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Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 748302, 14 pages
http://dx.doi.org/10.1155/2012/748302
Research Article

Spongiosa Primary Development: A Biochemical Hypothesis by Turing Patterns Formations

1Grupo de Investigación en Estudios y Aplicaciones de Ingeniería Mecánica (GEAMEC), Universidad Santo Tomás, Bogotá, Colombia
2Grupo de Modelado y Métodos Numéricos en Ingeniería (GNUM), Departamento de Ingeniería Mecánica y Mecatrónica, Facultad de Ingeniería, Universidad Nacional de Colombia, Bogotá, Colombia

Received 2 April 2012; Revised 24 May 2012; Accepted 5 June 2012

Academic Editor: Jérôme Noailly

Copyright © 2012 Oscar Rodrigo López-Vaca and Diego Alexander Garzón-Alvarado. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose a biochemical model describing the formation of primary spongiosa architecture through a bioregulatory model by metalloproteinase 13 (MMP13) and vascular endothelial growth factor (VEGF). It is assumed that MMP13 regulates cartilage degradation and the VEGF allows vascularization and advances in the ossification front through the presence of osteoblasts. The coupling of this set of molecules is represented by reaction-diffusion equations with parameters in the Turing space, creating a stable spatiotemporal pattern that leads to the formation of the trabeculae present in the spongy tissue. Experimental evidence has shown that the MMP13 regulates VEGF formation, and it is assumed that VEGF negatively regulates MMP13 formation. Thus, the patterns obtained by ossification may represent the primary spongiosa formation during endochondral ossification. Moreover, for the numerical solution, we used the finite element method with the Newton-Raphson method to approximate partial differential nonlinear equations. Ossification patterns obtained may represent the primary spongiosa formation during endochondral ossification.