A new finite element model for reduced order electromagneticmodeling

This paper introduces a new formulation suitable for direct model order reduction of finite element approximations of electromagnetic systems using Krylov subspace methods. The proposed formulation utilizes a finite element model of Maxwell's curl equations to generate a state-space representation of the electromagnetic system most suitable for the implementation of model order reduction techniques based on Krylov subspaces. It is shown that, with a proper selection of the finite element interpolation functions for the fields, the proposed formulation is equivalent to the commonly used approximation of the vector wave equation with tangentially continuous vector finite elements. This equivalence is exploited to improve the computational efficiency of the model order reduction process     

A high-order coupled finite element/boundary element torso model

Describes a high-order (cubic Hermite) coupled finite element/boundary element procedure for solving electrocardiographic potential problems to be ultimately used for solving forward and inverse problems on an anatomically accurate human torso. Details of both numerical procedures and the coupling between them are described. Test results, illustrating the accuracy and efficiency of this combination for both two-dimensional (2-D) and three-dimensional (3-D) problems, are also given     

A collocation-Galerkin finite element model of cardiac actionpotential propagation

A new computational method was developed for modeling the effects of the geometric complexity, nonuniform muscle fiber orientation, and material inhomogeneity of the ventricular wall on cardiac impulse propagation. The method was used to solve a modification to the FitzHugh-Nagumo system of equations. The geometry, local muscle fiber orientation, and material parameters of the domain were defined using linear Lagrange or cubic Hermite finite element interpolation. Spatial variations of time-dependent excitation and recovery variables were approximated using cubic Hermite finite element interpolation, and the governing finite element equations were assembled using the collocation method. To overcome the deficiencies of conventional collocation methods on irregular domains, Galerkin equations for the no-flux boundary conditions were used instead of collocation equations for the boundary degrees-of-freedom. The resulting system was evolved using an adaptive Runge-Kutta method. Converged two-dimensional simulations of normal propagation showed that this method requires less CPU time than a traditional finite difference discretization. The model also reproduced several other physiologic phenomena known to be important in arrhythmogenesis including: Wenckebach periodicity, slowed propagation and unidirectional block due to wavefront curvature, reentry around a fixed obstacle, and spiral wave reentry. In a new result, the authors observed wavespeed variations and block due to nonuniform muscle fiber orientation. The findings suggest that the finite element method is suitable for studying normal and pathological cardiac activation and has significant advantages over existing techniques     

A modified finite element method for analysis of finite periodicstructures

A modified finite element method with new solving algorithm is proposed to analyze electromagnetic problems of finite periodic structures. Dielectric-loaded parallel-plate waveguides with rectangular and triangular dielectric gratings are tackled as an example of the present approach. Numerical results are checked by the self-convergence test and by comparing with those obtained by other methods. Finally, the dependence of the scattering parameters on the frequency, the period number, and the grating height is analyzed and compared     

Sequential finite element model of tissue electropermeabilization

Permeabilization, when observed on a tissue level, is a dynamic process resulting from changes in membrane permeability when exposing biological cells to external electric field (E). In this paper we present a sequential finite element model of E distribution in tissue which considers local changes in tissue conductivity due to permeabilization. These changes affect the pattern of the field distribution during the high voltage pulse application. The presented model consists of a sequence of static models (steps), which describe E distribution at discrete time intervals during tissue permeabilization and in this way present the dynamics of electropermeabilization. The tissue conductivity for each static model in a sequence is determined based on E distribution from the previous step by considering a sigmoid dependency between specific conductivity and E intensity. Such a dependency was determined by parameter estimation on a set of current measurements, obtained by in vivo experiments. Another set of measurements was used for model validation. All experiments were performed on rabbit liver tissue with inserted needle electrodes. Model validation was carried out in four different ways: 1) by comparing reversibly permeabilized tissue computed by the model and the reversibly permeabilized area of tissue as obtained in the experiments; 2) by comparing the area of irreversibly permeabilized tissue computed by the model and the area where tissue necrosis was observed in experiments; 3) through the comparison of total current at the end of pulse and computed current in the last step of sequential electropermeabilization model; 4) by comparing total current during the first pulse and current computed in consecutive steps of a modeling sequence. The presented permeabilization model presents the first approach of describing the course of permeabilization on tissue level. Despite some approximations (ohmic tissue behavior) the model can predict the permeabilized volume of tissue, when exposed to electrical treatment. Therefore, the most important contribution and novelty of the model is its potentiality to be used as a tool for determining parameters for effective tissue permeabilization.     

A finite element model for describing the effect of muscle shortening on surface EMG

A finite-element model for the generation of single fiber action potentials in a muscle undergoing various degrees of fiber shortening is developed. The muscle is assumed fusiform with muscle fibers following a curvilinear path described by a Gaussian function. Different degrees of fiber shortening are simulated by changing the parameters of the fiber path and maintaining the volume of the muscle constant. The conductivity tensor is adapted to the muscle fiber orientation. In each point of the volume conductor, the conductivity of the muscle tissue in the direction of the fiber is larger than that in the transversal direction. Thus, the conductivity tensor changes point-by-point with fiber shortening, adapting to the fiber paths. An analytical derivation of the conductivity tensor is provided. The volume conductor is then studied with a finite-element approach using the analytically derived conductivity tensor. Representative simulations of single fiber action potentials with the muscle at different degrees of shortening are presented. It is shown that the geometrical changes in the muscle, which imply changes in the conductivity tensor, determine important variations in action potential shape, thus affecting its amplitude and frequency content. The model provides a new tool for interpreting surface EMG signal features with changes in muscle geometry, as it happens during dynamic contractions.     

A procedure for validating the finite element model of a piezoresistive ceramic pressure sensor

In this paper, we describe our experimental approach to the electromechanical characterization of thick-film resistors, the estimation of the resistive material's properties, and the validation of the finite element (FE) model used for the numerical analysis of ceramic pressure sensors (CPS). In order to improve the accuracy of the numerical models and increase the reliability of the simulation results a special test device containing all the essential construction details of the CPS was designed. Both the deflection of the ceramic diaphragm of the device under test and the resistance changes were measured. The numerical and experimental analyses of the specially designed test device indirectly confirmed the correctness of the FE model, which could be convenient for further virtual prototyping analyses.     

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.     

Three-dimensional finite element analysis of current density andtemperature distributions during radio-frequency ablation

This study analyzed the influence of electrode geometry, tissue-electrode angle, and blood flow on current density and temperature distribution, lesion size, and power requirements during radio-frequency ablation. The authors used validated three-dimensional finite element models to perform these analyses. They found that the use of an electrically insulating layer over the junction between electrode and catheter body reduced the chances of charring and coagulation. The use of a thermistor at the tip of the ablation electrodes did not affect the current density distribution. For longer electrodes, the lateral current density decreased more slowly with distance from the electrode surface. The authors analyzed the effects of three tissue-electrode angles: 0, 45, and 90°. More power was needed to reach a maximal tissue temperature of 95°C after 120 s when the electrode-tissue angle was 45°. Consequently, the lesions were larger and deeper for a tissue-electrode angle of 45° than for 0 and 90°. The lesion depth, volume, and required power increased with blood flow rate regardless of the tissue-electrode angle. The significant changes in power with the tissue-electrode angle suggest that it is safer and more efficient to ablate using temperature-controlled RF generators. The maximal temperature was reached at locations within the tissue, a fraction of a millimeter away from the electrode surface. These locations did not always coincide with the local current density maxima. The locations of these hottest spots and the difference between their temperature and the temperature read by a sensor placed at the electrode tip changed with blood flow rate and tissue-electrode angle     

A transition model for finite element simulation of kinematics of central nervous system white matter

Mechanical damage to axons is a proximal cause of deficits following traumatic brain injury and spinal cord injury. Axons are injured predominantly by tensile strain, and identifying the strain experienced by axons is a critical step toward injury prevention. White matter demonstrates complex nonlinear mechanical behavior at the continuum level that evolves from even more complex, dynamic, and composite behavior between axons and the "glial matrix" at the microlevel. In situ, axons maintain an undulated state that depends on the location of the white matter and the stage of neurodevelopment. When exposed to tissue strain, axons do not demonstrate pure affine or non-affine behavior, but instead transition from non-affine-dominated kinematics at low stretch levels to affine kinematics at high stretch levels. This transitional and predominant kinematic behavior has been linked to the natural coupling of axons to each other via the glial matrix. In this paper, a transitional kinematic model is applied to a micromechanics finite element model to simulate the axonal behavior within a white matter tissue subjected to uniaxial tensile stretch. The effects of the transition parameters and the volume fraction of axons on axonal behavior is evaluated and compared to previous experimental data and numerical simulations.     

A three-dimensional finite element model of human transthoracicdefibrillation: paddle placement and size

A detailed 3-D finite element model of the conductive anatomy of the human thorax has been constructed to quantitatively assess the current density distribution produced in the heart and thorax during transthoracic defibrillation. The model is based on a series of cross-sectional CT scans and incorporates isotropic conductivities for eight tissues and an approximation of the anisotropic conductivity of skeletal muscle. Current density distributions were determined and compared for four paddle pairs and two paddle sizes. The authors' results show that the myocardial current density distributions resulting from a defibrillation shock were fairly uniform for the paddle pairs and sizes examined in this study. Specific details of the spatial distribution of the current density magnitudes in the heart were found to depend on paddle placement and size. When the minimum current necessary to defibrillate was delivered, the maximum myocardial current density produced with any of the paddle sizes and positions examined was less than four times the minimum current density necessary to render a myocyte in a fibrillating heart inexcitable, and less than 40% of the damage threshold. These results suggest that common clinically used defibrillation paddle positions have a safety margin as large as 2.5 for current and ~6 for energy     

A two-dimensional time-domain finite element formulation for periodic structures

A formulation is presented for a two-dimensional time-domain finite-element method (FEM-TD) that incorporates periodic boundaries. The specifics of the method are shown for scattering problems, but it should be straightforward to extend it to radiation problems. The method solves for a transformed field variable (instead of solving directly for the electric field) in order to easily enable periodic boundary conditions in the time domain. The accuracy and stability of the method is demonstrated by a series of examples where the new formulation is compared with reference solutions. Very accurate results are obtained when the excitation (frequency range) and the geometry are such that no higher order Floquet modes are present. The accuracy is degraded in the presence of higher order modes due to the rather simple absorbing boundary condition that is used with the present formulation. The method is found to be stable even for angles of incidence close to grazing.     

Two-dimensional finite element charge-sheet model of a short-channel MOS transistor

A two-dimensional charge-sheet model for short-channel MOS transistors has been developed. The unique feature of the model is that the effect of channel inversion layer charge is included as a nonlinear integral boundary condition on the two-dimensional electrostatic field in the transistor. The average inversion layer charge density and source-drain current are obtained directly from the model rather than from the electron density or electron quasi-Fermi level. The model retains all of the physical detail of more complex two-dimensional models such as sensitivity to source-drain profile shape, channel profile, and oxide field shape. This allows the model to represent the changes in drain current associated with short-channel effects while still allowing simple comparison with long-channel models. For long-channel transistors, the results of this model are identical to Brews' long-channel charge-sheet model. The accuracy of this model is verified by modeling a sequence of transistors with channel lengths between 4.6 and 1.1 μm. In short-channel transistors, effects previously attributed to high field mobility are explained by simple two-dimensional electrostatics.The simulations produced using this model have been compared to experimental measurements on an array of n-channel MOSFETs; the model is in good agreement for transistors with channel lengths as short as 1.1 μm. In this verification process, the model represented accurately the onset of subthreshold current, channel-length-induced threshold voltage offset, and drain-field-induced output conductance changes.From studies of numerical accuracy, we conclude that the charge-sheet model can easily simulate drain current with an accuracy which exceeds that required for most applications. To obtain 5% accuracy for drain current, a 146 element mesh is sufficient. Refinement of the 146 element mesh to a 455 element mesh gives a current which is accurate to 0.16%. Average computer time for a high current solution is 2.5 min on a DEC-20.The numerical solutions were obtained using general-purpose software for solving elliptic partial differential equations. We have been able to solve problems with exact solutions to test the correctness and accuracy of our codes. We also can easily change the physics included in our model and the geometry of the transistor. The finite element method used allows refinement of oblique triangles which is important in achieving computational efficiency. The program is portable and has been run on a DEC-20, a VAX $\text{11}\text{780}$, a Cyber 175 and a Univac 1108.     

A note on hybrid finite element method for solving scatteringproblems

The hybrid finite-element formulation (HFEM) originated by P. Silvester and M.S. Hsieh (1971) is modified in such a way that it results in a sparse or uniformly banded matrix, rather than a partly full and partly sparse nonuniform matrix. The modification is accomplished by changing the sequence of matrix substitutions and substantially improves the computational efficiency and enhances the capability of the method, which is demonstrated by numerical examples. A comparison with other numerical techniques is presented     

A Gibbsian model for finite scanned arrays

A finite-by-infinite array of thin half-wave dipoles with H-plane scan is used to show the existence of a Gibbs' phenomenon-type standing wave in scan impedance (normalized by the infinite array value) over the elements of the array. The period of this wave is 0.5λ at broadside for λ/2 array spacing and increases as the scan angle increases by a grating lobe-type expression. A simple empirical model based on Gibbs oscillations is fitted to the scan-impedance wave; the model predicts the 1/(1-sin&thetas;₀) period variation, and should be useful for systems trades and for preliminary design purposes     

A new catheter design using needle electrode for subendocardial RF ablation of ventricular muscles: finite element analysis and in vitro experiments

Radio-frequency (RF) cardiac ablation has been very successful for treating arrhythmias related with atrioventricular junction and accessory pathways with successful cure rates of more than 90%. Even though ventricular tachycardia (VT) is a more serious problem, it is known to be rather difficult to cure VT using RF ablation. In order to apply RF ablation to VT, we usually need to create a deeper and wider lesion. Conventional RF ablation electrodes often fail to produce such a lesion. We propose a catheter-electrode design including one or more needle electrodes with a diameter of 0.5-1.0 mm and length of 2.0-10 mm to create a lesion large enough to treat VT. One temperature sensor could be placed at the middle of the needle electrode for temperature-controlled RF ablation. From finite element analyses and in vitro experiments, we found that the depth of a lesion is 1-2 mm deeper than the insertion depth of the needle and the width increases as we increase the diameter of the needle and the time duration. We showed that a single needle electrode can produce a lesion with about 10-mm width and any required depth. If a wider lesion is required, more than one needle with suggested structures can be used. Or, repeated RF ablations around a certain area using one needle could produce a cluster of lesions. In some cases, a catheter with both conventional electrode and needle electrode at its tip may be beneficial to take advantage of both types of electrode.     

A dual mesh scheme for finite element based reconstruction algorithms

The finite element (FE) method has found several applications in emerging imaging modalities, especially microwave imaging which has been shown to be potentially useful in a number of areas including thermal estimation. In monitoring temperature distributions, the biological phenomena of temperature variations of tissue dielectric properties is exploited. By imaging these properties and their changes during such therapies as hyperthermia, temperature distributions can be deduced using difference imaging techniques. The authors focus on a microwave imaging problem where the hybrid element (HE) method is used in conjunction with a dual mesh scheme in an effort to image complex wavenumbers, k(2). The dual mesh scheme is introduced to improve the reconstructed images of tissue properties and is ideally suited for systems using FE methods as their computational base. Since the electric fields typically vary rapidly over a given body when irradiated by high-frequency electromagnetic sources, a dense mesh is needed for these fields to be accurately represented. Conversely, k(2) may be fairly constant over subregions of the body which would allow for a less dense sampling of this parameter in those regions. In the dual mesh system employed, the first mesh, which is uniformly dense, is used for calculating the electric fields over the body whereas the second mesh, which is nonuniform and less dense, is used for representing the k(2) distribution within the region of interest. The authors examine the 2-D TM polarization case for a pair of dielectric distributions on both a large and small problem to demonstrate the flexibility of the dual mesh method along with some of the difficulties associated with larger imaging problems. Results demonstrate the capabilities of the dual mesh concept in comparison to a single mesh approach for a variety of test cases, suggesting that the dual mesh method is critical for FE based image reconstruction where rapidly varying physical quantities are used to recover smoother property profiles, as can occur in microwave imaging of biological bodies.     

基于有限元模型的三维集成电路热分析

基于有限元理论,对三维集成电路(3D-IC)进行了建模和仿真,研究了不同模型的热分布和计算复杂度.通过Gmsh软件创建3D-IC模型并生成网格化文件.利用Matlab软件提取有限元参数,获到模型的刚度矩阵.用层次矩阵(Hierarchical matrix,H-matrix)表示刚度矩阵,得到了不同模型刚度矩阵的求逆所消耗的存储空间和运算时间.结果表明:随着模型刚度矩阵行列数目的增加,所需要的运算时间和存储空间呈现线性变化关系.     

A comparison of formulations for the vector finite element analysisof waveguides

The principal formulations that have been proposed for finding the modes of waveguides by the finite element method are reviewed and compared. In each case, it is shown how Maxwell's equations may be reduced to matrix form using the method of weighted residuals. The formulations are compared from several points of view: their ability to handle spurious modes, lossy materials, and reentrant corners; the number of field components; and the properties of the matrices. Three benchmark problems are described and used to compare the formulations: a rectangular waveguide partially loaded with lossless dielectric; an air-filled, double-ridged waveguide; and a shielded image guide with either lossless or lossy dielectric