Figure 63)£ p ryblems.”” We consider here the one-dimensional case
he result jp which is expressed as follows
[ Kea") fle’) da’ = gle) + ele)
b
|, but mog'
upling light were f(z’) is the unknowndistribution of radioactivity
he seintilla.!
2"x2' PILOT B
tion in eff.
since, ult}.
Co®® coi.
by the fact that the amounts of radioaetivity sought in
the human body are unusually small. Hence, careful
study must be devoted to the selection of response kernels of width most appropriate to optimize the amount
of needed information.
: equation,
yields ap.
Experimentally our experience was gained with a fili-
form source (~0.7 mm width) consisting of a fine catheter ~200 cm long filled with uniform Cs!*’ microspheres
of about 0.2 nCi and shaped as a sequence of sinusoidal
waves of varying frequency and extending about 60 cm.
The detector was either a 3” diameter Nal crystal with
“ill-posed
Av. Res. 432 ps
three collimators or a cylindrical rod 2” diameter and
Av. ps/em 142
i
Average FWHM = 3.04cm
BOT
20
{0
oO
10
ot
20
CMS OF ROD
hic, 64—Proportionality between distance and transit time
l
T
t
REAL DISTRIBUTION
FWHM = 8.5 cm
oe
FWHM=1i.0 cm
-----FWHM =15.0 cm
T
TT
;
460
wo
i; \
50
°
RELATIVE AMOUNT OF ACTIVITY
mM
oO
Tr
25
60 em long covered bylead bricks separated from spaces
ranging from 1 to 5 em, as indicated in Figure 61.
Theresults concerning W4,;,, namely the effect of the
kernel width on the solution f(2"), are illustrated in Figure 65. As were all our results, they were obtained by the
smoothing technique, described elsewhere“) and programmed in a 3600 computer. Our f(z’), the true distribution, is shown bythesolid line; our calculated solu-
4°
0
10
20
30
cm
RELATIVE AMOUNT OF ACTIVITY
listribution®
lem of un
n equation,
appropriate Inanimate phantoms containing relatively
intense sources.
g(x) 1s the counting rate detected at the position x
In practice, the physical problem is further complicated
NANOSECONCS
oarameten
x’, We assumethat it can be determined very accurately
for practical purposes by prolonged measurements over
e(z) stands for the error whose limits are known from
knowledgeof g(x), althoughits actual value is unknown.
No detail can be given here of the methods of solving
this equation for f(x’) once K (z,x’) and g(x) are given.
lisplay sys.
entifies thet
unding thet
counting rate registered by the scintillator at x due to
the presence of an ‘ideal unit point source”situated at
and is subject to both statistical and experimentalerror.
with Al mylar reflector
ater in any
e detectior*
thicknesse*
dth of the!
per unit length of the body. The kernel K(z,z’) is the
60
Fic. 65.—Influence of kernel resolution on detail of f(z’)
MOK viet
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bt