All models with estrogen effects are osteoporosis-specific models, and their respective mathematical representations are outlined in Table . Several models do not consider dynamic estrogen levels . Instead, they model the effects of estrogen deficiency by altering RANKL, OPG, PTH, and TGF-β. and manually lower the OPG and TGF-β production parameters for osteoporotic scenarios. Two models with dynamic estrogen levels aim to determine the most effective therapeutic dose to prevent bone loss. In , periodic estrogen treatment is modeled with a linear increase in osteoclast removal. reformulates the model to be explicitly piecewise. Using the power law approach to illustrate, the osteoclast rate equation becomes