we a ee Ma
Id
v
x
a!
T
Tere erny
v
T
TUTCIYy
Tr TUTTryT Trt
PT rary rrr
“TTT
a
T
T
TYTTt
-
5
7
T
p
Yo/year. .
LL
Z
iE
ar
3
-
-
}
1e order
1
SN
10 oe
Pa
=
;
.
4
4
-
3
1 times ag
retentiog.
3
dt)}:
/dt)}
+4
°oO
—
=
=
2 107k
q
o
EF
(42,
Ld
lu
r
=
5
°
8-BODY SPECIFIC ACTIVITY
SQ
74
h
' (Time for)
"x
time
4
(tz =L2ty)
SQ
:
(Crossover time)
7
f
|
{
. (3 initial time
-J
J
V7 -TRABECULAR BONE
7\Vy7=8B
=3
o
subject:
=
=
® 10 Ey
°
=
CS
ia
|. Turnover
‘ surement
ZS
on
Ve~CORTICAL BONE
x
o
S-PLASMA SPECIFIC ACTIVITY
=—
~Z
a
4a
:
™
ui
.
[
°
calcium
then thy
—4|
ty = oe
iO '£
7
E
o that of
Se =
>
P
Ve
a
|
5
lO Le
(43}-
RADIUM IN ADULT
MAN
=
,
-
P
cortical
otal ref
He
0.1
S
—
\!
\
| cortul
Nl
1
col
10
as tol
100
{
J
toil
|
io?
7
_
trol
X
104
5
-oht
hi
ot
|
cul
10°
4
7
7
7
Ly te
108
DAYS AFTER !NJECTION
schowdl
hic. 56—-Summaryof the macroscopic model. Curves showthe bodyspecific activity B, the plasma specific activity S, the specific
activity of cortical bone V,, and the specific activity of trabecular bone V7 as given by the model. The parameter values are chosen
foapproximate the behavior of radium in normal adult man: b = 0.5, e = 0.18 day, 7k = 7 g calcium per day, « = 4 (theratio of
TENTIALgtheturnover rates of trabecular and cortical bone), 7 = 0.2 (the fraction of trabecular bone in the skeleton), and c = 1000 g calcium
SITION-2 (body caleium). The given values of b, e, and y& lead to the prediction that the final exponential rate will be 1%/year (assuming
&ce-invariance and no long-term discrimination), and this rate has been taken as the turnover rate of cortical bone by apposition-
Te-orption, Note that the areas underall four curves from time zero to time infinity are equal to each other and equal to ¢/nk,where
ry longe¢ is the aetivity injected (100° dose) and yk is the excretory plasma clearance in grams of calcium per day.
VY; =
“Mt
V ice
S= Se™
Shere
exponential rate constant of the model as a whole.
3. Then
(45)
(46)
[7
Wher .. and §, are the compartment and plasma
EDecitic Activities at the beginning of the equilibrium
aV.
dt
(47)
S= —\Vie' = XV;
80
—edV;, = -—ail
cn
Vi -
a(V
8)
= —al;
ait a
aV; — ¢caAV; = aS
vw
(48
(48)
(49)
~
ge calf
°- Now when transient equilibrium following a single
ir boné injec tion is finally reached,
_
allen
ddel in compartment.
period, which is here taken as ¢ = 0, and } is the final
ante,
Sel
a
liminudl
erm, EWhere S is the specific activity of the plasma, the central