84
scintillations, the spatial resolution would be limit
tion, obtained by taking readings everv 2 cm, shows the
advantages of the narrower collimation yielding a
Wie = 8.5 emvis-a-vis 11 and 15 em respectively. It 1s
seen that except for the area of the distribution between
15-21 em, the calculations could be considered satis-
timately by: (a) the dispersion due to the rod, (~
of its length);(b) the length of the luminesceni
tron track; and (¢) the energy interval of the Cor
electrons chosen for counting. The choice of the
will be the result of a compromise since the resolu
affected inversely by the square root of the gamn
energy (that is the numberof light photonspersc1
tion), whereas the statistical information is propo.
to the !» power of the numberof seintillations.
factory, since the errors in f(x’) are not more than 2 few
times those introduced in g(r). (Note that the tangible
error at 2’ < 10 em is due to having failed to inelude
g(x) readings for .« < 0, namely those bevond the spatial
limits of the distribution),
Before proceeding further, we must recall that even
if we had perfect photomultipliers and instantaneous
It is not unlikely that the choice will also dep«
whether detail of the function f(x’), or accuracy
integral [,° f(2’) dx’, is considered the more imp
information as far as the ultimate medical pur
concerned. Anillustration of what may happen 1s
in Figure 66 where the information given bythe }
ing curves is gathered in terms of radioactivity
Integrated Activity
an f(x)
Interval
on Fix)
fem)
:
0-14
14-44
44-54
eWHM = 15.0 cm
h=2cem
Ll
FWHM = 1L0cm
h=2cm
LO
~99
3.2
p
27
~10
42
4.8
.
~10
ercent Error
Experimental
FWHM = 85cm
Activity =2%
h=2cm
09
“1
3
~7
4.6
.
~2
Value of the
(uCi)
<0
0.9
~35
2.9
intervals of 14, 30, 10 em, to simulate dimensi
some organs within the body. It is seen that or
activity is sought over intervals larger than the
the errors drop sharply within acceptable limits.
A parameter of some practical importance is
terval h along g(x) at which readings are taken.
4.7
~?
ure 67 the effects of intervals between 1 and 4
shown for a resolution of 8.5 em; it is seen that a:
detail is concerned /. = 2 cm is best in thiscase. ]
lar experiments with a resolution of 15 em (Fig:
Fic. 66—Influenee of kernel resolution on accuracy of in-
tegral values of f(r") over 0-14. 14-44 and 44-54 em of extended
source.
FWHM = 8.5 cm
iN
50—
——— h=teom
Jot h=2cm
1
k
(\
60—
f
|
t
|
_
;
—-—n=3cm
h=4em
\
"
|
40-—
>
\\
:
k-
z=
O
<
5
uy) 20
:
P
|
r
4
‘|
=
oF
|
|
[il
f
‘
Hil
|
~
fy
o
if
} aN
YX #
ss
if
'
ii
i
re
=a
Hi
‘
te
fp to
0
IO
20
ft
:
i
H
,
VF
|
J
30
|
|
40
_|
L
50
DISTANCE (cm)
Fro. 67.—tiffect of & on details of f(x’) with Wi. = 8.5 em
|
60
7