The role of loading memory in bone adaptation simulations

The concept that bone responds to a time-averaged value of its current mechanical loading forms the basis for many computational bone adaptation algorithms. Some mathematical formulations have incorporated a quantification of the loading experienced during a single "average" day and thus implicitly assume that bone responds abruptly to changes in its loading history. To better reflect the time delays inherent in bone cell recruitment and activation processes, we included a fading memory of past loading. Implementing an exponentially fading memory with time constants of 5, 20, and 100 days, we simulated bone adaptations to abrupt and gradual changes in mechanical loading. Both an idealized single degree-of-freedom model and a finite element model of the proximal femur were studied. A time constant of 5 days produced time-dependent density changes that were negligibly different from those of the standard approach without memory. Models with higher time constants produced significant transient time lags (up to 8.1% difference) in the predicted short-term (3 months) bone density changes. A time constant of 100 days produced overshoots (by approximately 1%) of the eventual steady-state. All models predicted comparable long-term (after several years) steady-state adaptations. Future experimental analyses will be necessary to better determine appropriate fading memory time constants for bone under various loading conditions.