Spongiosa Primary Development: A Biochemical Hypothesis by Turing Patterns Formations

Oscar Rodrigo López-Vaca,Diego Alexander Garzón-Alvarado

doi:10.1155/2012/748302

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.

Highlights

Most of the long bones of the mammals skeletal system are developed from a process called endochondral growth [1,2,3,4]
We assume the existence of a reaction-diffusion system where two primary molecules are involved, such as vascular endothelial growth factor (VEGF) and model by metalloproteinase 13 (MMP13), which can lead to a stable pattern in time and unstable in space, similar to the patterns present in the structure of the trabecular bone during endochondral ossification
This means that when MMP13 and VEGF exist in all regions of the epiphyseal cartilage, having a high concentration of VEGF, there will be an adequate control of the invasion of endothelial cells, osteoclasts, chondroclasts, and osteoblasts, which are present in the primary ossification development [40]

Summary

Introduction

Most of the long bones of the mammals skeletal system are developed from a process called endochondral growth [1,2,3,4]. This process ends with the gradual production of bone from cartilage tissue during fetal development and postnatal growth. The ossification centers invade the cartilage gradually until it is completely replaced by bone tissue, except the articular surfaces. In this way, and eventually the bones reach their skeletal maturity [10]. The processes of endochondral development, growth, and elongation of the bones are made by the continuous addition of cartilage and subsequent replacement by bone tissue

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