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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS - 1963

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LEGAL NOTICE
This report was prepared as an account of
Government sponsored work. Neither the
United States, nor the Commission, nor any
person acting on behalf of the Commission:
· A. Makes any warranty or representa-
tion, expressed or implied, with respect to
the accuracy, completeness, or usefulness
of the information contained in this report,
or that the use of any information, appa-
ratus, method, or process disclosed in this
report may not infringe privately owned
rights; or
B. Assumes any liabilities with respect
to the use of, or for damages resulting from
the use of any information, apparatus,
method, or process disclosed in this report.
As used in the above, “person acting on
behalf of the Commission” includes any em-
ployee or contractor of the Commission, or
employee of such contractor, to the extent
that such employee or contractor of the
Commission, or employee of such contractor
prepares, disseminates, or provides access
to, any information pursuant to his employ-
ment or contract with the Commission, or
his employment with such contractor.
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ORNY P-1383
MASTER
Cant-6503/3-2-
26
COMPARISON OF VARIOUS METHODS OF RATE RECORDING*
JUL 20 1965 do
C. Craj.g Farris, M. M. Satterfield, P. fi. Bell, D. A. Foss
Oak Ridge National Laboratory
Oak Ridge, Tennessee
In nuclear medicine there is an inescapable need to record "counting
rate" versus time. The words "counting rate" are in quotation marks because
what is recorded is practically never a counting rate but some sort of average
over some time. Because of the randomess of nuclear events, it is impossible
to measure instantaneous counting rates.
Instead, regardless of the instru-
meutation used, an averaging approach must be used.
If the averaging is made over a few counts, the statistical variations
are large.
If many counts go into the averaging process, the average can
be quite accurate if the rate does not change significantly during the aver-
aging time.
This is the fundamental dilemma facing the designer of instruments
for count rate recording. If he desires a response fast enough to follow
rapid changes, he has to insure that there are enough counts in the memory
of his device (averaging over a sufficient number of counts) to prevent
“Research sponsored by V. S. Atomic Energy Commission under contract
with Union Carbide Corporation.
*counts are stored in a rate-measuring instrument, and the "storage
bin" is often referred to as the memory. The time a count stays in this
memory is called the memory time or memory duration. The memory can be
thought of as a time interval sliding along in time (or being moved along
in time-steps in some devices).
PATENT CLEARANCE OBTAINED. RELEASE TO
THE PUBLIC IS APPROVED. PROCEDURES
ARE ON FILE IN THE RECEIVING SECTION.
statistical variations from being so large that they mask the rapid changes
he is trying to record. This in itself forces a, slowing of response simply
because the instrument must wait to acquire the necessary number of counts.
The amount of faith that may be placed in s plot of count rate vs. time
is very simple to define. About two thirds of the time the actual indication
will be within VN of the true average of N counts in the memory. Only
five per cent of the time will the trace wander father than 2 VÑ away
from the average of N counts in the memory.
In a conventional rate-meter each pulse adds a small charge to the
capaciter of a "tank" circuit, and the charge leaks away exponentially through
a shunting resistance. The time constant of the decay is RC, the product
of the resistance and capacitance; thus the decay can be made fast or slow
as desired. Because the charges enter the tank with randon timing, the indi-
cated count rate will fluctuate, since it is measured by the instantaneous
charge on the capacitor. These fluctuations have a standard deviaticile trid
the exponential nature of the tank causes the S.D. to behave as if th: rabi
meter's "memory" contains the number of pulses that would accumulate in two
time constants.
In practical terms, if the count rate averages 100 pulses per second ,
and the rate-meter's time constant is 0.25 sec., the tank will look as if
it contains 50 pulses, with an S.D. of V50 = 7.1. The fractional standard
deviation is therefore 202, or about 14 percent. For the general case, F.S.D.
El
Thus the reliability of the reading delivered by :
V2 x RC x count rate
a couat-rate-meter can easily be determined 1f the time constant is know..
The exponential behavior also permits one to estimate how long one should
wait for a new reading to become trustworthy. In one time constant (sec. in
the above case) the indicator will have completed about 5/8 of the reeded change;
-3-
in 2 RC it will complete 7/8; in 3 RC about 95 percent. We can't expect a
"true"reading, therefore, until perhaps 4 time constants (98%) have elapsed.
And even then the reading, in the example cited, will be in erro: by 14 per-
cent or more about 1/3 of the time. It would be difficult to draw conclusions
from a record as shaky as this.
Now suppose we present this same rate-mater with a pulse rate of 10,000
100
per second. It will take just as long to reach ti reliable reading, but now
the S.D. will be only 1.4 percent of average ( = =
). This
V2 x 0.25 x 10,000
kind of indication we can trust.
سه سوده ... ممم منوف
Tais would suggest that, when recording with a conventional count-rate-
ملامین مع نسه ها نوش فرم به
meter, it is easy when there is a high counting rate. It also says that
rate recording is extremely uncertain with only 50 counts in the memory.
There have been attempts to circumvent the basic problem. They have
ت نها سه نما بعد
not been totally successful, and probably will never fully succeed. There
have been developed, however, several instruments that appear to be at
least somewhat better than conventional count-rate-meters.
These instruments have in common one major property. Unlike the
conventional count-rate-meter -- whose memory is indeterminate -- they
have definite memory content. Perhaps the simplest of these is a scaler
in which there is provision for recording, at the end of a chosen `ime
interval, the number of counts accumulated during that interval. After
recording, the scaler is reset and a now cycle is begun. The so-called
"digital-rate-meter" is nothing more than this. A multichannel analyzer
used in the "multi-scale" mode is also essentially the same.
In general, a change from a count rate meter to one of these devices
is a good thing. It can be shown that, for the same number of counts in
memory, a recording scaler has about twice the response speed of a count-
4-
rate-metor. Stated conversely, for the same response time, a recording
scaler will have twice the counts in its memory, with a statistical improve-
ment of about V2 in the reliability. Moreover, the statistical worth
of any plotted point can be easily estimated because the metiory content is
easily determined.
As previously noted, an estimate of the memory content of a count-rate-
meter -- and of the statistical worth of any part of a curve - Is easily
determined. Few people, liowever, will take the trouble to do this. The
chief reason seems to be that no one is willing to divide counts per minute
by 60.
It seems that on almost every commercially-available couat-rate-
meter the counting rate is given in counts per minute and the time constant
is noted in seconds. The average person, when faced by this remarkable mix-
ture of units, is quite willing to let "statistical validitys take care of
itself.
To pursue this unhappy situation further, it would seen there is a
se:sible answer that would be acceptab?3 tc clinicians and to instrument
manufacturers. (Each blames the other for this mess, incidentally.) When
the time unit of interest is the second, as in cardiac output and other
fast phenomena, it wou'd seen reasonable to give counting rate in counts
per second. This is probably reasonable also in slower processes such as
renal studies. For the slower work, however, it might make sense to give
the counting rate in counts per minute and the time constant to minutes or
decimal fractions thereof. In any event, if the courting rate and time
constant had the same time dimensions, people might be a bit more willing
to esimate the statistical validity of Wiggles in a curve rather than
groping for physiological explanations for them.
We have made a device, similar in principle to a recording scaler ex-
cept for two things: First, it averages over ten sub-intervals but changes
indication at each sub-interval. Second, it is made only with analog outa
put for driving a strip-chart-recorder. Then ter-unit memory provides the
same result as (with a digital-rate-meter) averaging over ten time later.
vals, advancing one time interval at the time and dropping one of the end.
This device we have called a "true-average" count-rate-meter.
To investigate the relative merits of the various devices, we have
constructed a device that exposes predeterruined amounts of a source to &
counter and is therefore a count rate function generator. Using this de-
vice, we have compared a conventional count-rate-meter, the "tre-average"
rate-meter, and a multi-channel scaler (which operates exactly as a "digital-
rate-meter" but with point readout).
We have come to the following conclusions:
1. If there is sufficient counting rate, any of the 3 devices, prop-
erly adjusted, will perform satisfactorily.
2. If there is not sufficient counting rate, nc ijpe of count-rate de-
vice will give satisfactory results.
3. At any counting rate, the "digital-rate-meter" and the "true-
average" rate-meter are both at least slightly better than the conventional
rate-meter.
4.
There is a final conclusion that is inescapable.
If the recorded
L
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trace of "counting rate" versus time -- obtained with any counting rate
measuring device -- is to be believed regarding rapid changes, the memory
or time constant must be short enough that the statistical variations are
highly evident in the recorded curve. Stated another way, if you are going
to believe rapid changes shown by the trace, there must be "hair" or "gress"
.
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on the curve.
The hair on the curve shows the system's response to t'ast
changes. (A posmiðle exception to this is the filtered-rate-meter of
Oldendorf.) on cardiac output curves obtained with count-rate-meters, lack
of hair on the curves indicates automatically and necessarily that there
18 serious distortion of the portrayal of the actual events.
In support of these conclusions, Figures i through 9 arc offered.
They show several comper isons made with the count-rate function generator.
(Additional comparisons of the pain formance of a count-rate-meter with
various time constants are shown in Reference 1.
In these earlier compari.
sons, the pattern was stored on magnetic tape and the same pattern was
played back for each comparison.) In each of these figures, unless other-
wise noted, the comparison was made between traces deemed the "best" that
the instrument had to offer. In some comparisons, this choice was difficult.
The effect of counting rats on a count-rate-meter's performance 18
shows 10 Fig. 1. The "true" curve was plotted at 1/50 real time with the
"true average" rate-meter. This illustration supports conclusions 1 and
2. With 300 to 600 counts in the memory, a rate-meter does passably well.
With 60 to 70 counts in the memory, it does poorly.
Figure 2 shows that the choice of "best" results 18 difficult, but
that traces with less smoothness are probably better. Figure 3 supports
Figure 1, with a different test pattern.
In a conparison of the three devices at nigh counting rate, Figure 4
shows that all three do very well. In Figure 5 the counting rate is re-
duced to one-tenth of that in Figure 4, and all three instruments are in
trouble. In Figure 6 the maximum counting rate 18 about three times that
of Figure 5. The three instruments perform fairly well, with no clear ad-
vantage for any one. (The vertical normalization for the digital-rate-meter
is slightly low.)
If there is any difference - End careful analysis or
large numbers of comparison indicates that there 18 a slight dirrerence, ..
It is only slight and 10 lavor of the "true-average" and "digitel" rate-
meters.
The effect of everaging time for the "true-average" rate-meter) og
the appearance of a curve 18 showa 10 Pigure 7. This shows how d£fficult
the choice of "best" 18. It also shows that the upper right hand trace to
Figure 7 Appears slightly more faithu then aay test trace 10 Figure 6.
In Figure 8, the "true-average" and conventional cout-rate-meters
are compared with about the same counts 10 the memory, on a suck renogram.
The true-average rate-meter gives slightly more faithful reproduction (a
point of inflection at 75% of maximum od the first rise and a slightly
smoother curve). Both curves in Figure 8 show enough hair to warrant con-
siderable confidence in them, yet the mean location of the trace care be aver-
aged by eye quite easily.
Figure 9 18 reprinted from Reference 1 and 18 lecluded to show the
firmness of conclusion 4. Io these curves, made by playing back the same
magnetic tape through a count-rate-meter with several time constants, only
the traces with "hair on the curve" have any promise at all of showing the
true events.
The results of our experiments are not strikingly in favor of anything
.
.
..
but high counting rates. It 18 imposs.ble to show, in a simple way, & strik-
ing superiority of the true -average and digital devices over the con-
ventional rate-meter. We are, however, 80 satisfied that there 18 a
definite superiority, and in our own work, we plan to use mostly the true-
average or digital ræte-meters.
8.
We believe that all devices currently in use for count-rate recording
Counse at least some distortion of the actual events. When the counting
ratio is high, however, all can be used properly. When the counting rate
1s low, none of them will do a good job. For fast changes to be believe
able, there must be hair on the curve; the statistical wiggles, however,
must not be do large that they totally mask real events. Only specious
reasoning vould lead one to put an tiedequate amunt of tracer activity
intia a patient and then to conceal the shakiness of the information by
smoothing the curve with an excessive time constant or time interval.
REFERENCE
Discussion pp 98-103 Dynamic Clinical Studies with Radioisotopes.
Edited by R. H. Kaise ley and W. N. Tauxe, United States Atomic mergy
Commission (TID 7678). Available from or ice of Technical Services,
Depamas tinent of Commerce, Washington, D. C. 20230 ($4.50).
1
13
Fig. 1. Count-rate-meter recordings of test pattera at 3 meximum counting
rates.
Fig. 2. Count-rate-meter recordings of test pattern 2 time constants.
Fig. 3. Count-rute-meter recordirigs of cardiac pattern at 3 maximum
counting rates.
Fig. 4. Comparison of three count-rate recording devices on the same test
pattern, at high counting rate. The "best" curve for each in-
strwent 18 used for this comparison.
Fig. 5. A comparison of the same devices uxed in Fig. 4, on the same
test pattern, at low counting rate.
Fig. 6. A comparison of three count-rate recording devices at "inter-
mediate" counting rates. ..
Fig. 7. A comparison, showing the effect of everaging time, for the
"true-average" rate-meter.
Fig. 8. A comparison between the "true-average" rate-meter (an experi-
mental device) and a conventional count-rate-meter on a renogram
test.
Fig. 9. Count-rate-meter recordings, with various time constants, obtained
with playback of magnetic tape. Reprinted from Reference l.
En

ORNL-DWG 65-2488
MAX COUNTING RATE
TEST PATTERN, "TRUE" CURVE
300 COUNTS PER SECOND MAX
-0.22 SEC TIME CONSTANT.
5 sec
PATTERN
TIME
250 sec
ACTUAL
TIME.
4000 COUNTS PER SECOND MAX
0.4 SEC TIME CONSTANT
3000 COUNTS PER SECOND MAX
0.4 SEC TIME CONSTANT
n
40
20
1020 30 40
40
20 30
TIME (sec)
TIME (sec)
Count Rate Meter Recordings of Test Pattern at 3 Max Counting Rates.
i statii si intretinbow
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ORAL-DWG 65-2190
1000 COUNTS PER SECOND MAX
0.1 SEC TIME CONSTANT
1000 COUNTS PER SECOND MAX
0.22 SEC TIME CONSTANT
0
5
10
15 20 25
TIME (sec)
30
35
40
0
5
10
15 20 25
TIME (sec)
30
35
40
TEST PATTERN "TRUE" CURVE
15 sec
PATTERN TIME
250 sec
ACTUAL TIME
AN
0 5 10 15 20 25 30 35 40
TIME (sec)
Count Rate Meter Recordings of Test Pattern 2 Time Constants.


CARDIAC PATTERN, "TRUE" CURVE
ORNL-DWG 65-2489
300 COUNTS PER SECOND MAX
-0.22 SEC TIME CONSTANT
5 sec
PATTERN
TIME
250 sec
+ ACTUAL
TIME
-
23
284
1000 COUNTS PER SECOND MAX
0.22 SEC TIME CONSTANT
231 28
3000 'COUNTS PER SECOND MAX
0.22 SEC TIME CONSTANT
231 281
30

0 10 20 30
0 10 20
TIME (sec)
TIME (sec)
Count Rate Meter Recordings of Cardiac Pattern at 3 Max Counting Rates.
mim
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CARDIAC PATTERN, "TRUE" CURVE
ORNL-DWG 65-2493
COUNT RATE METER
3000 COUNTS PER SECOND MAX
0.22 SEC TIME CONSTANT
5 sec
-PATTERN
TIME
250 sec
ACTUAL
TIME
234 281
234 281
"TRUE-AVERAGE" RATE METER
-3000 COUNTS PER SECOND MAX
0.5 SEC
- AVERAGING TIME-
"DIGITAL RATE METER"
3000 COUNTS PER SECOND MAX
0.4 SEC TIME INTERVAL
? 237 281
20
30
0
234 2812
10 20 30
TIME (sec)


TIME (sec)
..
.
CARDIAC PATTERN "TRUE" CURVE
5 sec
– PATTERN TIME
250 sec
ACTUAL TIME
ORNL-DWG 65-2191
COUNT RATE METER
300 COUNTS PER —
SECOND MAX
0.22 SEC TIME
CONSTANT
CC
234 281
231284.
"TRUE-AVERAGE"RATE METER
300 COUNTS PER
SECOND MAX
0.5 SEC ÁVERAGING
TIME
"DIGITAL RATE METER"
300 COUNTS PER
SECOND MAX
0.4 SEC TIME INTER
INTERNAL
1
15
o 5 10
TIME (sec)
234 281
20 25 30
0 5 10
TIME (sec)
15
231 28
20 25
30

momento de la
intens
itetindinici materiaime.com
een
ORNL-DWG 65-2192
CARDIAC PATTERN "TRUE" CURVE
COUNT RATE METER
– 1000 COUNTS PER SECOND MAX +
0.22 SEC
TIME CONSTANT
5 sec
PATTERN
TIME
250 sec
ACTUAL
TIME
YL234 287J
IT
1114 À 231 284
"TRUE-AVERAGE" RATE METER
– 1000 COUNTS PER SECOND MAX
0.5 SEC
AVERAGING TIME
· "DIGITAL RATE METER"
1000 COUNTS PER SECOND MAX
0.4 SEC
-TIME INTERVAL
CS
$ 234 281
10 20 30
TIME (sec)
10 20
TIME (sec)
30


1000 COUNTS PER SECOND MAX
0.5 SEC
AVERAGING TIME
ORNL-DWG 65-2186
1000 COUNTS PER SECOND MAX
ht
0.2 SEC
AVERAGING TIME
114 23 284
10
20 30
TIME (sec)
0
1 231_28
: 10 20
TIME (sec)
30

CARDIAC PATTERN, "TRUE" CURVE
5 sec
PATTERN TIME
250 sec
ACTUAL TIME
119. 23 _28
0 10 20 30
TIME (sec
"True -Average" Rate Meter on Cardiac Pattern.

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ORNL-DWG 65-2187
"TRUE-AVERAGE" RATE METER
300 COUNTS PER SECOND MAX
5 SEC AVERAGING TIME
COUNT RATE METER
300 COUNTS PER SEC MAX
2.2 SEC TIME CONSTANT
11
4
8
12
16 20
TIME (min)
24
28
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0
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12
16 20
TIME (min)
24
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32

✓ Renogrom Pattern
UNOLASSIFIED
Om-omg 63-mo

1200


ACTUAL CURVE
TIME CONSTANT : 0.1 vec
TIME CONSTANT: 0.22 sec
200
counts/wc
10 20
TIME (voc)



TME CONSTANT: 0.5 voc
TIME TONSTANT: 18c
TIME CONSTANT : 2.2 wc.

TIME CONSTANT : 5 sec
END
D
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DATE FILMED
19/13/65







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