Early in development, rudiments of the skeletal long bones are made of cartilage. Endochondral growth and ossification is the process by which the rudiment increases in length and the cartilage is replaced by bone. By adulthood, endochondral ossification normally halts at the ends of long bones, and a thin layer of articular cartilage is maintained. With aging, the subchondral bone front may advance, thinning the overlying cartilage. Osteoarthritis is associated with aging and is characterized by the thinning and progressive destruction of articular cartilage. Although the risk factors of osteoarthritis include hereditary factors, aging, trauma, and overuse, the exact role of biological and mechanical influences remains unclear.

Carter and coworkers (Carter, 1987;​ Carter, 1988;​ Carter et al., 1987b,c;​ Carter and Wong, 1990) have proposed that the process of endochondral ossification may be accelerated or decelerated in response to biological and mechanical factors. They have postulated that articular cartilage forms when endochondral ossification of the subchondral bone front is halted in response to a combination of high hydrostatic pressure and low shear stress near the joint surface. Osteoarthritic thinning of articular cartilage thus occurs when endochondral ossification of the subchondral bone is reinitiated, possibly in response to altered mechanical load. Previously, the above endochondral ossfication theory has been applied to models of ossification and cartilage preservation patterns during bone development and fracture healing, but it has not been used to describe endochondral bone growth. In addition, application of the above endochondral ossification theory to articular surfaces has not been examined in depth.

This thesis extends the endochondral ossification theory of Carter and coworkers to the processes of endochondral bone growth and articular cartilage layer development, maintenance and thinning. Computational models are used to simulate the response of cartilage to its biological and mechanical environment. An index of mechanobiological ossification stimulus is developed to mathematically combine the minimum hydrostatic (preserves cartilage) and maximum octahedral shear (promotes bone formation) stress which occurs within a region of cartilage during a complete loading cycle. The index of mechanobiological ossification stimulus allows predictions of temporal and spatial variations in endochondral ossification and cartilage preservation.

Theoretical and finite element models of endochondral growth and ossification are developed in a study of early long bone development (8 weeks gestation to 2 years after birth). This model incorporates both biological and mechanobiological influences on endochondral growth and ossification. A maturity index is formulated which reflects the progression of a region of cartilage through the sequence of endochondral ossification. The maturity index results correspond to histological distributions of proliferative, hypertrophic and mineralized cartilage in developing long bones. The model simulates growth of a bone rudiment, as well as developmental events including formation of the secondary ossific nucleus, growth plate and articular cartilage layer. In addition, bone remodeling algorithms have been included to simulate bone density changes during development.

A second study focused on the development and maintenance of articular cartilage thickness. Although several investigators agree that cartilage thickness is a reflection of mechanical loading, relationships between surface pressures and cartilage thickness have been difficult to establish. A finite element model of an idealized articular surface examines the effects of loading pressure magnitude, contact radius and cartilage thickness on the mechanical stresses within the cartilage layer. A threshold of mechanobiological ossification stimulus is assumed, below which endochondral ossification is assumed to halt. Final cartilage thickness is predicted to be the cartilage thickness at which the ossification stimulus calculated at the cartilage bone interface falls below the assumed threshold. A linear relationship between peak pressure magnitude and cartilage thickness is presented for a range of pressure contact areas. The results of this model suggest that for a given peak pressure magnitude, cartilage thickness decreases with decreasing pressure contact radius. In addition, cartilage thickness increases with increasing peak pressure magnitude. The pressure-thickness relationships presented in this thesis are consistent with several cartilage measurements reported in the literature.

A third study examined the role of mechanics in articular cartilage thinning and osteophyte formation which occur in osteoarthritis. A finite element model was used to calculate the stresses and index of mechanobiological ossification stimulus which occurred during uniform and non-uniform loading over a finite portion of an idealized articular surface. The results of this model suggest that the distribution and thickness of articular cartilage are dependent on the overall joint loading. Gradual decreases in thickness are predicted with gradual changes in pressure distribution magnitude within a complete loading cycle. However, ossification stimulus patterns consistent with subchondral advancement, cartilage thinning and osteophyte formation were predicted in response to loading cycles consisting of dramatically increased or decreased pressure magnitudes applied adjacent to baseline pressure magnitudes. The results of this study are consistent with the experimental findings of osteoarthritic thinning and osteophyte formation in response to a vastly different loading conditions such as traumatic overloading, joint immobilization and joint instability.

Several assumptions and material idealizations have been made in the interest of computational expense. However, this thesis successfully extends the endochondral ossification theory of Carter and colleagues to the processes of endochondral growth and articular cartilage development, maintenance and degeneration. In summary, the mechanical regulation of articular cartilage during adult life can be described by the same principles which guide endochondral growth and ossification during early development.