Anisotropic adaptive finite element method for modelling blood flow

In this study, we present an adaptive anisotropic finite element method (FEM) and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the SUPG formulation for the transient 3D incompressible Navier-Stokes equations which are discretised by linear finite elements for both the pressure and the velocity field. Given the pulsatile nature of the flow in blood vessels we have pursued adaptivity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical vessel and then to a porcine aorta with a stenosis bypassed by a graft. We demonstrate that the use of an anisotropic adaptive FEM can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with uniform meshes.     

Anisotropic adaptive finite element method for modelling blood flow

In this study, we present an adaptive anisotropic finite element method (FEM) and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the SUPG formulation for the transient 3D incompressible Navier–Stokes equations which are discretised by linear finite elements for both the pressure and the velocity field.

Given the pulsatile nature of the flow in blood vessels we have pursued adaptivity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical vessel and then to a porcine aorta with a stenosis bypassed by a graft. We demonstrate that the use of an anisotropic adaptive FEM can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with uniform meshes.     

Simulation of 3D tumor cell growth using nonlinear finite element method

We propose a novel parallel computing framework for a nonlinear finite element method (FEM)-based cell model and apply it to simulate avascular tumor growth. We derive computation formulas to simplify the simulation and design the basic algorithms. With the increment of the proliferation generations of tumor cells, the FEM elements may become larger and more distorted. Then, we describe a remesh and refinement processing of the distorted or over large finite elements and the parallel implementation based on Message Passing Interface to improve the accuracy and efficiency of the simulation. We demonstrate the feasibility and effectiveness of the FEM model and the parallelization methods in simulations of early tumor growth.     

Numerical analysis of an anastomotic device

The explicit dynamic finite element method was utilized to investigate the deformation behaviour of a woven wire mesh tubular device that is used in a side-to-side anastomotic procedure for achieving gastrointestinal anastomosis. The numerical model was initially verified by comparison to experimental results that were obtained using a specialized testing mechanism. Once validated, the finite element model (FEM) was parameterized to ascertain the influence of several device parameters on its deformation behaviour. The importance of these parameters, as related to its optimal design for use in minimally invasive surgery (MIS), was subsequently ascertained and discussed.     

Numerical Analysis of An Anastomotic Device

The explicit dynamic finite element method was utilized to investigate the deformation behaviour of a woven wire mesh tubular device that is used in a side-to-side anastomotic procedure for achieving gastrointestinal anastomosis. The numerical model was initially verified by comparison to experimental results that were obtained using a specialized testing mechanism. Once validated, the finite element model (FEM) was parameterized to ascertain the influence of several device parameters on its deformation behaviour. The importance of these parameters, as related to its optimal design for use in minimally invasive surgery (MIS), was subsequently ascertained and discussed.     

Singularity-free finite element model of bone through automated voxel-based reconstruction

Computed tomography (CT) provides both anatomical and density information about tissues. Bone is segmented by raw images and Finite Element Method (FEM) voxel-based meshing technique is achieved by matching each CT voxel to a single finite element (FE). As a consequence of the automated model reconstruction, unstable elements – i.e. elements insufficiently anchored to the whole model and thus potentially involved in partial rigid body motion – can be generated, a crucial problem in obtaining consistent FE models, hindering mechanical analyses. Through the classification of instabilities on topological connections between elements, a numerical procedure is proposed in order to avoid unconstrained models.     

FEM simulation of tapered cap floating sleeve antenna for hepatocellular carcinoma therapy

ABSTRACT

Malignant liver tumors are the sixth most common and deadly cancer in the world and the third most common cause of cancer mortality. Hepatocellular carcinoma (primary liver cancer) is one of the most common malignancies worldwide with one of the highest mortality rates. Microwave ablation (MWA) is a new, promising, and multidisciplinary technology designed to destroy unhealthy tissue of various natures by radiating electromagnetic waves with microwave antennas. The finite element method (FEM) has been used in the present work to generate the simulated models of tapered cap floating sleeve antenna for validation of its design concepts, because FEM allows modeling of complex geometries that cannot be solved by analytical methods or finite difference models. The performances have been evaluated in terms of objective metrics, ablation zone, antenna matching, power absorption and SAR pattern.     

Multispectral Plasmon-Induced Transparency Based on Asymmetric Metallic Nanoslices Array Metasurface

We propose a 3D metasurface structure with unsymmetrical metallic slices array. The tunable plasmon-induced transparency (PIT) effects and different electric field mode distributions could be realized by modulating the structure parameters and angle of incidence. The radiative and dark elements of the asymmetric metallic slices unit cell structure are analyzed. The transmission spectra and the electric fields distributions are studied by the finite element method (FEM). We demonstrate that PIT phenomena based on those metasurface array structures may have applications as tunable sensors and filters in nanophotonics and integrated optics.     

Calculation of protein form birefringence using the finite element method.

An approach based on the finite element method (FEM) is employed to calculate the optical properties of macromolecules, specifically form birefringence. Macromolecules are treated as arbitrarily shaped particles suspended in a solvent of refraction index n1. The form birefringence of the solution is calculated as the difference in its refractive index when all the particles of refractive index n2 are either parallel to or normal to the direction of the polarization of light. Since the particles of interest are small compared to the wavelength of light, a quasi-static approximation for the refractive index is used, i.e., that it is equal to the square root of the dielectric constant of the suspension. The average dielectric constant of the mixture is calculated using the finite element method. This approach has been tested for ellipsoidal particles and a good agreement with theoretical results has been obtained. Also, numerical results for the motor domains of ncd and kinesin, small arbitrarily shaped proteins with known x-ray structures, show reasonable agreement with the experimental data obtained from transient electric birefringence experiments.     

Constitutive model of brain tissue suitable for finite element analysis of surgical procedures.

Realistic finite element modelling and simulation of neurosurgical procedures present a formidable challenge. Appropriate, finite deformation, constitutive model of brain tissue is a prerequisite for such development. In this paper, a large deformation, linear, viscoelastic model, suitable for direct use with commercially available finite element software packages such as ABAQUS is constructed. The proposed constitutive equation is of polynomial form with time-dependent coefficients. The model requires four material constants to be identified. The material constants were evaluated based on unconfined compression experiment results. The analytical as well as numerical solutions to the unconfined compression problem are presented. The agreement between the proposed theoretical model and the experiment is good for compression levels reaching 30% and for loading velocities varying over five orders of magnitude. The numerical solution using the finite element method matched the analytical solution very closely.     

A modular software concept for individual numerical simulation (FEM) of the human mandible]

A new modular software concept for individual numerical simulation of the human mandible using the finite element method (FEM) is presented. The main task is an individual analysis of regional stress and stress-compatibility on the basis of computed tomographic data in individual patients. Simulation should, however, also be possible in parallel with biomechanical experiments, or for further research projects. For this purpose, rapid and uncomplicated generation of the FEM model, easy modification of input data, and short computation times are required. Practical use in the clinical setting makes appreciable additional demands on the individual software components.     

Finite element modeling of the breakage behavior of agricultural biomass pellets under different heights during handling and storage

It is very important to determine the amount of mechanical damage to biomass pellets during handling, transportation, and storage. However, it is difficult to determine the amount of damage to biomass pellets caused by existing external forces. However, a useful method is the finite element methods, which can be used in different engineering fields to simulate the posture of the material under defined boundary conditions. In this research, a drop test simulation of biomass pellet samples was performed by using the finite element method. An experimental study (compressive test) was carried out to measure some mechanical properties of the sample and use the obtained data in the finite element method simulation. The stress–strain curve of different biomass pellets was determined. Yield strength, Poisson’s ratio, ultimate strength and modulus of elasticity, and stress were identified. In the end, the maximum equivalent stress, highest contact force (generated normal force from target surface at impact), and shape of deformation of samples at impact were obtained from simulation results. The drop scenario was created with 25 steps after the impact site, and the FEM simulation was solved. The maximum stress value was 9.486 MPa, and the maximum generated force was 485.31 N. at step 8 of the FEM simulation. When the stress magnitudes were assessed, simulation outputs indicated that simulation stress values are inconsistent with experimental data.     

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.     

Numerical simulation of fibrous biomaterials with randomly distributed fiber network structure

This paper presents a computational framework to simulate the mechanical behavior of fibrous biomaterials with randomly distributed fiber networks. A random walk algorithm is implemented to generate the synthetic fiber network in 2D used in simulations. The embedded fiber approach is then adopted to model the fibers as embedded truss elements in the ground matrix, which is essentially equivalent to the affine fiber kinematics. The fiber–matrix interaction is partially considered in the sense that the two material components deform together, but no relative movement is considered. A variational approach is carried out to derive the element residual and stiffness matrices for finite element method (FEM), in which material and geometric nonlinearities are both included. Using a data structure proposed to record the network geometric information, the fiber network is directly incorporated into the FEM simulation without significantly increasing the computational cost. A mesh sensitivity analysis is conducted to show the influence of mesh size on various simulation results. The proposed method can be easily combined with Monte Carlo (MC) simulations to include the influence of the stochastic nature of the network and capture the material behavior in an average sense. The computational framework proposed in this work goes midway between homogenizing the fiber network into the surrounding matrix and accounting for the fully coupled fiber–matrix interaction at the segment length scale, and can be used to study the connection between the microscopic structure and the macro-mechanical behavior of fibrous biomaterials with a reasonable computational cost.     

On prediction of the strength levels and failure patterns of human vertebrae using quantitative computed tomography (QCT)-based finite element method

This paper presents an effective patient-specific approach for prediction of failure initiation and growth in human vertebra using the general framework of the quantitative computed tomography (QCT)-based finite element method (FEM). The studies were carried out on 13 vertebrae (lumbar and thoracic), excised from 3 cadavers with the average age of 42 years old. Initially, 4 samples were QCT scanned and the images were directly converted into voxel-based 3D finite element models for linear and nonlinear analyses. The equivalent plastic strains obtained from the nonlinear analyses were used to predict the occurrence of local failures and development of the failure patterns. In the linear analyses, the strain energy density measure was used to identify the critical elements and predict the failure patterns. Subsequently, the samples were destructively tested in uniaxial compression and the experimental load–displacement diagrams were obtained. The plain radiographic images of the tested samples were also examined for observation of the failure patterns. In continuation, the presence of osteolytic defects in vertebrae was simulated by creation of artificial cavities within 9 remaining samples using a computer numerical control (CNC) milling machine. The same protocol was followed for scanning, modeling, and destructive testing of these samples. A strong correlation was found between the predicted and measured strengths. Finally, a typical vertebroplasty treatment was simulated by injection of low-viscosity bone cement within 3 compressed samples. The failure patterns and the associated load levels for these samples were also predicted using the QCT voxel-based FEM.     

Incorporating chemical signalling factors into cell-based models of growing epithelial tissues

In this paper we present a comprehensive computational framework within which the effects of chemical signalling factors on growing epithelial tissues can be studied. The method incorporates a vertex-based cell model, in conjunction with a solver for the governing chemical equations. The vertex model provides a natural mesh for the finite element method (FEM), with node movements determined by force laws. The arbitrary Lagrangian-Eulerian formulation is adopted to account for domain movement between iterations. The effects of cell proliferation and junctional rearrangements on the mesh are also examined. By implementing refinements of the mesh we show that the finite element (FE) approximation converges towards an accurate numerical solution. The potential utility of the system is demonstrated in the context of Decapentaplegic (Dpp), a morphogen which plays a crucial role in development of the Drosophila imaginal wing disc. Despite the presence of a Dpp gradient, growth is uniform across the wing disc. We make the growth rate of cells dependent on Dpp concentration and show that the number of proliferation events increases in regions of high concentration. This allows hypotheses regarding mechanisms of growth control to be rigorously tested. The method we describe may be adapted to a range of potential application areas, and to other cell-based models with designated node movements, to accurately probe the role of morphogens in epithelial tissues.