Biphasic finite element contact analysis of the knee joint using an augmented Lagrangian method

Study on the poroelastic behaviors of the defected articular cartilage

This article presented the possible mechanism of arthritis damaged changes in cartilage's interstitial fluid flowing behavior. Firstly, the analytical solutions for the pore fluid pressure and velocity in the idealized cartilage defect model were obtained, which are employed to validate the finite element (FE) method. Then according to the MRI data, an articular cartilage FE model was developed to study the effects of defect characteristics on its poroelastic behaviors. The results showed the interstitial fluid pressure and velocity in defected articular cartilage is diminished, moreover, this trend is even more severe as the defect radius or thickness increased. As the development of osteoarthritis goes, the fluid velocity is decreased and cause the even serious nutrients loss.

The effect of distance between holes on the structural stability of subchondral bone in microfracture surgery: a finite element model study

Background

Microfracture is a surgical technique that involves creating multiple holes of 3–4 mm depth in the subchondral bone to recruit stem cells in the bone marrow to the lesion, inducing fibrocartilage repair and knee cartilage regeneration. Recently, it has been reported that increasing the exposed area of the lower cartilaginous bone (drilling a lot of holes) increases the outflow of stem cells, which is expected to affect the physical properties of the subchondral bone when the exposed area is large. The purpose of this study was to analyse the effect of the distance between the holes in the microfracture procedure on the structural stability of the osteochondral bone using a finite element method.

Methods

In this study, lateral aspects of the femoral knee, which were removed during total knee arthroplasty were photographed using microtomography. The model was implemented using a solitary walks program, which is a three-dimensional simplified geometric representation based on the basic microtomography data. A microfracture model was created by drilling 4 mm-deep holes at 1, 1.5, 2, 2.5, 3, 4, and 5 mm intervals in a simplified three-dimensional (3D) geometric femoral model. The structural stability of these models was analysed with the ABAQUS program. We compared the finite element model (FEM) based on the microtomography image and the simplified geometric finite element model.

Results

Von Mises stress of the subchondral bone plate barely increased, even when the distance between holes was set to 1 mm. Altering the distance between the holes had little impact on the structural stability of the subchondral bone plate. Safety factors were all below 1.

Conclusions

Although we did not confirm an optimal distance between holes, this study does provide reference data and an epidemiological basis for determining the optimal distance between the holes used in the microfracture procedure.

The Scaffold-Articular Cartilage Interface: A Combined In Vitro and In Silico Analysis Under Controlled Loading Conditions

The optimal method to integrate scaffolds with articular cartilage has not yet been identified, in part because of our lack of understanding about the mechanobiological conditions at the interface. Our objective was to quantify the effect of mechanical loading on integration between a scaffold and articular cartilage. We hypothesized that increased number of loading cycles would have a detrimental effect on interface integrity. The following models were developed: (i) an in vitro scaffold-cartilage explant system in which compressive sinusoidal loading cycles were applied for 14 days at 1 Hz, 5 days per week, for either 900, 1800, 3600, or 7200 cycles per day and (ii) an in silico inhomogeneous, biphasic finite element model (bFEM) of the scaffold-cartilage construct that was used to characterize interface micromotion, stress, and fluid flow under the prescribed loading conditions. In accordance with our hypothesis, mechanical loading significantly decreased scaffold-cartilage interface strength compared to unloaded controls regardless of the number of loading cycles. The decrease in interfacial strength can be attributed to abrupt changes in vertical displacement, fluid pressure, and compressive stresses along the interface, which reach steady-state after only 150 cycles of loading. The interfacial mechanical conditions are further complicated by the mismatch between the homogeneous properties of the scaffold and the depth-dependent properties of the articular cartilage. Finally, we suggest that mechanical conditions at the interface can be more readily modulated by increasing pre-incubation time before the load is applied, as opposed to varying the number of loading cycles.

Biomechanical Stimulus Based Strategies for Meniscus Tissue Engineering and Regeneration

Meniscus injuries are very common in the knee joint. Treating a damaged meniscus continues to be a scientific challenge in sport medicine because of its poor self-healing potential and few clinical therapeutic options. Tissue engineering strategies are very promising solutions for repairing and regenerating a damaged meniscus. Meniscus is exposed to a complex biomechanical microenvironment, and it plays a crucial role in meniscal development, growth, and repairing. Over the past decades, increasing attention has been focused on the use of biomechanical stimulus to enhance biomechanical properties of the engineered meniscus. Further understanding the influence of mechanical stimulation on cell proliferation and differentiation, metabolism, relevant gene expression, and pro/anti-inflammatory responses may be beneficial to enhance meniscal repair and regeneration. On the one hand, this review describes some basic information about meniscus; on the other hand, we sum up the various biomechanical stimulus based strategies applied in meniscus tissue engineering and how these factors affect meniscal regeneration. We hope this review will provide researchers with inspiration on tissue engineering strategies for meniscus regeneration in the future.

Tissue material properties and computational modelling of the human tibiofemoral joint: a critical review

Understanding how structural and functional alterations of individual tissues impact on whole-joint function is challenging, particularly in humans where direct invasive experimentation is difficult. Finite element (FE) computational models produce quantitative predictions of the mechanical and physiological behaviour of multiple tissues simultaneously, thereby providing a means to study changes that occur through healthy ageing and disease such as osteoarthritis (OA). As a result, significant research investment has been placed in developing such models of the human knee. Previous work has highlighted that model predictions are highly sensitive to the various inputs used to build them, particularly the mathematical definition of material properties of biological tissues. The goal of this systematic review is two-fold. First, we provide a comprehensive summation and evaluation of existing linear elastic material property data for human tibiofemoral joint tissues, tabulating numerical values as a reference resource for future studies. Second, we review efforts to model tibiofemoral joint mechanical behaviour through FE modelling with particular focus on how studies have sourced tissue material properties. The last decade has seen a renaissance in material testing fuelled by development of a variety of new engineering techniques that allow the mechanical behaviour of both soft and hard tissues to be characterised at a spectrum of scales from nano- to bulk tissue level. As a result, there now exists an extremely broad range of published values for human tibiofemoral joint tissues. However, our systematic review highlights gaps and ambiguities that mean quantitative understanding of how tissue material properties alter with age and OA is limited. It is therefore currently challenging to construct FE models of the knee that are truly representative of a specific age or disease-state. Consequently, recent tibiofemoral joint FE models have been highly generic in terms of material properties even relying on non-human data from multiple species. We highlight this by critically evaluating current ability to quantitatively compare and model (1) young and old and (2) healthy and OA human tibiofemoral joints. We suggest that future research into both healthy and diseased knee function will benefit greatly from a subject- or cohort-specific approach in which FE models are constructed using material properties, medical imagery and loading data from cohorts with consistent demographics and/or disease states.

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.

Shape of chondrocytes within articular cartilage affects the solid but not the fluid microenvironment under unconfined compression

Metabolic activity of the chondrocytes in articular cartilage is strongly related to their zone-specific shape and the composition and mechanical properties of their surrounding extracellular matrix (ECM). However the mechanisms by which cell shape influences the response of the ECM microenvironment to mechanical loading is yet to be elucidated. This relationship was studied using a biphasic multiscale finite element model of different shaped chondrocytes in the superficial and deep zones of the ECM during unconfined stress relaxation. For chondrocytes in the superficial zone, increasing the cell's initial aspect ratio (length/height) increased the deformation and solid stresses of the chondrocyte and pericellular matrix (PCM) during the loading phase; for chondrocytes in the deep zone the effect of the cell shape on the solid microenvironment was time and variable dependent. However, for superficial and deep zone chondrocytes the cell shape did not affect the fluid pressure and fluid shear stress. These results suggest that mechanotransduction of chondrocytes in articular cartilage may be regulated through the solid phase rather than the fluid phase, and that high stresses and deformations in the solid microenvironment in the superficial zone may be essential for the zone-specific biosynthetic activity of the chondrocyte. The biphasic multiscale computational analysis suggests that maintaining the cell shape is critical for regulating the microenvironment and metabolic activity of the chondrocyte in tissue engineering constructs.

STATEMENT OF SIGNIFICANCE

We investigated the effect of chondrocyte shape on the cellular microenvironment using a biphasic multiscale finite element analysis. Our study showed that cell shapes affects the solid but not the fluid microenvironment of the chondrocyte, and that maintaining the cell shape is critical for regulating the microenvironment and metabolic activity of the chondrocyte in native cartilage and tissue engineering constructs. As far as we know, this is the first study on the mechanotransduction mechanisms by which cell shape influences the response of the microenvironment to mechanical loading. This study is important for understanding cell mechanobiology, not only for regulation of cell phenotype in tissue engineered constructs but, as important, for understanding changes in normal chondrocyte function after post-traumatic injury and in the initiation and progression of osteoarthritis.

Focal cartilage defect compromises fluid-pressure dependent load support in the knee joint

A focal cartilage defect involves tissue loss or rupture. Altered mechanics in the affected joint may play an essential role in the onset and progression of osteoarthritis. The objective of the present study was to determine the compromised load support in the human knee joint during defect progression from the cartilage surface to the cartilage-bone interface. Ten normal and defect cases were simulated with a previously tested 3D finite element model of the knee. The focal defects were considered in both condyles within high load-bearing regions. Fluid pressurization, anisotropic fibril-reinforcement, and depth-dependent mechanical properties were considered for the articular cartilages and menisci. The results showed that a small cartilage defect could cause 25% reduction in the load support of the knee joint due to a reduced capacity of fluid pressurization in the defect cartilage. A partial-thickness defect could cause a fluid pressure decrease or increase in the remaining underlying cartilage depending on the defect depth. A cartilage defect also increased the shear strain at the cartilage-bone interface, which was more significant with a full-thickness defect. The effect of cartilage defect on the fluid pressurization also depended on the defect sites and contact conditions. In conclusion, a focal cartilage defect causes a fluid-pressure dependent load reallocation and a compromised load support in the joint, which depend on the defect depth, site, and contact condition.

Altered regional loading patterns on articular cartilage following meniscectomy are not fully restored by autograft meniscal transplantation

OBJECTIVE

To quantify the changes in regional dynamic loading patterns on tibial articular cartilage during simulated walking following medial meniscectomy and meniscal transplantation.

METHODS

Seven fresh frozen human cadaveric knees were tested under multidirectional loads mimicking the activity of walking, while the contact stresses on the tibial plateau were synchronously recorded using an electronic sensor. Each knee was tested for three conditions: intact meniscus, medial meniscectomy, and meniscal transplantation. The loading profiles at different locations were assessed and common loading patterns were identified at different sites of the tibial plateau using an established numerical algorithm.

RESULTS

Three regional patterns were found on the tibial plateau of intact knees. Following medial meniscectomy, the area of the first pattern which was located at the posterior aspect of the medial plateau was significantly reduced, while the magnitude of peak load was significantly increased by 120%. The second pattern which was located at the central-posterior aspects of the lateral plateau shifted anteriorly and laterally without changing its magnitude. The third pattern in the cartilage-to-cartilage contact region of the medial plateau was absent following meniscectomy. Meniscal transplantation largely restored the first pattern, but it did not restore the other two patterns.

CONCLUSION

There are site-dependent changes in regional loading patterns on both the medial and lateral tibial plateau following medial meniscectomy. Even when a meniscal autograft is used where the geometry and material properties are kept constant, the only region in which the loading pattern is restored is at posterior aspect of the medial plateau.

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.

Using a statistically calibrated biphasic finite element model of the human knee joint to identify robust designs for a meniscal substitute

This paper describes a methodology for selecting a set of biomechanical engineering design variables to optimize the performance of an engineered meniscal substitute when implanted in a population of subjects whose characteristics can be specified stochastically. For the meniscal design problem where engineering variables include aspects of meniscal geometry and meniscal material properties, this method shows that meniscal designs having simultaneously large radial modulus and large circumferential modulus provide both low mean peak contact stress and small variability in peak contact stress when used in the specified subject population. The method also shows that the mean peak contact stress is relatively insensitive to meniscal permeability, so the permeability used in the manufacture of a meniscal substitute can be selected on the basis of manufacturing ease or cost. This is a multiple objective problem with the mean peak contact stress over the population of subjects and its variability both desired to be small. The problem is solved by using a predictor of the mean peak contact stress across the tibial plateau that was developed from experimentally measured peak contact stresses from two modalities. The first experimental modality provided computed peak contact stresses using a finite element computational simulator of the dynamic tibial contact stress during axial dynamic loading. A small number of meniscal designs with specified subject environmental inputs were selected to make computational runs and to provide training data for the predictor developed below. The second experimental modality consisted of measured peak contact stress from a set of cadaver knees. The cadaver measurements were used to bias-correct and calibrate the simulator output. Because the finite element simulator is expensive to evaluate, a rapidly computable (calibrated) Kriging predictor was used to explore extensively the contact stresses for a wide range of meniscal engineering inputs and subject variables. The predicted values were used to determine the Pareto optimal set of engineering inputs to minimize peak contact stresses in the targeted population of subjects.

A biphasic finite element study on the role of the articular cartilage superficial zone in confined compression

The aim of this study was to investigate the role of the superficial zone on the mechanical behavior of articular cartilage. Confined compression of articular cartilage was modeled using a biphasic finite element analysis to calculate the one-dimensional deformation of the extracellular matrix (ECM) and movement of the interstitial fluid through the ECM and articular surface. The articular cartilage was modeled as an inhomogeneous, nonlinear hyperelastic biphasic material with depth and strain-dependent material properties. Two loading conditions were simulated, one where the superficial zone was loaded with a porous platen (normal test) and the other where the deep zone was loaded with the porous platen (upside down test). Compressing the intact articular cartilage with 0.2 MPa stress reduced the surface permeability by 88%. Removing the superficial zone increased the rate of change for all mechanical parameters and decreased the fluid support ratio of the tissue, resulting in increased tissue deformation. Apparent permeability linearly increased after superficial removal in the normal test, yet it did not change in the upside down test. Orientation of the specimen affected the time-dependent biomechanical behavior of the articular cartilage, but not equilibrium behavior. The two tests with different specimen orientations resulted in very different apparent permeabilities, suggesting that in an experimental study which quantifies material properties of an inhomogeneous material, the specimen orientation should be stated along with the permeability result. The current study provides new insights into the role of the superficial zone on mechanical behavior of the articular cartilage.

A biphasic multiscale study of the mechanical microenvironment of chondrocytes within articular cartilage under unconfined compression

Computational analyses have been used to study the biomechanical microenvironment of the chondrocyte that cannot be assessed by in vitro experimental studies; yet all computational studies thus far have focused on the effect of zonal location (superficial, middle, and deep) on the mechanical microenvironment of chondrocytes. The aim of this paper was to study the effect of both zonal and radial locations on the biomechanical microenvironment of chondrocytes in inhomogeneous cartilage under unconfined stress relaxation. A biphasic multiscale approach was employed and nine chondrocytes in different locations were studied. Hyperelastic biphasic theory and depth-dependent aggregate modulus and permeability of articular cartilage were included in the models. It was found that both zonal and radial locations affected the biomechanical stresses and strains of the chondrocytes. Chondrocytes in the mid-radial location had increased volume during the early stage of the loading process. Maximum principal shear stress at the interface between the chondrocyte and the extracellular matrix (ECM) increased with depth, yet that at the ECM-pericellular matrix (PCM) interface had an inverse trend. Fluid pressure decreased with depth, while the fluid pressure difference between the top and bottom boundaries of the microscale model increased with depth. Regardless of location, fluid was exchanged between the chondrocyte, PCM, and ECM. These findings suggested that even under simple compressive loading conditions, the biomechanical microenvironment of the chondrocytes, PCM and ECM was spatially dependent. The current study provides new insight on chondrocyte biomechanics.

Should a native depth-dependent distribution of human meniscus constitutive components be considered in FEA-models of the knee joint?

The depth-dependent matrix composition of articular cartilage is important for its mechanical behavior. It is unknown whether the depth-dependent matrix composition of a meniscus is similarly important for its load-bearing function. The present objective was to determine whether it is necessary to account for the native distribution of matrix components in the cross-sectional plane of the meniscus, when studying its mechanical behavior in numerical models. To address this objective, measured depth-dependent distribution of matrix contents in the human meniscus, and fitted visco-elastic mechanical properties of the collagen were used as input in FEA simulations of a knee joint. The importance of including the depth-dependent matrix component constitution in the meniscus was determined by comparing simulations with an axisymmetric representation of the knee joint, which incorporated either the depth-dependent matrix composition or homogenized matrix. Depth-dependent differences in water, collagen and proteoglycan contents were observed, but these were not significantly different. The anterior region, with significantly higher collagen content, was statistically stiffer than the posterior region. However, depth wise, stiffness did not correlate to the constitution of the tissue. GAG content was significantly higher in the posterior than in the anterior region. Visco-elastic properties of meniscus collagen were fitted against tensile test data. Simulations show that the distribution of stresses and strains in the cartilage is slightly low when the meniscus contains a depth-dependent constitution, but this difference is only modest. Therefore, this study suggests that knee joint mechanics is rather insensitive to the distribution of constitutive components in the cross section of the meniscus, and that the depth-dependent matrix distribution of the meniscus is not essential to be included in axisymmetric computational models of the knee joint.

A finite element implementation for biphasic contact of hydrated porous media under finite deformation and sliding

The study of biphasic soft tissue contact is fundamental to understand the biomechanical behavior of human diarthrodial joints. However, to date, only few biphasic finite element contact analyses for three-dimensional physiological geometries under finite deformation have been developed. The objective of this article is to develop a hyperelastic biphasic contact implementation for finite deformation and sliding problem. An augmented Lagrangian method was used to enforce the continuity of contact traction and fluid pressure across the contact interface. The finite element implementation was based on a general purpose software, COMSOL Multiphysics. The accuracy of the implementation is verified using example problems, for which solutions are available by alternative analyses. The implementation was proven to be robust and able to handle finite deformation and sliding.