A reduced order explicit dynamic finite element algorithm for surgical simulation

Reduced order modelling, in which a full system response is projected onto a subspace of lower dimensionality, has been used previously to accelerate finite element solution schemes by reducing the size of the involved linear systems. In the present work we take advantage of a secondary effect of such reduction for explicit analyses, namely that the stable integration time step is increased far beyond that of the full system. This phenomenon alleviates one of the principal drawbacks of explicit methods, compared with implicit schemes. We present an explicit finite element scheme in which time integration is performed in a reduced basis. Futhermore, we present a simple procedure for imposing inhomogeneous essential boundary conditions, thus overcoming one of the principal deficiencies of such approaches. The computational benefits of the procedure within a GPU-based execution framework are examined, and an assessment of the errors introduced is given. It is shown that speedups approaching an order of magnitude are feasible, without introduction of prohibitive errors, and without hardware modifications. The procedure may have applications in interactive simulation and medical image-guidance problems, in which both speed and accuracy are vital.     

A finite element model for radiofrequency ablation of themyocardium

A finite element model was developed to simulate the temperature distributions produced by radiofrequency catheter ablation. This model incorporated blood, myocardium and torso tissues. The Laplace equation was solved to determine the steady-state electric field. The heat generation in the tissues was then computed from the power density distribution and the bioheat equation was solved to determine the time-varying temperature distribution, taking into account the convective energy exchange at the blood-myocardium and torso-air interfaces. This model was used to predict the lesion depth and to evaluate the effects of electrode location, changes of the electrical and thermal conductivities, and the electrode radius on the thermally induced damage to the myocardium. Temperature distributions induced by radiofrequency ablation were found to be: i) not very sensitive to the reference electrode location, ii) more sensitive to electrical conductivity changes than to thermal conductivity changes, and iii) larger electrodes allow a current distribution at higher level of power with reducing the chance of impedance rise     

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 new method to generate a patient-specific finite element model of the human buttocks.

Finite element (FE) models are very efficient tools to study internal stresses in human structures that induce severe pressure sores. Unfortunately, methods currently used to generate FE models are not suitable for clinical application involving wheelchair users. A clinical-oriented method, based on calibrated-biplanar radiographs, was therefore developed to generate a subject-specific FE model of the buttocks in a non-weighted sitting position. The model was then used to analyze the stress distribution within the buttocks and compare two wheelchair seat cushions designs. Additional radiographs and pressure measurements in a weighted sitting position were acquired to validate the FE model experimentally. Results from the FE model were in good agreement with experimental data and related literature. An internal peak pressure of 45.3 kPa was observed while seated on a flat foam cushion, corresponding to an interface pressure of 23.6 kPa. Both pressures occurred underneath the ischial tuberosities. When compared to the flat foam cushion, the contoured foam cushion reduced internal and interface peak pressures by 18% and 33%, respectively. The method developed in this study has a great potential for clinical use. The FE model, by predicting realistic stress distributions, allows for the selection of a convenient wheelchair seat cushion.     

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 new finite element formulation for RF scattering by complexbodies of revolution

A formulation for and results of solving electromagnetic scattering from complex inhomogeneous axisymmetric bodies are presented. The approach presented uses the finite element method in the frequency domain. A node-based approach is used to solve for the three components of the electric or magnetic field. The finite element mesh is truncated using a three-dimensional vector absorbing boundary condition based on the Wilcox expansion theorem. A harmonic expansion of the near-field solution obtained from the finite element solution is used to compute the far fields and radar cross section     

A new global finite element analysis of planar balanced mixers

A new global fullwave analysis of complex planar balanced mixers is presented. The proposed technique is based on a 3D finite element method using edge elements. The simulated results for the study of two planar balanced mixers - one in the X-band and the other in the millimetric band - are compared to those obtained by measurements.     

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 new finite element approach to stress analysis in microfabrication technology

It is well known that the standard displacement-based finite element approach to viscoelastic stress analysis in microfabrication technology is susceptible to the volumetric locking and highly oscillatory pressure solutions. As an effective remedy for these problems, a new finite element approach based on separate weak statements for the displacement and pressure is proposed in this paper. Apart from the various existing techniques, the proposed approach is inherently free from the constraints imposed on the selection of discrete approximation spaces and permits a robust and stable discretisation based on piecewise linear Galerkin elements. The accuracy and stability of the proposed methodology has been tested in numerical experiments involving stress analysis problems from microfabrication deposition and native film growing processes.     

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.     

A nonlinear reduced order observer for permanent magnet synchronousmotors

This paper introduces a nonlinear reduced order observer for speed and rotor position estimation in permanent magnet synchronous motors (PMSMs). The observer is based on a model of the motor represented by stationary two-axes coordinates. The theoretical principles of the proposed observer are discussed. Sufficient conditions for convergence as well as convergence speed are established. The observer is designed and tested by simulation. The results show that the observer gives a good estimation of speed and rotor position. In addition, it has low sensitivity to torque disturbances and perturbations of the mechanical parameters     

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 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.     

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     

High spatial order finite element method to solve Maxwell's equations in time domain

This paper presents a finite element method with high spatial order for solving the Maxwell equations in the time domain. In the first part, we provide the mathematical background of the method. Then, we discuss the advantages of the new scheme compared to a classical finite-difference time-domain (FDTD) method. Several examples show the advantages of using the new method for different kinds of problems. Comparisons in terms of accuracy and CPU time between this method, the FDTD and the finite-volume time-domain methods are given as well.     

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 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.