A continuum model for the bio-mechanical interactions between living tissue and bio-resorbable graft after bone reconstructive surgery

Abstract

We introduce a two-constituent porous continuum as a model describing the long-term growth/resorption phenomena in bone tissues grafted with bio-resorbable materials as driven by mechanical loads. The proposed model is able to account for the interplay between mechanical and biological phenomena which are known to be important for the bone tissue synthesis and the resorption of both bone tissue and bio-material. In particular, in the presented model the Lagrangian apparent mass densities of the natural bone and of the artificial material evolve in time according to precise ordinary differential equations. These latter are obtained by postulating a growth/resorption law and suitable constitutive equations conceived to account for the influence on bone resorption and synthesis of the action of different applied external loads as mediated by biological stimulus. The considered constitutive equations are chosen on the basis of the known biological phenomena occurring in bone resorption and synthesis. We present some numerical simulations for rod-bones subjected to axial external load. These numerical simulations allow for the description of the most desirable situation in which a gradual resorption of the artificial material takes place together with the contemporary formation of new bone, finally giving rise to an almost complete replacement of the artificial material with natural living tissue. (C) 2011 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved

A 2‐D continuum model of a mixture of bone tissue and bio‐resorbable material for simulating mass density redistribution under load slowly variable in time

“…These equations have been obtained by postulating growth/resorption laws and constitutive equations which account for the influence on bone resorption and synthesis of the action of different applied external loads as mediated by biological stimulus. In this paper the above mentioned general model was used to account for the effects associated with the second dimension not considered in the previous papers [32,36]; these effects might be important in future validation of proposed model with respect to experimental tests. The size effect of the present 2D investigation consists in the influence of the boundary conditions; due to the lower stimulus at the borders, a more intense remodelling activity occurs far from the edges of the domain, which might be important in the case of metallic implants application.…”

“…This model has been formulated by [32,36] considering the mixture as linear elastic; a 3D spatial model was presented and was used by them to work out numerical examples in 1D space. This model is able to account for the interaction between mechanical and biological phenomena which are known to be important for the bone tissue synthesis and the resorption of both bone tissue and www.zamm-journal.org bio-material.…”

“…Therefore to describe some of the biological mechanisms occurring in bone/bio-resorbable material solid mixture we introduce a relation between the bone-tissue and bio-resorbable material mass densities and the density of active sensor cells, d(ρ b ), i.e. the number of osteocytes per unit volume which are able to measure the mechanical state and send the signal which will act as stimulus for the actor cells (such sensor cells are present only in living bone-tissue) [32,36]:…”

On the contribution of Angelo Luongo to Mechanics: in honor of his 60th birthday

“…In a recent workshop held at the M&MoCS center, concerning the critical role of applied external load, Prof. Luongo recognized as a double Hopf bifurcation the phenomenon which has been observed in bone tissue reconstruction. When this load is under a given threshold (see, e.g., [117][118][119]), then the reconstruction process cannot be completed, and there is a cavity formation; in other cases, either the bone is completely reconstructed (and the scaffold material is totally removed, which is the most desirable possibility), or the bioresorbable material remains trapped inside the reconstructed bone, which makes the final tissue weaker than what is desired. We expect that a careful study of the strongly nonlinear evolution equations which govern the proposed models by using MSM may supply a guidance to interesting engineering optimization problems.…”

Advanced finite element analysis of L4–L5 implanted spine segment

“…The biomechanical performances of the whole system implanted prosthesis-growing bone may be greatly improved by the application of such a technique, even if serious theoretical and experimental investigations are still needed [15][16][17][18]. In addition to this, another problem related to an implant application, i.e.…”