**3.2. Healthy trabecular structures in proximal femur**

The simulation results from initial random structure to an equilibrium state are shown in Fig. 4. In the diaphyseal region, random inner structures disappeared whereas the thickness of cortical bone increased with simulation step to the similar level observed in CT image (Fig.

4(g)). On the other hand, trabecular bone in the metaphyseal region, showing an isotropical random pattern at the initial (Fig. 4(a)), changed to an anisotropic, non-uniform structure. Bone volume was maintained in femoral head region A but decreased in neck region B reproducing Ward's triangle characteristic of trabecular structure in the proximal femur.

Osteocyte Apoptosis-Induced Bone Resorption

(13)

(14)

(15)

in Mechanical Remodeling Simulation – Computational Model for Trabecular Bone Structure 33

y = 397.81x + 27.425 r = 0.73 (p < 0.01)

0 0.2 0.4 0.6 0.8 1 Volume fraction

walking and the cane-assisted walking. In the infrequent walking condition, we wedged the interval with no loading into the daily loading condition; that is, the infrequent walking condition consisted of unloading of zero load and a part of the daily loading conditions. The proportion of unloading interval changed from 10 to 70% while the ratio of one-legged stance, abduction, and adduction were remained unchanged. In the simulation, the parameter of bone resorption and formation were represented with loading frequencies *fol*, *fab*, *fad*, and *funloading* as Eqs. (13) ~ (15). In the cane-assisted walking, we referred to the study on relative changes in muscle activity and kinetics during cane-assisted walking (Neumann et al., 1998). The cane use reduced the demand on the hip abductors and decreased joint compression forces related to muscle contraction in the contralateral side. We calculated joint force and hip abductor force at various rates of leaning force when using a cane (Fig. 6). That is, in the infrequent walking, the number of loading cycles per day decreased from the daily-loading condition (Table 1), while the same loading forces were applied to the femur; in the cane-assisted walking, the numbers of loading cycles per day remained unchanged but the loading forces were altered from the daily-loading condition (Kwon et al., 2010b).

0

200

400

Bone mineral density [mg/cm 3]

600

800

*ol c ol ab c ab ad c ad* \_\_ \_

*f f f fff f* 

*<sup>f</sup> AF f AF f AF AF fff f* 

*<sup>f</sup> AF f AF f AF AF fff f* 

The trabecular structure of the human proximal femur under the infrequent walking condition was shown for each rate of unloading interval and the initial, i.e., normal trabecular structure was also shown in Fig. 7. In the initial structure of Fig. 7(a), visible are all the normal groups of trabecular (Fig. 8), i.e. the compressive and tensile trabecular bones cross each other and the upper end of femur is completely occupied by cancellous tissue.

*ol ab ad unloading*

*ol r ol ab r ab ad r ad* \_\_ \_

*ol ab ad unloading*

*ol f ol ab f ab ad f ad* \_\_ \_

*ol ab ad unloading*

**Figure 5.** Bone mineral density vs. simulated volume fraction.

*c*

*r*

*f*

Even Ward's triangle shows some thin trabecular bone (Singh et al., 1970).


**Table 1.** Standard magnitude of force and frequency at each stance (daily-loading condition).

Regions A and B were subdivided to blocks of 10×10×10 voxels to compare local bone volume fraction in each block with local bone mineral density(Duchemin et al., 2008) i.e., averaged bone mineral density in the corresponding CT voxels referring to the phantoms of trabecular bone (B-mas 200). Trabecular bone volume fraction was correlated significantly with bone mineral density as shown in Fig. 5.

**Figure 4.** Simulated trabecular structure in human proximal femur and CT-image (Subject #1).

#### **3.3. Disuse mediated change in proximal femur**

To estimate the effect of weightlessness-induced osteocyte apoptosis in trabecular bone in proximal femur, two reduced weight-bearing conditions were considered here: the infrequent

Osteocyte Apoptosis-Induced Bone Resorption in Mechanical Remodeling Simulation – Computational Model for Trabecular Bone Structure 33

**Figure 5.** Bone mineral density vs. simulated volume fraction.

32 Apoptosis and Medicine

4(g)). On the other hand, trabecular bone in the metaphyseal region, showing an isotropical random pattern at the initial (Fig. 4(a)), changed to an anisotropic, non-uniform structure. Bone volume was maintained in femoral head region A but decreased in neck region B reproducing Ward's triangle characteristic of trabecular structure in the proximal femur.

> One-legged (*n=ol*)

Frequency *fn* [cycle/day] 6000 2000 2000

**Table 1.** Standard magnitude of force and frequency at each stance (daily-loading condition).

**Figure 4.** Simulated trabecular structure in human proximal femur and CT-image (Subject #1).

To estimate the effect of weightlessness-induced osteocyte apoptosis in trabecular bone in proximal femur, two reduced weight-bearing conditions were considered here: the infrequent

**3.3. Disuse mediated change in proximal femur** 

with bone mineral density as shown in Fig. 5.

Regions A and B were subdivided to blocks of 10×10×10 voxels to compare local bone volume fraction in each block with local bone mineral density(Duchemin et al., 2008) i.e., averaged bone mineral density in the corresponding CT voxels referring to the phantoms of trabecular bone (B-mas 200). Trabecular bone volume fraction was correlated significantly

J 24° -15° 56° J [N] 2317 1158 1548 H 28° -8° 35° H [N] 703 351 468

Abduction (*n=ab*)

Adduction (*n=ad*)

> walking and the cane-assisted walking. In the infrequent walking condition, we wedged the interval with no loading into the daily loading condition; that is, the infrequent walking condition consisted of unloading of zero load and a part of the daily loading conditions. The proportion of unloading interval changed from 10 to 70% while the ratio of one-legged stance, abduction, and adduction were remained unchanged. In the simulation, the parameter of bone resorption and formation were represented with loading frequencies *fol*, *fab*, *fad*, and *funloading* as Eqs. (13) ~ (15). In the cane-assisted walking, we referred to the study on relative changes in muscle activity and kinetics during cane-assisted walking (Neumann et al., 1998). The cane use reduced the demand on the hip abductors and decreased joint compression forces related to muscle contraction in the contralateral side. We calculated joint force and hip abductor force at various rates of leaning force when using a cane (Fig. 6). That is, in the infrequent walking, the number of loading cycles per day decreased from the daily-loading condition (Table 1), while the same loading forces were applied to the femur; in the cane-assisted walking, the numbers of loading cycles per day remained unchanged but the loading forces were altered from the daily-loading condition (Kwon et al., 2010b).

$$\Gamma\_c = \frac{f\_{ol}\Gamma\_{c\\_ol} + f\_{ab}\Gamma\_{c\\_ab} + f\_{ad}\Gamma\_{c\\_ad}}{f\_{ol} + f\_{ab} + f\_{ad} + f\_{unloading}} \tag{13}$$

$$AF\_r = \frac{f\_{ol}AF\_{r\\_ol} + f\_{ab}AF\_{r\\_ab} + f\_{ad}AF\_{r\\_ad}}{f\_{ol} + f\_{ab} + f\_{ad} + f\_{unloading}} \tag{14}$$

$$AF\_f = \frac{f\_{ol}AF\_{f\\_ol} + f\_{ab}AF\_{f\\_ab} + f\_{ad}AF\_{f\\_ad}}{f\_{ol} + f\_{ab} + f\_{ad} + f\_{unloading}} \tag{15}$$

The trabecular structure of the human proximal femur under the infrequent walking condition was shown for each rate of unloading interval and the initial, i.e., normal trabecular structure was also shown in Fig. 7. In the initial structure of Fig. 7(a), visible are all the normal groups of trabecular (Fig. 8), i.e. the compressive and tensile trabecular bones cross each other and the upper end of femur is completely occupied by cancellous tissue. Even Ward's triangle shows some thin trabecular bone (Singh et al., 1970).

Osteocyte Apoptosis-Induced Bone Resorption

in Mechanical Remodeling Simulation – Computational Model for Trabecular Bone Structure 35

Increasing the rate of unloading interval led to the increased bone loss, first in the femoral head and the greater trochanter. Ward's triangle was emptier in the case of higher rate of unloading frequency. Subsequently, the secondary compressive group disappeared and the principal tensile group became thinner with further increasing of the rate of unloading. When unloading level increased up to 70%, the principal compressive group little remained

Figure 9 shows the trabecular structure changes under cane-assisted walking conditions. Using cane decreased joint compression forces related to muscle contraction in the contralateral side. Bone loss attracts attention on the greater trochanter group and Ward's triangle became clear when reducing hip abductor forces. Subsequent disappearing of the secondary compressive group and the thinning of the principal tensile group were observed with further increasing. This is similar to those observed for the infrequent walking. However, bone loss in the trabecular femoral head differed from that under the infrequent

Clinically, the correlation of bed rest (reducing loading frequency) and muscle activity has been reported. The disuse due to bed rest with diseases accompanies with reduced muscle activity, and then leads to the cane use for walking. Thus, we simulated the trabecular remodeling by combining the two reduced weight-bearing conditions. Figure 10 shows that trabecular loss increased with increasing in the rate of unloading interval. Combination of reductions of loading frequency and loading forces relatively accentuated the structure of principal compressive and principal tensile groups and enhanced the thinning of the secondary compressive trabecular bone. Therefore, empty Ward's triangle is clearly observed. Further increase in the rate of unloading interval led to a marked reduction of tensile trabecular bone and discontinued the principal tensile group. Thus, the tensile trabecular bone is observed only in the upper part of the femoral head, where trabeculae are still comparable in density to the principal compressive trabeculae. Finally, even the

although the greater trochanter group was still observed clearly.

walking condition. The hip joint load will be involved in this difference.

**Figure 8.** Trabecular structure pattern of human femur.

principal compressive group became less obvious.

**Figure 6.** Diagram for boundary conditions of cane-assisted walk.

**Figure 7.** Simulated trabecular structure under infrequent walking.

Increasing the rate of unloading interval led to the increased bone loss, first in the femoral head and the greater trochanter. Ward's triangle was emptier in the case of higher rate of unloading frequency. Subsequently, the secondary compressive group disappeared and the principal tensile group became thinner with further increasing of the rate of unloading. When unloading level increased up to 70%, the principal compressive group little remained although the greater trochanter group was still observed clearly.

Figure 9 shows the trabecular structure changes under cane-assisted walking conditions. Using cane decreased joint compression forces related to muscle contraction in the contralateral side. Bone loss attracts attention on the greater trochanter group and Ward's triangle became clear when reducing hip abductor forces. Subsequent disappearing of the secondary compressive group and the thinning of the principal tensile group were observed with further increasing. This is similar to those observed for the infrequent walking. However, bone loss in the trabecular femoral head differed from that under the infrequent walking condition. The hip joint load will be involved in this difference.

**Figure 8.** Trabecular structure pattern of human femur.

34 Apoptosis and Medicine

**Figure 6.** Diagram for boundary conditions of cane-assisted walk.

**Figure 7.** Simulated trabecular structure under infrequent walking.

Clinically, the correlation of bed rest (reducing loading frequency) and muscle activity has been reported. The disuse due to bed rest with diseases accompanies with reduced muscle activity, and then leads to the cane use for walking. Thus, we simulated the trabecular remodeling by combining the two reduced weight-bearing conditions. Figure 10 shows that trabecular loss increased with increasing in the rate of unloading interval. Combination of reductions of loading frequency and loading forces relatively accentuated the structure of principal compressive and principal tensile groups and enhanced the thinning of the secondary compressive trabecular bone. Therefore, empty Ward's triangle is clearly observed. Further increase in the rate of unloading interval led to a marked reduction of tensile trabecular bone and discontinued the principal tensile group. Thus, the tensile trabecular bone is observed only in the upper part of the femoral head, where trabeculae are still comparable in density to the principal compressive trabeculae. Finally, even the principal compressive group became less obvious.

Osteocyte Apoptosis-Induced Bone Resorption

in Mechanical Remodeling Simulation – Computational Model for Trabecular Bone Structure 37

Trabecular structure of the proximal femur is remodeled differently in response to various forms of mechanical stimulation (Wolff, 1986; Carter, 1987). In this study, we investigated that the structure changes of human trabecular bone under the reduced weight-bearing conditions by a surface remodeling model (Kwon et al., 2010a), in which osteocyte apoptosis plays a crucial role below a physiological strain range (Gu et al., 2005). The reduced weightbearing conditions were imposed by assuming infrequent and/or cane-assisted walking. Depending on the reduced weight-bearing conditions, the trabecular structure reached different equilibrium structures even if the same initial structure and model parameters are used. In all cases, trabecular bone loss occurred in relation to the mechanical stimuli, although there was a regional difference in the pattern of bone loss between the two conditions. In the infrequent and cane-assisted walking conditions, significant bone loss

In the results of imposing the condition combining two reduced weight-bearing conditions, we found out the clinically observed trabecular structure in osteoporotic human proximal femur. The description for degree of osteoporotic trabecular structure (Singh Index) is shown in Table 2. The present stimulations showed that decreasing mechanical stimuli enhanced the degree of osteoporosis along with the grade defined by Singh et al. (1970). Figure 10 shows trabecular loss at various degrees of unloading. In the initial structure (Fig. 10 (a)), all groups of trabecular bones are visible, which corresponds to Grade 6 in Singh index. The compressive and tensile trabeculae intersect each other and the upper end of the femur is completely occupied by cancellous rich structure. Ward's triangle is not clearly delineated and there are some thin trabeculae in it. With increasing the proportion of unloading, there occurs an apparent accentuation of the structure of the principal compressive and principal tensile groups, while the secondary compressive trabeculae became thinner (Grade 5, Fig. 10 (b)~(c)). As a result, an empty region appears in Ward's triangle. Further increase in the proportion of unloading leads to the marked reduction in the tensile trabecular bones (Grade 4, Fig. 10 (d)~(e)); in due course, discontinuity occurs in the principal tensile group. At the stages of Fig. 10 (e) and (f), the tensile trabeculae are seen

Grade 6 All the normal trabecular groups are visible and the upper end of the femur

Grade 4 Principal tensile trabeculae are markedly reduced in number but can still be observed in lateral cortex to the upper part of the femoral neck. Grade 3 There is a break in the continuity of the principal tensile trabeculae opposite the greater trochanter. This grade indicates definite osteoporosis. Grade 2 Only the principal compressive trabeculae stand out prominently; the others

Grade 1 Even the principal compressive trabeculae are markedly reduced in number

Grade 5 The structure of principal tensile and principal compressive trabeculae is

seems to be completely occupied by trabecular bone.

accentuated. Ward's triangle appears prominent.

have been resorbed more or less completely.

and are no longer prominent.

**Table 2.** Singh Index

occurred in the great trochanter and in the femoral head, respectively.

**Figure 9.** Simulated trabecular structures under cane-assisted walking

**Figure 10.** Simulated trabecular structures under infrequent cane-assisted walking.

Trabecular structure of the proximal femur is remodeled differently in response to various forms of mechanical stimulation (Wolff, 1986; Carter, 1987). In this study, we investigated that the structure changes of human trabecular bone under the reduced weight-bearing conditions by a surface remodeling model (Kwon et al., 2010a), in which osteocyte apoptosis plays a crucial role below a physiological strain range (Gu et al., 2005). The reduced weightbearing conditions were imposed by assuming infrequent and/or cane-assisted walking. Depending on the reduced weight-bearing conditions, the trabecular structure reached different equilibrium structures even if the same initial structure and model parameters are used. In all cases, trabecular bone loss occurred in relation to the mechanical stimuli, although there was a regional difference in the pattern of bone loss between the two conditions. In the infrequent and cane-assisted walking conditions, significant bone loss occurred in the great trochanter and in the femoral head, respectively.

In the results of imposing the condition combining two reduced weight-bearing conditions, we found out the clinically observed trabecular structure in osteoporotic human proximal femur. The description for degree of osteoporotic trabecular structure (Singh Index) is shown in Table 2. The present stimulations showed that decreasing mechanical stimuli enhanced the degree of osteoporosis along with the grade defined by Singh et al. (1970). Figure 10 shows trabecular loss at various degrees of unloading. In the initial structure (Fig. 10 (a)), all groups of trabecular bones are visible, which corresponds to Grade 6 in Singh index. The compressive and tensile trabeculae intersect each other and the upper end of the femur is completely occupied by cancellous rich structure. Ward's triangle is not clearly delineated and there are some thin trabeculae in it. With increasing the proportion of unloading, there occurs an apparent accentuation of the structure of the principal compressive and principal tensile groups, while the secondary compressive trabeculae became thinner (Grade 5, Fig. 10 (b)~(c)). As a result, an empty region appears in Ward's triangle. Further increase in the proportion of unloading leads to the marked reduction in the tensile trabecular bones (Grade 4, Fig. 10 (d)~(e)); in due course, discontinuity occurs in the principal tensile group. At the stages of Fig. 10 (e) and (f), the tensile trabeculae are seen


#### **Table 2.** Singh Index

36 Apoptosis and Medicine

**Figure 9.** Simulated trabecular structures under cane-assisted walking

**Figure 10.** Simulated trabecular structures under infrequent cane-assisted walking.

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 osteoporotic change of trabecular bone structure.

Osteocyte Apoptosis-Induced Bone Resorption

in Mechanical Remodeling Simulation – Computational Model for Trabecular Bone Structure 39

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).

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

**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.
