Bone Remodeling as a Hybrid Cellular Automaton Optimization Process

Biological structures are continually adapting to changes in their physical environment. In bones, for example, it has been widely accepted that mineral tissue is resorbed in regions exposed to low mechanical stimulus, whereas new bone is deposited where the stimulus is high. This process of functional adaptation is thought to enable bone to perform its mechanical functions with a minimum of mass. Many theoretical models for bone remodeling use this concept as part of the strategy to simulate bone structural adaptation. These models imply the existence of an equilibrium state where the bone structure is adapted to the environment and no net remodeling is required. The first practical computational models were developed under the assumption of isotropy of the trabecular structure in the continuum level. Despite the similarities in density distribution with in-vivo bone, no convergent solution was possible to obtain. Recent models have been developed to consider the anisotropic nature of the trabecular bone in the continuum level making use of optimization principles; however, despite of some mechanical aspects reflected by these idealized microstructures, they just represent a mathematical abstraction of the trabecular architecture. The objective of this investigation is to develop an algorithm that incorporates tissue-level mechanisms of bone functional adaptation compatible with both phenomenological and optimization approaches. This technique makes use of the cellular automaton paradigm and concepts of structural optimization. The algorithm also incorporates the finite element method to perform structural analysis over a design domain that represents the bone structure. This design domain is composed of a lattice of sensor cells or cellular automata. These cells activate local processes of formation and resorption with changes in their relative variable mass. Parameters of the proposed algorithm include mechanotransduction of the mechanical stimulus and intracellular communication. This algorithm has been applied to a variety of tissue-level models which exhibit self trabeculation for all parameters applied. The resulting trabecular structure is also incorporated into a continuum level model in which the anisotropic nature of the trabecular bone is determined by direct simulation and not by a mathematical approximation.