: ey , : : ae tena MthateA da ol eleanetl neilethos Lad S alee {t should be emphasized that this approach to the | 0OO-——-—— rn 228747228 Rq Pi Thorotrast problem is not intended to accord very aceuritely with a metabolic model expressed in terms of compartments constrained by long biological half-lives, ance this, in general, is not how Thorotrast: behaves. “t evidence Is more in accord with a model whichpic- - wes the Thorotrast as a diphasic material containing a eertiib proportion of the activity trapped within the particles, and the remainder in a relatively rapidly I t I 0.90-~ — ° | Si | x 0 sol metabolizing pool outside the particles. In such a case as this, the mathematical treatment presented here is a ~ [ simple but not unreasonable approach to the problem, at least for the soft tissues. To the extent that it is over~implified, its inadequacies should reveal themselves in tle different values of the retention coefficients (or -tendy state activity ratios) fi and f. calculated from experiments of different durations. 1 Th in short-term experiments (<1 year), most of the activity of #8Ra and *8Th is associated with atoms of ivpe I, and, therefore, the caleulated values of fi and fs should describe mainly the behavior of the injection material, At much later times (>>2 years), however, a -jenificant proportion of theRa atoms are of type IT, und most of the “8Th atoms are of types II and HI. In lise eases, therefore, the calculated values of fi and fe — npoule, shoud principally deseribe the behavior of the radioaetive atoms generated im vivo. The quantitative inter- pretation of f; and fe is thus fraught with difficulty. | Nevertheless, from a studyof their values for different tissues, it should be possible to gain at least a reasonable qualitative picture of the overall metabolism of 7%Ra / and @8Th in the whole body, since values of fi and fe suiuler than unity imply a “wash-out” of the daughter i-tope concerned, while values in excess of unity imply «net gain or “wash-in” of that isotope from other tis- 20 With the above qualifications in mind, and adopting the definitions given in Table 54, and from the varia- tion of the coefficients of the Bateman equations with time (see Figure 88), we can write for the activity in a fi<<uc sample at any time after administration of the 30 TIME 'N YEARS 40 50 Fic. 89.—In vitro activity ratios °**Th:™Ra:Th in Thorotrast at different times after the preparation date. 2287 9 2281 (4) 1.e., The ratios of activities at the time of sampling are implied in this equation. The suffix § refers to the tissue sample, and the suffix T to a Thorotrast sample containing, at the timeof injection, the sameactivities of °’Th and its daughter isotopes as were actually administered. At very late times when [??Ra/?”Th]- is equal to unity, fi has the desired property of expressing the *8Ra/?®Th ratio in the tissue at the timeof radioactive steadystate. Solving for fe , from Eq. (3) we obtain C/A fe = (5) fe + a fs + | It should be noted that, at very early times when Cy &X Co 0, and cz, & 1, Eq. (5) ean be expressed in a form similar to Iq. (4), i-e., _ OSTTES, fr = 28D 4 23h 22Th |g 7 2arPph ee At times greater than about 10 years when c; < 1, it is readily shown that fs can be expressed in the form 228 28h (6) Thorotrast: ior ?®Th: A = ado (1) tor "8Ra: B (2) I P 10 for “’8Th: C GA ofiby + aBofibe =aaA offer + aB ofifoce + aC feces . Solving for fi ; from Eq. (2) we obtain f, ; = A . ae + Pia Bi ‘Ao (3) It is interesting to note that, from the time of manufacture of the Thorotrast, the ratio ?°Th/Rajy takes many more than 6 half-lives of 28Th to approach closely the value unity (Figure 89) and even after 20 years, is still about 5% below radioactive equilibrium. The ratio [28Th/28Ra]y in Eq. (6), therefore, remains a significant correction factor to the ratio ?°Th/**Rajg until many more than 20 years from the time of manufactureof the Thorotrast, ae cy i sv ose iz