Effect of cement volume on biomechanical response of a spine segment treated with a PEEK polymer implant: a finite element comparative study with vertebroplasty.

In the current study, a 3D finite element study was performed to investigate the biomechanical response of an osteoporotic spine segment treated with a novel transpedicular implant (V-STRUT©, Hyprevention, France) made of PEEK (polyetheretherketone) material combined with either injections of 2, 3, 4, 5 and 6 cc of cement. The objective was to assess numerically the biomechanical performance of the implant in combination with different doses of the injected bone cement and to compare its performance with the gold standard vertebroplasty (VP) technique. A female (69 yo) was selected and a 3D finite element model of an osteoporotic spine segment was built based on a Computed Tomography (CT) scan performed from T12 to L2 with corresponding intervertebral discs and ligaments. A heterogeneous distribution of bone material properties was assigned to the bone using grey scale levels. Bilateral ellipsoid geometries of the inserted cement were retained for the V-STRUT and VP models based on experimental observation performed on different patients treated with the V-STRUT device. The current study demonstrated an optimal dose of 4 cc of bilaterally injected cement for the V-STRUT and VP techniques to restore the treated segment and confirmed that the V-STRUT device in combination with bone cement is superior to VP alone in establishing the normal stiffness and in reducing the applied stress to the immediately adjacent vertebral levels.

Finite element investigation of the influence of a new transpedicular vertebral implant positioning on biomechanical responses of the spine segment.

The optimal positioning of an implant into a living organ such as femurs and vertebra is still an open problem. In particular, vertebral implant position has a significant impact on the results on spine behaviour after treatment in terms of stiffness, range of motion (ROM), wear, loosening and failure. In the current work, a 3D finite element analysis was conducted to investigate the positioning parameters of a novel transpedicular implant (V-STRUT©, Hyprevention, France) in terms of placement of the implant in the treated vertebra. The implant was designed in order to strength osteoporotic vertebral body and the related spine segment under compressive load. The effects of the axial and sagittal positions of the implant in the treated vertebra was investigated in terms of stress and stiffness variations. A 3D finite element model of an osteoporotic spine segment was built based on a Computed Tomography (CT) scan of an osteoporotic female (69 yo). The model is composed of T12, L1 and L2 vertebrae and corresponding intervertebral discs and ligaments. The bone tissue was modeled as a heterogeneous material with properties assigned based on the grey scale levels. The intervertebral discs were modeled using two regions describing the annulus and the nucleus and linear beam elements with specific stiffness each were used representing each ligament. The simulations indicated that the sagittal position (distance d) plays a role on the stress distribution. The closer the implant to the interior wall the lower the stress applied to the spine segment. Nevertheless, the axial plane position (distance h) have limited effects on the stress applied to the bone with a higher stress applied to the device (subjected to a higher bending load). These results can have direct clinical implications when dealing with the optimal placement of the implant. It is also possible to select a particular position in order to assign a given (target) stiffness for a patient.

Effect of a new transpedicular vertebral device for the treatment or prevention of vertebral compression fractures: A finite element study.

BACKGROUND: A finite element study was performed to investigate the biomechanical performance of a novel transpedicular implant (V-STRUT©, Hyprevention, France) made of PEEK (polyetheretherketone) material in terms of strengthening the osteoporotic vertebra and the thoraco-lumbar spine. The objective was to assess numerically the efficacy of the implant to reduce the stress distribution within bone and absorb part of the stress by the implant thanks to its optimized material selection close to that of normal bone. METHODS: A numerical model was generated based on a scan of an osteoporotic patient. The model is composed of three consecutive vertebrae and intervertebral discs. A heterogeneous distribution of bone material properties was assigned to the bone. In order to investigate the rationale of the device material selection, three FE models were developed (i) without the device to serve a reference model, (ii) with device made in Titanium material and (iii) with device made in PEEK material. Stiffness and stress distribution within the spine segment were computed and compared in order to assess the implants' performances. FINDINGS: The results obtained by the simulations indicated that the novel transpedicular implant made of PEEK material provided support to the superior vertebral endplate, restored the thoraco-lumbar spine segment stiffness and reduced the stress applied to the vertebrae under the compressive load. INTERPRETATION: Implant geometry in combination with its material properties are very important factors to restore vertebral strength and stiffness and limiting the risk of fracture at the same vertebra or adjacent ones.

Multiscale approach incorporating tropocollagen scale to assess the effect of molecular age-related modifications on elastic constants of cortical bone based on finite element and homogenization methods.

With osteoporosis and aging, structural changes occur at all hierarchical levels of bone from the molecular scale to the whole tissue, which requires multiscale modeling to analyze the effect of these modifications on the mechanical behavior of bone and its remodeling process. In this paper, a novel hybrid multiscale model for cortical bone incorporating the tropocollagen molecule based on the combination of finite element method and different homogenization techniques was developed. The objective was to investigate the influence of age-related structural alterations that occur at the molecular level, namely the decrease in both molecular diameter (due to the loss of hydration) and number of hydrogen bonds, on mechanical properties of the bone tissue. The proposed multiscale hierarchical approach is divided in two phases: (i) in Step 0, a realistic 3D finite element model for tropocollagen was used to estimate the effective elastic properties at the molecular scale as a function of the collagen molecule's degree of hydration (represented by its external diameter) and the number of its intramolecular hydrogen bonds, and (ii) in Steps 1-10, the effective elastic constants at the higher scales from mineralized fibril to continuum cortical bone tissue were predicted analytically using homogenization equations. The results obtained in healthy mature cortical bone at different scales are in good agreement with the experimental data and multiscale models reported in the literature. Moreover, our model made it possible to visualize the influence of the two parameters (molecular diameter and number of hydrogen bonds) that represent the main age-related alterations at the molecular scale on the mechanical properties of cortical bone, at its different hierarchical levels. Keywords: Bone aging, multiscale model, tropocollagen, cortical bone, finite element modeling, homogenization method.

A multiscale four-layer finite element model to predict the effects of collagen fibers on skin behavior under tension.

Human skin is a complex multilayered multiscale material that exhibits nonlinear and anisotropic mechanical behavior. It has been reported that its macroscopic behavior in terms of progression of wrinkles induced by aging is strongly dependent on its microscopic composition in terms of collagen fibers in the dermis layer. In the present work, a multiscale four-layer 2D finite element model of the skin was developed and implemented in Matlab code. The focus here was to investigate the effects of dermal collagen on the macroscopic mechanical behavior of the skin. The skin was modeled by a continuum model composed of four layers: the Stratum Corneum, the epidermis, the dermis, and the hypodermis. The geometry of the different layers of the skin was represented in a 2D model with their respective thicknesses and material properties taken from literature data. The macroscopic behavior of the dermis was modeled with a nonlinear multiscale approach based on a multiscale elastic model of collagen structure going from cross-linked molecules to the collagen fiber, combined with a Mori-Tanaka homogenization scheme. The model includes the nonlinear elasticity of the collagen fiber density, the fiber radius, the undulation, and the fiber orientation. An axial tension was applied incrementally to the lateral surfaces of the skin model. A parametric study was performed in order to investigate the effect of the collagen constituents on the macroscopic skin mechanical behavior in terms of the predicted macroscopic stress-strain curve of the skin. The results of the FE computations under uniaxial tension showed that the different layers undergo different strains, leading to a difference in the transversal deformation at the top surface. In addition, the parametric study revealed a strong correlation between macroscopic skin elasticity and its collagen structure.

Mesh-independent damage model for trabecular bone fracture simulation and experimental validation.

We propose in this study a two-dimensional constitutive model for trabecular bone combining continuum damage with embedded strong discontinuity. The model is capable of describing the three failure phases of trabecular bone tissue which is considered herein as a quasi-brittle material with strains and rotations assumed to be small and without viscous, thermal or other non-mechanical effects. The finite element implementation of the present model uses constant strain triangle (CST) elements. The displacement jump vector is implicitly solved through a return mapping algorithm at the local (finite element) level, while the global equilibrium equations are dealt with by Newton-Raphson method. The performance, accuracy and applicability of the proposed model for trabecular bone fracture are evaluated and validated against experimental measurements. These comparisons include both global and local aspects through numerical simulations of three-point bending tests performed on 10 single bovine trabeculae in the quasi-static regime.

Parametric investigation of the effects of load level on fatigue crack growth in trabecular bone based on artificial neural network computation.

This study reports the development of an artificial neural network computation model to predict the accumulation of crack density and crack length in cancellous bone under a cyclic load. The model was then applied to conduct a parametric investigation into the effects of load level on fatigue crack accumulation in cancellous bone. The method was built in three steps: (1) conducting finite element simulations to predict fatigue growth of different three-dimensional micro-computed tomography cancellous bone specimens considering input combinations based on a factorial experimental design; (2) performing a training stage of an artificial neural network based on the results of step 1; and (3) applying the trained artificial neural network to rapidly predict the crack density and the crack length growth for cancellous bone under a cyclic loading for a given applied apparent strain, cycle frequency, bone volume fraction, bone density and apparent elastic modulus.

Numerical modeling of the effects hydration and number of hydrogen bonds on the mechanical properties of the tropocollagen molecule.

Bone aging involves structural and molecular modifications, especially at the level of type I tropocollagen. This macromolecule shows two main age-related alterations, which are the decrease of both molecular diameter (due to the loss of hydration) and number of hydrogen bonds. In this work, it is proposed to investigate the influence of these two parameters (molecular diameter and number of hydrogen bonds) on the mechanical behavior of tropocollagen using finite element method. To this end, a novel three-dimensional finite element model of collagen molecule accounting for hydrogen bonds was developed. Then, a numerical design of experiments for the diameter of tropocollagen and variations in the number of hydrogen bonds has been established. The mechanical properties ("load-strain" curve and apparent Young's modulus) of the collagen molecule were obtained by employing the proposed model to uniaxial tensile tests. The parametric study demonstrates that the mechanical properties of tropocollagen are slightly affected by the rate of hydration but considerably affected by variation of the number of hydrogen bonds. Finally, a fitted analytical function was deduced from the above results showing effects of the two parameters (hydration rate and hydrogen bonds) on the apparent Young's modulus of tropocollagen. This study could be useful to understand the influence of structural age modifications of tropocollagen on the macroscopic mechanical properties of bone.

On dynamic behavior of bone: Experimental and numerical study of porcine ribs subjected to impact loads in dynamic three-point bending tests.

This study covers the characterization of the dynamic behavior of isolated porcine ribs based on experimental and numerical approaches. A Split Hopkinson Pressure Bar (SHPB) setup for three-point bending tests was used. Data of 20 tests were considered to be comprehensible for experimental characterization, thereby, showing an influence of strain rate on both time for fracture and amplitudes of force response. A three-dimensional porcine rib model was generated from the DICOM (Digital Imaging and Communication in Medicine) images of High-Resolution peripheral Quantitative Computed Tomography (HR-pQCT) scans. Material properties having been fitted by power law regression equations based on apparent density were assigned to the numerical rib. A modified elastic-plastic constitutive law, capable of considering the effects of strain rate was adopted. An incremental and stress-state dependent damage law, capable of considering effects of strain rate on fracture propagation, non-linear damage accumulation and instabilities was coupled to the constitutive law. The Finite Element (FE) model shows high efficiency in predicting both force-displacement curve and the fracture patterns of tested ribs. Predictions prove the ability of the proposed model to investigate the fracture behavior of human ribs under dynamic loads.

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.

Age and gender effects on bone mass density variation: finite elements simulation.

Bone remodeling is a physiological process by which bone constantly adapts its structure to changes in long-term loading manifested by interactions between osteoclasts and osteoblasts. This process can be influenced by many local factors, via effects on bone cells differentiation and proliferation, which are produced by bone cells and act in a paracrine or autocrine way. The aim of the current work is to provide mechanobiological finite elements modeling coupling both cellular activities and mechanical behavior in order to investigate age and gender effects on bone remodeling evolution. A series of computational simulations have been performed on a 2D and 3D human proximal femur. An age- and gender-related impacts on bulk density alteration of trabecular bone have been noticed, and the major actors responsible of this phenomenon have been then discussed.

Osteoporosis drug effects on cortical and trabecular bone microstructure: a review of HR-pQCT analyses.

With the development of new non-invasive analytical techniques and particularly the advent of high-resolution peripheral quantitative computed tomography (HRpQCT) it is possible to assess cortical and trabecular bone changes under the effects of ageing, diseases and treatments. In the present study, we reviewed the treatment-related effects on bone parameters assessed by HRpQCT imaging. We identified 12 full-length articles published in peer-reviewed journals describing treatment-induced changes assessed by HRpQCT. The design of these studies varied a lot in terms of duration and methodology: some of them were open-labelled, others were double-blind, placebo-controlled or double-blind, double-dummy, active controlled. In addition, the sample size in these studies ranged from 11 to 324 patients. Motion artifacts occurring during data acquisition were sometimes a real challenge particularly at the radius leading sometimes to exclude the analysis at the radius due to the uninterpretability of microstructural parameters. Responses to therapies were treatment-specific and divergent effects in cortical and trabecular bone with antiresorptive or anabolic agents were observed. Standardization of bone microarchitecture parameters (including porosity) and bone strength estimates by finite element analysis (FEA) are mandatory. The additional value of microarchitecture and FEA estimates changes with therapies in terms of improvement in fracture outcomes which have to be adequately assessed in clinical trials with fracture end point. Data from these reviewed studies advance our understanding of the microstructural consequences of osteoporosis and highlight potential differences in bone quality outcomes within therapies.

A multiscale modelling of bone ultrastructure elastic proprieties using finite elements simulation and neural network method.

Bone is a living material with a complex hierarchical structure which entails exceptional mechanical properties, including high fracture toughness, specific stiffness and strength. Bone tissue is essentially composed by two phases distributed in approximately 30-70%: an organic phase (mainly type I collagen and cells) and an inorganic phase (hydroxyapatite-HA-and water). The nanostructure of bone can be represented throughout three scale levels where different repetitive structural units or building blocks are found: at the first level, collagen molecules are arranged in a pentameric structure where mineral crystals grow in specific sites. This primary bone structure constitutes the mineralized collagen microfibril. A structural organization of inter-digitating microfibrils forms the mineralized collagen fibril which represents the second scale level. The third scale level corresponds to the mineralized collagen fibre which is composed by the binding of fibrils. The hierarchical nature of the bone tissue is largely responsible of their significant mechanical properties; consequently, this is a current outstanding research topic. Scarce works in literature correlates the elastic properties in the three scale levels at the bone nanoscale. The main goal of this work is to estimate the elastic properties of the bone tissue in a multiscale approach including a sensitivity analysis of the elastic behaviour at each length scale. This proposal is achieved by means of a novel hybrid multiscale modelling that involves neural network (NN) computations and finite elements method (FEM) analysis. The elastic properties are estimated using a neural network simulation that previously has been trained with the database results of the finite element models. In the results of this work, parametric analysis and averaged elastic constants for each length scale are provided. Likewise, the influence of the elastic constants of the tissue constituents is also depicted. Results highlight that intelligent numerical methods are powerful and accurate procedures to deal with the complex multiscale problem in the bone tissue with results in agreement with values found in literature for specific scale levels.

Prediction of denosumab effects on bone remodeling: A combined pharmacokinetics and finite element modeling.

Denosumab is a fully human monoclonal antibody that inhibits receptor activator of nuclearfactor-kappa B ligand (RANKL). This key mediator of osteoclast activities has been shown to inhibit osteoclast differentiation and hence, to increase bone mineral density (BMD) in treated patients. In the current study, we develop a computer model to simulate the effects of denosumab treatments (dose and duration) on the proximal femur bone remodeling process quantified by the variation in proximal femur BMD. The simulation model is based on a coupled pharmacokinetics model of denosumab with a pharmacodynamics model consisting of a mechanobiological finite element remodeling model which describes the activities of osteoclasts and osteoblasts. The mechanical behavior of bone is described by taking into account the bone material fatigue damage accumulation and mineralization. A coupled strain-damage stimulus function is proposed which controls the level of bone cell autocrine and paracrine factors. The cellular behavior is based on Komarova et al.׳s (2003) dynamic law which describes the autocrine and paracrine interactions between osteoblasts and osteoclasts and computes cell population dynamics and changes in bone mass at a discrete site of bone remodeling. Therefore, when an external mechanical stress is applied, bone formation and resorption is governed by cell dynamics rather than by adaptive elasticity approaches. The proposed finite element model was implemented in the finite element code Abaqus (UMAT routine). In order to perform a preliminary validation, in vivo human proximal femurs were selected and scanned at two different time intervals (at baseline and at a 36-month interval). Then, a 3D FE model was generated and the denosumab-remodeling algorithm was applied to the scans at t0 simulating daily walking activities for a duration of 36 months. The predicted results (density variation) were compared to existing published ones performed on a human cohort (FREEDOM).

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.

Effect of material and structural factors on fracture behaviour of mineralised collagen microfibril using finite element simulation.

Bone is a multiscale heterogeneous material and its principal function is to support the body structure and to resist mechanical loads without fracturing. Numerical modelling of biocomposites at different length scales provides an improved understanding of the mechanical behaviour of structures such as bone, and also guides the development of multiscale mechanical models. Here, a three-dimensional nano-scale model of mineralised collagen microfibril based on the finite element method was employed to investigate the effect of material and structural factors on the mechanical equivalent of fracture properties. Fracture stress and damping capacity as functions of the number of cross-links were obtained under tensile loading conditions for different densities and Young's modulus of the mineral phase. The results show that the number of cross-links and the density of mineral as well as Young's modulus of mineral have an important influence on the strength of mineralised collagen microfibrils which in turn clarify the bone fracture on a macroscale.

Connecting mechanics and bone cell activities in the bone remodeling process: an integrated finite element modeling.

Bone adaptation occurs as a response to external loadings and involves bone resorption by osteoclasts followed by the formation of new bone by osteoblasts. It is directly triggered by the transduction phase by osteocytes embedded within the bone matrix. The bone remodeling process is governed by the interactions between osteoblasts and osteoclasts through the expression of several autocrine and paracrine factors that control bone cell populations and their relative rate of differentiation and proliferation. A review of the literature shows that despite the progress in bone remodeling simulation using the finite element (FE) method, there is still a lack of predictive models that explicitly consider the interaction between osteoblasts and osteoclasts combined with the mechanical response of bone. The current study attempts to develop an FE model to describe the bone remodeling process, taking into consideration the activities of osteoclasts and osteoblasts. The mechanical behavior of bone is described by taking into account the bone material fatigue damage accumulation and mineralization. A coupled strain-damage stimulus function is proposed, which controls the level of autocrine and paracrine factors. The cellular behavior is based on Komarova et al.'s (2003) dynamic law, which describes the autocrine and paracrine interactions between osteoblasts and osteoclasts and computes cell population dynamics and changes in bone mass at a discrete site of bone remodeling. Therefore, when an external mechanical stress is applied, bone formation and resorption is governed by cells dynamic rather than adaptive elasticity approaches. The proposed FE model has been implemented in the FE code Abaqus (UMAT routine). An example of human proximal femur is investigated using the model developed. The model was able to predict final human proximal femur adaptation similar to the patterns observed in a human proximal femur. The results obtained reveal complex spatio-temporal bone adaptation. The proposed FEM model gives insight into how bone cells adapt their architecture to the mechanical and biological environment.

Multiscale approach including microfibril scale to assess elastic constants of cortical bone based on neural network computation and homogenization method.

The complexity and heterogeneity of bone tissue require a multiscale modeling to understand its mechanical behavior and its remodeling mechanisms. In this paper, a novel multiscale hierarchical approach including microfibril scale based on hybrid neural network (NN) computation and homogenization equations was developed to link nanoscopic and macroscopic scales to estimate the elastic properties of human cortical bone. The multiscale model is divided into three main phases: (i) in step 0, the elastic constants of collagen-water and mineral-water composites are calculated by averaging the upper and lower Hill bounds; (ii) in step 1, the elastic properties of the collagen microfibril are computed using a trained NN simulation. Finite element calculation is performed at nanoscopic levels to provide a database to train an in-house NN program; and (iii) in steps 2-10 from fibril to continuum cortical bone tissue, homogenization equations are used to perform the computation at the higher scales. The NN outputs (elastic properties of the microfibril) are used as inputs for the homogenization computation to determine the properties of mineralized collagen fibril. The mechanical and geometrical properties of bone constituents (mineral, collagen, and cross-links) as well as the porosity were taken in consideration. This paper aims to predict analytically the effective elastic constants of cortical bone by modeling its elastic response at these different scales, ranging from the nanostructural to mesostructural levels. Our findings of the lowest scale's output were well integrated with the other higher levels and serve as inputs for the next higher scale modeling. Good agreement was obtained between our predicted results and literature data.

Nanomechanical properties of mineralised collagen microfibrils based on finite elements method: biomechanical role of cross-links.

Hierarchical structures in bio-composites such as bone tissue have many scales or levels and synergic interactions between the different levels. They also have a highly complex architecture in order to fulfil their biological and mechanical functions. In this study, a new three-dimensional (3D) model based on the finite elements (FEs) method was used to model the relationship between the hierarchical structure and the properties of the constituents at the sub-structure scale (mineralised collagen microfibrils) and to investigate their apparent nanomechanical properties. The results of the proposed FE simulations show that the elastic properties of microfibrils depend on different factors such as the number of cross-links, the mechanical properties and the volume fraction of phases. The results obtained under compression loading at a small deformation < 2% show that the microfibrils have a Young's modulus (Ef) ranging from 0.4 to 1.16 GPa and a Poisson's ratio ranging from 0.26 to 0.3. These results are in excellent agreement with experimental data (X-ray, AFM and MEMS) and molecular simulations.