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

Angela Madeo; Tomasz Lekszycki; Francesco dellʼIsola

doi:10.1016/j.crme.2011.07.004

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

Angela Madeo ^1,² ; Tomasz Lekszycki ^3,^2,⁴ ; Francesco dellʼIsola ^5,^6,²

¹ Laboratoire de génie civil et ingénierie environnementale, université de Lyon–INSA, bâtiment Coulomb, 69621 Villeurbanne cedex, France
² International Center M& MOCS, University of LʼAquila, Palazzo Caetani, Cisterna di Latina, Italy
³ Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw, Poland
⁴ Warsaw Medical University, Lindleya 4, 02-005 Warszawa, Poland
⁵ Dipartimento di Ingegneria Strutturale e Geotecnica, Università di Roma La Sapienza, Via Eudossiana 18, 00184 Roma, Italy
⁶ Laboratorio Strutture e Materiali Intelligenti, Fondazione Tullio Levi-Civita, Via S. Pasquale snc, Cisterna di Latina, Italy

Comptes Rendus. Mécanique, Volume 339 (2011) no. 10, pp. 625-640.

Résumé

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.

Reçu le : 2010-10-14
Accepté le : 2011-07-19
Publié le : 2011-08-18

DOI : 10.1016/j.crme.2011.07.004

Mots clés : Biomechanics, ODEs governing growth/resorption, Coupling between mechanical and biological stimuli, Artificial bio-resorbable material, Continuum solid-mixture model, Load-induced replacement of artificial material with natural bone tissue, Numerical simulations

Affiliations des auteurs :

Angela Madeo ^{1, 2} ; Tomasz Lekszycki ^{3, 2, 4} ; Francesco dellʼIsola ^{5, 6, 2}

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     author = {Angela Madeo and Tomasz Lekszycki and Francesco dell'Isola},
     title = {A continuum model for the bio-mechanical interactions between living tissue and bio-resorbable graft after bone reconstructive surgery},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {625--640},
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Angela Madeo; Tomasz Lekszycki; Francesco dellʼIsola. A continuum model for the bio-mechanical interactions between living tissue and bio-resorbable graft after bone reconstructive surgery. Comptes Rendus. Mécanique, Volume 339 (2011) no. 10, pp. 625-640. doi : 10.1016/j.crme.2011.07.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2011.07.004/

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