The effect of body weight on the knee joint biomechanics based on subject-specific finite element-musculoskeletal approach.

Knee osteoarthritis (OA) and obesity are major public health concerns that are closely intertwined. This intimate relationship was documented by considering obesity as the most significant preventable risk factor associated with knee OA. To date, however, the effects of obesity on the knee joint's passive-active structure and cartilage loading have been inconclusive. Hence, this study investigates the intricate relationship between obesity and knee OA, centering on the biomechanical changes in knee joint active and passive reactions during the stance phase of gait. Using a subject-specific musculoskeletal and finite element approach, muscle forces, ligament stresses, and articular cartilage contact stresses were analyzed among 60 individuals with different body mass indices (BMI) classified under healthy weight, overweight, and obese categories. Our predicted results showed that obesity significantly influenced knee joint mechanical reaction, increasing muscle activations, ligament loading, and articular cartilage contact stresses, particularly during key instances of the gait cycle-first and second peak loading instances. The study underscores the critical role of excessive body weight in exacerbating knee joint stress distribution and cartilage damage. Hence, the insights gained provide a valuable biomechanical perspective on the interaction between body weight and knee joint health, offering a clinical utility in assessing the risks associated with obesity and knee OA.

Knee joint biomechanics and cartilage damage prediction during landing: A hybrid MD-FE-musculoskeletal modeling.

Understanding the mechanics behind knee joint injuries and providing appropriate treatment is crucial for improving physical function, quality of life, and employability. In this study, we used a hybrid molecular dynamics-finite element-musculoskeletal model to determine the level of loads the knee can withstand when landing from different heights (20, 40, 60 cm), including the height at which cartilage damage occurs. The model was driven by kinematics-kinetics data of asymptomatic subjects at the peak loading instance of drop landing. Our analysis revealed that as landing height increased, the forces on the knee joint also increased, particularly in the vastus muscles and medial gastrocnemius. The patellar tendon experienced more stress than other ligaments, and the medial plateau supported most of the tibial cartilage contact forces and stresses. The load was mostly transmitted through cartilage-cartilage interaction and increased with landing height. The critical height of 126 cm, at which cartilage damage was initiated, was determined by extrapolating the collected data using an iterative approach. Damage initiation and propagation were mainly located in the superficial layers of the tibiofemoral and patellofemoral cartilage. Finally, this study provides valuable insights into the mechanisms of landing-associated cartilage damage and could help limit joint injuries and improve training programs.

Effect of Surgical Design Variations on the Knee Contact Behavior during Anterior Cruciate Ligament Reconstruction.

In this study, we aimed to develop an in-silico synthesis of the effect of critical surgical design parameters on articular contact behavior for a bone-patellar-tendon-bone anterior cruciate ligament reconstruction (ACL-R) surgery. A previously developed finite element model of the knee joint consisting of all relevant soft tissues was employed. The knee model was further updated with additional features to develop the parametric FE model of the biomechanical experiments that depicted the ACL-R surgery. The parametricity was created involving femoral tunnel architecture (orientations and locations) and graft fixation characteristics (pretension and angle of fixation). A global sensitivity analysis based on variance decomposition was used to investigate the contribution of the surgical parameters to the uncertainty in response to the ACL-R joint. Our examinations indicated that the total contact force was primarily influenced by either combined or individual action of the graft pretension and fixation angle, with a modest contribution of the graft insertion sites. The joint contact center and area were affected mainly by the angle of fixation and the tunnel placements. Graft pretension played the dominant role in the maximum contact pressure variability, an observation that has been well-documented in the literature. Interestingly, the joint contact behavior was almost insensitive to the tunnel's coronal and sagittal orientations. Our data provide an evaluation of how the surgical parameters affect the knee joint's contact behavior after ACL-R and may provide additional information to better explain the occurrence of osteoarthritis as an aftermath of such surgery.

Surrogate modeling of articular cartilage degradation to understand the synergistic role of MMP-1 and MMP-9: a case study.

A characteristic feature of arthritic diseases is cartilage extracellular matrix (ECM) degradation, often orchestrated by the overexpression of matrix metalloproteinases (MMPs) and other proteases. The interplay between fibril level degradation and the tissue-level aggregate response to biomechanical loading was explored in this work by a computational multiscale cartilaginous model. We considered the relative abundance of collagenases (MMP-1) and gelatinases (MMP-9) in surrogate models, where the diffusion (spatial distribution) of these enzymes and the subsequent, co-localized fibrillar damage were spatially randomized with Latin Hypercube Sampling. The computational model was constructed by incorporating the results from prior molecular dynamics simulations (tensile test) of microfibril degradation into a hyper-elastoplastic fibril-reinforced cartilage model. Including MMPs-mediated collagen fibril-level degradation in computational models may help understand the ECM pathomechanics at the tissue level. The mechanics of cartilage tissue and fibril show variations in mechanical integrity depending on the different combinations of MMPs-1 and 9 with a concentration ratio of 1:1, 3:1, and 1:3 in simulated indentation tests. The fibril yield (local failure) was initiated at 20.2 ± 3.0 (%) and at 23.0 ± 2.8 (%) of bulk strain for col 1:gel 3 and col 3: gel 1, respectively. The reduction in failure stress (global response) was 39.8% for col 1:gel 3, 37.5% for col 1:gel 1, and 36.7% for col 3:gel 1 compared with the failure stress of the degradation free tissue. These findings indicate that cartilage's global and local mechanisms of failure largely depend on the relative abundance of the two key enzymes-collagenase (MMP-1) and gelatinase (MMP-9) and the spatial characteristics of diffusion across the layers of the cartilage ECM.

Multiscale Characterization of Type I Collagen Fibril Stress-Strain Behavior under Tensile Load: Analytical vs. MD Approaches.

Type I collagen is one of the most important proteins in the human body because of its role in providing structural support to the extracellular matrix of the connective tissues. Understanding its mechanical properties was widely investigated using experimental testing as well as molecular and finite element simulations. In this work, we present a new approach for defining the properties of the type I collagen fibrils by analytically formulating its response when subjected to a tensile load and investigating the effects of enzymatic crosslinks on the behavioral response. We reveal some of the shortcomings of the molecular dynamics (MD) method and how they affect the obtained stress-strain behavior of the fibril, and we prove that not only does MD underestimate the Young's modulus and the ultimate tensile strength of the collagen fibrils, but also fails to detect the mechanics of some stretching phases of the fibril. We prove that non-crosslinked fibrils have three tension phases: (i) an initial elastic deformation corresponding to the collagen molecule uncoiling, (ii) a linear regime related to the stretching of the backbone of the tropocollagen molecules, and (iii) a plastic regime dominated by molecular sliding. We also show that for crosslinked fibrils, the second regime can be subdivided into three sub-regimes, and we define the properties of each regime. We also prove, analytically, the alleged MD quadratic relation between the ultimate tensile strength of the fibril and the concentration of enzymatic crosslinks (ß).

Biomechanical Characteristics of the Knee Joint during Gait in Obese versus Normal Subjects.

Knee osteoarthritis (OA) is a growing source of pain and disability. Obesity is the most important avoidable risk factor underlying knee OA. The processes by which obesity impacts osteoarthritis are of tremendous interest to osteoarthritis researchers and physicians, where the joint mechanical load is one of the pathways generally thought to cause or intensify the disease process. In the current work, we developed a hybrid framework that simultaneously incorporates a detailed finite element model of the knee joint within a musculoskeletal model to compute lower extremity muscle forces and knee joint stresses in normal-weight (N) and obese (OB) subjects during the stance phase gait. This model accounts for the synergy between the active musculature and passive structures. In comparing OB subjects and normal ones, forces significantly increased in all muscle groups at most instances of stance. Mainly, much higher activation was computed with lateral hamstrings and medial gastrocnemius. Cartilage contact average pressure was mostly supported by the medial plateau and increased by 22%, with a larger portion of the load transmitted via menisci. This medial compartment experienced larger relative movement and cartilage stresses in the normal subjects and continued to do so with a higher level in the obese subjects. Finally, the developed bioengineering frame and the examined parameters during this investigation might be useful clinically in evaluating the initiation and propagation of knee OA.

Sensitivity analysis of the knee ligament forces to the surgical design variation during anterior cruciate ligament reconstruction: a finite element analysis.

The purpose of this study is to understand the effect of essential surgical design parameters on collateral and cruciate ligaments behavior for a Bone-Patellar-Tendon-Bone (BPTB) anterior cruciate ligament reconstruction (ACL-R) surgery. A parametric finite element model of biomechanical experiments depicting the ACL-R surgery associated with a global sensitivity analysis was adopted in this work. The model parameters were six intraoperative variables, two-quadrant coordinates of femoral tunnel placement, femoral tunnel sagittal and coronal angles, graft pretension, and the joint angle at which the BPTB graft is tensioned (fixation angle). Our results indicated that cruciate ligaments (posterior cruciate ligament (PCL) and graft) were mainly sensitive to graft pretension (23%), femoral tunnel sites (56%), and the angle at which the surgeon decided to fix the graft (14%). The collateral ligaments (medial and lateral) were also affected by the same set of surgical parameters as the cruciate ligaments except for graft pretension. The output data of this study may help to identify a better role for the ACL-R intraoperative variables in optimizing the knee joint ligaments' postsurgical functionality.

An in vitro investigation to understand the synergistic role of MMPs-1 and 9 on articular cartilage biomechanical properties.

Matrix metalloproteinases (MMPs) play a crucial role in enzymatically digesting cartilage extracellular matrix (ECM) components, resulting in degraded cartilage with altered mechanical loading capacity. Overexpression of MMPs is often caused by trauma, physiologic conditions and by disease. To understand the synergistic impact MMPs have on cartilage biomechanical properties, MMPs from two subfamilies: collagenase (MMP-1) and gelatinase (MMP-9) were investigated in this study. Three different ratios of MMP-1 (c) and MMP-9 (g), c1:g1, c3:g1 and c1:g3 were considered to develop a degradation model. Thirty samples, harvested from bovine femoral condyles, were treated in groups of 10 with one concentration of enzyme mixture. Each sample was tested in a healthy state prior to introducing degradative enzymes to establish a baseline. Samples were subjected to indentation loading up to 20% bulk strain. Both control and treated samples were mechanically and histologically assessed to determine the impact of degradation. Young's modulus and peak load of the tissue under indentation were compared between the control and degraded cartilage explants. Cartilage degraded with the c3:g1 enzyme concentration resulted in maximum 33% reduction in stiffness and peak load compared to the other two concentrations. The abundance of collagenase is more responsible for cartilage degradation and reduced mechanical integrity.

Multiscale modeling of knee ligament biomechanics.

Knee connective tissues are mainly responsible for joint stability and play a crucial role in restraining excessive motion during regular activities. The damage mechanism of these tissues is directly linked to the microscale collagen level. However, this mechanical connection is still unclear. During this investigation, a multiscale fibril-reinforced hyper-elastoplastic model was developed and statistically calibrated. The model is accounting for the structural architecture of the soft tissue, starting from the tropocollagen molecule that forms fibrils to the whole soft tissue. Model predictions are in agreement with the results of experimental and numerical studies. Further, damage initiation and propagation in the collagen fiber were computed at knee ligaments and located mainly in the superficial layers. Results indicated higher crosslink density required higher tensile stress to elicit fibril damage. This approach is aligned with a realistic simulation of a damaging process and repair attempt. To the best of our knowledge, this is the first model published in which the connective tissue stiffness is simultaneously predicted by encompassing the mesoscopic scales between the molecular and macroscopic levels.

Computational frame of ligament in situ strain in a full knee model.

The biomechanical function of connective tissues in a knee joint is to stabilize the kinematics-kinetics of the joint by augmenting its stiffness and limiting excessive coupled motion. The connective tissues are characterized by an in vivo reference configuration (in situ strain) that would significantly contribute to the mechanical response of the knee joint. In this work, a novel iterative method for computing the in situ strain at reference configuration was presented. The framework used an in situ strain gradient approach (deformed reference configuration) and a detailed finite element (FE) model of the knee joint. The effect of the predicted initial configuration on the mechanical response of the joint was then investigated under joint axial compression, passive flexion, and coupled rotations (adduction and internal), and during the stance phase of gait. The inclusion of the reference configuration has a minimal effect on the knee joint mechanics under axial compression, passive flexion, and at two instances (0% and 50%) of the stance phase of gait. However, the presence of the ligaments in situ strains significantly increased the joint stiffness under passive adduction and internal rotations, as well as during the other simulated instances (25%, 75% and 100%) of the stance phase of gait. Also, these parameters substantially altered the local loading state of the ligaments and resulted in better agreement with the literature during joint flexion. Therefore, the proposed computational framework of ligament in situ strain will help to overcome the challenges in considering this crucial biological aspect during knee joint modeling. Besides, the current construct is advantageous for a better understanding of the mechanical behavior of knee ligaments under physiological and pathological states and provide relevant information in the design of reconstructive treatments and artificial grafts.

A multiscale synthesis: characterizing acute cartilage failure under an aggregate tibiofemoral joint loading.

Knee articular cartilage is characterized by a complex mechanical behavior, posing a challenge to develop an efficient and precise model. We argue that the cartilage damage, in general, can be traced to the fibril level as a plastic deformation, defined as micro-defects. To investigate these micro-defects, we have developed a detailed finite element model of the entire healthy tibiofemoral joint (TF) including a multiscale constitutive model which considers the structural hierarchies of the articular cartilage. The net model was simulated under physiological loading conditions to predict joint response under 2000 N axial compression and damage initiation under high axial loading (max 7 KN) when the TF joint flexed to 30°. Computed results sufficiently agreed with earlier experimental and numerical studies. Further, initiation and propagation of damage in fibrils were computed at the tibial cartilage located mainly in the superficial and middle layers. Our simulation results also indicated that the stiffer the fibril is (higher cross-link densities), the higher the contact stress required to elicit a fibril yield and the higher the rate of yielding as a function of increased contact stress. To the best of our knowledge, this is the first model that combines macro-continuum joint mechanics and micromechanics at the tissue level. The computational construct presented here serves as a simulation platform to explore the interplay between acute cartilage damage and micromechanics characteristics at the tropocollagen level.

The effect of fibrillar degradation on the mechanics of articular cartilage: a computational model.

The pathogenesis and pathophysiological underpinnings of cartilage degradation are not well understood. Either mechanically or enzymatically mediated degeneration at the fibril level can lead to acute focal injuries that will, overtime, cause significant cartilage degradation. Understanding the relationship between external loading and the basic molecular structure of cartilage requires establishing a connection between the fibril-level defects and its aggregate effect on cartilage. In this work, we provide a multiscale constitutive model of cartilage to elucidate the effect of two plausible fibril degradation mechanisms on the aggregate tissue: tropocollagen crosslink failure (ß) and a generalized surface degradation (δ). Using our model, the mechanics of aggregate tissue shows differed yield stress and post-yield behavior after crosslink failure and surface degradation compared to intact cartilage, and the tissue-level aggregate behaviors are different from the fibrillar behaviors observed in the molecular dynamics simulations. We also compared the effect of fibrillar defects in terms of crosslink failure and surface degradation in different layers of cartilage within the macroscale tissue construct during a simulated nanoindentation test. Although the mechanical properties of cartilage tissue were largely contingent upon the mechanical properties of the fibril, the macroscale mechanics of cartilage tissue showed ~ 10% variation in yield strain (tissue yield strain: ~ 27 to ~ 37%) compared to fibrillar yield strain (fibrillar yield strain: ~ 16 to ~ 26%) for crosslink failure and ~ 7% difference for the surface degradation (yield strain variations at the tissue: ~ 30 to ~ 37% and fibril: ~ 24 to ~ 26%) at the superficial layer. The yield strain was further delayed in middle layers at least up to 30% irrespective of the failure mechanisms. The cartilage tissue appeared to withstand more strain than the fibrils. The degeneration mechanisms of fibril differentially influenced the aggregate mechanics of cartilage, and the deviation may be attributed to fiber-matrix interplay, depth-dependent fiber orientation and fibrillar defects with different degradation mechanisms. The understanding of the aggregate stress-strain behavior of cartilage tissue, cartilage degradation and its underlying biomechanical factors is important for developing engineering approaches and therapeutic interventions for cartilage pathologies.

Anterior laxity, graft-tunnel interaction and surgical design variations during anterior cruciate ligament reconstruction: A probabilistic simulation of the surgery.

Anterior cruciate ligament (ACL) reconstructive surgeries, employing a total of 48 models, were conducted by virtually removing the ACL and then modeling the surgical preparation, tunnel architecture, graft pre-tensioning and fixation angle of a bone-patellar-tendon-bone autograft. Multifactorial sensitivity analyses were performed to assess the relative influence of these surgical factors on the intraoperative joint laxity, graft-tunnel contact mechanics and graft forces. The sensitivity results indicated that the combined variation in tunnel architecture and graft pre-tension at the time of fixation accounts for most of the estimated variance of the three outcomes. Joint laxity was largely influenced by tunnel placement with a modest contribution of the pre-tensioning force. However, variations in pre-tensioning force yielded a significant effect on both the in tunnel and intra-articular graft forces. Tunnel directions played the dominant role in the expressions of the contact shear between the graft and tunnel aperture in the fully extended and reconstructed joint. Given the proposed significance of the shear mediated graft abrasion at the graft-tunnel aperture, these sensitivity results are consistent with the general observation in the Multicenter ACL Revision Study (MARS), femoral tunnel architecture is most correlated with incidences of graft failures. Tunnel direction and graft pre-tension had similar effect on the estimated variance of the contact pressure in the fully extended joint. Data derived from the 48 ACL reconstructed models indicated that the anatomic surgical design may not be the only design that recovers the healthy joint laxity. In the context of the design of prospective studies, our findings highlight the need to include the graft tension and not fixation angle at the time of fixation as a variable in the evaluation of the surgery.

A multi-scale elasto-plastic model of articular cartilage.

Collagen damage is one of the earliest signs of cartilage degeneration and the onset of osteoarthritis (OA), but the connection between the microscale damage and macroscale tissue function is unclear. We argue that a multiscale model can help elucidate the biochemical and mechanical underpinnings of OA by connecting the microscale defects in collagen fibrils to the macroscopic cartilage mechanics. We investigated this connection using a multiscale fibril reinforced hyperelastoplastic (MFRHEP) model that accounts for the structural architecture of the soft tissue, starting from tropocollagen molecules that form fibrils, and moving to the complete soft tissue. This model was driven by reported experimental data from unconfined compression testing of cartilage. The model successfully described the observed transient response of the articular cartilage in unconfined and indentation tests with low and high loading rates. We used this model to understand damage initiation and propagation as a function of the cross-link density between tropocollagen molecules. This approach appeared to provide a realistic simulation of damage when compared with certain published studies. The current construct presents the first attempt to express the aggregate cartilage damage in terms of the cross-link density at the microfibril level.