Model developments for in silico studies of the lumbar spine biomechanics

Premi extraordinari doctorat curs 2008-2009, àmbit Enginyeria IndustrialLa present tesi investiga l'ús de la modelització amb elements finits per a l'estudi de la biomecànica lumbar per a l'avaluació clínica. Els estudis bibliogràfics del capítol 1 mostren relacions funcionals clares entre les forces externes i les estructures i formes del teixit lumbar. Els estudis clínics demostraren que independentment del seu origen, el dolor lumbar pot veure's empitjorat per sobrecàrregues dels teixits. Les mesures experimentals són insuficients per descriure la distribució de càrrega entre els diferents teixits lumbars, és així que s'han utilitzat models d'elements finits. No obstant, la fiabilitat dels models a l'hora de predir les càrregues locals en els teixits no ha estat demostrada, essent aquest un dels objectes d'estudi.En el Capítol 2 s'elaborà un model bisegment de la columna lumbar. El model inicial es completà incloent el còrtex vertebral, una definició complerta de les juntes sinovials, les plaques terminals de cartílag i una descripció millorada de l'estructura de l'anell. Es van simular càrregues simplificades per als estudis in vitro per calcular les distribucions de tensions, deformacions i energia. El model bisegment és vàlid per interpretar les distribucions de càrrega funcionals a L3-L5 en el cas d'estructures conegudes de teixit, però el conjunt de la geometria L3-L5 necessitava ser millorat.Així al Capítol 3 es creà un model geomètric bisegment precís de L3-L5. El nou model incloïa les corregides: dimensions i formes, alçades de disc, localitzacions del nucli, formes posteriors de l'os, i distribució dels lligaments. Després de comparar a nivell biomecànic l'antiga geometria amb la nova, els resultats mostraren que els rols relatius dels teixits modelats depenen de la geometria. En general, les distribucions de càrrega predites eren més fisiològiques en el nou model. En canvi, ambdós models, reprodueixen rangs experimentals de moviment, així doncs la seva validació hauria de tenir en compte les transferències de càrrega locals.El Capítol 4 es centra en la variabilitat dels angles creuats del col·lagen de l'anell. Es crearen quatre models bisegment amb organitzacions d'anell fibrós basats en la bibliografia comparant-se sota diverses càrregues. A més es proposà un paràmetre d'estabilització de l'anell per analogia a un tub de parets gruixudes. La biomecànica del model depenia en gran mesura de l'organització de l'anell fibrós, però el paràmetre d'estabilització era soviet contradictori amb les tensions i forces predites. Així, s'assumí que la geometria de la columna i l'organització de l'anell fibrós estaven lligades. Les xarxes d'anell de col·lagen adaptades es poden determinar numèricament, però els models d'anell haurien d'estar bastats en relacions mecanobiològiques.Al Capítol 5 es presenta un model de disc artificial acoblat amb el model de L3-L5. Models bisegment amb i sense implant van ser comparats amb càrregues controlades per força o desplaçament, incloent o no l'aproximació del pes del cos. La rigidesa de la pròtesi alterava generalment les distribucions de càrrega i les rotacions controlades per desplaçament conduint a grans efectes adjacents. Incloent el pes del cos les condicions de contorn semblaven més fisòlogiques que sense. Malgrat la rigidesa del nou disc, aquest sembla més prometedor que altres dispositius comercials.En aquesta tesi s'han creat sis models nous elements finits de la columna lumbar osteoligamentosa. Les simulacions han mostrat que l'ús fiable dels models requereix d'una descripció precisa de les càrregues locals i respostes mecàniques de teixits. Les prediccions locals van estar limitades qualitativament degudes al desconeixement de les estructures de teixit tou, equacions constitutives i condicions de contorn. En canvi, els models poden ser emprats com a laboratoris in silico per superar aquestes limitacions. Basat en la informació numèrica i experimental, s'ha proposat un procediment jeràrquic per al desenvolupament qualitativament fiable de models elements finits de la columna lumbar.This PhD thesis investigated the use of finite element modelling to study lumbar spine biomechanics for clinical assessment. Bibliographic studies reported in the first Chapter showed clear functional relations between external forces and lumbar spine tissue structures and shapes. Clinical research revealed that independently of its origin, low back pain may be worsened by altered tissue mechanical environments. Experimental measurements alone cannot truly describe the load distributions between the different lumbar spine tissues. Thus, finite element models have been used in the past. But model reliability in predicting local tissue loadings is still not manifest and has been explored in this thesis as described in the following chapters.In Chapter 2, a L3-L5 lumbar spine bi-segment model was built. An initial model was completed to include the vertebral cortex, a full definition of the facet joints, the cartilage endplates, and an improved description of the annulus fibre-reinforced structure. Simplified load-cases used for in vitro studies were simulated to calculate stress and strain energy distributions. Predictions within the L3-L5 lumbar spine bi-segment model could be interpreted in terms of functional load distributions related to known tissue structures, but the overall L3-L5 bisegment model geometry needed further update.Thus, in Chapter 3, a geometrically accurate L3-L5 lumbar spine bi-segment model was created. The new model included corrected L3 and L5 body shapes and dimensions, corrected disc heights and nucleus placements, corrected posterior bone shapes, dimensions, and orientations, and corrected ligament distributions. The new and old geometries were biomechanically compared. Results showed that the relative roles of modelled tissues greatly depend on the geometry. Predicted load distributions were generally more physiological in the new model. However, new and old models could both reproduce experimental ranges of motion, meaning that their validation should take into account local load transfers.Chapter 4 focuses on the variability of the annulus collagen criss-cross angles. Four bi-segment models with literature-based annulus fibre organizations were created and compared under diverse loads. Moreover, an annulus stabilization parameter was proposed by analogy to a thick walled pipe. Model biomechanics greatly depended on the annulus fibre organization, but annulus stabilization parameter was often contradictory with the predicted stresses and strains. Spine geometry and annulus fibrous organization were hypothesized to be linked together. Adapted annulus collagen networks may be numerically determined, but annulus modelling should be based on mechano-biological relationships.In Chapter 5, a case-study of a novel artificial disc design coupled with the L3-L5 lumbar spine model is presented. Bi-segment models with and without implant were compared under load- or displacement-controlled rotations, with or without body-weight like load. Prosthesis stiffness generally altered the load distributions and displacement-controlled rotations led to strong adjacent level effects. Including body weight-like loads seemed to give more realistic results. Although the novel disc substitute is too stiff, it is more promising than other existing commercial devices.In this thesis, six new osteoligamentous lumbar spine bi-segment finite element models were created. Simulations showed that reliable use of lumbar spine finite element models requires precise descriptions of local tissue loading and response. Local predictions were qualitatively mainly limited by a lack of knowledge about soft tissue structural organisations, constitutive equations, and boundary conditions. However, models can be used as in silico laboratories to overcome such limitations. A hierarchical procedure for the development of qualitatively reliable lumbar spine finite element models was proposed based on available numerical and experimental inputs.Award-winningPostprint (published version

Significance of the collagen criss-cross angle distributions in lumbar annuli fibrosi as revealed by finite element simulations

In the human lumbar spine, annulus fibr osus (AF) fibres la rgely contribute to intervertebral disc (IVD) stability, and deta iled annulus models are required to obtain reliable predictions of lumbar spine biom echanics by finite element (FE) modelling. However, different definitions of collagen orientation coexist in the literature for healthy human lumbar AFs and are indiscrimi nately used in mode lling. Therefore, four AF fibre-induced anisotropy models were bu ilt from reported anatomical descriptions and inserted in a L3-L5 lumbar bi-segment FE model. AF models were respectively characterized by radial, tange ntial, radial and tangentia l, and no fibre orientation gradients. IVD local biomechanics was studied under axial rotation and axial compression. A new parameter, i.e. the Fi bre Contribution Qual ity parameter, was computed in the anterior, lateral, postero-l ateral and posterior AFs of each model, in function of fibre stresses, load distributions, and matrix shear strains. Locally, each AF model behaved differently, affecting the IVD biomechanics. The Fibre Contribution Quality (FCQ) parameter established a direct link between local AF fibre organization and loading, while other biomechanical data did not. It was conc luded that local AF fibre orientations should be modelled in rela tion to other segment characteristics. The proposed FCQ parameter could be used to examine such relations, being, therefore particularly relevant to patient-specifi c models or artificial disc designs.Postprint (published version

Regional annulus fibre orientations used as a tool for the calibration of lumbar intervertebral disc finite element models

The highly organized collagen network of human lumbar a nnulus fibrosus (AF) is fundamental to preserve the mechanical inte grity of the interverte bral discs. In the healthy AF, fibres are embedded in a hydrated matrix and arranged in a criss-cross fashion, giving an anisotropic structure capab le to undergo large st rains. Quantitative anatomical examinations revealed particular fibre orientation patterns, possibly coming from regional adaptations of the AF mechan ics. Based on such hypothesis, this study aimed to show that the regional differen ces in AF mechanical behaviour can be reproduced by considering only fibre orientatio n changes. Using the finite element (FE) method, AF matrix was modelled as a poro-hy perelastic material, where the porous solid was treated as a comp ressible continuum following a Neo-Hookean constitutive law. Strain-dependent permeability was assumed and all material parameters were taken from the literature. Fibre reinforcement wa s accounted for by adding an extra-term to the porous matrix strain energy density func tion, only active along th e fibre directions. Through such term, fibre orientations were then adjusted, to reproduce AF tensile behaviours measured for four different regi ons: posterior outer (PO), anterior outer (AO), posterior inner (PI) and anterior inne r (AI). Curve calibrations resulted in the following optimal angles, calculated with respect to the circumferential axis: 28º for PO, 23º for AO, 43º for PI and 31º for AI. In average, we obtained fibres 30% more transversal in the inner than in the outer AF against 38% as measured by Cassidy et al. (1989). Fibres more axial in the posterior than in the anterior AF were also measured by Holzapfel et al. (2005), with angle values comparable to our computed average values. Since all the hyperelastic and fluid-phase material parameters remained unchanged throughout the AF, calibration based only on fibre patterns variations may be an effective tool to calibrate the regional AF mechanics in a realistic way.Postprint (published version

Estabilización de fracturas Schatzker I de la meseta tibial. Estudio numérico comparativo mediante elementos finitos. Placas bloqueadas vs tornillos canulados

ResumenObjetivoLa estabilización quirúrgica de las fracturas SchatzkerI de meseta tibial se realiza principalmente mediante la colocación de tornillos canulados o mediante la aplicación de una placa con tornillos bloqueados proximales. En el postoperatorio, los pacientes realizan generalmente una descarga de 6 u 8 semanas. Usando el método de elementos finitos (EF), este estudio intenta analizar si la carga inmediata del paciente después de la cirugía genera un exceso de desplazamiento interfragmentario (DI).MétodosUtilizando un modelo validado de EF de paciente sano, el modelo tibial se reprodujo geométricamente, y se realizó una fractura SchatzkerI tipo a partir de radiografías y TAC de diferentes pacientes. Se modelizaron tornillos canulados de 6,5mm y una placa Polyax (Biomet Inc, EE.UU.), implantándose virtualmente en la tibia fracturada, y aplicando una fuerza de 400N, equivalente a 80kg de peso del paciente en bipedestación. Los DI se calcularon a partir del desplazamientos de diferentes nodos en el área fractuaria.ResultadosLos DI máximos calculados con la placa Polyax y los tornillos canulados fueron de 0,1-0,15mm y 0,25-0,3mm, respectivamente. Sin embargo, aplicando un peso de un 20% existía riesgo de fractura por compresión con los tornillos canulados. Con la placa Polyax se obtuvo una mejor distribución de las cargas, manteniéndose en zona segura por debajo de 100Mpa con la aplicación del 50% del peso del paciente.ConclusiónEste estudio sugiere que ambos sistemas tienen un resultado similar en cuanto al DI, pero la placa realiza una mejor distribución de las cargas en la zona de la fractura, permitiendo la carga parcial inmediata de un 50% del peso del paciente.AbstractObjectiveSurgical stabilization of split fractures of the lateral tibial plateau may involve percutaneous insertion of cannulated screws or more invasive implantation of locked plating systems. In any case, six to eight weeks of non-weight-bearing are recommended. By using the finite element (FE) method, this study aimed to assess whether immediate weight bearing can generate excessive interfragmentary motions (IM).MethodsA validated femur-tibia FE model of a healthy patient was used. The tibia model was reconverted into geometry, and a SchatzkerI fracture was re-created based on patient x-rays. Cannulated 6.5mm cancellous bone screws, and a Polyax tibial locked plating system (Biomet Inc, USA) were modelled, and virtually implanted into the fractured tibia geometry. An axial force of 400N pressed the femur model against the tibial plateau, simulating the weight of an 80Kg patient in bipedal stance. IM were calculated as the displacements between two nodes initially superimposed in the fracture areaResultsMaximum IM calculated with the Polyax and with the cannulated screw fixations were around 0.1-0.15mm, and 0.25-0.3mm, respectively. Both systems led to similar IM up to 80-90% of applied body weight. However, applying over 20% of the simulated body weight might lead to a risk of compression bone fracture. With the Polyax system, bone stresses were better distributed, and remained below 100MPa at 30% of body weight. Maximum stresses in the implants were about half the reported strength for the alloy simulated.ConclusionThis study suggested that IM caused by weight bearing might not impede bone healing in a fracture stabilized with either a Polyax locked plating system or cannulated screws. However, cannulated screw systems could lead to harmful load concentrations in the bone with immediate weight bearing. Plate systems will allow around 50% of immediate weight bearing

A micro-macro evaluation of the vertebral bony endplate permeability based on computational fluid dynamics

The intrinsic permeability is an important parameter that describes the resistance of a porous structure to fluid flo w. It has a key role in poroelastic finite element models of spinal segments, especially at the vertebral endplate, i.e. the interface between intervertebral disc and vertebra. In the understanding of the properties of the complex endplate system, an expli cit evaluation for permeability of subchondral bone is missing. Thus, a new method wa s proposed to evaluate the intrinsic permeability of the bony endplate. CT - based reconstruction s of the bony endplate from a lumbar vertebra were analyzed using computational fluid dynamics , and the i ntrinsic permeability and porosity of the structure were calculated. Results showed that the permeability did not depend on the fluid flow direction, and was statistically similar for both the superior and inferior endplates . Permeability values varied within the range of trabecular bone, while porosity values w ere lower than trabecular bone characteristic values. Finally, i ntrins ic permeability correlated well with porosity through the Kozeny - Karman model, which offer s perspectives for parametric studies involving degenerative or age - related changes at the disc - bone interface.Postprint (published version

Muscular tension significantly affects stability in standing posture

Muscular co-contraction is a strategy commonly used by elders with the aim to increase stability. However, co-contraction leads to stiffness which in turns reduces stability. Some literature seems to suggest an opposite approach and to point out relaxation as a way to improve stability. Teaching relaxation is therefore becoming the aim of many studies letting unclear whether tension or relaxation are the most effective muscular strategy to improve stability. Relaxation is a misleading concept in our society. It is often confused with rest, while it should be addressed during stressing tasks, where it should aim to reduce energetic costs and increase stability. The inability to relax can be related to sub-optimal neuro-motor control, which can lead to increased stresses. Research question The objective of the study is to investigate the effect of voluntary muscle contraction and relaxation over the stability of human standing posture, answering two specific research questions: (1) Does the muscular tension have an impact on stability of standing posture? (2) Could this impact be estimated by using a minimally invasive procedure? Methods By using a force plate, we analysed the displacement of the center of pressure of 30 volunteers during state of tension and relaxation in comparison with a control state, and with open and closed eyes. Results We found that tension significantly reduced the stability of subjects (15 out of 16 parameters, p¿<¿0.003). Significance Our results show that daily situations of stress can lead to decreased stability. Such a loss might actually increase the risk of chronic joint overload or fall. Finally, breathing has direct effect over the management of pain and stress, and the results reported here point out the need to explicitly explore the troubling fact that a large portion of population might not be able to properly breath.Peer ReviewedPostprint (published version

The interplay between biochemical mediators and mechanotransduction in chondrocytes: Unravelling the differential responses in primary knee osteoarthritis.

In primary or idiopathic osteoarthritis (OA), it is unclear which factors trigger the shift of articular chondrocyte activity from pro-anabolic to pro-catabolic. In fact, there is a controversy about the aetiology of primary OA, either mechanical or inflammatory. Chondrocytes are mechanosensitive cells, that integrate mechanical stimuli into cellular responses in a process known as mechanotransduction. Mechanotransduction occurs thanks to the activation of mechanosensors, a set of specialized proteins that convert physical cues into intracellular signalling cascades. Moderate levels of mechanical loads maintain normal tissue function and have anti-inflammatory effects. In contrast, mechanical over- or under-loading might lead to cartilage destruction and increased expression of pro-inflammatory cytokines. Simultaneously, mechanotransduction processes can regulate and be regulated by pro- and anti-inflammatory soluble mediators, both local (cells of the same joint, i.e., the chondrocytes themselves, infiltrating macrophages, fibroblasts or osteoclasts) and systemic (from other tissues, e.g., adipokines). Thus, the complex process of mechanotransduction might be altered in OA, so that cartilage-preserving chondrocytes adopt a different sensitivity to mechanical signals, and mechanic stimuli positively transduced in the healthy cartilage may become deleterious under OA conditions. This review aims to provide an overview of how the biochemical exposome of chondrocytes can alter important mechanotransduction processes in these cells. Four principal mechanosensors, i.e., integrins, Ca2+ channels, primary cilium and Wnt signalling (canonical and non-canonical) were targeted. For each of these mechanosensors, a brief summary of the response to mechanical loads under healthy or OA conditions is followed by a concise overview of published works that focus on the further regulation of the mechanotransduction pathways by biochemical factors. In conclusion, this paper discusses and explores how biological mediators influence the differential behaviour of chondrocytes under mechanical loads in healthy and primary OA

In-Vitro and In-Silico Investigation of Dynamic Compression on Cartilage Endplate Cells in Agarose

INTRODUCTION: The cartilage endplate (CEP) covers the top and bottom of the intervertebral disc (IVD) and acts to transmit compressive loads and transport water, nutrients, and waste in and out of the disc. Early cartilage endplate (CEP) degeneration is likely to play a key role in IVD degeneration, but little is known about CEP mechanobiology and its changes in degeneration. Investigating these changes is essential to elucidate how the CEP contributes to IVD pathology. METHODS: In-vitro: Bovine-tail CEP cells were expanded until passage three. Afterwards, a 1:1 mixture of CEP cells and agarose was pipetted into silicon molds to create 2% agarose and 1x107 cells/ml carriers, 6 mm diameter and 3 mm thickness, and cultured two days for phenotype recovery. Cell-agarose carriers were placed in custom-made chambers, stimulated with 10 ng/ml TGF-β1 throughout the entirety of the experiment and dynamically compressed up to 7% strain for one hour at 1.5 Hz every day for up to 14 days. Those not dynamically loaded experienced the constant weight of the chamber lid exerting ~5.1 Pa per carrier. Carriers were collected on Days 0, 7, and 14 for downstream analysis of cell viability, gene expression, and glycosaminoglycan (GAG) content. In-silico: A 2D axisymmetric porohyperelastic, compressible, Neo-Hookean finite element model (FEM) of a cell-agarose carrier was developed in Abaqus using literature-derived material properties and loaded with dynamic compression as in the in-vitro experiment. A previously developed mechanotransduction network model was used to predict protein activation levels by initial mechanoreceptor perturbations standing for dynamic compression (α5β1, αvβ3), physioosmotic pressure (TRPV4), tensile strain (αvβ5), plus chondrogenic media (TGF-β). Predicted protein activation was normalized by baseline conditions. RESULTS: After seven and 14 days of culture, cell-agarose carriers in all conditions demonstrated significantly increased expression of anabolic genes aggrecan (ACAN) 2-200x, collagen II (COL II) 31000x, and GAG/DNA content 2.5-5x, alongside decreased expression of catabolic gene matrix metalloproteinase 3 (MMP3). Reaction forces from FEM (0.07N) matched force data collected during loading (0.06N). The FEM showed that hydrostatic pressure varies from center to edge of carrier. General trends of increased/decreased gene expression and protein activation matched between experimental and network model results. DISCUSSION & CONCLUSIONS: A novel framework coupling 3D cell culture with in-silico methods is presented, in which the FEM provides details about loads experienced at each point within the carrier, while the network model uses these mechanical cues and environmental perturbations to predict protein expression and identify key proteins for future analysis. Keywords: Intervertebral disc / spine and their disorders, Biomechanics / biophysical stimuli and mechanotransductio

Cartilaginous endplates: A comprehensive review on a neglected structure in intervertebral disc research

The cartilaginous endplates (CEP) are key components of the intervertebral disc (IVD) necessary for sustaining the nutrition of the disc while distributing mechanical loads and preventing the disc from bulging into the adjacent vertebral body. The size, shape, and composition of the CEP are essential in maintaining its function, and degeneration of the CEP is considered a contributor to early IVD degeneration. In addition, the CEP is implicated in Modic changes, which are often associated with low back pain. This review aims to tackle the current knowledge of the CEP regarding its structure, composition, permeability, and mechanical role in a healthy disc, how they change with degeneration, and how they connect to IVD degeneration and low back pain. Additionally, the authors suggest a standardized naming convention regarding the CEP and bony endplate and suggest avoiding the term vertebral endplate. Currently, there is limited data on the CEP itself as reported data is often a combination of CEP and bony endplate, or the CEP is considered as articular cartilage. However, it is clear the CEP is a unique tissue type that differs from articular cartilage, bony endplate, and other IVD tissues. Thus, future research should investigate the CEP separately to fully understand its role in healthy and degenerated IVDs. Further, most IVD regeneration therapies in development failed to address, or even considered the CEP, despite its key role in nutrition and mechanical stability within the IVD. Thus, the CEP should be considered and potentially targeted for future sustainable treatments

Immuno-modulatory effects of intervertebral disc cells

Low back pain is a highly prevalent, chronic, and costly medical condition predominantly triggered by intervertebral disc degeneration (IDD). IDD is often caused by structural and biochemical changes in intervertebral discs (IVD) that prompt a pathologic shift from an anabolic to catabolic state, affecting extracellular matrix (ECM) production, enzyme generation, cytokine and chemokine production, neurotrophic and angiogenic factor production. The IVD is an immune-privileged organ. However, during degeneration immune cells and inflammatory factors can infiltrate through defects in the cartilage endplate and annulus fibrosus fissures, further accelerating the catabolic environment. Remarkably, though, catabolic ECM disruption also occurs in the absence of immune cell infiltration, largely due to native disc cell production of catabolic enzymes and cytokines. An unbalanced metabolism could be induced by many different factors, including a harsh microenvironment, biomechanical cues, genetics, and infection. The complex, multifactorial nature of IDD brings the challenge of identifying key factors which initiate the degenerative cascade, eventually leading to back pain. These factors are often investigated through methods including animal models, 3D cell culture, bioreactors, and computational models. However, the crosstalk between the IVD, immune system, and shifted metabolism is frequently misconstrued, often with the assumption that the presence of cytokines and chemokines is synonymous to inflammation or an immune response, which is not true for the intact disc. Therefore, this review will tackle immunomodulatory and IVD cell roles in IDD, clarifying the differences between cellular involvements and implications for therapeutic development and assessing models used to explore inflammatory or catabolic IVD environments