On a Class of Bone Cell-Based Remodeling Laws with Spatial Fading Influence of Stimuli

In the present paper the class of cell-based bone remodeling laws is considered. The fundamental assumption is that of fading in space influence on actor cells osteocytes functioning as sensors. The actor cells — osteoclasts and osteoclasts are responsible for the changes of bone micro-structure. The model proposed in the previous publications of other authors, is based on the assumption of exponential influence function and density of strain energy as the stimulus to which the osteocytes are sensitive, see [11, 12, 14]. As the result of the adaptation according to such remodeling law the porous material is created. The topology of the micro-structure of this material is dependent on the mechanical loading conditions and the characteristics of the interactions of cells. The aim of the present work was to examine if this phenomenon is characteristic only for this specific law or represents a rather general property associated with the hypothesis of fading influence of the cells. Different influence functions were examined for different functionals selected to represent the stimulus. It follows from the these considerations that the fading influence of the cells plays fundamental role for the remodeling process and the creation of trabecular structure. Such structures were obtained for several adaptation laws based on different influence functions and functionals representing the stimulus. They were compared with the results obtained for the adaptation law proposed and discussed in [11, 12, 14]. The numerical calculations suggest that the idea of spatial fading influence of the cells can be possibly combined in future with the results of the research on the biological mechanisms of the bone remodeling to propose more sophisticated models.