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|