382 research outputs found

    Composite Finite Elements for Trabecular Bone Microstructures

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    In many medical and technical applications, numerical simulations need to be performed for objects with interfaces of geometrically complex shape. We focus on the biomechanical problem of elasticity simulations for trabecular bone microstructures. The goal of this dissertation is to develop and implement an efficient simulation tool for finite element simulations on such structures, so-called composite finite elements. We will deal with both the case of material/void interfaces (complicated domains) and the case of interfaces between different materials (discontinuous coefficients). In classical finite element simulations, geometric complexity is encoded in tetrahedral and typically unstructured meshes. Composite finite elements, in contrast, encode geometric complexity in specialized basis functions on a uniform mesh of hexahedral structure. Other than alternative approaches (such as e.g. fictitious domain methods, generalized finite element methods, immersed interface methods, partition of unity methods, unfitted meshes, and extended finite element methods), the composite finite elements are tailored to geometry descriptions by 3D voxel image data and use the corresponding voxel grid as computational mesh, without introducing additional degrees of freedom, and thus making use of efficient data structures for uniformly structured meshes. The composite finite element method for complicated domains goes back to Wolfgang Hackbusch and Stefan Sauter and restricts standard affine finite element basis functions on the uniformly structured tetrahedral grid (obtained by subdivision of each cube in six tetrahedra) to an approximation of the interior. This can be implemented as a composition of standard finite element basis functions on a local auxiliary and purely virtual grid by which we approximate the interface. In case of discontinuous coefficients, the same local auxiliary composition approach is used. Composition weights are obtained by solving local interpolation problems for which coupling conditions across the interface need to be determined. These depend both on the local interface geometry and on the (scalar or tensor-valued) material coefficients on both sides of the interface. We consider heat diffusion as a scalar model problem and linear elasticity as a vector-valued model problem to develop and implement the composite finite elements. Uniform cubic meshes contain a natural hierarchy of coarsened grids, which allows us to implement a multigrid solver for the case of complicated domains. Besides simulations of single loading cases, we also apply the composite finite element method to the problem of determining effective material properties, e.g. for multiscale simulations. For periodic microstructures, this is achieved by solving corrector problems on the fundamental cells using affine-periodic boundary conditions corresponding to uniaxial compression and shearing. For statistically periodic trabecular structures, representative fundamental cells can be identified but do not permit the periodic approach. Instead, macroscopic displacements are imposed using the same set as before of affine-periodic Dirichlet boundary conditions on all faces. The stress response of the material is subsequently computed only on an interior subdomain to prevent artificial stiffening near the boundary. We finally check for orthotropy of the macroscopic elasticity tensor and identify its axes.Zusammengesetzte finite Elemente für trabekuläre Mikrostrukturen in Knochen In vielen medizinischen und technischen Anwendungen werden numerische Simulationen für Objekte mit geometrisch komplizierter Form durchgeführt. Gegenstand dieser Dissertation ist die Simulation der Elastizität trabekulärer Mikrostrukturen von Knochen, einem biomechanischen Problem. Ziel ist es, ein effizientes Simulationswerkzeug für solche Strukturen zu entwickeln, die sogenannten zusammengesetzten finiten Elemente. Wir betrachten dabei sowohl den Fall von Interfaces zwischen Material und Hohlraum (komplizierte Gebiete) als auch zwischen verschiedenen Materialien (unstetige Koeffizienten). In klassischen Finite-Element-Simulationen wird geometrische Komplexität typischerweise in unstrukturierten Tetraeder-Gittern kodiert. Zusammengesetzte finite Elemente dagegen kodieren geometrische Komplexität in speziellen Basisfunktionen auf einem gleichförmigen Würfelgitter. Anders als alternative Ansätze (wie zum Beispiel fictitious domain methods, generalized finite element methods, immersed interface methods, partition of unity methods, unfitted meshes und extended finite element methods) sind die zusammengesetzten finiten Elemente zugeschnitten auf die Geometriebeschreibung durch dreidimensionale Bilddaten und benutzen das zugehörige Voxelgitter als Rechengitter, ohne zusätzliche Freiheitsgrade einzuführen. Somit können sie effiziente Datenstrukturen für gleichförmig strukturierte Gitter ausnutzen. Die Methode der zusammengesetzten finiten Elemente geht zurück auf Wolfgang Hackbusch und Stefan Sauter. Man schränkt dabei übliche affine Finite-Element-Basisfunktionen auf gleichförmig strukturierten Tetraedergittern (die man durch Unterteilung jedes Würfels in sechs Tetraeder erhält) auf das approximierte Innere ein. Dies kann implementiert werden durch das Zusammensetzen von Standard-Basisfunktionen auf einem lokalen und rein virtuellen Hilfsgitter, durch das das Interface approximiert wird. Im Falle unstetiger Koeffizienten wird die gleiche lokale Hilfskonstruktion verwendet. Gewichte für das Zusammensetzen erhält man hier, indem lokale Interpolationsprobleme gelöst werden, wozu zunächst Kopplungsbedingungen über das Interface hinweg bestimmt werden. Diese hängen ab sowohl von der lokalen Geometrie des Interface als auch von den (skalaren oder tensorwertigen) Material-Koeffizienten auf beiden Seiten des Interface. Wir betrachten Wärmeleitung als skalares und lineare Elastizität als vektorwertiges Modellproblem, um die zusammengesetzten finiten Elemente zu entwickeln und zu implementieren. Gleichförmige Würfelgitter enthalten eine natürliche Hierarchie vergröberter Gitter, was es uns erlaubt, im Falle komplizierter Gebiete einen Mehrgitterlöser zu implementieren. Neben Simulationen einzelner Lastfälle wenden wir die zusammengesetzten finiten Elemente auch auf das Problem an, effektive Materialeigenschaften zu bestimmen, etwa für mehrskalige Simulationen. Für periodische Mikrostrukturen wird dies erreicht, indem man Korrekturprobleme auf der Fundamentalzelle löst. Dafür nutzt man affin-periodische Randwerte, die zu uniaxialem Druck oder zu Scherung korrespondieren. In statistisch periodischen trabekulären Mikrostrukturen lassen sich ebenfalls Fundamentalzellen identifizieren, sie erlauben jedoch keinen periodischen Ansatz. Stattdessen werden makroskopische Verschiebungen zu denselben affin-periodischen Randbedingungen vorgegeben, allerdings durch Dirichlet-Randwerte auf allen Seitenflächen. Die Spannungsantwort des Materials wird anschließend nur auf einem inneren Teilbereich berechnet, um künstliche Versteifung am Rand zu verhindern. Schließlich prüfen wir den makroskopischen Elastizitätstensor auf Orthotropie und identifizieren deren Achsen

    A novel approach for tetrahedral-element-based finite element simulations of anisotropic hyperelastic intervertebral disc behavior

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    Intervertebral discs are microstructurally complex spinal tissues that add greatly to the flexibility and mechanical strength of the human spine. Attempting to provide an adjustable basis for capturing a wide range of mechanical characteristics and to better address known challenges of numerical modeling of the disc, we present a robust finite-element-based model formulation for spinal segments in a hyperelastic framework using tetrahedral elements. We evaluate the model stability and accuracy using numerical simulations, with particular attention to the degenerated intervertebral discs and their likely skewed and narrowed geometry. To this end, 1) annulus fibrosus is modeled as a fiber-reinforced Mooney-Rivlin type solid for numerical analysis. 2) An adaptive state-variable dependent explicit time step is proposed and utilized here as a computationally efficient alternative to theoretical estimates. 3) Tetrahedral-element-based FE models for spinal segments under various loading conditions are evaluated for their use in robust numerical simulations. For flexion, extension, lateral bending, and axial rotation load cases, numerical simulations reveal that a suitable framework based on tetrahedral elements can provide greater stability and flexibility concerning geometrical meshing over commonly employed hexahedral-element-based ones for representation and study of spinal segments in various stages of degeneration

    Mechanical modelling of the abdominal wall and biomaterials for hernia surgery

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    Abdominal surgery for hernia repair is based on the implantation of a synthetic mesh in the defect area which aims at reinforcing the damaged wall. This clinical intervention is common in today's society and, in unfavorable cases such as obese patients or patients with large defects, could lead to a number of problems that reduce the quality of life of patients. The most common problems are the appearance of fibrosis, the hernia recurrence and occurrence of abdominal discomfort due to poor compliance between the host tissue and the prosthesis. Currently, surgeons have no definitive and universally accepted guidelines for the selection of the appropriate prosthesis for each patient and type of defect. Therefore, the choice of one or another mesh, and their placement in case of anisotropic meshes, is a decision to be taken by the surgeons according to their experience. This thesis aims to study the abdominal hernia surgery from the continuum mechanics point of view. However, for the supply and validation of the generated models, it is necessary to perform an experimental study in an animal model. Since this is a multidisciplinary problem, the study approached was developed in collaboration with the Translational Research Group in Biomaterials and Tissue Engineering at the University of Alcalá de Henares (Madrid). The final goal of hernia surgery is that the prosthesis ensures adequate tissular integration, being capable, among other things, to reproduce the mechanical behaviour of the healthy abdominal wall and to absorb the stresses due to the physiological loads to which the abdomen is subjected. Therefore, in addition to addressing the study in animal models to analyze the integration on the wall, the mechanical modelling of the abdominal wall and the biomaterials used in hernia repair is essential. For this, the construction of an ``in silico'' model of the human abdomen has been developed. Due to the diversity of commercial products on the market, this thesis focusses on the study of three representative prostheses, specifically Surgipro, Optilene and Infinit. These meshes are characterized by different geometric parameters and are made of different materials. In this work, the mechanical properties of the prostheses have been determined experimentally and different constitutive models, that reproduce the patterns of the mechanical behaviour observed in both, the abdominal muscle and implanted biomaterials, have been proposed. Specifically, the numerical modelling of the response of the abdominal muscle, including both active and passive responses, and prostheses have been approached within the framework of the nonlinear hyperelasticity in large deformations. The latter approach of this thesis aims to model, using the finite element method, the mechanical response of the wall with the implanted mesh. A complete model of the human abdomen has been defined from nuclear magnetic resonance imaging. This complete model allows differentiating the main anatomical units of the abdomen and it is used to simulate the passive and active responses. Furthermore, this model allows the study of the response of the healthy wall and the analysis of the final mechanical response of the herniated human abdomen to the placement of different prostheses. In summary, this thesis establishes a methodology to the automation of computational models for personalized surgical procedures in order to select the most appropriate mesh for each patient as well as the appropriate placement on the defect in the case of anisotropic prostheses

    Use of Brain Biomechanical Models for Monitoring Impact Exposure in Contact Sports

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    Head acceleration measurement sensors are now widely deployed in the field to monitor head kinematic exposure in contact sports. The wealth of impact kinematics data provides valuable, yet challenging, opportunities to study the biomechanical basis of mild traumatic brain injury (mTBI) and subconcussive kinematic exposure. Head impact kinematics are translated into brain mechanical responses through physics-based computational simulations using validated brain models to study the mechanisms of injury. First, this article reviews representative legacy and contemporary brain biomechanical models primarily used for blunt impact simulation. Then, it summarizes perspectives regarding the development and validation of these models, and discusses how simulation results can be interpreted to facilitate injury risk assessment and head acceleration exposure monitoring in the context of contact sports. Recommendations and consensus statements are presented on the use of validated brain models in conjunction with kinematic sensor data to understand the biomechanics of mTBI and subconcussion. Mainly, there is general consensus that validated brain models have strong potential to improve injury prediction and interpretation of subconcussive kinematic exposure over global head kinematics alone. Nevertheless, a major roadblock to this capability is the lack of sufficient data encompassing different sports, sex, age and other factors. The authors recommend further integration of sensor data and simulations with modern data science techniques to generate large datasets of exposures and predicted brain responses along with associated clinical findings. These efforts are anticipated to help better understand the biomechanical basis of mTBI and improve the effectiveness in monitoring kinematic exposure in contact sports for risk and injury mitigation purposes

    Investigation of Primary Blast Injury and Protection using Sagittal and Transverse Finite Element Head Models

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    The prevalence of blast related mild traumatic brain injury (mTBI) in recent military conflicts, attributed in part to an increased exposure to improvised explosive devices (IEDs), requires further understanding to develop methods to mitigate the effects of primary blast exposure. Although general blast injury has been studied extensively since the 1950’s, many aspects of mTBI remain unclear, including specific injury mechanisms and injury criteria. The purpose of this work was to develop finite element models to investigate primary blast injury to the head in the loading regimes relevant to mTBI, to use the models to determine the response of the brain tissue, and ultimately to investigate the effectiveness of helmets on response mitigation. Since blast is inherently a wave dominated phenomena, finite element models require relatively small elements to resolve complex pressure wave transmission and reflections in order to accurately predict tissue response. Furthermore, mesh continuity between the tissue structures is necessary to ensure accurate wave transmission. The computational limitations present in analyzing a full three dimensional blast head model led to the development of sagittal and transverse planar models, which provide a fully coupled analysis with the required mesh resolution while remaining computationally feasible. The models consist of a single layer of solid hexahedral elements, and include all of the relevant tissues in the head including the skin, muscle, skull, cerebrospinal fluid, and brain. The sagittal and transverse models were validated using head kinematics against experimental data on Hybrid III head-forms exposed to free-field blast. The peak head accelerations of the models was in close agreement to the experimental data, and the HIC15 predictions were in reasonable agreement. In addition, the models were validated for intracranial pressure using experimental data from cadaveric heads exposed to shock tube loading. The intracranial pressures predicted by the sagittal and transverse models was in good agreement at the frontal, temporal, and parietal locations, and in fair agreement at the occipital location. A simplified three dimensional ellipsoid study was undertaken to verify that sagittal and transverse planar models are capable of representing a three dimensional shape. This investigation confirmed that the pressures predicted by the planar models are accurate at the frontal, temporal, and parietal locations, although underpredicted at the occipital location due to three dimensional wave superposition that becomes significant at the occipital region. The sagittal and transverse models were run at three representative blast load cases, corresponding to 5 kg of C4 at 3, 3.5, and 4 m standoff distances, and the resulting intracranial strains and pressures were investigated. The sagittal and transverse models report peak principal strains of 0.035 – 0.062 and 0.053 – 0.087 respectively. In comparison to the available threshold values of principal strain in the literature, the strains predicted by the models are generally low. While the strains reported by the models in primary blast are small, the strain rates are significantly greater (ranging from 226 – 571 s-1) than those seen in typical automotive or blunt impact scenarios. Furthermore, the models report that significant levels of intracranial pressure, on the order of several atmospheres, can be generated in the brain tissue during primary blast exposure. The peak pressures in the brain tissue for both models typically exceeded the existing injury thresholds for intracranial that are available in the literature. However, these existing criteria were generally developed for automotive crash scenarios, so may not be suitable for the short durations inherent to blast. The magnitudes of intracranial pressure increased significantly with increasing blast load severity, while changes in principal strain were relatively small, and peak strains were low in all three load cases, suggesting that pressure may be a more appropriate injury response metric for blast injury. The sagittal and transverse models were outfitted with various military helmet configurations and materials to investigate the influence of helmet visors, foam lining presence and density, and Kevlar material stiffness on the protective properties of the helmet. The peak head accelerations and intracranial pressures were compared for low and high intensity blast loads. In general, the presence of a helmet resulted in reduced peak head accelerations, and a greater reduction was reported with the addition of a half-visor and full-visor. The presence of a visor significantly reduced positive intracranial pressures in all cases, although increased the maximum negative pressures in some cases. The effects of the foam lining material was not as significant to the model response as the helmet visor configurations, but in general, a lower density foam provided better load mitigation. In cases where there was no foam lining, pressure wave reflections in the air gap between the helmet and head were found to cause greater intracranial pressures in adjacent brain tissue, although the magnitudes of these increased pressures were generally lower than the incident compressive pressures caused by the initial wave impact

    Numerical modelling of the growth and remodelling phenomena in biological tissues

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    Living biological tissues are complex structures that have the capacity of evolving in response to external loads and environmental stimuli. The adequate modelling of soft biological tissue behaviour is a key issue in successfully reproducing biomechanical problems through computational analysis. This study presents a general constitutive formulation capable of representing the behaviour of these tissues through finite element simulation. It is based on phenomenological models that, used in combination with the generalized mixing theory, can numerically reproduce a wide range of material behaviours. First, the passive behaviour of tissues is characterized by means of hyperelastic and finite-strain damage models. A new generalized damage model is proposed, providing a flexible and versatile formulation that can reproduce a wide range of tissue behaviour. It can be particularized to any hyperelastic model and requires identifying only two material parameters. Then, the use of these constitutive models with generalized mixing theory in a finite-strain framework is described and tools to account for the anisotropic behaviour of tissues are put forth. The active behaviour of tissues is characterized through constitutive models capable of reproducing the growth and remodelling phenomena. These are built on the hyperelastic and damage formulations described above and, thus, represent the active extension of the passive tissue behaviour. A growth model considering biological availability is used and extended to include directional growth. In addition, a novel constitutive model for homeostatic-driven turnover remodelling is presented and discussed. This model captures the stiffness recovery that occurs in healing tissues, understood as a recovery or reversal of damage in the tissue, which is driven by both mechanical and biochemical stimuli. Finally, the issue of correctly identifying the material parameters for computational modelling is addressed. An inverse method using optimization techniques is developed to facilitate the identification of these parameters.Els teixits biològics vius són estructures complexes que tenen la capacitat d'evolucionar en resposta a càrregues externes i estímuls ambientals. El modelat adequat del comportament del teixit biològic tou és un tema clau per poder reproduir amb èxit problemes biomecànics mitjançant anàlisi computacional. Aquest estudi presenta una formulació constitutiva general capaç de representar el comportament d'aquests teixits mitjançant la simulació amb elements finits. Es basa en models fenomenològics que, usats en combinació amb la teoria de mescles generalitzada, permeten reproduir numèricament un ampli ventall de comportaments materials. Primer, el comportament passiu dels teixits es caracteritza amb models hiperelàstics i de dany en grans deformacions. Es proposa un model generalitzat de dany que proporciona una formulació versàtil i flexible per poder reproduir una extensa gamma de conductes de teixits. Pot ser particularitzat amb qualsevol model hiperelàstic i requereix identificar tan sols dos paràmetres materials. Llavors, es descriu l'ús d'aquests models constitutius en conjunt amb la teoria generalitzada de mescles, desenvolupada en el marc de grans deformacions, i es presenten eines que permeten incorporar les propietats anisòtropes dels teixits. El comportament actiu dels teixits es caracteritza mitjançant models constitutius capaços de reproduir els fenòmens de creixement i remodelació. Aquests es construeixen sobre les formulacions d'hiperelasticitat i dany descrites anteriorment i, per tant, suposen l'extensió activa del comportament passiu del teixit. Es fa servir un model de creixement que té en compte la disponibilitat biològica de l'organisme, que després s'amplia per incloure dany direccional en el model. També es presenta i analitza un nou model constitutiu per al remodelat per renovació tendint a l’homeòstasi (homeostatic-driven turnover remodelling). Aquest model captura la recuperació de rigidesa que s'observa en teixits que es guareixen. Aquí, el remodelat s'entén com la recuperació o inversió del dany en el teixit i és motivat tant per estímuls mecànics com bioquímics. Finalment, s'aborda el tema de la identificació correcta dels paràmetres materials per al modelat computacional. Es desenvolupa un mètode invers que fa ús de tècniques d'optimització per facilitar la identificació d'aquests paràmetre

    Computational biomechanics of acute myocardial infarction and its treatment

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    The intramyocardial injection of biomaterials is an emerging therapy for myocardial infarction. Computational methods can help to study the mechanical effect s of biomaterial injectates on the infarcted heart s and can contribute to advance and optimise the concept of this therapy. The distribution of polyethylene glycol hydrogel injectate delivered immediately after the infarct induction was studied using rat infarct model. A micro-structural three-dimensional geometrical model of the entire injectate was reconstructed from histological micro graphs. The model provides a realistic representation of biomaterial injectates in computational models at macroscopic and microscopic level. Biaxial and compression mechanical testing was conducted for healing rat myocardial infarcted tissue at immediate (0 day), 7, 14 and 28 days after infarction onset. Infarcts were found to be mechanically anisotropic with the tissue being stiffer in circumferential direction than in longitudinal direction. The 0, 7, 14 and 28 days infarcts showed 443, 670, 857 and 1218 kPa circumferential tensile moduli. The 28 day infarct group showed a significantly higher compressive modulus compared to the other infarct groups (p= 0.0055, 0.028, and 0.018 for 0, 7 and 14 days groups). The biaxial mechanical data were utilized to establish material constitutive models of rat healing infarcts. Finite element model s and genetic algorithms were employed to identify the parameters of Fung orthotropic hyperelastic strain energy function for the healing infarcts. The provided infarct mechanical data and the identified constitutive parameters offer a platform for investigations of mechanical aspects of myocardial infarction and therapies in the rat, an experimental model extensively used in the development of infarct therapies. Micro-structurally detailed finite element model of a hydrogel injectate in an infarct was developed to provide an insight into the micromechanics of a hydrogel injectate and infarct during the diastolic filling. The injectate caused the end-diastolic fibre stresses in the infarct zone to decrease from 22.1 to 7.7 kPa in the 7 day infarct and from 35.7 to 9.7 kPa in the 28 day infarct. This stress reduction effect declined as the stiffness of the biomaterial increased. It is suggested that the gel works as a force attenuating system through micromechanical mechanisms reducing the force acting on tissue layers during the passive diastolic dilation of the left ventricle and thus reducing the stress induced in these tissue layers

    Micro-Computed Tomography-Based Finite Element Analysis Of The Mechanical Integrity Of In Vivo Biodegradable Magnesium-Alloy Screw And Surrounding Bone

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    The anterior cruciate ligament (ACL) tear, the most common knee injury, affects 100,000 to 200,000 persons in the US annually. Surgical repair is employed to restore the knee to its full range of motion. In the surgery, an interference screw is used to a secure a soft tissue graft that is used to replace the torn ACL. In 2012, orthopedic devices for knees accounted for the largest share of the $29.2 billion overall revenue for orthopedic devices. Biodegradable implants are expected to lead growth in the orthopedic sector by increasing the quality of life and decreasing recovery time after orthopedic injury for athletes and non-athletes and aging, osteoporotic, osteoarthritic and obese populations. Magnesium-based orthopedic devices, including interference screws, are being investigated because of their ability to provide high strength as a metal, but degrade like a polymer. One objective of this study was to compare the pull-out forces of an unnamed magnesium-alloy against a commercially available copolymer, 82:18 PLLA:PLGA, in woven bone using finite element analysis. The reaction forces in bone and displacement of the screws were used to assess the overall performance of each material in a pull-out test. The second objective of this work was to develop and evaluate micro-computed tomography-based finite element models of in vivo biodegradable screws of the unnamed magnesium-alloy over time in rabbit femurs. Several foundational observations were made about modeling in vivo degrading magnesium devices with a micro-CT to FEA protocol. The results of this work have shown that an unnamed biodegradable magnesium-alloy and a biodegradable 82:18 PLLA:PLGA copolymer performed equally in nodal displacement and that the Mg-based device only outperformed the copolymer in Emin woven bone

    Multi-scale biomechanical study of transport phenomena in the intervertebral disc

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    Intervertebral disc (IVD) degeneration is primarily involved in back pain, a morbidity that strongly affects the quality of life of individuals nowadays. Lumbar IVDs undergo stressful mechanical loads while being the largest avascular tissues in our body: Mechanical principles alone cannot unravel the intricate phenomena that occur at the cellular scale which are fundamental for the IVD regeneration. The present work aimed at coupling biomechanical and relevant molecular transport processes for disc cells to provide a mechanobiological finite element framework for a deeper understanding of degenerative processes and the planning of regenerative strategies. Given the importance of fluid flow within the IVD, the influence of poroelastic parameters such as permeabilities and solid-phase stiffness of the IVD subtissues was explored. A continuum porohyperelastic material model was then implemented. The angles of collagen fibers embedded in the annulus fibrosus (AF) were calibrated. The osmotic pressure of the central nucleus pulposus (NP) was also taken into account. In a parallel study of the human vertebral bone, microporomechanics was used together with experimental ultrasonic tests to characterize the stiffness of the solid matrix, and to provide estimates of poroelastic coefficients. Fluid dynamics analyses and microtomographic images were combined to understand the fluid exchanges at the bone-IVD interface. The porohyperelastic model of a lumbar IVD with poroelastic vertebral layers was coupled with a IVD transport model of three solutes - oxygen, lactate and glucose - interrelated to reproduce the glycolytic IVD metabolism. With such coupling it was possible to study the effect of deformations, fluid contents, solid-phase stiffness, permeabilities, pH, cell densities of IVD subtissues and NP osmotic pressure on the solute transport. Moreover, cell death governed by glucose deprivation and lactate accumulation was included to explore the mechanical effect on cell viability. Results showed that the stiffness of the AF had the most remarkable role on the poroelastic behavior of the IVD. The permeability of the thin cartilage endplate and the NP stiffness were also relevant. The porohyperelastic model was shown to reproduce the local AF mechanics, provided the fiber angles were calibrated regionally. Such back-calculation led to absolute values of fibers angles and to a global IVD poromechanical behavior in agreement with experiments in literature. The inclusion of osmotic pressure in the NP also led to stress values under confined compression comparable to those measured in healthy and degenerated NP specimens. For the solid bone matrix, axial and transverse stiffness coefficients found experimentally in the present work agreed with universal mass density-elasticity relationships, and combined with continuum microporomechanics provided poroelastic coefficients for undrained and drained cases. The effective permeability of the vertebral bony endplate calculated with fluid dynamics was highly correlated with the porosity measured in microtomographic images. The coupling of transport and porohyperelastic models revealed a mechanical effect acting under large volume changes and high compliance, favored by healthy rather than degenerated IVD properties. Such effect was attributed to strain-dependent diffusivities and diffusion distances and was shown to be beneficial for IVD cells due to the load-dependent increases of glucose levels. Cell density, NP osmotic pressure and porosity were the most important parameters affecting the coupled mechano-transport of metabolites. This novel study highlights the restoration of both cellular and mechanical factors and has a great potential impact for novel designs of treatments focused on tissue regeneration. It also provides methodological features that could be implemented in clinical image-based tools and improve the multiscale understanding of the human spine mechanobiology
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