Computational Mechanobiological Model Combining Epiphyseal, Apophyseal, and Appositional Growth and Inner Bone Remodeling of the Juvenile Femur

In silico models for simulating bone growth based on mechanical or non-mechanical epigenetic factors are widely used. In this study, a well-known mechanobiological model, which states that octahedral shear stress accelerates longitudinal bone growth and hydrostatic stress retards it, is applied to a finite element model of the femur of an 8-year-old boy. Proximal and distal epiphyseal plates as well as the growth plate of the greater trochanter, cartilaginous growth at the femoral isthmus, and appositional bone growth are included in the model. Furthermore, changes in the density of the cancellous bone in the metaphyses are modeled based on Wolff's law using compressive stresses as the mechanical stimulus. Muscle forces during a dynamic gait cycle were determined for nine discrete loading cases by optimizing to minimize bending stress. The highest stresses in the femoral shaft were determined as medial compressive stresses with a maximum of −33.2 MPa. Highest internal axial load in the shaft was 985 N during loading response. The simulated bone growth resulted in an increase in femur length of 23.7 mm and a decrease in femoral neck angle by −1.4°, anteversion angle by −2.4°, and lateral distal femur angle by −1.6° per year. Growth of the apophysis of the greater trochanter resulted in an unchanged articulo-trochanteric distance. The bone remodeling led to an increase in bone density, particularly in the medial proximal metaphysis. The consideration of different growth mechanisms allowed a comprehensive simulation of femoral growth with high agreement with anthropometric data. Possible applications are the simulation of the correction of deformities.