Interpretação do comportamento e funcionamento da remodelação óssea através de modelos matemáticos

Abstract

Bone is a living tissue constantly renewing itself as it is capable to adapt its geometry and internal structure in response to mechanical and physiological demands. Bone adaptation consists of reabsorption of old bone and formation of new one. This adaptation is also called bone remodeling. The goal of bone remodeling is to prevent the accumulation of microdamage to minimize the possibility of bone fracture and keep mineral homeostasis of bone. The bone remodeling mechanism includes complex processes that depend on factors like biochemical interactions, coordination of the basic multicellular unit (BMU) activities and the feedback from mechanical stimuli. The BMU is composed by osteoblasts and osteoclasts. Achieving new insights about the bone remodeling machinery has been curtailed by the complexity of this mechanism. In vivo or in vitro tests alone fail to provide new hypotheses. To better understand this mechanism, it is useful to develop new mathematical models for the integration of theoretical knowledge in mathematical expressions that allow us to understand the most relevant interactions and to develop virtual simulations to formulate new hypotheses. I present in this work, a review of some mathematical and computational models for the bone remodeling proposed to date. There are two areas of study for development of mathematical models: a mechanical level and metabolic level. Mathematical models developed at these two levels can aim at describing the behavior and function of bone remodeling. After that, a new mathematical model will be created and will includes mechanical and metabolic factors. Moreover, the simulation of different scenario like disease, treatment and mechanical stimulation will be simulated by the new mathematical model. The results generated by the new model are compared with the results of the models reviewed in this thesis. These comparisons show that the results are qualitatively similar between the new model and the model of the other authors.

Date of Award	May 2011
Original language	Portuguese
Awarding Institution	Universidade Católica Portuguesa
Supervisor	Braga, José J. C. da Costa Pinto (Supervisor) & Jorge M. B. S. Rebelo (Co-Supervisor)