Non-linear bone remodelling: an existence and uniqueness result

Abstract

Several models have been proposed in order to be able to predict the correct density and stress distributions on long bones. Most of them are of an empiric and/or experimental nature. A few are related to optimization techniques, in the framework of elasticity theory. In this work, we establish an existence and uniqueness result for a modified Cowin–Hegedus model. This models is of great importance not only because it is one of the most sophisticated including a great number of the existing models, but also because it is set in the framework of adaptive elasticity theory giving a sound basis for the development of robust numerical methods. Copyright © 2000 John Wiley & Sons, Ltd.

Analysis of a bone remodeling model

“…During the last ten years, some papers dealt with mathematical issues of these models as the existence and uniqueness of weak solutions under some quite strong assumptions (see, e.g., [14,15,16,17,19]), the analysis of an asymptotic rod model ( [6,7,8,9]) or the numerical stability of finite element models ( [11]). Here, our aim is to continue [16], providing the numerical analysis of a fully discrete algorithm and performing some numerical simulations which demonstrate its accuracy and its behavior.…”

Analysis of a bone remodeling model

“…During the last ten years, some papers dealt with mathematical issues of these models as the existence and uniqueness of weak solutions under some quite strong assumptions (see, e.g., [14,15,16,17,19]), the analysis of an asymptotic rod model ( [6,7,8,9]) or the numerical stability of finite element models ( [11]). Here, our aim is to continue [16], providing the numerical analysis of a fully discrete algorithm and performing some numerical simulations which demonstrate its accuracy and its behavior.…”

Analysis of a bone remodeling model

“…During the last ten years, some papers dealt with mathematical issues of these models as the existence and uniqueness of weak solutions under some quite strong assumptions (see, e.g., [14,15,16,17,19]), the analysis of an asymptotic rod model ( [6,7,8,9]) or the numerical stability of finite element models ( [11]). Here, our aim is to continue [16], providing the numerical analysis of a fully discrete algorithm and performing some numerical simulations which demonstrate its accuracy and its behavior.…”

Analysis of a bone remodeling model

“…During the last ten years, some papers dealt with mathematical issues of these models as the existence and uniqueness of weak solutions under some quite strong assumptions (see, e.g., [14,15,16,17,19]), the analysis of an asymptotic rod model ( [6,7,8,9]) or the numerical stability of finite element models ( [11]). Here, our aim is to continue [16], providing the numerical analysis of a fully discrete algorithm and performing some numerical simulations which demonstrate its accuracy and its behavior.…”