Bee RE catia ate a at ailaelate, 72 Case (a) = (1 — pyerr Case (b) 4 = | (35) r(2 ~ Hake (= be (a) o”° = 2.9 (left hand intercept) - ¢, = 23 years For radium, 6 = 0.5, soo = 8.4 4, Thefinal exponential in case (b) has a lower rate constant than case (a), which allows a choice as to the best fit for data. (a) leads to \ & 6/t, = 2.5 %/year for Ca, Sr and Ra in man. (b) produces a common X= 1.5%/year for approximately the same input data. % From this point on, consider only case (b)—the power function times an exponeniial. (b) Ifo” = 2.0, then « = 4.0 X= 145%/year t, = 23 years (ec) From the considerable spread in t} one can only conclude that X is the« 1 %/year. 12. For case (b) above, the power function t exponential, the effective rate constant for re at a time f after radium intake is [(1/R)(dR/d. 5. The average specific activity of the bodyis then B=! 0(i + )e™[ease (b)] cortical bone by apposition-resorption. 7. Then if the apposition-resorption rate of trabecu- lar boneis o times that of the cortical bone, the specific activity of trabecular bone is (38) where the first bracket (c'’) normalizes the whole expression for Vy so that For ¢ = 35 years X= 1%/year a weight) that is trabecular is designated by 7,tl ratio of the specific activity of cortical bone to the bodyis given by once o has been chosen. 8. Nowthe ratio of trabecular specific activity to body specific activity, V;/B, may be compared with data for radium in man and “Sr in man: a _ gighee ; (40) intake on semilogarithmic graph paper. (See Llovd’s report on radium in man.°” 10. The time at which V7 crosses and starts falling below B is P= SG (Vr = B), (41) 11. Lloyd’s plot of the MIT radium vertebrae is fitted by ro Pe et l—-—+r JUSTIFICATION FOR CONSTANT EQUATING 2X WITH FINAL CORTICAL EXPON. APPO> RESORPTION 9. Expression (40) is exponential so that V,7/B can be plotted as a straight line vs. time since tracer L = (1 — b) log. « _. This expression insures that the sum of the « and trabecular activity always equals the to tained activity [compare (40) and (43)]. It fits J plot for humanradium quite well. The expressions above for Vr, Ve, and B are for radium in man in Figure 56. RATE bo 1 B 0 termines the initial uptake of activity in the trabeculae effective = 2.4%/year of the average rate constant in 20 radium + some 30 to 40 years after intake. 13. If the fraction of the skeleton (by « Ve This is another application of the area rule. It de- ite b = 0.5 This agrees with Keane and Evans’®”’ measu i Vrdat= | Bat = | Sdt = q/nk. (39) a b effective =k (37) 6. We associate \ in Step 5 with the turnoverrate of Vr = (0) 2 et + ee™ A = 0.63 %/, An equally good fit would be From expression (42) it is clear that at ver times after injection the power function (and d tion) can be neglected and \ Is the dominantt: 1. Consider the behavior of the parallel mx which a number of bone compartments exchan: cium directly with the blood plasma. A particulz compartment, 7, has specific activity, V;, calciu and calcium transfer rate (due to apposition-: tion), a;. The behavior of V; is given by Cj dV; dt —a(V; —_ S),