Biomaterials 26 (2005) 6788–6797 Mathematical modelling of the distribution of newly formed bone in bone tissue engineering Laurent Pothuaud a , Jean-Christophe Fricain a,b , Stephane Pallu a , Reine Bareille a , Martine Renard c , Marie-Christine Durrieu a , Michel Dard d , Michel Vernizeau e , Joelle Ame ´de´e a, a INSERM U577, Universite ´ Victor Segalen Bordeaux 2, 33076 Bordeaux Cedex, France b UFR Odontologie, Universite ´ Victor Segalen Bordeaux 2, Bordeaux, France c CIT, CHU de Bordeaux, Bordeaux, France d Biomet-Merck Biomaterials, Darmstadt, Germany e Biomet-France, Valence, France Received 24 September 2004; accepted 11 April 2005 Available online 13 June 2005 Abstract New bone formation in bone substitutes is usually investigated by histomorphometric global analysis. This study provide mathematical modelling approach of new bone formation in the use of osteoinductive and functionalized biomaterials for bo tissue engineering. We discuss here the repartition and the probability to get new bone formation inside Biphasic Calcium (BCP) loaded with autologous osteogenic cells, functionalized with a cyclo RGD peptide, after implantation in rabbits for 2 weeks. This local analysis allowed us to complement classical global findings and to demonstrate that after 2 weeks of imp the probability ofnew bone formation was significantly higher in RGD-grafted BCP and that new formed bone was largely distributed from the edge to the centre of the implant. While no significant differences were obtained after 4 weeks of imp between RGD-grafted and non-grafted materials, distribution ofnew boneformation insideRGD-grafted materialswas significantly more homogeneous as demonstrated by our mathematical modelling approach. In conclusion, localanalysis of new bone formation inside macroporous substitutes coupled with mathematical modelling constitutes a potential quantitative a for the evaluation of the osteoconductive and osteoinductive characteristics of such biomaterials. r 2005 Elsevier Ltd. All rights reserved. Keywords: RGD peptide; Animal model; Image analysis; Modelling 1. Introduction With advancesin understandingtissue–material interactions [1,2] and bioengineering, several strategies can be exploited to develop efficient bone substitutes, based on macroporousbiomaterials, when they are associated with stem cells [3,4] or osteoinductive factors [5].The application of relevant exploration methods to analyze the amount of new bone formation in such biomaterials is absolutely required to evaluate their osteoconductive and osteoinductive properties. The bone defect treatment usually requires the use of bioactivematerialssuch as calcium carbonate [6,7], hydroxyapatite [8], bioglass [9], tricalcium phosphate [10,11],orbiphasicceramicsofhydroxyapatiteand b-tricalcium phosphate [12,13].These materialsare biocompatibleandhaveosteoconductiveproperties because they serve as a scaffold for osteoblastic cells [3].However,none of these materials have osteoinduc- tive properties like autograft which is still the reference processfor defecthealing.While autogeneous bone ARTICLE IN PRESS www.elsevier.com/locate/biomaterials 0142-9612/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.biomaterials.2005.04.002 Corresponding author. Tel.: +33 557571737; fax: +33 556900517. E-mail address: joelle.amedee@bordeaux.inserm.fr (J. Ame ´de´e).