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.     

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.     

Parallel splitting solvers for the isogeometric analysis of the Cahn-Hilliard equation

Abstract

Modeling tumor growth in biological systems is a challenging problem with important consequences for diagnosis and treatment of various forms of cancer. This growth process requires large simulation complexity due to evolving biological and chemical processes in living tissue and interactions of cellular and vascular constituents in living organisms. Herein, we describe with a phase-field model, namely the Cahn-Hilliard equation the intricate interactions between the tumors and their host tissue. The spatial discretization uses highly-continuous isogeometric elements. For fast simulation of the time-dependent Cahn-Hilliard equation, we employ an alternating directions implicit methodology. Thus, we reduce the original problems to Kronecker products of 1?D matrices that can be factorized in a linear computational cost. The implementation enables parallel multi-core simulations and shows good scalability on shared-memory multi-core machines. Combined with the high accuracy of isogeometric elements, our method shows high efficiency in solving the Cahn-Hilliard equation on tensor-product meshes.     

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.     

Patient-specific finite element model of the spine and spinal cord to assess the neurological impact of scoliosis correction: preliminary application on two cases with and without intraoperative neurological complications

Scoliosis is a 3D deformation of the spine and rib cage. For severe cases, surgery with spine instrumentation is required to restore a balanced spine curvature. This surgical procedure may represent a neurological risk for the patient, especially during corrective maneuvers. This study aimed to computationally simulate the surgical instrumentation maneuvers on a patient-specific biomechanical model of the spine and spinal cord to assess and predict potential damage to the spinal cord and spinal nerves. A detailed finite element model (FEM) of the spine and spinal cord of a healthy subject was used as reference geometry. The FEM was personalized to the geometry of the patient using a 3D biplanar radiographic reconstruction technique and 3D dual kriging. Step by step surgical instrumentation maneuvers were simulated in order to assess the neurological risk associated to each maneuver. The surgical simulation methodology implemented was divided into two parts. First, a global multi-body simulation was used to extract the 3D displacement of six vertebral landmarks, which were then introduced as boundary conditions into the personalized FEM in order to reproduce the surgical procedure. The results of the FEM simulation for two cases were compared to published values on spinal cord neurological functional threshold. The efficiency of the reported method was checked considering one patient with neurological complications detected during surgery and one control patient. This comparison study showed that the patient-specific hybrid model reproduced successfully the biomechanics of neurological injury during scoliosis correction maneuvers.     

Microtubular Protofilament Analysis Based on Molecular Level Tubulin Interaction

Nonlinear microstructure of the microtubules (MTs) plays an important role in their mechanical properties. Despite the extensive efforts into the development of continuum models for microtubules, a mesoscale finite element model that can link the molecular level information to the overall performance of microtubules is still missing. The aim of this study is to develop a molecular dynamics model (MDM), finite element model (FEM) and structural mechanics beam model (SMBM) for tubulins of protofilament (PF). In MDM, the backbone atoms of α-tubulin were fixed while the backbone atoms of β-tubulin were attached to a molecular dynamics (MD) atom through a virtual spring. In FEM, both α and β tubulins are modeled as spherical shells and adjacent tubulins are connected by linear springs. The spherical shells were framed as beams in SMBM. Corresponding parameters such as the elasticity of tubulin-tubulin interaction (TTI) and the stiffness of springs and beam are derived from MD simulation. Marginal differences in the force-deflection curve among the FEM, the MDM and SMBM indicate the good accuracy in describing the mechanical properties of microtubules. Simulation results show that the protofilament behaves non-linearly under tension and torsion but linearly under bending. Deformation pattern of a PF from the SMBM frame bending can be well captured by the classical Euler-Bernouli beam theory and the flexural rigidity derived from FEM is in good agreement with SMBM. These findings lend compelling credence in our developed models of PF to deepen our understanding of the underlying mechanism of statics and dynamics of MTs. In perspective our approach provides a tool for the analysis of MTs mechanical behavior under different conditions.     

A study of trace and minor elements in the solid tumor model 3924A hepatoma before and after treatment with 5-fluorouracil

The changes in the concentrations of a number of trace elements have been determined by neutron activation analysis in a solid tumor model, blood and its host liver, following 5-fluorouracil administration. Studies have also been carried out for non-tumor bearing animals after 5-fluorouracil. The changes in some of the trace elements parallel destructive changes found in the tumor. Studies are in progress to determine if changes in the urinary concentrations of these trace elements parallel the time sequence of the destructive changes found in the tumor. The potential clinical usefulness of these trace elements are being evaluated along with other biological markers which may eventually be utilized to assess the therapeutic effectiveness of different treatment modalities as well as monitor the patient for possible reoccurrence of the cancer following treatment.     

A strain-based finite element model for calcification progression in aortic valves

Calcific aortic valve disease (CAVD) is a serious disease affecting the aging population. A complex interaction between biochemicals, cells, and mechanical cues affects CAVD initiation and progression. In this study, motivated by the progression of calcification in regions of high strain, we developed a finite element method (FEM) based spatial calcification progression model. Several cardiac cycles of transient structural FEM simulations were simulated. After each simulation cycle, calcium deposition was placed in regions of high circumferential strain. Our results show the radial expansion of calcification as spokes starting from the attachment region, agreeing very well with the reported clinical data.     

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.     

Nonlinear simulation of tumor necrosis,neo-vascularization and tissue invasion via an adaptive finite-element/level-set method

We present a multi-scale computer simulator of cancer progression at the tumoral level, from avascular stage growth, through the transition from avascular to vascular growth (neo-vascularization), and into the later stages of growth and invasion of normal tissue. We use continuum scale reaction-diffusion equations for the growth component of the model, and a combined continuum-discrete model for the angiogenesis component. We use the level set method for describing complex topological changes observed during growth such as tumor splitting and reconnection, and capture of healthy tissue inside the tumor. We use an adaptive, unstructured finite element mesh that allows for finely resolving important regions of the computational domain such as the necrotic rim, the tumor interface and around the capillary sprouts. We present full nonlinear, two-dimensional simulations, showing the potential of our virtual cancer simulator. We use microphysical parameters characterizing malignant glioma cells, obtained from recent in vitro experiments from our lab and from clinical data, and provide insight into the mechanisms leading to infiltration of the brain by the cancer cells. The results indicate that diffusional instability of tumor mass growth and the complex interplay with the developing neo-vasculature may be powerful mechanisms for tissue invasion.     

A CT-based high-order finite element analysis of the human proximal femur compared to in-vitro experiments

The prediction of patient-specific proximal femur mechanical response to various load conditions is of major clinical importance in orthopaedics. This paper presents a novel, empirically validated high-order finite element method (FEM) for simulating the bone response to loads. A model of the bone geometry was constructed from a quantitative computerized tomography (QCT) scan using smooth surfaces for both the cortical and trabecular regions. Inhomogeneous isotropic elastic properties were assigned to the finite element model using distinct continuous spatial fields for each region. The Young's modulus was represented as a continuous function computed by a least mean squares method. p-FEMs were used to bound the simulation numerical error and to quantify the modeling assumptions. We validated the FE results with in-vitro experiments on a fresh-frozen femur loaded by a quasi-static force of up to 1500 N at four different angles. We measured the vertical displacement and strains at various locations and investigated the sensitivity of the simulation. Good agreement was found for the displacements, and a fair agreement found in the measured strain in some of the locations. The presented study is a first step toward a reliable p-FEM simulation of human femurs based on QCT data for clinical computer aided decision making.     

Transient three-dimensional modeling of soil water and solute transport with simultaneous root growth,root water and nutrient uptake

A three-dimensional solute transport model was developed and linked to a three-dimensional transient model for soil water flow and root growth. The simulation domain is discretized into a grid of finite elements by which the soil physical properties are spatially distributed. Solute transport modeling includes passive and active nutrient uptake by roots as well as zero- and first-order source/sink terms. Root water uptake modeling accounts for matric and osmotic potential effects on water and passive nutrient uptake. Root age effects on root water and nutrient uptake activity have been included, as well as the influence of nutrient deficiency and ion toxicity on root growth. Examples illustrate simulations with different levels of model complexity, depending on the amount of information available to the user. At the simplest level, root growth is simulated as a function of mechanical soil strength only. Application of the intermediate level with root water and nutrient uptake simulates the influence of timing and amount of NO3 application on leaching. The most comprehensive level includes simulation of root and shoot growth as influenced by soil water and nutrient status, temperature, and dynamic allocation of assimilate to root and shoot.     

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.     

A multiscale model for eccentric and concentric cardiac growth through sarcomerogenesis

We present a novel computational model for maladaptive cardiac growth in which kinematic changes of the cardiac chambers are attributed to alterations in cytoskeletal architecture and in cellular morphology. We adopt the concept of finite volume growth characterized through the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. The functional form of its growth tensor is correlated to sarcomerogenesis, the creation and deposition of new sarcomere units. In response to chronic volume-overload, an increased diastolic wall strain leads to the addition of sarcomeres in series, resulting in a relative increase in cardiomyocyte length, associated with eccentric hypertrophy and ventricular dilation. In response to chronic pressure-overload, an increased systolic wall stress leads to the addition of sacromeres in parallel, resulting in a relative increase in myocyte cross sectional area, associated with concentric hypertrophy and ventricular wall thickening. The continuum equations for both forms of maladaptive growth are discretized in space using a nonlinear finite element approach, and discretized in time using the implicit Euler backward scheme. We explore a generic bi-ventricular heart model in response to volume- and pressure-overload to demonstrate how local changes in cellular morphology translate into global alterations in cardiac form and function.