A finite element formulation and program to study transient swelling and load-carriage in healthy and degenerate articular cartilage

Relative contribution of articular cartilage's constitutive components to load support depending on strain rate

Cartilage is considered a biphasic material in which the solid is composed of proteoglycans and collagen. In biphasic tissue, the hydraulic pressure is believed to bear most of the load under higher strain rates and its dissipation due to fluid flow determines creep and relaxation behavior. In equilibrium, hydraulic pressure is zero and load bearing is transferred to the solid matrix. The viscoelasticity of the collagen network also contributes to its time-dependent behavior, and the osmotic pressure to load bearing in equilibrium. The aim of the present study was to determine the relative contributions of hydraulic pressure, viscoelastic collagen stress, solid matrix stiffness and osmotic pressure to load carriage in cartilage under transient and equilibrium conditions. Unconfined compression experiments were simulated using a fibril-reinforced poroviscoelastic model of articular cartilage, including water, fibrillar viscoelastic collagen and non-fibrillar charged glycosaminoglycans. The relative contributions of hydraulic and osmotic pressures and stresses in the fibrillar and non-fibrillar network were evaluated in the superficial, middle and deep zone of cartilage under five different strain rates and after relaxation. Initially upon loading, the hydraulic pressure carried most of the load in all three zones. The osmotic swelling pressure carried most of the equilibrium load. In the surface zone, where the fibers were loaded in tension, the collagen network carried 20 % of the load for all strain rates. The importance of these fibers was illustrated by artificially modifying the fiber architecture, which reduced the overall stiffness of cartilage in all conditions. In conclusion, although hydraulic pressure dominates the transient behavior during cartilage loading, due to its viscoelastic nature the superficial zone collagen fibers carry a substantial part of the load under transient conditions. This becomes increasingly important with higher strain rates. The interesting and striking new insight from this study suggests that under equilibrium conditions, the swelling pressure generated by the combination of proteoglycans and collagen reinforcement accounts cartilage stiffness for more than 90 % of the loads carried by articular cartilage. This finding is different from the common thought that load is transferred from fluid to solid and is carried by the aggregate modulus of the solid. Rather, it is transformed from hydraulic to osmotic swelling pressure. These results show the importance of considering both (viscoelastic) collagen fibers as well as swelling pressure in studies of the (transient) mechanical behavior of cartilage.

Finite element modeling of soft tissues: material models, tissue interaction and challenges

BACKGROUND

Musculoskeletal soft tissues, such as articular cartilage, ligaments, knee meniscus and intervertebral disk, have a complex structure, which provides elasticity and capability to support and distribute the body loads. Soft tissues describe an inhomogeneous and multiphasic structure, and exhibit a nonlinear, time-dependent behavior. Their mechanical response is governed by a substance composed of protein fiber-rich and proteoglycan-rich extracellular matrix and interstitial fluid. Protein fibers (e.g. collagen) give the tissue direction dependent stiffness and strength. To investigate these complex biological systems, the use of mathematical tools is well established, alone or in combination with experimental in vitro and in vivo tests. However, the development of these models poses many challenges due to the complex structure and mechanical response of soft tissues.

METHODS

Non-systematic literature review.

FINDINGS

This paper provides a summary of different modeling strategies with associated material properties, contact interactions between articulating tissues, validation and sensitivity of soft tissues with special focus on knee joint soft tissues and intervertebral disk. Furthermore, it reviews and discusses some salient clinical findings of reported finite element simulations.

INTERPRETATION

Model studies extensively contributed to the understanding of functional biomechanics of soft tissues. Models can be effectively used to elucidate clinically relevant questions. However, users should be aware of the complexity of such tissues and of the capabilities and limitations of these approaches to adequately simulate a specific in vivo or in vitro phenomenon.

A review of the combination of experimental measurements and fibril-reinforced modeling for investigation of articular cartilage and chondrocyte response to loading

The function of articular cartilage depends on its structure and composition, sensitively impaired in disease (e.g. osteoarthritis, OA). Responses of chondrocytes to tissue loading are modulated by the structure. Altered cell responses as an effect of OA may regulate cartilage mechanotransduction and cell biosynthesis. To be able to evaluate cell responses and factors affecting the onset and progression of OA, local tissue and cell stresses and strains in cartilage need to be characterized. This is extremely challenging with the presently available experimental techniques and therefore computational modeling is required. Modern models of articular cartilage are inhomogeneous and anisotropic, and they include many aspects of the real tissue structure and composition. In this paper, we provide an overview of the computational applications that have been developed for modeling the mechanics of articular cartilage at the tissue and cellular level. We concentrate on the use of fibril-reinforced models of cartilage. Furthermore, we introduce practical considerations for modeling applications, including also experimental tests that can be combined with the modeling approach. At the end, we discuss the prospects for patient-specific models when aiming to use finite element modeling analysis and evaluation of articular cartilage function, cellular responses, failure points, OA progression, and rehabilitation.

Comparison of four methods to simulate swelling in poroelastic finite element models of intervertebral discs

Osmotic phenomena influence the intervertebral disc biomechanics. Their simulation is challenging and can be undertaken at different levels of complexity. Four distinct approaches to simulate the osmotic behaviour of the intervertebral disc (a fixed boundary pore pressure model, a fixed osmotic pressure gradient model in the whole disc or only in the nucleus pulposus, and a swelling model with strain-dependent osmotic pressure) were analysed. Predictions were compared using a 3D poroelastic finite element model of a L4-L5 spinal unit under three different loading conditions: free swelling for 8 h and two daily loading cycles: (i) 200 N compression for 8 h followed by 500 N compression for 16 h; (ii) 500 N for 8 h followed by 1000 N for 16 h. Overall, all swelling models calculated comparable results, with differences decreasing under greater loads. Results predicted with the fixed boundary pore pressure and the fixed osmotic pressure in the whole disc models were nearly identical. The boundary pore pressure model, however, cannot simulate differential osmotic pressures in disc regions. The swelling model offered the best potential to provide more accurate results, conditional upon availability of reliable values for the required coefficients and material properties. Possible fields of application include mechanobiology investigations and crack opening and propagation. However, the other approaches are a good compromise between the ease of implementation and the reliability of results, especially when considering higher loads or when the focus is on global results such as spinal kinematics.

A human knee joint model considering fluid pressure and fiber orientation in cartilages and menisci

Articular cartilages and menisci are generally considered to be elastic in the published human knee models, and thus the fluid-flow dependent response of the knee has not been explored using finite element analysis. In the present study, the fluid pressure and site-specific collagen fiber orientation in the cartilages and menisci were implemented into a finite element model of the knee using fibril-reinforced modeling previously proposed for articular cartilage. The geometry of the knee was obtained from magnetic resonance imaging of a healthy young male. The bones were considered to be elastic due to their greater stiffness compared to that of the cartilages and menisci. The displacements obtained for fast ramp compression were essentially same as those for instantaneous compression of equal magnitude with the fluid being trapped in the tissues, which was expected. However, a clearly different pattern of displacements was predicted by an elastic model using a greater Young's modulus and a Poisson's ratio for nearly incompressible material. The results indicated the influence of fluid pressure and fiber orientation on the deformation of articular cartilage in the knee. The fluid pressurization in the femoral cartilage was somehow affected by the site-specific fiber directions. The peak fluid pressure in the femoral condyles was reduced by three quarters when no fibril reinforcement was assumed. The present study indicates the necessity of implementing the fluid pressure and anisotropic fibril reinforcement in articular cartilage for a more accurate understanding of the mechanics of the knee.

Relative contributions of strain-dependent permeability and fixed charged density of proteoglycans in predicting cervical disc biomechanics: a poroelastic C5-C6 finite element model study

Disc swelling pressure (P(swell)) facilitated by fixed charged density (FCD) of proteoglycans (P(fcd)) and strain-dependent permeability (P(strain)) are of critical significance in the physiological functioning of discs. FCD of proteoglycans prevents any excessive matrix deformation by tissue stiffening, whereas strain-dependent permeability limits the rate of stress transfer from fluid to solid skeleton. To date, studies involving the modeling of FCD of proteoglycans and strain-dependent permeability have not been reported for the cervical discs. The current study objective is to compare the relative contributions of strain-dependent permeability and FCD of proteoglycans in predicting cervical disc biomechanics. Three-dimensional finite element models of a C5-C6 segment with three different disc compositions were analyzed: an SPFP model (strain-dependent permeability and FCD of proteoglycans), an SP model (strain-dependent permeability alone), and an FP model (FCD of proteoglycans alone). The outcomes of the current study suggest that the relative contributions of strain-dependent permeability and FCD of proteoglycans were almost comparable in predicting the physiological behavior of the cervical discs under moment loads. However, under compression, strain-dependent permeability better predicted the in vivo disc response than that of the FCD of proteoglycans. Unlike the FP model (least stiff) in compression, motion behavior of the three models did not vary much from each other and agreed well within the standard deviations of the corresponding in vivo published data. Flexion was recorded with maximum P(fcd) and P(strain), whereas minimum values were found in extension. The study data enhance the understanding of the roles played by the FCD of proteoglycans and strain-dependent permeability and porosity in determining disc tissue swelling behavior. Degenerative changes involving strain-dependent permeability and/or loss of FCD of proteoglycans can further be studied using an SPFP model. Future experiments are necessary to support the current study results.

The mechanical response of the lumbar spine to different combinations of disc degenerative changes investigated using randomized poroelastic finite element models

Degeneration of the intervertebral disc is related to progressive changes in the disc tissue composition and morphology, such as water loss, disc height loss, endplate calcification, osteophytosis. These changes may be present separately or, more frequently, in various combinations. This work is aimed to the biomechanical investigation of a wide range of clinical scenarios of disc degeneration, in which the most common degenerative changes are present in various combinations. A poroelastic non-linear finite element model of the healthy L4-L5 human spine segment was employed and randomly scaled to represent ten spine segments from different individuals. Six different degenerative characteristics (water loss in the nucleus pulposus and annulus fibrosus; calcification and thickness reduction of endplate cartilage; disc height loss; osteophyte formation; diffuse sclerosis) were modeled in 30 randomly generated models, 10 for each overall degree of degeneration (mild, moderate, severe). For each model, a daily loading cycle including 8 h of rest, 16 h in the standing position with superimposed two flexion-extension motion cycles was simulated. A tendency to an increase of stiffness with progressing overall degeneration was observed, in compression, flexion and extension. Hence, instability for mild degeneration was not predicted. Facet forces and fluid loss decreased with disc degeneration. Nucleus, annulus and endplate degeneration, disc height loss, osteophytosis and diffuse sclerosis all induced a statistically significant decrease in the total daily disc height variation, facet force and flexibility in flexion-extension. Therefore, grading systems for disc degeneration should include all the degenerative changes considered in this work, since all of them had a significant influence on the spinal biomechanics.

The role of lubricin in the mechanical behavior of synovial fluid

Synovial fluid is a semidilute hyaluronate (HA) polymer solution, the rheology of which depends on HA-protein interactions, and lubricin is a HA-binding protein found in synovial fluid and at cartilage surfaces, where it contributes to boundary lubrication under load. Individuals with genetic deficiency of lubricin develop precocious joint failure. The role of lubricin in synovial fluid rheology is not known. We used a multiple-particle-tracking microrheology technique to study the molecular interactions between lubricin and HA in synovial fluid. Particles (200 nm mean diameter) embedded in normal and lubricin-deficient synovial fluid samples were tracked separately by using multiple-particle-tracking microrheology. The time-dependent ensemble-averaged mean-squared displacements of all of the particles were measured over a range of physiologically relevant frequencies. The mean-squared displacement correlation with time lag had slopes with values of unity for simple HA solutions and for synovial fluid from an individual who genetically lacked lubricin, in contrast to slopes with values less than unity (alpha approximately 0.6) for normal synovial fluid. These data correlated with bulk rheology studies of the same samples. We found that the subdiffusive and elastic behavior of synovial fluid, at physiological shear rates, was absent in fluid from a patient who lacks lubricin. We conclude that lubricin provides synovial fluid with an ability to dissipate strain energy induced by mammalian locomotion, which is a chondroprotective feature that is distinct from boundary lubrication.

Influence of a Superficial Tangential Zone Over Repairing Cartilage Defects: Implications for Tissue Engineering

The superficial tangential zone (STZ) plays a critical role in normal cartilage function but is not yet a focus for designing tissue-engineered constructs for cartilage repair. Without material properties of sufficient quality in this zone, transplanted constructs in vivo may have little chance of survival. This finite element study investigates the impact of the superficial tangential zone on the mechanical function of normal articular surfaces as well as those with transplanted constructs. The zone is modeled as a thin transversely isotropic material with strain dependent permeability. The analyses predict that a normal transversely isotropic STZ placed over a repair region reduces the axial compression (55-68%) of, and the rate of fluid loss (45-82%) from the articular surface. A reduction was also found in von Mises stress (26-57%), axial strain (22-56%), and radial strain (69-73%), and an increase in fluid pressure (19-45%) in repair tissue under the STZ. Incorporating a quality superficial tangential zone in tissue-engineered constructs may be a critical factor in achieving mechanical environments conducive for successful cartilage repairs.