Dissipation energy as a stimulus for cortical bone adaptation

We present a finite element study of a poroelastic rectangular beam subjected to oscillatory bending loads. This geometric model is chosen for simplicity, as an idealized representation of cortical bone. We then propose the use of the dissipation energy of the poroelastic flow as a mechanical stimulus for bone adaptation, and show that it can predict the effect of frequency of the applied load. Surface adaptation in the model depends on the weighted average of the mechanical stimulus in a "zone of influence" near each surface point, in order to incorporate the non-locality in the mechanotransduction of osteocytes present in the lacunae. We show that the dissipation energy stimulus and the resulting increase in second moment of inertia of the cross section increase linearly with frequency in the low frequency range (less than 10 Hz) and saturate at the higher frequency range (greater than 10 Hz). Similar non-linear adaptation frequency response also has been observed in numerous experiments. Our framework is readily extended to the modeling of cortical bone using actual bone geometries.