Publisher Correction: Quantitative Evaluation of the Mechanical Risks Caused by Focal Cartilage Defects in the Knee.

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The effect of fixed charge density and cartilage swelling on mechanics of knee joint cartilage during simulated gait.

The effect of swelling of articular cartilage, caused by the fixed charge density (FCD) of proteoglycans, has not been demonstrated on knee joint mechanics during simulated walking before. In this study, the influence of the depth-wise variation of FCD was investigated on the internal collagen fibril strains and the mechanical response of the knee joint cartilage during gait using finite element (FE) analysis. The FCD distribution of tibial cartilage was implemented from sodium (23Na) MRI into a 3-D FE-model of the knee joint ("Healthy model"). For comparison, models with decreased FCD values were created according to the decrease in FCD associated with the progression of osteoarthritis (OA) ("Early OA" and "Advanced OA" models). In addition, a model without FCD was created ("No FCD" model). The effect of FCD was studied with five different collagen fibril network moduli of cartilage. Using the reference fibril network moduli, the decrease in FCD from "Healthy model" to "Early OA" and "Advanced OA" models resulted in increased axial strains (by +2 and +6%) and decreased fibril strains (by -3 and -13%) throughout the stance, respectively, calculated as mean values through cartilage depth in the tibiofemoral contact regions. Correspondingly, compared to the "Healthy model", the removal of the FCD altogether in "NoFCD model" resulted in increased mean axial strains by +16% and decreased mean fibril strains by -24%. This effect was amplified as the fibril network moduli were decreased by 80% from the reference. Then mean axial strains increased by +6, +19 and +49% and mean fibril strains decreased by -9, -20 and -32%, respectively. Our results suggest that the FCD in articular cartilage has influence on cartilage responses in the knee during walking. Furthermore, the FCD is suggested to have larger impact on cartilage function as the collagen network degenerates e.g. in OA.

Quantitative Evaluation of the Mechanical Risks Caused by Focal Cartilage Defects in the Knee.

Focal cartilage lesions can proceed to severe osteoarthritis or remain unaltered even for years. A method to identify high risk defects would be of utmost importance to guide clinical decision making and to identify the patients that are at the highest risk for the onset and progression of osteoarthritis. Based on cone beam computed tomography arthrography, we present a novel computational model for evaluating changes in local mechanical responses around cartilage defects. Our model, based on data obtained from a human knee in vivo, demonstrated that the most substantial alterations around the defect, as compared to the intact tissue, were observed in minimum principal (compressive) strains and shear strains. Both strain values experienced up to 3-fold increase, exceeding levels previously associated with chondrocyte apoptosis and failure of collagen crosslinks. Furthermore, defects at the central regions of medial tibial cartilage with direct cartilage-cartilage contact were the most vulnerable to loading. Also locations under the meniscus experienced substantially increased minimum principal strains. We suggest that during knee joint loading particularly minimum principal and shear strains are increased above tissue failure limits around cartilage defects which might lead to osteoarthritis. However, this increase in strains is highly location-specific on the joint surface.

Spatial variation of fixed charge density in knee joint cartilage from sodium MRI - Implication on knee joint mechanics under static loading.

The effects of fixed charge density (FCD) and cartilage swelling have not been demonstrated on cartilage mechanics on knee joint level before. In this study, we present how the spatial and local variations of FCD affects the mechanical response of the knee joint cartilage during standing (half of the body weight, 13 minutes) using finite element (FE) modeling. The FCD distribution of tibial cartilage of an asymptomatic subject was determined using sodium (23Na) MRI at 7T and implemented into a 3-D FE-model of the knee joint (Subject-specific model, FCD: 0.18±0.08 mEq/ml). Tissue deformation in the Subject-specific model was validated against experimental, in vivo loading of the joint conducted with a MR-compatible compression device. For comparison, models with homogeneous FCD distribution (homogeneous model) and FCD distribution obtained from literature (literature model) were created. Immediately after application of the load (dynamic response), the variations in FCD had minor effects on cartilage stresses and strains. After 13 minutes of standing, the spatial and local variations in FCD had most influence on axial strains. In the superficial tibial cartilage in the Subject-specific model, axial strains were increased up to +13% due to smaller FCD (mean -11%), as compared to the homogeneous model. Compared to the literature model, those were decreased up to -18% due to greater FCD (mean +7%). The findings demonstrate that the spatial and local FCD variations in cartilage modulates strains in knee joint cartilage. Thereby, the results highlight the mechanical importance of site-specific content of proteoglycans in cartilage.

Three dimensional patient-specific collagen architecture modulates cartilage responses in the knee joint during gait.

Site-specific variation of collagen fibril orientations can affect cartilage stresses in knee joints. However, this has not been confirmed by 3-D analyses. Therefore, we present a novel method for evaluation of the effect of patient-specific collagen architecture on time-dependent mechanical responses of knee joint cartilage during gait. 3-D finite element (FE) models of a human knee joint were created with the collagen architectures obtained from T2 mapped MRI (patient-specific model) and from literature (literature model). The effect of accuracy of the implementation of collagen fibril architecture into the model was examined by using a submodel with denser FE mesh. Compared to the literature model, fibril strains and maximum principal stresses were reduced especially in the superficial/middle regions of medial tibial cartilage in the patient-specific model after the loading response of gait (up to -413 and -26%, respectively). Compared to the more coarsely meshed joint model, the patient-specific submodel demonstrated similar strain and stress distributions but increased values particularly in the superficial cartilage regions (especially stresses increased >60%). The results demonstrate that implementation of subject-specific collagen architecture of cartilage in 3-D modulates location- and time-dependent mechanical responses of human knee joint cartilage. Submodeling with more accurate implementation of collagen fibril architecture alters cartilage stresses particularly in the superficial/middle tissue.

Implementation of subject-specific collagen architecture of cartilage into a 2D computational model of a knee joint--data from the Osteoarthritis Initiative (OAI).

A subject-specific collagen architecture of cartilage, obtained from T(2) mapping of 3.0 T magnetic resonance imaging (MRI; data from the Osteoarthritis Initiative), was implemented into a 2D finite element model of a knee joint with fibril-reinforced poroviscoelastic cartilage properties. For comparison, we created two models with alternative collagen architectures, addressing the potential inaccuracies caused by the nonoptimal estimation of the collagen architecture from MRI. Also two models with constant depth-dependent zone thicknesses obtained from literature were created. The mechanical behavior of the models were analyzed and compared under axial impact loading of 846N. Compared to the model with patient-specific collagen architecture, the cartilage model without tangentially oriented collagen fibrils in the superficial zone showed up to 69% decrease in maximum principal stress and fibril strain and 35% and 13% increase in maximum principal strain and pore pressure, respectively, in the superficial layers of the cartilage. The model with increased thickness for the superficial and middle zones, as obtained from the literature, demonstrated at most 73% increase in stress, 143% increase in fibril strain, and 26% and 23% decrease in strain and pore pressure, respectively, in the intermediate cartilage. The present results demonstrate that the computational model of a knee joint with the collagen architecture of cartilage estimated from patient-specific MRI or literature lead to different stress and strain distributions. The findings also suggest that minor errors in the analysis of collagen architecture from MRI, for example due to the analysis method or MRI resolution, can lead to alterations in knee joint stresses and strains.