Implementation of a compliant custom made knee musculoskeletal model in Opensim

Common musculoskeletal models often resort to simplified rigid joint models that do not account for the articular response to internal and external load. Thus, they are not able to capture fine articular behaviour, reducing their clinical applicability. To face this problem, the development of deformable joint models is required. In this perspective, recent publications proposed explicit formulations of the joint compliance, modelling the human joint and knee in particular as a deformable multibody system, featuring ligaments and cartilage direct representation. Known limits of these approaches include the need for optimization of numerous parameters, complication of scaling procedure, requiring manual positioning of muscle and ligaments insertions and manual scaling and segmentation from medical imaging. Both of these aspects are crucial since the musculoskeletal analysis is reported to be sensitive to the involved parameters. Overall, the state of art lacks a middle ground between rigid joint models, and deformable joint models based on an explicit formulation. While common multibody models implement a one degree of freedom spatial knee, deformable articulations often rely on six degrees of freedom joints, that require a proper modelling of the complex musculotendon and ligamentous structures. Moreover, the standard musculoskeletal analysis pipeline calculates muscle activation and joint loads imposing the experimental acquisition of the kinematic data (namely, the Inverse Kinematics procedure). In other words, loads involved in the analysis are not known a priori, forcing an initial evaluation of the subject movement with a rigid joint definition. This clearly makes the utilization of deformable models in the context of gait analysis not trivial, requiring the definition of new strategies, for example the insertion in a proper loop of the kinematics reconstruction, the muscle actuation calculation, and finally the joint deformation. An example of this kind of approach was proposed by Colin Smith et al. with Opensim JAM, which relies on a modified pipeline for the musculoskeletal analysis of a full-body model with a 6-DoF knee joint implementation. Here, the procedure consists of a minimization problem that comprehend the knee secondary kinematics, muscle activations, and joint loads. However, it still requires a preliminary analysis executed with a rigid joint definition. Our aim is to propose a different approach to the problem, implementing an implicit formulation of a deformable knee model, rather than an explicit formulation. The scaling operation for this model is equivalent to the standard procedure, without the necessity of further adjustments, like the already cited muscle insertion positioning, or manual scaling from medical images. This was done by manipulating the spline functions that describe the secondary kinematics at the knee articulation, using a compliance map of the knee joint, obtained from an experimental procedure on six cadaveric legs. The overall pipeline was executed in MATLAB, using Opensim API. Moreover, to evaluate the impact of the initial rigid kinematic chain used for the Inverse Kinematics and Static Optimization operations on the final knee deformation, two different knee models were studied. The first one implements a six degrees of freedom deformable knee model, with only one not-resisted coordinate (namely the flexion-extension rotation). Since the internal-external rotation is reported to be less resisted, along with the flexion-extension one, the second model implements a six degrees of freedom deformable knee model, with two not-resisted coordinates (namely, flexion-extension, and internal-external rotation).