Tetrahedral Element Meshes Research Articles

Variations of Middle Cerebral Artery Hemodynamics Due to Aneurysm Clipping Surgery

Abstract Cerebral aneurysms are potentially life-threatening cerebrovascular conditions where a weakened blood vessel in the brain bulges or protrudes over time. The most common way to treat aneurysms is surgical clipping, an approach where blood flow to the aneurysm is blocked by a permanently placed clip on the artery. However, not all aneurysms are identical; thus, there has been a need for patient-specific treatment options, where each aneurysm is treated based on its individual characteristics. Computational fluid dynamics (CFD) modeling can offer insights to predict how different treatment procedures will affect cerebral hemodynamics. In that regard, the goal of this pilot study was to investigate the flow characteristics and hemodynamic parameters in cerebral arteries before and after neurosurgical clipping. For this purpose, two patient-specific cerebral artery geometries with at least one aneurysm at the middle cerebral artery bifurcation were selected from an online dataset. A companion postclipping model was created for each geometry by removing the aneurysm from the original geometry. Tetrahedral mesh elements were then generated and CFD simulations were conducted to compare the blood velocity profile, secondary flow, flow streamline, and wall shear stress in the computational models with and without aneurysm. Results showed that the clipping treatment led to changes in the velocity profiles, secondary flow structures, and wall shear stress in the middle cerebral artery. In conclusion, our results suggest that CFD modeling can assist in predicting hemodynamic parameters prior to treatment, thus facilitating more tailored planning for each patient’s treatment.

Computations and measurements of the magnetic polarizability tensor characterisation of highly conducting and magnetic objects

PurposeThe ability to characterise highly conducting objects, that may also be highly magnetic, by the complex symmetric rank–2 magnetic polarizability tensor (MPT) is important for metal detection applications including discriminating between threat and non-threat objects in security screening, identifying unexploded anti-personnel landmines and ordnance and identifying metals of high commercial value in scrap sorting. Many everyday non-threat items have both a large electrical conductivity and a magnetic behaviour, which, for sufficiently weak fields and the frequencies of interest, can be modelled by a high relative magnetic permeability. This paper aims to discuss the aforementioned idea.Design/methodology/approachThe numerical simulation of the MPT for everyday non-threat highly conducting magnetic objects over a broad range of frequencies is challenging due to the resulting thin skin depths. The authors address this by employing higher order edge finite element discretisations based on unstructured meshes of tetrahedral elements with the addition of thin layers of prismatic elements. Furthermore, computer aided design (CAD) geometrical models of the non-threat and threat object are often not available and, instead, the authors extract the geometrical features of an object from an imaging procedure.FindingsThe authors obtain accurate numerical MPT characterisations that are in close agreement with experimental measurements for realistic physical objects. The assessment of uncertainty shows the impact of geometrical and material parameter uncertainties on the computational results.Originality/valueThe authors present novel computations and measurements of MPT characterisations of realistic objects made of magnetic materials. A novel assessment of uncertainty in the numerical predictions of MPT characterisations for uncertain geometry and material parameters is included.

Computational modeling of sigmoid functionally graded material (SFGM) plate

The first-order shear deformation theory (FSDT) was used to explore the natural frequency response of functionally graded piezoelectric plates subjected to static electrical and mechanical strain in this present study. A monomorph model for a functionally graded piezoelectric plate with material properties that change according to sigmoid law with respect to plate thickness has been considered. A three-dimensional finite element model with a free tetrahedral element mesh was created using COMSOL 4.2 Multiphysics® software, with each node having three degrees of freedom. Variations in the FGPM plate’s free vibration boundary conditions, composition, and geometry have all been investigated. In free vibration analysis, non-dimensional natural frequency of FGPM plate initially decreasing considerably and then remaining almost constant with the increase in volume fraction index when material property graded by power law. When material properties are varied by sigmoid law, with an increase in volume fraction index, the non-dimensional natural frequency of FGPM plates remains virtually constant. FGPM plates have a lower non-dimensional natural frequency if the thickness to width ratio is greater. Non-dimensional natural frequencies of Clamped-Clamped FGPM plates (C–C–C–C) are greater compared to Clamped-Free FGPM (C–F–C–F) and Simply Supported Free FGPM (S–F–S–F).

Designing & simulation of a lightweight hip implant stem: an FEM based approach

ABSTRACT Total hip arthroplasty is a widely used surgical intervention widely used in entire world. Objective of this paper is to develop a hollow lightweight costeffective model of hip implant stem using CAD and optimise it for better results than the already existing designs. The study therefore focuses on designing and simulation of a lightweight, cost-effective and durable model of prosthetic hip implant. The developed design is optimised in such a way that revascularisation in bone tissue reduces the weight of the implant stem. This is done by punching holes in the distal end of the design module. Standard boundary conditions are applied using ASTM F2996-13 with tetrahedral mesh elements for static structural analysis. From comparative study between three Ti6Al4V models (viz. solid model, model with 3 mm holes and model with 4.5 mm holes), it can be stated that the model with 3 mm holes was superior. This model showcases lower weight as well as lower values of all the static structural analysis performed. Model with 3 mm holes was approximately 15% lighter than solid reference model and experiences around 100 MPa lesser Von Mises stress than that experienced by model with hole sizes of 4.5 mm.

Numerical prediction of fatigue life of an A356-T6 alloy wheel considering the influence of casting defect and mean stress

A fatigue prediction method considering shrinkage cavity, secondary dendrite arm spacing (SDAS) and mean stress level is presented in the paper. Firstly, the casting process of an aluminum alloy wheel is simulated based on ProCAST software. And the data of SDAS and porosity of different parts are predicted based on the solidification process. Then the data mapping algorithm between tetrahedral mesh elements is developed to realize the unidirectional transformation of microcosmic data from a cast model to a static mechanical model. And the radial loading mechanical analysis model of a wheel containing microcosmic information is further established. According to the specific mechanical and fatigue parameters of each node, the fatigue life prediction model is established by Fesafe software. Based on the self-developed Transfer Couple Data (TCD) software, the integrated coupling method of the three software prediction models is realized, and the method is further used to realize a precise prediction of the radial fatigue life of a wheel considering effects of shrinkage cavity, SDAS and mean stress. Compared with the experimental results, after considering the microcosmic influence, the predicted position of the minimum life is unchanged, and the predicted life value is more accurate after considering the microcosmic influence. The proposed method lays a solid foundation of the optimization design and lightweight design of aluminum alloy wheels.

Numerical analysis on the thermal hydraulic effect of wrapped wire spacer in a four rod fuel bundle

Abstract The application of relatively simple and cheap wrapped wire spacer in the European supercritical-water-cooled reactor has been proposed in order to provide enhanced heat transfer in the fuel assembly without unacceptable penalty in pressure loss. The wires cause twisting flow in fuel assembly, which means the coolant flows not only straight in the axial direction but has a significant transverse velocity component and strong mixing between neighbouring sub-channels occurs. The aim of this ongoing research is to numerically investigate the effect of wrapped wire spacers on thermal hydraulics of turbulent coolant flow and its heat transfer in a small bundle with four fuel rods. One bare and six wired geometry with different wire pitches (1–6 turn(s) of wires) have been studied. Unstructured volume mesh of tetrahedral elements with fine near wall boundary mesh of prism elements for fluid domain and structured mesh of hexahedral elements for solid domains of fuel rods, wires, etc. have been used to discretize the computational domain. After an extensive mesh and turbulence model sensitivity study, the M4 mesh resolution and the most advanced BSL Reynolds Stress turbulence model were selected for the further CFD calculations. The validation of the model with 3 turns of wires has been performed. The wires generate significant amount of transverse velocity and decrease the wall temperature most in corner sub-channels which was hottest in bare geometry. The heat transfer coefficient has been increased also most in corner sub-channels by 60–145% depending on the number of turns of wires. The other two types of sub-channel showed moderated (wall type) or negligible (central type) decrease in wall temperature and enhancement in heat transfer. Temperature hot spots with moderate values have been identified on the wall of fuel rods. The optimal technical choice from thermal hydraulic sense seems to be three turns of wires due to the pressure drop is only 18% higher than in bare geometry but maximum wall temperature is 32 °C lower while the average heat transfer coefficient is 95% higher where it is most needed, in the corner sub-channels. For these thermal benefits, the 18% penalty in the pressure drop seems to be acceptable. The outcome of this technical optimization needs further confirmation by an economic analysis while the possible long term effect of revealed hot spots on integrity of fuel rod cladding has to be investigated as well.

Modeling hemodynamics in intracranial aneurysms: Comparing accuracy of CFD solvers based on finite element and finite volume schemes.

Image-based computational fluid dynamics (CFD) has shown potential to aid in the clinical management of intracranial aneurysms, but its adoption in the clinical practice has been missing, partially because of lack of accuracy assessment and sensitivity analysis. To numerically solve the flow-governing equations, CFD solvers generally rely on 2 spatial discretization schemes: finite volume (FV) and finite element (FE). Since increasingly accurate numerical solutions are obtained by different means, accuracies and computational costs of FV and FE formulations cannot be compared directly. To this end, in this study, we benchmark 2 representative CFD solvers in simulating flow in a patient-specific intracranial aneurysm model: (1) ANSYS Fluent, a commercial FV-based solver, and (2) VMTKLab multidGetto, a discontinuous Galerkin (dG) FE-based solver. The FV solver's accuracy is improved by increasing the spatial mesh resolution (134k, 1.1m, 8.6m, and 68.5m tetrahedral element meshes). The dGFE solver accuracy is increased by increasing the degree of polynomials (first, second, third, and fourth degree) on the base 134k tetrahedral element mesh. Solutions from best FV and dGFE approximations are used as baseline for error quantification. On average, velocity errors for second-best approximations are approximately 1cm/s for a [0,125]cm/s velocity magnitude field. Results show that high-order dGFE provides better accuracy per degree of freedom but worse accuracy per Jacobian nonzero entry as compared with FV. Cross-comparison of velocity errors demonstrates asymptotic convergence of both solvers to the same numerical solution. Nevertheless, the discrepancy between underresolved velocity fields suggests that mesh independence is reached following different paths.

Transport of phase space densities through tetrahedral meshes using discrete flow mapping

Discrete flow mapping was recently introduced as an efficient ray based method determining wave energy distributions in complex built up structures. Wave energy densities are transported along ray trajectories through polygonal mesh elements using a finite dimensional approximation of a ray transfer operator. In this way the method can be viewed as a smoothed ray tracing method defined over meshed surfaces. Many applications require the resolution of wave energy distributions in three-dimensional domains, such as in room acoustics, underwater acoustics and for electromagnetic cavity problems. In this work we extend discrete flow mapping to three-dimensional domains by propagating wave energy densities through tetrahedral meshes. The geometric simplicity of the tetrahedral mesh elements is utilised to efficiently compute the ray transfer operator using a mixture of analytic and spectrally accurate numerical integration. The important issue of how to choose a suitable basis approximation in phase space whilst maintaining a reasonable computational cost is addressed via low order local approximations on tetrahedral faces in the position coordinate and high order orthogonal polynomial expansions in momentum space.

A multi-moment finite volume method for incompressible Navier–Stokes equations on unstructured grids: Volume-average/point-value formulation

A robust and accurate finite volume method (FVM) is proposed for incompressible viscous fluid dynamics on triangular and tetrahedral unstructured grids. Differently from conventional FVM where the volume integrated average (VIA) value is the only computational variable, the present formulation treats both VIA and the point value (PV) as the computational variables which are updated separately at each time step. The VIA is computed from a finite volume scheme of flux form, and is thus numerically conservative. The PV is updated from the differential form of the governing equation that does not have to be conservative but can be solved in a very efficient way. Including PV as the additional variable enables us to make higher-order reconstructions over compact mesh stencil to improve the accuracy, and moreover, the resulting numerical model is more robust for unstructured grids.We present the numerical formulations in both two and three dimensions on triangular and tetrahedral mesh elements. Numerical results of several benchmark tests are also presented to verify the proposed numerical method as an accurate and robust solver for incompressible flows on unstructured grids.

Dynamic homogenization of split-ring metamaterials by Floquet–Bloch decomposition

We apply a novel dynamic homogenization technique to determine the frequency-dependent effective permeability of split-rings arrays. The Floquet–Bloch decomposition of Maxwell equations in this metamaterial is applied when the wavelength is much bigger than the material’s period. We replace the inclusion with a closed ring, and numerically simulate the model by nodal finite elements and a reasonable number of tetrahedral mesh elements. Our results show a good agreement with an analytical permeability law for 2D structures. This work also proposes an accurate method to model the magnetic field in the unit cell.

A method for rapid production of subject specific finite element meshes for electrical impedance tomography of the human head

Finite element (FE) methods are widely used in electrical impedance tomography (EIT) to enable rapid image reconstruction of different tissues based on their electrical conductivity. For EIT of brain function, anatomically-accurate (head-shaped) FE meshes have been shown to improve the quality of the reconstructed images. Unfortunately, given the lack of a computational protocol to generate patient-specific meshes suitable for EIT, production of such meshes is currently ad hoc and therefore very time consuming. Here we describe a robust protocol for rapid generation of patient-specific FE meshes from MRI or CT scan data. Most of the mesh generation process is automated and uses freely available user-friendly software. Other necessary custom scripts are provided as supplementary online data and are fully documented. The patient scan data is segmented into four surfaces: brain, cerebrospinal fluid, skull and scalp. The segmented surfaces are then triangulated and used to generate a global mesh of tetrahedral elements. The resulting meshes exhibit high quality when tested with different criteria and were validated in computational simulations. The proposed protocol provides a rapid and practicable method for generation of patient-specific FE meshes of the human head that are suitable for EIT. This method could eventually be extended to other body regions and might confer benefits with other imaging techniques such as optical tomography or EEG inverse source imaging.

Numerical fatigue 3D-FE modeling of indirect composite-restored posterior teeth

Objective In restored teeth, stresses at the tooth–restoration interface during masticatory processes may fracture the teeth or the restoration and cracks may grow and propagate. The aim was to apply numerical methodologies to simulate the behavior of a restored tooth and to evaluate fatigue lifetimes before crack failure. Materials and methods Using a CAD–FEM procedure and fatigue mechanic laws, the fatigue damage of a restored molar was numerically estimated. Tessellated surfaces of enamel and dentin were extracted by applying segmentation and classification algorithms, to sets of 2D image data. A user-friendly GUI, which enables selection and visualization of 3D tessellated surfaces, was developed in a MatLab ® environment. The tooth-boundary surfaces of enamel and dentin were then created by sweeping operations through cross-sections. A class II MOD cavity preparation was then added into the 3D model and tetrahedral mesh elements were generated. Fatigue simulation was performed by combining a preliminary static FEA simulation with classical fatigue mechanical laws. Results Regions with the shortest fatigue-life were located around the fillets of the class II MOD cavity, where the static stress was highest. Significance The described method can be successfully adopted to generate detailed 3D-FE models of molar teeth, with different cavities and restorative materials. This method could be quickly implemented for other dental or biomechanical applications.

SU‐GG‐I‐132: Refinements to the Deformation Model of an Anthropomorphic Computer Generated Breast Phantom

Purpose: We have previously developed a method for generating synthetic mammograms and breast tomosynthesis images of an anthropomorphic computer generated breast phantom. Mammographic compression of the phantom was simulated based upon a finite element (FE) deformation model. Currently, the compressed phantom is affected by artifacts arising during deformation. In this paper we investigate two refinements to the deformation model. Method and Materials: The mammographic compression simulation involves three steps. First, the undeformed voxel phantom is transformed into a mesh of tetrahedral elements, with each element encompassing several hundred voxels. Decimation reduces the computational complexity of the finite element model. Second, an FE deformation model is applied resulting in a deformed mesh. Finally, the deformed phantom is voxelized by interpolation. Each voxel in the undeformed and deformed phantoms encode a single tissue type. To reduce deformation artifacts we supersampled the deformed phantom during interpolation; uniformly spaced 3×3×3 sub‐voxel sampling points were used for each deformed voxel. In addition, we introduced rules governing the assignment of the tissue type to each voxel in the deformed phantom. Each voxel is now assigned the tissue type most frequently referred to by the supersampling points. These refinements were evaluated by analyzing phantoms whose interior consisted of regularly spaced parallel planes. Results: Without supersampling, 33.6% of the undeformed phantom voxels were not used during interpolation; supersampling reduced the number to 0.2%. The refined rules governing the tissue assignment improved the smoothness of the boundaries between simulated tissues; particularly near the interface between the breast phantom and air, where previously voxels incorrectly assigned as air produced noticeable artifacts. Conclusion: The refinements of the phantom compression model improve the simulation of tissue structures. This is especially important for the simulation of small structures (e.g., microcalcifications).

56LBA Prediction of response to preoperative chemoradiotherapy in rectal cancer by multiplex kinase activity profiling

A fatigue prediction method considering shrinkage cavity, secondary dendrite arm spacing (SDAS) and mean stress level is presented in the paper. Firstly, the casting process of an aluminum alloy wheel is simulated based on ProCAST software. And the data of SDAS and porosity of different parts are predicted based on the solidification process. Then the data mapping algorithm between tetrahedral mesh elements is developed to realize the unidirectional transformation of microcosmic data from a cast model to a static mechanical model. And the radial loading mechanical analysis model of a wheel containing microcosmic information is further established. According to the specific mechanical and fatigue parameters of each node, the fatigue life prediction model is established by Fesafe software. Based on the self-developed Transfer Couple Data (TCD) software, the integrated coupling method of the three software prediction models is realized, and the method is further used to realize a precise prediction of the radial fatigue life of a wheel considering effects of shrinkage cavity, SDAS and mean stress. Compared with the experimental results, after considering the microcosmic influence, the predicted position of the minimum life is unchanged, and the predicted life value is more accurate after considering the microcosmic influence. The proposed method lays a solid foundation of the optimization design and lightweight design of aluminum alloy wheels.

Physically Based Node Distributions For Mesh Generation

A new physically based approach to mesh generation is proposed, which uses the variants of Monte-Carlo (MC) technique. The mesh nodes are treated as interacting particles and their positions are determined using energy minimization. When the approach is extended with the grand-canonical MC scheme the optimization is performed for both the number of particles and their positions. It is shown how a molecular dynamics technique can be applied to accelerate the convergence of the simulations. Local mesh refinement can be achieved with appropriate node spacing functions. The final mesh is created by connecting the generated node distributions with constrained Delaunay triangulation. Well-shaped triangular or tetrahedral mesh elements are usually obtained. The proposed method is simple, flexible, and works in an identical way in spaces of any number of dimensions.

MRI Guided 3D Mesh Generation and Registration for Biological Modeling

An accurate three-dimensional (3D) mesh of biological models is fundamental for analysis and treatment simulations. Generally noninvasive magnetic resonance image (MRI) data are taken as the input for the simulation. The topologic relationship of anatomy is extracted from MR images through segmentation processes. To accelerate the biological modeling phase, template surface and volume meshes are generated based on MR images and∕or anatomical atlases (e.g., brain atlas, etc.). The boundary surfaces are extracted from segmented regions on the image slices, which are used as the input for 3D volume mesh generation. An intuitive graphic user interface was developed for biomedical applications. It integrated MRI data manipulation with surface mesh and volume mesh generators. Image volume and mesh geometries are registered in the MRI working space. As the core component of the system, a robust 3D mesh generation approach is presented. It is capable of describing irregular geometries exhibiting concave and convex surfaces. It uses deltahedral building blocks for volume mesh generation and creates high-quality, regular-shaped tetrahedral mesh elements. The approach supports multiple levels of localized refinement without reducing the overall mesh quality. The validity of this new mesh generation strategy and implementation is demonstrated via the medical applications in brain vasculature modeling, multimodality imaging for breast cancer detection, and numerous anatomically accurate models presented. Multiple material boundaries are preserved in each mesh with fidelity.

An Analysis of the Basic Space-Charge-Limited Emission Algorithm in a Finite-Element Electrostatic Gun Code

Beam currents computed with a general-purpose gun code can exhibit puzzling behavior as the mesh is refined. To understand such behavior, we analyze the convergence, with respect to element size, of the basic space-charge-limited (SCL) emission algorithm in a one-dimensional (1-D) finite-element electrostatic gun model. With the current density fixed at the Child's law value, we find that the relative error of the potential at the first vertex adjacent to the cathode does not converge to zero, but rather increases as the mesh is refined. Convergence of the basic SCL emission algorithm, which depends on said error, is due instead to the increasing sensitivity of the potential to the current density. The current density converges slowly from above to the Child's law value, with a maximum error of 2.7% and ultimately with a sublinear convergence rate of 2/3. Tests on a three-dimensional parallel plate geometry with unstructured meshes of tetrahedral elements demonstrate that insight from the 1-D model applies to a general-purpose code. The behavior is similar to the 1-D model, but with a maximum error of 4.3%. Thus, using an unstructured mesh instead of a smooth structured mesh introduces only a modest additional error to the beam current. Based on the analysis of the 1-D model, we present two scaled SCL emission algorithms. The first exhibits linear convergence from below. The second limits the maximum error to 0.9%. Similar scalings can be employed in general-purpose gun codes to improve the accuracy of the computed beam current.

Three Dimensional And Thermal TransientAnalysis Of Sedimentary Rocks

This work presents the implementation of a finite element code for the thermal transient analysis of sedimentary rocks. This analysis provides a means to assess the thermal history in sedimentary rocks, assisting the studies of hydrocarbon generation and migration processes. The unstructured 3D mesh of tetrahedral elements provides the discrete model. An iterative driver using an edge-by-edge data structure solves the resulting system of equations at each time step. This strategy provides considerable improvements in terms of CPU time and memory demand. This combination enables the study of complex 3D problems, a key issue to basin analysis.

Coupling Of CFD And CSD Methodologies For Modeling BlastAnd Structural Response

This paper describes recent algorithm developments and applications of a program that couples parallel Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) methodologies. FEFL098 is the CFD code used while DYNA3D handles the CSD portion. FEFL098 solves the time-dependent compressible Euler and Reynolds-Averaged Navier-Stokes equations on an unstructured mesh of tetrahedral elements. DYNA3D solves explicitly the large deformation, large strain formulation equations on an unstructured grid composed of bricks and hexahedral elements. While the initial coupled algorithm used the so-called glued-mesh approach, where the CFD and CSD faces match identically, failure of this approach to model severe structural deformation, as well as crack propagation in steel and concrete, led us to the development of the so-called embedded-mesh approach. Here, the CSD objects float through the CFD domain. While each approach has its own advantages, limitations, and deficiencies, the embedded approach was proven to be superior for the class of problems modeled here. Critical application of both approaches are described, including weapon detonation and fragmentation, airblast interaction with a reinforced concrete wall, and fragment/airblast interaction with a steel wall. The final application models the interaction of an external airblast with a generic steel ship.

Development And Applications Of An Embedded CSD ApproachFor Coupled CFD/CSD Modeling Of Blastlstructure Interactions

This paper describes recent developments and select applications of a program that couples parallel Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) methodologies. FEFL098 is the CFD code used while DYNA3D handles the CSD portion. FEFL098 solves the time-dependent, compressible Euler and Reynolds-Averaged Navier-Stokes equations on an unstructured mesh of tetrahedral elements. DYNA3D solves explicitly the large deformation, large strain formulation equations on an unstructured grid composed of bricks and hexahedral elements. The initial algorithm constructed to model the coupled processes used the so-called glued-mesh approach, where the CFD and CSD faces match identically. Failure of this approach to model severe structural deformations in steel plates, as well as crack growth and propagation in steel and concrete, led us to the development of the so-called embedded-mesh approach, where the CSD mesh float through the CFD domain. While each approach has its own advantages, limitations and deficiencies, the embedded approach was proven to be superior for the class of problems modeled here. Critical applications of both approaches are described, including weapon detonation and fragmentation, airblast interaction with a reinforced concrete wall, and fragmentlairblast interactions with steel wall structures including a generic steel ship hull and a steel tower. Transactions on the Built Environment vol 71, © 2004 WIT Press, www.witpress.com, ISSN 1743-3509