68
TABLE 23.
VALUES FOR THE INTEGRAL foto Fe dt
Ay WIL. 0.693
Tia, YE...
0.231 , 0.099
i
3
1.919
2.889
3.176
3.327
3.339
3.339
3.339
3.339
2.010
3.163
3.716
4.330
4.574
4.639
4.643
4.643
7
0.046
0.020
15
0.0092
35
75
| 2.053
3.318
4.067
5.282}
6.349
7.514
8.873
9.484
2.055
3.326
4.086
5.346
6.518
7.839
9.761
11.04
T, yr
0.2
1
2
5
10
20
50
100
TABLE 24.
Ay yr... ee. 0.693
Tis, YT wee
1
2.037 2.047
3.259 3.2908
3.918 4.019
4.862 5.127
5.475 6.023
5.852 6.815
5.983 7.412
5.987 7.518
0.500
0.154
0.010
0.0002!
—
—
—
Vattrs ror T7-°-7eAT
0.231
0.099
0.046
0.020
0.0092
3
7
i5
35
75
TABLE 25.
0.794
0.388
0.102
0.0198]
0.0012!
—
—
0.906
0.505
0.198
0.074
0.0170
0.00046]
—
0.955
0.561
0.258
0.126
0.0490
0.0065
0.00040)
0.980
0.591
0.293
0.163
0.0823}
0.0238}
0.0054}
0.991
0.604
0.310
0.182
0. 1022
0.0408
0.0159
0.693
0.231
0.099
0.046
0.020
0.0092
T1;2, YT... eee eee
1
3
7
15
35
75
T,yr
2.50
2.35
2.352
2.31
2.31
2.31
2.31
1.52
1.25
1.10
1.08
1.07
1.07
1.07
1.23
0.893
0.679
0.616
0.596
0.593
0.593
1.11
0.746
0.494
0.403
0.362
0.347
0.346
1.05
0.672
0.399
0.290
0.233
0.201
0.195
1.02
@.642
0.359
0.242
0.174
0.131
0.117
11. Therefore, Augs for the region as a whole is
given by a times Table 25.
12. Conclusions (a) For reasonable remodeling rates
the average augmentation rate is almost independent
of the time since adolescence over the major portion
of the humanlife-span. For example, for a resorptionapposition rate of X
4.6%/year the augmentation
rate would be within the limits 11.8 + 1.3%/year
from T = 8 yearsto T = o, or from say age 25 onwards.
of this distribution would far outweigh those
older members.
(c) We, therefore, have a successful quant
description of the continual creation of enough
bene to provide an overall augmentation rate
practically independent of age. This is true
stasis of the adult skeleton due to remodeling.
(d) Therefore, it is consistent to consider the
jected tracer, even though individual bone
elements are aging and their local augmentatio
are decreasing with their increasing age.
(e) If we assume that the dependence o
augmentation rate upon bone age which we ot
for dogs, step 7, ean be used for bone in man
same age, then it follows that an apposition-res
rate of 4.6%/year implies an augmentation )
11%/year, The sum of these two rates is about
year, which is the observed A; value for norma
man.
(f) Therefore, about 70% (11/15) of the lon
tracer activity would be associated with augmer
and only 30% (4.6/15) with apposition. Thi
mentational activity would not, however, be ob.
\X Times Tasie 23 + Tapue 24
A,r. eee,
1
2
5
10
20
50
100
would have this low a rate. Very likely, it wi
considered as the diffuse component. The rest
bone volume would contain a distribution of bor
and the augmentation rates of the younger m
adult skeleton as age-invariant with respect
T,yrI
1
2
5
10
20
50
100
rate of 40-year-old bone would only be 2.2‘
However, only 16% of-the region of bone a:
(b) If we let 7 = 40 years, the local augmentation
associated with a uniform diffuse component but
instead be located in bone only a few years old
tensities perhaps as much as 10 times the diffuse |
apparent in 40-year-old bone.
(g) The age distribution (step 5) msures that
AT “<1, as it is for young adult dogs, then therea large area of bone with a relatively uniform :
component. However, for older dogs and ma
distribution of local augmentation rates is much
One expects blotchy autoradiographs as we fou
*Ca in man, with what uniform diffuse activityt!
representing only a small fraction of the overal
mentation rate.
Improvement on Step 7
Because bone less than 0.2 year old (about the
to form a human haversian system) is in the imm:
neighborhood of bone formation, it would be
accurate to use the formula for augmentation raage with a lower limit of 0.2 year. Bone younger
0.2 year would then not contribute to augment
but would be included in apposition. (See Table =
Then Figure 52 is a times Table 26.
The exclusion of bone less than 10 weeks of age|