The primary mechanical function of bones is to provide rigid levers for muscles to pull against and to remain as light as possible to allow for efficient locomotion. To accomplish this function, bones must adapt their shape and architecture efficiently. Bone tissue during skeletal growth and development continuously adjusts its mass and architecture to changing mechanical environments.
The trabecular structure in bone is the result of a dynamic remodeling process controlled by mechanical loads.
In this study, the process of adaptive bone remodeling is investigated mathematically and simulated by a finite element model. Bone tissue is described as continuous material with variable mass density. Topology optimization and cellular automata models are adopted with the aim to characterize the osteocytes located within the bone as sensors of mechanical signals.
An implemented optimization process provides structures resembling actual trabecular architectures and aligning them with the actual principal stress orientation. Two cost indices are derived from the structural optimization task of simultaneously minimizing the weight and maximizing the stiffness of the investigated domain. A trabecular architecture characterized by the highest structural efficiency is showed as result of the proposed optimal control process.
Optimal control PID control Finite element method (FEM) Bone functional adaptation Minimum mass Maximum stiffness
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This research was partially funded by Sapienza University of Rome under Progetto di Ateneo 2004 grant no. C26A044385, Progetto di Ateneo 2005 grant no. C26A059503 and Progetto di Università 2008 grant no. C26A08E7B3.
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