= ee FT ein ca ah a ea, ell tan wleae Naheaaa s 70 Aug, = 13%/year or Ag = 22%/year. Despite his low ratio of diffuse/uniform label of 0.11, about 55% of the A-value is augmentation according to Table 27. (d) The assumption of random remodeling together with an augmentation rate which dependssolely on the age of each bone volume element (300° %/year, where ¢ is bone age in years) leads to a bone model which answers a numberof outstanding questions. (1) For remodeling rates of about 4%/vear or greater, there can be age-invariance of tracer retention over most of the adult life-span in spite of the local decrease of augmentation rate with bone age. (2) The ratio diffuse/uniform label is seen to depend both on remodeling rate and on age at tracer intake. (3) For older dogs and menit is clear that the ratio diffuse/uniform label can be as low as 0.1 in spite of the fact that over half the value of A; is due to augmentation. The calculation that a significant fraction of A; can be in augmentational hotspots removes what had appeared to be a serious discrepancy between data and model. Therefore, it would be most interesting to obtain experimental verification of the high fraction of As that should be due to augmentational hotspots in older animals. This experiment should involve both “Ca and double tetracycline labeling of an older dog or man. THE GENERATION DISTRIBUTION OF REMODELING BONE The assumption of random remodeling ean be tested by examining microradiographs for the presence of overlapping haversian systems. If the remodeling rate is a constant, \ (years—!) and if remodeling occurs at locations governed entirely by chance, then at u time T after adolescence there should be volume fractions of bone versus generation as shown in Figure 51 and Table 28. Generation 0 is the original bone formed during growth, generation 1 is once remodeled bone, etc. TABLE 28. Bone generation 0 1 2 3 4 5 6 Fraction or THE Bone VoLUME OccUPIED RY Eacuo GENERATION OF BONE AT 0 0.2 0.6 1 2 100% 0% 0% 0% 0% 0% 0% 82% 17% 1% 0% 0% 0% 0% 55% 34% 10% 1.5% 0.1% 9% 0% 37% 37% 19% 6% 1% 0.1% 0% 13% 28% 280% 19%, 9% a 1% | ! This table summarizes Figure 51 which erated iteratively on a calculator from the ser: Oh osor sSokor 0 2 3 4 5 6 which is identical to radioactive series decay. T constant \ is the same for each bone fraction, so the Bateman equations break down. For the case in radioactive series decay in w successive \’s are equal, Evans" shows 1 first daughter would peak at AT = 1. From J it appears likely that the second daughter wo at XT = 2, ete. Furthermore, although the calculation of Figure 51 is slightly in error, the of generation 0 bone should equal that of gen at AT = 1 when 1 peaks, and generation 2 shot generation 1 at AT’ = 2 when the amountof gc 2 peaks, etc. Table 28 has been adjusted to sh: relations. Note thatif ¥ = 4.6%/year, \T = 2 wou: at T = 43 years or about age 60, and 1%of 1 volume would be sixth generation bone. Perhaps a morelikely situation would be X = year observed at AT = 1 or 50 vears after ado or age ubout 68 years. In this case, perhaps generations would be detectable, 0-3, with t generation occupying 6% of the volume. (One would be fourth generation bone.) Careful microradiographie observation of th. bution of overlapping haversian systems migh whether this model of random remodeling is \ the distribution of generations is not as wide as ‘J predicts—that is, if the required proportions higher generations of bone are not found in pr: then resorption is not random but favors olde If true, this would be an important finding b dosimetry and for an understanding of the | signal which calls for resorption at a particular adult bone not subjected to a changing pattern o TURNOVER AND SURFACE-TO-VOLUME RATIO Can the Ratio of Trabecular Turnover to | Turnover be Related to the Respective Surface-toRatios? This would be an attractive hypothesis fo1 bone because it would imply that an osteoblast osteoclast does not know whetherit is on a sur: cortical bone or of trabecular bone. The fra. apposition surface and resorption surface would same everywhere (provided there was no cha stress which called for adaptive remodeling). Jowsey’s observations of surface activity in di é: