Modeling of Bone Adaptation
We know that bone is a living tissue and it undergoes a complex process of adaptation in response to its chemical and mechanical environment. A number of researchers have observed that bone adaptation depends strongly on the mechanical loading, specifically on the magnitude and frequency, number of cycles, number of bouts, time between the bouts etc. Numerical models have been used to predict bone adaptation, but most of the existing work in the literature (a) cannot predict the adaptation response on a real model of cortical bone, (b) does not provide any quantitative comparisons of the predictions to existing experimental results, and (c) does not account for the effect of the various loading parameters on the adaptation response. We develop a finite element (FE) based framework to simulate the external adaptation response of rat ulna. The FE meshes were generated from actual geometric data. Growth is realized by normal displacement of the surface nodes of the FE model using a phenomenological growth law. We investigate the use of elastic and poroelastic material models and mechanical stimuli to efficiently simulate the bone growth. We show that the numerical model can predict the effect of magnitude and number of bouts of loading on the growth response, by modeling the bone as an elastic material and using strain energy density as the stimulus. We also show that the effects of frequency of loading on the adaptation response can be simulated by using a poroelastic material model and incorporating a new frequency-dependent mechanical stimulus, which was developed based on thermodynamic considerations. Numerical results from a parametric study are used to describe the effects of the different parameters of the growth law on the adaptation response.