**4. Conclusions**

In this chapter, described was the mathematical model of bone remodeling extending the established previously (Adachi et al., 1997) based on the mechanostat theory (Duncan & Turner, 1995; Frost, 2003; Hughes et al., 2010). Extension was the bone resorption-dominant response in low strain range by disuse and formation-dominant response in overuse windows. The osteocyte apoptosis in the low strain range due to weightlessness was a key aspect in the extended model, and the targeted remodeling was in the high strain range for bone formation. Trabecular structure in human proximal femur was simulated using the model extended and the reproduced trabecular structure exhibited good agreement with that in the actual femur more reasonably by taking the osteocyte apoptosis in low strain range and the targeted remodeling in high strain range. Especially, the consideration of osteocyte apoptosis was crucial in the mathematical model of bone remodeling model in reproducing the healthy normal bone structure and in simulation the disuse-mediated osteoporotic bone structure. The former was demonstrated by comparison of simulated volume fraction and the X-ray CT bone mineral density. For the latter, disuse-accelerated bone loss was examined for infrequent and cane-assisted walking conditions. The osteoporotic trabecular structure was examined in terms of Singh Index, a diagnostic criterion for the stage of progression of osteoporosis. This competence of the model was coming from the effect of osteoporosis due to less mechanical stimulus and its result of bone loss acceleration, and the present remodeling model is effective in bone remodeling simulation under reduced loading condition.

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In conclusion, the effect of osteocyte apoptosis on bone resorption is inevitable aspect in the computer simulation of bone remodeling.
