Finite element analysis of cardiac defibrillation currentdistributions

We have developed a two-dimensional finite element model of the canine heart and thorax to examine different aspects of the distribution of current through cardiac tissue during defibrillation. This model allows us to compare various electrode configurations for the implantable cardioverter/defibrillator. Since we do not yet know the electrical criteria to apply for predicting defibrillation thresholds, such as the minimum current density required for defibrillation or the critical mass if indeed such quantities are applicable, we measured defibrillation energy in dogs to determine the voltages to apply to the model for calculating current distributions. By analyzing isopotential contours, current lines, power distributions, current density histograms, and cumulative current distributions, we estimated the critical fraction and threshold current density for defibrillation, compared various electrode configurations, and assessed the sensitivity of the defibrillation threshold to electrode position, patch size, and tissue conductivity. We found that blood can shunt defibrillation current away from the myocardium, particularly in configurations using a two-electrode catheter, that myocardial tissue conductivity strongly affects the current distributions, and that epicardial patch size is more important that subcutaneous patch size. Our results are consistent with successful defibrillation requiring that 80 +/- 5% of the heart must be rendered inexcitable by a current density of 35 +/- 5 mA/cm2 or greater. This two-dimensional, isotropic model has allowed us to analyze some of the determinants of defibrillation, but more detailed interpretation of experimental data may require the extension of the model to three dimensions.     

切向气流下激光对旋转靶热烧蚀的数值模拟

针对连续激光辐照表面存在切向气流的旋转靶目标,数值求解温度场分布以及热烧蚀效应。首先,综合切向气流、固液相变和目标旋转的影响,给出柱坐标下三维瞬态热传导方程,建立激光对旋转靶目标的热烧蚀模型。其次,分析热烧蚀过程中,物质在固态、固液态和液态之间的转化关系,提出一种改进的“单元生死法”处理旋转烧蚀过程中的边界移动问题,并采用有限容积法数值求解热烧蚀模型。最后,数值模拟温度场分布和热烧蚀效应,分析靶目标旋转速率对温度场分布和热烧蚀效应的影响。分析结果表明:靶目标的旋转,导致最大烧蚀深度不断减小,圆柱面的烧蚀区域逐渐增加,并对温度场分布产生一定影响。     

Numerical model for radio-frequency ablation of the endocardium andits experimental validation

A theoretical model for the study of the radiofrequency (RF) ablation technique is presented. The model relies on a finite-element time-domain calculation of the temperature distribution in a block of tissue, resulting from the flow of RF (<1 MHz) electrical current. A thermal damage function is used to calculate the extent of the lesion on the basis of the temperature elevation and the duration of exposure. This work extends the model proposed by D.E. Haines and D.D. Watson (PACE, vol.12, p.962-76, 1989) by including a more realistic and variable geometry, the cooling effect of the blood flow and a transient analysis. Furthermore, the nonlinearity caused by the temperature dependence of the tissue properties is also considered. The complexity of the model being appreciable, an experiment demonstrating its validity is also described. While remaining workable, the experiment is sophisticated enough to lead to convincing conclusions. It consists in measuring the temperature distribution and the time-dependent electrode resistance during “ablation” of a tissue-equivalent material. Various electrode configurations and electrical excitations are investigated. In all cases, the experimental results agree reasonably well with the numerical calculations. This confirms that the model is accurate for the investigation of RF ablation     

Thermal-electrical modeling for epicardial atrial radiofrequency ablation

Epicardial radiofrequency ablation is increasingly being used for intraoperative treatment of atrial fibrillation. However, the effect of different parameters on the lesion characteristics has not been sufficiently characterized. We used a finite element model to calculate the temperature distribution in the atrial tissue under different conditions during a constant voltage radiofrequency ablation. Our simulation results show that although in the case of a thin atrium the lesion was less deep for a thin atrium, it was easier to achieve transmurality. While considering a thinner atrium, the location of the hottest point of the lesion shifted from the electrode tip to epicardial surface. This effect was due to the convective cooling of the circulating blood inside the atrium. This convective cooling phenomenon has almost negligible effects for atria thicker than 3 mm. The variability of the cooling values has no significant effect on the lesion, even for thin atria (1-2 mm). Increasing the electrode insertion depth (ID) in the tissue produced larger lesions. However, for thinner atria (thickness <2 mm), this increase in the ID reduced the lesion width. It was also proved that the presence of a fat layer between the electrode and the atrial tissue decreased significantly the lesion dimensions.     

Noncontact radio-frequency ablation for obtaining deeper lesions

Radio-frequency (RF) cardiac catheter ablation has been very successful for treating some cardiac arrhythmias, however, the success rate for ventricular tachycardias is still not satisfactory. Some existing methods for developing deeper lesions include active cooling of the electrode and modifying the electrode shape. We propose a method of noncontact ablation, to solve this problem. We apply 120 W of power through an 8-mm electrode for a 120-s duration, with distances from 0 to 3 mm between electrode and myocardium, to create lesions in myocardium. We apply flow rates of 1, 3, and 5 L/min to determine their effect. Results show that with an optimal distance from 0.5 to 1.5 mm between electrode and myocardium, we increase lesion depth from 7.5 mm for contact ablation to 9.5 mm for noncontact ablation. For different flow rates, the optimal distance various. The effect of flow rate is not obvious. Higher flow rate does not lead to a deeper lesion.     

Modeling bipolar phase-shifted multielectrode catheter ablation

Atrial fibrillation (AFIB) is a common clinical problem affecting approximately 0.5-1% of the United States population. Radio-frequency (RF) multielectrode catheter (MEC) ablation has successes in curing AFIB. We utilized finite-element method analysis to determine the myocardial temperature distribution after 30 s, 80 degrees C temperature-controlled unipolar ablation using three 7F 12.5-mm electrodes with 2-mm interelectrode spacing MEC. Numerical results demonstrated that cold spots occurred at the edges of the middle electrode and hot spots at the side electrodes. We introduced the bipolar phase-shifted technique for RF energy delivery of MEC ablation. We determined the optimal phase-shift (phi) between the two sinusoidal voltage sources of a simplified two-dimensional finite-element model. At the optimal phi, we can achieve a temperature distribution that minimizes the difference between temperatures at electrode edges. We also studied the effects of myocardial electric conductivity (sigma), thermal conductivity (k), and the electrode spacing on the optimal phi. When we varied sigma and kappa from 50% to 150%, optimal phi ranged from 29.5 degrees to 23.5 degrees, and in the vicinity of 26.5 degrees, respectively. The optimal phi for 3-mm spacing MEC was 30.5 degrees. We show the design of a simplified bipolar phase-shifted MEC ablation system.     

Dynamic thermoelectric model of a light-emitting structure with a current spreading layer

The non-stationary thermoelectric model of the axisymmetric heterostructure of a light-emitting device is considered taking into account positive feedback mechanisms and the effect of the current-spreading-layer resistance. Taking into account the current localization effect, the nonuniform distribution of the heterojunction current density over the heterostructure area is determined. The non-stationary thermal conductivity equation with temperature-dependent current density flowing into the heterojunction is solved by the numerical–analytical iterative method. Based on the developed model, the current density, temperature, and thermomechanical stress distributions for the heterojunction plane are determined.     

Thermalelectro-feedback model for multi-emitter finger power heterojunction bipolar transistor. Part I: Temperature profile

Poor thermal conductivity of GaAs, a self-heating phenomenon which results in the rapid rise of device temperature, is the major factor that limits and even degrades the electrical performance of GaAs-based heterojunction bipolar transistor (HBT) operated at high power densities. On the basis of this consideration, a numerical model is presented to study the interaction mechanism between the thermal and electrical behavior of AlGaAs/GaAs HBT with multiple-emitter fingers. The model mainly comprises a numerical model applicable for multi-finger HBT that solves the three-dimensional heat transfer equation. The device design parameters that influence the temperature profile and current distribution of the device are identified, and optimization concerning the device performance is made.     

Nonlinear thermal model of a heterojunction-based light-emitting diode

A mathematical nonlinear thermal model of a heterojunction-based light-emitting diode (LED) is considered; the model makes it possible to estimate the nonuniformity of the current and temperature distributions in the active region of the heterostructure with the LED efficiency and the temperature dependence of the thermal-conductivity coefficient in the structure taken into account. A numerical-analytical iteration method is used to solve a set of equations that includes solving a nonlinear time-independent equation of thermal conductivity with the density of electrical power converted to heat dependent on the LED efficiency and an equation of electrothermal feedback, under conditions of a constant value for the average current density over the active region of the structure. The results of theoretical and experimental studies into the dependence of the p-n junction-to-case thermal resistance on the forward current are represented for high-power light-emitting diodes.     

Determination of the temperature distribution of Hall plates by a relaxation method

A numerical method is presented for the solution of the temperature distribution of Hall plates. Here the treatment is done in two-dimensional space, on the assumption that the conductivity and Hall coefficient of a Hall plate are invariable with temperature. Numerical examples of the following cases are solved concurrently with the derivation of the algorithm: (1) different Hall angles, (2) different sizes and different thermal conductivities of the control electrode, (3) different thermal conductivities of the semiconductor material, (4) with or without a Peltier effect, and (5) with or without finite Hall electrodes. The results show (1) that the temperature distributions, being affected by the thermal conduction of the control electrode, are almost dissimilar with the electric field distributions, and (2) that, when finite Hall electrodes are attached, the analogies become lost.     

Estimation of temperature distribution inside tissues heated byinterstitial RF electrode hyperthermia systems

The computational method presented relies on a semi-infinite tissue model. The needle-shaped RF electrodes are modeled with elongated spheroids. The heat transfer problem is treated in three dimensions. The localized current fields set up inside the tissue from the discrete implants are computed by using electrostatic methods, and the bioheat diffusion equation under a steady-state condition is solved to determine the temperature distributions inside superficial tissues. A Green's-function technique is applied to solve the bioheat transfer equation. The heat removal due to blood circulation is also taken into account. Analytical techniques are used to treat the singularities in the vicinity of implanted electrodes. Numerical results are presented for several electrode configurations     

Radio-frequency heating of the cornea: theoretical model and in vitro experiments

We present a theoretical model for the study of cornea heating with radio-frequency currents. This technique is used to reshape the cornea to correct refractive disorders. Our numerical model has allowed the study of the temperature distributions in the cornea and to estimate the dimensions of the lesion. The model incorporates a fragment of cornea, aqueous humor, and the active electrode placed on the cornea surface. The finite element method has been used to calculate the temperature distribution in the cornea by solving a coupled electric-thermal problem. We analyzed by means of computer simulations the effect of: a) temperature influence on the tissue electrical conductivity; b) the dispersion of the biological characteristics; c) the anisotropy of the cornea thermal conductivity; d) the presence of the tear film; and e) the insertion depth of the active electrode in the cornea, and the results suggest that these effects have a significant influence on the temperature distributions and thereby on the lesion dimensions. However, the cooling of the aqueous humor in the endothelium or the realistic value of the cornea curvature did not have a significant effect on the temperature distributions. An experimental model based on the lesions created in rabbit eyes has been used in order to compare the theoretical and experimental results. There is a tendency toward the agreement between experimental and theoretical results, although we have observed that the theoretical model overestimates the lesion dimension.     

Micromachined Hot-Wire Thermal Conductivity Probe for Biomedical Applications

This paper presents the design, fabrication, numerical simulation, and experimental validation of a micromachined probe that measures thermal conductivity of biological tissues. The probe consists of a pair of resistive line heating elements and resistance temperature detector sensors, which were fabricated by using planar photolithography on a glass substrate. The numerical analysis revealed that the thermal conductivity and diffusivity can be determined by the temperature response induced by the uniform heat flux in the heating elements. After calibrating the probe using a material (agar gel) of known thermal conductivity, the probe was deployed to calculate the thermal conductivity of Crisco. The measured value is in agreement with that determined by the macro-hot-wire probe method to within 3%. Finally, the micro thermal probe was used to investigate the change of thermal conductivity of pig liver before and after RF ablation treatment. The results show an increase in thermal conductivity of liver after the RF ablation.     

Temperature-controlled and constant-power radio-frequency ablation: what affects lesion growth?

Radio-frequency (RF) catheter ablation is the primary interventional therapy for the treatment of many cardiac tachyarrhythmias. Three-dimensional finite element analysis of constant-power (CPRFA) and temperature-controlled RF ablation (TCRFA) of the endocardium is performed. The objectives are to study: 1) the lesion growth with time and 2) the effect of ground electrode location on lesion dimensions and ablation efficiency. The results indicate that: a) for TCRFA: i) lesion growth was fastest during the first 20 s, subsequently the lesion growth slowed reaching a steady state after 100 s, ii) positioning the ground electrode directly opposite the catheter tip (optimal) produced a larger lesion, and iii) a constant tip temperature maintained a constant maximum tissue temperature; b) for CPRFA: i) the lesion growth was fastest during the first 20 s and then the lesion growth slowed; however, the lesion size did not reach steady state even after 600 s suggesting that longer durations of energy delivery may result in wider and deeper lesions, ii) the temperature-dependent electrical conductivity of the tissue is responsible for this continuous lesion growth, and iii) an optimal ground electrode location resulted in a slightly larger lesion and higher ablation efficiency.     

Three-dimensional computer model of electric fields in internaldefibrillation

The automatic internal defibrillator delivers a low-energy shock directly to the heart. Optimal strategies for these shock deliveries are determined by studying a three-dimensional computer model of the electric fields produced by initial defibillation electrodes. A finite-element analysis technique is used to calculate energy and current density distributions in three commonly used electrode configurations: (1) patch-patch (PP), (2) catheter-patch (CP), and (3) catheter-catheter (CC). analysis of these simulations indicates that : (1) the PP and CP configurations are more effective at channeling energy to the myocardium than the CC configuration; (2) small electrodes and the edges of the electrodes give rise to high local current densities which might cause damage to the myocardium: (3) energy delivered to the myocardium is not significantly altered for different electrode placements tested; (4) electrode size influences current density distribution, especially near the electrodes; and (5) energy distribution is sensitive to the relative conductances of the myocardial tissue and blood     

Finite element analyses of uniform current density electrodes for radio-frequency cardiac ablation

The high current density at the edge of a metal electrode causes hot spots, which can lead to charring or blood coagulation formation during radio-frequency (RF) cardiac ablation. We used finite element analysis to predict the current density distribution created by several electrode designs for RF ablation. The numerical results demonstrated that there were hot spots at the edge of the conventional tip electrode and the insulating catheter. By modifying the shape of the edge of the 5-mm tip electrode, we could significantly reduce the high current density at the electrode-insulator interface. We also studied the current density distribution produced by a cylindrically shaped electrode. We modified the shape of a cylindrical electrode by recessing the edge and filled in a coating material so that the overall structure was still cylindrical. We analyzed the effects of depth of recess and the electrical conductivity of the added material. The results show that more uniform current density can be accomplished by recessing the electrode, adding a curvature to the electrode, and by coating the electrode with a resistive material.     

A High-Precision,Low-Voltage Pulsed Field Ablation Device with Capability of Minimally Invasive Surgery

Pulsed field ablation is a novel approach to treating 33.5 million patients with atrial fibrillation and offers a tissue-specific advantage over conventional radiofrequency ablation and cryoablation. However, for complex structural targets in the heart, current electrodes often damage non-target areas due to inaccurate ablation and have to employ electrical pulses with amplitudes of several kilovolts. Herein, materials and designs of a catheter-integrated microelectrode and sensors that can be used for high-precision and low-voltage pulsed field ablation through minimally invasive operation on a large animal model, is reported. The device with a new electrode configuration supports point-by-point ablation with a width of 3.8 mm (≈1/10 that of a typical ablation electrode) for individual lesions at the voltage of 300 V (an order of magnitude reduction compared to the current state-of-the-art). More impressively, the integrated catheter allows for pulsed field ablation on the large animal heart through minimally invasive surgery and blocks the electrical conduction pathway on the heart, which is the key to treating atrial fibrillation. This catheter-integrated device will enhance the efficiency and safety of pulsed field ablation, especially for complex cardiac structures, thus facilitating its move to the clinic.     

Weighted least-squares criteria for electrical impedance tomography

Methods are developed for the design of electrical impedance tomographic reconstruction algorithms with specified properties. Assuming a starting model with constant conductivity or some other specified background distribution, an algorithm with the following properties is found. (1) The optimum constant for the starting model is determined automatically. (2) The weighted least-squares error between the predicted and measured power dissipation data is as small as possible. (3) The variance of the reconstructed conductivity from the starting model is minimized. (4) Potential distributions with the largest volume integral of gradient squared have the least influence on the reconstructed conductivity, and therefore distributions most likely to be corrupted by contact impedance effects are deemphasized. (5) Cells that dissipate the most power during the current injection tests tend to deviate least from the background value. For a starting model with nonconstant conductivity, the reconstruction algorithm has analogous properties.     

Thermal modeling of a wafer in a rapid thermal processor

A model, using geometric optics, has been developed to calculate the illumination of a wafer inside a rapid thermal processor. The main parameters of the model are: the processing chamber geometry, the lamp number and location, the reflector characteristics, and the wafer temperature. Each incident light component, i.e., direct or reflected, is identified, its contribution to the illumination of the wafer is calculated through a 3D analytical model, and the corresponding contour maps are depicted. Then, the heat diffusion equation is numerically solved in two dimensions, and thermal maps of a Si wafer are given versus various experimental conditions, such as the effect of patterning the reflectors, of individually adjusting the electrical power applied to each lamp, and the impact of rotating the wafer or using crossed lamp banks. The latter method, while being easy to implement, is shown to give excellent thermal uniformity     

Transcranial direct current stimulation: estimation of the electric field and of the current density in an anatomical human head model

This paper investigates the spatial distribution of the electric field and of the current density in the brain tissues induced by transcranial direct current stimulation of the primary motor cortex. A numerical method was applied on a realistic human head model to calculate these field distributions in different brain structures, such as the cortex, the white matter, the cerebellum, the hippocampus, the medulla oblongata, the pons, the midbrain, and the thalamus. The influence of varying the anode area, the cathode area, and the injected current was also investigated. An electrode area as the one typically used in clinical practice (i.e., both electrodes equal to 35 cm(2)) resulted into complex and diffuse amplitude distributions over all the examined brain structures, with the region of maximum induced field being below or close to the anode. Variations in either the anode or cathode area corresponded to changes in the field amplitude distribution in all the brain tissues, with the former variation producing more diffuse effects. Variations in the injected current resulted, as could be expected, in linearly correlated changes in the field amplitudes.