' Ra nib " . : ke WL me oh a ee oeNi ad Bo atid dicta aiea oteahthdlbh tlce 79 we have associated with the apposition-resorption atc in cortical bone. » |xnowing the latter, we know the amount of L. itv in hotspots a few weeks after injection. The bout: activity involved in new bone formation and gecondary mineralization in cortical bone is “einead Auc = (1 — vr) (66) ‘here e( 1 — 7) is the amount of cortical calcium \ is the fraction being renewed per unit time ( / is the time integral of plasma specifie activity. ~ 1. From expression (19), 1 ne I=] 0 Sdt= = (1 — R). nk (67) List of Symbols Capital letters indicate functions of time since tracer injection. Augs Augmentation rate, the kinetic A-value calculated 5 days after injection for bone in which there is no apposition. Fractional retention of tracer in body. Plasma specific activity. c Plasma specific activity under continuous tracer intake. The rate of tracer intake into blood. Radius of osteon canal. Fractional rate of closure of osteon canal. Mass of calcium per unit length of osteon being RRA |. The final exponential of the macroscopic model, normal man, keeping in mind that the macroscopic and microscopic models must be internally consistent. T FR. «ROXNECTION WITH THE MICROSCOPIC MODEL ‘The asymptote of the integral at! = @ is Ane = a(“) a= 2) nk | n bone (not a function of time). Number of osteons per unit area of bone which A Activity per unit length of osteon. (69) "\ «, Similarly, the total activity mvolved in bone (63 formation in trabecular bone is of 0 the‘| ap Aur = a(%) oT (70) " formation, one can 7. From the section on osteon An the average hotspot intensity and the distri- fal an! Wibon. s. nowing both the total activity and the hotspot rlivity, one obtains the activity not connected with banc formation. This calculation must then agree with the direct calculation of the overall augmentation rate (65 ‘in the section on osteon formation. . Expressions (69) and (70) give the fraction of the injected activity which deposits in hotspots due to bone formation. They do not give the fraction of the retained activity (the current body burden) in hotSpots. If hotspots showlittle diminution for a month or so. then the two figures can be quite different. The }Cininution in hotspots at times shortly after injection reqiures further experimental investigation. Also, the effect of soft tissue uptake has not yet been included. CONCLUSION The preliminary model outlined above promises to Provide a framework into which the data listed in _ ! -uommary of background information can be fitted. tainty ©... must now attempt to find the best parameters for i V D A f T a,8 At ly V; Ci a; Vie Se Auc Aur B Vr = \/Ne th a >. Therefore, (68 ) nor = g/nk. laid down per unit time. Gramscalcium per em’ of bone. Time for forming an osteon. Number of forming osteons per unit area of start forming per unit time. The time integral of S from 0 to ¢. Specific activity of some compartment in bone. Microcurie-days per cm’ of bone surface. Depth of Rowland’s exchange on bone surface. A volumefraction of bone. The time since skeletal formation (a person’s age minus about 18 years). Used to express augmentation rate as a function of bone age. KXinetic A-value calculated at timef. Equilibration time for model in which a power funetion is followed by an exponential [Case (a)]. Specific activity of 7** compartment. Calcium content of 2** compartment. Calcium transfer rate of 7** compartment. Vat beginning of period of transient equilib- rium. S at beginning of period of transient equilibrium. Activity in bone formation hotspots m cortical bone. Activity in bone formation hotspots in trabecular bone. Body specific activity (uCi/gea). ‘Trabecular specific activity. Cortical specific activity. Activity injected. Bodycaletum. Turnover timeof initial pool (days). betal