Computational modelling of articular joints with biphasic cartilage: recent advances, challenges and opportunities.

Biphasic models have been widely used to simulate the time-dependent biomechanical response of soft tissues. Modelling techniques of joints with biphasic weight-bearing soft tissues have been markedly improved over the last decade, enhancing our understanding of the function, degenerative mechanism and outcomes of interventions of joints. This paper reviews the recent advances, challenges and opportunities in computational models of joints with biphasic weight-bearing soft tissues. The review begins with an introduction of the function and degeneration of joints from a biomechanical aspect. Different constitutive models of articular cartilage, in particular biphasic materials, are illustrated in the context of the study of contact mechanics in joints. Approaches, advances and major findings of biphasic models of the hip and knee are presented, followed by a discussion of the challenges awaiting to be addressed, including the convergence issue, high computational cost and inadequate validation. Finally, opportunities and clinical insights in the areas of subject-specific modeling and tissue engineering are provided and discussed.

A computational approach to determine key anatomic landmarks on pelvis and its application to acetabular orientation assessment and hip computational biomechanics.

The determination of anatomic landmarks on the pelvis is an important procedure in orthopaedics, computational biomechanics and morphometrics. This study aimed to develop a robust method for determining the anatomic landmarks on the pelvis and demonstrate the application of the method in assessing the native acetabular orientation and developing multiscale computational modelling for hip biomechanics. Two Matlab algorithms, named "Pelvisor" and "Acetabulor", were developed to determine four anatomic landmarks on the pelvis and assess the acetabular orientation in the natural hip. The algorithms were then applied to: (1) assess the native acetabular orientations for a cohort of subjects; (2) develop a multiscale computational modelling to investigate the biomechanical behaviour of the biphasic cartilage in the natural hip joint. Results showed that the present method can accurately determine the key anatomic landmarks on the pelvis and assess the acetabular orientation in the natural hip joint. Significant differences in acetabular inclination and anteversion between males and females were identified, with larger orientations in females. The interstitial fluid pressure in the cartilage supported over 90% of loading during gait, and the stresses and strains within the solid matrix of the cartilage were as low as 1.8 MPa and 0.12, respectively.

Multiscale modelling for investigating the long-term time-dependent biphasic behaviour of the articular cartilage in the natural hip joint.

A better understanding of the time-dependent biomechanical behaviour of the biphasic hip articular cartilage (AC) under physiological loadings is important to understand the onset of joint pathology and guide the clinical treatment. Current computational studies for the biphasic hip AC were usually limited to short-term duration or using elaborate loading. The present study aimed to develop a multiscale computational modelling to investigate the long-term biphasic behaviour of the hip AC under physiological loadings over multiple gait cycles. Two-scale computational modelling including a musculoskeletal model and a finite element model of the natural hip was created. These two models were then combined and used to investigate the biphasic behaviour of hip AC over 80 gait cycles. The results showed that the interstitial fluid pressure in the AC supported over 89% of the loading during gait. When the contact area was located at the AC centre, the contact pressure and fluid pressure increased over time from the first cycle to the 80th cycle, while when the contact area approached the edge, these pressures decreased first dramatically and then slowly over time. The peak stresses and strains in the solid matrix of the AC remained at a low level and increased over time from the first cycle to the 80th cycle. This study demonstrated that the long-term temporal variations of the biphasic behaviour of hip AC under physiological loadings are significant. The methodology has potentially important implications in the biomechanical studies of human cartilage and supporting the development of cartilage substitution.

Multiscale biomechanics of the biphasic articular cartilage in the natural hip joint during routine activities.

BACKGROUND AND OBJECTIVE: The investigation of the biomechanical behaviour of the articular cartilage (AC) under physiological loading is important to understand the joint function and onset of pathologies. This study aimed to develop a multiscale computational modelling approach and apply the approach to investigate the time-dependant biphasic behaviour of the AC in the natural hip joint under repetitive physiological loading over 80 cycles amongst six routine activities. METHODS: A subject-specific musculoskeletal multibody dynamics (MBD) model was developed based on the anthropometry and motion capture data collected for a male subject. A corresponding FE model of the natural hip joint with biphasic AC was created based on the bone geometries exported from the MBD model. A multiscale computational modelling was then developed to couple the MBD model and the FE model and used to investigate the time-dependant biphasic behaviour of the AC under subject-specific physiological loading over 80 cycles amongst six routine activities. RESULTS: The results showed that for all the activities considered, the interstitial fluid pressure in the AC supported over 80% of the loading. The maximum values of the peak contact pressure and peak fluid pressure for the whole cycle increased firstly and then remained stable over time from the 1st cycle to the 80th cycle. At these instants, the contact areas were located at the centre region of the AC. By contrast, when the contact area was located at the edge of the AC, these peak pressures were found to increase over time for some of the activities (squat, ascending stairs, descending stairs) but decrease for the other activities (normal walking, standing up, sitting down). CONCLUSION: This study for the first time developed a multiscale computational modelling approach to couple a musculoskeletal MBD model of the body and a detailed FE model of the natural hip joint with biphasic AC, which enabled the evaluation of time-dependant biphasic behaviour of the AC under realistic physiological loading conditions. The study may have important implications in biomechanical studies of human cartilage to understand the joint function and biomechanical factors related to joint disease, and to support the development of cartilage substitution.

Comparison of Kinematics and Contact Mechanics in Normal Knee and Total Knee Replacements: A Computational Investigation.

An objective of total knee replacement (TKR) is to restore the mechanical function of a normal knee. Joint kinematics and contact mechanics performance are two of the primary indices that indicate the success of TKR devices. The aim of this study was to compare the kinematics and contact mechanics of TKR and normal knee joints. An experimentally evaluated finite-element (FE) knee model was developed and used to investigate the performance of four TKR designs (fixed cruciate-retaining (CR), mobile CR, posterior-stabilized (PS), medial pivot design (MP)) and the normal knee joint during a gait cycle. The predicted kinematic results showed that the MP design presented similar kinematics to those of the normal knee joint and did not demonstrate paradoxical motion of the femur. A considerably larger contact area and lower contact pressure were found on the normal knee joint (1315 mm2, and 14.8 MPa, respectively) than on the TKRs, which was consistent with the previous in-vivo fluoroscopic investigation. The mobile CR and PS designs exhibited the smallest and greatest contact pressures of the four TKR designs, respectively. The results of the present study help to understand the kinematics and contact mechanics in the TKR during the gait cycle, and provide comprehensive information about the performance of the normal knee joint.

Development of a finite element musculoskeletal model with the ability to predict contractions of three-dimensional muscles.

Representation of realistic muscle geometries is needed for systematic biomechanical simulation of musculoskeletal systems. Most of the previous musculoskeletal models are based on multibody dynamics simulation with muscles simplified as one-dimensional (1D) line-segments without accounting for the large muscle attachment areas, spatial fibre alignment within muscles and contact and wrapping between muscles and surrounding tissues. In previous musculoskeletal models with three-dimensional (3D) muscles, contractions of muscles were among the inputs rather than calculated, which hampers the predictive capability of these models. To address these issues, a finite element musculoskeletal model with the ability to predict contractions of 3D muscles was developed. Muscles with realistic 3D geometry, spatial muscle fibre alignment and muscle-muscle and muscle-bone interactions were accounted for. Active contractile stresses of the 3D muscles were determined through an efficient optimization approach based on the measured kinematics of the lower extremity and ground force during gait. This model also provided stresses and strains of muscles and contact mechanics of the muscle-muscle and muscle-bone interactions. The total contact force of the knee predicted by the model corresponded well to the in vivo measurement. Contact and wrapping between muscles and surrounding tissues were evident, demonstrating the need to consider 3D contact models of muscles. This modelling framework serves as the methodological basis for developing musculoskeletal modelling systems in finite element method incorporating 3D deformable contact models of muscles, joints, ligaments and bones.

The contact mechanics and occurrence of edge loading in modular metal-on-polyethylene total hip replacement during daily activities.

The occurrence of edge loading in hip joint replacement has been associated with many factors such as prosthetic design, component malposition and activities of daily living. The present study aimed to quantify the occurrence of edge loading/contact at the articulating surface and to evaluate the effect of cup angles and edge loading on the contact mechanics of a modular metal-on-polyethylene (MoP) total hip replacement (THR) during different daily activities. A three-dimensional finite element model was developed based on a modular MoP bearing system. Different cup inclination and anteversion angles were modelled and six daily activities were considered. The results showed that edge loading was predicted during normal walking, ascending and descending stairs activities under steep cup inclination conditions (≥55°) while no edge loading was observed during standing up, sitting down and knee bending activities. The duration of edge loading increased with increased cup inclination angles and was affected by the cup anteversion angles. Edge loading caused elevated contact pressure at the articulating surface and substantially increased equivalent plastic strain of the polyethylene liner. The present study suggested that correct positioning the component to avoid edge loading that may occur during daily activities is important for MoP THR in clinical practice.

The influence of the representation of collagen fibre organisation on the cartilage contact mechanics of the hip joint.

The aim of this study was to develop a finite element (FE) hip model with subject-specific geometry and biphasic cartilage properties. Different levels of detail in the representation of fibre reinforcement were considered to evaluate the feasibility to simplify the complex depth-dependent fibre pattern in the native hip joint. A FE model of a cadaveric hip with subject-specific geometry was constructed through micro-computed-tomography (µCT) imaging. The cartilage was assumed to be biphasic and fibre-reinforced with different levels of detail in the fibre representation. Simulations were performed for heel-strike, mid-stance and toe-off during walking and one-leg-stance over 1500s. It was found that the required level of detail in fibre representation depends on the parameter of interest. The contact stress of the native hip joint could be realistically predicted by simplifying the fibre representation to being orthogonally reinforced across the whole thickness. To predict the fluid pressure, depth-dependent fibre organisation is needed but specific split-line pattern on the surface of cartilage is not necessary. Both depth-dependent and specific surface fibre orientations are required to simulate the strains.

The effect of cup outer sizes on the contact mechanics and cement fixation of cemented total hip replacements.

One important loosening mechanism of the cemented total hip arthroplasty is the mechanical overload at the bone-cement interface and consequent failure of the cement fixation. Clinical studies have revealed that the outer diameter of the acetabular component is a key factor in influencing aseptic loosening of the hip arthroplasty. The aim of the present study was to investigate the influence of the cup outer diameter on the contact mechanics and cement fixation of a cemented total hip replacement (THR) with different wear penetration depths and under different cup inclination angles using finite element (FE) method. A three-dimensional FE model was developed based on a typical Charnley hip prosthesis. Two acetabular cup designs with outer diameters of 40 and 43 mm were modelled and the effect of cup outer diameter, penetration depth and cup inclination angle on the contact mechanics and cement fixation stresses in the cemented THR were studied. The results showed that for all penetration depths and cup inclination angles considered, the contact mechanics in terms of peak von Mises stress in the acetabular cup and peak contact pressure at the bearing surface for the two cup designs were similar (within 5%). However, the peak von Mises stress, the peak maximum principal stress and peak shear stress in the cement mantle at the bone-cement interface for the 43 mm diameter cup design were predicted to be lower compared to those for the 40 mm diameter cup design. The differences were predicted to be 15-19%, 15-22% and 18-20% respectively for different cup penetration depths and inclination angles, which compares to the clinical difference of aseptic loosening incidence of about 20% between the two cup designs.

Geometric parameterisation of pelvic bone and cartilage in contact analysis of the natural hip: an initial study.

Parameterised finite element models of the human hip have the potential to allow controlled analysis of the effect of individual geometric features on the contact mechanics of the joint. However, the challenge lies in defining a set of parameters which sufficiently capture the joint geometry in order to distinguish between individuals. In this study, a simple set of parameters to describe the geometries of acetabulum and cartilage in the hip were extracted from two segmentation-based models, which were then used to generate the parameterised finite element models for the two subjects. The contact pressure and contact area at the articular surface predicted from the parameterised finite element models were compared with the results from the segmentation-based models. The differences in the predicted results between the parameterised models and segmentation-based models were found to be within 11% across seven activities simulated. In addition, the parameterised models were able to replicate features of the contact pressure/area fluctuations over the loading cycle that differed between the two subjects. These results provide confidence that the parameterised approach could be used to generate representative finite element models of the human hip for contact analysis. Such a method has the potential to be used to systematically evaluate geometric features that can be captured from simple clinical measurements and provide a cost- and time-effective approach for stratification of the acetabular geometries in the patient population.

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.

Influence of clearance on the time-dependent performance of the hip following hemiarthroplasty: a finite element study with biphasic acetabular cartilage properties.

Hip hemiarthroplasty is a common treatment for femoral neck fracture. However, the acetabular cartilage may degenerate after hemiarthroplasty leading to postoperative failure and the need for revision surgery. The clearance between the acetabular cartilage and head of the prosthesis is one of the potential reasons for this failure. In this study, the influence of joint clearance on the biomechanical function of a generic hip model in hemiarthroplasty was investigated using biphasic numerical simulation. Both a prolonged loading period of 4000 s and dynamic gait load of 10 cycles were considered. It was found that a larger clearance led to a higher stress level, a faster reduction in load supported by the fluid and a faster cartilage consolidation process. Additionally, the mechanical performance of the acetabular cartilage in the natural model was similar to that in the hemiarthroplasty model with no clearance but different from the hemiarthroplasty models with clearances of 0.5mm and larger. The results demonstrated that a larger clearance in hip hemiarthroplasty is more harmful to the acetabular cartilage and prosthesis heads with more available dimensions (i.e. smaller increments in diameter) could be manufactured for surgeons to achieve a lower clearance, and reduced contact stress in hemiarthroplasty surgeries.

Contact mechanics of modular metal-on-polyethylene total hip replacement under adverse edge loading conditions.

Edge loading can negatively impact the biomechanics and long-term performance of hip replacements. Although edge loading has been widely investigated for hard-on-hard articulations, limited work has been conducted for hard-on-soft combinations. The aim of the present study was to investigate edge loading and its effect on the contact mechanics of a modular metal-on-polyethylene (MoP) total hip replacement (THR). A three-dimensional finite element model was developed based on a modular MoP bearing. Different cup inclination angles and head lateral microseparation were modelled and their effect on the contact mechanics of the modular MoP hip replacement were examined. The results showed that lateral microseparation caused loading of the head on the rim of the cup, which produced substantial increases in the maximum von Mises stress in the polyethylene liner and the maximum contact pressure on both the articulating surface and backside surface of the liner. Plastic deformation of the liner was observed under both standard conditions and microseparation conditions, however, the maximum equivalent plastic strain in the liner under microseparation conditions of 2000 µm was predicted to be approximately six times that under standard conditions. The study has indicated that correct positioning the components to avoid edge loading is likely to be important clinically even for hard-on-soft bearings for THR.

Experimental validation of finite element modelling of a modular metal-on-polyethylene total hip replacement.

Finite element models are becoming increasingly useful tools to conduct parametric analysis, design optimisation and pre-clinical testing for hip joint replacements. However, the verification of the finite element model is critically important. The purposes of this study were to develop a three-dimensional anatomic finite element model for a modular metal-on-polyethylene total hip replacement for predicting its contact mechanics and to conduct experimental validation for a simple finite element model which was simplified from the anatomic finite element model. An anatomic modular metal-on-polyethylene total hip replacement model (anatomic model) was first developed and then simplified with reasonable accuracy to a simple modular total hip replacement model (simplified model) for validation. The contact areas on the articulating surface of three polyethylene liners of modular metal-on-polyethylene total hip replacement bearings with different clearances were measured experimentally in the Leeds ProSim hip joint simulator under a series of loading conditions and different cup inclination angles. The contact areas predicted from the simplified model were then compared with that measured experimentally under the same conditions. The results showed that the simplification made for the anatomic model did not change the predictions of contact mechanics of the modular metal-on-polyethylene total hip replacement substantially (less than 12% for contact stresses and contact areas). Good agreements of contact areas between the finite element predictions from the simplified model and experimental measurements were obtained, with maximum difference of 14% across all conditions considered. This indicated that the simplification and assumptions made in the anatomic model were reasonable and the finite element predictions from the simplified model were valid.

The effect of cup inclination and wear on the contact mechanics and cement fixation for ultra high molecular weight polyethylene total hip replacements.

The present study aimed to investigate individual and combined influences of the cup inclination and wear on the contact mechanics and fixation of a Charnley hip replacement using finite element method. The effects of cup inclination and penetration on the contact mechanics of articulating bearings as well as the stress within the cement and at the bone-cement interface were examined. The maximum contact pressure and the von Mises stress on the cup were reduced by ~30% and ~20% respectively when even a small penetration occurred. However, no large differences were found between different cup penetration depths with regards to either the contact pressure or the von Mises stress. The von Mises stress at the bone-cement interface was predicted almost unaltered with an increased cup inclination angle to 55° for a cup penetration to 4mm. These predictions suggest that the contact mechanics and the cement stress are insensitive to the cup inclination and wear under these normal conditions investigated, therefore explaining the robustness of the Charnley hip implant. An increase in the cup inclination angle to 65°, coupled with a maximum penetration of 4mm, resulted in a large increase in the maximum von Mises stress at the bone-cement interface.