Sensitivities of medial meniscal motion and deformation to material properties of articular cartilage, meniscus and meniscal attachments using design of experiments methods

Effect of meniscus modelling assumptions in a static tibiofemoral finite element model: importance of geometry over material

Finite element studies of the tibiofemoral joint have increased use in research, with attention often placed on the material models. Few studies assess the effect of meniscus modelling assumptions in image-based models on contact mechanics outcomes. This work aimed to assess the effect of modelling assumptions of the meniscus on knee contact mechanics and meniscus kinematics. A sensitivity analysis was performed using three specimen-specific tibiofemoral models and one generic knee model. The assumptions in representing the meniscus attachment on the tibia (shape of the roots and position of the attachment), the material properties of the meniscus, the shape of the meniscus and the alignment of the joint were evaluated, creating 40 model instances. The values of material parameters for the meniscus and the position of the root attachment had a small influence on the total contact area but not on the meniscus displacement or the force balance between condyles. Using 3D shapes to represent the roots instead of springs had a large influence in meniscus displacement but not in knee contact area. Changes in meniscus shape and in knee alignment had a significantly larger influence on all outcomes of interest, with differences two to six times larger than those due to material properties. The sensitivity study demonstrated the importance of meniscus shape and knee alignment on meniscus kinematics and knee contact mechanics, both being more important than the material properties or the position of the roots. It also showed that differences between knees were large, suggesting that clinical interpretations of modelling studies using single geometries should be avoided.

Polynomial chaos expansion based sensitivity analysis of predicted knee reactions-assessing the influence of the primary ligaments in distraction based models

Computational knee models have shown that predicted condylar reactions are sensitive to the utilized ligament mechanical parameters. These models, however, are computationally expensive with multiple sources of uncertainty. Traditional uncertainty analysis using Monte-Carlo (MC) inspired methods are costly to perform. The purpose of this study was to use two example calibrated knee models to compare quasi-MC versus polynomial chaos expansion (PCE) sensitivity analyses of predicted condylar reactions that included uncertainty in the mechanical parameters of the ligaments. PCE was practically identical versus quasi-MC with 95% and 98% reductions in model evaluations for analyses with 10 and 6 uncertain variables, respectively.

Effect of surface matching mismatch of focal knee articular prosthetic on tibiofemoral contact stress using finite element analysis

Aims

Focal knee arthroplasty is an attractive alternative to knee arthroplasty for young patients because it allows preservation of a large amount of bone for potential revisions. However, the mechanical behaviour of cartilage has not yet been investigated because it is challenging to evaluate in vivo contact areas, pressure, and deformations from metal implants. Therefore, this study aimed to determine the contact pressure in the tibiofemoral joint with a focal knee arthroplasty using a finite element model.

Methods

The mechanical behaviour of the cartilage surrounding a metal implant was evaluated using finite element analysis. We modelled focal knee arthroplasty with placement flush, 0.5 mm deep, or protruding 0.5 mm with regard to the level of the surrounding cartilage. We compared contact stress and pressure for bone, implant, and cartilage under static loading conditions.

Results

Contact stress on medial and lateral femoral and tibial cartilages increased and decreased, respectively, the most and the least in the protruding model compared to the intact model. The deep model exhibited the closest tibiofemoral contact stress to the intact model. In addition, the deep model demonstrated load sharing between the bone and the implant, while the protruding and flush model showed stress shielding. The data revealed that resurfacing with a focal knee arthroplasty does not cause increased contact pressure with deep implantation. However, protruding implantation leads to increased contact pressure, decreased bone stress, and biomechanical disadvantage in an in vivo application.

Conclusion

These results show that it is preferable to leave an edge slightly deep rather than flush and protruding.

The Interplay of Biomechanical and Biological Changes Following Meniscus Injury

PURPOSE OF REVIEW

Meniscus injury often leads to joint degeneration and post-traumatic osteoarthritis (PTOA) development. Therefore, the purpose of this review is to outline the current understanding of biomechanical and biological repercussions following meniscus injury and how these changes impact meniscus repair and PTOA development. Moreover, we identify key gaps in knowledge that must be further investigated to improve meniscus healing and prevent PTOA.

RECENT FINDINGS

Following meniscus injury, both biomechanical and biological alterations frequently occur in multiple tissues in the joint. Biomechanically, meniscus tears compromise the ability of the meniscus to transfer load in the joint, making the cartilage more vulnerable to increased strain. Biologically, the post-injury environment is often characterized by an increase in pro-inflammatory cytokines, catabolic enzymes, and immune cells. These multi-faceted changes have a significant interplay and result in an environment that opposes tissue repair and contributes to PTOA development. Additionally, degenerative changes associated with OA may cause a feedback cycle, negatively impacting the healing capacity of the meniscus. Strides have been made towards understanding post-injury biological and biomechanical changes in the joint, their interplay, and how they affect healing and PTOA development. However, in order to improve clinical treatments to promote meniscus healing and prevent PTOA development, there is an urgent need to understand the physiologic changes in the joint following injury. In particular, work is needed on the in vivo characterization of the temporal biomechanical and biological changes that occur in patients following meniscus injury and how these changes contribute to PTOA development.

Thinner tuberosity osteotomy is more resistant to axial load in medial open-wedge distal tuberosity proximal tibial osteotomy: A biomechanical study

BACKGROUND

The purpose of this study was to investigate axial load resistance of the tibia depending on the thickness of tibial tuberosity osteotomy in medial open-wedge distal tuberosity proximal tibial osteotomy (OWDTO). The hypothesis is that a thin tibial tuberosity osteotomy shows high axial load resistance of the tibia.

METHODS

The OWDTO model was constructed from imitation bones of the tibia. Distal tibial tuberosity osteotomy was performed with thicknesses of 7, 14, and 21 mm (n = 5 for each group). Cyclic axial-load fatigue tests were performed to investigate the strain at five measurement points on the OWDTO model. An axial-load failure test was also performed to investigate the maximum strain for failure.

RESULTS

The 7-mm OWDTO model showed a significantly lower stain range than the 14-mm model at the middle part of the lateral hinge (P = 0.0263, mean difference: -852.6 με), posterior part (P = 0.0465, mean difference: -1040.0 με), posterior tibial cortex (P < 0.0001, mean difference: -583.4 με), and plate (P = 0.0029, mean difference: -121.6 με). There were no significant differences in the strain at the tibial tuberosity between the groups. The axial load for complete failure was significantly higher in the 7-mm model than in the 21-mm model (P = 0.0010, mean difference: 2577.0 N). The failure points were at the lateral hinges.

CONCLUSIONS

Thinner distal tibial tuberosity osteotomy is more resistant to axial load and may be recommended for the prevention of tibial and lateral hinge fractures after OWDTO.

Osteoarthritic meniscal entheses exhibit altered collagen fiber orientation

PURPOSE/AIM

The knee menisci are vital for maintaining the stability of the joint, allowing for force distribution, and protecting the underlying articular cartilage during loading. Each meniscus is attached to the underlying bone via two ligamentous entheses composed of collagen fibers that are continuous throughout all four zones of the attachment: ligament, uncalcified fibrocartilage, calcified fibrocartilage, and subchondral bone. The collagen fibers of the meniscal entheses are important for proper functionality of the entheses, particularly in preventing meniscal extrusion which is a common hallmark of osteoarthritis. The goal of this work was to assess changes in collagen fiber orientation present in osteoarthritic knee joints.

MATERIALS AND METHODS

Entheses were harvested from patients undergoing total knee arthroplasties and prepared histological sections were stained with picrosirius red to identify collagen fiber angle and fiber deviation.

RESULTS

In the calcified fibrocartilage the collagen fibers of the lateral anterior enthesis inserted at significantly (p < 0.1) shallower angles, and the fiber deviation was significantly (p < 0.1) less compared to the lateral posterior enthesis. These differences in the calcified fibrocartilage may occur as an adaptation to loading regimes of the osteoarthritic joint. When compared to the collagen fiber orientation of healthy entheses, collagen fibers in osteoarthritic tissue inserted at shallower insertion angles and demonstrated higher levels of deviation.

CONCLUSIONS

Changes to meniscal enthesis collagen fiber orientation with end stage osteoarthritis could offer an explanation for the change in functionality of diseased tissue and may contribute to meniscal extrusion and ultimately the degeneration of articular cartilage.

Evolution of knowledge on meniscal biomechanics: a 40 year perspective

Background

Knowledge regarding the biomechanics of the meniscus has grown exponentially throughout the last four decades. Numerous studies have helped develop this knowledge, but these studies have varied widely in their approach to analyzing the meniscus. As one of the subcategories of mechanical phenomena Medical Subject Headings (MeSH) terms, mechanical stress was introduced in 1973. This study aims to provide an up-to-date chronological overview and highlights the evolutionary comprehension and understanding of meniscus biomechanics over the past forty years.

Methods

A literature review was conducted in April 2021 through PubMed. As a result, fifty-seven papers were chosen for this narrative review and divided into categories; Cadaveric, Finite element (FE) modeling, and Kinematic studies.

Results

Investigations in the 1970s and 1980s focused primarily on cadaveric biomechanics. These studies have generated the fundamental knowledge basis for the emergence of FE model studies in the 1990s. As FE model studies started to show comparable results to the gold standard cadaveric models in the 2000s, the need for understanding changes in tissue stress during various movements triggered the start of cadaveric and FE model studies on kinematics.

Conclusion

This study focuses on a chronological examination of studies on meniscus biomechanics in order to introduce concepts, theories, methods, and developments achieved over the past 40 years and also to identify the likely direction for future research. The biomechanics of intact meniscus and various types of meniscal tears has been broadly studied. Nevertheless, the biomechanics of meniscal tears, meniscectomy, or repairs in the knee with other concurrent problems such as torn cruciate ligaments or genu-valgum or genu-varum have not been extensively studied.

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.

Effects of the material properties of a focal knee articular prosthetic on the human knee joint using computational simulation

BACKGROUND

Localized cartilage defects are related to joint pain and reduced function to the development of osteoarthritis. The mechanical properties of the implant for treatment do influence its longevity. Therefore, we aimed to evaluate the effect of material properties' variations of anatomically shaped focal knee implants in the knee joint using numerical finite element analysis.

METHODS

Computational simulations were performed for different cases including an intact knee, a knee with a focal cartilage defect, and a knee fitted with a focal articular prosthetic having three distinct mechanical properties: cobalt-chromium, pyrolytic carbon, and polyethylene. Femoral cartilage, tibial cartilage, and menisci contact pressures were evaluated under the load. In addition, bone stress was evaluated to investigate the stress shielding effect.

RESULTS

Compared with the intact model, the contact stress of the focal implant model was increased; on the femoral lateral cartilage by 14%, on medial and lateral tibial cartilages by nine percent and 10%, on medial and lateral menisci by 23% and 20%. In contrast, the focal implant model had no effect on the menisci but contact stress on the tibial cartilage increased compared with the intact model. The BioPoly model showed the lowest contact stress on femoral and tibial cartilages. Additionally, the cobalt-chromium model showed the lowest bone stress that improved the load-sharing effect.

CONCLUSIONS

The results suggested that implant material properties are an important parameter in the design of a focal implant. The polyethylene model potentially restored the intact knee contact mechanics and it reduced the risk of physiological damage to the articular cartilage.

A comprehensive testing protocol for macro-scale mechanical characterization of knee articular cartilage with documented experimental repeatability

Articular cartilage mechanics has been extensively studied with various approaches and mechanical characterization strategies. However testing protocols can be highly varying and difficult to reproduce, particularly for specimen-specific analyses. Detailed knowledge of testing protocols is important for reliable use in concordant finite element analyses. This study presents a detailed, robust procedure for cartilage testing-with multiple regions and per sample repeatability data. Samples were taken from femur, tibia and patella of a human cadaver knee and tested in unconfined compression, confined compression and uniaxial tension. Each test was repeated three times. The testing protocols provide elastic and time dependent characterization data. Results, for example equilibrium modulus of 0.28 (0.0024) MPa for patella under unconfined compression indicate that variability is well controlled and that protocol(s) presented here can generate repeatable specimen-specific data. As per the authors' knowledge this is the first study to report in-depth uncertainty assessment of the experimental procedures for multi-region knee cartilage characterization.

Constitutive modeling of menisci tissue: a critical review of analytical and numerical approaches

Menisci are fibrocartilaginous disks consisting of soft tissue with a complex biomechanical structure. They are critical determinants of the kinematics as well as the stability of the knee joint. Several studies have been carried out to formulate tissue mechanical behavior, leading to the development of a wide spectrum of constitutive laws. In addition to developing analytical tools, extensive numerical studies have been conducted on menisci modeling. This study reviews the developments of the most widely used continuum models of the meniscus mechanical properties in conjunction with emerging analytical and numerical models used to study the meniscus. The review presents relevant approaches and assumptions used to develop the models and includes discussions regarding strengths, weaknesses, and discrepancies involved in the presented models. The study presents a comprehensive coverage of relevant publications included in Compendex, EMBASE, MEDLINE, PubMed, ScienceDirect, Springer, and Scopus databases. This review aims at opening novel avenues for improving menisci modeling within the framework of constitutive modeling through highlighting the needs for further research directed toward determining key factors in gaining insight into the biomechanics of menisci which is crucial for the elaborate design of meniscal replacements.

Effects of lateral opening wedge and medial closing wedge distal femoral osteotomies on axial load stability

BACKGROUND

The stability of the current distal femoral osteotomy is insufficient for early weight bearing and bone healing. The purpose of this study was to test the stability of medial closing wedge- (MCW-) and lateral opening wedge-distal femoral osteotomies (LOW-DFO), which have improved with the recent advances in technology.

METHODS

We used composite bone models with MCW-DFO, improved with biplanar osteotomy technique and a Tomofix™ MDF plate, or LOW-DFO improved with biplanar osteotomy technique, a Tomofix™ LDF plate, and a β-TCP bone substitute, BONISH® graft. A cyclic axial loading test was employed to evaluate the strain on a plate and hinge point. The breaking axial load was measured.

RESULTS

Tensile strain on the plate produced by cyclic axial loading was significantly lower for LOW-DFO (2.0 ± 0.8 MPa) than for MCW-DFO (3.9 ± 1.6 MPa, P < .05). Compressive strain on the hinge point produced by cyclic axial loading was lower for LOW-DFO (6.6 ± 2.9 MPa) than for MCW-DFO (7.7 ± 4.6 MPa,). The maximum breaking axial load was significantly higher for LOW-DFO (5511 ± 945 N) than for MCW-DFO (4303 ± 518 N, P < .05).

CONCLUSIONS

LOW-DFO improved with recent advanced technology was superior to MCW-DFO improved with advanced technology in both cyclic axial loading test and breaking axial load test. This suggests that LOW-DFO facilitates earlier weight bearing and bone healing than does MCW-DFO.

Effects of a Medial Knee Unloading Implant on Tibiofemoral Joint Mechanics During Walking

The Atlas™ unicompartmental knee system is a second-generation extra-articular unloading implant for patients with mild to moderate medial knee osteoarthritis. The technology acts to reduce a portion of the weight-bearing load exerted on the medial knee during physical activity thereby, reducing the mechanical stress imposed on a degenerative joint. The purpose of the present study was to evaluate the effects of the Atlas™ on tibiofemoral joint mechanics during walking. A computer-aided design assembly of the Atlas™ was virtually implanted on the medial aspect of a previously validated finite element tibiofemoral joint model. Data for knee joint forces and moments from an anthropometrically matched male were applied to the model to quasi-statically simulate the stance phase of gait. Predictions of tibiofemoral joint mechanics were computed pre- and post-virtual implantation of the Atlas™. Compressive force in the medial tibiofemoral compartment was reduced by a mean of 53%, resulting in the decrement of mean cartilage-cartilage and cartilage-meniscus von Mises stress by 31% and 32%, respectively. The Atlas™ was not predicted to transfer net loading to the lateral compartment. The tibiofemoral joint model exhibited less internal-external rotation and anterior-posterior translation post-Atlas™, indicating a change in the kinematic environment of the knee. From a biomechanical perspective, extra-articular joint unloading may serve as a treatment option for patients recalcitrant to conservative care. Evaluation of mechanical changes in the tibiofemoral joint demonstrate the potential treatment mechanism of the Atlas™, in accordance with the available clinical data. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 37:2149-2156, 2019.

Design optimization of high tibial osteotomy plates using finite element analysis for improved biomechanical effect

Background

High tibial osteotomy (HTO) is a common treatment for moderate osteoarthritis of the medial compartment in the knee joint by the translation of the force center toward the lateral compartment. However, the stability of a short plate such as Puddu used in this procedure was not as effective as other long plates such as Tomofix. No previous studies have used a rigorous and systematic design optimization method to determine the optimal shape of short HTO plate. Therefore, the purpose of this study is to evaluate the improved biomechanical stability of a short HTO plate by using design optimization and finite element (FE) analysis.

Methods

A FE model of HTO was subjected to physiological and surgical loads in the tibia. Taguchi-style L27 orthogonal arrays were used to identify the most significant factors for optimizing the design parameters. The optimal design variables were calculated using the nondominated sorting genetic algorithm II. Plate and bone stresses and wedge micromotions in the initial and optimized designs were chosen as the comparison indices.

Results

Optimal designed HTO plate showed the decreased micromotions over the initial HTO plate with enhanced plate stability. In addition, increased bone stress and decreased plate stress supported the positive effect on stress shielding compared to initial HTO plate design. The results yielded a new short HTO design while demonstrating the feasibility of design optimization and potential improvements to biomechanical stability in HTO design. The newly developed short HTO plate throughout the optimization and computational simulation showed the improved biomechanical effect as good as the golden standard, TomoFix, does.

Conclusions

This study showed that plate design has a strong influence on the stability after HTO. This study demonstrated that the optimized short plates had low stress shielding effect and less micromotion because of its improvement in biomechanical performances. Our result showed that design optimization is an effective tool for HTO plate design. This information can aid future developments in HTO plate design and can be expanded to other implant designs.

Multi-objective design optimization of high tibial osteotomy for improvement of biomechanical effect by using finite element analysis

Medial opening wedge high tibial osteotomy (HTO) makes the proximal tibia a highly unstable structure and causes plates and screws to be the potential sources for mechanical failure. However, asymmetrical callus and incomplete bone formations underneath the plates (TomoFix) have been recent concerns in clinical and experimental studies related to HTO due to the high stiffness. The purpose of this study was to evaluate the biomechanical effect of the TomoFix plate system with respect to changes in design using a computational simulation. A parametric three-dimensional model of HTO was constructed from medical image data. The design parameters for the HTO plate were evaluated to investigate their influence on biomechanical effects, and the most significant factors were determined using Taguchi-style L27 orthogonal arrays. Multi-objective optimization was used to identify the wedge micromotion stability without the stress shielding effect that occurs in the bone plate. The initial design showed that the high stiffness of the plate caused stress shielding on the bone and plate. However, the optimal design led to sharing the stress and load with the bone plate to eliminate stress shielding. In addition, the stability required for the plate could be found in the micromotions of the wedge for the optimal design. The optimal condition of design parameters was successfully determined using the Taguchi and multi-objective optimization method, which was shown to eliminate stress shielding effects. The results showed that an optimal design demonstrated the feasibility of design optimization and improvements in biomechanical stability for HTO. © 2018 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:2956-2965, 2018.

The influence of a change in the meniscus cross-sectional shape on the medio-lateral translation of the knee joint and meniscal extrusion

OBJECTIVE

The purpose of this study was to evaluate the influence of a change in the meniscus cross sectional shape on its position and on the biomechanics of a knee joint.

METHODS

One main finite element model of a left knee joint was created on the basis of MRI images. The model consisted of bones, articular cartilages, menisci and ligaments. Eight variants of this model with an increased or decreased meniscus height were then prepared. Nonlinear static analyses with a fixed flexion/extension movement for a compressive load of 1000 N were performed. The additional analyses for those models with a constrained medio-lateral relative bone translation allowed for an evaluation of the influence of this translation on a meniscus external shift.

RESULTS

It was observed that a decrease in the meniscus height caused a decrease in the contact area, together with a decrease in the contact force between the flattened meniscus and the cartilage. For the models with an increased meniscus height, a maximal value of force acting on the meniscus in a medio-lateral direction was obtained. The results have shown that the meniscus external shift was approximately proportional to the meniscus slope angle, but that relationship was modified by a medio-lateral relative bone translation. It was found that the translation of the femur relative to the tibia may be dependent on the geometry of the menisci.

CONCLUSIONS

The results have suggested that a change in the meniscus geometry in the cross sectional plane can considerably affect not only the meniscal external shift, but also the medio-lateral translation of the knee joint as well as the congruency of the knee joint.

Validation of a computational knee joint model using an alignment method for the knee laxity test and computed tomography

BACKGROUND

Computational models have been identified as efficient techniques in the clinical decision-making process. However, computational model was validated using published data in most previous studies, and the kinematic validation of such models still remains a challenge. Recently, studies using medical imaging have provided a more accurate visualization of knee joint kinematics.

OBJECTIVE

The purpose of the present study was to perform kinematic validation for the subject-specific computational knee joint model by comparison with subject's medical imaging under identical laxity condition.

METHODS

The laxity test was applied to the anterior-posterior drawer under 90° flexion and the varus-valgus under 20° flexion with a series of stress radiographs, a Telos device, and computed tomography. The loading condition in the computational subject-specific knee joint model was identical to the laxity test condition in the medical image.

RESULTS

Our computational model showed knee laxity kinematic trends that were consistent with the computed tomography images, except for negligible differences because of the indirect application of the subject's in vivo material properties.

CONCLUSIONS

Medical imaging based on computed tomography with the laxity test allowed us to measure not only the precise translation but also the rotation of the knee joint. This methodology will be beneficial in the validation of laxity tests for subject- or patient-specific computational models.

Reducing uncertainty when using knee-specific finite element models by assessing the effect of input parameters

Little is known about knee-specific factors that influence contact mechanics. Finite Element (FE) models offer a powerful tool to study contact mechanics, but there often exists ambiguity in the exact values of the inputs (e.g., tissue properties), which can result in a range of output values. Our objective was to quantify the reduction in the range of output values (defined herein as "uncertainty") from FE models of the human knee joint when known pre-defined values are used for clinically measurable inputs. To achieve this goal, we applied a statistically augmented FE approach to three human cadaveric knees for which full geometric and kinematic data were available. Two sets of conditions were simulated: All model inputs, clinically measurable or not, were varied to represent a "normal" patient population (Condition 1); subsets of clinically measurable variable inputs were fixed at specific values (called "patient derived inputs," or PDIs) while the other variables were varied over "normal" values (Condition 2). We found that by fixing body mass index and the anterior-posterior position of the meniscal-bony insertion points, model output uncertainty was reduced by one- to three-fifths. The magnitude of uncertainty reduction was strongly influenced by the individual knee. It was observed that knees with great anterior-posterior translation during gait had greater reductions in uncertainty when PDIs were used. This study represents the first step in developing FE models of the human knee joint based on inputs that can be derived from patients in a clinical setting. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:2233-2242, 2017.

Current concepts on structure-function relationships in the menisci

The menisci are intricately organized structures that perform many tasks in the knee. We review their structure and function and introduce new data about their tibial and femoral surfaces. As the femur and tibia approach each other when the knee is bearing load, circumferential tension develops in the menisci, enabling the transmission of compressive load between the femoral and tibial cartilage layers. A low shear modulus is necessary for the tissue to adapt its shape to the changing radius of the femur as that bone moves relative to the tibia during joint articulation. The organization of the meniscus facilitates its functions. In the outer region of the menisci, intertwined collagen fibrils, fibers, and fascicles with predominantly circumferential orientation are prevalent; these structures are held together by radial tie fibers and sheets. Toward the inner portion of the menisci, there is more proteoglycan and the structure becomes more cartilage-like. The transition between these structural forms is gradual and seamless. The flexible roots, required for rigid body motion of the menisci, meld with both the tibia and the outer portion of the menisci to maintain continuity for resistance to the circumferential tension. Our new data demonstrate that the femoral and tibial surfaces of the menisci are structurally analogous to the surfaces of articular cartilage, enabling consistent modes of lubrication and load transfer to occur at the interfacing surfaces throughout motion. The structure and function of the menisci are thus shown to be strongly related to one another: form clearly complements function.

The Influence of Articular Cartilage Thickness Reduction on Meniscus Biomechanics

OBJECTIVE

Evaluation of the biomechanical interaction between meniscus and cartilage in medial compartment knee osteoarthritis.

METHODS

The finite element method was used to simulate knee joint contact mechanics. Three knee models were created on the basis of knee geometry from the Open Knee project. We reduced the thickness of medial cartilages in the intact knee model by approximately 50% to obtain a medial knee osteoarthritis (OA) model. Two variants of medial knee OA model with congruent and incongruent contact surfaces were analysed to investigate the influence of congruency. A nonlinear static analysis for one compressive load case was performed. The focus of the study was the influence of cartilage degeneration on meniscal extrusion and the values of the contact forces and contact areas.

RESULTS

In the model with incongruent contact surfaces, we observed maximal compressive stress on the tibial plateau. In this model, the value of medial meniscus external shift was 95.3% greater, while the contact area between the tibial cartilage and medial meniscus was 50% lower than in the congruent contact surfaces model. After the non-uniform reduction of cartilage thickness, the medial meniscus carried only 48.4% of load in the medial compartment in comparison to 71.2% in the healthy knee model.

CONCLUSIONS

We have shown that the change in articular cartilage geometry may significantly reduce the role of meniscus in load transmission and the contact area between the meniscus and cartilage. Additionally, medial knee OA may increase the risk of meniscal extrusion in the medial compartment of the knee joint.

Computational model-based probabilistic analysis of in vivo material properties for ligament stiffness using the laxity test and computed tomography

The objective of this paper was to evaluate in vivo material properties in order to address technical aspects of computational modeling of ligaments in the tibiofemoral joint using a probabilistic method. The laxity test was applied to the anterior-posterior drawer under 30° and 90° of flexion with a series of stress radiographs, a Telos device, and computed tomography. Ligament stiffness was investigated using sensitivity analysis based on the Monte-Carlo method with a subject-specific finite element model generated from in vivo computed tomography and magnetic resonance imaging data, subjected to laxity test conditions. The material properties of ligament stiffness and initial ligament strain in a subject-specific finite element model were optimized to minimize the differences between the movements of the tibia and femur in the finite element model and the computed tomography images in the laxity test. The posterior cruciate ligament was the most significant factor in flexion and posterior drawer, while the anterior cruciate ligament primarily was the most significant factor for the anterior drawer. The optimized material properties model predictions in simulation and the laxity test were more accurate than predictions based on the initial material properties in subject-specific computed tomography measurement. Thus, this study establishes a standard for future designs in allograft, xenograft, and artificial ligaments for anterior cruciate ligament and posterior cruciate ligament injuries.

A Computational Efficient Method to Assess the Sensitivity of Finite-Element Models: An Illustration With the Hemipelvis

Assessing the sensitivity of a finite-element (FE) model to uncertainties in geometric parameters and material properties is a fundamental step in understanding the reliability of model predictions. However, the computational cost of individual simulations and the large number of required models limits comprehensive quantification of model sensitivity. To quickly assess the sensitivity of an FE model, we built linear and Kriging surrogate models of an FE model of the intact hemipelvis. The percentage of the total sum of squares (%TSS) was used to determine the most influential input parameters and their possible interactions on the median, 95th percentile and maximum equivalent strains. We assessed the surrogate models by comparing their predictions to those of a full factorial design of FE simulations. The Kriging surrogate model accurately predicted all output metrics based on a training set of 30 analyses (R2 = 0.99). There was good agreement between the Kriging surrogate model and the full factorial design in determining the most influential input parameters and interactions. For the median, 95th percentile and maximum equivalent strain, the bone geometry (60%, 52%, and 76%, respectively) was the most influential input parameter. The interactions between bone geometry and cancellous bone modulus (13%) and bone geometry and cortical bone thickness (7%) were also influential terms on the output metrics. This study demonstrates a method with a low time and computational cost to quantify the sensitivity of an FE model. It can be applied to FE models in computational orthopaedic biomechanics in order to understand the reliability of predictions.

Probabilistic evaluation of the material properties of the in vivo subject-specific articular surface using a computational model

This article used probabilistic analysis to evaluate material properties of the in vivo subject-specific tibiofemoral (TF) joint model. Sensitivity analysis, based on a Monte Carlo (MC) method, was performed using a subject-specific finite element (FE) model generated from in vivo computed tomography (CT) and magnetic resonance imaging (MRI) data, subjected to two different loading conditions. Specifically, the effects of inherent uncertainty in ligament stiffness, horn attachment stiffness, and articular surface material properties were assessed using multifactorial global sensitivity analysis. The MRI images were taken before and after axial compression, and when the flexion condition had been maintained at up to 90 degree flexion in the subject-specific knee joint. The loading conditions of the probabilistic subject-specific FE model (axial compression and 90 degree flexion) were similar to the MRI acquisition setup. We were able to detect the influence of material parameters while maintaining the potential effect of parametric interactions. Throughout the in silico property optimization, a subject-specific FE model was used and less sensitive parameters were eliminated in the global sensitivity method. Soft tissue material properties were estimated using an optimization procedure that involved the minimization of the differences between the kinematics predicted by the subject-specific model and those obtained through in vivo subject-specific data. The results of this approach suggest that the articular surface mechanical properties could be found by using in vivo measurements, which clarifies the valuable tool for future subject-specific studies related to TF joint scaffolds, allografts and biologics. © 2016 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 105B: 1390-1400, 2017.

Probabilistic Approach for Determining the Material Properties of Meniscal Attachments In Vivo Using Magnetic Resonance Imaging and a Finite Element Model

The material properties of in vivo meniscal attachments were evaluated using a probabilistic finite element (FE) model and magnetic resonance imaging (MRI). MRI scans of five subjects were collected at full extension and 30°, 60°, and 90° flexion. One subject with radiographic evidence of no knee injury and four subjects with Kellgren-Lawrence score of 1 or 2 (two each) were recruited. Isovoxel sagittal three-dimensional cube sequences of the knee were acquired in extension and flexion. Menisci movement in flexion was investigated using sensitivity analysis based on the Monte Carlo method in order to generate a subject-specific FE model to evaluate significant factors. The material properties of horn attachment in the five-subject FE model were optimized to minimize the differences between meniscal movements in the FE model and MR images in flexion. We found no significant difference between normal and patient knees in flexion with regard to movement of anterior, posterior, medial, and lateral menisci or changes in height morphology. At 90° flexion, menisci movement was primarily influenced by posterior horn stiffness, followed by anterior horn stiffness, the transverse ligament, and posterior cruciate ligament. The optimized material properties model predictions for menisci motion were more accurate than the initial material properties model. The results of this approach suggest that the material properties of horn attachment, which affects the mobile characteristics of menisci, could be determined in vivo. Thus, this study establishes a basis for a future design method of attachment for tissue-engineered replacement menisci.

A Comprehensive Specimen-Specific Multiscale Data Set for Anatomical and Mechanical Characterization of the Tibiofemoral Joint

Understanding of tibiofemoral joint mechanics at multiple spatial scales is essential for developing effective preventive measures and treatments for both pathology and injury management. Currently, there is a distinct lack of specimen-specific biomechanical data at multiple spatial scales, e.g., joint, tissue, and cell scales. Comprehensive multiscale data may improve the understanding of the relationship between biomechanical and anatomical markers across various scales. Furthermore, specimen-specific multiscale data for the tibiofemoral joint may assist development and validation of specimen-specific computational models that may be useful for more thorough analyses of the biomechanical behavior of the joint. This study describes an aggregation of procedures for acquisition of multiscale anatomical and biomechanical data for the tibiofemoral joint. Magnetic resonance imaging was used to acquire anatomical morphology at the joint scale. A robotic testing system was used to quantify joint level biomechanical response under various loading scenarios. Tissue level material properties were obtained from the same specimen for the femoral and tibial articular cartilage, medial and lateral menisci, anterior and posterior cruciate ligaments, and medial and lateral collateral ligaments. Histology data were also obtained for all tissue types to measure specimen-specific cell scale information, e.g., cellular distribution. This study is the first of its kind to establish a comprehensive multiscale data set for a musculoskeletal joint and the presented data collection approach can be used as a general template to guide acquisition of specimen-specific comprehensive multiscale data for musculoskeletal joints.

Material properties of individual menisci and their attachments obtained through inverse FE-analysis

Meniscal properties for computational methods have already been proposed. However, it is well known that there is high intra subject variability in the material properties of soft tissues and that disruption of the fiber network alters the biomechanics of the meniscus. Therefore, the objective of this study was to establish a non invasive method to determine the material properties of the individual menisci and their attachments using inverse FE-analyses. In a previous study, the 3D displacements of the meniscus and its attachments under axial joint loads were determined for intact porcine knees. To simulate the experimental response in individual FE-analyses (n=5), an anisotropic, hyperelastic meniscus matrix was embedded in a poroelastic model. During a particle swarm optimization, the difference between the force applied to the meniscus during the experiment and the femoral surface reaction force of the FE model at equilibrium was minimized by varying four material parameters. Afterwards, a prediction error was determined to describe how well the material parameter fit to each of the three displacement directions. Additionally, the stresses occurring in the meniscus were evaluated. The error of the material parameter optimization was on average 6.5±4.4%. The best fitting material parameter combination revealed an error of 1.2%. The highest stresses occurred in the region between the pars intermedia and posterior horn of the meniscus. The individual material properties of the meniscus were successfully obtained with a combination of previously reported, noninvasively measured 3D displacements and inverse FE-analyses. The methodology presented in this study is a promising contribution to the detection of degeneration within the meniscus.

A statistically-augmented computational platform for evaluating meniscal function

Meniscal implants have been developed in an attempt to provide pain relief and prevent pathological degeneration of articular cartilage. However, as yet there has been no systematic and comprehensive analysis of the effects of the meniscal design variables on meniscal function across a wide patient population, and there are no clear design criteria to ensure the functional performance of candidate meniscal implants. Our aim was to develop a statistically-augmented, experimentally-validated, computational platform to assess the effect of meniscal properties and patient variables on knee joint contact mechanics during the activity of walking. Our analysis used Finite Element Models (FEMs) that represented the geometry, kinematics as based on simulated gait and contact mechanics of three laboratory tested human cadaveric knees. The FEMs were subsequently programmed to represent prescribed meniscal variables (circumferential and radial/axial moduli-Ecm, Erm, stiffness of the meniscal attachments-Slpma, Slamp) and patient variables (varus/valgus alignment-VVA, and articular cartilage modulus-Ec). The contact mechanics data generated from the FEM runs were used as training data to a statistical interpolator which estimated joint contact data for untested configurations of input variables. Our data suggested that while Ecm and Erm of a meniscus are critical in determining knee joint mechanics in early and late stance (peak 1 and peak 3 of the gait cycle), for some knees that have greater laxity in the mid-stance phase of gait, the stiffness of the articular cartilage, Ec, can influence force distribution across the tibial plateau. We found that the medial meniscus plays a dominant load-carrying role in the early stance phase and less so in late stance, while the lateral meniscus distributes load throughout gait. Joint contact mechanics in the medial compartment are more sensitive to Ecm than those in the lateral compartment. Finally, throughout stance, varus-valgus alignment can overwhelm these relationships while the stiffness of meniscal attachments in the range studied have minimal effects on the knee joint mechanics. In summary, our statistically-augmented, computational platform allowed us to study how meniscal implant design variables (which can be controlled at the time of manufacture or implantation) interact with patient variables (which can be set in FEMs but cannot be controlled in patient studies) to affect joint contact mechanics during the activity of simulated walking.

Subject-specific finite element modeling of the tibiofemoral joint based on CT, magnetic resonance imaging and dynamic stereo-radiography data in vivo

In this paper, we present a new methodology for subject-specific finite element modeling of the tibiofemoral joint based on in vivo computed tomography (CT), magnetic resonance imaging (MRI), and dynamic stereo-radiography (DSX) data. We implemented and compared two techniques to incorporate in vivo skeletal kinematics as boundary conditions: one used MRI-measured tibiofemoral kinematics in a nonweight-bearing supine position and allowed five degrees of freedom (excluding flexion-extension) at the joint in response to an axially applied force; the other used DSX-measured tibiofemoral kinematics in a weight-bearing standing position and permitted only axial translation in response to the same force. Verification and comparison of the model predictions employed data from a meniscus transplantation study subject with a meniscectomized and an intact knee. The model-predicted cartilage-cartilage contact areas were examined against "benchmarks" from a novel in situ contact area analysis (ISCAA) in which the intersection volume between nondeformed femoral and tibial cartilage was characterized to determine the contact. The results showed that the DSX-based model predicted contact areas in close alignment with the benchmarks, and outperformed the MRI-based model: the contact centroid predicted by the former was on average 85% closer to the benchmark location. The DSX-based FE model predictions also indicated that the (lateral) meniscectomy increased the contact area in the lateral compartment and increased the maximum contact pressure and maximum compressive stress in both compartments. We discuss the importance of accurate, task-specific skeletal kinematics in subject-specific FE modeling, along with the effects of simplifying assumptions and limitations.

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.

Deleterious effects of osteoarthritis on the structure and function of the meniscal enthesis

OBJECTIVE

The ability of menisci to prevent osteoarthritis (OA) is dependent on the integrity of the complex meniscal entheses, the attachments of the menisci to the underlying subchondral bone (SB). The goal of this study was to determine mechanical and structural changes in meniscal entheses after the onset of OA.

DESIGN

Healthy and osteoarthritic meniscal entheses were evaluated for changes in histomorphological characteristics, mineralization, and mechanical properties. Glycosaminoglycans (GAG) and calcium in the insertion were evaluated with histological staining techniques. The extent of calcium deposition was assessed and tidemark (TM) integrity was quantified. Changes in the mineralized zone of the insertion were examined using micro-computed tomography (μCT) to determine bone mineral density, cortical zone thickness, and mineralization gradient. Mechanical properties of the entheses were measured using nano-indentation techniques to obtain material properties based on viscoelastic analysis.

RESULTS

GAG thickness in the calcified fibrocartilage (CFC) zone and calcium content were significantly greater in osteoarthritic anterior meniscal entheses. TM integrity was significantly decreased in OA tissue, particularly in the medial anterior (MA) enthesis. The mineralized zone of osteoarthritic meniscal entheses was significantly thicker than in healthy entheses and showed decreased bone mineral density. Fitting of mineralization data to a sigmoidal Gompertz function revealed a lower rate of increase in mineralization in osteoarthritic tissue. Analysis of viscoelastic mechanical properties revealed increased compliance in osteoarthritic tissue.

CONCLUSIONS

These data suggest that significant changes occur at meniscal enthesis sites with the onset of OA. Mechanical and structural changes in meniscal entheses may contribute to meniscal extrusion, which has been shown to increase the progression of OA.

Finite element model of the knee for investigation of injury mechanisms: development and validation

Multiple computational models have been developed to study knee biomechanics. However, the majority of these models are mainly validated against a limited range of loading conditions and/or do not include sufficient details of the critical anatomical structures within the joint. Due to the multifactorial dynamic nature of knee injuries, anatomic finite element (FE) models validated against multiple factors under a broad range of loading conditions are necessary. This study presents a validated FE model of the lower extremity with an anatomically accurate representation of the knee joint. The model was validated against tibiofemoral kinematics, ligaments strain/force, and articular cartilage pressure data measured directly from static, quasi-static, and dynamic cadaveric experiments. Strong correlations were observed between model predictions and experimental data (r > 0.8 and p < 0.0005 for all comparisons). FE predictions showed low deviations (root-mean-square (RMS) error) from average experimental data under all modes of static and quasi-static loading, falling within 2.5 deg of tibiofemoral rotation, 1% of anterior cruciate ligament (ACL) and medial collateral ligament (MCL) strains, 17 N of ACL load, and 1 mm of tibiofemoral center of pressure. Similarly, the FE model was able to accurately predict tibiofemoral kinematics and ACL and MCL strains during simulated bipedal landings (dynamic loading). In addition to minimal deviation from direct cadaveric measurements, all model predictions fell within 95% confidence intervals of the average experimental data. Agreement between model predictions and experimental data demonstrates the ability of the developed model to predict the kinematics of the human knee joint as well as the complex, nonuniform stress and strain fields that occur in biological soft tissue. Such a model will facilitate the in-depth understanding of a multitude of potential knee injury mechanisms with special emphasis on ACL injury.

In vivo assessment of weight-bearing knee flexion reveals compartment-specific alterations in meniscal slope

PURPOSE

The purpose of this study was to determine the effects of flexion angle on meniscal slope during partial weight-bearing knee flexion.

METHODS

Forty-eight sagittal sequences were performed on 12 patients (6 male patients, 6 female patients; 25.7 ± 10.5 years) during partial weight bearing in an open magnetic resonance imaging (MRI) scanner at full extension, 60°, 90°, and maximum knee flexion. A previously published method was used to measure the meniscal slope for each compartment using manual digitalization. A general linear model was used to test for effects of compartment and flexion angle on meniscal slope.

RESULTS

The mean maximum flexion angle achieved was 125° ± 10.5°. A significant main effect of compartment (P < .01) and flexion angle (P < .01) on meniscal slope was observed. A significant interaction between compartment and angle was also detected (P < .01). Specifically, the lateral meniscal slope was significantly more horizontal than the medial meniscus slope at full extension (P = .017) but significantly more posterior at all other angles. In addition, the lateral meniscus displayed a greater change in posterior slope across the range of motion compared with the medial meniscus. Significant correlations were found in medial meniscal slope at full extension and at maximum knee flexion (P = .031).

CONCLUSIONS

The results showed that meniscal slope in healthy knees increased significantly with knee flexion for both menisci, with significantly greater changes in the lateral meniscus. Furthermore, a lack of correlation was observed between the meniscal slope in extension and the meniscal slope at increasing flexion angles, questioning the efficacy of measuring the meniscal slope only in extension as commonly described. Overall, this study has provided valuable insight into how meniscal slope changes with knee motion.

Internal pressure of human meniscal root attachments during loading

This study investigated the internal fluid pressure of human cadaver meniscal root attachments. A pressure micro-sensor was implanted inside each attachment site. Tibiofemoral joints were compressed to 2× body weight at various flexion angles and pressure recorded for 20 min. The anterior cruciate ligament (ACL) was then transected and joints retested. Lastly, a longitudinal incision of the lateral posterior (LP) horn was made and the joint retested. Ramp pressure was defined as the pressure when 2× body weight was reached, and equilibrium pressure was recorded at the end of the hold period. The medial posterior (MP) attachment was subjected to greater ramp pressure than the medial anterior (p = 0.002) and greater equilibrium pressure than all other root attachment sites (p < 0.001). Flexion angle had a significant effect on pressure as full extension was greatest at ramp (p = 0.040). Transection of the ACL decreased ramp pressure in the LP attachment (p = 0.025) and increased equilibrium pressure (p = 0.031) in the MP attachment. The results suggest that repair strategies should be developed which reconstruct the MP attachments to be sufficient to withstand large pressures. Furthermore, since meniscal pressure is highest at full extension, this fact should be considered when prescribing rehabilitation following repair of an attachment.

Using Design of Experiments Methods for Assessing Peak Contact Pressure to Material Properties of Soft Tissue in Human Knee

Contact pressure in the knee joint is a key element in the mechanisms of knee pain and osteoarthritis. Assessing the contact pressure in tibiofemoral joint is a challenging mechanical problem due to uncertainty in material properties. In this study, a sensitivity analysis of tibiofemoral peak contact pressure to the material properties of the soft tissue was carried out through fractional factorial and Box-Behnken designs. The cartilage was modeled as linear elastic material, and in addition to its elastic modulus, interaction effects of soft tissue material properties were added compared to previous research. The results indicated that elastic modulus of the cartilage is the most effective factor. Interaction effects of axial/radial modulus with elastic modulus of cartilage, circumferential and axial/radial moduli of meniscus were other influential factors. Furthermore this study showed how design of experiment methods can help designers to reduce the number of finite element analyses and to better interpret the results.

Risk factors for meniscal tears: a systematic review including meta-analysis

STUDY DESIGN

Systematic review with meta-analysis.

OBJECTIVES

To review and critically appraise the literature for factors that increase the risk for meniscal tears.

BACKGROUND

Meniscal tears are an important cause of disability and time lost from work, and are associated with a 4-fold increase in the long-term risk of knee osteoarthritis. Knowledge of the risk factors that lead to meniscal tears can help to correctly diagnose knee injuries and is important to the development of prevention strategies for knee osteoarthritis.

METHODS

A search of the Cochrane Database of Systematic Reviews, MEDLINE, and Embase, from 1950 to January 2012, and a hand search of reference lists of all initially selected studies, without restriction on language or date of publication, were conducted. Prospective, retrospective, and case-control studies that included individuals over 16 years of age, who had no previous meniscal injuries or surgeries, were selected. A meta-analysis for 17 risk factors was performed. Where considerable heterogeneity among studies was present or the data did not provide sufficient information to perform a meta-analysis, a qualitative synthesis was conducted.

RESULTS

Eleven studies, with a total of 7358 participants, were selected for systematic review. Data were available for meta-analysis for 10 of the 11 studies. Qualitative analysis was conducted using data from 3 of the 11 studies. Results showed strong evidence that age (older than 60 years), gender (male), work-related kneeling and squatting, and climbing stairs (greater than 30 flights) were risk factors for degenerative meniscal tears. We also found strong evidence that playing soccer and playing rugby were strong risk factors for acute meniscal tears. Waiting longer than 12 months between the anterior cruciate ligament injury and reconstructive surgery was a strong risk factor for a medial meniscal tear but not for a lateral meniscal tear.

CONCLUSION

The literature indicates a number of risk factors leading to either degenerative or acute meniscal tears, with some of these factors being potentially modifiable.

LEVEL OF EVIDENCE

Prognosis, level 2a.

From meniscus to bone: a quantitative evaluation of structure and function of the human meniscal attachments

Meniscus efficacy at promoting joint congruity and preventing osteoarthritis hinges on enthesis integrity. Gross-scale tensile testing, histomorphometry and magnetic resonance imaging reveal significant differences between the four attachments, implying that each must endure a unique mechanical environment, which dictates their structure. However, little data exists to elucidate how these interfaces have adapted to their complex loading environment, particularly on a relevant scale, as the enthesis transitions through several unique zones in less than a millimeter. In our study we leveraged nanoindentation to determine viscoelastic material properties through the transition zones. Additionally, we employed histological techniques to evaluate the enthesis structure, including collagen organization and interdigitation morphometry. Mechanical evaluation revealed the medial posterior insertion site to be significantly more compliant than others. Collagen fiber orientation and dispersion as well as interdigitation morphometry were significantly different between attachments sites. These findings are clinically relevant as a disproportionate amount of enthesis failure occurs in the medial posterior attachment. Also, meniscal enthesis structure and function will need to be considered in future reparative and replacement strategies in order to recreate native meniscus mechanics and prevent osteoarthritis propagation.

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.

Recent advances in computational mechanics of the human knee joint

Computational mechanics has been advanced in every area of orthopedic biomechanics. The objective of this paper is to provide a general review of the computational models used in the analysis of the mechanical function of the knee joint in different loading and pathological conditions. Major review articles published in related areas are summarized first. The constitutive models for soft tissues of the knee are briefly discussed to facilitate understanding the joint modeling. A detailed review of the tibiofemoral joint models is presented thereafter. The geometry reconstruction procedures as well as some critical issues in finite element modeling are also discussed. Computational modeling can be a reliable and effective method for the study of mechanical behavior of the knee joint, if the model is constructed correctly. Single-phase material models have been used to predict the instantaneous load response for the healthy knees and repaired joints, such as total and partial meniscectomies, ACL and PCL reconstructions, and joint replacements. Recently, poromechanical models accounting for fluid pressurization in soft tissues have been proposed to study the viscoelastic response of the healthy and impaired knee joints. While the constitutive modeling has been considerably advanced at the tissue level, many challenges still exist in applying a good material model to three-dimensional joint simulations. A complete model validation at the joint level seems impossible presently, because only simple data can be obtained experimentally. Therefore, model validation may be concentrated on the constitutive laws using multiple mechanical tests of the tissues. Extensive model verifications at the joint level are still crucial for the accuracy of the modeling.

Subject-specific analysis of joint contact mechanics: application to the study of osteoarthritis and surgical planning

Advances in computational mechanics, constitutive modeling, and techniques for subject-specific modeling have opened the door to patient-specific simulation of the relationships between joint mechanics and osteoarthritis (OA), as well as patient-specific preoperative planning. This article reviews the application of computational biomechanics to the simulation of joint contact mechanics as relevant to the study of OA. This review begins with background regarding OA and the mechanical causes of OA in the context of simulations of joint mechanics. The broad range of technical considerations in creating validated subject-specific whole joint models is discussed. The types of computational models available for the study of joint mechanics are reviewed. The types of constitutive models that are available for articular cartilage are reviewed, with special attention to choosing an appropriate constitutive model for the application at hand. Issues related to model generation are discussed, including acquisition of model geometry from volumetric image data and specific considerations for acquisition of computed tomography and magnetic resonance imaging data. Approaches to model validation are reviewed. The areas of parametric analysis, factorial design, and probabilistic analysis are reviewed in the context of simulations of joint contact mechanics. Following the review of technical considerations, the article details insights that have been obtained from computational models of joint mechanics for normal joints; patient populations; the study of specific aspects of joint mechanics relevant to OA, such as congruency and instability; and preoperative planning. Finally, future directions for research and application are summarized.

The Effect of Ligament Modeling Technique on Knee Joint Kinematics: A Finite Element Study

Finite element (FE) analysis has become an increasingly popular technique in the study of human joint biomechanics, as it allows for detailed analysis of the joint/tissue behavior under complex, clinically relevant loading conditions. A wide variety of modeling techniques have been utilized to model knee joint ligaments. However, the effect of a selected constitutive model to simulate the ligaments on knee kinematics remains unclear. The purpose of the current study was to determine the effect of two most common techniques utilized to model knee ligaments on joint kinematics under functional loading conditions. We hypothesized that anatomic representations of the knee ligaments with anisotropic hyperelastic properties will result in more realistic kinematics. A previously developed, extensively validated anatomic FE model of the knee developed from a healthy, young female athlete was used. FE models with 3D anatomic and simplified uniaxial representations of main knee ligaments were used to simulate four functional loading conditions. Model predictions of tibiofemoral joint kinematics were compared to experimental measures. Results demonstrated the ability of the anatomic representation of the knee ligaments (3D geometry along with anisotropic hyperelastic material) in more physiologic prediction of the human knee motion with strong correlation (r ≥ 0.9 for all comparisons) and minimum deviation (0.9º ≤ RMSE ≤ 2.29°) from experimental findings. In contrast, non-physiologic uniaxial elastic representation of the ligaments resulted in lower correlations (r ≤ 0.6 for all comparisons) and substantially higher deviation (2.6° ≤ RMSE ≤ 4.2°) from experimental results. Findings of the current study support our hypothesis and highlight the critical role of soft tissue modeling technique on the resultant FE predicted joint kinematics.

A computational modeling approach for investigating soft tissue balancing in bicruciate retaining knee arthroplasty

Bicruciate retaining knee arthroplasty, although has shown improved functions and patient satisfaction compared to other designs of total knee replacement, remains a technically demanding option for treating severe cases of arthritic knees. One of the main challenges in bicruciate retaining arthroplasty is proper balancing of the soft tissue during the surgery. In this study biomechanics of soft tissue balancing was investigated using a validated computational model of the knee joint with high fidelity definitions of the soft tissue structures along with a Taguchi method for design of experiments. The model was used to simulate intraoperative balancing of soft tissue structures following the combinations suggested by an orthogonal array design. The results were used to quantify the corresponding effects on the laxity of the joint under anterior-posterior, internal-external, and varus-valgus loads. These effects were ranked for each ligament bundle to identify the components of laxity which were most sensitive to the corresponding surgical modifications. The resulting map of sensitivity for all the ligament bundles determined the components of laxity most suitable for examination during intraoperative balancing of the soft tissue. Ultimately, a sequence for intraoperative soft tissue balancing was suggested for a bicruciate retaining knee arthroplasty.

Forces acting on the anterior meniscotibial ligaments

PURPOSE

The purpose of this study was to investigate the forces occurring in human anterior meniscotibial attachment structures under various loading conditions.

METHODS

Twelve human knee joints were exposed to eight loading conditions (tibial rotations and varus/valgus stress) using a previously described knee joint simulator. Subsequently, the joints were axially compressed (1,000 N at 0° 30° and 60° knee flexion) using a materials testing machine. Then, we performed a tensile test to failure of the ligaments. Finally, we used the strains that occurred during the loading tests and the force-elongation diagrams obtained from the tensile test to recursively assess the resulting forces.

RESULTS

In the anterior meniscotibial ligaments, we found maximum mean strains of 3.8 ± 2.3% under external moments and 1.5 ± 0.9% for axial compression. With an ultimate load of 454 ± 220 N for the anterolateral meniscotibial ligament and 397 ± 275 N for the anteromedial meniscotibial ligament, we estimated maximum forces of up to 50.2 N for the knee simulator tests and 22.6 N for the axial compression tests.

CONCLUSIONS

The low forces found in the meniscal ligaments suggest that for normal daily activities, meniscal replacement implants and allografts do not require a very rigid fixation at their bony insertions. However, it remains unknown, what level of force occurs in the meniscotibial ligaments under traumatic situations or impact knee loads. Furthermore, the results of the present study could help to optimize meniscal re-fixation and to improve the properties of meniscal replacement materials, such as tissue-engineered artificial menisci. Moreover, the results could be used for the validation of finite element models of the knee joint with the main focus on the meniscus and its biomechanical relevance for tibiofemoral contact pressure.

[Anterior meniscotibial ligaments. Forces under various load conditions]

The main biomechanical function of the knee meniscus is to enlarge the contact area of the tibiofemoral joint leading to a reduction in articular cartilage contact stress. The meniscal attachments are essential for converting the axial load into circumferential tension in the meniscal periphery. Consequently, meniscal substitutes need sufficient anchorage to the tibial plateau to adequately restore the biomechanical function of a replaced meniscus. Therefore the aim of the present study was to investigate the loads acting on the anterior meniscotibial attachments under various joint loads.

Impact of measurement errors on the determination of the linear modulus of human meniscal attachments

For the development of meniscal substitutes and related finite element models it is necessary to know the mechanical properties of the meniscus and its attachments. Measurement errors can falsify the determination of material properties. Therefore the impact of metrological and geometrical measurement errors on the determination of the linear modulus of human meniscal attachments was investigated. After total differentiation the error of the force (+0.10%), attachment deformation (-0.16%), and fibre length (+0.11%) measurements almost annulled each other. The error of the cross-sectional area determination ranged from 0.00%, gathered from histological slides, up to 14.22%, obtained from digital calliper measurements. Hence, total measurement error ranged from +0.05% to -14.17%, predominantly affected by the cross-sectional area determination error. Further investigations revealed that the entire cross-section was significantly larger compared to the load-carrying collagen fibre area. This overestimation of the cross-section area led to an underestimation of the linear modulus of up to -36.7%. Additionally, the cross-sections of the collagen-fibre area of the attachments significantly varied up to +90% along their longitudinal axis. The resultant ratio between the collagen fibre area and the histologically determined cross-sectional area ranged between 0.61 for the posterolateral and 0.69 for the posteromedial ligament. The linear modulus of human meniscal attachments can be significantly underestimated due to the use of different methods and locations of cross-sectional area determination. Hence, it is suggested to assess the load carrying collagen fibre area histologically, or, alternatively, to use the correction factors proposed in this study.

Reconsideration on the use of elastic models to predict the instantaneous load response of the knee joint

Fluid pressurization in articular cartilages and menisci plays an important role in the mechanical function of the knee joint. However, fluid pressure has not been incorporated in previous finite element modelling of the knee, instead elastic models of the knee are widely used. It is believed that an elastic model can be used to predict the instantaneous load response of the knee as long as large effective moduli for the cartilaginous tissues are used. In the present study, the instantaneous response of the knee was obtained from a proposed model including fluid pressure and fibril reinforcement in the cartilaginous tissues. The results were then compared with those obtained from an elastic model using the effective modulus method. It was found that the deformations and contact pressures predicted by the two models were substantially different. An unconfined compression of a tissue disc was used to help understand the issue. It was clear that a full equivalence between the instantaneous and elastic responses could not be established even for this simple case. A partial equivalence in stress could be conditionally established for a given unconfined compression, but it was not valid for a different magnitude of compression. The instantaneous deformation of the intact tissues in the joint was even more difficult to determine using the effective modulus method. The results thus obtained were further compromised because of the uncertainty over the choice of effective modulus. The tissue non-linearity was one of the factors that made it difficult to establish the equivalence in stress. The pressurized tissue behaved differently from a solid material when non-linear fibril reinforcement was presented. The direct prediction of the instantaneous response using the proposed poromechanical model had the advantage of determining the fluid pressure and incompressible deformation.

Contact forces in several TKA designs during squatting: A numerical sensitivity analysis

Total knee arthroplasty (TKA) is a very successful procedure, but pain or difficulties during activities still persist in patients. Patient outcomes in TKA surgery can be affected by implant design, alignment or patient-related anatomical factors. This paper presents a numerical sensitivity analysis of several TKA types: a fixed bearing, posterior stabilized prosthesis, a high flexion fixed bearing guided motion prosthesis, a mobile bearing prosthesis and a hinge prosthesis. Each prosthesis was virtually implanted on the same cadaver leg model and it underwent a loaded squat, in 10s, between 0° and 120°, similar to several previous experimental tests performed on knee kinematics simulators. The aim of this examination was to investigate the sensitivity of the patello-femoral (PF) and tibio-femoral (TF) contact forces to patient-related anatomical factors, and component position in the different implant types. The following parameters were used for the sensitivity study: the proximo-distal patellar position, the patellar component tilting, the tibial component position and orientation, the locations of the medial and lateral collateral ligaments with respect to femur and tibia and the patellar tendon length. The sensitivity analysis showed that PF contact forces are mostly affected by patella height (increases up to 67% for one TKA type in patella-alta configuration), by an anterior tibial component translation (increases up to 30%), and by patellar component tilting (increases up to 29%); TF contact forces are mostly affected by the anterior displacement of the insertion points of the medial collateral ligament with respect to the reference position (increases up to 48%).

Regional and zonal histo-morphological characteristics of the lapine menisci

The menisci have crucial weight-bearing roles in the knee. Regional variations in structure and cellularity of the meniscus have only been minimally investigated. Therefore, the goal of this study was to illustrate the regional cell density, tissue area, and structure of healthy lapine menisci. Skeletally mature Flemish Giant rabbits were used for this study. Upon sacrifice, menisci were removed, fixed in formalin, and cryosectioned. Histological analysis was performed for the detection of sulfated glycosaminoglycans (GAG), collagen Types I and II, cellular density, and tissue area. ANOVA and paired t tests were used for testing of statistical significance. Glycosaminoglycan coverage of the medial meniscus significantly varied between regions, with the anterior region demonstrating significantly more GAG coverage than the posterior region. Inter- and intra-meniscal comparisons revealed variations between zones, with trends that outer zones of the medial menisci had less GAG coverage. Collagen Types I and II had marked characteristics and varying degrees of coverage across regions. Tissue area varied between regions for both medial and lateral menisci. Cellular density was dependent on region in the lateral meniscus. This is the first study to illustrate regional and zonal variation in glycosaminoglycan coverage, size, and cellular density for healthy lapine meniscal tissue. This data provides baseline information for future investigations in meniscal injury models in rabbits.

The effect of connective tissue material uncertainties on knee joint mechanics under isolated loading conditions

Although variability in connective tissue parameters is widely reported and recognized, systematic examination of the effect of such parametric uncertainties on predictions derived from a full anatomical joint model is lacking. As such, a sensitivity analysis was performed to consider the behavior of a three-dimensional, non-linear, finite element knee model with connective tissue material parameters that varied within a given interval. The model included the coupled mechanics of the tibio-femoral and patello-femoral degrees of freedom. Seven primary connective tissues modeled as non-linear continua, articular cartilages described by a linear elastic model, and menisci modeled as transverse isotropic elastic materials were included. In this study, a multi-factorial global sensitivity analysis is proposed, which can detect the contribution of influential material parameters while maintaining the potential effect of parametric interactions. To illustrate the effect of material uncertainties on model predictions, exemplar loading conditions reported in a number of isolated experimental paradigms were used. Our findings illustrated that the inclusion of material uncertainties in a coupled tibio-femoral and patello-femoral model reveals biomechanical interactions that otherwise would remain unknown. For example, our analysis revealed that the effect of anterior cruciate ligament parameter variations on the patello-femoral kinematic and kinetic response sensitivities was significantly larger, over a range of flexion angles, when compared to variations associated with material parameters of tissues intrinsic to the patello-femoral joint. We argue that the systematic sensitivity framework presented herein will help identify key material uncertainties that merit further research and provide insight on those uncertainties that may not be as relative to a given response.

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.