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

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.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.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.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.