A penetration-based finite element method for hyperelastic 3D biphasic tissues in contact. Part II: finite element simulations

The penetration method allows for the efficient finite element simulation of contact between soft hydrated biphasic tissues in diarthrodial joints. Efficiency of the method is achieved by separating the intrinsically nonlinear contact problem into a pair of linked biphasic finite element analyses, in which an approximate, spatially and temporally varying contact traction is applied to each of the contacting tissues. In Part I of this study, we extended the penetration method to contact involving nonlinear biphasic tissue layers, and demonstrated how to derive the approximate contact traction boundary conditions. The traction derivation involves time and space dependent natural boundary conditions, and requires special numerical treatment. This paper (Part II) describes how we obtain an efficient nonlinear finite element procedure to solve for the biphasic response of the individual contacting layers. In particular, alternate linearization of the nonlinear weak form, as well as both velocity-pressure, v-p, and displacement-pressure, u-p, mixed formulations are considered. We conclude that the u-p approach, with linearization of both the material law and the deformation gradients, performs best for the problem at hand. The nonlinear biphasic contact solution will be demonstrated for the motion of the glenohumeral joint of the human shoulder joint.     

Biomechanical analysis and comparison of 12 dental implant systems using 3D finite element study

Finite element analysis plays an important role in dental implant design. The objective of this study was to show the effect of the overall geometry of dental implants on their biomechanics after implantation. In this study, 12 dental implants, with the same length, diameter and screw design, were simulated from different implant systems. Numerical model of right mandibular incisor bone segment was generated from CT data. The von-Mises stress distributions and the total deformation distributions under vertical/lateral load were compared for each implant by scores ranking method. The implants with cylindrical shapes had highest scores. Results indicated that cylindrical shape represented better geometry over taper implant. This study is helpful in choosing the optimal dental implant for clinical application and also contributes to individual implant design. Our study could also provide reference for choice and modification of dental implant in any other insertion sites and bone qualities.     

A 3D finite element model of an implanted scapula: importance of a multiparametric validation using experimental data

In order to help to understand the loosening phenomenon around gleno?d prostheses, a 3D finite element model of a previously tested implanted scapula has been developed. The construction of the model was done using CT scans of the tested scapula. Different bone material properties were tested and shell elements or 8 nodes hexaedric elements were used to model the cortical bone. Surface contact elements were introduced on one hand between the bone and the lower part of the plate of the implant, and on the other, between the loading metallic ball and the upper surface of the implant. The results of the model were compared with those issued from in vitro experiments carried out on the same scapula. The evaluation of the model was done for nine cases of loading of 500 N distributed on the implant, in terms of strains (principal strains of six spots around peripheral cortex of the gleno?d) and displacement of four points positioned on the implant. The best configuration of the model presented here, fits with experiments for most of the strains (difference lower than 150microdef) but it seems to be still too stiff (mainly in the lower part). Nevertheless, we want, in this paper, to underline the importance of doing a multiparametric validation for such a model. Indeed, some models can give correct results for one case of loading but bad results for another kind of loading, some others can give good results for one kind of compared parameters (like strains for instance) but bad results for the other one (like displacements).     

Maxillary expansion treatment using bone anchors: development and validation of a 3D finite element model

Objective: Develop a finite element (FE) model of a skull to perform biomechanical studies of maxillary expansion using bone anchors (BA).

Materials and methods: A skull model was developed and assigned material properties based on Hounsfield unit (HU) values of cone-beam computerized tomography (CBCT) images. A 3 mm diameter cylindrical BA was modelled and inserted in the palatal bone. A 4 mm transverse displacement was applied on the anchor. An evaluation on the effect on local stresses of BA implantation inclination angle was performed.

Results: Proper displacement results and strain–stress trends for the expansion process were present. Stress distribution patterns were similar as reported in the literature. No significant difference between BA inclination angles was found.

Conclusion: This work leads to a better understanding and prediction of craniofacial and maxillary bone remodelling during ME with BA treatments and is a first step towards the development of patient specific treatments.     

Maxillary expansion treatment using bone anchors: development and validation of a 3D finite element model

OBJECTIVE: Develop a finite element (FE) model of a skull to perform biomechanical studies of maxillary expansion using bone anchors (BA). MATERIALS AND METHODS: A skull model was developed and assigned material properties based on Hounsfield unit (HU) values of cone-beam computerized tomography (CBCT) images. A 3 mm diameter cylindrical BA was modelled and inserted in the palatal bone. A 4 mm transverse displacement was applied on the anchor. An evaluation on the effect on local stresses of BA implantation inclination angle was performed. RESULTS: Proper displacement results and strain-stress trends for the expansion process were present. Stress distribution patterns were similar as reported in the literature. No significant difference between BA inclination angles was found. CONCLUSION: This work leads to a better understanding and prediction of craniofacial and maxillary bone remodelling during ME with BA treatments and is a first step towards the development of patient specific treatments.     

Development of a 3D finite element model of lens microcirculation

Background

It has been proposed that in the absence of a blood supply, the ocular lens operates an internal microcirculation system. This system delivers nutrients, removes waste products and maintains ionic homeostasis in the lens. The microcirculation is generated by spatial differences in membrane transport properties; and previously has been modelled by an equivalent electrical circuit and solved analytically. While effective, this approach did not fully account for all the anatomical and functional complexities of the lens. To encapsulate these complexities we have created a 3D finite element computer model of the lens.

Methods

Initially, we created an anatomically-correct representative mesh of the lens. We then implemented the Stokes and advective Nernst-Plank equations, in order to model the water and ion fluxes respectively. Next we complemented the model with experimentally-measured surface ionic concentrations as boundary conditions and solved it.

Results

Our model calculated the standing ionic concentrations and electrical potential gradients in the lens. Furthermore, it generated vector maps of intra- and extracellular space ion and water fluxes that are proposed to circulate throughout the lens. These fields have only been measured on the surface of the lens and our calculations are the first 3D representation of their direction and magnitude in the lens.

Conclusion

Values for steady state standing fields for concentration and electrical potential plus ionic and fluid fluxes calculated by our model exhibited broad agreement with observed experimental values. Our model of lens function represents a platform to integrate new experimental data as they emerge and assist us to understand how the integrated structure and function of the lens contributes to the maintenance of its transparency.     

Density-based load estimation using two-dimensional finite element models: a parametric study

A parametric investigation was conducted to determine the effects on the load estimation method of varying: (1) the thickness of back-plates used in the two-dimensional finite element models of long bones, (2) the number of columns of nodes in the outer medial and lateral sections of the diaphysis to which the back-plate multipoint constraints are applied and (3) the region of bone used in the optimization procedure of the density-based load estimation technique. The study is performed using two-dimensional finite element models of the proximal femora of a chimpanzee, gorilla, lion and grizzly bear. It is shown that the density-based load estimation can be made more efficient and accurate by restricting the stimulus optimization region to the metaphysis/epiphysis. In addition, a simple method, based on the variation of diaphyseal cortical thickness, is developed for assigning the thickness to the back-plate. It is also shown that the number of columns of nodes used as multipoint constraints does not have a significant effect on the method.     

Density-based load estimation using two-dimensional finite element models: a parametric study

A parametric investigation was conducted to determine the effects on the load estimation method of varying: (1) the thickness of back-plates used in the two-dimensional finite element models of long bones, (2) the number of columns of nodes in the outer medial and lateral sections of the diaphysis to which the back-plate multipoint constraints are applied and (3) the region of bone used in the optimization procedure of the density-based load estimation technique. The study is performed using two-dimensional finite element models of the proximal femora of a chimpanzee, gorilla, lion and grizzly bear. It is shown that the density-based load estimation can be made more efficient and accurate by restricting the stimulus optimization region to the metaphysis/epiphysis. In addition, a simple method, based on the variation of diaphyseal cortical thickness, is developed for assigning the thickness to the back-plate. It is also shown that the number of columns of nodes used as multipoint constraints does not have a significant effect on the method.     

A numerical study of the Belousov-Zhabotinskii reaction using Galerkin finite element methods

The Belousov-Zhabotinskii reaction has been modelled by Field and Noyes [5] as a pair of nonlinear parabolic equations. Previous studies of these, both theoretical and numerical, have assumed wave solutions travelling with constant velocity leading to a simplification of the mathematical model in the form of a system of ordinary differential equations. In the present study a finite element Galerkin method is used directly on the original parabolic system for a range of parameter values.     

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.     

3D finite element model of the diabetic neuropathic foot: A gait analysis driven approach

Diabetic foot is an invalidating complication of diabetes that can lead to foot ulcers. Three-dimensional (3D) finite element analysis (FEA) allows characterizing the loads developed in the different anatomical structures of the foot in dynamic conditions. The aim of this study was to develop a subject specific 3D foot FE model (FEM) of a diabetic neuropathic (DNS) and a healthy (HS) subject, whose subject specificity can be found in term of foot geometry and boundary conditions. Kinematics, kinetics and plantar pressure (PP) data were extracted from the gait analysis trials of the two subjects with this purpose. The FEM were developed segmenting bones, cartilage and skin from MRI and drawing a horizontal plate as ground support. Materials properties were adopted from previous literature. FE simulations were run with the kinematics and kinetics data of four different phases of the stance phase of gait (heel strike, loading response, midstance and push off). FEMs were then driven by group gait data of 10 neuropathic and 10 healthy subjects. Model validation focused on agreement between FEM-simulated and experimental PP.     

Modeling the biomechanics of the mandible: a three-dimensional finite element study.

Three-dimensional finite element models of a partially edentulated human mandible were generated to calculate the mechanical response to simulated isometric biting and mastication loads. The level of mesh refinement was established via a convergence test and showed that a model with over 30,000 degrees of freedom was required to obtain analysis accuracy. The functional loading cases included muscle loading based on an algorithm that assigns muscle forces in accordance with muscle cross-sectional area, while maintaining static equilibrium. Results were found for isometric application of unilateral and bilateral bite and mastication loading, and two different sets of displacement boundary conditions were imposed at the condyles. The mechanical response is shown in terms of displacements, principal strains, and a new measure called the 'mechanical intensity scalar'. For each load case studied, there was substantial bending in the molar region of the corpus and high tensile strains in the anterior portion of the ramus.     

Failure locus of the anterior cruciate ligament: 3D finite element analysis

Anterior cruciate ligament (ACL) disruption is a common injury that is detrimental to an athlete's quality of life. Determining the mechanisms that cause ACL injury is important in order to develop proper interventions. A failure locus defined as various combinations of loadings and movements, internal/external rotation of femur and valgus and varus moments at a 25^o knee flexion angle leading to ACL failure was obtained. The results indicated that varus and valgus movements were more dominant to the ACL injury than femoral rotation. Also, Von Mises stress in the lateral tibial cartilage during the valgus ACL injury mechanism was 83% greater than that of the medial cartilage during the varus mechanism of ACL injury. The results of this study could be used to develop training programmes focused on the avoidance of the described combination of movements which may lead to ACL injury.     

Failure locus of the anterior cruciate ligament: 3D finite element analysis

Anterior cruciate ligament (ACL) disruption is a common injury that is detrimental to an athlete's quality of life. Determining the mechanisms that cause ACL injury is important in order to develop proper interventions. A failure locus defined as various combinations of loadings and movements, internal/external rotation of femur and valgus and varus moments at a 25(o) knee flexion angle leading to ACL failure was obtained. The results indicated that varus and valgus movements were more dominant to the ACL injury than femoral rotation. Also, Von Mises stress in the lateral tibial cartilage during the valgus ACL injury mechanism was 83% greater than that of the medial cartilage during the varus mechanism of ACL injury. The results of this study could be used to develop training programmes focused on the avoidance of the described combination of movements which may lead to ACL injury.     

Mechanical characterisation of in vivo human skin using a 3D force-sensitive micro-robot and finite element analysis

The complex mechanical properties of skin have been the subject of much study in recent years. Several experimental methods developed to measure the mechanical properties of skin in vivo, such as suction or torsion, are unable to measure skin’s anisotropic characteristics. An experiment characterising the mechanical properties of in vivo human skin using a novel force-sensitive micro-robot is presented. The micro-robot applied in-plane deformations to the anterior forearm and the posterior upper arm. The behaviour of the skin in each area is highly nonlinear, anisotropic, and viscoelastic. The response of the upper arm skin is very dependent on the orientation of the arm. A finite element model consisting of an Ogden strain energy function and quasi-linear viscoelasticity was developed to simulate the experiments. An orthogonal initial stress field, representing the in vivo skin tension, was used as an additional model parameter. The model simulated the experiments accurately with an error-of-fit of 17.5% for the anterior lower forearm area, 6.5% for the anterior upper forearm and 9.3% for the posterior upper arm. The maximum in vivo tension in each area determined by the model was 6.2 Nm⁻¹ in the anterior lower forearm, 11.4 Nm⁻¹ in anterior upper forearm and 5.6 Nm⁻¹ in the posterior upper arm. The results also show that a finite element model with a neo-Hookean strain energy function cannot simulate the experiments with the same accuracy.     

Failure analysis of a new post-and-core restoration system using the finite element method

Human teeth with substantial coronal defects are subject to reconstruction by means of post-and-core restorations. Typically, such a restoration comprises a slightly cylindrical post onto which an abutment of varying shape, depending on the designated restoration, is attached. As clinical results are not satisfactory to date, a new post-and-core design which makes use of positive locking (rather than relying on chemical bonding agents for retention in the residual root) was proposed. Using proprietary burs, an inversely conical hole is machined into the root, into which the prefabricated post-and-core restoration is inserted. This part can be spread at the bottom to match the cavity's undercut form, resulting in a positive lock which can only be separated by destruction of root, restoration or both. Another key feature of this system is a ring/groove geometry which is able to absorb the wedging forces created by said spreading and the stress of loading of the restoration which arises from mascatory forces. To assess the properties, especially in terms of the stress imposed on the remaining tooth at highest possible loading, both finite element simulations and in vitro failure tests were performed and the findings compared. The results suggest that the parameters of the finite element simulations are in good agreement with reality. As calculated and measured force levels immediately before failure of the restoration are high, the introduced new geometry has significant advantages over the classical restoration.     

A novel methodology for generating 3D finite element models of the hip from 2D radiographs

Finite element (FE) modelling has been proposed as a tool for estimating fracture risk and patient-specific FE models are commonly based on computed tomography (CT). Here, we present a novel method to automatically create personalised 3D models from standard 2D hip radiographs. A set of geometrical parameters of the femur were determined from seven a–p hip radiographs and compared to the 3D femoral shape obtained from CT as training material; the error in reconstructing the 3D model from the 2D radiographs was assessed. Using the geometry parameters as the input, the 3D shape of another 21 femora was built and meshed, separating a cortical and trabecular compartment. The material properties were derived from the homogeneity index assessed by texture analysis of the radiographs, with focus on the principal tensile and compressive trabecular systems. The ability of these FE models to predict failure load as determined by experimental biomechanical testing was evaluated and compared to the predictive ability of DXA. The average reconstruction error of the 3D models was 1.77 mm (±1.17 mm), with the error being smallest in the femoral head and neck, and greatest in the trochanter. The correlation of the FE predicted failure load with the experimental failure load was r²=64% for the reconstruction FE model, which was significantly better (p<0.05) than that for DXA (r²=24%). This novel method for automatically constructing a patient-specific 3D finite element model from standard 2D radiographs shows encouraging results in estimating patient-specific failure loads.     

A generic 3D finite element model of tree anchorage integrating soil mechanics and real root system architecture

Understanding the mechanism of tree anchorage in a forest is a priority because of the increase in wind storms in recent years and their projected recurrence as a consequence of global warming. To characterize anchorage mechanisms during tree uprooting, we developed a generic finite element model where real three-dimensional (3D) root system architectures were represented in a 3D soil. The model was used to simulate tree overturning during wind loading, and results compared with real data from two poplar species (Populus trichocarpa and P. deltoides). These trees were winched sideways until failure, and uprooting force and root architecture measured. The uprooting force was higher for P. deltoides than P. trichocarpa, probably due to its higher root volume and thicker lateral roots. Results from the model showed that soil type influences failure modes. In frictional soils, e.g., sandy soils, plastic failure of the soil occurred mainly on the windward side of the tree. In cohesive soils, e.g., clay soils, a more symmetrical slip surface was formed. Root systems were more resistant to uprooting in cohesive soil than in frictional soil. Applications of this generic model include virtual uprooting experiments, where each component of anchorage can be tested individually.     

3D finite element model of biofilm detachment using real biofilm structures from CLSM data

In this work, a three‐dimensional model of fluid–structure interactions (FSI) in biofilm systems is developed in order to simulate biofilm detachment as a result of mechanical processes. Therein, fluid flow past the biofilm surface results in a mechanical load on the structure which in turn causes internal stresses in the biofilm matrix. When the strength of the matrix is exceeded parts of the structure are detached. The model is used to investigate the influence of several parameters related to the mechanical strength of the biofilm matrix, Young's modulus, Reynolds number, and biofilm structure on biofilm detachment. Variations in biofilm strength and flow conditions significantly influence the simulation outcome. With respect to structural properties the model is widely independent from a change of Young's modulus. A further result of this work indicates that the change of biofilm structure due to growth or other processes will significantly change the stress distribution in the biofilm and thereby the detachment rate. An increase of the mechanical load by increasing fluid flow results in a flat surface of the remaining biofilm structure. It is concluded that the change of structure during biofilm development is the key determinant in terms of the detachment behavior. Biotechnol. Bioeng. 2009;103: 177–186. © 2008 Wiley Periodicals, Inc.