An in silico model for woven bone adaptation to heavy loading conditions in murine tibia

Existing in silico models for lamellar bone adaptation to mechanical loading are unsuitable for predicting woven bone growth. This anomaly is due to the difference in mechanobiology of the woven bone with respect to that of the lamellar bone. The present study is aimed at developing an in silico bone-adaptation model for woven bone at cellular and tissue levels. The diffusion of Ca²⁺ ions reaching lining cells from the osteocytic network and the bone cortex in response to a mechanical loading on the cortical bone has been considered as a stimulus. The diffusion of ions within osteocytic network has been computed with a lacunar-canalicular network (LCN) in which bone cells are uniformly arranged. Strain energy density is assumed to regulate ion flow within the network when the induced normal strain is above a threshold level. If the induced strain exceeds another higher threshold level, then the strain with a power constant is additionally assumed to regulate the stimulus. The intracellular flow of Ca²⁺ ions within the LCN has been simulated using Fick's laws of diffusion, using a finite element method. The ion diffusion from bone cortex to vesicles has been formulated as a normal strain with a power constant. The stimuli reaching the surface cells are assumed to form the new bone. The mathematical model closely predicts woven bone growth in mouse and rat tibia for various in vivo loading conditions. This model is the first to predict woven bone growth at tissue and cellular levels in response to heavy mechanical loading.