Biomechanical study of intervertebral disc degeneration

Degeneration and age affect the biomechanics of the intervertebral disc, by reducing its stiffness, flexibility and shock absorption capacities against daily movement and spinal load. The biomechanical characterization of intervertebral discs is achieved by conducting mechanical testing to vertebra-disc-vertebra segments and applying axial, shear, bend and torsion loads, statically or dynamically, with load magnitudes corresponding to the physiological range. However, traditional testing does not give a view of the load and deformation states of the disc components: nucleus pulposus, annulus fibrosus and endplate. Thus, the internal state of stress and strains of the disc can only be predicted by numerical methods, one of which is the finite element method. The objective of this thesis was, to study the biomechanics of degenerated intervertebral discs to load conditions in compression, bending and torsion, by using mechanical testing and a finite element model of disc degeneration, based on magnetic resonance imaging (MRI). Therefore, lumbar discs obtained from cadavers corresponding to spinal levels L2-L3 and L4-L5 with mild to severe degeneration were used. Intervertebral osteochondrosis and spondylosis deformans were identified, being the disc space collapse, the most striking feature. Next, all discs were tested to static and dynamic load conditions, the results gained corresponded to the disc stiffness (in compression, bending and torsion), stress relaxation and dynamic response. Of these, the stiffness response was used to validate the disc model. The testing results suggest that discs with advanced degeneration over discs with mild degeneration are, less rigid in compression, less stiffer under bending and torsion, showed less radial bulge, and reduce their viscoelastic and damping properties. This study shows that degeneration has an impact on the disc biomechanical properties which can jeopardize normal functionality. Development of one finite element model of disc degeneration started by choosing a MRI of a L2-L3 disc. Segmentation of vertebra bone and disc materials followed, and were based on pixel brightness and radiology fundamentals, then a finite element mesh was created to account for the disc irregular shape. The disc materials were modeled as hyperelastic and the bone materials were modeled as orthotropic and isotropic. Adjustment of material properties was based on integrity of the annulus fibrosus, giving a stiffness value matching that of a mild degeneration disc. Then, validation of the model was performed, and included a study of the distributions of stress and strain under loads of compression, bending and torsion. The results from all load simulations show that the disc undergoes large deformations. In contrast, the vertebrae are subjected to higher stress but with negligible deformations. In compression, the model predicted formation of symmetrical disc bulge which agree with the testing behavior. The nucleus pulposus showed to be the principal load carrier with negative principal stresses and strains. In bending and torsion, the annulus fibrosus showed to be the principal load carrier with large symmetrical principal strains and stresses for the former loading and large shearing for the latter. The study showed the importance of soft tissue deformation, mostly noticed in advanced degeneration. In contrast, the higher stresses in the vertebra over those of the intervertebral disc showed the relevance of bone predisposition to fracture. Such kind of studies, should contribute to the understanding of the biomechanics of the intervertebral disc.La degeneración y edad afectan la biomecánica del disco intervertebral, reduciendo la capacidad de rigidez, flexibilidad y atenuación de impactos, contra el movimiento y carga del raquis. La caracterización biomecánica del disco se realiza con ensayos mecánicos a segmentos de vértebra-disco-vértebra y aplicando cargas axiales, cortantes, flexión y torsión, estáticas ó dinámicas, con magnitudes de carga según el intervalo fisiológico. Sin embargo, las pruebas tradicionales no dan una visión de los estados de carga y deformación de los componentes del disco: núcleo pulposo, anillo fibroso y placa terminal. Por lo tanto, el estado interno de esfuerzos y deformaciones del disco, solo puede ser predicho con métodos numéricos, uno de los cuales es el método de elemento finito. El objetivo de esta tesis fue, estudiar la biomecánica de discos intervertebrales degenerados a las condiciones de carga en compresión, flexión y torsión, mediante el uso de ensayos mecánicos y de un modelo de elementos finitos de la degeneración de disco, basado en imágenes con resonancia magnética (MRI). Por lo tanto, se usaron discos lumbares L2-L3 y L4-L5 obtenidos de cadáveres, con degeneración leve a severa. Se identificó osteocondrosis intervertebral y espondilosis deformante, siendo el colapso del espacio intervertebral el aspecto más relevante. Luego, todos los discos fueron ensayados a condiciones de carga estática y dinámica, y los resultados correspondieron a la rigidez del disco (a compresión, flexión y torsión), a la relajación de tensiones y a la respuesta dinámica. De éstos, la rigidez fue usada para validar el modelo de disco. Los resultados de los ensayos sugieren que los discos con degeneración avanzada sobre aquellos con degeneración leve son, menos rigidos a compresión, menos rigidos a flexión y torsión, presentan menor protuberancia radial, y reducen sus propiedades viscoelásticas y de amortiguamiento. El estudio muestra que la degeneración impacta las propiedades biomecánicas del disco, poniendo en riesgo la funcionalidad normal. El desarollo de un modelo de elementos finitos de la degeneración de disco inició eligiendo una secuencia de resonancia magnética de un disco L2-L3. La segmentación de los materiales del disco y de las vértebras se realizó basado en intensidad de brillo del pixel y en fundamentos de radiología, y se creó una malla de elementos finitos correspondiente a la forma irregular del disco. Los materiales del disco se modelaron como hiperelásticos y los tejidos óseos se modelaron como materiales ortotrópicos e isotrópicos. El ajuste de propiedades de los materiales fue basado en la integridad del anillo fibroso, y dio una rigidez correspondiente a la de un disco con degeneración leve. Luego, se realizó la validación del modelo, e incluyó un estudio de las distribuciones de esfuerzo y deformación a las condiciones de carga en compresión, flexión y torsión. Los resultados de todas las simulaciones de carga mostraron que el disco es sometido a grandes deformaciones. En contraste, las vértebras fueron sometidas a mayores esfuerzos pero con deformaciones insignificantes. En compresión, el modelo predijo la formación de una protuberancia radial simétrica, en concordancia con la experimentación. El núcleo pulposo mostró ser el portador principal de carga, con tensiones y deformaciones principales negativas. En flexión y torsión, el anillo fibroso mostró ser el portador principal de carga, con grandes deformaciones y tensiones principales simétricas para la primera carga, y con grandes tensiones cortantes para la segunda carga. El estudio mostró la importancia de las deformaciones de los tejidos blandos, principalmente notados en la degeneración avanzada. Por el contrario, las tensiones mayores en los cuerpos vertebrales sobre aquellas del disco intervertebral mostraron la relevancia de la predisposición a las fracturas óseas. Este tipo de estudio debe contribuir a la comprensión de la biomecánica del disco intervertebral

Finite Element Modelling of Human Lumbar Spine

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Finite element modeling and simulation of degeneration and hydrotraction therapy of human lumbar spine segments

A large percent of population is affected by low back pain problems all over the world, starting from the degeneration of the lumbar spinal structure, caused generally by ageing and mechanical overloading. If the degeneration is not too advanced, surgical treatments can be avoid, by applying conservative treatments, like traction therapies. Dry traction is a well-known method, however, often happens that instead of the traction effect and stress relaxation, the compression increases in the discs due to muscle activities. This verifies the importance of the suspension hydro-traction therapy, where the muscles are completely relaxed. The aim of this study was doubled: to model and simulate numerically the age-related and accidental degenerations of lumbar functional spinal units (FSU) and to simulate the mechanical answer of the more or less degenerated lumbar segments for the hydro-traction treatment, by using FE method. The basic question was: how to unload the disc to regain or improve its functional and metabolic ability. FE simulations of the mechanical behaviour of human lumbar FSUs with life-long agerelated and sudden accidental degenerations are presented for tension and compression. Compressive material constants were obtained from the literature, tensional material moduli were determined by parameter identification, using in vivo measured global elongations of segments as control parameters. 3D FE models of a typical FSU of lumbar part L3-S1 were developed extended to several nonlinear and nonsmooth unilateral features of intervertebral discs, ligaments, articular facet joints and attachments. The FE model was validated both for compression and tension, by comparing the numerical calculations with experimental results. The weightbath hydrotraction therapy decreases pain, increases joint flexibility, and improves the quality of life of patients with cervical or lumbar discopathy. Numerical simulations were investigated to clear the biomechanical effects of hydrotraction treatment of more or less degenerated segments to improve the efficiency of the non-invasive conservative treatment

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

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

The influence of over-distraction on biomechanical response of cervical spine post anterior interbody fusion: a comprehensive finite element study

Introduction: Anterior cervical discectomy and fusion (ACDF) has been considered as the gold standard surgical treatment for cervical degenerative pathologies. Some surgeons tend to use larger-sized interbody cages during ACDF to restore the index intervertebral disc height, hence, this study evaluated the effect of larger-sized interbody cages on the cervical spine with ACDF under both static and cyclic loading.Method: Twenty pre-operative personalized poro-hyperelastic finite element (FE) models were developed. ACDF post-operative models were then constructed and four clinical scenarios (i.e., 1) No-distraction; 2) 1 mm distraction; 3) 2 mm distraction; and 4) 3 mm distraction) were predicted for each patient. The biomechanical responses at adjacent spinal levels were studied subject to static and cyclic loading. Non-parametric Friedman statistical comparative tests were performed and the p values less than 0.05 were reflected as significant.Results: The calculated intersegmental range of motion (ROM) and intradiscal pressure (IDP) from 20 pre-operative FE models were within the overall ranges compared to the available data from literature. Under static loading, greater ROM, IDP, facet joint force (FJF) values were detected post ACDF, as compared with pre-op. Over-distraction induced significantly higher IDP and FJF in both upper and lower adjacent levels in extension. Higher annulus fibrosus stress and strain values, and increased disc height and fluid loss at the adjacent levels were observed in ACDF group which significantly increased for over-distraction groups.Discussion: it was concluded that using larger-sized interbody cages (the height of ≥2 mm of the index disc height) can result in remarkable variations in biomechanical responses of adjacent levels, which may indicate as risk factor for adjacent segment disease. The results of this comprehensive FE investigation using personalized modeling technique highlight the importance of selecting the appropriate height of interbody cage in ACDF surgery

Biomechanical modelling of the whole human spine for dynamic analysis

Developing computational models of the human spine has been a hot topic in biornechanical research for a couple of decades in order to have an understanding of the behaviour of the whole spine and the individual spinal parts under various loading conditions. The objectives of this thesis are to develop a biofidefic multi-body model of the whole human spine especially for dynamic analysis of impact situations, such as frontal impact in a car crash, and to generate finite element (FE) models of the specific spinal parts to investigate causes of injury of the spinal components. As a proposed approach, the predictions of the multi-body model under dynamic impact loading conditions, such as reaction forces at lumbar motion segments, were utilised not only to have a better understanding of the gross kinetics and kinematics of the human spine, but also to constitute the boundary conditions for the finite element models of the selected spinal components. This novel approach provides a versatile, cost effective and powerful tool to analyse the behaviour of the spine under various loading conditions which in turn helps to develop a better understanding of injury mechanisms

Development of a biomimetic finite element model of the intervertebral disc diseases and regeneration

Tese de doutoramento do Programa Doutoral em Engenharia BiomédicaDegenerative Disc Disease is one of the largest health problems faced worldwide, based on lost working time and associated costs. This is the driving force for the development of a biomimetic Finite Element (FE) model of the Intervertebral Disc (IVD), which is a multiphasic and highly inhomogeneous structure. A great amount of experimental and numerical works have studied the IVD and proven that it presents osmo-poro-hyper-visco-elastic behavior, with high influence of the anisotropic behavior of collagen fibers. Poroelastic models of the IVD are mostly implemented in commercial FE-packages, which means that the accessibility to the source algorithm is often circumscribed. In order to approach to the biomechanical behavior of the IVD in the Human spine with higher flexibility and accuracy, an innovative poroelastic formulation implemented on a home-developed open-source FE solver is addressed and validated throughout this work. Numerical simulations were mostly devoted to the analysis of the non-degenerated Human IVD time-dependent behavior, using a geometrically accurate FE model of a full motion segment (MS), constructed with quadratic 27 nodes hexaedral elements. The results of the tests performed for creep assessment were inside the scope of the experimental and numerical literature data, with remarkable improvements of the numerical accuracy when compared with some previously published results obtained with the commercial FE-package ABAQUS®. Previously unpublished experimental data from the research partners at VUmc (Amsterdam, The Netherlands) were also analyzed and compared with the MS FE model, which proved to reproduce satisfactorily to the physiological and non-physiological conditions of those experimental tests. The IVD biomechanical behavioral is complex and dependent on multiple factors. The numerical simulations with the present MS FE model, using the home-developed open-source FE solver, demonstrated potential to biomimitize the IVD and thus contribute to the advance of the knowledge on its biomechanics.A Doença Degenerativa dos Discos é um dos maiores problemas de saúde enfrentados a nível mundial, a nível de tempo de trabalho perdido e custos associados. Esta é a motivação para o desenvolvimento de um modelo biomimético de Elementos Finitos (EF) do Disco Intervertebral (DIV), que é uma estrutura multifásica e altamente heterogénea. Um grande número de trabalhos, experimentais e numéricos, estudou o DIV e provou que este apresenta comportamento osmo-poro-hiper-visco-elástico, com influência significativa do comportamento anisotrópico das fibras de colagénio. Os modelos poroelásticos do DIV têm sido frequentemente implementados em programas comerciais de EF, o que significa que o acesso ao algoritmo-fonte é circunscrito. Para obter uma aproximação mais flexível e rigorosa ao comportamento biomecânico do DIV, uma formulação poroelástica inovadora foi implementada num programa de EF de acesso livre, desenvolvido internamente. Esta formulação é descrita e validada ao longo do presente trabalho. As simulações numéricas foram quase totalmente dedicadas à análise do comportamento do DIV Humano não-degenerado, que se sabe ser fortemente dependente do factor tempo. Para esse feito, foi utilizado um modelo de EF geométrico correcto de um segmento móvel (SM) completo, construído com elementos quadráticos hexaédricos de 27 nós. Os resultados dos testes levados a cabo para análise do comportamento do DIV em termos de fluência ficaram dentro do espectro dos resultados experimentais e numéricos disponíveis na literatura. Foram, inclusivé, registadas melhorias notáveis em relação a alguns trabalhos que utilizaram ABAQUS®, um programa de EF comericalmente disponível. Foram também analisados dados experimentais não publicados dos parceiros de investigação da VUmc (Amesterdão, Holanda). A comparação com o modelo EF do SM demonstrou que este modelo reproduz satisfactoriamente as condições dos testes experimentais, sejam elas condições fisiológicas ou não-fisiológicas. O comportamento biomecânico do DIV é complexo e dependente de múltiplos factores. As simulações numéricas levadas a cabo com o modelo EF do SM, utilizando o programa de EF de acesso livre desenvolvido internamente, demonstraram potencial para biomimetizar o DIV e assim contribuir para o avanço do conhecimento da sua biomecânica

A Constitutive Model for the Annulus of Human Intervertebral Disc: Implications for Developing a Degeneration Model and Its Influence on Lumbar Spine Functioning

The study of the mechanical properties of the annulus fibrosus of the intervertebral discs is significant to the study on the diseases of lumbar intervertebral discs in terms of both theoretical modelling and clinical application value. The annulus fibrosus tissue of the human intervertebral disc (IVD) has a very distinctive structure and behaviour. It consists of a solid porous matrix, saturated with water, which mainly contains proteoglycan and collagen fibres network. In this work a mathematical model for a fibred reinforced material including the osmotic pressure contribution was developed. This behaviour was implemented in a finite element (FE) model and numerical characterization and validation, based on experimental results, were carried out for the normal annulus tissue. The characterization of the model for a degenerated annulus was performed, and this was capable of reproducing the increase of stiffness and the reduction of its nonlinear material response and of its hydrophilic nature. Finally, this model was used to reproduce the degeneration of the L4L5 disc in a complete finite element lumbar spine model proving that a single level degeneration modifies the motion patterns and the loading of the segments above and below the degenerated disc