@article{RusconiVallerianiDunlopetal.2009, author = {Rusconi, Marco and Valleriani, Angelo and Dunlop, John William Chapman and Kurths, J{\"u}rgen and Weinkamer, Richard}, title = {Insights into the control of trabecular bone remodelling obtained by a Markov model}, issn = {8756-3282}, doi = {10.1016/j.bone.2009.03.467}, year = {2009}, language = {en} } @article{RusconiVallerianiDunlopetal.2012, author = {Rusconi, Marco and Valleriani, Angelo and Dunlop, John William Chapman and Kurths, J{\"u}rgen and Weinkamer, Richard}, title = {Quantitative approach to the stochastics of bone remodeling}, series = {epl : a letters journal exploring the frontiers of physics}, volume = {97}, journal = {epl : a letters journal exploring the frontiers of physics}, number = {2}, publisher = {EDP Sciences}, address = {Mulhouse}, issn = {0295-5075}, doi = {10.1209/0295-5075/97/28009}, pages = {6}, year = {2012}, 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.}, language = {en} }