8th. World Congress on Computational Mechanics (WCCM8) 5th European Congress on Computational Methods in Applied Sciences and Engineeering (ECCOMAS 2008) June 30 –July 5, 2008 Venice, Italy UNDERSTANDING THE PROCESS OF FORCE-INDUCED BONE GROWTH AND ADAPTATION BY A MATHEMATICAL MODEL Solvey Maldonado *1 , Rolf Findeisen 2 and Frank Allg ¨ ower 1 1 Institute for Systems Theory and Automatic Control University of Stuttgart, Pfaffenwaldring 9,70550 Stuttgart,Germany maldonado@ist.uni-stuttgart.de, allgower@ist.uni-stuttgart.de 2 Institute for Automation Engineering Otto-Von-Guericke-Universit¨ at Magdeburg, 39106 Magdeburg, Germany rolf.findeisen@ovgu.de, Key Words: Mathematical Modeling, Bone Cells, Mechanotransduction, NO, PGE 2 , Bone Adaptation. INTRODUCTION Mathematical modeling offers a powerful tool to predict the influence of multiple and simultaneous factors on biological processes. It also offers the possibility to study and to analyze bone tissue as a dynamic complex system. Additionally, mechanical stimulation has been recognized as a potential regulator factor involved in development, growth, maintenance and function of the skeleton [1]. Our research is focused on understanding the process of force-induced bone growth and adaptation. In this work, a mathematical model is employed to consider multiple and simultaneous effects of mechanical force and local factors during a bone remodeling cycle. Bone as a living tissue, has the ability to self-repair and adapt in response to new biophysical de- mands. The complex and hierarchical bone structure has attracted the interest of different scientific communities, studying and developing conceptual and computational models trying to shed light into the phenomenon of bone growth, development and maintenance. Additionally, research studies have been conducted in order to understand and identify the mechanisms bone uses to transduce the mechan- ical loads (gravity, physical activity) into biochemical signals. Taking the conceptual framework of bone as a highly regulated system, proposed in the mechanostat theory and the functional adaptation concept, we constructed a mathematical model describing the bone dynamics at the tissue, cellular and signaling transduction level [7]. The model encompasses three layers of abstraction, from the biochemical signaling in response to mechanical stimulation, passing through the formation and resorption activities of bone cells (metabolic mechanisms), up to a basic description of the bone thickness growth and adaptation at the tissue level (mechanical part). The mechanobio- logical phenomena of the bone tissue is based on the hypothesis of osteocyte cells functioning as the bone mechanotransducers. Specifically, osteocytes formed an interfacing layer between the functional