Mathematical Model for Osteobstruction in Bone Regeneration Mechanisms: A Headway in Skeletal Tissue Engineering

Abstract

In this paper, we formulate a mathematical model for the evaluation of parameters responsible for the retardation and eventual acceleration of bone regeneration on the contralateral side of the mandible of experimental animals, following the discovery of a new mechanism of bone regeneration called the osteobstruction mechanism (a negative mechanism of bone regeneration as opposed to the well established and extensively documented positive mechanisms such as osteogenesis, osteoinduction and osteoconduction). This osteobstructive mechanism was demonstrated by episodes of overtaking and reovertaking on single photon emission computed tomography (SPECT) following evaluation of osteoblastic activities in a sequential animal experiment to validate both the Ogunsalu sandwich technique (a double guided tissue technique; D-GTR) and the interceed membrane technique (a single guided tissue regeneration technique; S-GTR) utilizing SPECT, histological and histomorphometric evaluation. This work is now given special attention in terms of mathematical analysis because of limited experimental observations since experiments cannot be observed infinitely. Mathematical modelling is as such essential to generalize the results of this osteobstructive mechanism in bone regeneration. We utilize the Fisher's equation to describe bone cell mobilization during bone regeneration by two different techniques: the Ogunsalu sandwich bone regeneration technique (D-GTR) and the S-GTR.