The role of mechanics in bone tissue maintenance has been recognized for well over a hundred years. However, the relative importance of mechanics compared to nutritional, hormonal and genetic factors has yet to be established. Today, a woman’s lifetime risk of death as a consequence of osteoporotic fracture is equivalent to her combined risk of death from breast, ovarian, and endometrial cancer. Understanding the relationship between mechanical forces and bone response will allow us to recommend effective treatments to combat the devastating effects of age-related bone loss.

Mathematical theories describe the relationship between mechanical stimuli and bone adaptive response. Theories of bone remodeling provide a framework for understanding and evaluating this physical phenomena and can predict the response of bone to altered loading. To date, the validation of remodeling theories has been largely subjective and qualitative, and the model parameters have only been estimated from clinical data. These parameters include the homeostatic set-point, the weight factor of number of cycles compared to the magnitude of load, and the rates of bone apposition and resorption. Improving estimates of the values of these parameters is essential to defining the relationship between mechanical stimuli and bone response, ultimately providing a viable clinical tool for assessing exercise treatment protocols.

The calcaneus, a large irregularly shaped bone in the hind foot, was selected as a site to evaluate bone adaptation theories. The calcaneus was chosen because it is an important clinical site for assessing skeletal status, it is sensitive to alterations in activity levels, and daily loading of the calcaneus is quantifiable using insole force sensors. In this dissertation a numerical model of the calcaneus is developed to be used with current imaging and novel activity monitoring techniques for evaluating mathematical theories of bone adaptation and predicting bone adaptive changes with altered activity.

The first study presented in this dissertation develops and validates a contact-coupled finite element model of the foot relating external, measurable daily loading to internal calcaneal stresses and strains. This model was used with cineradiographic gait data to examine the loading on the calcaneus throughout the gait cycle. Analyses showed that peak calcaneal loading occurs at 70% of the stance phase of walking and 60% of the stance phase of running. The temporal profiles of force generation corresponded with the temporal pattern of the moment about the ankle joint produced by the ground reaction force vector. The ligament, tendon, and joint contact forces scaled with the external moment, that for the walking and running velocities studied, had a scale factor of two. The results of this study also established a 1:​4 scaling between the strain energy generated at walking compared to running, at the velocities evaluated. A timed-temporal occurrence during the gait cycle of peak strain energy allowed several simplifying assumptions for implementing this problem in a remodeling simulation.

The second study applies the mathematical model of bone adaptation to the finite element model of the calcaneus. In order to assess the contribution of mechanics to calcaneal morphology and density, the effect of different lifetime activity levels including running, moderate and intense exercise intervention, and age-related decreases in activity levels. The simulations predicted that lifetime exercisers had substantially increased bone density over sedentary individuals. The simulations of moderate exercise intervention predicted density increases from 0.8 to 2.8% after one year, while intense exercise resulted in more substantial gains of 2.5 to 8.5%. Simulations of age-related bone loss suggested that over a 20% decrease in bone density between the ages of 30 to 65 could be explained by a diminishing activity level.

In the third study, physiological adaptation rates were determined based on clinical data of calcaneal bone loss during bedrest. Regional density heterogeneity in the calcaneus resulted in different volumetric resorption rates and absolute quantities of bone lost. The percentage of bone lost varied by 33% when a 5 mm diameter region-of-interest was used. Even when larger regions-of-interest were utilized, the percent of bone lost varied by 10% and the absolute density change varied by over 200%.

This dissertation establishes a numerical model of the calcaneus to quantitatively examine mathematical theories of bone remodeling by providing the critical link between external forces acting on the foot during daily activity and the in vivo calcaneal stresses. This work provides a framework for designing clinical studies and evaluating their results. Future work should include design of longitudinal exercise studies that monitor daily loading, combined with high precision volumetric bone imaging to evaluate the in vivo responses to altered loading. Extension of this work will allow us to predict bone adaptive response and make recommendations for patient-specific exercise treatment.