**2.4. Integrated mathematical model and simulation procedures for bone remodeling**

The mathematical models of bone remodeling established in low, physiological, and high strain ranges were integrated by introducing transition regions. In the transition regions between low and physiological range (*εdu* < *εc < εpl*) or between physiological and high range (*εpu* < *εc < εol*), the probabilities of bone resorption or formation in each window were combined as a linearly weighed sum as given by Eqs. (10)-(12) resulting the resultant probability *f*\* of bone resorption/formation.

 LS c du c du c du LS c du c pl pl du pl du \* c c c pl c pu c pu c pu c HS pu c ol ol du ol pu HS P ε ε εε εε 1 P <sup>Γ</sup> ε εε εε εε f Γ ,ε Γ ε εε εε εε 1 Γ P ε εε εε εε P *f f f* ol c ε ε (10) \*\* \* ( , ) ( ( , ) 0) *f cc cc Pf f* (11)

$$P\_r^\* = f^\*(\Gamma\_{\varepsilon'} \varepsilon\_c) \left( f^\*(\Gamma\_{\varepsilon'} \varepsilon\_c) < 0 \right) \tag{12}$$

Using this integrated model, trabecular bone structure was simulated by the following procedures.

