A three-dimensional inverse finite element analysis of the heel pad

Quantification of plantar tissue behavior of the heel pad is essential in developing computational models for predictive analysis of preventive treatment options such as footwear for patients with diabetes. Simulation based studies in the past have generally adopted heel pad properties from the literature, in return using heel-specific geometry with material properties of a different heel. In exceptional cases, patient-specific material characterization was performed with simplified two-dimensional models, without further evaluation of a heel-specific response under different loading conditions. The aim of this study was to conduct an inverse finite element analysis of the heel in order to calculate heel-specific material properties in situ. Multidimensional experimental data available from a previous cadaver study by Erdemir et al. ("An Elaborate Data Set Characterizing the Mechanical Response of the Foot," ASME J. Biomech. Eng., 131(9), pp. 094502) was used for model development, optimization, and evaluation of material properties. A specimen-specific three-dimensional finite element representation was developed. Heel pad material properties were determined using inverse finite element analysis by fitting the model behavior to the experimental data. Compression dominant loading, applied using a spherical indenter, was used for optimization of the material properties. The optimized material properties were evaluated through simulations representative of a combined loading scenario (compression and anterior-posterior shear) with a spherical indenter and also of a compression dominant loading applied using an elevated platform. Optimized heel pad material coefficients were 0.001084 MPa (μ), 9.780 (α) (with an effective Poisson's ratio (ν) of 0.475), for a first-order nearly incompressible Ogden material model. The model predicted structural response of the heel pad was in good agreement for both the optimization (<1.05% maximum tool force, 0.9% maximum tool displacement) and validation cases (6.5% maximum tool force, 15% maximum tool displacement). The inverse analysis successfully predicted the material properties for the given specimen-specific heel pad using the experimental data for the specimen. The modeling framework and results can be used for accurate predictions of the three-dimensional interaction of the heel pad with its surroundings.     

Trabecular bone fracture healing simulation with finite element analysis and fuzzy logic

Trabecular bone fractures heal through intramembraneous ossification. This process differs from diaphyseal fracture healing in that the trabecular marrow provides a rich vascular supply to the healing bone, there is very little callus formation, woven bone forms directly without a cartilage intermediary, and the woven bone is remodelled to form trabecular bone. Previous studies have used numerical methods to simulate diaphyseal fracture healing or bone remodelling, however not trabecular fracture healing, which involves both tissue differentiation and trabecular formation. The objective of this study was to determine if intramembraneous bone formation and remodelling during trabecular bone fracture healing could be simulated using the same mechanobiological principles as those proposed for diaphyseal fracture healing. Using finite element analysis and the fuzzy logic for diaphyseal healing, the model simulated formation of woven bone in the fracture gap and subsequent remodelling of the bone to form trabecular bone. We also demonstrated that the trabecular structure is dependent on the applied loading conditions. A single model that can simulate bone healing and remodelling may prove to be a useful tool in predicting musculoskeletal tissue differentiation in different vascular and mechanical environments.     

Comparison of microCT and an inverse finite element approach for biomechanical analysis: results in a mesenchymal stem cell therapeutic system for fracture healing

An important concern in the study of fracture healing is the ability to assess mechanical integrity in response to candidate therapeutics in small-animal systems. In recent reports, it has been proposed that microCT image-derived densitometric parameters could be used as a surrogate for mechanical property assessment. Recently, we have proposed an inverse methodology that iteratively reconstructs the modulus of elasticity of the lumped soft callus/hard callus region by integrating both intrinsic mechanical property (from biomechanical testing) and geometrical information (from microCT) within an inverse finite element analysis (FEA) to define a callus quality measure. In this paper, data from a therapeutic system involving mesenchymal stem cells is analyzed within the context of comparing traditional microCT densitometric and mechanical property metrics. In addition, a novel multi-parameter regression microCT parameter is analyzed as well as our inverse FEA metric. The results demonstrate that the inverse FEA approach was the only metric to successfully detect both longitudinal and therapeutic responses. While the most promising microCT-based metrics were adequate at early healing states, they failed to track late-stage mechanical integrity. In addition, our analysis added insight to the role of MSCs by demonstrating accelerated healing and was the only metric to demonstrate therapeutic benefits at late-stage healing. In conclusion, the work presented here indicates that microCT densitometric parameters are an incomplete surrogate for mechanical integrity. Additionally, our inverse FEA approach is shown to be very sensitive and may provide a first-step towards normalizing the often challenging process of assessing mechanical integrity of healing fractures.     

Dynamic analysis of a simplified bone model during the process of fracture healing

The dynamic analysis of fracture healing is tackled numerically by means of a bone model which uses the finite element method. The model is of non-uniform cross-sectional area and moment of inertia. Shear and rotatory inertia are taken into account. Considerable variation of the upper natural frequencies is observed as the healing process progresses. The practical implications, as well as present limitations, of the technique are examined.     

A finite element analysis methodology for representing the articular cartilage functional structure

Recognising that the unique biomechanical properties of articular cartilage are a consequence of its structure, this paper describes a finite element methodology which explicitly represents this structure using a modified overlay element model. The validity of this novel concept was then tested by using it to predict the axial curling forces generated by cartilage matrices subjected to saline solutions of known molality and concentration in a novel experimental protocol. Our results show that the finite element modelling methodology accurately represents the intrinsic biomechanical state of the cartilage matrix and can be used to predict its transient load-carriage behaviour. We conclude that this ability to represent the intrinsic swollen condition of a given cartilage matrix offers a viable avenue for numerical analysis of degenerate articular cartilage and also those matrices affected by disease.     

A numerical approach to the biomechanical analysis of bone fracture healing

Investigations are reported in the literature, by means of experimental, analytical and numerical methods, concerning the biomechanical properties of bone. However, the evolutionary phenomena of bone fracture healing does not have a large reference literature. This work investigates and describes the behaviour of inclined human femur fractures with external fixation up to complete healing. A numerical formulation based on the finite element method has been adopted. Geometric configuration is defined using data from a magnetic resonance process applied to a femur in vivo. A three dimensional model has been developed by adopting an orthotropic material law for cortical bone and an isotropic law for the fracture gap zone. Stress and strain reponses of the bone and fixation device are investigated with reference to the evolutionary behaviour of the healing tissue.     

A finite element model of an anthropomorphic test device lower limb to assess risk of injuries during vertical accelerative loading

Improvised explosive devices (IEDs) were used extensively to target occupants of military vehicles during the conflicts in Iraq and Afghanistan (2003–2011). War fighters exposed to an IED attack were highly susceptible to lower limb injuries. To appropriately assess vehicle safety and make informed improvements to vehicle design, a novel Anthropomorphic Test Device (ATD), called the Warrior Injury Assessment Manikin (WIAMan), was designed for vertical loading. The main objective of this study was to develop and validate a Finite Element (FE) model of the WIAMan lower limb (WIAMan-LL). Appropriate materials and contacts were applied to realistically model the physical dummy. Validation of the model was conducted based on experiments performed on two different test rigs designed to simulate the vertical loading experienced during an under-vehicle explosion. Additionally, a preliminary evaluation of the WIAMan and Hybrid-III test devices was performed by comparing force responses to post-mortem human surrogate (PMHS) corridors. The knee axial force recorded by the WIAMan-LL when struck on the plantar surface of the foot (2 m/s) fell mostly within the PMHS corridor, but the corresponding data predicted by the Hybrid-III was almost 60% higher. Overall, good agreements were observed between the WIAMan-LL FE predictions and experiments at various pre-impact speeds ranging from 2 m/s up to 5.8 m/s. Results of the FE model were backed by mean objective rating scores of 0.67–0.76 which support its accuracy relative to the physical lower limb dummy. The observations and objective rating scores show the model is validated within the experimental loading conditions. These results indicate the model can be used in numerical studies related to possible dummy design improvements once additional PMHS data is available. The numerical lower limb is currently incorporated into a whole body model that will be used to evaluate the vehicle design for underbody blast protection.     

A sub-domain inverse finite element characterization of hyperelastic membranes including soft tissues

Quantification of the mechanical behavior of hyperelastic membranes in their service configuration, particularly biological tissues, is often challenging because of the complicated geometry, material heterogeneity, and nonlinear behavior under finite strains. Parameter estimation thus requires sophisticated techniques like the inverse finite element method. These techniques can also become difficult to apply, however, if the domain and boundary conditions are complex (e.g. a non-axisymmetric aneurysm). Quantification can alternatively be achieved by applying the inverse finite element method over sub-domains rather than the entire domain. The advantage of this technique, which is consistent with standard experimental practice, is that one can assume homogeneity of the material behavior as well as of the local stress and strain fields. In this paper, we develop a sub-domain inverse finite element method for characterizing the material properties of inflated hyperelastic membranes, including soft tissues. We illustrate the performance of this method for three different classes of materials: neo-Hookean, Mooney Rivlin, and Fung-exponential.     

A three-dimensional finite element analysis of the upper tibia

A three-dimensional finite element model of the proximal tibia has been developed to provide a base line for further modeling of prosthetic resurfaced tibiae. The geometry for the model was developed by digitizing coronal and transverse sections made with the milling machine, from one fresh tibia of average size. The load is equally distributed between the medial and lateral compartments over contact areas that were reported in the literature. An indentation test has been used to measure the stiffness and the ultimate strength of cancellous bone in four cadaver tibiae. These values provided the statistical basis for characterising the inhomogeneous distribution of the cancellous bone properties in the proximal tibia. All materials in the model were assumed to be linearly elastic and isotropic. Mechanical properties for the cortical bone and cartilage have been taken from the literature. Results have been compared with strain gage tests and with a two-dimensional axisymmetric finite element model both from the literature. Qualitative comparison between trabecular alignment, and the direction of the principal compressive stresses in the cancellous bone, showed a good relationship. Maximum stresses in the cancellous bone and cortical bone, under a load which occurs near stance phase during normal gait, show safety factors of approximately eight and twelve, respectively. The load sharing between the cancellous bone and the cortical bone has been plotted for the first 40 mm distally from the tibial eminence.     

Material properties of the ovine mitral valve anterior leaflet in vivo from inverse finite element analysis

We measured leaflet displacements and used inverse finite-element analysis to define, for the first time, the material properties of mitral valve (MV) leaflets in vivo. Sixteen miniature radiopaque markers were sewn to the MV annulus, 16 to the anterior MV leaflet, and 1 on each papillary muscle tip in 17 sheep. Four-dimensional coordinates were obtained from biplane videofluoroscopic marker images (60 frames/s) during three complete cardiac cycles. A finite-element model of the anterior MV leaflet was developed using marker coordinates at the end of isovolumic relaxation (IVR; when the pressure difference across the valve is approximately 0), as the minimum stress reference state. Leaflet displacements were simulated during IVR using measured left ventricular and atrial pressures. The leaflet shear modulus (G(circ-rad)) and elastic moduli in both the commisure-commisure (E(circ)) and radial (E(rad)) directions were obtained using the method of feasible directions to minimize the difference between simulated and measured displacements. Group mean (+/-SD) values (17 animals, 3 heartbeats each, i.e., 51 cardiac cycles) were as follows: G(circ-rad) = 121 +/- 22 N/mm2, E(circ) = 43 +/- 18 N/mm2, and E(rad) = 11 +/- 3 N/mm2 (E(circ) > E(rad), P < 0.01). These values, much greater than those previously reported from in vitro studies, may result from activated neurally controlled contractile tissue within the leaflet that is inactive in excised tissues. This could have important implications, not only to our understanding of mitral valve physiology in the beating heart but for providing additional information to aid the development of more durable tissue-engineered bioprosthetic valves.     

Cement flow during impaction allografting: a finite element analysis

Cement intrusion into cancellous or impacted bone is not well understood. We adopted an engineering mechanics approach to predict the effect of surgical variables on the cement intrusion into impacted cancellous bone, used for the revision of failed total hip replacement with the impaction allografting technique. Specifically, a three-dimensional finite element model was used to determine the effects of cement viscosity, the magnitude and duration of pressurization, and the distribution of the porosity along the femur on cement intrusion. The overall averaged mean intrusion depth difference between the finite element model prediction and the cadaveric measurements was 1.1mm. The depth of penetration increased with higher pressurization pressure, duration of pressurization, and earlier stem insertion (lower viscosity), but maintained a similar profile. The distribution of the porosity along the femur determined the intrusion profile. Cement viscosity, the applied pressure or the duration of the pressurization can be adjusted to limit the cement volume injected into the medullary canal and therefore prevent the cement from reaching the endosteal surface.     

Multi-scale finite element modelling at the posterior lumbar vertebra: analysis of pedicle stresses due to pars fracture

Multi-scale finite element (FE) model is a cost-effective way to analyse stress response of micro-level structures to the changes in loading at macro-level. This study deals with the development of a multi-scale model of a human vertebra and stress changes in the pedicle at high resolution after a gross fracture at the posterior neural arch. Spondylolysis (pars fracture) is a painful condition occurring in the vertebral neural arch and common especially among the athletic young population. The fracture of the pars significantly alters load distribution and load transfer characteristics at the neural arch. Structural changes in the posterior vertebra due to the new loading patterns can trigger secondary complications. Clinical reports have shown the association of pedicle hypertrophy or pedicle fracture with unilateral pars fractures. However, the biomechanical consequences of pars fracture and its effect on the pedicle have never been studied in detail. Therefore, we prepared a multi-scale model of posterior vertebra with continuum laminar complex model combined with micro-FE model of a pedicle section. The results showed that stress at the contralateral pars and pedicle increased after unilateral pars fracture simulation. High-stress regions were found around the outer boundaries of the pedicle. This model and information are helpful in understanding the stress changes in the pedicle and can be used for adaptive remodelling studies.     

Comparison of plate-screw systems used in mandibular fracture reduction: finite element analysis

A finite element model of the human dentate mandible has been developed to provide a comparison of fixation systems used currently for fracture reduction. Volume domains for cortical bone, cancellous bone, and teeth were created and meshed in ANSYS 8.0 based on IGES curves created from computerized tomography data. A unilateral molar clench was loaded on the model with a fracture gap simulated along the symphysis. Results based on Von Mises stress in cortical and cancellous bone surrounding the screws, and on fracture surface spatial fixation, show some relative differences between different screw-plate systems, yet all were judged to be appropriate in their reduction potential.     

A finite element analysis of masticatory stress hypotheses

Understanding how the skull transmits and dissipates forces during feeding provides insights into the selective pressures that may have driven the evolution of primate skull morphology. Traditionally, researchers have interpreted masticatory biomechanics in terms of simple global loading regimes applied to simple shapes (i.e., bending in sagittal and frontal planes, dorsoventral shear, and torsion of beams and cylinders). This study uses finite element analysis to examine the extent to which these geometric models provide accurate strain predictions in the face and evaluate whether simple global loading regimes predict strains that approximate the craniofacial deformation pattern observed during mastication. Loading regimes, including those simulating peak loads during molar chewing and those approximating the global loading regimes, were applied to a previously validated finite element model (FEM) of a macaque (Macaca fascicularis) skull, and the resulting strain patterns were compared. When simple global loading regimes are applied to the FEM, the resulting strains do not match those predicted by simple geometric models, suggesting that these models fail to generate accurate predictions of facial strain. Of the four loading regimes tested, bending in the frontal plane most closely approximates strain patterns in the circumorbital region and lateral face, apparently due to masseter muscle forces acting on the zygomatic arches. However, these results indicate that no single simple global loading regime satisfactorily accounts for the strain pattern found in the validated FEM. Instead, we propose that FE models replace simple cranial models when interpreting bone strain data and formulating hypotheses about craniofacial biomechanics.     

A voxel-based formulation for contact finite element analysis

To date, voxel-based finite element models have not been feasible for contact problems, owing to the inherent stair-step boundary discontinuities. New preprocessing techniques are reported herein to mesh these boundaries smoothly, for purposes of contact stress analysis. Further, new techniques are reported to concentrate the mesh resolution automatically near the articular surface, thus reducing the problem size to levels compatible with executing nonlinear problems on contemporary engineering workstations. Close approximations to Hertzian analytical solutions were obtained for spherical and cylindrical geometries meshed in this manner, and an illustrative anatomical contact problem of the human hip joint is presented.     

Three-dimensional finite element analysis of the foot during standing--a material sensitivity study

Information on the internal stresses/strains in the human foot and the pressure distribution at the plantar support interface under loading is useful in enhancing knowledge on the biomechanics of the ankle-foot complex. While techniques for plantar pressure measurements are well established, direct measurement of the internal stresses/strains is difficult. A three-dimensional (3D) finite element model of the human foot and ankle was developed using the actual geometry of the foot skeleton and soft tissues, which were obtained from 3D reconstruction of MR images. Except the phalanges that were fused, the interaction among the metatarsals, cuneiforms, cuboid, navicular, talus, calcaneus, tibia and fibula were defined as contact surfaces, which allow relative articulating movement. The plantar fascia and 72 major ligaments were simulated using tension-only truss elements by connecting the corresponding attachment points on the bone surfaces. The bony and ligamentous structures were embedded in a volume of soft tissues. The encapsulated soft tissue was defined as hyperelastic, while the bony and ligamentous structures were assumed to be linearly elastic. The effects of soft tissue stiffening on the stress distribution of the plantar surface and bony structures during balanced standing were investigated. Increases of soft tissue stiffness from 2 and up to 5 times the normal values were used to approximate the pathologically stiffened tissue behaviour with increasing stages of diabetic neuropathy. The results showed that a five-fold increase in soft tissue stiffness led to about 35% and 33% increase in the peak plantar pressure at the forefoot and rearfoot regions, respectively. This corresponded to about 47% decrease in the total contact area between the plantar foot and the horizontal support surface. Peak bone stress was found at the third metatarsal in all calculated cases with a minimal increase of about 7% with soft tissue stiffening.     

Biomechanical properties of the rat sclera obtained with inverse finite element modeling

Biomechanics and Modeling in Mechanobiology - It is widely accepted that biomechanics plays an important role in glaucoma pathophysiology, but the mechanisms involved are largely unknown. Rats are...     

A contact-coupled finite element analysis of the natural adult hip

A non-linear two-dimensional finite element model was used to study phenomena of stress redistribution in the natural adult hip resulting from parametric material property variations in the juxtarticular regions of the femoral head. Despite the geometrical simplifications employed, the intra-articular contact stresses (computed using the FEAP program) were found to be in reasonable qualitative agreement with previous in vitro data for the case of a normal hip. Generalized sclerotic changes in the subchondral plate, as reflected either in apparent modulus increases or in plate thickening, were found to have only minor effects on the computed contact stress distribution, although stress levels within the plate itself were markedly influenced. Localized subchondral plate sclerosis, by contrast, led to marked stress elevations in the cartilage immediately overlying the stiffened bone. Cartilage modulus increases caused increased load uptake for a given imposed deformation, but involved stress distribution increases which were very nearly linearly proportional to the increases in resultant load magnitude. Friction coefficient elevations had no noticeable effects on normal contact stress or upon overall load transmission, but involved complex, possibly slip-related, changes in intra-articular and cartilaginous shear stresses.