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.

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.

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.

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.

Effect of bone inhomogeneity on tibiofemoral contact mechanics during physiological loading.

It is not known how inhomogeneous mechanical properties of bone affect contact mechanics and cartilage response during physiological loading of the knee joint. In this study, a finite element model of a cadaver knee joint was constructed based on quantitative computed tomography (QCT). The mechanical properties of bone were altered and their effect on tibiofemoral contact mechanics and cartilage stresses, strains and pore pressures were evaluated during the first 20% of stance. For this purpose, models with rigid, homogeneous and inhomogeneous bones were created. When bone was modeled to be rigid, the resulting contact pressures were substantially higher in the medial side of the joint, as compared to the non-rigid bones. Similar changes were revealed also in stresses, strains and pore pressures throughout the cartilage depth at the cartilage-cartilage contact area. Furthermore, the mechanical response of medial tibial cartilage was found to be highly dependent on the bone properties. When Young׳s modulus in the model with homogeneous bone was 5GPa, cartilage mechanical response approached to that of the model with inhomogeneous bone. Finally, when the apparent bone mineral densities were decreased globally in the inhomogeneous bone, stresses, strains and pore pressures were decreased at all layers of medial tibial cartilage. Similar changes were observed also in cartilage-cartilage contact area of the lateral compartment but with a lesser extent. These results indicate that during physiological loading Young׳s modulus of bone has a substantial influence on cartilage stresses and strains, especially in the medial compartment.

Characterization of site-specific biomechanical properties of human meniscus-Importance of collagen and fluid on mechanical nonlinearities.

Meniscus adapts to joint loads by depth- and site-specific variations in its composition and structure. However, site-specific mechanical characteristics of intact meniscus under compression are poorly known. In particular, mechanical nonlinearities caused by different meniscal constituents (collagen and fluid) are not known. In the current study, in situ indentation testing was conducted to determine site-specific elastic, viscoelastic and poroelastic properties of intact human menisci. Lateral and medial menisci (n=26) were harvested from the left knee joint of 13 human cadavers. Indentation tests, using stress-relaxation and dynamic (sinusoidal) loading protocols, were conducted for menisci at different sites (anterior, middle, posterior, n=78). Sample- and site-specific axisymmetric finite element models with fibril-reinforced poroelastic properties were fitted to the corresponding stress-relaxation curves to determine the mechanical parameters. Elastic moduli, especially the instantaneous and dynamic moduli, showed site-specific variation only in the medial meniscus (p<0.05 between the sites). The instantaneous and dynamic elastic moduli of the anterior horn were significantly (p<0.05) greater in the medial than lateral meniscus. The phase angle showed no statistically significant variation between the sites (p>0.05). The values for the strain-dependent fibril network modulus (nonlinear behaviour of collagen) were significantly different (p<0.05) between all sites in the medial menisci. Additionally, there was a significant difference (p<0.01) in the strain-dependent fibril network modulus between the lateral and medial anterior horns. The initial permeability was significantly different (p<0.05) in the medial meniscus only between the middle and posterior sites. For the strain-dependent permeability coefficient, only anterior and middle sites showed a significant difference (p<0.05) in the medial meniscus. This parameter demonstrated a significant difference (p<0.05) between lateral and medial menisci at the anterior horns. Our results reveal that under in situ indentation loading, medial meniscus shows more site-dependent variation in the mechanical properties as compared to lateral meniscus. In particular, anterior horn of medial meniscus was the stiffest and showed the most nonlinear mechanical behaviour. The nonlinearity was related to both collagen fibrils and fluid.

Deformation of articular cartilage during static loading of a knee joint--experimental and finite element analysis.

Novel conical beam CT-scanners offer high resolution imaging of knee structures with i.a. contrast media, even under weight bearing. With this new technology, we aimed to determine cartilage strains and meniscal movement in a human knee at 0, 1, 5, and 30 min of standing and compare them to the subject-specific 3D finite element (FE) model. The FE model of the volunteer׳s knee, based on the geometry obtained from magnetic resonance images, was created to simulate the creep. The effects of collagen fibril network stiffness, nonfibrillar matrix modulus, permeability and fluid flow boundary conditions on the creep response in cartilage were investigated. In the experiment, 80% of the maximum strain in cartilage developed immediately, after which the cartilage continued to deform slowly until the 30 min time point. Cartilage strains and meniscus movement obtained from the FE model matched adequately with the experimentally measured values. Reducing the fibril network stiffness increased the mean strains substantially, while the creep rate was primarily influenced by an increase in the nonfibrillar matrix modulus. Changing the initial permeability and preventing fluid flow through noncontacting surfaces had a negligible effect on cartilage strains. The present results improve understanding of the mechanisms controlling articular cartilage strains and meniscal movements in a knee joint under physiological static loading. Ultimately a validated model could be used as a noninvasive diagnostic tool to locate cartilage areas at risk for degeneration.

Importance of depth-wise distribution of collagen and proteoglycans in articular cartilage--a 3D finite element study of stresses and strains in human knee joint.

Proteoglycans and collagen fibrils are distributed inhomogeneously throughout the depth of articular cartilage, providing the tissue with its unique depth-dependent properties and directly influencing local tissue deformations and stresses in in vitro/in situ. The aim of this study was to investigate the importance of the proteoglycan and collagen distributions for cartilage stresses and strains resulting from dynamic joint loading (i.e., a simulated gait cycle) and mechanical equilibrium in a knee joint. A 3D finite element model of a human knee joint including femoral and tibial cartilages and menisci was created. In order to characterize the effects of collagen orientation, collagen distribution and proteoglycan distribution on knee joint stresses and strains, five fibril-reinforced poroviscoelastic models with different depth-wise tissue structure were created. For each model strains and stresses were evaluated at four different depths in the medial tibial compartment during a gait cycle (simulating walking) and at mechanical equilibrium (simulating standing). The model with arcade-like collagen fibril architecture predicted substantially lower stresses than the homogeneous model, especially during dynamic joint loading. The depth-wise proteoglycan gradient caused a substantial increase in stresses and axial strains in the superficial layer, and reduced stresses and strains in the deep layer under static loading. The effect of fibril volume density distribution was minor during both dynamic joint loading and at mechanical equilibrium. The present study emphasizes the importance of the arcade-like collagen fibril orientation for cartilage function in a human knee joint. However, we suggest that, for practical reasons, a constant fibril volume density may be used in 3D models of knee joints, whereas a realistic depth-wise proteoglycan distribution should be applied when simulating the cartilage response during mechanical equilibrium.

Effect of superficial collagen patterns and fibrillation of femoral articular cartilage on knee joint mechanics-a 3D finite element analysis.

Collagen fibrils of articular cartilage have specific depth-dependent orientations and the fibrils bend in the cartilage surface to exhibit split-lines. Fibrillation of superficial collagen takes place in osteoarthritis. We aimed to investigate the effect of superficial collagen fibril patterns and collagen fibrillation of cartilage on stresses and strains within a knee joint. A 3D finite element model of a knee joint with cartilage and menisci was constructed based on magnetic resonance imaging. The fibril-reinforced poroviscoelastic material properties with depth-dependent collagen orientations and split-line patterns were included in the model. The effects of joint loading on stresses and strains in cartilage with various split-line patterns and medial collagen fibrillation were simulated under axial impact loading of 1000 N. In the model, the collagen fibrils resisted strains along the split-line directions. This increased also stresses along the split-lines. On the contrary, contact and pore pressures were not affected by split-line patterns. Simulated medial osteoarthritis increased tissue strains in both medial and lateral femoral condyles, and contact and pore pressures in the lateral femoral condyle. This study highlights the importance of the collagen fibril organization, especially that indicated by split-line patterns, for the weight-bearing properties of articular cartilage. Osteoarthritic changes of cartilage in the medial femoral condyle created a possible failure point in the lateral femoral condyle. This study provides further evidence on the importance of the collagen fibril organization for the optimal function of articular cartilage.

Alterations in structure and properties of collagen network of osteoarthritic and repaired cartilage modify knee joint stresses.

Organization of the collagen network is known to be different in healthy, osteoarthritic and repaired cartilage. The aim of the study was to investigate how the structure and properties of collagen network of cartilage modulate stresses in a knee joint with osteoarthritis or cartilage repair. Magnetic resonance imaging (MRI) at 1.5 T was conducted for a knee joint of a male subject. Articular cartilage and menisci in the knee joint were segmented, and a finite element mesh was constructed based on the two-dimensional section in sagittal projection. Then, the knee joint stresses were simulated under impact loads by implementing the structure and properties of healthy, osteoarthritic and repaired cartilage in the models. During the progression of osteoarthritis, characterized especially by the progressive increase in the collagen fibrillation from the superficial to the deeper layers, the stresses were reduced in the superficial zone of cartilage, while they were increased in and under menisci. Increased fibril network stiffness of repair tissue with randomly organized collagen fibril network reduced the peak stresses in the adjacent tissue and strains at the repair-adjacent cartilage interface. High collagen fibril strains were indicative of stress concentration areas in osteoarthritic and repaired cartilage. The collagen network orientation and stiffness controlled the stress distributions in healthy, osteoarthritic and repaired cartilage. The evaluation of articular cartilage function using clinical MRI and biomechanical modeling could enable noninvasive estimation of osteoarthritis progression and monitoring of cartilage repair. This study presents a step toward those goals.