Multilevel finite element modeling for the prediction of local cellular deformation in bone

The underlying mechanisms by which bone cells respond to mechanical stimuli or how mechanical loads act on osteocytes housed in lacunae in bone are not well understood. In this study, a multilevel finite element (FE) approach is applied to predict local cell deformations in bone tissue. The local structure of the matrix dictates the local mechanical environment of an osteocyte. Cell deformations are predicted from detailed linear FE analysis of the microstructure, consisting of an arrangement of cells embedded in bone matrix material. This work has related the loads applied to a whole femur during the stance phase of the gait cycle to the strain of a single lacuna and of canaliculi. The predicted bone matrix strains around osteocyte lacunae and canaliculi were nonuniform and differed significantly from the macroscopically measured strains. Peak stresses and strains in the walls of the lacuna were up to six times those in the bulk extracellular matrix. Significant strain concentrations were observed at sites where the process meets the cell body.     

A nonlinear viscoelastic finite element model of polyethylene

A nonlinear viscoelastic finite element model of ultra-high molecular weight polyethylene (UHMWPE) was developed in this study. Eight cylindrical specimens were machined from ram extruded UHMWPE bar stock (GUR 1020) and tested under constant compression at 7% strain for 100 sec. The stress strain data during the initial ramp up to 7% strain was utilized to model the instantaneous stress-strain response using a Mooney-Rivlin material model. The viscoelastic behavior was modeled using the time-dependent relaxation in stress seen after the initial maximum stress was achieved using a stored energy formulation. A cylindrical model of similar dimensions was created using a finite element analysis software program. The cylinder was made up of hexahedral elements, which were given the material properties utilizing the instantaneous stress-strain curve and the energy-relaxation curve obtained from the experimental data. The cylinder was compressed between two flat rigid bodies that simulated the fixtures of the testing machine. Experimental stress-relaxation, creep and dynamic testing data were then used to validate the model. The mean error for predicted versus experimental data for stress relaxation at different strain levels was 4.2%. The mean error for the creep test was 7% and for dynamic test was 5.4%. Finally, dynamic loading in a hip arthroplasty was modeled and validated experimentally with an error of 8%. This study establishes a working finite element material model of UHMWPE that can be utilized to simulate a variety of postoperative arthroplasty conditions.     

Extramuscular myofascial force transmission: experiments and finite element modeling

The specific purpose of the present study was to show that extramuscular myofascial force transmission exclusively has substantial effects on muscular mechanics. Muscle forces exerted at proximal and distal tendons of the rat extensor digitorium longus (EDL) were measured simultaneously, in two conditions (1) with intact extramuscular connections (2) after dissecting the muscles' extramuscular connections to a maximum extent without endangering circulation and innervation (as in most in situ muscle experiments). A finite element model of EDL including the muscles' extramuscular connections was used to assess the effects of extramuscular myofascial force transmission on muscular mechanics, primarily to test if such effects lead to distribution of length of sarcomeres within muscle fibers. In condition (1), EDL isometric forces measured at the distal and proximal tendons were significantly different (F(dist) > F(prox), DeltaF approximates maximally 40% of the proximal force). The model results show that extramuscular myofascial force transmission causes distributions of strain in the fiber direction (shortening in the proximal, lengthening in the distal ends of fibers) at higher lengths. This indicates significant length distributions of sarcomeres arranged in series within muscle fibers. Stress distributions found are in agreement with the higher distal force measured, meaning that the muscle fiber is no longer the unit exerting equal forces at both ends. Experimental results obtained in condition (2) showed no significant changes in the length-force characteristics (i.e., proximo-distal force differences were maintained). This shows that a muscle in situ has to be distinguished from a muscle that is truly isolated in which case the force difference has to be zero. We conclude that extramuscular myofascial force transmission has major effects on muscle functioning.     

Analyzing the interplay between single cell rheology and force generation through large deformation finite element models

In this study, experimental results of single cell spreading between two parallel microplates are exploited through finite element modeling. Axisymmetric computations at finite strains are performed to extract the mechanical properties of the cell which can account for cell shape evolution and traction force generation. Our model includes two distinct components representing the cortex associated with the bilayer membrane on the one hand, and the rest of the cell on the other hand. The former is modeled as a homogeneous hyperelastic material described by a slightly compressible Gent strain energy function, while the latter is idealized either as a quasi-incompressible Newtonian fluid or as another homogeneous hyperelastic material. The kinetics of spreading is ensured by a stapling procedure defined from experimental observations. Material parameters are then optimized to match the simulation closely with the experimental data. In particular, the elastic modulus of the cortex is estimated at about 1,000?Pa in both models, while the cell interior is characterized by a viscosity of 1,000?Pa.s in the biphasic model, or by an elastic modulus of about 100?Pa in the hyperelastic one. These results are in good agreement with G(') and G(') measurements carried out previously in the same parallel plates setup and estimated at the typical rate of cell straining. Moreover, stresses are found to concentrate at the edge of the cell-substrate contact area. These observations allow explaining the relationship between cell spreading and force increase since spreading and the consequent straining of the cell mechanical structure could be the source of the force applied by the cell on its substrate. They could also explain, in a very simple manner, why force-sensitive focal contacts concentrate at the cell edges.     

Transient finite element modeling of functional electrical stimulation

Transcutaneous functional electrical stimulation is commonly used for strengthening muscle. However, transient effects during stimulation are not yet well explored. The effect of an amplitude change of the stimulation can be described by static model, but there is no differency for different pulse duration. The aim of this study is to present the finite element (FE) model of a transient electrical stimulation on the forearm. Discrete FE equations were derived by using a standard Galerkin procedure. Different tissue conductive and dielectric properties are fitted using least square method and trial and error analysis from experimental measurement. This study showed that FE modeling of electrical stimulation can give the spatial-temporal distribution of applied current in the forearm. Three different cases were modeled with the same geometry but with different input of the current pulse, in order to fit the tissue properties by using transient FE analysis. All three cases were compared with experimental measurements of intramuscular voltage on one volunteer.     

Merging of intersecting triangulations for finite element modeling

Surface mesh generation over intersecting triangulations is a problem common to many branches of biomechanics. A new strategy for merging intersecting triangulations is described. The basis of the method is that object surfaces are represented as the zero-level iso-surface of the distance-to-surface function defined on a background grid. Thus, the triangulation of intersecting objects reduces to the extraction of an iso-surface from an unstructured grid. In a first step, a regular background mesh is constructed. For each point of the background grid, the closest distance to the surface of each object is computed. Background points are then classified as external or internal by checking the direction of the surface normal at the closest location and assigned a positive or negative distance, respectively. Finally, the zero-level iso-surface is constructed. This is the final triangulation of the intersecting objects. The overall accuracy is enhanced by adaptive refinement of the background grid elements. The resulting surface models are used as support surfaces to generate three-dimensional grids for finite element analysis. The algorithms are demonstrated by merging arterial branches independently reconstructed from contrast-enhanced magnetic resonance images and by adding extra features such as vascular stents. Although the methodology is presented in the context of finite element analysis of blood flow, the algorithms are general and can be applied in other areas as well.     

A finite element model of cell deformation during magnetic bead twisting.

Magnetic twisting cytometry probes mechanical properties of an adherent cell by applying a torque to a magnetic bead that is tightly bound to the cell surface. Here we have used a three-dimensional finite element model of cell deformation to compute the relationships between the applied torque and resulting bead rotation and lateral bead translation. From the analysis, we computed two coefficients that allow the cell elastic modulus to be estimated from measurements of either bead rotation or lateral bead translation, respectively, if the degree of bead embedding and the cell height are known. Although computed strains in proximity of the bead can be large, the relationships between applied torque and bead rotation or translation remain virtually linear up to bead rotations of 15 degrees, above which geometrical nonlinearities become significant. This appreciable linear range stands in contrast to the intrinsically nonlinear force-displacement relationship that is observed when cells are indented during atomic force microscopy. Finally, these computations support the idea that adhesive forces are sufficient to keep the bead firmly attached to the cell surface throughout the range of working torques.     

Porohyperelastic finite element modeling of abdominal aortic aneurysms

Abdominal aortic aneurysm (AAA) is the gradual weakening and dilation of the infrarenal aorta. This disease is progressive, asymptomatic, and can eventually lead to rupture--a catastrophic event leading to massive internal bleeding and possibly death. The mechanical environment present in AAA is currently thought to be important in disease initiation, progression, and diagnosis. In this study, we utilize porohyperelastic (PHE) finite element models (FEMs) to investigate how such modeling can be used to better understand the local biomechanical environment in AAA. A 3D hypothetical AAA was constructed with a preferential anterior bulge assuming both the intraluminal thrombus (ILT) and the AAA wall act as porous materials. A parametric study was performed to investigate how physiologically meaningful variations in AAA wall and ILT hydraulic permeabilities affect luminal interstitial fluid velocities and wall stresses within an AAA. A corresponding hyperelastic (HE) simulation was also run in order to be able to compare stress values between PHE and HE simulations. The effect of AAA size on local interstitial fluid velocity was also investigated by simulating maximum diameters (5.5 cm, 4.5 cm, and 3.5 cm) at the baseline values of ILT and AAA wall permeability. Finally, a cyclic PHE simulation was utilized to study the variation in local fluid velocities as a result of a physiologic pulsatile blood pressure. While the ILT hydraulic permeability was found to have minimal affect on interstitial velocities, our simulations demonstrated a 28% increase and a 20% decrease in luminal interstitial fluid velocity as a result of a 1 standard deviation increase and decrease in AAA wall hydraulic permeability, respectively. Peak interstitial velocities in all simulations occurred on the luminal surface adjacent to the region of maximum diameter. These values increased with increasing AAA size. PHE simulations resulted in 19.4%, 40.1%, and 81.0% increases in peak maximum principal wall stresses in comparison to HE simulations for maximum diameters of 35 mm, 45 mm, and 55 mm, respectively. The pulsatile AAA PHE FEM demonstrated a complex interstitial fluid velocity field the direction of which alternated in to and out of the luminal layer of the ILT. The biomechanical environment within both the aneurysmal wall and the ILT is involved in AAA pathogenesis and rupture. Assuming these tissues to be porohyperelastic materials may provide additional insight into the complex solid and fluid forces acting on the cells responsible for aneurysmal remodeling and weakening.     

Dynamic finite element modeling of poroviscoelastic soft tissue

Clinical evidences relative to biomechanical factors have demonstrated their important contribution to the behaviour of soft tissues. Finite element (FE) analysis is used to study the mechanical behaviour of soft tissue because it can provide numerical solutions to problems that are intractable to analytic solutions. This study focuses on the development of a FE model of a poroelastic biological tissue, which incorporates the viscoelastic material behaviour, finite deformation and inertial effect. The FE formulation is based on the weak form derived from the governing equation, and Newmark-beta method as well as Newton's method is incorporated into the implicit non-linear solutions. One-dimensional analytical solutions were used to verify the theoretical formulation and the numerical implementation of the proposed model. This study was further extended to analyze two-dimensional biomechanical models and the results clearly demonstrate the importance of including finite deformation, viscoelasticity and inertial effects.     

Computer-integrated finite element modeling of human middle ear

 The objective of this study was to produce an improved finite element (FE) model of the human middle ear and to compare the model with human data. We began with a systematic and accurate geometric modeling technique for reconstructing the middle ear from serial sections of a freshly frozen temporal bone. A geometric model of a human middle ear was constructed in a computer-aided design (CAD) environment with particular attention to geometry and microanatomy. Using the geometric model, a working FE model of the human middle ear was created using previously published material properties of middle ear components. This working FE model was finalized by a cross-calibration technique, comparing its predicted stapes footplate displacements with laser Doppler interferometry measurements from fresh temporal bones. The final FE model was shown to be reasonable in predicting the ossicular mechanics of the human middle ear. Received: 18 February 2002 / Accepted: 6 June 2002 The preparation of temporal bone histological sections of Robert K. Dyer, Jr., MD is gratefully recognized. The Whitaker Foundation supported this work (Research Grant RG-98-0305).     

A novel two-layer, coupled finite element approach for modeling the nonlinear elastic and viscoelastic behavior of human erythrocytes

A novel finite element approach is presented to simulate the mechanical behavior of human red blood cells (RBC, erythrocytes). As the RBC membrane comprises a phospholipid bilayer with an intervening protein network, we propose to model the membrane with two distinct layers. The fairly complex characteristics of the very thin lipid bilayer are represented by special incompressible solid shell elements and an anisotropic viscoelastic constitutive model. Properties of the protein network are modeled with an isotropic hyperelastic third-order material. The elastic behavior of the model is validated with existing optical tweezers studies with quasi-static deformations. Employing material parameters consistent with literature, simulation results are in excellent agreement with experimental data. Available models in literature neglect either the surface area conservation of the RBC membrane or realistic loading conditions of the optical tweezers experiments. The importance of these modeling assumptions, that are both included in this study, are discussed and their influence quantified. For the simulation of the dynamic motion of RBC, the model is extended to incorporate the cytoplasm. This is realized with a monolithic fully coupled fluid-structure interaction simulation, where the fluid is described by the incompressible Navier–Stokes equations in an arbitrary Lagrangian Eulerian framework. It is shown that both membrane viscosity and cytoplasm viscosity have significant influence on simulation results. Characteristic recovery times and energy dissipation for varying strain rates in dynamic laser trap experiments are calculated for the first time and are found to be comparable with experimental data.     

A transversely isotropic viscoelastic constitutive equation for brainstem undergoing finite deformation

The objective of this study was to define the constitutive response of brainstem undergoing finite shear deformation. Brainstem was characterized as a transversely isotropic viscoelastic material and the material model was formulated for numerical implementation. Model parameters were fit to shear data obtained in porcine brainstem specimens undergoing finite shear deformation in three directions: parallel, perpendicular, and cross sectional to axonal fiber orientation and determined using a combined approach of finite element analysis (FEA) and a genetic algorithm (GA) optimizing method. The average initial shear modulus of brainstem matrix of 4-week old pigs was 12.7 Pa, and therefore the brainstem offers little resistance to large shear deformations in the parallel or perpendicular directions, due to the dominant contribution of the matrix in these directions. The fiber reinforcement stiffness was 121.2 Pa, indicating that brainstem is anisotropic and that axonal fibers have an important role in the cross-sectional direction. The first two leading relative shear relaxation moduli were 0.8973 and 0.0741, respectively, with corresponding characteristic times of 0.0047 and 1.4538 s, respectively, implying rapid relaxation of shear stresses. The developed material model and parameter estimation technique are likely to find broad applications in neural and orthopaedic tissues.     

Modified Bilston nonlinear viscoelastic model for finite element head injury studies

This paper proposes a modified nonlinear viscoelastic Bilston model (Bilston et al., 2001, Biorheol., 38, pp. 335-345). for the modeling of brain tissue constitutive properties. The modified model can be readily implemented in a commercial explicit finite element (FE) code, PamCrash. Critical parameters of the model have been determined through a series of rheological tests on porcine brain tissue samples and the time-temperature superposition (TTS) principle has been used to extend the frequency to a high region. Simulations by using PamCrash are compared with the test results. Through the use of the TTS principle, the mechanical and rheological behavior at high frequencies up to 10(4) rads may be obtained. This is important because the properties of the brain tissue at high frequencies and impact rates are especially relevant to studies of traumatic head injury. The averaged dynamic modulus ranges from 130 Pa to 1500 Pa and loss modulus ranges from 35 Pa to 800 Pa in the frequency regime studied (0.01 rads to 3700 rads). The errors between theoretical predictions and averaged relaxation test results are within 20% for strains up to 20%. The FEM simulation results are in good agreement with experimental results. The proposed model will be especially useful for application to FE analysis of the head under impact loads. More realistic analysis of head injury can be carried out by incorporating the nonlinear viscoelastic constitutive law for brain tissue into a commercial FE code.     

3D finite element modeling of pelvic organ prolapse

Objectives: The purpose of this study is to develop a validated 3D finite element model of the pelvic floor system which can offer insights into the mechanics of anterior vaginal wall prolapse and have the ability to assess biomedical device treatment methods. The finite element results should accurately mimic the clinical findings of prolapse due to intra-abdominal pressure (IAP) and soft tissues impairment conditions. Methods: A 3D model of pelvic system was created in Creo Parametric 2.0 based on MRI Images, which included uterus, cervix, vagina, cardinal ligaments, uterosacral ligaments, and a simplified levator plate and rectum. The geometrical model was imported into ANSYS Workbench 14.5. Mechanical properties of soft tissues were based on experimental data of tensile test results from current literature. Studies were conducted for IAP loadings on the vaginal wall and uterus, increasing from lowest to extreme values. Results: Anterior vaginal wall collapse occurred at an IAP value corresponding to maximal valsalva and showed similar collapsed shape as clinical findings. Prolapse conditions exhibited high sensitivity to vaginal wall stiffness, whereas healthy tissues was found to support the vagina against prolapse. Ligament impairment was found to have only a secondary effect on prolapse.     

Explicit finite element modeling of total knee replacement mechanics

Joint kinematics and contact mechanics dictate the success of current total knee replacement (TKR) devices. Efficient computer models present an effective way of evaluating these characteristics. Predicted contact stress and area due to articulations at the tibio-femoral and patello-femoral interfaces indicate potential clinical performance. Previous finite element (FE) knee models have generally been used to predict contact stresses and/or areas during static or quasi-static loading conditions. Explicit dynamic FE analyses have recently been used to efficiently predict TKR kinematics and contact mechanics during dynamic loading conditions. The objective of this study was to develop and experimentally validate an explicit FE TKR model that incorporates tibio-femoral and patello-femoral articulations. For computational efficiency, we developed rigid body analyses that can reasonably reproduce the kinematics, contact pressure distribution, and contact area of a fully deformable system. Results from the deformable model showed that the patello-femoral and tibio-femoral kinematics were in good agreement with experimental knee simulator measurements. Kinematic results from the rigid body analyses were nearly identical to those from the fully deformable model, and the contact pressure and contact area correlation was acceptable given the great reduction in analysis time. Component mesh density studied had little effect on the predicted kinematics, particularly for the patellar component, and small effects on the predicted contact pressure and area. These analyses have shown that, at low computational cost, a force-control dynamic simulation of a gait cycle can yield useful and predictable results.     

A power-law rheology-based finite element model for single cell deformation

Physical forces can elicit complex time- and space-dependent deformations in living cells. These deformations at the subcellular level are difficult to measure but can be estimated using computational approaches such as finite element (FE) simulation. Existing FE models predominantly treat cells as spring-dashpot viscoelastic materials, while broad experimental data are now lending support to the power-law rheology (PLR) model. Here, we developed a large deformation FE model that incorporated PLR and experimentally verified this model by performing micropipette aspiration on fibroblasts under various mechanical loadings. With a single set of rheological properties, this model recapitulated the diverse micropipette aspiration data obtained using three protocols and with a range of micropipette sizes. More intriguingly, our analysis revealed that decreased pipette size leads to increased pressure gradient, potentially explaining our previous counterintuitive finding that decreased pipette size leads to increased incidence of cell blebbing and injury. Taken together, our work leads to more accurate rheological interpretation of micropipette aspiration experiments than previous models and suggests pressure gradient as a potential determinant of cell injury.     

Sensitivity of the tibio-femoral response to finite element modeling parameters

A generic finite element (FE) model of the lower limb was used to study the knee response in-vivo during a one-legged hop. The approach uses an explicit FE code and a combination of estimated muscle forces and measured three-dimensional tibio-femoral kinematics and ground reaction force as input to the FE model. The sensitivity of the simulated tibio-femoral response to variations of key geometric and material parameters was investigated by performing a total of 38 different simulations. The amplitudes of both kinematic and kinetic responses were affected by the change of these parameters. For the current approach, the results suggest that while cartilage mechanical and geometric properties are very important for the estimation of tibio-femoral cartilage pressure, they have limited effects on the overall kinematic response. The study may help to better define the relative importance of modeling parameters for the development of subject-specific models.     

Hyper-viscoelastic damage modeling of whole blood clot under large deformation

Biomechanics and Modeling in Mechanobiology - Blood clots play a diametric role in our bodies as they are both vital as a wound sealant, as well as the source for many devastating diseases. In...     

Analyzing taphonomic deformation of ankylosaur skulls using retrodeformation and finite element analysis

Taphonomic deformation can make the interpretation of vertebrate fossil morphology difficult. The effects of taphonomic deformation are investigated in two ankylosaurid dinosaur taxa, Euoplocephalus tutus (to investigate effects on our understanding of intraspecific variation) and Minotaurasaurus ramachandrani (to investigate the validity of this genus). The ratio of orbit maximum rostrocaudal length to perpendicular height is used as a strain ellipse, which can be used to determine if ankylosaur skull fossils have been dorsoventrally compacted during fossilization and diagenesis. The software program Geomagic is used to retrodeform three-dimensional (3D) digital models of the ankylosaur skulls. The effects of sediment compaction are modeled using finite element analysis, and the resulting strain distributions are compared with the retrodeformed models as a test of the retrodeformation method. Taphonomic deformation can account for a large amount of intraspecific variation in Euoplocephalus, but finite element analysis and retrodeformation of Minotaurasaurus shows that many of its diagnostic features are unlikely to result from deformation.