Informing phenomenological structural bone remodelling with a mechanistic poroelastic model

Studies suggest that fluid motion in the extracellular space may be involved in the cellular mechanosensitivity at play in the bone tissue adaptation process. Previously, the authors developed a mesoscale predictive structural model of the femur using truss elements to represent trabecular bone, relying on a phenomenological strain-based bone adaptation algorithm. In order to introduce a response to bending and shear, the authors considered the use of beam elements, requiring a new formulation of the bone adaptation drivers. The primary goal of the study presented here was to isolate phenomenological drivers based on the results of a mechanistic approach to be used with a beam element representation of trabecular bone in mesoscale structural modelling. A single-beam model and a microscale poroelastic model of a single trabecula were developed. A mechanistic iterative adaptation algorithm was implemented based on fluid motion velocity through the bone matrix pores to predict the remodelled geometries of the poroelastic trabecula under 42 different loading scenarios. Regression analyses were used to correlate the changes in poroelastic trabecula thickness and orientation to the initial strain outputs of the beam model. Linear (R(2) > 0.998) and third-order polynomial (R(2) > 0.98) relationships were found between change in cross section and axial strain at the central axis, and between beam reorientation and ratio of bending strain to axial strain, respectively. Implementing these relationships into the phenomenological predictive algorithm for the mesoscale structural femur has the potential to produce a model combining biofidelic structure and mechanical behaviour with computational efficiency.