Long bones grow by the process of endochondral ossification in which a cartilage template, or anlage, grows and is replaced by bone. This process is regulated by biological factors such as genetic make-up, hormones, and systemic chemical agents, and by mechanical factors such as joint loads and muscle contractions which impose stresses and strains on the developing bone. Previous studies have used multiaxial stress invariants to characterize the effects of multiaxial cyclic loading on endochondral bone growth. In particular it has been proposed that cyclic hydrostatic compression inhibits growth and ossification, whereas cyclic octahedral shear stress promotes growth and ossification (Carter et al., 1987). These mechanobiological principles have been used to predict ossification patterns in long bones. Previous studies, however, did not examine progression of the growth front and changes in growth front morphology and overall bone shape. The effects of multiaxial static stresses on growth and ossification have also not been examined.

The purpose of this research is to use mechanobiological principles to predict the rates of growth and the progression of the growth front in long bones during endochondral ossification. Both the rate and direction of growth at the growth front determine the morphology of the whole bone. This thesis first introduces a finite element method for simulating growth front progression in both static and cyclic loading conditions. These mechanobiological principles are then applied to bone morphogenesis in five different studies:​ a phalangeal joint, the bicondylar angle of the distal femur, the formation of coxa valga in the proximal femur during developmental dysplasia of the hip, the formation of anteversion in the proximal femur in cerebral palsy, and the change in growth front morphology after formation of the secondary center. Each study highlights a different aspect of the mechanobiological principles and their implementation into finite element growth simulations.

This thesis demonstrates that mechanobiological principles can be applied to many different aspects of bone morphogenesis to explain changes in bone morphology. The results have implications in clinical treatments of bone deformities and explaining skeletal variations in various species throughout evolution.