# Gradient mechanical environments modulate intra-osteonal fluid flow: a three-dimensional finite element study

## TL;DR

This study uses a 3D model to show how mechanical forces and blood pressure affect fluid flow in bone, which is important for bone health and disease.

## Contribution

A novel 3D finite element model with gradient boundary conditions to quantify fluid flow in bone under various mechanical and vascular conditions.

## Key findings

- Peak pore pressure, fluid velocity, and fluid shear stress increased linearly with strain magnitude.
- Relaxing outer wall constraints significantly reduced pore pressure, fluid velocity, and fluid shear stress.
- Elevated pulsatile blood pressure increased pore pressure but had minimal effect on fluid velocity and shear stress.

## Abstract

Interstitial fluid flow within the osteonal lacunar-canalicular system (LCS) is crucial for osteocyte mechanotransduction and bone remodeling. This study aims to develop a three-dimensional finite element model of an osteon with gradient-varying boundary conditions to systematically investigate how mechanical loading, outer wall constraints, and pulsatile blood pressure modulate intra-osteonal fluid flow.

This study constructs a three-dimensional finite element model to systematically analyze the dynamic responses of fluid flow behavior under gradient boundary conditions. Gradient parametric analyses were performed by varying: (1) axial strain amplitudes (250–5000 με) to simulate different activity levels; (2) radial displacement constraints at the outer wall (0– 0.042 μm) to represent confinement by surrounding tissues; and (3) pulsatile blood pressure amplitudes (A = 0–2.5) at the inner wall to mimic physiological to hypertensive conditions. The resulting pore pressure, fluid velocity, and fluid shear stress (FSS) distributions were analyzed.

All parameters exhibited axisymmetric distributions. Peak pore pressure, fluid velocity, and FSS increased nearly linearly with strain magnitude, ranging from 1.7×104 to 1.4×105 Pa, 1.69×10-8 to 3.50×10-8 m/s, and 0.34 to 6.5 Pa, respectively. Relaxation of outer wall constraints from fully constrained (0 μm) to fully elastic (0.042 μm) significantly reduced all three parameters. Elevated pulsatile blood pressure markedly increased intra-osteonal pore pressure (from 2.7×104 to 6.5×104 Pa) but had minimal effect on velocity and FSS. A subsequent multiscale validation using an explicit LCS model showed that the macro-scale poroelastic model accurately captures global trends, while local FSS within canaliculi is amplified by a factor of 1.5–2.5.

The gradient boundary condition approach effectively quantifies the differential and synergistic effects of mechanical load, structural constraint, and vascular pressure on the osteonal fluid environment. These findings provide a quantitative framework for understanding mechanotransduction in bone and may inform clinical strategies for managing bone adaptation and disease.