Coupling of multibody models and finite element models to investigate the role of muscles in the in silico prediction of femoral fracture risk

Femoral fractures pose a significant challenge to public health, especially in light of the increasing number of elderly subjects affected by osteoporosis worldwide. In this context, when aiming to predict femoral fracture in silico, it is still not clear whether muscles actions have a protective effect on the fracture risk or, on the contrary, those increase the fracture risk. Hence, aiming to evaluate the contribution of muscles forces in this context, this thesis focused on exploring various approaches described in the literature to transfer muscles forces from a multibody model to a finite element (FE) model of the femur. In particular, several methods to constrain the FE model were analysed. An Opensim-derived simplified musculoskeletal model was used to simulate a static pose and calculate the muscle forces directly acting on the femur. These forces were then applied to a femur's FE model simulating a fall on the side, by constraining the femur in five different ways based on literature studies. The FE model comprised a force applied on the centre of the femoral head with a frictionless contact defined between the greater trochanter and a rigid plane. Distally, the following five constraint cases were considered: 1) the reference case boundary conditions, where the diaphysis nodes were linked to the knee centre, modelled as a hinge, through beams elements; 2) all the nodes in the distal portion of the femur were fully constrained; 3) three nodes in the mid-diaphysis were fully constrained; 4) one node near the patella groove was constrained in antero-posterior displacements, the most distal node of the medial condyle was fully constrained, and the most distal node at the lateral condyle was constrained in antero-posterior and cranio-caudal displacements; 5) the node on the femoral head’s surface, referred to as the hip contact node, was constrained in antero-posterior and cranio-caudal displacements; additionally, one node near the patella groove was fully constrained, and a node on the distal lateral epicondyle was constrained in antero-posterior displacement. All these models were also compared to the reference model, where case 1) boundary conditions were applied but without any muscles forces applied. Principal strains represented the references biomechanical variables considered to perform the comparisons. The five cases considered with applied muscle forces showed 0.247%(±0.343%), 0.248%(±0.341%), 0.232%(±0.313%), 0.285%(±0.390%), 0.085%(±0.207%) average values for the maximum principal strain, and -0.253%(±0.346%), -0.254%(±0.343%), -0.238%(±0.313%), -0.290%(±0.392%), -0.087%(±0.130%) average values for the minimum principal strains. The FE model without muscles forces instead showed 0.248%(±0.333%) and -0.253%(±0.335%) average values for the maximum and minimum principal strains, respectively.