Comput Math Methods Med - Spongiosa primary development: a biochemical hypothesis by Turing patterns formations.

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Resumo

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.

Resumo Limpo

propos biochem model describ format primari spongiosa architectur bioregulatori model metalloproteinas mmp vascular endotheli growth factor vegf assum mmp regul cartilag degrad vegf allow vascular advanc ossif front presenc osteoblast coupl set molecul repres reactiondiffus equat paramet ture space creat stabl spatiotempor pattern lead format trabecula present spongi tissu experiment evid shown mmp regul vegf format assum vegf negat regul mmp format thus pattern obtain ossif may repres primari spongiosa format endochondr ossif moreov numer solut use finit element method newtonraphson method approxim partial differenti nonlinear equat ossif pattern obtain may repres primari spongiosa format endochondr ossif

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