A. Shirazi-Adl

A Fibril-Network-Reinforced Biphasic Model of Cartilage in Unconfined Compression

Cartilage mechanical function relies on a composite structure of a collagen fibrillar network entrapping a proteoglycan matrix. Previous biphasic or poroelastic models of this tissue, which have approximated its composite structure using a homogeneous solid phase, have experienced difficulties in describing measured material responses. Progress to date in resolving these difficulties has demonstrated that a constitutive low that is successful for one test geometry (confined compression) is not necessarily successful for another (unconfined compression). In this study, we hypothesize that an alternative fibril-reinforced composite biphasic representation of cartilage can predict measured material responses and explore this hypothesis by developing and solving analytically a fibril-reinforced biphasic model for the case of uniaxial unconfined compression with frictionless compressing platens. The fibrils were considered to provide stiffness in tension only. The lateral stiffening provided by the fibril network dramatically increased the frequency dependence of disk rigidity in dynamic sinusoidal compression and the magnitude of the stress relaxation transient, in qualitative agreement with previously published data. Fitting newly obtained experimental stress relaxation data to the composite model allowed extraction of mechanical parameters from these tests, such as the rigidity of the fibril network, in addition to the elastic constants and the hydraulic permeability of the remaining matrix. Model calculations further highlight a potentially important difference between homogeneous and fibril-reinforced composite models. In the latter type of model, the stresses carried by different constituents can be dissimilar, even in sign (compression versus tension) even though strains can be identical. Such behavior, resulting only from a structurally physiological description, could have consequences in the efforts to understand the mechanical signals that determine cellular and extracellular biological responses to mechanical loads in cartilage.

Nonlinear analysis of cartilage in unconfined ramp compression using a fibril reinforced poroelastic model

OBJECTIVE To develop a biomechanical model for cartilage which is capable of capturing experimentally observed nonlinear behaviours of cartilage and to investigate effects of collagen fibril reinforcement in cartilage. DESIGN A sequence of 10 or 20 steps of ramp compression/relaxation applied to cartilage disks in uniaxial unconfined geometry is simulated for comparison with experimental data. BACKGROUND Mechanical behaviours of cartilage, such as the compression-offset dependent stiffening of the transient response and the strong relaxation component, have been previously difficult to describe using the biphasic model in unconfined compression. METHODS Cartilage is modelled as a fluid-saturated solid reinforced by an elastic fibrillar network. The latter, mainly representing collagen fibrils, is considered as a distinct constituent embedded in a biphasic component made up mainly of proteoglycan macromolecules and a fluid carrying mobile ions. The Youngs modulus of the fibrillar network is taken to vary linearly with its tensile strain but to be zero for compression. Numerical computations are carried out using a finite element procedure, for which the fibrillar network is discretized into a system of spring elements. RESULTS The nonlinear fibril reinforced poroelastic model is capable of describing the strong relaxation behaviour and compression-offset dependent stiffening of cartilage in unconfined compression. Computational results are also presented to demonstrate unique features of the model, e.g. the matrix stress in the radial direction is changed from tensile to compressive due to presence of distinct fibrils in the model. RELEVANCE Experimentally observed nonlinear behaviours of cartilage are successfully simulated, and the roles of collagen fibrils are distinguished by using the proposed model. Thus this study may lead to a better understanding of physiological responses of individual constituents of cartilage to external loads, and of the roles of mechanical loading in cartilage remodelling and pathology.

Poroelastic creep response analysis of a lumbar motion segment in compression

The nonlinear three-dimensional poroelastic creep response of a lumbar motion segment under a constant axial compression (400, 1200, or 2000 N) is investigated for a period of 2 h. The role of facet joints, strain-dependent variable permeability, boundary pore pressure, and coupled sagittal rotation on response is studied. Biomechanics of annulus excision, nucleotomy, and facetectomy are also investigated. Both material and geometric nonlinearities are considered. The annulus bulk is modelled as a nonhomogeneous composite of collagenous fibers and annulus bulk. As time progresses, axial displacement increases, pore pressure decreases, annulus bulk undergoes larger compressive stresses, fiber layers become slack, and facets carry larger loads. Surgical alterations markedly soften the temporal response and increase facets forces. In contrast, the strain-dependent variable permeability and boundary pore pressure stiffen the response and decrease forces on the facets. Changes in the nucleus fluid content, facet joints, boundary pore pressure, and disc permeability markedly influence the lumbar biomechanics.

Finite element analysis of human knee joint in varus-valgus

OBJECTIVE: The overall response, load transmission, role of ligaments, and state of stress in various components under varus-valgus moments in the intact and collateral-deficient tibiofemoral joint are investigated. DESIGN: A non-linear finite element model consisting of bony structures (tibia and femur), their articular cartilage layers, medial and lateral menisci and four primary ligaments (cruciates and collaterals) is utilized. BACKGROUND: Valgus and varus stresses are among the primary mechanisms of injury to knee ligaments. Several in vitro studies have investigated the role of ligaments in resisting such loads and on the way deficiency in either collateral may affect the response. METHODS: Cartilage layers are isotropic while menisci are non-homogeneous composite. The articulation of cartilage layers with each other and with the intervening menisci and the wrapping of the medial collateral ligament around the tibial edge are treated as large displacement frictionless contact problems. The non-linear elastostatic response of the joint at full extension is computed under varus-valgus moments applied to the femur with the tibia fixed. Cases simulating deficiency in collaterals and constraint on femoral axial rotation are also studied. RESULTS: The response is non-linear with large coupled axial rotations, internal in varus and external in valgus. In intact and collateral-deficient states, the joint shows varus or valgus openings so that the articulation occurs at one plateau only, medial in varus and lateral in valgus. Large tensile forces in cruciates in collateral-cut models generate higher compression penalty on the loaded plateau. CONCLUSIONS: Collaterals are the primary load-bearing structures; their absence would substantially increase primary laxities, coupled axial rotations, forces in cruciates, and articular contact forces. Good agreement with measurements is found. RELEVANCE: Detailed knowledge of joint biomechanics is essential in the diagnosis, prevention and treatment of observed disorders. Absence of collateral ligaments increases the loads in cruciates and contact stresses transmitted through cartilage layers and menisci, and thus places the affected components at more risk, especially when varus-valgus is accompanied by other modes of loading as well.

A fibril reinforced nonhomogeneous poroelastic model for articular cartilage: inhomogeneous response in unconfined compression

The depth dependence of material properties of articular cartilage, known as the zonal differences, is incorporated into a nonlinear fibril-reinforced poroelastic model developed previously in order to explore the significance of material heterogeneity in the mechanical behavior of cartilage. The material variations proposed are based on extensive observations. The collagen fibrils are modeled as a distinct constituent which reinforces the other two constituents representing proteoglycans and water. The Youngs modulus and Poissons ratio of the drained nonfibrillar matrix are so determined that the aggregate compressive modulus for confined geometry fits the experimental data. Three nonlinear factors are considered, i.e. the effect of finite deformation, the dependence of permeability on dilatation and the fibril stiffening with its tensile strain. Solutions are extracted using a finite element procedure to simulate unconfined compression tests. The features of the model are then demonstrated with an emphasis on the results obtainable only with a nonhomogeneous model, showing reasonable agreement with experiments. The model suggests mechanical behaviors significantly different from those revealed by homogeneous models: not only the depth variations of the strains which are expected by qualitative analyses, but also, for instance, the relaxation-time dependence of the axial strain which is normally not expected in a relaxation test. Therefore, such a nonhomogeneous model is necessary for better understanding of the mechanical behavior of cartilage.

Role of cartilage collagen fibrils networks in knee joint biomechanics under compression.

Collagen fibrils networks in knee cartilage and menisci change in content and structure from a region to another. While resisting tension, they influence global joint response as well as local strains particularly at short-term periods. To investigate the role of fibrils networks in knee joint mechanics and in particular cartilage response, a novel model of the knee joint is developed that incorporates the cartilage and meniscus fibrils networks as well as depth-dependent properties in cartilage. The joint response under up to 2000N compression is investigated for conditions simulating the absence in cartilage of deep fibrils normal to subchondral bone or superficial fibrils parallel to surface as well as localized split of cartilage at subchondral junction or localized damage to superficial fibrils at loaded areas. Deep vertical fibrils network in cartilage play a crucial role in stiffening (by 10%) global response and protecting cartilage by reducing large strains (from maximum of 102% to 38%), in particular at subchondral junction. Superficial horizontal fibrils protect the tissue mainly from excessive strains at superficial layers (from 27% to 8%). Local cartilage split at base disrupts the normal function of vertical fibrils at the affected areas resulting in higher strains. Deep fibrils, and to a lesser extent superficial fibrils, play dominant mechanical roles in cartilage response under transient compression. Any treatment modality attempting to repair or regenerate cartilage defects involving partial or full thickness osteochondral grafts should account for the crucial role of collagen fibrils networks and the demanding mechanical environment of the tissue.

Load-bearing role of facets in a lumbar segment under sagittal plane loadings

In the present work, the load-bearing role of the facet joints in a lumbar I2-3 segment is quantitatively determined by means of a three dimensional nonlinear finite element program. The analysis accounts for both material and geometric nonlinearities and treats the facet articulation as a nonlinear moving contact problem. The disc nucleus is considered as an inviscid incompressible fluid and the annulus as a composite of collagenous fibres embedded in a matrix of ground substance. The spinal ligaments are modelled as a collection of nonlinear axial elements. The loadings consist of axial compression and sagittal plane shears and bending moments, acting alone or combined. The results show that in pure compression, the external axial force is transmitted primarily by the intervertebral disc. The facet joints carry only a small percentage of the force. However, the facet joints carry large forces in extension, whereas in small flexion they carry none. Addition of compression tends to increase these contact forces in extension while it has no effect on them in flexion. In extension, the forces on the facet joints are transmitted by both the articular surfaces and the capsular ligaments. Although in small flexion the facets carry no load, large contact forces are predicted to develop as the segment is flexed beyond 7-8 degrees. These forces are of the same magnitude as those computed under large extension rotation and are oriented nearly in the horizontal plane with negligible component in the axial direction. The horizontal components of the contact forces generated during articulation are often larger than the axial components which directly resist the applied compressive force. The axial components of the contact forces, therefore, grossly underestimate the total forces acting on the facets. The transfer of forces from one facet to the adjacent one occurs through distinct areas in flexion and in extension loadings. That is, on the superior articular surface, the contact area shifts from the upper tip in large flexion to the lower margin in extension. On the inferior articular surface, the contact area shifts from the upper and central regions in large flexion to the lower tip in extension.

Muscle activity, internal loads, and stability of the human spine in standing postures: combined model and in vivo studies.

Study Design. The load in active and passive spinal components as well as the stability margin in standing postures ± load in hands are studied using both computational model and in vivo studies. Objective. To investigate muscle activity, spinal loads, and system stability in standing postures. Summary of Background Data. Study of the human trunk yields a redundant system, the satisfactory solution of which remains yet to be done. Existing biomechanical models are often oversimplified or attempt to solve the problem by equilibrium of loads at only one cross section along the spine. Methods. In vivo measurements are performed to obtain kinematics (by skin markers) as input data into model and EMG activity (by surface electrodes) for validation of predictions. A thoracolumbar model, while accounting for nonlinear ligamentous properties and trunk musculature, solved the redundant active-passive system by a novel kinematics-based approach that used both the posture and gravity/external loads as input data. In both studies, neutral standing posture was considered with weights up to 380 N held in hands with arms extended close to the body either in front or on sides. Results. Predicted muscle forces were in satisfactory agreement with measured EMG activities. The activity in extensor muscles significantly increased with the load magnitude when held in front, a trend that disappeared as loads were held on sides. Abdominal muscles remained relatively silent. Large compression forces of ∼2000 N were computed in lower lumbar levels when 380 N was held in front. Coactivity in abdominal muscles markedly increased internal loads and stability margin. Conclusion. A tradeoff exists between lower loads in passive tissues (i.e., tissue risk of failure) and higher stability margins as both increase with greater muscle coactivation. Greater muscle activity observed under load held in front did not necessarily yield larger stability margin as the position of load appeared to play an important role as well. The strength of the proposed model is in realistic consideration of both passive-active structures under postures and gravity/external loads, yielding results that satisfy kinematics, equilibrium, and stability requirements in all directions along the spine.

Dynamics of human lumbar intervertebral joints. Experimental and finite-element investigations.

To improve our understanding of the dynamic characteristics of the human lumbar spine, both experimental and finite-element methods are required. The experimental methods included measurement of the axial steady state response, resonant frequencies, and damping of seven lumbar motion segments under an upper-body mass of 40 kg. The influence of the presence of posterior elements and different magnitudes of compression preload on the response was also studied. To supplement the measurements, linear and nonlinear, axisymmetric, and threedimensional finite-element models of a L2-L3 disc-vertebra unit were developed to predict the free and forcedvibration responses. The step and harmonic loadings in the axial direction were considered for the forced-vibration analysis. The effect of the presence of the body mass and compression preloads were also examined. The results of experimental and finite-element studies were in good agreement with each other. They indicated that the system resonant frequencies are reduced considerably with the addition of a body mass of 40 kg and increase significantly (P < .005) as the compression preload increases. The compliance at both low and resonant frequencies decreases with increasing compression preload. Under preloads of not more than 680 N, removal of the facet joints tends to decrease slightly the segmental resonant frequencies irrespective of the magnitude of compression preload (P < .1). The finite-element model studies show quasistatic response under harmonic loads with periods much larger than the fundamental period of the segment and under step loads with slow rising times. Under a step load without the body mass, the nucleus pressure varies with both location and time and reaches a maximum of about 2.5 times that under equivalent static load. The addition of a 40-kg mass, in this case, renders a single degree-of-freedom response, with the pressure remaining nearly constant with location inside the nucleus. The stresses and strains throughout the segment in this case increase approximately twofold in comparison with equivalent static values. Partial or complete removal of the disc nucleus considerably decreases the resonant frequency and increases the corresponding segmental response amplitude (ie, compliance). The results indicate that the most vulnerable element under axial vibration loads is the cancellous bone adjacent to the nucleus space. Fatigue fracture of bone as a cumulative trauma and the subsequent loss of nucleus content likely initiates or accelerate the segmental degenerative processes. The annulus fibers do not appear to be vulnerable to rupture when the segment is subjected to pure

Biomechanics of changes in lumbar posture in static lifting

Study Design. In vivo measurements and model studies are combined to investigate the role of lumbar posture in static lifting tasks. Objectives. Identification of the role of changes in the lumbar posture on muscle forces, internal loads, and system stability in static lifting tasks with and without load in hands. Summary of Background Data. Despite the recognition of the causal role of lifting in spinal injuries, the advantages of preservation or flattening of the lumbar lordosis while performing lifting tasks is not yet clear. Methods. Kinematics of the spine and surface EMG activity of selected muscles were measured in 15 healthy subjects under different forward trunk flexion angles and load cases. Apart from the freestyle lumbar posture, subjects were instructed to take either lordotic or kyphotic posture as well. A kinematics-based method along with a nonlinear finite element model were interactively used to compute muscle forces, internal loads and system stability margin under postures, and loads considered in in vivo investigations. Results. In comparison with the kyphotic postures, the lordotic postures increased the pelvic rotation, active component of extensor muscle forces, segmental axial compression and shear forces at L5-S1, and spinal stability margin while decreasing the passive muscle forces and segmental flexion moments. Conclusion. Alterations in the lumbar lordosis in lifting resulted in significant changes in the muscle forces and internal spinal loads. Spinal shear forces at different segmental levels were influenced by changes in both the disc inclinations and extensor muscle lines of action as the posture altered. Considering internal spinal loads and active-passive muscle forces, the current study supports the freestyle posture or a posture with moderate flexion as the posture of choice in static lifting tasks.