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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

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