Double site-bond percolation model for biomaterial implants

TL;DR

This paper introduces a double site-bond percolation model to simulate vascularization, resorption, and mechanical stability of biomaterial implants in bones, distinguishing biological and physical influences.

Contribution

It develops a novel dual-network percolation model that captures the dynamic transformation and interaction of biological and physical processes in bone implants.

Findings

Model successfully differentiates biological and physical parameters.

Numerical simulations demonstrate percolation regimes relevant to implant stability.

Framework applicable to two-dimensional implant scenarios.

Abstract

We present a double site-bond percolation model to account, on the one hand, for the vascularization and/or resorption of biomaterial implant in bones and, on the other hand, for its mechanical continuity. The transformation of the implant into osseous material, and the dynamical formation/destruction of this osseous material is accounted for by creation and destruction of links and sites in two, entangled, networks. We identify the relevant parameters to describe the implant and its evolution, and separate their biological or chemical origin from their physical one. We classify the various phenomena in the two regimes, percolating or non-percolating, of the networks. We present first numerical results in two dimensions.