Simulation of orthotropic microstructure remodelling of cancellous bone.

Abstract

A computational model of adaptive bone remodelling is formulated as an optimization problem of instantaneous changes in microstructure that minimize a functional describing the structure quality rate. Microstructure is locally described by a set of scalar geometric parameters. Macroscopic (continuum) elastic properties are assumed orthotropic and expressed as known functions of the geometric parameters. Strain energy is considered the quality measure of bone at given load conditions. The instantaneous rate of geometric parameters is postulated to minimize the rate of the quality functional. An optimization problem is formulated in the continuum description and then it is discretized both in space and time. Numerical simulations predict bone remodelling for femur without and with a hip endoprosthesis.