Influence of interstitial fluid pressure, porosity, loading magnitude, and anisotropy in cortical bone adaptation

Adaptive elasticity in cortical bone has traditionally been modeled using Strain Energy Density (SED). Recent studies have highlighted the importance of interstitial fluid in bone adaptation, yet no research has quantified the role of interstitial fluid pressure and its effects, specifically incorporating both SED and interstitial fluid pressure in the adaptation process. This study introduces a novel formulation combining theory of porous media and theory of adaptive elasticity that considers both SED and interstitial fluid's pressure in cortical bone adaptation. The formulation is solved using ANSYS Fluent and a MATLAB script, and sensitivity analyses were conducted, analyzing various porosities, loading magnitudes, anisotropic properties of cortical bone, and involvement coefficients of interstitial fluid's pressure. This study reveals that bones with different vascular porosities (PV) tend to achieve similar density distributions under uniform loading over time. This highlights the significant role of interstitial fluid pressure in accelerating the convergence to optimal bone properties, especially in specimens with larger PV porosities. The findings emphasize the importance of fluid pressure in bone remodeling, aligning with previous studies. Furthermore, this study demonstrates that considering transversely isotropic material properties can significantly alter the remodeling configuration compared to isotropic material properties. This highlights the importance of accurately representing the anisotropic nature of cortical bone in models to better predict its adaptive responses. However, aspects such as fluid density variations and bone geometry changes remain unexplored, suggesting directions for future research. Overall, this research enhances the understanding of cortical bone adaptation and its mechanical interactions.