Bone’s microarchitecture, strength and density change throughout our lifetime through the natural process of bone adaptation. With age, the mechanisms that normally maintain bone’s mechanical competence are disrupted and rapid bone loss ensues. In an attempt to understand these mechanisms, many theories and computational models were developed. But to date, few of these models have been rigorously tested in vivo. The first objective of this thesis was to develop a computational technique to validate bone adaptation models in vivo. Specifically, an inverse problem was defined that identifies participant-specific bone adaptation parameters from high-resolution computed tomography (CT) image data of changing bone microarchitecture. The inverse problem was based on a model of advection and mean curvature flow (curvature-driven bone adaptation). The inverse technique was accurate for synthetic data that exactly obeyed the curvature-driven model;​ it was insensitive and robust to small amounts of salt-and-pepper.

Based on a solver that was accurate for data that obeyed the curvature-driven model, it was possible to test the model itself on longitudinal in vivo data. Sixteen astronauts who spent between four and seven months on the International Space Station received high-resolution peripheral quantitative computed tomography (HR-pQCT) scans before and after flight. The inverse problem was solved for each participant, and bone samples were simulated to match the HR-pQCT images at each measurement. Predicted and observed static morphometry (trabecular thickness, separation, number and bone volume fraction) agreed well, but dynamic morphometry (bone formation and resorption rates) indicated a poor fit.

While the mean curvature model did not predict local bone adaptation in astronauts, a framework was developed that will allow researchers to test any model in vivo on a participant-specific basis. The inverse problem is versatile and general and could easily be adjusted for other models (i.e., strain-driven or other geometric flows). By rigorously testing hypotheses regarding bone adaptation in vivo, researchers will better understand the mechanisms of bone loss in space and on Earth.