A multi-scale study of the hip joint mechanics using rigid-body inverse dynamics and finite element analysis

Coxarthrosis (CA) is a non-inflammatory degenerative disease of the hip joint that provokes the destruction of the articular cartilage and bone growth, all in all resulting in pain and patient disability. Primary CA commonly affects old people due to cartilage ageing, but appears at an early age in about 20% of the cases, possibly caused by joint deformities and undue mechanical loads. However, deformities only explain up to 30% of the cases of juvenile CA [1]. Recently, it was suggested that juvenile CA could be caused by pathological loads transmitted to the hip joint cartilage, even in patients with apparently normal hip morphologies. In particular, Sanchez et al. [2] developed different finite element (FE) models of the hip joint, and their results strongly suggested that specific combinations of normal range anatomical angles provoke high cartilage stresses during daily activities. However, the confirmation of these results depends significantly on the boundary loads applied onto the FE model. Hence, the goal of this study is to calculate the pressure within the cartilage during a patient’s activity (in this case gait), based upon the movement kinematics and foot-ground contact forces captured in the laboratory. A multi-scale approach was developed for this purpose, which combined a musculoskeletal rigid body model of the entire human body and a FE model of the hip joint with a deformable cartilage. The process required acquiring proper boundary conditions for the FE model from the data calculated with the rigid body model. The workflow of the whole process is shown in Fig. 1. Figure 1. Workflow of the multi-scale modelling of the hip joint mechanics. Both the rigid body and the FE models corresponded to healthy subjects. In order to capture the subject’s movement, a set of 21 markers were placed on a volunteer and their trajectories were measured by means of 14 infrared cameras. The foot-ground contact forces were recorded using 2 force plates. All data was sampled at 100 Hz. The captured movement was reproduced on the rigid body model, which consisted on 12 segments (HAT –head, arms, trunk–, pelvis, 2 thighs, 2 shanks, 2 calcaneus, 2 talus and 2 toes) and had 23 degrees of A. Peiret, E. Bosch, G. Serrancoli, J. Noailly and J.M. Font-Llagunes. 2 freedom. The model was implemented on the OpenSim software [3]. The muscle forces FM were estimated solving an inverse dynamics problem together with an optimization approach that minimized the sum of squares of muscle activations. Finally, Lagrange multipliers allowed to obtain the joint forces FJ. For the FE calculations, a previously developed osteoligamentous hip joint model was used [2]. Bones were linear elastic, and cartilage tissues were considered as hyperelastic NeoHookean materials, with material parameter values taken from [4]. The boundary conditions for the FE model were calculated with the coordinates q, the forces of the muscles attached to the femur (FM) and the knee joint force (FJ) and torque (MJ). To avoid singularity in the FE system to solve, the pelvis was immobilized and a distribution of inertial forces was applied to the femur. These inertial forces emulate the movement of the bone at a specific instant, see Fig. 1. The d’Alembert inertial force Fd'Al= –ma was implemented as a body force applied to the femur elements, whose value depends on their location. Therefore, the body force B considering the gravity force was given by: