A new model of bone remodeling and turnover set up in the framework of generalized continuum mechanics

Abstract

In the past few decades, numerous studies have attempted to address the various phenomena that take place simultaneously during bone remodeling. Drawing from Frost’s “mechanostat theory,” multiple phenomenological models of varying complexity have been developed to describe bone remodeling in terms of evolution of bone porosity, tissue properties, and mineralization. The main goal of this paper is to present the general theory of a novel macroscopic and comprehensive model of bone remodeling accounting for the interactions of mechanics and biochemistry at the microscale. Two independent remodeling mechanisms are considered: the rotation of the material axes and the turnover of bone material. The former mechanism is related to the change of orientation of bone microstructure. Bone turnover refers to the dynamic process of bone resorption by osteoclasts, formation of unmineralized bone by osteoblasts, and mineralization. The model is set up in the framework of generalized continuum mechanics. The evolution of bone tissue is thus described through its macroscopic deformation as well as macroscopic variables related to the orientation of bone microstructure and bone tissue composition (porosity, unmineralized and mineralized bone matrix). Thermodynamically consistent evolution laws of bone material are obtained by enforcing suitable statements of the virtual power principle and of the dissipation principle. Moreover, additional constitutive hypotheses are formulated to develop a phenomenological law of bone turnover. The turnover model is discussed on the basis of a number of numerical simulations. Although the model can capture the main features of bone turnover, it cannot describe satisfactorily the complexity of the underlying biological crosstalk, highlighting the need of a more refined mechanobiological constitutive theory of bone turnover.