ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

BIOCHEMICAL MODEL TO PREDICT THE ONSET OF THE
PRIMARY SPONGIOSA ARCHITECTURE USING A REACTION-
DIFFUSION SYSTEM
1. ABSTRACT
O. R. López-Vaca 1 and D.A. Garzón-Alvarado 2
In this work we propose a biochemical model that describe the formation of primary
spongiosa architecture by means of a bioregulator model that include two molecular
factors VEGF (vascular endothelial growth factor) and MMP13 (matrix
metalloproteinase 13) release by hypertrophic chondrocytes during the endochondral
growth. It is supposed that MMP13 regulates the cartilage degradation, and VEGF allow
the vascularization and ossification front progress by means of osteoblastic cells present
on the woven bone. The coupling of this set of molecules is represented by means of
reaction-diffusion equations with parameters in the Turing space. These equations
determine a time-stable spatial pattern, similar to the patterns present on the primary
spongiosa. The experimental evidence has shown that MMP13 regulates the VEGF
expression, and we hypothesized that VEGF negatively regulates the MMP13
expression. Of this way, the ossifications patterns obtained may represent the formation
of the primary spongiosa. To the numerical simulation was used the finite element
method with the Newton-Raphson method to approximate the no-linear partial
differential equations. As a result we obtained a mathematical model capable of
reproduce with detail the architecture 3D of the primary spongiosa, including the effect
of molecular factors VEGF and MMP13, and allowing the variation of the porosity and
trabecular thickness.
2. INTRODUCTION
Most of the long bones of the mammals skeletal system are developed from a process
called endochondral growth[1–4]. In the process of endochondral development, growth
and elongation of the bones are made by the continuous addition of cartilage and
subsequent replacement by bone tissue.
During the differentiation process of chondrocytes the matrix composition changes
dramatically, through the production of other components such as collagen type X, the
expression of metalloproteinases and subsequent calcification. At the same time the
blood vessels invade the calcified cartilage bringing osteoblasts which build immature
bone. Chondrocytes in the growth plate are subjected to the influence of excess
extracellular factors including systemic and soluble local factors as well as extracellular
1
Professor, Department of Mechanical Engineering, Universidad Santo Tomás. Bogotá-Colombia,
oscarlopez@usantotomas.edu.co.
2
Professor, Department of Mechanical and Mechatronics Engineering, Universidad Nacional de
Colombia. Bogotá-Colombia