This study aims to numerically investigate the influence of low-intensity pulsed mechanical impact, simulating extracorporeal shockwave therapy, on the stress and strain state of the osteon system in cortical bone tissue. The focus is on assessing the mechanical conditions that trigger either bone resorption or remodeling processes. A three-dimensional structural-mechanical model of a single osteon and an osteon conglomerate was developed using the movable cellular automaton method. This particle mechanics approach incorporated a poroelastic constitutive model based on Biot’s theory to account for the interstitial fluid in the bone matrix. The osteon was represented as a multi-layered cylinder with depth-dependent permeability of the lamellae. The validation of the single osteon model demonstrated good agreement with reference data for pore pressure distribution. The analysis of remodeling conditions was based on thresholds for mean stress, equivalent shear strain, and interstitial fluid pressure. The calculated anisotropy of the effective elastic moduli for the osteon system between extreme orientations (parallel and perpendicular to the osteon axis) was found to be less than 20%, justifying the use of isotropic models at the macroscale. Simulations revealed that the pulsed mechanical impact with an energy flux density (EFD) of 0.05–0.1 mJ/mm2 applied perpendicularly to the osteon axis induced adequate fluid pressure for stem cell migration in 80% of the Haversian canal volume. Concurrently, mean stress levels (0.04–0.2 MPa) conducive to osteoblast differentiation were generated in the lamellar region. In contrast, loading parallel to the osteon axis produced this beneficial environment in only 30% of the canal volume. EFD levels exceeding 0.25 mJ/mm2 generated critical tensile stresses, potentially leading to microdamage at the osteon boundaries. As a conclusion, the findings suggest that the extracorporeal application of the mechanic impact, directed perpendicular to the bone surface at a medium intensity range, is the most effective protocol for promoting targeted bone regeneration.

Alexey Y. Smolin, Doctor of Physics and Mathematics, Professor; e-mail: asmolin@ispms.ru; https://orcid.org/0000-0003-0213-1701; AuthorID: 203461

Galina M. Eremina, Candidate of Physics and Mathematics Scientific Researcher; e-mail: anikeeva@ispms.ru; https://orcid.org/0000-0003-3346-367X; AuthorID: 676130