Dynamic relationships of trabecular bone density, architecture, and strength in a computational model of osteopenia.

A computational model was developed to study the effects of short- and long-term periods of disuse osteopenia and repair to elucidate the interrelationships between bone mass, architecture, and strength. The model is one in which the sequence of structural change events is followed in time. This temporal feature contrasts with studies of real trabecular tissue which are necessarily cross-sectional in nature and do not lend themselves to insights into the dynamic nature of the structural changes with time. In the model it was assumed that the stimulus for bone adaptation to mechanical load is the local mechanical strain rate, according to which the trabecular surfaces are differentially formed and resorbed. The effects of mechanical loading and unloading (disuse) on the cancelous bone properties were studied. The bone mass, architecture, and elastic stiffness were shown to be strongly dependent upon the period of the unloading phase, as well as the period of the reloading phase. Mechanical stiffness is demonstrated computationally to be a multivalued function of bone mass, if architecture is not accounted for. The model shows how the same value of trabecular bone mass can be associated with two or more distinct values of biomechanical stiffness. This result is the first explicit demonstration of how bone mass, architecture, and strength are related under dynamical load-bearing conditions. The results explain the empirical observation that bone mass can account for about 65% of the observed variation in bone strength, but that by incorporating measures of bony architecture into the analysis, the predictability is increased to 94%. The computational model may be used to explore the effects of different loading regimes on mass, architecture, and strength, and potentially for assistance in designing both animal and clinical bone loss studies.