62 the cortex which determines the time constant of the final exponential of the system as a whole. (See sec- tion on justification for equating the final exponential rate constant A in the retention function with the rate of apposition-resorptionin cortical bone.) (c) Sections 2(c), 3(b) and £(b) can now be combined to relate the final exponential of the modified power function or multi-exponential model directly with the rate of apposition-resorption in cortical bone. (i) Finally, having determined the tracer u trabeculae, the tracer uptake in the cortex is de by the requirement that the total tracer upta equal that for the body as a whole with w calculation was started. (j) The effect of soft tissue uptakeis still to uated. 5. Results (d) A corollary to 4(c) is that the retention curves This new bone model provides a solution for outstanding problems in the literature: tial. This is a reasonable possibility in view of exist- bone turnover (a few percent/year) measured of all the alkaline earth elements in adult man must have the same time constant for their final exponening data. This time constant must also agree with the best estimates of cortiéal turnover in man by the method of tetracycline labeling. (e) Nowthe turnover rates \ and od determine the amount of new bone that is heing formed in the cortex and in trabeculae at the time of tracer intake. Therefore, they determine the amount of activity in intense hotspots. The distribution of this activity among osteons growing at different rates is treated in the section on detailed uptakein osteons. (f) If we assume that the rates of turnover have been constant and that the remodeling has been random as to location in each kind of bone, then \ and od determine the distribution of bone ages within the cortex and the trabeculae, respectively. Knowing these distributions one can calculate the augmentation rate for cortex and trabeculae (see the section on age distribution of augmentation rates). Knowing both the augmentation rates and the apposition rates, one can then add them to obtain the addition rates or A-values for cortical and trabecular bone and for the skeleton as a whole. These A-values determine the tracer uptake; they must agree with direct measurements of A-values by kinetic studies. (g) The relative uptake of tracer in cortical and trabecular bone is also determined by the area requirement for age-invariant systems [2(a)]: the area under the trabecular curve of specific activity must equal the area under the cortical curve. The final ex- ponential for trabeculae has already been specified to be o times that for cortex (and body). Therefore, with a retention function of the type e'(t + €)%e-™ (2) the area requirement determines the relative uptake in trabeculae as compared to cortex once o has been agreed upon. (h) Sections (f) and (g) give independent values for the ratio of tracer uptake in trabeculae as compared to cortex. They must agree for the macroscopic model to be consistent with the microscopie model. (a) It shows that one can reconcile the low eycline labeling with the high rate of long-term uptake (15%/year) measured bycalcium kinet difference between the two rates is shown by th to be produced both bythe diffuse component a wide distribution of augmentational hotsp: uptake of activity in fully calcified regions : which are—due to remodeling—much young the skeleton as a whole. (b) It shows that the measurements of “‘bo: over’ from Sr uptake in fallout-labeled s! are much lower than calcium kinetic measu. because the latter are calculated only about fr after injection, whereas the fallout measui pertain to an average residence time of sever: after intake in a system for which the appare dence time increases with the period of the o tions. (c) The model demonstrates that it is pos+ construct a system which is age-invariant in res measurements of the whole-body retention of jected tracer in spite of the fact that the ind microscopic bone volumes are not age-invario cause their local rates of augmentation and dim decrease as bone ages. The rates of resorptu apposition in the adult human skeleton, howev just sufficient to keep creating enough new b maintain the rates of augmentation and dim in the skeleton as a whole at constant levels thro: most of adult life (see Figure 52). The model is, fore, macroscopically steady state but microsco non-steadystate. The osteoblasts and osteoclasts, through the: tinuous production of new bone, produce a home in the calcium metabolism of the skeletal syste: whole, in spite of the aging of the individual u bone of which it is made. (d) The modelfinally explains howit is poss! have a very lowratio of the diffuse to uniform and at the same time to have more than half kinetic A-value produced by the process of diffu: existing, fully-mineralized bone. We recogniz