Time evolution of deformation in a human cartilage under cyclic loading

Recent imaging has revealed that in vivo contact deformations of human knee cartilage under physiological loadings are surprisingly large—typically on the order of 10%, but up to 20 or 30% of tibiofemora cartilage thickness depending on loading conditions. In this paper we develop a biphasic, large deformation, non-linear poroelastic model of cartilage that can accurately represent the time dependence and magnitude of cyclic cartilage deformations in vivo. The model takes into account cartilage tension–compression nonlinearity and a new constitutive relation in which the compressive stiffness and hydraulic permeability of the cartilage adjusts in response to the strain-dependent aggrecan concentration. The model predictions are validated using experimental test results on osteochondral plugs obtained from human cadavers. We find that model parameters can be optimised to give an excellent fit to the experimental data. Using typical hydraulic conductivity and stiffness parameters for healthy cartilage, we find that the experimentally observed transient and steady state tissue deformations under cyclic loading and unloading can be reproduced by the model. Steady state tissue deformations are shown to cycle between 10% (exudation strain) and 20% (total strain) in response to the cyclic test loads. At steady-state cyclic loading, the pore fluid exuded from the tissue is exactly equal to the pore fluid imbibed by the tissue during each load cycle

Osteoporotic bone fracture healing under the locking compression plate system

Abstract Osteoporosis is highly prevalent and a costly disease predicted to affect 1,555 million worldwide by 2050, and the total cost of osteoporotic fractures worldwide could reach US$131 billion by 2025. These statistics clearly affirm the significant economic burden of osteoporotic fractures to the community, and the need for the development of improved fracture treatments. Studies over the last decade reveal that, even though osteoporosis may not necessarily lead to non-union, it is associated with delayed fracture healing due to impaired mecho-regulation and angiogenesis in osteoporotic condition. Despite the advances in locking compression plate (LCP) technology, the operative treatment in osteoporotic fractures remains a challenge for an orthopaedic surgeon, often with unpredictable outcomes. Therefore, it becomes necessary to bridge the 'information gap' between osteoporosis and its effect on fracture healing, and so enables healing progression prediction under different fracture geometries and fixation configurations. By using a computational model of fracture healing, this paper demonstrates that fracture healing can be significantly delayed due to impaired mechano-regulation as a result of osteoporosis, and the impact of osteoporosis on fracture healing can be mitigated by adjusting the configuration of the LCP system to allow a certain degree of interfragmentary movement (IFM) without compromising overall fixation stability

Computational modelling of the mechanical environment of the early stage of fracture healing using structural engineering techniques

Bone healing is a complex biological process which is regulated by mechanical micro-environment caused by inter-fragmentary movement (IFM). IFM generated interstitial fluid flow within the fracture callus could potentially not only affect the mesenchymal stem cells migration and differentiation during the healing, but also enhance nutrient transport within the callus tissue. In this study, a three dimensional poroelastic finite element model of a human tibia was developed to study the mechanical behaviour of the fracture callus due to IFM at the early stage of fracture. The biophysical stimuli were characterised with three main parameters involved in the healing process: octahedral shear strain, interstitial fluid velocity and pressure. The proposed algorithm represents a first step towards to the development of a powerful simulation tool for fracture healing

The spatio-temporal mechanical environment of healthy and injured human cartilage during sustained activity and its role in cartilage damage

Recently we presented a computational model of articular cartilage calibrated for normal human tissue explants. This model was able to capture the transient deformation of cartilage experiencing a cyclic load. The model takes into account the tension-compression nonlinearity of the cartilage and incorporates the dependency of the compressive stiffness and fluid permeability of cartilage on the deformation-dependent aggrecan concentration in cartilage tissue. As such it represents a leading constitutive model of articular cartilage. Here we build on the previous study to develop an experimentally validated computational model to simulate mechanical consolidation response of intact and previously injured cartilage under sustained static loading, to develop our understanding of the implications for rates of tissue damage. We see that the type of prior injuries compromise the cartilage function in different ways. Relatively rapid consolidation is predicted for cartilage with a complete meniscectomy and that with a full thickness defect, indicating the inability of cartilage with such injuries to sustain interstitial fluid pressurisation for long periods of time, as does uninjured cartilage. By comparing the consolidation response of articular cartilage predicted by computational model against experimental measurements of the apparent friction coefficient following static loading, we find a strong linear positive correlation exists between cartilage degree of consolidation (DoC) and friction coefficient at the joint. As the DoC of articular cartilages can be estimated in vivo via medical imaging, the DoC can be used as an index to non-invasively evaluate the apparent friction coefficient between opposing cartilage surfaces, and so estimate the likelihood of frictional surface wear and/or cartilage damag

Investigation of role of cartilage surface polymer brush border in lubrication of biological joints

Although experimental evidence has suggested that the polymer brush border (PBB) on the cartilage surface is important in regulating fluid permeability in the contact gap, the current theoretical understanding of joint lubrication is still limited. To address this research gap, a multiscale cartilage contact model that includes PBB, in particular its effect on the fluid permeability of the contact gap, is developed in this study. Microscale modeling is employed to estimate the permeability of the contact gap. This permeability is classified into two categories: For a gap size > 1 µm, the flow resistance is assumed to be dominated by the cartilage roughness; for gap size < 1 µm, flow resistance is assumed to be dominated by the surface polymers extending beyond the collagen network of the articular cartilage. For gap sizes of less than 1 µm, the gap permeability decreases exponentially with increasing aggrecan concentration, whereas the aggrecan concentration varies inversely with the gap size. Subsequently, the gap permeability is employed in a macroscale cartilage contact model, in which both the contact gap space and articular cartilage are modeled as two interacting poroelastic systems. The fluid exchange between these two media is achieved by imposing pressure and normal flux continuity boundary conditions. The model results suggest that PBB can substantially enhance cartilage lubrication by increasing the gap fluid load support (e.g., by 26 times after a 20-min indentation compared with the test model without a PBB). Additionally, the fluid flow resistance of PBB sustains the cartilage interstitial fluid pressure for a relatively long period, and hence reduces the vertical deformation of the tissue. Furthermore, it can be inferred that a reduction in the PBB thickness impairs cartilage lubrication ability

Computational study on synovial fluid flow behaviour in cartilage contact gap under osteoarthritic condition

This study numerically investigates the pathological changes of fluid flow in cartilage contact gap due to the changes in cartilage surface roughness and synovial fluid characteristics in osteoarthritic (OA) condition. First, cartilage surface topographies in both healthy and OA conditions are constructed using a numerical approach with consideration of both vertical and horizontal roughness. Then, constitutive equations for synovial fluid viscosity are obtained through calibration against previous experimental data. Finally, the roughness and synovial fluid information are input into the gap flow model to predict the gap permeability. The results show that the rougher surface of OA cartilage tends to decrease gap permeability by around 30%–60%. More importantly, with the reduction in gap size, the decrease in gap permeability becomes more significant, which could result in an early fluid ultrafiltration into the tissue. Moreover, it is demonstrated that the pathological synovial fluid has more deleterious effects on the gap permeability than the OA cartilage surface, as it could potentially increase the gap permeability by a few hundred times for pressure gradients less than 106 Pa/m, which could inhibit the fluid ultrafiltration into the tissue. The outcomes from this research indicate that the change in fluid flow behaviour in contact gap in OA condition could significantly affect the function of articular joints

A coupled contact model of cartilage lubrication in the mixed-mode regime under static compression

This study presents a coupled cartilage contact model, in which the contact gap and cartilage tissue are modelled as two poroelastic systems, linked by pressure and normal flux continuity boundary conditions. Using a tibial plug under indentation as a proof-of-concept model, the predictions support the weeping lubrication theory under static compression. Specifically, the interstitial fluid would exude from the underlying cartilage into the contact gap to extend the mixed-mode duration by > 20-fold compared to a no fluid exudation counterpart. Moreover, the traditional contact model, that does not consider the contact gap and cartilage fluid exchange, potentially overestimates the interstitial fluid pressure compared to the proposed coupled model. Parametric studies suggest that the increasing viscosity of synovial fluid prolongs the gap fluid pressurisation, while increasing the asperity stiffness reduces the gap fluid pressure but increases contact gap height

A probabilistic failure risk approach to the problem of articular cartilage lubrication

Background and Objective The geometrical and mechanical properties that characterise the cartilage contact gap are uncertain and spatially varied. To date the effects of such uncertainties on cartilage lubrication have not been explored. Using a probabilistic approach, the purpose of this study is to numerically investigate the influence of surficial cartilage glycoaminoglycan (GAG) content on joint lubrication behaviour. Gap asperity stiffness and polymer brush border (PBB) thickness are affected by the uncertainty of surficial GAG concentration, and so their correlated effects in maintaining hydrodynamic joint lubrication are investigated. Methods Correlated sampling data are first generated by Monte Carlo simulation. These data are used as inputs for the cartilage contact model, which includes three distinctive features of cartilage tissue (tension-compression nonlinearity, aggrecan dependent permeability and compressive modulus) and fluid flow resistance effects of PBB on cartilage surface. The degree of hydrodynamic lubrication after thirty minutes of constant loading is used as an indicator for assessing the lubrication performance at the contact interface. Results The increase of PBB thickness with GAG concentration enhances the hydrodynamic lubrication component in the cartilage contact gap, whereas increasing the asperity stiffness with GAG concentration impairs hydrodynamic lubrication. GAG loss rate increases with the rise of GAG concentration. More aggrecan shedding through the surface could result in a thicker and denser PBB, and therefore enhance the lubrication performance in mixed-mode regime. On the other hand, higher GAG content makes the asperities stiffer, which may impede contact gap closure, and thus encourage gap fluid loss and impair the lubrication performance of cartilage. Conclusion The lubrication performance of cartilage varies with the physiological conditions of the joint. Since a range of variables are internally related, the outcomes on joint lubrication are difficult to predict. A probabilistic approach accounting for the uncertainties can potentially result in more accurate evaluations of joint lubrication performance

Life-cycle modelling of concrete cracking and reinforcement corrosion in concrete bridges: A case study

The development of effective life cycle management strategies for transport infrastructure assets is of importance for meeting the defined public policies and levels of service. In the last decades, much progress has been made in assessing the life-cycle performance of bridges using reliability-based approaches. However, the goal of developing a comprehensive life-cycle performance assessment framework for bridges has not been fully achieved. This is due to the uncertainties surrounding model parameters as well as the correlation between these parameters (e.g. the complex correlation between the reinforcement corrosion and the concrete cracking). It becomes more challenging due to the limited access to bridge inspection data by bridge research communities resulting from confidentiality issues. Using a typical highway concrete bridge as a case study, the present study systematically investigated the impact of concrete crack induced reinforcement corrosion on the serviceability of concrete bridges by developing an engineering reliability-based approach involving an auto-regressive crack propagation model and a steel corrosion prediction model. The model parameters were calibrated using the eight-year inspection data of an operating bridge. The influence of different external environments in the reinforcement corrosion, ultimately the residual life of the bridges, was also investigated through conducting a series of parametric studies. Based on the collected bridge inspection data, the model results predict that, although the surface crack of a RC bridge is repairable through periodic maintenance, the corrosion of the steel bars in the bridge still continues over time with a corrosion rate which depends on different maintenance intervention cycle periods (Tcycle). For example, reducing Tcycle from 12 years to 4 years could potentially prolong the service life of the bridge by around 15 years. The developed model could assist bridge managers to estimate the optimal Tcycle to prolong the service life of bridges

The investigation of fluid flow in cartilage contact gap

Synovial fluid flow in articular joint capsule plays an important role during mixed mode lubrication. However, the actual fluid flow behaviour during cartilage contact has not been fully understood so far. This is due to the difficulties in measuring the gap permeability using conventional experimental techniques. The problem becomes further complicated with consideration of the cartilage surface roughness. Here a validated numerical study was developed to quantify the gap permeability of lateral synovial fluid flow. Both macro- and micro-scale gap flow models were created based on Darcy's law at the macro-scale and the Navier-stokes equation at the micro-scale. To generate model inputs, the cartilage topography was numerically synthesised based on the experimental measurements of bovine medial tibia cartilage surface roughness using Dektak Stylus Profilers. The experimental results show that the average roughness height Ra is 1.97 μm and root-mean-square roughness height Rq is 2.44 μm, while the correlation lengths of the secondary and tertiary undulations are round 100 μm and 20 μm, respectively. The numerical results indicate that the contact gap height and fluid pressure gradient are two critical parameters which significantly affect the gap permeability. As the contact gap closes, there is a decrease in gap permeability, and most importantly, the gap permeability is also very sensitive to the fluid pressure gradient. Furthermore, with gap closure, the permeability of the contact gap gradually approaches that of the cartilage tissue, at which point the contact gap is functional closed. This occurs at a contact gap height around 1 μm and fluid pressure gradient below 5 × 105 Pa/m in this study