for the saline to concentrate on the targeted coagulation zone. Firstly, we conducted ex vivo experiments in order to characterize the monopolar coagulation zones. We observed that they are practically impermeable to the infused saline. On the basis of this finding, we built theoretical models and conducted computer simulations to assess the feasibility of our hypothesis. Temperature distributions during bipolar ablations with and without previous monopolar coagulation zones were obtained. The results showed that in the case of monopolar coagulation zones the temperature of the tissue took longer to reach 100 degrees C. Since this temperature value is related to rise of impedance, and the time necessary for this process is directly related to the volume of the coagulation zone, our results suggest that monopolar sealing would allow larger coagulation zones to be created. Future experimental studies should confirm this benefit.

Theoretical modeling for radiofrequency ablation: state-of-the-art and challenges for the future

Radiofrequency ablation is an interventional technique that in recent years has come to be employed in very different medical fields, such as the elimination of cardiac arrhythmias or the destruction of tumors in different locations. In order to investigate and develop new techniques, and also to improve those currently employed, theoretical models and computer simulations are a powerful tool since they provide vital information on the electrical and thermal behavior of ablation rapidly and at low cost. In the future they could even help to plan individual treatment for each patient. This review analyzes the state-of-the-art in theoretical modeling as applied to the study of radiofrequency ablation techniques. Firstly, it describes the most important issues involved in this methodology, including the experimental validation. Secondly, it points out the present limitations, especially those related to the lack of an accurate characterization of the biological tissues. After analyzing the current and future benefits of this technique it finally suggests future lines and trends in the research of this area.

Bio-heat transfer model of deep brain stimulation induced temperature changes

There is a growing interest in the use of chronic deep brain stimulation (DBS) for the treatment of medically refractory movement disorders and other neurological and psychiatric conditions. Fundamental questions remain about the physiologic effects and safety of DBS. Previous basic research studies have focused on the direct polarization of neuronal membranes by electrical stimulation. The goal of this paper is to provide information on the thermal effects of DBS using finite element models to investigate the magnitude and spatial distribution of DBS induced temperature changes. The parameters investigated include: stimulation waveform, lead selection, brain tissue electrical and thermal conductivity, blood perfusion, metabolic heat generation during the stimulation. Our results show that clinical deep brain stimulation protocols will increase the temperature of surrounding tissue by up to 0.8 deg C depending on stimulation/tissue parameters.

Automatic control of finite element models for temperature-controlled radiofrequency ablation

BACKGROUND

The finite element method (FEM) has been used to simulate cardiac and hepatic radiofrequency (RF) ablation. The FEM allows modeling of complex geometries that cannot be solved by analytical methods or finite difference models. In both hepatic and cardiac RF ablation a common control mode is temperature-controlled mode. Commercial FEM packages don't support automating temperature control. Most researchers manually control the applied power by trial and error to keep the tip temperature of the electrodes constant.

METHODS

We implemented a PI controller in a control program written in C++. The program checks the tip temperature after each step and controls the applied voltage to keep temperature constant. We created a closed loop system consisting of a FEM model and the software controlling the applied voltage. The control parameters for the controller were optimized using a closed loop system simulation.

RESULTS

We present results of a temperature controlled 3-D FEM model of a RITA model 30 electrode. The control software effectively controlled applied voltage in the FEM model to obtain, and keep electrodes at target temperature of 100 degrees C. The closed loop system simulation output closely correlated with the FEM model, and allowed us to optimize control parameters.

DISCUSSION

The closed loop control of the FEM model allowed us to implement temperature controlled RF ablation with minimal user input.

Influence of electrical and thermal properties on RF ablation of breast cancer: is the tumour preferentially heated?

Background

Techniques based on radio frequency (RF) energy have many applications in medicine, in particular tumour ablation. Today, mammography screening detects many breast cancers at an early stage, facilitating treatment by minimally invasive techniques such as radio frequency ablation (RFA). The breast cancer is mostly surrounded by fat, which during RFA-treatment could result in preferential heating of the tumour due to the substantial differences in electrical parameters. The object of this study was to investigate if this preferential heating existed during experimental in vitro protocols and during computer simulations.

Methods

Excised breast material from four patients with morphologically diagnosed breast cancers were treated with our newly developed RFA equipment. Subsequently, two finite element method (FEM) models were developed; one with only fat and one with fat and an incorporated breast cancer of varying size. The FEM models were solved using temperature dependent electrical conductivity versus constant conductivity, and transient versus steady-state analyses.

Results

Our experimental study performed on excised breast tissue showed a preferential heating of the tumour, even if associated with long tumour strands. The fat between these tumour strands was surprisingly unaffected. Furthermore, the computer simulations demonstrated that the difference in electrical and thermal parameters between fat and tumour tissue can cause preferential heating of the tumour. The specific absorption rate (SAR) distribution changed significantly when a tumour was present in fatty tissue. The degree of preferential heating depended on tissue properties, tumour shape, and placement relative to the electrode. Temperature dependent electrical conductivity increased the thermal lesion volume, but did not change the preferential heating. Transient solutions decreased the thermal lesion volume but increased the preferential heating of the tumour.

Conclusion

Both the computer model and the in vitro study confirmed that preferential heating of the tumour during RFA exists in breast tissue. However, the observed preferential heating in the in vitro studies were more pronounced, indicating that additional effects other than the difference in tissue parameters might be involved. The existing septa layers between the cancer tissue and the fatty tissue could have an additional electrical or thermal insulating effect, explaining the discrepancy between the in vitro study and the computer model.

A finite element method model to simulate laser interstitial thermo therapy in anatomical inhomogeneous regions

BACKGROUND

Laser Interstitial ThermoTherapy (LITT) is a well established surgical method. The use of LITT is so far limited to homogeneous tissues, e.g. the liver. One of the reasons is the limited capability of existing treatment planning models to calculate accurately the damage zone. The treatment planning in inhomogeneous tissues, especially of regions near main vessels, poses still a challenge. In order to extend the application of LITT to a wider range of anatomical regions new simulation methods are needed. The model described with this article enables efficient simulation for predicting damaged tissue as a basis for a future laser-surgical planning system. Previously we described the dependency of the model on geometry. With the presented paper including two video files we focus on the methodological, physical and mathematical background of the model.

METHODS

In contrast to previous simulation attempts, our model is based on finite element method (FEM). We propose the use of LITT, in sensitive areas such as the neck region to treat tumours in lymph node with dimensions of 0.5 cm - 2 cm in diameter near the carotid artery. Our model is based on calculations describing the light distribution using the diffusion approximation of the transport theory; the temperature rise using the bioheat equation, including the effect of microperfusion in tissue to determine the extent of thermal damage; and the dependency of thermal and optical properties on the temperature and the injury. Injury is estimated using a damage integral. To check our model we performed a first in vitro experiment on porcine muscle tissue.

RESULTS

We performed the derivation of the geometry from 3D ultrasound data and show for this proposed geometry the energy distribution, the heat elevation, and the damage zone. Further on, we perform a comparison with the in-vitro experiment. The calculation shows an error of 5% in the x-axis parallel to the blood vessel.

CONCLUSIONS

The FEM technique proposed can overcome limitations of other methods and enables an efficient simulation for predicting the damage zone induced using LITT. Our calculations show clearly that major vessels would not be damaged. The area/volume of the damaged zone calculated from both simulation and in-vitro experiment fits well and the deviation is small. One of the main reasons for the deviation is the lack of accurate values of the tissue optical properties. In further experiments this needs to be validated.

Thermal modeling of lesion growth with radiofrequency ablation devices

BACKGROUND

Temperature is a frequently used parameter to describe the predicted size of lesions computed by computational models. In many cases, however, temperature correlates poorly with lesion size. Although many studies have been conducted to characterize the relationship between time-temperature exposure of tissue heating to cell damage, to date these relationships have not been employed in a finite element model.

METHODS

We present an axisymmetric two-dimensional finite element model that calculates cell damage in tissues and compare lesion sizes using common tissue damage and iso-temperature contour definitions. The model accounts for both temperature-dependent changes in the electrical conductivity of tissue as well as tissue damage-dependent changes in local tissue perfusion. The data is validated using excised porcine liver tissues.

RESULTS

The data demonstrate the size of thermal lesions is grossly overestimated when calculated using traditional temperature isocontours of 42 degrees C and 47 degrees C. The computational model results predicted lesion dimensions that were within 5% of the experimental measurements.

CONCLUSION

When modeling radiofrequency ablation problems, temperature isotherms may not be representative of actual tissue damage patterns.

A new mathematical approach to the diffusion approximation theory for selective photothermolysis modeling and its implication in laser treatment of port-wine stains

BACKGROUND AND OBJECTIVES

Monte Carlo (MC) simulations of light-tissue interactions and analytical solutions for the diffusion approximation theory have been used to determine the optimal laser wavelength and radiant exposure to treat port-wine stains (PWS). Both approaches suggest that optimal parameters are a wavelength of 585 or 595-nm with pulse times of 0.45-20 milliseconds. However, which parameters are optimal is still unclear. As differences in vessel size and in temperature distribution within vessels appeared to be the main reasons for the varied responses to the same laser treatments, we sought to develop a solution to the diffusion approximation in order to calculate temperature distribution and the resulting coagulation pattern within specific blood vessels.

STUDY DESIGN/MATERIALS AND METHODS

The light and heat diffusion equations were simultaneously solved with the finite element method (FEM). The latent heat of evaporation was included in the thermal analysis. The temperature and coagulation patterns across specific blood vessels, within a heterogeneous medium, were calculated for laser wavelengths of 585 and 595-nm with clinical parameters.

RESULTS

At 1.2 mm deep, the calculations predicted that vessels ranging from 50 to 100 microm in diameter would be coagulated from top to bottom, small vessels (10 microm) would be spared, and vessels larger than 150 microm would be partially coagulated. Coagulation across vessels was more uniform for the 595-nm than for the 585-nm wavelength. Maximal temperatures did not exceed 100 degrees C because of the inclusion of latent heat in the thermal calculations.

CONCLUSIONS

To study laser treatments of PWS with the diffusion approximation, FEM is an effective method to calculate the coagulation patterns within specific blood vessels. To improve coagulation efficacy at 585 and 595-nm wavelengths, the radiant exposure should be increased without increasing the irradiance.