Tetrahedral Finite Element Meshes Research Articles

Reduction in the Computational Complexity of Calculating Losses on Eddy Currents in a Hydrogen Fuel Cell Using the Finite Element Analysis

This paper considers the issues of the reduction in the computational complexity of the numerical problem and the requirements of the computer memory size when calculating the power of the eddy currents in a hydrogen fuel cell based on a proton exchange membrane. The study was performed on a model problem based on a geometric pattern of a hydrogen fuel cell of typical dimensions and characteristics operating at a nominal load in steady-state conditions. The power of the eddy currents was calculated using a numerical model based on a tetrahedral finite element mesh and a mathematical model of a quasi-stationary electromagnetic field in the classical formulation through the vector magnetic potential. The requirements for the minimum degree of the geometric model approximation by a finite element mesh to achieve mesh stability of the computational problem results were defined. The paper considers issues of finite element order selection, the method of ordering, and the solution of the systems of linear algebraic equations (SLAEs). It shows the techniques for determining the accuracy of the calculated SLAE solution obtained by the direct method, as well as the effectiveness of the low-rank approximation of the SLAE to reduce the computational complexity of the computational problem solution and reduce the requirements for the amount of computer memory needed, considering the reduced accuracy of the SLAE solutions.

Three-dimensional inversion for sparse potential data using first-order system least squares with application to gravity anomalies in Western Queensland

SUMMARY We present an inversion algorithm tailored for point gravity data. As the data are from multiple surveys, it is inconsistent with regards to spacing and accuracy. An algorithm design objective is the exact placement of gravity observations to ensure no interpolation of the data is needed prior to any inversion. This is accommodated by discretization using an unstructured tetrahedral finite-element mesh for both gravity and density with mesh nodes located at all observation points and a first-order system least-squares (FOSLS) formulation for the gravity modelling equations. Regularization follows the Bayesian framework where we use a differential operator approximation of an exponential covariance kernel, avoiding the usual requirement of inverting large dense covariance matrices. Rather than using higher order basis functions with continuous derivatives across element faces, regularization is also implemented with a FOSLS formulation using vector-valued property function (density and its gradient). Minimization of the cost function, comprised of data misfit and regularization, is achieved via a Lagrange multiplier method with the minimum of the gravity FOSLS functional as a constraint. The Lagrange variations are combined into a single equation for the property function and solved using an integral form of the pre-conditioned conjugate gradient method (I-PCG). The diagonal entries of the regularization operator are used as the pre-conditioner to minimize computational costs and memory requirements. Discretization of the differential operators with the finite-element method (FEM) results in matrix systems that are solved with smoothed aggregation algebraic multigrid pre-conditioned conjugate gradient (AMG-PCG). After their initial setup, the AMG-PCG operators and coarse grid solvers are reused in each iteration step, further reducing computation time. The algorithm is tested on data from 23 surveys with a total of 6519 observation points in the Mt Isa–Cloncurry region in north–west Queensland, Australia. The mesh had about 2.5 million vertices and 16.5 million cells. A synthetic case was also tested using the same mesh and error measures for localized concentrations of high and low densities. The inversion results for different parameters are compared to each other as well as to lower order smoothing. Final inversion results are shown with and without depth weighting and compared to previous geological studies for the Mt Isa–Cloncurry region.

Patient-specific computational flow modelling for assessing hemodynamic changes following fenestrated endovascular aneurysm repair

ObjectiveThis study aimed to develop an accessible patient-specific computational flow modelling pipeline for evaluating the hemodynamic performance of fenestrated endovascular aneurysm repair (fEVAR), with the hypothesis that computational flow modelling can detect aortic branch hemodynamic changes associated with fEVAR graft implantation. MethodsPatients who underwent fEVAR for juxtarenal aortic aneurysms with the Cook ZFEN were retrospectively selected. Using open-source SimVascular software, preoperative and postoperative visceral aortic anatomy was manually segmented from computed tomography angiograms. Three-dimensional geometric models were then discretized into tetrahedral finite element meshes. Patient-specific pulsatile in-flow conditions were derived from known supraceliac aortic flow waveforms and adjusted for patient body surface area, average resting heart rate, and blood pressure. Outlet boundary conditions consisted of three-element Windkessel models approximated from physiologic flow splits. Rigid wall flow simulations were then performed on preoperative and postoperative models with the same inflow and outflow conditions. We used SimVascular's incompressible Navier-Stokes solver to perform blood flow simulations on a cluster using 72 cores. ResultsPreoperative and postoperative flow simulations were performed for 10 patients undergoing fEVAR with a total of 30 target vessels (20 renal stents, 10 mesenteric scallops). Postoperative models required a higher mean number of mesh elements to reach mesh convergence (3.2 ± 1.8 × 106 vs 2.6 ± 1.1 × 106; P = .005) with a longer mean computational time (10.3 ± 6.3 hours vs 7.8 ± 3.5 hours; P = .04) compared with preoperative models. fEVAR was associated with small but statistically significant increases in mean peak proximal aortic arterial pressure (140.3 ± 11.0 mm Hg vs 136.9 ± 8.7 mm Hg; P = .02) and peak renal artery pressure (131.6 ± 14.8 mm Hg vs 128.9 ± 11.8 mm Hg; P = .04) compared with preoperative simulations. No differences were observed in peak pressure in the celiac, superior mesenteric, or distal aortic arteries (P = .17-.96). When measuring blood flow, the only observed difference was an increase in peak renal flow rate after fEVAR (17.5 ± 3.8 mL/s vs 16.9 ± 3.5 mL/s; P = .04). fEVAR was not associated with changes in the mean pressure or the mean flow rate in the celiac, superior mesenteric, or renal arteries (P = .06-.98). Stenting of the renal arteries did not induce significant changes time-averaged wall shear stress in the proximal renal artery (23.4 ± 8.1 dynes/cm2 vs 23.2 ± 8.4 dynes/cm2; P = .98) or distal renal artery (32.7 ± 13.9 dynes/cm2 vs 29.6 ± 11.8 dynes/cm2; P = .23). In addition, computational visualization of cross-sectional velocity profiles revealed low flow disturbances associated with protrusion of renal graft fabric into the aortic lumen. ConclusionsIn a pilot study involving a selective cohort of patients who underwent uncomplicated fEVAR, patient-specific flow modelling was a feasible method for assessing the hemodynamic performance of various two-vessel fenestrated device configurations and revealed subtle differences in computationally derived peak branch pressure and blood flow rates. Structural changes in aortic flow geometry after fEVAR do not seem to affect computationally estimated renovisceral branch perfusion or wall shear stress adversely. Additional studies with invasive angiography or phase contrast magnetic resonance imaging are required to clinically validate these findings. (JVS–Vascular Science 2021;2:53-69.) Clinical RelevanceUsing a computational flow modelling for assessing the hemodynamic performance of fenestrated endovascular aneurysm repair (fEVAR), this real-world, patient-specific study included 10 participants and found that structural changes in aortic flow geometry after fEVAR did not seem to adversely impact estimated renal or visceral branch perfusion metrics (eg, peak and mean arterial pressure and flow rates) or wall shear stress. These findings overall support the ongoing clinical use of commercially available fEVAR devices for repair of juxtarenal aortic aneurysms, and provides a computational framework for future evaluation of fEVAR configurations in a preoperative or postoperative settings.

Patient-Specific Computational Flow Modelling for Assessing Hemodynamic Changes Following Fenestrated Endovascular Aneurysm Repair

Abstract Objective This study aimed to develop an accessible patient-specific computational flow modelling pipeline for evaluating the hemodynamic performance of fenestrated endovascular aneurysm repair (fEVAR), with the hypothesis that computational flow modelling can detect aortic branch hemodynamic changes associated with fEVAR graft implantation. Methods Patients who underwent fEVAR for juxtarenal aortic aneurysms with the Cook ZFEN were retrospectively selected. Using open-source SimVascular software, preoperative and postoperative visceral aortic anatomy was manually segmented from computed tomography angiograms. Three-dimensional geometric models were then discretized into tetrahedral finite element meshes. Patient-specific pulsatile in-flow conditions were derived from known supraceliac aortic flow waveforms and adjusted for patient body surface area, average resting heart rate, and blood pressure. Outlet boundary conditions consisted of three-element Windkessel models approximated from physiologic flow splits. Rigid wall flow simulations were then performed on preoperative and postoperative models with the same inflow and outflow conditions. We used SimVascular's incompressible Navier-Stokes solver to perform blood flow simulations on a cluster using 72 cores. Results Preoperative and postoperative flow simulations were performed for 10 patients undergoing fEVAR with a total of 30 target vessels (20 renal stents, 10 mesenteric scallops). Postoperative models required a higher mean number of mesh elements to reach mesh convergence (3.2 ± 1.8 × 106 vs 2.6 ± 1.1 × 106; P = .005) with a longer mean computational time (10.3 ± 6.3 hours vs 7.8 ± 3.5 hours; P = .04) compared with preoperative models. fEVAR was associated with small but statistically significant increases in mean peak proximal aortic arterial pressure (140.3 ± 11.0 mm Hg vs 136.9 ± 8.7 mm Hg; P = .02) and peak renal artery pressure (131.6 ± 14.8 mm Hg vs 128.9 ± 11.8 mm Hg; P = .04) compared with preoperative simulations. No differences were observed in peak pressure in the celiac, superior mesenteric, or distal aortic arteries (P = .17-.96). When measuring blood flow, the only observed difference was an increase in peak renal flow rate after fEVAR (17.5 ± 3.8 mL/s vs 16.9 ± 3.5 mL/s; P = .04). fEVAR was not associated with changes in the mean pressure or the mean flow rate in the celiac, superior mesenteric, or renal arteries (P = .06-.98). Stenting of the renal arteries did not induce significant changes time-averaged wall shear stress in the proximal renal artery (23.4 ± 8.1 dynes/cm2 vs 23.2 ± 8.4 dynes/cm2; P = .98) or distal renal artery (32.7 ± 13.9 dynes/cm2 vs 29.6 ± 11.8 dynes/cm2; P = .23). In addition, computational visualization of cross-sectional velocity profiles revealed low flow disturbances associated with protrusion of renal graft fabric into the aortic lumen. Conclusions In a pilot study involving a selective cohort of patients who underwent uncomplicated fEVAR, patient-specific flow modelling was a feasible method for assessing the hemodynamic performance of various two-vessel fenestrated device configurations and revealed subtle differences in computationally derived peak branch pressure and blood flow rates. Structural changes in aortic flow geometry after fEVAR do not seem to affect computationally estimated renovisceral branch perfusion or wall shear stress adversely. Additional studies with invasive angiography or phase contrast magnetic resonance imaging are required to clinically validate these findings. (JVS–Vascular Science 2021;▪:1-17.) Clinical Relevance Using a computational flow modelling for assessing the hemodynamic performance of fenestrated endovascular aneurysm repair (fEVAR), this real-world, patient-specific study included 10 participants and found that structural changes in aortic flow geometry after fEVAR did not seem to adversely impact estimated renal or visceral branch perfusion metrics (eg, peak and mean arterial pressure and flow rates) or wall shear stress. These findings overall support the ongoing clinical use of commercially available fEVAR devices for repair of juxtarenal aortic aneurysms, and provides a computational framework for future evaluation of fEVAR configurations in a preoperative or postoperative settings.

Finite-element analysis of top-casing electric source method for imaging hydraulically active fracture zones

Imaging hydraulically active fracture zones (HAFZ) is of paramount importance to subsurface resource extraction, geologic storage, and hazardous waste disposal. We have developed advanced 3D finite-element (FE) electrical imaging algorithms for HAFZ in the presence of a steel-cased well. The algorithms use tetrahedral FE meshes in the simulation domain and coarse rectangular finite-difference meshes in the imaging domain. This heterogeneous dual-mesh approach is well suited to modeling the multiscale earth model due to steel-cased wells. We find that the algorithms accurately and efficiently simulate surface electric field measurements over a 3D HAFZ at depth when one end point of a surface electric source is connected to a wellhead. For brevity, this configuration is called the top-casing electric source method. By replacing a hollow cased well with a solid prism, we improve our computational efficiency without affecting the solution accuracy. The sensitivity of the top-casing source method to HAFZ highly depends on the continuity of a steel-cased well because it makes currents preferentially flow to HAFZ. The sensitivity also depends on conductivity structures around the well because they control current leaking from the steel-cased well. We find that the method can image a localized HAFZ and detect changes in its width and height. The imaging results are improved when a volume of the imaging domain is constrained from geomechanical perspectives. A primary advantage of the method is the fact that the sources and receivers are placed on the surface, thus not interrupting the well operation.

Fast tetrahedral mesh generation and segmentation of an atlas-based heart model using a periodic uniform grid

Abstract A fast procedure for generation of regular tetrahedral finite element mesh for objects with complex shape cavities is proposed. The procedure like LBIE-Mesher can generate tetrahedral meshes for the volume interior to a polygonal surface, or for an interval volume between two surfaces having a complex shape and defined in STL-format. This procedure consists of several stages: generation of a regular tetrahedral mesh that fills the volume of the required object; generation of clipping for the uniform grid parts by a boundary surface; shifting vertices of the boundary layer to align onto the surface.We present a sequential and parallel implementation of the algorithm and compare their performance with existing generators of tetrahedral grids such as TetGen, NETGEN, and CGAL. The current version of the algorithm using the mobile GPU is about 5 times faster than NETGEN. The source code of the developed software is available on GitHub.

Full field modeling of recrystallization: Effect of intragranular strain gradients on grain boundary shape and kinetics

The effect of stored energy field heterogeneity on the microstructure evolution during static recrystallization (SRX) was assessed by performing three dimensional (3D) full field simulations. These simulations were performed by using the Level set (LS) method in a finite element (FE) framework with unstructured tetrahedral FE mesh. An extension of classical LS-FE for SRX was developed to account for average stored energies in zones adjacent to grain boundaries (GBs) in each grain. Annihilation of dislocations by a passing GB was taken into account. The results of 3D simulations were analyzed to compare the “per interface” LS model to the usual “per grain” LS method (with averaging stored energy per grain). Recrystallization is faster at the beginning of the heat treatment when using the “per interface” model. The analysis of the evolution of grain volume and grain surface scattering reveals that the “per interface” approach results in complex shapes of grains which are closer to those observed in experiments. Local simulations for few grains with refined FE mesh were also performed to study the effect of stored energy heterogeneity along interfaces, and even higher complexity of grain topology was observed compared to the results of “per interface” computations.

Personalized computational modeling of left atrial geometry and transmural myofiber architecture

Atrial fibrillation (AF) is a supraventricular tachyarrhythmia characterized by complete absence of coordinated atrial contraction and is associated with an increased morbidity and mortality. Personalized computational modeling provides a novel framework for integrating and interpreting the role of atrial electrophysiology (EP) including the underlying anatomy and microstructure in the development and sustenance of AF. Coronary computed tomography angiography data were segmented using a statistics-based approach and the smoothed voxel representations were discretized into high-resolution tetrahedral finite element (FE) meshes. To estimate the complex left atrial myofiber architecture, individual fiber fields were generated according to morphological data on the endo- and epicardial surfaces based on local solutions of Laplace’s equation and transmurally interpolated to tetrahedral elements. The influence of variable transmural microstructures was quantified through EP simulations on 3 patients using 5 different fiber interpolation functions. Personalized geometrical models included the heterogeneous thickness distribution of the left atrial myocardium and subsequent discretization led to high-fidelity tetrahedral FE meshes. The novel algorithm for automated incorporation of the left atrial fiber architecture provided a realistic estimate of the atrial microstructure and was able to qualitatively capture all important fiber bundles. Consistent maximum local activation times were predicted in EP simulations using individual transmural fiber interpolation functions for each patient suggesting a negligible effect of the transmural myofiber architecture on EP. The established modeling pipeline provides a robust framework for the rapid development of personalized model cohorts accounting for detailed anatomy and microstructure and facilitates simulations of atrial EP.

English

The maximum angle condition of J. L. Synge was originally introduced in interpolation theory and further used in finite element analysis and applications for triangular and later also for tetrahedral finite element meshes. In this paper we present some of its generalizations to higher-dimensional simplicial elements. In particular, we prove optimal interpolation properties of linear simplicial elements in ℝd that degenerate in some way.

Efficient conformal tetrahedral finite element mesh generation for moving objects with contact by mesh adaptation

Efficient conformal tetrahedral finite element mesh generation for moving objects with contact by mesh adaptation

A tetrahedral mesh generation approach for 3D marine controlled-source electromagnetic modeling

3D finite-element (FE) mesh generation is a major hurdle for marine controlled-source electromagnetic (CSEM) modeling. In this paper, we present a FE discretization operator (FEDO) that automatically converts a 3D finite-difference (FD) model into reliable and efficient tetrahedral FE meshes for CSEM modeling. FEDO sets up wireframes of a background seabed model that precisely honors the seafloor topography. The wireframes are then partitioned into multiple regions. Outer regions of the wireframes are discretized with coarse tetrahedral elements whose maximum size is as large as a skin depth of the regions. We demonstrate that such coarse meshes can produce accurate FE solutions because numerical dispersion errors of tetrahedral meshes do not accumulate but oscillates. In contrast, central regions of the wireframes are discretized with fine tetrahedral elements to describe complex geology in detail. The conductivity distribution is mapped from FD to FE meshes in a volume-averaged sense. To avoid excessive mesh refinement around receivers, we introduce an effective receiver size. Major advantages of FEDO are summarized as follow. First, FEDO automatically generates reliable and economic tetrahedral FE meshes without adaptive meshing or interactive CAD workflows. Second, FEDO produces FE meshes that precisely honor the boundaries of the seafloor topography. Third, FEDO derives multiple sets of FE meshes from a given FD model. Each FE mesh is optimized for a different set of sources and receivers and is fed to a subgroup of processors on a parallel computer. This divide and conquer approach improves the parallel scalability of the FE solution. Both accuracy and effectiveness of FEDO are demonstrated with various CSEM examples.

Method for the explicit insertion of microstructure in Cellular Automata Finite Element (CAFE) models based on an irregular tetrahedral Finite Element mesh: Application in a multi-scale Finite Element Microstructure MEshfree framework (FEMME)

Multiscale models are needed in simulations of mechanical and thermal properties that consider the microstructural heterogeneity of materials, in which a coupling is essential between the numerical models that deal with the different scales. In the class of cellular automata-finite element (CA-FE) or CAFE models, the use of a regular FE mesh restricts the model versatility due to the limited variety of engineering problems that can be simulated with such meshes. A novel methodology is proposed to create the homogeneous cells of the CA model from a mesh that is formed by irregular tetrahedrons. The result is more versatile and capable of modelling complex geometries, improving its applicability. The problem is solved through a subdivision algorithm that creates homogeneous tetrahedral cells, using a methodology to insert microstructures that can be described by particles, pores or fibres. Its use is demonstrated in a multi-scale Finite Element Microstructure MEshfree (FEMME) framework to calculate the elastic strains caused by microstructural features (pores); the method is shown to have a significantly lower computational cost than finite element simulations of equivalent levels of discretization.

The in situ mechanics of trabecular bone marrow: the potential for mechanobiological response.

Bone adapts to habitual loading through mechanobiological signaling. Osteocytes are the primary mechanical sensors in bone, upregulating osteogenic factors and downregulating osteoinhibitors, and recruiting osteoclasts to resorb bone in response to microdamage accumulation. However, most of the cell populations of the bone marrow niche,which are intimately involved with bone remodeling as the source of bone osteoblast and osteoclast progenitors, are also mechanosensitive. We hypothesized that the deformation of trabecular bone would impart mechanical stress within the entrapped bone marrow consistent with mechanostimulation of the constituent cells. Detailed fluid-structure interaction models of porcine femoral trabecular bone and bone marrow were created using tetrahedral finite element meshes. The marrow was allowed to flow freely within the bone pores, while the bone was compressed to 2000 or 3000 microstrain at the apparent level.Marrow properties were parametrically varied from a constant 400 mPas to a power law rule exceeding 85 Pas. Deformation generated almost no shear stress or pressure in the marrow for the low viscosity fluid, but exceeded 5 Pa when the higher viscosity models were used. The shear stress was higher when the strain rate increased and in higher volume fraction bone. The results demonstrate that cells within the trabecular bone marrow could be mechanically stimulated by bone deformation, depending on deformation rate, bone porosity, and bone marrow properties. Since the marrow contains many mechanosensitive cells, changes in the stimulatory levels may explain the alterations in bone marrow morphology with aging and disease, which may in turn affect the trabecular bone mechanobiology and adaptation.

SU-D-BRF-06: A Brachytherapy Simulator with Realistic Haptic Force Feedback and Real-Time Ultrasounds Image Simulation for Training and Teaching

Purpose: Surgical procedures require dexterity, expertise and repetition to reach optimal patient outcomes. However, efficient training opportunities are usually limited. This work presents a simulator system with realistic haptic force-feedback and full, real-time ultrasounds image simulation. Methods: The simulator is composed of a custom-made Linear-DELTA force-feedback robotic platform. The needle tip is mounted on a force gauge at the end effector of the robot, which responds to needle insertion by providing reaction forces. 3D geometry of the tissue is using a tetrahedral finite element mesh (FEM) mimicking tissue properties. As the needle is inserted/retracted, tissue deformation is computed using a mass-tensor nonlinear visco-elastic FEM. The real-time deformation is fed to the L-DELTA to take into account the force imparted to the needle, providing feedback to the end-user when crossing tissue boundaries or needle bending. Real-time 2D US image is also generated synchronously showing anatomy, needle insertion and tissue deformation. The simulator is running on an Intel I7 6- core CPU at 3.26 MHz. 3D tissue rendering and ultrasound display are performed on a Windows 7 computer; the FEM computation and L-DELTA control are executed on a similar PC using the Neutrino real-time OS. Both machines communicate through an Ethernet link.more » Results: The system runs at 500 Hz for a 8333-tetrahedron tissue mesh and a 100-node angular spring needle model. This frame rate ensures a relatively smooth displacement of the needle when pushed or retracted (±20 N in all directions at speeds of up to 2 m/s). Unlike commercially-available haptic platforms, the oblong workspace of the L-DELTA robot complies with that required for brachytherapy needle displacements of 0.1m by 0.1m by 0.25m. Conclusion: We have demonstrated a real-life, realistic brachytherapy simulator developed for prostate implants (LDR/HDR). The platform could be adapted to other sites or training for other types of needle-based procedures.« less

Finite element mesh generation for subsurface simulation models

This paper introduces a methodology for creating geometrically consistent subsurface simulation models, and subsequently tetrahedral finite element (FE) meshes, from geometric entities generated in...

A projection hybrid finite volume/element method for low-Mach number flows

The purpose of this article is to introduce a projection hybrid finite volume/element method for low-Mach number flows of viscous or inviscid fluids. Starting with a 3D tetrahedral finite element mesh of the computational domain, the equation of the transport-diffusion stage is discretized by a finite volume method associated with a dual mesh where the nodes of the volumes are the barycenters of the faces of the initial tetrahedra. The transport-diffusion stage is explicit. Upwinding of convective terms is done by classical Riemann solvers as the Q-scheme of van Leer or the Rusanov scheme. Concerning the projection stage, the pressure correction is computed by a piecewise linear finite element method associated with the initial tetrahedral mesh. Passing the information from one stage to the other is carefully made in order to get a stable global scheme. Numerical results for several test examples aiming at evaluating the convergence properties of the method are shown.

A balanced accumulation scheme for parallel PDE solvers

We present a tailored load balancing technique that addresses specific performance issues in the boundary data accumulation algorithm for non-overlapping domain decompositions. The technique is used to speed up a parallel conjugate gradient algorithm with an algebraic multigrid preconditioner to solve a potential problem on an unstructured tetrahedral finite element mesh. The optimized accumulation algorithm significantly improves the performance of the parallel solver and we show up to 50 % runtime improvements over the standard approach in benchmark runs with up to 48 MPI processes. The load balancing problem itself is a global optimization problem that is solved approximately by local optimization algorithms in parallel that require no communication during the optimization process.

An Optimised Linear Mechanical Model for Estimating Brain Shift Caused by Meningioma Tumours

Estimation of brain deformation plays an important role in computer-aided therapy and image-guided neurosurgery systems. Tumour growth can cause brain deformation and change stress distribution in the brain. Biomechanical models exist that use a finite element method to estimate brain shift caused by tumour growth. Such models can be categorised as linear and non-linear models, both of which assume finite deformation of the brain after tumour growth. Linear models are easy to implement and fast enough to for applications such as IGS where the time is a great of concern. However their accuracy highly dependent on the parameters of the models in this paper, we proposed an optimisation approach to improve a naive linear model to achieve more precise estimation of brain displacements caused by tumour growth. The optimisation process has improved the accuracy of the model by adapting the brain model parameters according to different tomour sizes.We used patient-based tetrahedron finite element mesh with proper material properties for brain tissue and appropriate boundary conditions in the tumour region. Anatomical landmarks were determined by an expert and were divided into two different sets for evaluation and optimisation. Tetrahedral finite element meshes were used and the model parameters were optimised by minimising the mean square distance between the predicted locations of the anatomical landmarks derived from Brain Atlas images and their actual locations on the tumour images. Our results demonstrate great improvement in the accuracy of an optimised linear mechanical model that achieved an accuracy rate of approximately 92%.

Interactive deformable models with quadratic bases in Bernstein–Bézier-form

We present a physically based interactive simulation technique for de formable objects. Our method models the geometry as well as the displacements using quadratic basis functions in Bernstein–Bezier form on a tetrahedral finite element mesh. The Bernstein–Bezier formulation yields significant advantages compared to approaches using the monomial form. The implementation is simplified, as spatial derivatives and integrals of the displacement field are obtained analytically avoiding the need for numerical evaluations of the elements’ stiffness matrices. We introduce a novel traversal accounting for adjacency in order to accelerate the reconstruction of the global matrices. We show that our proposed method can compensate the additional effort introduced by the co-rotational formulation to a large extent. We validate our approach on several models and demonstrate new levels of accuracy and performance in comparison to current state-of-the-art.

Numerical and Experimental Models of the Mandible

This study aimed to validate a numerical model of an intact mandible for further development of a new TMJ implant. Numerical and experimental models of the biomechanics of the mandible were elaborated to characterize the human temporomandibular joint and to approach the development of a condyle implant. The model of the mandible was obtained through the use of a polymeric replica of a human cadaveric mandible and through 3D geometry acquisition. The three-dimensional finite element model was generated as a tetrahedral finite element mesh. The level of mesh refinement was established via a convergence test and a model with more than 50,000 degrees of freedom was required to obtain analysis accuracy. The functional loading cases included muscle loading in four different load boundary conditions. The same boundary conditions were applied to the experimental model. The strains were measured with an experimental procedure using electric resistance strain gauges applied on the external surface of the mandible. The mechanical response is shown and discussed in terms of strains, principal numerical and measured strains. This study proved that FE models of the mandible can reproduce experimental strains within an overall agreement of 10%. The FE models correctly reproduced bone strains under different load configurations and therefore can be used for the design of a novel TMJ implant considering other load configurations and bone mechanical properties.