Biphasic Analysis of Cartilage Stresses in the Patellofemoral Joint

A novel knee joint model in FEBio with inhomogeneous fibril-reinforced biphasic cartilage simulating tissue mechanical responses during gait: data from the osteoarthritis initiative

We developed a novel knee joint model in FEBio to simulate walking. Knee cartilage was modeled using a fibril-reinforced biphasic (FRB) formulation with depth-wise collagen architecture and split-lines to account for cartilage structure. Under axial compression, the knee model with FRB cartilage yielded contact pressures, similar to reported experimental data. Furthermore, gait analysis with FRB cartilage simulated spatial and temporal trends in cartilage fluid pressures, stresses, and strains, comparable to those of a fibril-reinforced poroviscoelastic (FRPVE) material in Abaqus. This knee joint model in FEBio could be used for further studies of knee disorders using physiologically relevant loading.

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.

A Finite Element Algorithm for Large Deformation Biphasic Frictional Contact Between Porous-Permeable Hydrated Soft Tissues

The frictional response of porous and permeable hydrated biological tissues such as articular cartilage is significantly dependent on interstitial fluid pressurization. To model this response, it is common to represent such tissues as biphasic materials, consisting of a binary mixture of a porous solid matrix and an interstitial fluid. However, no computational algorithms currently exist in either commercial or open-source software that can model frictional contact between such materials. Therefore, this study formulates and implements a finite element algorithm for large deformation biphasic frictional contact in the open-source finite element software FEBio. This algorithm relies on a local form of a biphasic friction model that has been previously validated against experiments, and implements the model into our recently-developed surface-to-surface (STS) contact algorithm. Contact constraints, including those specific to pressurized porous media, are enforced with the penalty method regularized with an active-passive augmented Lagrangian scheme. Numerical difficulties specific to challenging finite deformation biphasic contact problems are overcome with novel smoothing schemes for fluid pressures and Lagrange multipliers. Implementation accuracy is verified against semi-analytical solutions for biphasic frictional contact, with extensive validation performed using canonical cartilage friction experiments from prior literature. Essential details of the formulation are provided in this paper, and the source code of this biphasic frictional contact algorithm is made available to the general public.

Guide to mechanical characterization of articular cartilage and hydrogel constructs based on a systematic in silico parameter sensitivity analysis

Osteoarthritis is a whole joint disease with cartilage degeneration being an important manifestation. Tissue engineering treatment is a solution for repairing cartilage defects by implantation of chondrocyte-laden hydrogel constructs within the defect. In silico models have recently been introduced to simulate and optimize the design of these constructs. These models require accurate knowledge on the mechanical properties of the hydrogel constructs and cartilage explants, which are challenging to obtain due to their anisotropic structure and time-dependent behaviour. We performed a systematic in silico parameter sensitivity analysis to find the most efficient unconfined compression testing protocols for mechanical characterization of hydrogel constructs and cartilage explants, with a minimum number of tests but maximum identifiability of the material parameters. The construct and explant were thereby modelled as porohyperelastic and fibril-reinforced poroelastic materials, respectively. Three commonly used loading regimes were simulated in Abaqus (ramp, relaxation and dynamic loading) with varying compressive strain magnitudes and rates. From these virtual experiments, the resulting material parameters were obtained for each combination using a numerical inverse identification scheme. For hydrogels, maximum sensitivity to the different material parameters was found when using a single step ramp loading (20% compression with 10%/s rate) followed by 15 min relaxation. For cartilage explants, a two-stepped ramp loading (10% compression with 10%/s rate and 10% compression with 1%/s rate), each step followed by 15 min relaxation, yielded the maximum sensitivity to the different material parameters. With these protocols, the material parameters could be retrieved with the lowest amount of uncertainty (hydrogel: < 2% and cartilage: < 6%). These specific results and the overall methodology can be used to optimize mechanical testing protocols to yield reliable material parameters for in silico models of cartilage and hydrogel constructs.

Lateral Extra-articular Tenodesis Alters Lateral Compartment Contact Mechanics under Simulated Pivoting Maneuvers: An In Vitro Study

BACKGROUND

There is concern that utilization of lateral extra-articular tenodesis (LET) in conjunction with anterior cruciate ligament (ACL) reconstruction (ACLR) may disturb lateral compartment contact mechanics and contribute to joint degeneration.

HYPOTHESIS

ACLR augmented with LET will alter lateral compartment contact mechanics in response to simulated pivoting maneuvers.

STUDY DESIGN

Controlled laboratory study.

METHODS

Loads simulating a pivot shift were applied to 7 cadaveric knees (4 male; mean age, 39 ± 12 years; range, 28-54 years) using a robotic manipulator. Each knee was tested with the ACL intact, sectioned, reconstructed (via patellar tendon autograft), and, finally, after augmenting ACLR with LET (using a modified Lemaire technique) in the presence of a sectioned anterolateral ligament and Kaplan fibers. Lateral compartment contact mechanics were measured using a contact stress transducer. Outcome measures were anteroposterior location of the center of contact stress (CCS), contact force from anterior to posterior, and peak and mean contact stress.

RESULTS

On average, augmenting ACLR with LET shifted the lateral compartment CCS anteriorly compared with the intact knee and compared with ACLR in isolation by a maximum of 5.4 ± 2.3 mm (P < .001) and 6.0 ± 2.6 mm (P < .001), respectively. ACLR augmented with LET also increased contact force anteriorly on the lateral tibial plateau compared with the intact knee and compared with isolated ACLR by a maximum of 12 ± 6 N (P = .001) and 17 ± 10 N (P = .002), respectively. Compared with ACLR in isolation, ACLR augmented with LET increased peak and mean lateral compartment contact stress by 0.7 ± 0.5 MPa (P = .005) and by 0.17 ± 0.12 (P = .006), respectively, at 15° of flexion.

CONCLUSION

Under simulated pivoting loads, adding LET to ACLR anteriorized the CCS on the lateral tibial plateau, thereby increasing contact force anteriorly. Compared with ACLR in isolation, ACLR augmented with LET increased peak and mean lateral compartment contact stress at 15° of flexion.

CLINICAL RELEVANCE

The clinical and biological effect of increased anterior loading of the lateral compartment after LET merits further investigation. The ability of LET to anteriorize contact stress on the lateral compartment may be useful in knees with passive anterior subluxation of the lateral tibia.

Tissue engineered autologous cartilage-bone grafts for temporomandibular joint regeneration

Joint disorders can be detrimental to quality of life. There is an unmet need for precise functional reconstruction of native-like cartilage and bone tissues in the craniofacial space and particularly for the temporomandibular joint (TMJ). Current surgical methods suffer from lack of precision and comorbidities and frequently involve multiple operations. Studies have sought to improve craniofacial bone grafts without addressing the cartilage, which is essential to TMJ function. For the human-sized TMJ in the Yucatan minipig model, we engineered autologous, biologically, and anatomically matched cartilage-bone grafts for repairing the ramus-condyle unit (RCU), a geometrically intricate structure subjected to complex loading forces. Using image-guided micromilling, anatomically precise scaffolds were created from decellularized bone matrix and infused with autologous adipose-derived chondrogenic and osteogenic progenitor cells. The resulting constructs were cultured in a dual perfusion bioreactor for 5 weeks before implantation. Six months after implantation, the bioengineered RCUs maintained their predefined anatomical structure and regenerated full-thickness, stratified, and mechanically robust cartilage over the underlying bone, to a greater extent than either autologous bone-only engineered grafts or acellular scaffolds. Tracking of implanted cells and parallel bioreactor studies enabled additional insights into the progression of cartilage and bone regeneration. This study demonstrates the feasibility of TMJ regeneration using anatomically precise, autologous, living cartilage-bone grafts for functional, personalized total joint replacement. Inclusion of the adjacent tissues such as soft connective tissues and the TMJ disc could further extend the functional integration of engineered RCUs with the host.

Finite Element Modelling Simulated Meniscus Translocation and Deformation during Locomotion of the Equine Stifle

Simple Summary

Meniscal tears are one of the most common soft tissue injuries in the equine stifle joint. To date no optimal treatment strategy to heal meniscal tissue is available. Accordingly, there is a need to improve treatment for meniscal injuries and thus to identify appropriate translational animal models. A possible alternative to animal experimentation is the use of finite element modelling (FEMg). FEMg allows simulation of time dependent changes in tissues resulting from biomechanical strains. We developed a finite element model (FEM) of the equine stifle joint to identify pressure peaks and simulate translocation and deformation of the menisci at different joint angles under loading conditions. The FEM model was tested across a range of motion of approximately 30°. Pressure load was higher overall in the lateral meniscus than in the medial meniscus. Accordingly, the simulation showed higher translocation and deformation throughout the whole range of motion in the lateral compared to the medial meniscus. The results encourage further refinement of this FEM model for studying loading patterns on menisci and articular cartilages as well as the resulting mechanical stress in the subchondral bone. A functional FEM model can not only help identify segments in the femoro–tibial joint which are predisposed to injury, but also provide better understanding of the progression of certain stifle disorders, simulate treatment/surgery effects and to optimize implant/transplant properties in order to most closely resemble natural tissue.

Abstract

We developed a finite element model (FEM) of the equine stifle joint to identify pressure peaks and simulate translocation and deformation of the menisci. A series of sectional magnetic resonance images (1.5 T) of the stifle joint of a 23 year old Shetland pony gelding served as basis for image segmentation. Based on the 3D polygon models of femur, tibia, articular cartilages, menisci, collateral ligaments and the meniscotibial ligaments, an FEM model was generated. Tissue material properties were assigned based on data from human (Open knee(s) project) and bovine femoro-tibial joint available in the literature. The FEM model was tested across a range of motion of approximately 30°. Pressure load was overall higher in the lateral meniscus than in the medial. Accordingly, the simulation showed higher translocation and deformation in the lateral compared to the medial meniscus. The results encourage further refinement of this model for studying loading patterns on menisci and articular cartilages as well as the resulting mechanical stress in the subchondral bone (femur and tibia). A functional FEM model can not only help identify segments in the stifle which are predisposed to injury, but also to better understand the progression of certain stifle disorders, simulate treatment/surgery effects and to optimize implant/transplant properties.

Parametric finite element model of medial patellofemoral ligament reconstruction model development and clinical validation

Background

Currently, there is uncertainty regarding the long-term outcome of medial patellofemoral ligament reconstructions (MPFLr). Our objectives were: (1) to develop a parametric model of the patellofemoral joint (PFJ) enabling us to simulate different surgical techniques for MPFLr; (2) to determine the negative effects on the PFJ associated with each technique, which could be related to long-term deterioration of the PFJ.

Methods

A finite element model of the PFJ was created based on CT data from 24 knees with chronic lateral patellar instability. Patella contact pressure and maximum MPFL-graft stress at five angles of knee flexion (0, 30, 60, 90 and 120°) were analysed in three types of MPFLr: anatomic, non-anatomic with physiometric behaviour, and non-anatomic with non-physiometric behaviour.

Results

An increase in patella contact pressure was observed at 0 and 30° of knee flexion after both anatomic and non-anatomic MPFLr with physiometric behaviour. In both reconstructions, the ligament was tense between 0 and 30° of knee flexion, but at 60, 90 and 120°, it had no tension. In the third reconstruction, the behaviour was completely the opposite.

Conclusion

A parametric model of the PFJ enables us to evaluate different types of MPFLr throughout the full range of motion of the knee, regarding the effect on the patellofemoral contact pressure, as well as the kinematic behaviour of the MPFL-graft and the maximum MPFL-graft stress.

Electronic supplementary material

The online version of this article (10.1186/s40634-019-0200-x) contains supplementary material, which is available to authorized users.

Regulation of Cell Behavior by Hydrostatic Pressure

Hydrostatic pressure (HP) regulates diverse cell behaviors including differentiation, migration, apoptosis, and proliferation. Abnormal HP is associated with pathologies including glaucoma and hypertensive fibrotic remodeling. In this review, recent advances in quantifying and predicting how cells respond to HP across several tissue systems are presented, including tissues of the brain, eye, vasculature and bladder, as well as articular cartilage. Finally, some promising directions on the study of cell behaviors regulated by HP are proposed.

Computational simulation of the multiphasic degeneration of the bone-cartilage unit during osteoarthritis via indentation and unconfined compression tests

It has been experimentally proposed that the discrete regions of articular cartilage, along with different subchondral bone tissues, known as the bone-cartilage unit, are biomechanically altered during osteoarthritis degeneration. However, a computational framework capturing all of the dominant changes in the multiphasic parameters has not yet been developed. This article proposes a new finite element model of the bone-cartilage unit by combining several validated, nonlinear, depth-dependent, fibril-reinforced, and swelling models, which can computationally simulate the variations in the dominant parameters during osteoarthritis degeneration by indentation and unconfined compression tests. The mentioned dominant parameters include the proteoglycan depletion, collagen fibrillar softening, permeability, and fluid fraction increase for approximately non-advanced osteoarthritis. The results depict the importance of subchondral bone tissues in fluid distribution within the bone-cartilage units by decreasing the fluid permeation and pressure (up to a maximum of 100 kPa) during osteoarthritis, supporting the notion that subchondral bones might play a role in the pathogenesis of osteoarthritis. Furthermore, the osteoarthritis composition-based studies shed light on the significant biomechanical role of the calcified cartilage, which experienced a maximum change of 70 kPa in stress, together with relative load contributions of articular cartilage constituents during osteoarthritis, in which the osmotic pressure bore around 70% of the loads after degeneration. To conclude, the new insights provided by the results reveal the significance of the multiphasic osteoarthritis simulation and demonstrate the functionality of the proposed bone-cartilage unit model.

Analyzing the effects of instillation volume on intravesical delivery using biphasic solute transport in a deformable geometry

Ailments of the bladder are often treated via intravesical delivery-direct application of therapeutic into the bladder through a catheter. This technique is employed hundreds of thousands of times every year, but protocol development has largely been limited to empirical determination. Furthermore, the numerical analyses of intravesical delivery performed to date have been restricted to static geometries and have not accounted for bladder deformation. This study uses a finite element analysis approach with biphasic solute transport to investigate several parameters pertinent to intravesical delivery including solute concentration, solute transport properties and instillation volume. The volume of instillation was found to have a substantial impact on the exposure of solute to the deeper muscle layers of the bladder, which are typically more difficult to reach. Indeed, increasing the instillation volume from 50-100 ml raised the muscle solute exposure as a percentage of overall bladder exposure from 60-70% with higher levels achieved for larger instillation volumes. Similar increases were not seen for changes in solute concentration or solute transport properties. These results indicate the role that instillation volume may play in targeting particular layers of the bladder during an intravesical delivery.

Rate-dependent crack nucleation in cartilage under microindentation

This study investigates rate-dependent crack nucleation in cartilage under microindentation using a poroviscoelastic framework and nano/microscopic images. Localized crack failure was induced at known locations and at different loading rates via microindentation with an axisymmetric sphero-conical indenter. Finite element (FE) modeling was used to reproduce results of microindentation tests within a poroviscoelastic framework. Scanning electron microscopy (SEM) was used to examine nano- and microscale structural features of crack surfaces. Microindentation results showed rate-dependent crack nucleation in cartilage. In particular, critical total work required for crack nucleation was larger at the slow loading rate compared to the fast loading rate. FE results suggested that viscoelastic relaxation of cartilage was a major contributor to the rate dependency and that tensile stresses localized at the indenter tip was a governing factor in crack nucleation. SEM images combined with microindentation and FE results suggested that the solid matrix in the vicinity of the tip experienced relatively large relaxation and kinematic fiber rearrangement at the slow loading rate in comparison to the fast loading rate. These findings extend current understanding of rate-dependent failure mechanisms in cartilage.

Minimal medical imaging can accurately reconstruct geometric bone models for musculoskeletal models

Accurate representation of subject-specific bone anatomy in lower-limb musculoskeletal models is important for human movement analyses and simulations. Mathematical methods can reconstruct geometric bone models using incomplete imaging of bone by morphing bone model templates, but the validity of these methods has not been fully explored. The purpose of this study was to determine the minimal imaging requirements for accurate reconstruction of geometric bone models. Complete geometric pelvis and femur models of 14 healthy adults were reconstructed from magnetic resonance imaging through segmentation. From each complete bone segmentation, three sets of incomplete segmentations (set 1 being the most incomplete) were created to test the effect of imaging incompleteness on reconstruction accuracy. Geometric bone models were reconstructed from complete sets, three incomplete sets, and two motion capture-based methods. Reconstructions from (in)complete sets were generated using statistical shape modelling, followed by host-mesh and local-mesh fitting through the Musculoskeletal Atlas Project Client. Reconstructions from motion capture-based methods used positional data from skin surface markers placed atop anatomic landmarks and estimated joint centre locations as target points for statistical shape modelling and linear scaling. Accuracy was evaluated with distance error (mm) and overlapping volume similarity (%) between complete bone segmentation and reconstructed bone models, and statistically compared using a repeated measure analysis of variance (p<0.05). Motion capture-based methods produced significantly higher distance error than reconstructions from (in)complete sets. Pelvis volume similarity reduced significantly with the level of incompleteness: complete set (92.70±1.92%), set 3 (85.41±1.99%), set 2 (81.22±3.03%), set 1 (62.30±6.17%), motion capture-based statistical shape modelling (41.18±9.54%), and motion capture-based linear scaling (26.80±7.19%). A similar trend was observed for femur volume similarity. Results indicate that imaging two relevant bone regions produces overlapping volume similarity >80% compared to complete segmented bone models, and improve analyses and simulation over current standard practice of linear scaling musculoskeletal models.

The mechanics of focal chondral defects in the hip

There is a mean incidence of osteoarthritis (OA) of the hip in 8% of the overall population. In the presence of focal chondral defects, defined as localized damage to the articular cartilage, there is an increased risk of symptomatic progression toward OA. This relationship between chondral defects and subsequent development of OA has led to substantial efforts to develop effective procedures for surgical cartilage repair. This study examined the effects of chondral defects and labral delamination on cartilage mechanics in the dysplastic hip during the gait cycle using subject-specific finite element analysis. Models were generated from volumetric CT data and analyzed with simulated chondral defects at the chondrolabral junction on the posterior acetabulum during five distinct points in the gait cycle. Focal chondral defects increased maximum shear stress on the osteochondral surface of the acetabular cartilage, when compared to the intact case. This effect was amplified with labral delamination. Additionally, chondral defects increased the first principal Lagrange strain on the articular surface of the acetabular cartilage and labrum. Labral delamination relieved some of this tensile strain. As defect size was increased, contact stress increased in the medial zone of the acetabulum, while it decreased anteriorly. The results suggest that in the presence of chondral defects and labral delamination the cartilage experiences elevated tensile strains and shear and contact stress, which could lead to further damage of the cartilage, and subsequent arthritic progression. The framework presented here will serve as the procedure for future finite element studies on cartilage mechanics in hips with varying disease states with simulated chondral defects and labral tears.

Relative contribution of articular cartilage's constitutive components to load support depending on strain rate

Cartilage is considered a biphasic material in which the solid is composed of proteoglycans and collagen. In biphasic tissue, the hydraulic pressure is believed to bear most of the load under higher strain rates and its dissipation due to fluid flow determines creep and relaxation behavior. In equilibrium, hydraulic pressure is zero and load bearing is transferred to the solid matrix. The viscoelasticity of the collagen network also contributes to its time-dependent behavior, and the osmotic pressure to load bearing in equilibrium. The aim of the present study was to determine the relative contributions of hydraulic pressure, viscoelastic collagen stress, solid matrix stiffness and osmotic pressure to load carriage in cartilage under transient and equilibrium conditions. Unconfined compression experiments were simulated using a fibril-reinforced poroviscoelastic model of articular cartilage, including water, fibrillar viscoelastic collagen and non-fibrillar charged glycosaminoglycans. The relative contributions of hydraulic and osmotic pressures and stresses in the fibrillar and non-fibrillar network were evaluated in the superficial, middle and deep zone of cartilage under five different strain rates and after relaxation. Initially upon loading, the hydraulic pressure carried most of the load in all three zones. The osmotic swelling pressure carried most of the equilibrium load. In the surface zone, where the fibers were loaded in tension, the collagen network carried 20 % of the load for all strain rates. The importance of these fibers was illustrated by artificially modifying the fiber architecture, which reduced the overall stiffness of cartilage in all conditions. In conclusion, although hydraulic pressure dominates the transient behavior during cartilage loading, due to its viscoelastic nature the superficial zone collagen fibers carry a substantial part of the load under transient conditions. This becomes increasingly important with higher strain rates. The interesting and striking new insight from this study suggests that under equilibrium conditions, the swelling pressure generated by the combination of proteoglycans and collagen reinforcement accounts cartilage stiffness for more than 90 % of the loads carried by articular cartilage. This finding is different from the common thought that load is transferred from fluid to solid and is carried by the aggregate modulus of the solid. Rather, it is transformed from hydraulic to osmotic swelling pressure. These results show the importance of considering both (viscoelastic) collagen fibers as well as swelling pressure in studies of the (transient) mechanical behavior of cartilage.