Finite element analysis of bone remodelling with piezoelectric effects using an open-source framework

Bone tissue exhibits piezoelectric properties and thus is capable of transforming mechanical stress into electrical potential. Piezoelectricity has been shown to play a vital role in bone adaptation and remodelling processes. Therefore, to better understand the interplay between mechanical and electrical stimulation during these processes, strain-adaptive bone remodelling models without and with considering the piezoelectric effect were simulated using the Python-based open-source software framework. To discretise numerical attributes, the finite element method (FEM) was used for the spatial variables and an explicit Euler scheme for the temporal derivatives. The predicted bone apparent density distributions were qualitatively and quantitatively evaluated against the radiographic scan of a human proximal femur and the bone apparent density calculated using a bone mineral density (BMD) calibration phantom, respectively. Additionally, the effect of the initial bone density on the resulting predicted density distribution was investigated globally and locally. The simulation results showed that the electrically stimulated bone surface enhanced bone deposition and these are in good agreement with previous findings from the literature. Moreover, mechanical stimuli due to daily physical activities could be supported by therapeutic electrical stimulation to reduce bone loss in case of physical impairment or osteoporosis. The bone remodelling algorithm implemented using an open-source software framework facilitates easy accessibility and reproducibility of finite element analysis made.

     

Finite element thermal analysis of bone cement for joint replacements

A finite element technique was developed to investigate the thermal behavior of bone cement in joint replacement procedures. Thermal tests were designed and performed to provide the parameters in a kinetic model of bone cement exothermic polymerization. The kinetic model was then coupled with an energy balance equation using a finite element formulation to predict the temperature history and polymerization development in the bone-cement-prosthesis system. Based on the temperature history, the possibility of the thermal bone necrosis was then evaluated. As a demonstration, the effect of cement mantle thickness on the thermal behavior of the system was investigated. The temperature profiles in the bone-cement-prosthesis system have shown that the thicker the cement, the higher the peak temperature in the bone. In the 7 mm thick cement case, a peak temperature of over 55 degrees C was predicted. These high temperatures occurred in a small region near the bone/cement interface. No damage was predicted in the 3 mm and 5 mm cement mantle thickness cases. Although thermal damage was predicted in the bone for the 7 mm mantle thickness case, the amount of thermal necrosis predicted was minimal. If more cement is used in the surgical procedure, more heat will be generated and the potential for thermal bone damage may rise. The systems should be carefully selected to reduce thermal tissue damage when more cement is used. The methodology developed in this paper provides a numerical tool for the quantitative simulation of the thermal behavior of bone-cement-prosthesis designs.     

Finite element analysis of a three-dimensional open-celled model for trabecular bone

Based on a regular array of cubic unit cells, each containing a body-centered spherical void, we created an idealized three-dimensional model for both subchondral trabecular bone and a class of porous foams. By considering only face-to-face stacking of unit cells, the inherent symmetry was such that, except at the surface, the displacements and stresses within any one unit cell were representative of the entire porous structure. Using prescribed displacements the model was loaded in both uniaxial compressive strain and uniaxial shear strain. Based on the response to these loads, we found the tensor of elastic constants for an equivalent homogeneous elastic solid with cubic symmetry. We then compared the predicted modulus with our experimental values for bovine trabecular bone and literature values for an open-celled latex rubber foam.     

Finite element analysis for the evaluation of protective functions of helmets against ballistic impact

The ballistic impact of a human head model protected by a Personnel Armor System Ground Troops Kevlar^® helmet is analysed using the finite element method. The emphasis is to examine the effect of the interior cushioning system as a shock absorber in mitigating ballistic impact to the head. The simulations of the frontal and side impacts of the full metal jacket (FMJ) and fragment-simulating projectile (FSP) were carried out using LS-DYNA. It was found that the Kevlar^® helmet with its interior nylon and leather strap was able to defeat both the FMJ and FSP without the projectiles penetrating the helmet. However, the head injuries caused by the FMJ impact can be fatal due to the high stiffness of the interior strap. The bulge section at the side of the Kevlar^® helmet had more room for deformation that resulted in less serious head injuries.     

Finite element modeling of trabecular bone damage

This paper presents a finite element-based, computational model for analysis of structural damage to trabecular bone tissues. A modulus reduction method was formulated from elasto-plasticity theory, and was used to account for site-specific trabecular bone tissue damage. Trabecular bone tissue damage is illustrated using a large-scale, anatomically accurate, two-dimensional, microstructural finite element model of a human thoracic vertebral body. Four models with varying specifications for damage accumulation were subjected to compressive loading and unloading cycles. The numerical results and experimental validation demonstrated that the modulus reduction method reproduced the non-linear mechanical behaviour of vertebal trabecular bone. The iterative computational approach presented provides a methodology to study trabecular bone damage, and should provide researchers with a computational approach to study bone fracture and repair and to predict vertebral fragility.     

Finite element evaluation of the AIA shear specimen for bone

An elastic-plastic finite element analysis is performed on the AIA shear specimen to evaluate its effectiveness to yield ultimate shear strength values. The effect of geometry, material properties, and yield criteria are discussed in the light of applications to human femoral cortical bone. Specimen dimensions are noted as follows: W, width, D, hole diameter and H, distance between holes. As the H/D ratio increases the stress distribution tends more toward pure shear at the same time the overshoot in the shear distribution increases. An H/D ratio equal to 1.2-1.5 is optimal. The H/W parameter does not affect the overshoot noticeably but it does slightly affect the purity of shear. The material parameters do affect the performance of the shear specimen. However, the effect of the material parameters are far more pronounced in the anisotropic case than it is in the isotropic case. In the isotropic case, the Young modulus does not affect the overshoot. The increase in Poisson's ratio does slightly decrease the overshoot. For the anisotropic case, the increase in the ratio of shear modulus to Young modulus in the transverse direction (G/E2) results in an increase in the overshoot (in the shear distribution). The increase in the ratio of the Young modulus in the transverse direction to that of the axial direction (E2/E1) also results in an increase in the overshoot. Creating a notch at the top of the hole is shown to have the effect of decreasing the overshoot. Its effect on the purity of the shear is rather slight. It is found that plasticity is initiated at the sides of the two holes where the tensile normal stresses are maximum. The plastic region first expands around the perimeter of the hole then radially outward; and finally, it expands into the significant region. If the W/H parameter is less than 5, a sizable portion of the width of the specimen around the hole can go plastic with the significant region still being in the elastic state. Such a situation can cause tearing of the specimen across the width. A W/H ratio of 6 or more can prevent that danger. It is also found that the onset of plasticity brings about higher overshoot and higher purity of shear. The notched shear specimen performs better in actual tests and is more reliable in producing shear failures. The shear strength results obtained from AIA shear tests tend to confirm those shear strength results obtained from torsion tests.     

Finite element analysis of covered microstents

Currently available neuroendovascular devices are inadequate for effective treatment of many wide-necked or fusiform intracranial aneurysms and intracranial carotid-cavernous fistulae (CCF). Placing a covered microstent across the intracranial aneurysm neck and CCF rent could restore normal vessel morphology by preventing blood flow into the aneurysm lumen or CCF rent. To fabricate covered microstents, our research group has developed highly flexible ultra thin (approximately 150 microm) silicone coverings and elastomerically captured them onto commercially available metal stents without stitching. Preliminary in vivo studies were conducted by placing these covered microstents in the common carotid artery of rabbits. The feasibility of using covered stents was demonstrated. However, the cover affected the deployment pressure and the stents failed occasionally during deployment due to tearing of the cover. Appropriate modeling of covered stents will assist in designing suitable coverings, and help to reduce the failure rate of covered microstents. The purpose of this study is to use the finite element method to determine the mechanical properties of the covered microstent and investigate the effects of the covering on the mechanical behavior of the covered microstent. Variations in the mechanical properties of the covered microstent such as deployment pressure, elastic recoil and longitudinal shortening due to change in thickness and material properties of the cover have been investigated. This work is also important for custom design of covered microstents such as adding cutout holes to save adjacent perforating arteries.     

Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques

In this study, we investigate if finite element (FE) analyses of human trabecular bone architecture based on 168 μm images can provide relevant information about the bone mechanical characteristics. Three human trabecular bone samples, one taken from the femoral head, one from the iliac crest, and one from the lumbar spine, were imaged with micro-computed tomography (micro-CT) using a 28 μm resolution. After reconstruction the resolution was coarsened to 168 μm. First, all reconstructions were thresholded and directly converted to FE-models built of hexahedral elements. For the coarser resolutions of two samples, this resulted in a loss of trabecular connections and a subsequent loss of stiffness. To reduce this effect, a tetrahedral element meshing based on the marching cubes algorithm, as well as a modified hexahedron meshing, which thresholds the image such that load carrying bone mass is preserved, were employed. For each sample elastic moduli and tissue Von Mises stresses of the three different 168 μm models were compared to those from the hexahedron 28 μm model. For one sample the hexahedron meshing at 168 μm produced excellent results. For the other two samples the results obtained from the hexahedral models at 168 μm resolution were poor. Considerably better results were attained for these samples when using the mass-compensated or tetrahedron meshing techniques. We conclude that the accuracy of the FE-models at 168 μm strongly depends on the bone morphology, in particular its trabecular thickness. A substantial loss of trabecular connections during the hexahedron meshing process indicates that poor FE results will be obtained. In this case the tetrahedron or mass-compensated hexahedron meshing techniques can reduce the loss of connections and produce better results than the plain hexahedron meshing techniques.     

Finite element modelling of polymethylmethacrylate flow through cancellous bone

A mathematical model based on the Finite Element Method is developed to simulate the non-linear flow of acrylic bone cement through cancellous bone. The cancellous bone bed is modelled as a bed of parallel capillaries filled with equal spaced toroidal trabeculae. By manipulating the relative size of the torus and the capillary, the flow within bone of varying porosity is simulated. An apparent permeability based on the volume weighted average viscosity and Darcy's law is developed to describe the flow of the acrylic through the cancellous bone bed. The model predicts a cancellous bone permeability of 5.6 x 10(-9)-8.3 x 10(-9) m2 for linear flow. The non-linear behavior of the acrylic cement results in an increase of apparent permeability when compared to the permeability computed for linear flow. Estimates of penetration are achieved by running the model in a quasi-steady state fashion with pressure applied over a fixed time increment. Close agreement is shown between model predictions of penetration depth and experimental results available in the literature.     

Finite element simulation of the mechanical impact of computer work on the carpal tunnel syndrome

Carpal tunnel syndrome (CTS) is a clinical disorder resulting from the compression of the median nerve. The available evidence regarding the association between computer use and CTS is controversial. There is some evidence that computer mouse or keyboard work, or both are associated with the development of CTS. Despite the availability of pressure measurements in the carpal tunnel during computer work (exposure to keyboard or mouse) there are no available data to support a direct effect of the increased intracarpal canal pressure on the median nerve.     

Finite element displacement analysis of a lung

There is considerable physiological evidence that the regional variation in pleural pressure and expansion of the lung is largely determined by gravity. In this paper a method is given based on the technique of finite elements which determines theoretically the mechanical behaviour of a lung-shaped body loaded by its own weight. The results of this theoretical analysis have been compared with actual measurements of alveolar size and pleural pressures in animal lungs.     

Investigating the mechanical response of paediatric bone under bending and torsion using finite element analysis

Fractures of bone account 25% of all paediatric injuries (Cooper et al. in J Bone Miner Res 19:1976–1981, 2004.  https://doi.org/10.1359/JBMR.040902). These can be broadly categorised into accidental or inflicted injuries. The current clinical approach to distinguish between these two is based on the clinician’s judgment, which can be subjective. Furthermore, there is a lack of studies on paediatric bone to provide evidence-based information on bone strength, mainly due to the difficulties of obtaining paediatric bone samples. There is a need to investigate the behaviour of children’s bones under external loading. Such data will critically enhance our understanding of injury tolerance of paediatric bones under various loading conditions, related to injuries, such as bending and torsional loads. The aim of this study is therefore to investigate the response of paediatric femora under two types of loading conditions, bending and torsion, using a CT-based finite element approach, and to determine a relationship between bone strength and age/body mass of the child. Thirty post-mortem CT scans of children aged between 0 and 3 years old were used in this study. Two different boundary conditions were defined to represent four-point bending and pure torsional loads. The principal strain criterion was used to estimate the failure moment for both loading conditions. The results showed that failure moment of the bone increases with the age and mass of the child. The predicted failure moment for bending, external and internal torsions were 0.8–27.9, 1.0–31.4 and 1.0–30.7 Nm, respectively. To the authors’ knowledge, this is the first report on infant bone strength in relation to age/mass using models developed from modern medical images. This technology may in future help advance the design of child, car restrain system, and more accurate computer models of children.     

Finite element prediction of fatigue damage growth in cancellous bone

Cyclic stresses applied to bones generate fatigue damage that affects the bone stiffness and its elastic modulus. This paper proposes a finite element model for the prediction of fatigue damage accumulation and failure in cancellous bone at continuum scale. The model is based on continuum damage mechanics and incorporates crack closure effects in compression. The propagation of the cracks is completely simulated throughout the damaged area. In this case, the stiffness of the broken element is reduced by 98% to ensure no stress-carrying capacities of completely damaged elements. Once a crack is initiated, the propagation direction is simulated by the propagation of the broken elements of the mesh. The proposed model suggests that damage evolves over a real physical time variable (cycles). In order to reduce the computation time, the integration of the damage growth rate is based on the cycle blocks approach. In this approach, the real number of cycles is reduced (divided) into equivalent blocks of cycles. Damage accumulation is computed over the cycle blocks and then extrapolated over the corresponding real cycles. The results show a clear difference between local tensile and compressive stresses on damage accumulation. Incorporating stiffness reduction also produces a redistribution of the peak stresses in the damaged region, which results in a delay in damage fracture.     

New three-dimensional model based on finite element method of bone nanostructure: single TC molecule scale level

At the macroscopic scale, the bone mechanical behavior (fracture, elastic) depends mainly on its components’ nature at the nanoscopic scale (collagen, mineral). Thus, an understanding of the mechanical behavior of the elementary components is demanded to understand the phenomena that can be observed at the macroscopic scale. In this article, a new numerical model based on finite element method is proposed in order to describe the mechanical behavior of a single Tropocollagen molecule. Furthermore, a parametric study with different geometric properties covering the molecular composition and the rate hydration influence is presented. The proposed model has been tested under tensile loading. While focusing on the entropic response, the geometric parameter variation effect on the mechanical behavior of Tropocollagen molecule has been revealed using the model. Using numerical and experimental testing, the obtained numerical simulation results seem to be acceptable, showing a good agreement with those found in literature.     

Finite element analysis of blood clots based on the nonlinear visco-hyperelastic model

Mechanical thrombectomy has become the standard treatment for patients with an acute ischemic stroke. In this approach, to remove blood clots, mechanical force is applied using thrombectomy devices, in which the interaction between the clot and the device could significantly affect the clot retrieval performance. It is expected that the finite element method (FEM) could visualize the mechanical interaction by the visualization of the stress transmission from the device to the clot. This research was aimed at verifying the constitutive theory by implementing FEM based on the visco-hyperelastic theory, using a three-dimensional clot model. We used the visco-hyperelastic FEM to reproduce the mechanical behavior of blood clots, as observed in experiments. This study is focused on the mechanical responses of clots under tensile loading and unloading because in mechanical thrombectomy, elongation is assumed to occur locally on the clots during the retrieval process. Several types of cylindrical clots were created by changing the fibrinogen dose. Tensile testing revealed that the stiffness (E_0.45-value) of clots with fibrinogen could be more than three times higher than that of clots without fibrinogen. It was also found that the stiffness was not proportional to the fibrinogen dose. By fitting to the theoretical curve, it was revealed that the Mooney-Rivlin model could reproduce the hyperelastic characteristics of clots well. From the stress-relaxation data, the three-chain Maxwell model could accurately fit the experimental viscoelastic data. FEM, taking the theoretical models into account, was then carried out, and the results matched well with the experimental visco-hyperelastic characteristics of clots under tensile load, reproducing the mechanical hysteresis during unloading, the stress dependence on the strain rate, and the time-dependent stress decrease in the stress-relaxation test.     

Finite element analysis of microelectrotension of cell membranes

Electric fields can be focused by micropipette-based electrodes to induce stresses on cell membranes leading to tension and poration. To date, however, these membrane stress distributions have not been quantified. In this study, we determine membrane tension, stress, and strain distributions in the vicinity of a microelectrode using finite element analysis of a multiscale electro-mechanical model of pipette, media, membrane, actin cortex, and cytoplasm. Electric field forces are coupled to membranes using the Maxwell stress tensor and membrane electrocompression theory. Results suggest that micropipette electrodes provide a new non-contact method to deliver physiological stresses directly to membranes in a focused and controlled manner, thus providing the quantitative foundation for micreoelectrotension, a new technique for membrane mechanobiology.     

Finite element investigation of the loading rate effect on the spinal load-sharing changes under impact conditions

Sudden deceleration and frontal/rear impact configurations involve rapid movements that can cause spinal injuries. This study aimed to investigate the rotation rate effect on the L2–L3 motion segment load-sharing and to identify which spinal structure is at risk of failure and at what rotation velocity the failure may initiate?Five degrees of sagittal rotations at different rates were applied in a detailed finite-element model to analyze the responses of the soft tissues and the bony structures until possible fractures. The structural response was markedly different under the highest velocity that caused high peaks of stresses in the segment compared to the intermediate and low velocities. Under flexion, the stress was concentrated at the upper pedicle region of L2 and fractures were firstly initiated in this region and then in the lower endplate of L2. Under extension, maximum stress was located in the lower pedicle region of L2 and fractures started in the left facet joint, then they expanded in the lower endplate and in the pedicle region of L2. No rupture has resulted at the lower or intermediate velocities. The intradiscal pressure was higher under flexion and decreased when the endplate was fractured, while the contact forces were greater under extension and decreased when the facet surface was cracked. The highest ligaments stresses were obtained under flexion and did not reach the rupture values. The endplate, pedicle and facet surface represented the potential sites of bone fracture. Results showed that spinal injuries can result at sagittal rotation velocity exceeding 0.5°/ms.     

Finite element analysis of heel pad with insoles

To design optimal insoles for reduction of pedal tissue trauma, experimental measurements and computational analyses were performed. To characterize the mechanical properties of the tissues, indentation tests were performed. Pedal tissue geometry and morphology were obtained from magnetic resonance scan of the subject's foot. Axisymmetrical finite element models of the heel of the foot were created with 1/4 of body weight load applied. The stress, strain and strain energy density (SED) fields produced in the pedal tissues were computed. The effects of various insole designs and materials on the resulting stress, strain, and SED in the soft pedal tissues were analyzed. The results showed: (a) Flat insoles made of soft material provide some reductions in the maximum stress, strain and SED produced in the pedal tissues. These maximum values were computed near the calcaneus. (b) Flat insoles, with conical/cylindrical reliefs, provided more reductions in these maximum values than without reliefs. (c) Custom insoles, contoured to match the pedal geometry provide most reductions in the maximum stress, strain and SED. Also note, the maximum stress, strain and SED computed near the calcaneus were found to be about 10 times the corresponding peak values computed on the skin surface. Based on the FEA analysis, it can be concluded that changing insole design and using different material can significantly redistribute the stress/strain inside the heel pad as well as on the skin surface.     

Finite element scaling analysis of human craniofacial growth

The study of form change is central to traditional cephalometric research. Unfortunately, traditional cephalometric studies operate within systems of measurement that are based on registration and orientation. Measurements produced in registered systems are insufficient for the craniofacial biologist who is interested in locating morphological differences between forms. In this article we apply a registration-free method called finite element scaling analysis in a study of the form change occurring during growth of the normal human craniofacial complex. The method provides form change data that can be summarized at various morphological levels. Twenty normal male individuals are used to analyze the form change that occurs from age 4 to ages 5, 7, 8, 9, 10, 12, 13, and 15 years. The magnitude and direction of growth expressed as shape and size change specific to craniofacial landmarks are presented. Although exceptions occur, our analysis shows that localized size change is, on the average, greater than localized shape change. The relation between size and shape change during growth shows allometry (shape change increasing during growth along with size change) but at a lesser magnitude and slower rate. We conclude that although shape change occurs throughout ontogeny, the magnitude and rate of shape change in relation to size change diminishes as age increases. This analysis represents new insights into the understanding of human craniofacial growth at various levels of morphological integration.     

Finite element analysis of ramming in Ovis canadensis

The energy produced during the ramming of bighorn sheep (Ovis canadensis) would be expected to result in undesirable stresses in their frontal skull, which in turn would cause brain injury; yet, this animal seems to suffer no ill effects. In general, horn is made of an α-keratin sheath covering a bone. Despite volumes of data on the ramming behavior of Ovis canadensis, the extent to which structural components of horn and horn-associated structure or tissue absorb the impact energy generated by the ramming event is still unknown. This study investigates the hypothesis that there is a mechanical relationship present among the ramming event, the structural constituents of the horn, and the horn-associated structure. The three-dimensional complex structure of the bighorn sheep horn was successfully constructed and modeled using a computed tomography (CT) scan and finite element (FE) method, respectively. Three different three-dimensional quasi-static models, including a horn model with trabecular bone, a horn model with compact bone that instead of trabecular bone, and a horn model with trabecular bone as well as frontal sinuses, were studied. FE simulations were used to compare distributions of principal stress in the horn and the frontal sinuses and the strain energy under quasi-static loading conditions. It was noticed that strain energy due to elastic deformation of the complex structure of horn modeled with trabecular bone and with trabecular bone and frontal sinus was different. In addition, trabecular bone in the horn distributes the stresses over a larger volume, suggesting a mechanical link between the structural constituents and the ramming event. This phenomenon was elucidated through the principal stress distribution in the structure. This study will help designers in choosing appropriate material combinations for the successful design of protective structures against a similar impact.