Biphasic Cartilage Layers Research Articles

Biphasic investigation of contact mechanics in natural human hips during activities.

The aim of this study was to determine the cartilage contact mechanics and the associated fluid pressurisation of the hip joint under eight daily activities, using a three-dimensional finite element hip model with biphasic cartilage layers and generic geometries. Loads with spatial and temporal variations were applied over time and the time-dependent performance of the hip cartilage during walking was also evaluated. It was found that the fluid support ratio was over 90% during the majority of the cycles for all the eight activities. A reduced fluid support ratio was observed for the time at which the contact region slid towards the interior edge of the acetabular cartilage, but these occurred when the absolute level of the peak contact stress was minimal. Over 10 cycles of gait, the peak contact stress and peak fluid pressure remained constant, but a faster process of fluid exudation was observed for the interior edge region of the acetabular cartilage. The results demonstrate the excellent function of the hip cartilage within which the solid matrix is prevented from high levels of stress during activities owing to the load shared by fluid pressurisation. The findings are important in gaining a better understanding of the hip function during daily activities, as well as the pathology of hip degeneration and potential for future interventions. They provide a basis for future subject-specific biphasic investigations of hip performance during activities.

The influence of size, clearance, cartilage properties, thickness and hemiarthroplasty on the contact mechanics of the hip joint with biphasic layers

Computational models of the natural hip joint are needed to examine and optimise tissue sparing interventions where the natural cartilage remains part of the bearing surfaces. Although the importance of interstitial fluid pressurisation in the performance of cartilage has long been recognized, few studies have investigated the time dependent interstitial fluid pressurisation in a three dimensional natural hip joint model. The primary aim of this study was to develop a finite element model of the natural hip incorporating the biphasic cartilage layers that was capable of simulating the joint response over a prolonged physiological loading period. An initial set of sensitivity studies were also undertaken to investigate the influence of hip size, clearance, cartilage properties, thickness and hemiarthroplasty on the contact mechanics of the joint. The contact stress, contact area, fluid pressure and fluid support ratio were calculated and cross-compared between models with different parameters to evaluate their influence. It was found that the model predictions for the period soon after loading were sensitive to the hip size, clearance, cartilage aggregate modulus, thickness and hemiarthroplasty, while the time dependent behaviour over 3000s was influenced by the hip clearance and cartilage aggregate modulus, permeability, thickness and hemiarthroplasty. The modelling methods developed in this study provide a basic platform for biphasic simulation of the whole hip joint onto which more sophisticated material models or other input parameters could be added in the future.

Contact problem for a thin elastic layer with variable thickness: Application to sensitivity analysis of articular contact mechanics

In the framework of the recently developed asymptotic models for tibio-femoral contact incorporating frictionless elliptical contact interaction between thin elastic, viscoelastic, or biphasic cartilage layers, we apply an asymptotic modeling approach for analytical evaluating the sensitivity of crucial parameters in joint contact mechanics due to small variations in the thicknesses of the contacting cartilage layers. The four term asymptotic expansion for the normal displacement at the contact surface is explicitly derived, which recovers the corresponding solution obtained previously for the 2D case in the compressible case. It was found that to minimize the influence of the cartilage thickness non-uniformity on the force–displacement relationship, the effective thicknesses of articular layers should be determined from a special optimization criterion.

Mathematical modeling of linear viscoelastic impact: Application to drop impact testing of articular cartilage

In recent years, a number of experimental studies have been conducted to investigate the mechanical behavior and damage mechanisms of articular cartilage under impact loading. Some experimentally observed results have been explained using a non-linear viscoelastic impact model. At the same time, there is the need of simple mathematical models, which allow comparing experimental results obtained in drop impact testing with impact loads of different weights and incident velocities. The objective of this study was to investigate theoretically whether the main features of articular impact could be qualitatively predicted using a linear viscoelastic theory or the linear biphasic theory. Based on the short-time asymptotic solution of the contact problem for a thin biphasic layer [Ateshian GA, Lai WM, Zhu WB, Mow VC. An asymptotic solution for the contact of two biphasic cartilage layers. Journal of Biomechanics 1994;27(11):1347–1360.], an asymptotic model for blunt impact of articular cartilage is developed, which is mathematically equivalent to the Maxwell impact model. In the present paper, exact analytical solutions are obtained for the main parameters of the Kelvin–Voigt and Maxwell impact models. Perturbation analysis of the impact process according to the standard viscoelastic solid model is performed. Asymptotic solutions are obtained for the drop weight impact test. The dependence of the coefficient of restitution on the impactor parameters has been studied in detail.

Development of an asymptotic modeling methodology for tibio-femoral contact in multibody dynamic simulations of the human knee joint

A new methodology for modeling articular tibio-femoral contact based on the recently developed asymptotic model of frictionless elliptical contact interaction between thin biphasic cartilage layers is presented. The developed mathematical model of articular contact is extended to the case of contact between arbitrary viscoelastic incompressible coating layers. The approach requires use of the smooth contact surface geometry and efficient contact points detection methods. A generalization of the influence surface theory based method for representing articular surfaces from the unstructured noisy surface data is proposed. The normal contact forces are determined analytically based on the exact solution for elliptical contact between thin cartilage layers modeled as viscoelastic incompressible layers. The effective geometrical characteristics of articular surfaces are introduced for use in the developed asymptotic models of elliptical contact between articular surfaces.

Frictionless elliptical contact of thin viscoelastic layers bonded to rigid substrates

A three-dimensional unilateral contact problem for thin viscoelastic layers bonded to rigid substrates shaped like elliptic paraboloids is considered. Two cases are studied: (a) Poisson’s ratios of the layer materials are not very close to 0.5 and (b) the layer materials are incompressible with Poisson’s ratio of 0.5. Poisson’s ratios are assumed to be time independent. In the present paper we derive the general solutions to the problems of elliptical contact between thin compressible or incompressible layers of arbitrary viscoelastic materials. The approach is based on the analytical method developed by the authors for the elliptical contact of thin biphasic cartilage layers. The obtained analytical solution is valid for monotonically increasing loading conditions.

A general solution of the axisymmetric contact problem for biphasic cartilage layers

A unilateral axisymmetric contact problem for articular cartilage layers is considered. The articular cartilages bonded to subchondral bones are modeled as biphasic materials consisting of a solid phase and a fluid phase. It is assumed that the subchondral bones are rigid and shaped like bodies of revolution with arbitrary convex profiles. The obtained closed-form analytical solution is valid over time periods compared with the typical diffusion time and can be used for increasing loading.

Elliptical contact of thin biphasic cartilage layers: Exact solution for monotonic loading

A three-dimensional unilateral contact problem for articular cartilage layers is considered in the framework of the biphasic cartilage model. The articular cartilages bonded to subchondral bones are modeled as biphasic materials consisting of a solid phase and a fluid phase. It is assumed that the subchondral bones are rigid and shaped like elliptic paraboloids. The obtained analytical solution is valid for monotonically increasing loading conditions.

Functional adaptation of human joints to mechanical stimuli

Objective This study tests the hypothesis that functional adaptation occurs in human joints, and that substantial differences in joint ‘loading history’ explain the phenotypic variability observed in human cartilage morphology.Method We examined 18 triathletes (nine men and nine women) who had been physically active throughout life (training for >10h per week for the last 3 years), and 18 volunteers that had never been physically active on a regular basis. The right knee joints were imaged with a previously validated fat-suppressed gradient-echo MR sequence. Cartilage volume, thickness, joint surface areas, and normalized cartilage signal intensity were determined with post-processing software, specifically designed for these applications.ResultsThe knee joint cartilage thickness, and signal intensity were not significantly different between athletes and inactive volunteers, but male athletes displayed significantly larger knee joint surfaces (P< 0.01; +8.8%). Female athletes displayed a significantly larger medial tibia (P< 0.05; +18.9%), the difference in the total knee surface area reaching borderline significance (P=0.08; +7.0%).ConclusionsThe results suggest that joint size can be modulated during growth, but that (opposite to muscle and bone) the thickness of the cartilage does not adapt to mechanical stimulation. This finding may reveal a general principle in the development and functional adaptation of diarthrodial joints, elucidating an important mechanism for reducing mechanical stress in biphasic cartilage layers.

A note on an asymptotic solution for the contact of two biphasic cartilage layers in a loaded synovial joint at rest

Retaining the first terms of asymptotic expansions and assuming zero gradient of the contact pressure at the contact edge in the perpendicular direction to the edge, Ateshian et al. (1994, J. Biomechanics 27, 1347–1360; 1992, Adv. Bioeng. ASME 22, 191–194) have presented an asymptotic axially symmetric and plane strain solutions to the contact problems of the two thin biphasic cartilage layers in the synovial joint (with the synovial fluid film in between already depleted), subjected to a sudden normal load. Both the immediate and an early time response to a step loading have been analysed. The present note shows that the contact width thus obtained immediately after the load application differs from the numerical values for a dry frictionless contact of incompressible single-phase elastic layers available in the literature. The difference increases with the decreasing contact width-to-layer thickness ratio. It is proposed to improve the above solutions by releasing zero pressure gradient condition at the contact edge and calculating the instantaneous contact widths from the equations proposed for the corresponding case by Matthewson (1981, J. Mech. Phys. Solids 29, 89–113) and Meijers (1967, Appl. Sci. Res. 18, 353–383) that approximate better the numerical values. The instantaneous rate of change in the contact width is then obtained for a step load varying in time.

Contact Creep of Biphasic Cartilage Layers

Integral transform methods are used to solve the contact creep problem between two identical cylindrical biphasic cartilage layers bonded to rigid impermeable subchondral bone substrates. The biphasic model employed for cartilage consists of a binary mixture of an incompressible porous-permeable solid phase and an incompressible fluid phase. Solutions are obtained as a function of time, from the instantaneous to the equilibrium responses of the tissue. A significant result of this analysis is that under application of a step load, fluid pressurization may support upward of 96 percent of the total applied load for more congruent joints, shielding the solid collagen-proteoglycan matrix of the tissue from excessive stresses during physiological loading durations. The protection imparted by interstitial fluid pressurization to the solid collagen-proteoglycan matrix of cartilage is investigated, and the influence of material properties and osteoarthritic changes on the potential loss of this protective effect is discussed.

Articular joint mechanics with biphasic cartilage layers under dynamic loading.

The composition and amount of extracellular matrix produced by chondrocytes are thought to be influenced by the stress and strain states in the vicinity of the chondrocytes. During daily activities, such as walking and running, articular joints are loaded dynamically. In the present study, a solution is proposed to simulate the responses of a joint under dynamic loading. In order to show the characteristics of the proposed solution, numerical simulations were carried out, in which the contact radius, the relative approach displacement between the centers of the contacting bodies, or the contact force were controlled. As a result of the history-dependent material properties of the articular cartilage, the predicted parameters changed nonperiodically, when the controlled parameters varied periodically. For a constant load, the contact radius and the relative displacement between the contacting bodies were predicted to increase at decreasing rates. When the contact force was varied dynamically, the predicted mean values of the contact radius, the relative displacement between the contacting bodies, and the contact pressure at the center of the contact area depended on the amplitude and the duration of the loading. When the relative displacement between the contacting bodies was controlled, the amplitudes and the cycling frequency must be limited to avoid a loss of contact between the articular joint surfaces. The proposed solution is valid for a long but limited time period, the exact extent of which is yet to be determined. It can be used to simulate the effects associated with cartilage degeneration in diseases such as osteoarthritis.

Evaluation of the finite element software ABAQUS for biomechanical modelling of biphasic tissues

The biphasic cartilage model proposed by Mow et al. (1980)has proven successful to capture the essential mechanical features of articular cartilage. In order to analyse the joint contact mechanics in real, anatomical joints, the cartilage model needs to be implemented into a suitable finite element code to approximate the irregular surface geometries of such joints. However, systematic and extensive evaluation of the capacity of commercial software for modelling the contact mechanics with biphasic cartilage layers has not been made. This research was aimed at evaluating the commercial finite element software ABAQUS for analysing biphasic soft tissues. The solutions obtained using ABAQUS were compared with those obtained using other finite element models and analytical solutions for three numerical tests: an unconfined indentation test, a test with the contact of a spherical cartilage surface with a rigid plate, and an axi-symmetric joint contact test. It was concluded that the biphasic cartilage model can be implemented into the commercial finite element software ABAQUS to analyse practical joint contact problems with biphasic articular cartilage layers.

An improved solution for the contact of two biphasic cartilage layers

The purpose of this study was to present a solution for the contact of two biphasic cartilage layers which can be used for dynamic loading, is not restricted to predictions over small time periods, and predicts biologically meaningful changes in contact areas over time. The proposed solution was based on the work of Ateshian et al. (1994, J. Biomechanics 27, 1347–1360) who retained the first term of an asymptotic expansion and used an approximate integration which is valid for short time periods. The solution proposed here uses an exact integration, is valid over long time periods, and can be used for increasing loading. The new solution corrects a limitation of the work by Ateshian et al., which manifests itself immediately (i.e. at time t = 0 ±s): the rate of change in the contact radius (and therefore, the contact area) is increasing in Ateshian et al.'s solution for a constant force, whereas it is decreasing in the new solution. An increasing rate of change in the contact radius suggests that the contact radius (area) is unbounded, and a steady-state solution cannot be reached, which is physically not correct for the contact of two joint surfaces. In the new solution, the contact radius reaches a steady-state value given sufficient time.

Modeling axi-symmetrical joint contact with biphasic cartilage layers—An asymptotic solution

The articular contact surfaces in human and animal joints are highly variable. Articular cartilage thickness and the material properties of the cartilage vary as a function of location in the joint and may also change in the pathologic state. In order to study practical joint contact problems, we extended the model for the contact of two biphasic cartilage layers proposed by Ateshian et al. [ J. Biomechanics 27, 1347–1360 (1994)] by combining the assumption of the kinetic relationship from classical contact mechanics with the joint contact model for biphasic articular cartilage. In order to illustrate the characteristics of the proposed model, the contact problem was solved numerically for different curvatures of the contact surfaces, and for different thicknesses and material properties of the cartilage layers. Each cartilage layer was assumed to have constant thickness within the contact region. The contact radius, the relative displacement between the contacting bodies, contact pressure, and the stress distributions within the cartilage layers were calculated by applying a step load for a time period of 200 s. The contact radius was found to be sensitive to the change in thickness of the cartilage, and was not very sensitive to the change in the material property of the cartilage. The peak effective stress and the maximal shear stress were predicted to occur at the cartilage-bone interface for all simulated cases, which is in agreement with other theoretical research and supports the experimental findings in the literature on the origins of cartilage damage. For articular cartilage layers of different thicknesses, the stresses in the thick layer were found to be higher than those in the thin layer. Compared to other models of joint contact, the present model offers more possibilities for investigating practical applications, such as simulating the effects associated with cartilage degeneration in diseases such as osteoarthritis, and comparing theoretical predictions with experimental measurements of pressure distribution and contact area in joints.

An asymptotic solution for the contact of two biphasic cartilage layers

This study addresses the hypothesis that interstitial fluid plays a major role in the load support mechanism of articular cartilage. An asymptotic solution is presented for two contacting biphasic cartilage layers under compression. This solution is valid for identical thin (i.e. ε= h′ a′ 0 ⪡ 1 ), frictionless cartilage layers, and for the ‘early’ time response (i.e. t′⪡ (h′) 2 H Ak ) after the application of a step load. An equilibrium asymptotic solution is also presented (i.e. t′→∞). Here h′ is the thickness, a′ 0 is a characteristic contact radius, H A is the aggregate modulus and k is the permeability of the cartilage layer. A main conclusion from this analysis is that the fluid phase of cartilage plays a major role in providing load support during the first 100–200 s after contact loading. Further, the largest component of stress in cartilage is the hydrostatic pressure developed in the interstitial fluid. For tissue fluid volume fraction (porosity) in the range 0.6≤ Φ f≤0.8, k = O(10 −15 m 4/Ns) and H A=O(1 MPa), the peak magnitude of the principal effective (or elastic) stress may be as low as 14% of the peak hydrostatic pressure within the tissue, or the contact stress at the surface. In effect, the interstitial fluid shields the solid matrix from high normal stresses and strains. The asymptotic solution also shows that pressure-sensitive film measurements of intra-articular contact stress do not measure the elastic stress at the surface, but they rather provide a measure of the interstitial fluid pressure. Finally, this analysis provides strong support for the hypothesis that, if sudden loading causes shear failure within the cartilage-bone layer structure, this failure would take place at the cartilage-bone interface, and the plane of failure would be either parallel or perpendicular to this interface.