A lumped model for long bone behavior based on poroelastic deformation and Darcy flow

Area of Science:

• Biomechanics
• Materials Science
• Fluid Dynamics

Background:

• Compact bone exhibits complex behavior influenced by fluid flow and its porous elastic structure.
• Previous studies have noted the importance of pressure history but lacked a simplified model.
• Understanding bone's poroelastic properties is crucial for predicting its mechanical response.

Purpose of the Study:

• To develop a simplified, lumped model for compact bone behavior.
• To investigate the coupled effects of bone fluid flow and poroelasticity.
• To highlight the significance of pressure history, particularly pressure impulse, on bone displacement.

Main Methods:

• Modeling compact bone as a layered poroelastic structure.
• Utilizing Darcy's model (1856) for fluid flow in channels.
• Incorporating Biot's model (1941) for fluid changes within the porous solid.
• Predicting normal pressure versus displacement (stress-strain curve).

Main Results:

• The simplified model predicts normal pressure versus displacement, yielding a stress-strain curve.
• Bone displacement is parametrically dependent on porosity, permeability, and crucially, pressure history.
• The pressure impulse (integral of pressure over time) is identified as a key factor influencing bone displacement.

Conclusions:

• The developed lumped model offers a simplified yet effective approach to understanding compact bone mechanics.
• Fluid flow dynamics, as described by Darcy and Biot, are integral to bone's elastic response.
• The findings align with previous detailed numerical simulations and experimental results, validating the simplified model.