Contribution of collagen degradation and proteoglycan depletion to cartilage degeneration in primary and secondary osteoarthritis: an in silico study.

OBJECTIVES: Current experimental approaches cannot elucidate the effect of maladaptive changes on the main cartilage constituents during the degeneration process in osteoarthritis (OA). In silico approaches, however, allow creating 'virtual knock-out' cases to elucidate these effects in a constituent-specific manner. We used such an approach to study the main mechanisms of cartilage degeneration in different mechanical loadings associated with the following OA etiologies: (1) physiological loading of degenerated cartilage, (2) injurious loading of healthy intact cartilage and (3) physiological loading of cartilage with a focal defect. METHODS: We used the recently developed Cartilage Adaptive REorientation Degeneration (CARED) framework to simulate cartilage degeneration associated with primary and secondary OA (OA cases (1)-(3)). CARED incorporates numerical description of tissue-level cartilage degeneration mechanisms in OA, namely, collagen degradation, collagen reorientation, fixed charged density loss and tissue hydration increase following mechanical loading. We created 'virtual knock-out' scenarios by deactivating these degenerative processes one at a time in each of the three OA cases. RESULTS: In the injurious loading of intact and physiological loading of degenerated cartilage, collagen degradation drives degenerative changes through fixed charge density loss and tissue hydration rise. In contrast, the two later mechanisms were more prominent in the focal defect cartilage model. CONCLUSION: The virtual knock-out models reveal that injurious loading to intact cartilage and physiological loading to degenerated cartilage induce initial degenerative changes in the collagen network, whereas, in the presence of a focal cartilage defect, mechanical loading initially causes proteoglycans (PG) depletion, before changes in the collagen fibril network occur.

Machine learning augmented near-infrared spectroscopy: In vivo follow-up of cartilage defects.

OBJECTIVE: To assess the potential of near-infrared spectroscopy (NIRS) for in vivo arthroscopic monitoring of cartilage defects. METHOD: Sharp and blunt cartilage grooves were induced in the radiocarpal and intercarpal joints of Shetland ponies and monitored at baseline (0 weeks) and at three follow-up timepoints (11, 23, and 39 weeks) by measuring near-infrared spectra in vivo at and around the grooves. The animals were sacrificed after 39 weeks and the joints were harvested. Spectra were reacquired ex vivo to ensure reliability of in vivo measurements and for reference analyses. Additionally, cartilage thickness and instantaneous modulus were determined via computed tomography and mechanical testing, respectively. The relationship between the ex vivo spectra and cartilage reference properties was determined using convolutional neural network. RESULTS: In an independent test set, the trained networks yielded significant correlations for cartilage thickness (ρ = 0.473) and instantaneous modulus (ρ = 0.498). These networks were used to predict the reference properties at baseline and at follow-up time points. In the radiocarpal joint, cartilage thickness increased significantly with both groove types after baseline and remained swollen. Additionally, at 39 weeks, a significant difference was observed in cartilage thickness between controls and sharp grooves. For the instantaneous modulus, a significant decrease was observed with both groove types in the radiocarpal joint from baseline to 23 and 39 weeks. CONCLUSION: NIRS combined with machine learning enabled determination of cartilage properties in vivo, thereby providing longitudinal evaluation of post-intervention injury development. Additionally, radiocarpal joints were found more vulnerable to cartilage degeneration after damage than intercarpal joints.

Comparison of material models for anterior cruciate ligament in tension: from poroelastic to a novel fibril-reinforced nonlinear composite model.

Computational models of the knee joint are useful for evaluating stresses and strains within the joint tissues. However, the outcome of those models is sensitive to the material model and material properties chosen for ligaments, the collagen reinforced tissues connecting bone to bone. The purpose of this study was to investigate different compositionally motivated material models and further to develop a model that can accurately reproduce experimentally measured stress-relaxation data of bovine anterior cruciate ligament (ACL). Tensile testing samples were extracted from ACLs of bovine knee joints (N = 10) and subjected to a three-step stress-relaxation test at the toe region. Data from the experiments was averaged and one average finite element model was generated to replicate the experiment. Poroelastic and different fibril-reinforced poro(visco)elastic material models were applied, and their material parameters were optimized to reproduce the experimental force-time response. Material models with only fluid flow mediated relaxation were not able to capture the stress-relaxation behavior (R2 = 0.806, 0.803 and 0.938). The inclusion of the viscoelasticity of the fibrillar network improved the model prediction (R2 = 0.978 and 0.976), but the complex stress-relaxation behavior was best captured by a poroelastic model with a nonlinear two-relaxation-time strain-recruited viscoelastic fibrillar network (R2 = 0.997). The results suggest that in order to replicate the multi-step stress-relaxation behavior of ACL in tension, the fibrillar network formulation should include the complex nonlinear viscoelastic phenomena.

12 Degrees of Freedom Muscle Force Driven Fibril-Reinforced Poroviscoelastic Finite Element Model of the Knee Joint.

Accurate knowledge of the joint kinematics, kinetics, and soft tissue mechanical responses is essential in the evaluation of musculoskeletal (MS) disorders. Since in vivo measurement of these quantities requires invasive methods, musculoskeletal finite element (MSFE) models are widely used for simulations. There are, however, limitations in the current approaches. Sequentially linked MSFE models benefit from complex MS and FE models; however, MS model's outputs are independent of the FE model calculations. On the other hand, due to the computational burden, embedded (concurrent) MSFE models are limited to simple material models and cannot estimate detailed responses of the soft tissue. Thus, first we developed a MSFE model of the knee with a subject-specific MS model utilizing an embedded 12 degrees of freedom (DoFs) knee joint with elastic cartilages in which included both secondary kinematic and soft tissue deformations in the muscle force estimation (inverse dynamics). Then, a muscle-force-driven FE model with fibril-reinforced poroviscoelastic cartilages and fibril-reinforced poroelastic menisci was used in series to calculate detailed tissue mechanical responses (forward dynamics). Second, to demonstrate that our workflow improves the simulation results, outputs were compared to results from the same FE models which were driven by conventional MS models with a 1 DoF knee, with and without electromyography (EMG) assistance. The FE model driven by both the embedded and the EMG-assisted MS models estimated similar results and consistent with experiments from literature, compared to the results estimated by the FE model driven by the MS model with 1 DoF knee without EMG assistance.

Machine learning methods to support personalized neuromusculoskeletal modelling.

Many biomedical, orthopaedic, and industrial applications are emerging that will benefit from personalized neuromusculoskeletal models. Applications include refined diagnostics, prediction of treatment trajectories for neuromusculoskeletal diseases, in silico design, development, and testing of medical implants, and human-machine interfaces to support assistive technologies. This review proposes how physics-based simulation, combined with machine learning approaches from big data, can be used to develop high-fidelity personalized representations of the human neuromusculoskeletal system. The core neuromusculoskeletal model features requiring personalization are identified, and big data/machine learning approaches for implementation are presented together with recommendations for further research.

Comparison of water, hydroxyproline, uronic acid and elastin contents of bovine knee ligaments and patellar tendon and their relationships with biomechanical properties.

Mechanical material properties of ligaments originate from their biochemical composition and structural organization. However, it is not yet fully elucidated how biochemical contents vary between knee ligaments and patellar tendon (PT) and how they relate with mechanical properties. The purpose of this study was to compare water, collagen, proteoglycan and elastin contents between bovine knee ligaments and PT and correlate them with tensile material properties. Hydroxyproline (collagen), uronic acid (proteoglycan) and elastin contents per wet and dry weights were measured using colorimetric biochemical methods for bovine knee ligament and PT samples (n = 10 knees). Direct comparison and correlation with multiple linear regression were performed against biomechanical properties measured in our earlier study. Anterior cruciate ligament (ACL) and PT exhibited lower hydroxyproline content per wet weight compared with other ligaments (p < 0.05). Cruciate ligaments had higher uronic acid content per dry weight compared with collateral ligaments (p < 0.05). Posterior cruciate ligament had higher elastin content than ACL (p < 0.05). Higher hydroxyproline content per wet weight implied higher Young's modulus, strength and toughness. Quantitatively, higher elastin content per wet weight predicted higher toe region nonlinearity and Young's modulus whereas higher uronic acid content per dry weight predicted lower Young's modulus, yield stress and toughness. Differences between ligaments in biochemical composition highlight differences in their physiological function and loading regimes. As expected, collagen content showed similar trend with stiffness and strength. The predictive role of proteoglycan and elastin contents on the mechanical properties might indicate their important functional role in ligaments.

EMG-Assisted Muscle Force Driven Finite Element Model of the Knee Joint with Fibril-Reinforced Poroelastic Cartilages and Menisci.

Abnormal mechanical loading is essential in the onset and progression of knee osteoarthritis. Combined musculoskeletal (MS) and finite element (FE) modeling is a typical method to estimate load distribution and tissue responses in the knee joint. However, earlier combined models mostly utilize static-optimization based MS models and muscle force driven FE models typically use elastic materials for soft tissues or analyze specific time points of gait. Therefore, here we develop an electromyography-assisted muscle force driven FE model with fibril-reinforced poro(visco)elastic cartilages and menisci to analyze knee joint loading during the stance phase of gait. Moreover, since ligament pre-strains are one of the important uncertainties in joint modeling, we conducted a sensitivity analysis on the pre-strains of anterior and posterior cruciate ligaments (ACL and PCL) as well as medial and lateral collateral ligaments (MCL and LCL). The model produced kinematics and kinetics consistent with previous experimental data. Joint contact forces and contact areas were highly sensitive to ACL and PCL pre-strains, while those changed less cartilage stresses, fibril strains, and fluid pressures. The presented workflow could be used in a wide range of applications related to the aetiology of cartilage degeneration, optimization of rehabilitation exercises, and simulation of knee surgeries.

Quantifying Subresolution 3D Morphology of Bone with Clinical Computed Tomography.

The aim of this study was to quantify sub-resolution trabecular bone morphometrics, which are also related to osteoarthritis (OA), from clinical resolution cone beam computed tomography (CBCT). Samples (n = 53) were harvested from human tibiae (N = 4) and femora (N = 7). Grey-level co-occurrence matrix (GLCM) texture and histogram-based parameters were calculated from CBCT imaged trabecular bone data, and compared with the morphometric parameters quantified from micro-computed tomography. As a reference for OA severity, histological sections were subjected to OARSI histopathological grading. GLCM and histogram parameters were correlated to bone morphometrics and OARSI individually. Furthermore, a statistical model of combined GLCM/histogram parameters was generated to estimate the bone morphometrics. Several individual histogram and GLCM parameters had strong associations with various bone morphometrics (|r| > 0.7). The most prominent correlation was observed between the histogram mean and bone volume fraction (r = 0.907). The statistical model combining GLCM and histogram-parameters resulted in even better association with bone volume fraction determined from CBCT data (adjusted R2 change = 0.047). Histopathology showed mainly moderate associations with bone morphometrics (|r| > 0.4). In conclusion, we demonstrated that GLCM- and histogram-based parameters from CBCT imaged trabecular bone (ex vivo) are associated with sub-resolution morphometrics. Our results suggest that sub-resolution morphometrics can be estimated from clinical CBCT images, associations becoming even stronger when combining histogram and GLCM-based parameters.

Effect of centrifugal force on the development of articular neocartilage with bovine primary chondrocytes.

A lot has been invested into understanding how to assemble cartilage tissue in vitro and various designs have been developed to manufacture cartilage tissue with native-like biological properties. So far, no satisfactory design has been presented. Bovine primary chondrocytes are used to self-assemble scaffold-free constructs to investigate whether mechanical loading by centrifugal force would be useful in manufacturing cartilage tissue in vitro. Six million chondrocytes were laid on top of defatted bone disks placed inside an agarose well in 50-ml culture tubes. The constructs were centrifuged once or three times per day for 15 min at a centrifugal force of 771×g for up to 4 weeks. Control samples were cultured under the same conditions without exposure to centrifugation. The samples were analysed by (immuno)histochemistry, Fourier transform infrared imaging, micro-computed tomography, biochemical and gene expression analyses. Biomechanical testing was also performed. The centrifuged tissues had a more even surface covering a larger area of the bone disk. Fourier transform infrared imaging analysis indicated a higher concentration of collagen in the top and bottom edges in some of the centrifuged samples. Glycosaminoglycan contents increased along the culture, while collagen content remained at a rather constant level. Aggrecan and procollagen α1(II) gene expression levels had no significant differences, while procollagen α2(I) levels were increased significantly. Biomechanical analyses did not reveal remarkable changes. The centrifugation regimes lead to more uniform tissue constructs, whereas improved biological properties of the native tissue could not be obtained by centrifugation.

Interrelationship of cartilage composition and chondrocyte mechanics after a partial meniscectomy in the rabbit knee joint - Experimental and numerical analysis.

Site-specific and depth-dependent properties of cartilage were implemented within a finite element (FE) model to determine if compositional or structural changes in the tissue could explain site-specific alterations of chondrocyte deformations due to cartilage loading in rabbit knee joints 3 days after a partial meniscectomy (PM). Depth-dependent proteoglycan (PG) content, collagen content and collagen orientation in the cartilage extracellular matrix (ECM), and PG content in the pericellular matrix (PCM) were assessed with microscopic and spectroscopic methods. Patellar, femoral groove and samples from both the lateral and medial compartments of the femoral condyle and tibial plateau were extracted from healthy controls and from the partial meniscectomy group. For both groups and each knee joint site, axisymmetric FE models with measured properties were generated. Experimental cartilage loading was applied in the simulations and chondrocyte volumes were compared to the experimental values. ECM and PCM PG loss occurred within the superficial cartilage layer in the PM group at all locations, except in the lateral tibial plateau. Collagen content and orientation were not significantly altered due to the PM. The FE simulations predicted similar chondrocyte volume changes and group differences as obtained experimentally. Loss of PCM fixed charge density (FCD) decreased cell volume loss, as observed in the medial femur and medial tibia, whereas loss of ECM FCD increased cell volume loss, as seen in the patella, femoral groove and lateral femur. The model outcome, cell volume change, was also sensitive to applied tissue geometry, collagen fibril orientation and loading conditions.

Comparison of elastic, viscoelastic and failure tensile material properties of knee ligaments and patellar tendon.

The knee ligaments and patellar tendon function in concert with each other and other joint tissues, and are adapted to their specific physiological function via geometry and material properties. However, it is not well known how the viscoelastic and quasi-static material properties compare between the ligaments. The purpose of this study was to characterize and compare these material properties between the knee ligaments and patellar tendon. Dumbbell-shaped tensile test samples were cut from bovine knee ligaments (ACL, LCL, MCL, PCL) and patellar tendon (PT) and subjected to tensile testing (n = 10 per ligament type). A sinusoidal loading test was performed at 8% strain with 0.5% strain amplitude using 0.1, 0.5 and 1 Hz frequencies. Subsequently, an ultimate tensile test was performed to investigate the stress-strain characteristics. At 0.1 Hz, the phase difference between stress and strain was higher in LCL compared with ACL, PCL and PT (p < 0.05), and at 0.5 Hz that was higher in LCL compared with all other ligaments and PT (p < 0.05). PT had the longest toe-region strain (p < 0.05 compared with PCL and MCL) and MCL had the highest linear and strain-dependent modulus, and toughness (p < 0.05 compared with ACL, LCL and PT). The results indicate that LCL is more viscous than other ligaments at low-frequency loads. MCL was the stiffest and toughest, and its modulus increased most steeply at the toe-region, possibly implying a greater amount of collagen. This study improves the knowledge about elastic, viscoelastic and failure properties of the knee ligaments and PT.

Poisson's ratio of bovine meniscus determined combining unconfined and confined compression.

Poisson's ratio has not been experimentally measured earlier for meniscus in compression. It is however an important intrinsic material property needed in biomechanical analysis and computational models. In this study, equilibrium Poisson's ratio of bovine meniscus (n = 6) was determined experimentally by combining stress-relaxation measurements in unconfined and confined compression geometries. The average Young's modulus, aggregate modulus and Poisson's ratio were 0.182 ±â€¯0.086 MPa, 0.252 ±â€¯0.089 MPa and 0.316 ±â€¯0.040, respectively. These moduli are consistent with previously determined values, but the Poisson's ratio is higher than determined earlier for meniscus in compression through biomechanical modelling analysis. This new experimentally determined Poisson's ratio value could be used in the analysis of biomechanical data as well as in computational finite element analysis when the Poisson's ratio is needed as an input for the analysis.

Composition, structure and tensile biomechanical properties of equine articular cartilage during growth and maturation.

Articular cartilage undergoes structural and biochemical changes during maturation, but the knowledge on how these changes relate to articular cartilage function at different stages of maturation is lacking. Equine articular cartilage samples of four different maturation levels (newborn, 5-month-old, 11-month-old and adult) were collected (N = 25). Biomechanical tensile testing, Fourier transform infrared microspectroscopy (FTIR-MS) and polarized light microscopy were used to study the tensile, biochemical and structural properties of articular cartilage, respectively. The tensile modulus was highest and the breaking energy lowest in the newborn group. The collagen and the proteoglycan contents increased with age. The collagen orientation developed with age into an arcade-like orientation. The collagen content, proteoglycan content, and collagen orientation were important predictors of the tensile modulus (p < 0.05 in multivariable regression) and correlated significantly also with the breaking energy (p < 0.05 in multivariable regression). Partial least squares regression analysis of FTIR-MS data provided accurate predictions for the tensile modulus (r = 0.79) and the breaking energy (r = 0.65). To conclude, the composition and structure of equine articular cartilage undergoes changes with depth that alter functional properties during maturation, with the typical properties of mature tissue reached at the age of 5-11 months.

Functional effects of an interpenetrating polymer network on articular cartilage mechanical properties.

OBJECTIVE: Depletion of glycosaminoglycans (GAGs) and degradation of collagen network are early hallmarks of osteoarthritis (OA). Currently, there are no chondroprotective therapies that mitigate the loss of GAGs or effectively restore the collagen network. Recently, a novel polymeric cartilage supplement was described that forms a charged interpenetrating polymer network (IPN) reconstituting the hydrophilic properties of the extracellular matrix (ECM). To investigate the mechanism by which this hydrophilic IPN improves articular cartilage material properties, a finite element (FE) model is used to evaluate the IPN's effect on the fibrillar collagen network, nonfibrillar matrix, and interstitial fluid flow. METHODS: Bovine osteochondral plugs were degraded with chondroitinase ABC to selectively decrease GAG content. Samples were mechanically tested before and after IPN treatment using unconfined testing geometry and stress-relaxation protocol. Every measurement was modeled separately using a fibril-reinforced poroviscoelastic FE model. Measurement replication was achieved by optimizing the following model parameters: initial and strain-dependent fibril network modulus (Ef0, Efε, respectively), nonfibrillar matrix modulus (Enf), initial permeability (k0) and strain-dependent permeability factor (M). RESULTS: Based on the FE model results, treatment of native and GAG depleted cartilage with the hydrophilic IPN increases the ECM stiffness and impedes fluid flow. The IPN did not alter the stiffness of fibrillary network. Cartilage permeability and the strain-dependent permeability factor decreased with increasing IPN w/v%. CONCLUSIONS: The IPN reconstitutes cartilage material properties primarily by augmenting the hydrophilic ECM. This reinforcement of the solid phase also affects the fluid phase reestablishing low permeability.

Tissue viscoelasticity is related to tissue composition but may not fully predict the apparent-level viscoelasticity in human trabecular bone - An experimental and finite element study.

Trabecular bone is viscoelastic under dynamic loading. However, it is unclear how tissue viscoelasticity controls viscoelasticity at the apparent-level. In this study, viscoelasticity of cylindrical human trabecular bone samples (n=11, male, age 18-78 years) from 11 proximal femurs were characterized using dynamic and stress-relaxation testing at the apparent-level and with creep nanoindentation at the tissue-level. In addition, bone tissue elasticity was determined using scanning acoustic microscope (SAM). Tissue composition and collagen crosslinks were assessed using Raman micro-spectroscopy and high performance liquid chromatography (HPLC), respectively. Values of material parameters were obtained from finite element (FE) models by optimizing tissue-level creep and apparent-level stress-relaxation to experimental nanoindentation and unconfined compression testing values, respectively, utilizing the second order Prony series to depict viscoelasticity. FE simulations showed that tissue-level equilibrium elastic modulus (Eeq) increased with increasing crystallinity (r=0.730, p=.011) while at the apparent-level it increased with increasing hydroxylysyl pyridinoline content (r=0.718, p=.019). In addition, the normalized shear modulus g1 (r=-0.780, p=.005) decreased with increasing collagen ratio (amide III/CH2) at the tissue-level, but increased (r=0.696, p=.025) with increasing collagen ratio at the apparent-level. No significant relations were found between the measured or simulated viscoelastic parameters at the tissue- and apparent-levels nor were the parameters related to tissue elasticity determined with SAM. However, only Eeq, g2 and relaxation time τ1 from simulated viscoelastic values were statistically different between tissue- and apparent-levels (p<.01). These findings indicate that bone tissue viscoelasticity is affected by tissue composition but may not fully predict the macroscale viscoelasticity in human trabecular bone.

Early in situ changes in chondrocyte biomechanical responses due to a partial meniscectomy in the lateral compartment of the mature rabbit knee joint.

We determined the biomechanical responses of chondrocytes to indentation at specific locations within the superficial zone of cartilage (i.e. patellar, femoral groove, femoral condylar and tibial plateau sites) taken from female New Zealand white rabbits three days after a partial meniscectomy in the lateral compartment of a knee joint. Confocal laser scanning microscopy combined with a custom indentation system was utilized to image chondrocyte responses at sites taken from ten contralateral and experimental knee joints. Cell volume, height, width and depth changes, global, local axial and transverse strains and Young׳s moduli were determined. Histological assessment was performed and proteoglycan content from the superficial zone of each site was determined. Relative to contralateral group cells, patellar, femoral groove and lateral femoral condyle cells in the experimental group underwent greater volume decreases (p < 0.05), due to smaller lateral expansions (with greater decreases in cell height only for the lateral femoral condyle cells; p < 0.05) whereas medial femoral and medial tibial plateau cells underwent smaller volume decreases (p < 0.05), due to less deformation in cell height (p < 0.05). Proteoglycan content was reduced in the patellar (p > 0.05), femoral groove, medial femoral condyle and medial tibial plateau experimental sites (p < 0.05). The findings suggest: (i) cell biomechanical responses to cartilage loading in the rabbit knee joint can become altered as early as 3 days after a partial meniscectomy, (ii) are site-specific, and (iii) occur before alterations in tissue mechanics or changes detectable with histology.

Site-specific cell-tissue interactions in rabbit knee joint articular cartilage.

Relationships between cartilage structure and superficial in situ chondrocyte deformations were investigated from 6 different knee joint locations (n=10 knees). Depth dependent cartilage structure and composition were quantified with microscopic/microspectroscopic methods. Medial tibial cartilages had the lowest superficial collagen content, highest collagen orientation angle, and highest proteoglycan content in the pericellular matrix relative to that in the extracellular matrix, coupled with the largest chondrocyte deformations. In contrast, femoral groove and lateral tibial cartilages had the highest superficial collagen contents, lowest collagen orientation angles, and low normalized proteoglycan contents in the pericellular matrix, coupled with the smallest chondrocyte deformations. To study cell-tissue interactions further, observations (n=57) from all locations were pooled and a multivariable linear regression was performed. Cell width deformations (R2=0.57) correlated with collagen orientation angle (standardized regression coefficient ß=0.398) and collagen content (ß=-0.402). Cell height deformations (R2=0.52) also correlated with collagen orientation (ß=-0.248) and collagen content (ß=0.455). Cell volume change upon cartilage compression (R2=0.41) correlated with collagen content (ß=0.435) and proteoglycan content (ß=0.279). In conclusion, higher collagen and proteoglycan contents combined with lower collagen orientation angle in the extracellular matrix were related to reductions in superficial chondrocyte deformations. Also, a steep gradient of proteoglycan content from the extracellular to the pericellular matrix was associated with increased cell deformation, particularly in the medial tibial plateau cartilage.

Optimal graft stiffness and pre-strain restore normal joint motion and cartilage responses in ACL reconstructed knee.

Anterior cruciate ligament (ACL) rupture leads to abnormal loading of the knee joint and increases the risk of osteoarthritis. It is unclear how different ACL reconstruction techniques affect knee joint motion and mechanics. As the in vivo measurement of knee joint loading is not possible, we used finite element analysis to assess the outcome of ACL reconstruction techniques. Effects of different ACL reconstruction techniques on knee joint mechanics were studied using six models during gait; with 1) healthy ACL, 2) ACL rupture, 3) single bundle ACL reconstruction, 4) double bundle ACL reconstruction, 5) weakened (softer) single bundle reconstruction and 6) single bundle reconstruction with less pre-strain. Early in the gait, the ACL rupture caused substantially increased tibial translation in the anterior direction as well as a smaller but increased lateral translation and internal tibial rotation. ACL rupture substantially reduced average stresses and strains, while local peak stresses and strains could be either increased or decreased. Single bundle and double bundle reconstructions restored joint motion close to normal levels. However, cartilage strains and stresses were elevated during the entire gait cycle. Models with modulated graft stiffness and pre-strain restored the joint motion and cartilage stresses and strains close to the normal, healthy levels. Results suggest that rather than the choice of reconstruction technique, stiffness and pre-strain of the ACL reconstruction affect the motion and mechanics of the operated knee. We suggest that an optimal choice of graft properties might help restore normal knee joint function and cartilage responses, thus, minimizing the risk of osteoarthritis.

Highly nonlinear stress-relaxation response of articular cartilage in indentation: Importance of collagen nonlinearity.

Modern fibril-reinforced computational models of articular cartilage can include inhomogeneous tissue composition and structure, and nonlinear mechanical behavior of collagen, proteoglycans and fluid. These models can capture well experimental single step creep and stress-relaxation tests or measurements under small strains in unconfined and confined compression. Yet, it is known that in indentation, especially at high strain velocities, cartilage can express highly nonlinear response. Different fibril reinforced poroelastic and poroviscoelastic models were used to assess measured highly nonlinear stress-relaxation response of rabbit articular cartilage in indentation. Experimentally measured depth-dependent volume fractions of different tissue constituents and their mechanical nonlinearities were taken into account in the models. In particular, the collagen fibril network was modeled using eight separate models that implemented five different constitutive equations to describe the nonlinearity. These consisted of linear elastic, nonlinear viscoelastic and multiple nonlinear elastic representations. The model incorporating the most nonlinearly increasing Young׳s modulus of collagen fibrils as a function of strain captured best the experimental data. Relative difference between the model and experiment was ~3%. Surprisingly, the difference in the peak forces between the experiment and the model with viscoelastic collagen fibrils was almost 20%. Implementation of the measured volume fractions did not improve the ability of the model to capture the measured mechanical data. These results suggest that a highly nonlinear formulation for collagen fibrils is needed to replicate multi-step stress-relaxation response of rabbit articular cartilage in indentation with high strain rates.

Importance of Patella, Quadriceps Forces, and Depthwise Cartilage Structure on Knee Joint Motion and Cartilage Response During Gait.

In finite-element (FE) models of the knee joint, patella is often omitted. We investigated the importance of patella and quadriceps forces on the knee joint motion by creating an FE model of the subject's knee. In addition, depthwise strains and stresses in patellar cartilage with different tissue properties were determined. An FE model was created from subject's magnetic resonance images. Knee rotations, moments, and translational forces during gait were recorded in a motion laboratory and used as an input for the model. Three material models were implemented into the patellar cartilage: (1) homogeneous model, (2) inhomogeneous (arcadelike fibrils), and (3) random fibrils at the superficial zone, mimicking early stages of osteoarthritis (OA). Implementation of patella and quadriceps forces into the model substantially reduced the internal-external femoral rotations (versus without patella). The simulated rotations in the model with the patella matched the measured rotations at its best. In the inhomogeneous model, maximum principal stresses increased substantially in the middle zone of the cartilage. The early OA model showed increased compressive strains in the superficial and middle zones of the cartilage and decreased stresses and fibril strains especially in the middle zone. The results suggest that patella and quadriceps forces should be included in moment- and force-driven FE knee joint models. The results indicate that the middle zone has a major role in resisting shear forces in the patellar cartilage. Also, early degenerative changes in the collagen network substantially affect the cartilage depthwise response in the patella during walking.