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),