Quantitative approach to the stochastics of bone remodeling

¹ Center for Dynamics of Complex Systems, Department of Mathematics, University of Potsdam Karl-Liebknecht-Str. 24, 14476 Potsdam, Germany, EU
² Max Planck Institute of Colloids and Interfaces, Department of Theory and Bio-Systems Science Park Golm, 14424 Potsdam, Germany, EU
³ Max Planck Institute of Colloids and Interfaces, Department of Biomaterials - Science Park Golm, 14424 Potsdam, Germany, EU
⁴ Humboldt-Universität zu Berlin and Potsdam Institute for Climate Impact Research Telegrafenberg A31, 14473 Potsdam, Germany, EU
⁵ Institute for Complex Systems and Mathematical Biology, University of Aberdeen Aberdeen AB24 3UE, UK, EU

^a marco.rusconi@bccn-berlin.de

Received: 22 July 2011
Accepted: 29 November 2011

Abstract

During life bones constantly adapt their structure to their mechanical environment via a mechanically controlled process called bone remodeling. For trabecular bone, this process modifies the thickness of each trabecula leading occasionally to full resorption. We describe the irreversible dynamics of the trabecular thickness distribution (TTD) by means of a Markov chain discrete in space and time. By using thickness data from adult patients, we derive the transition probabilities in the chain. This allows a quantification, in terms of geometrical quantities, of the control of bone remodeling and thus to determine the evolution of the TTD with age.