An Approach for Time-dependent Bone Modeling and Remodeling-application: a Preliminary Remodeling Simulation

In a companion paper, we presented a time-dependent theory for bone modeling and remodeling in response to a daily loading history. This paper represents a preliminary attempt to use the theory to determine the distribution of bone density within the adult proximal femur under an assumed normal loading history. Subsequent functional adaptation of the internal structure due to changes in the loading history are then determined. Throughout this preliminary study, the external geometry of the proximal femur is considered to be fixed, i.e., changes in the external shape are neither stimulated nor allowed. Linear and trilinear (dead-zone nonlinearity) rate remodeling laws were compared. Computer emulations using two-dimensional finite element models were successful in creating a normal-appearing distribution of bone tissue when remodeling was initiated from a solid structure of homogeneous bone density. Subsequent reduction in the loading history caused regional bone atrophy. Reinstatement of the normal loading history caused a generalized increase in bone mass but resulted in a slightly different bone distribution than was calculated for a constant loading history. These results demonstrate the utility of the remodeling theory and are consistent with the hypothesis that similar stress-related phenomena are responsible for both normal morphogenesis and functional adaptation in response to changes in the bone loading.