Validation of a personalized ligament-constraining discrete element framework for computing ankle joint contact mechanics

BACKGROUND AND OBJECTIVE

Computer simulations of joint contact mechanics have great merit to improve our current understanding of articular ankle pathology. Owed to its computational simplicity, discrete element analysis (DEA) is an encouraging alternative to finite element analysis (FEA). However, previous DEA models lack subject-specific anatomy and may oversimplify the biomechanics of the ankle. The objective of this study was to develop and validate a personalized DEA framework that permits movement of the fibula and incorporates personalized cartilage thickness as well as ligamentous constraints.

METHODS

A linear and non-linear DEA framework, representing cartilage as compressive springs, was established, verified, and validated. Three-dimensional (3D) bony ankle models were constructed from cadaveric lower limb CT scans imaged during application of weight (85 kg) and/or torque (10 Nm). These 3D models were used to generate cartilage thickness and ligament insertion sites based on a previously validated statistical shape model. Ligaments were modelled as non-linear tension-only springs. Validation of contact stress prediction was performed using a simple, axially constrained tibiotalar DEA model against an equivalent FEA model. Validation of ligamentous constraints compared the final position of the ankle mortise to that of the cadaver after application of torque and sequential ligament sectioning. Finally, a combined ligamentous-constraining DEA model was validated for predicted contact stress against an equivalent ligament-constraining FEA model.

RESULTS

The linear and non-linear DEA model reproduced a mean articular contact stress within 0.36 MPa and 0.39 MPa of the FEA calculated stress, respectively. With respect to the ligamentous validation, the DEA ligament-balancing algorithm could reproduce the position of the distal fibula within the ankle mortise to within 0.97 mm of the experimental observed distal fibula. When combining the ligament-constraining and contact stress algorithm, DEA was able to reproduce a mean articular contact stress to within 0.50 MPa of the FEA calculated contact stress.

CONCLUSION

The DEA framework presented herein offers a computationally efficient alternative to FEA for the prediction of contact stress in the ankle joint, manifesting its potential to enhance the mechanical understanding of articular ankle pathologies on both a patient-specific and population-wide level. The novelty of this model lies in its personalized nature, inclusion of the distal tibiofibular joint and the use of non-linear ligament balancing to maintain the physiological ankle joint articulation.

Radiographically successful periacetabular osteotomy does not achieve optimal contact mechanics in dysplastic hips

BACKGROUND

Optimal correction of hip dysplasia via periacetabular osteotomy may reduce osteoarthritis development by reducing damaging contact stress. The objective of this study was to computationally determine if patient-specific acetabular corrections that optimize contact mechanics can improve upon contact mechanics resulting from clinically successful, surgically achieved corrections.

METHODS

Preoperative and postoperative hip models were retrospectively created from CT scans of 20 dysplasia patients treated with periacetabular osteotomy. A digitally extracted acetabular fragment was computationally rotated in 2-degree increments around anteroposterior and oblique axes to simulate candidate acetabular reorientations. From discrete element analysis of each patient's set of candidate reorientation models, a mechanically optimal reorientation that minimized chronic contact stress exposure and a clinically optimal reorientation that balanced improving mechanics with surgically acceptable acetabular coverage angles was selected. Radiographic coverage, contact area, peak/mean contact stress, and peak/mean chronic exposure were compared between mechanically optimal, clinically optimal, and surgically achieved orientations.

FINDINGS

Compared to actual surgical corrections, computationally derived mechanically/clinically optimal reorientations had a median[IQR] 13[4-16]/8[3-12] degrees and 16[6-26]/10[3-16] degrees more lateral and anterior coverage, respectively. Mechanically/clinically optimal reorientations had 212[143-353]/217[111-280] mm2 more contact area and 8.2[5.8-11.1]/6.4[4.5-9.3] MPa lower peak contact stresses than surgical corrections. Chronic metrics demonstrated similar findings (p ≤ 0.003 for all comparisons).

INTERPRETATION

Computationally selected orientations achieved a greater mechanical improvement than surgically achieved corrections; however, many predicted corrections would be considered acetabular over-coverage. Identifying patient-specific corrections that balance optimizing mechanics with clinical constraints will be necessary to reduce the risk of osteoarthritis progression after periacetabular osteotomy.

Contribution of joint tissue properties to load-induced osteoarthritis

Objective

Clinical evidence suggests that abnormal mechanical forces play a major role in the initiation and progression of osteoarthritis (OA). However, few studies have examined the mechanical environment that leads to disease. Thus, using a mouse tibial loading model, we quantified the cartilage contact stresses and examined the effects of altering tissue material properties on joint stresses during loading.

Design

Using a discrete element model (DEA) in conjunction with joint kinematics data from a murine knee joint compression model, the magnitude and distribution of contact stresses in the tibial cartilage during joint loading were quantified at levels ranging from 0 to 9 N in 1 N increments. In addition, a simplified finite element (FEA) contact model was developed to simulate the knee joint, and parametric analyses were conducted to investigate the effects of altering bone and cartilage material properties on joint stresses during compressive loading.

Results

As loading increased, the peak contact pressures were sufficient to induce fibrillations on the cartilage surfaces. The computed areas of peak contact pressures correlated with experimentally defined areas of highest cartilage damage. Only alterations in cartilage properties and geometry caused large changes in cartilage contact pressures. However, changes in both bone and cartilage material properties resulted in significant changes in stresses induced in the bone during compressive loading.

Conclusions

The level of mechanical stress induced by compressive tibial loading directly correlated with areas of biological change observed in the mouse knee joint. These results, taken together with the parametric analyses, are the first to demonstrate both experimentally and computationally that the tibial loading model is a useful preclinical platform with which to predict and study the effects of modulating bone and/or cartilage properties on attenuating OA progression. Given the direct correlation between computational modeling and experimental results, the effects of tissue-modifying treatments may be predicted prior to in vivo experimentation, allowing for novel therapeutics to be developed.

Development and validation of a kinematically-driven discrete element model of the patellofemoral joint

Quantifying the complex loads at the patellofemoral joint (PFJ) is vital to understanding the development of PFJ pain and osteoarthritis. Discrete element analysis (DEA) is a computationally efficient method to estimate cartilage contact stresses with potential application at the PFJ to better understand PFJ mechanics. The current study validated a DEA modeling framework driven by PFJ kinematics to predict experimentally-measured PFJ contact stress distributions. Two cadaveric knee specimens underwent quadriceps muscle [215 N] and joint compression [350 N] forces at ten discrete knee positions representing PFJ positions during early gait while measured PFJ kinematics were used to drive specimen-specific DEA models. DEA-computed contact stress and area were compared to experimentally-measured data. There was good agreement between computed and measured mean and peak stress across the specimens and positions (r = 0.63-0.85). DEA-computed mean stress was within an average of 12% (range: 1-47%) of the experimentally-measured mean stress while DEA-computed peak stress was within an average of 22% (range: 1-40%). Stress magnitudes were within the ranges measured (0.17-1.26 MPa computationally vs 0.12-1.13 MPa experimentally). DEA-computed areas overestimated measured areas (average error = 60%; range: 4-117%) with magnitudes ranging from 139 to 307 mm² computationally vs 74-194 mm² experimentally. DEA estimates of the ratio of lateral to medial patellofemoral stress distribution predicted the experimental data well (mean error = 15%) with minimal measurement bias. These results indicate that kinematically-driven DEA models can provide good estimates of relative changes in PFJ contact stress.

Joint contact stresses calculated for acetabular dysplasia patients using discrete element analysis are significantly influenced by the applied gait pattern

Gait modifications in acetabular dysplasia patients may influence cartilage contact stress patterns within the hip joint, with serious implications for clinical outcomes and the risk of developing osteoarthritis. The objective of this study was to understand how the gait pattern used to load computational models of dysplastic hips influences computed joint mechanics. Three-dimensional pre- and post-operative hip models of thirty patients previously treated for hip dysplasia with periacetabular osteotomy (PAO) were developed for performing discrete element analysis (DEA). Using DEA, contact stress patterns were calculated for each pre- and post-operative hip model when loaded with an instrumented total hip, a dysplastic, a matched control, and a normal gait pattern. DEA models loaded with the dysplastic and matched control gait patterns had significantly higher (p = 0.012 and p < 0.001) average pre-operative maximum contact stress than models loaded with the normal gait. Models loaded with the dysplastic and matched control gait patterns had nearly significantly higher (p = 0.051) and significantly higher (p = 0.008) average pre-operative contact stress, respectively, than models loaded with the instrumented hip gait. Following PAO, the average maximum contact stress for DEA models loaded with the dysplastic and matched control patterns decreased, which was significantly different (p < 0.001) from observed increases in maximum contact stress calculated when utilizing the instrumented hip and normal gait patterns. The correlation between change in DEA-computed maximum contact stress and the change in radiographic measurements of lateral center-edge angle were greatest (R2 = 0.330) when utilizing the dysplastic gait pattern. These results indicate that utilizing a dysplastic gait pattern to load DEA models may be a crucial element to capturing contact stress patterns most representative of this patient population.

Discrete element analysis is a valid method for computing joint contact stress in the hip before and after acetabular fracture

Evaluation of abnormalities in joint contact stress that develop after inaccurate reduction of an acetabular fracture may provide a potential means for predicting the risk of developing post-traumatic osteoarthritis. Discrete element analysis (DEA) is a computational technique for calculating intra-articular contact stress distributions in a fraction of the time required to obtain the same information using the more commonly employed finite element analysis technique. The goal of this work was to validate the accuracy of DEA-computed contact stress against physical measurements of contact stress made in cadaveric hips using Tekscan sensors. Four static loading tests in a variety of poses from heel-strike to toe-off were performed in two different cadaveric hip specimens with the acetabulum intact and again with an intentionally malreduced posterior wall acetabular fracture. DEA-computed contact stress was compared on a point-by-point basis to stress measured from the physical experiments. There was good agreement between computed and measured contact stress over the entire contact area (correlation coefficients ranged from 0.88 to 0.99). DEA-computed peak contact stress was within an average of 0.5 MPa (range 0.2-0.8 MPa) of the Tekscan peak stress for intact hips, and within an average of 0.6 MPa (range 0-1.6 MPa) for fractured cases. DEA-computed contact areas were within an average of 33% of the Tekscan-measured areas (range: 1.4-60%). These results indicate that the DEA methodology is a valid method for accurately estimating contact stress in both intact and fractured hips.