Monofractal and Multifractal Approach for the Fractal Modeling of the Porous Structure of the Trabecular Bone Matrix

Abstract

Fractal geometry presents a comprehensive mathematical richness capable of describing different aspects of irregular growth phenomena of which the bone structure is an example. In this context we can mention osteoporosis, which is a disease that reaches the bones. It is characterized when the amount of bone mass decreases substantially and develops hollow bones, fine and extremely sensitive, more subject to fractures. It is a variation in the density of the trabecular bone, or a variation in the quantity of trabeculae. Generic modeling of an irregular structure, such as that of the trabeculae of bone, will allow an analytical description of the phenomena resulting from the structure of these trabeculae within the models of bone growth, bone remodeling, osseointegration, etc. In this way, the theoretical models of these phenomena may incorporate the fractal aspects of the trabeculae, explaining them more appropriately, as well as the properties deriving from their geometry in a general way. The objective of this work is to develop a methodology for the measurement of void volume variation and volume variation of trabecular bone material based on fractals.