**3.4. Importance of osteocyte apoptosis-induced bone resorption in remodeling simulation**

To evaluate the advantage of including low and high strain ranges, we performed the simulation assuming the response model defined for physiological strain range to the entire strain range including low and high strain ranges, referred to physiological response-only model hereafter. Results by physiological range-only model were compared with that obtained by the present integrated model considering individual response model for low and high strain ranges. This physiological response-only model determines the trabecular structure only by relative non-uniformity of strain distribution over all the strain range with no local acceleration of bone resorption and formation. Figure 12(a) shows the distribution of initial equivalent strain. Diaphyseal structure was formed with the loss of trabecular bone both integrated and physiological response-only models (Fig. 12(b)). However, bone resorption occurred to the higher degree in the integrated model, especially in low strain regions as clearly shown in dashed circles of Fig. 12(b). Figure 13 shows the simulation result for change of volume fraction in ward's triangle region at each model. The integrated model was reached to equilibrium state, faster than physiological response-only model. Ward's triangle region has a low strain range, as seen in Fig. 12(a). Figure 14 shows the histogram of number of trabecular bone elements against initial equivalent strain distribution for both simulation models. In the low strain range below 100*με*, as much as 43, 37, and 46% of trabecular bone preserved in the physiological response-only model were resorbed by the integrated model in different subjects of #1, #2, and #3, respectively. In low strain regions at the initial, the integrated model could reproduce more suitable trabecular structure by taking the characteristic response in low strain range into account. Furthermore, the correlation between bone volume fraction simulated and bone mineral density by CT image was higher in the integrated model than that in the physiological response-only model (Fig. 15).

38 Apoptosis and Medicine

**simulation** 

osteoporotic change of trabecular bone structure.

only in the upper part of the femoral head, where the trabeculae are still comparable in density to the principal compressive trabeculae (Grade 3). Finally, even the principal compressive group ceases to stand out (Grade 2, Fig. 10 (g)) and decreases markedly in number (Grade 1, Fig. 10 (h)). Therefore, the present remodeling model has the competence to study the trabecular bone loss in disuse-mediated osteoporosis, where bone resorptiondominant remodeling due to less mechanical stimuli should be characterized reasonably and sufficiently. That is introduced into the present model by considering the effect of osteocyte apoptosis under low strain stimuli, and it is essential in predicting the

**Figure 11.** Equivalent stress and strain distributions in normal and osteoporotic femurs.

Finite element analyses were conducted for normal and osteoporotic human femurs obtained by remodeling simulation, and trabecular bone stress and strain were examined for a spherical volume of interest in the femoral head (Rietbergen et al., 2003). Figure 11 shows the distribution of voxel at different stress/strain for the normal femur of Fig. 10(a) and an osteoporotic femur of Fig. 10 (b) that is obtained under the disuse loading condition of reduced loading frequency and force. Solid and broken blue lines distinguish the stress/strain distribution for osteoporotic femur under standard and disuse loading conditions, respectively. Trabecular bone stress and strain in the osteoporotic femur were distributed more uniformly than those in the normal femur. In the osteoporotic femur, trabecular bones orthogonal to the alignment of the principal compressive group (non-principal trabeculae) are relatively-scarce because osteocytes in those trabeculae, especially in non-principal group originally exposed to relatively small loading, are susceptible to apoptosis when subjected to the disuse condition, resulting in scarcely distributed non-principal trabeculae. Consequently, trabeculae undergoing relatively-low stress/strain decrease and the peaks of stress and strain distributions increased in the osteoporotic femur. Trabeculae in principal compressive group are likely to preserve their role of relatively high load-bearing even under the disuse condition.

**3.4. Importance of osteocyte apoptosis-induced bone resorption in remodeling** 

To evaluate the advantage of including low and high strain ranges, we performed the simulation assuming the response model defined for physiological strain range to the entire strain range including low and high strain ranges, referred to physiological response-only

**Figure 12.** Initial stress distribution and simulated trabecular structures.

Osteocyte Apoptosis-Induced Bone Resorption

in Mechanical Remodeling Simulation – Computational Model for Trabecular Bone Structure 41

**Figure 15.** Bone mineral density at proximal femur by CT and simulated volume fraction by integrated

and physiological response-only models.

**Figure 13.** Volume fraction in Ward's triangle during remodeling simulation.

**Figure 14.** Number of trabecular bone elements in simulated proximal femur against initial equivalent strain levels before disuse-mediated remodeling.

**Figure 13.** Volume fraction in Ward's triangle during remodeling simulation.

**Figure 14.** Number of trabecular bone elements in simulated proximal femur against initial equivalent

strain levels before disuse-mediated remodeling.

**Figure 15.** Bone mineral density at proximal femur by CT and simulated volume fraction by integrated and physiological response-only models.
