IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-28, NO. 4, DECEMBER 1979

Microprocessor-Based Flow MeasurementUsing a Positron Active Tracer

HANNU HEUSALA AND RISTO MYLLYLA

Abstract Methods for liquid-flow measurement based on thetransit time of a positron active source are described, and theaccuracy of each method is estimated. A microprocessor-basedsystem and a TTL integrator for studying a positron active flow isconstructed. The theoretical and experimental studies show that thevelocity of a point source, 111 kBq (3pCi) Na22-isotope (4, 1 mm)inside a metal pipe (4 42 mm) can be measured using annihilationcoincidence detection (detector pairs 1 m apart) and microprocessorelectronics with inaccuracies of 0.2, 0.5, 0.7 percent for velocities 0.1,0.5, and 1.0 m/s, respectively, at the 95 percent level of significance.Greater accuracy can be achieved by increasing the activity of thesource.

I. INTRODUCTION

POSITRON annihilation coincidence detection (ACD)is known in emission transaxial reconstruction tomo-

graphy [1] and the pulse velocity method using singlephoton counting (SPC) in determination of the mean velo-city of liquid flow [2]. These methods are used in the presentwork for velocity determination in the case of positronactivity [3]. The main aim is to find a way of studying thevelocity profile of liquid flow in a pipe, with special referenceto pulp flow in paper manufacture. A microprocessor-basedinstrument and a TTL integrator have been constructed foranalyzing the ACD signal and resolving the transit time ofapositron active source.

First, some timing techniques are discussed theoretically.The standard deviation of measured transit times for fourdifferent techniques are calculated. Then the velocitymeasurement accuracy of those techniques are comparedtheoretically assuming the timing signals are triangulars.Two different kinds of electronic apparatus are used forstudying experimentally the ACD-timing signals and thetheory developed.

II. METHODS FOR TRANSIT TIME MEASUREMENTOF POSITRON ACTIVITY

If a tracer is detected using the ACD method, the coinci-dent pulses from two detector pairs form the pulse ratesignal r(t) shown in Fig. 1. This is based on the properties ofpositron annihilation radiation containing two coincidentgamma rays of a certain energy of 0.511 MeV which areemitted in opposite directions, so that the ACD signal isdetected only if the source of radiation lies in the volume

Manuscript received May 10, 1979; revised August 6, 1979. This workwas supported by grants from Tauno Tonning Foundation, Academy ofFinland, Oulun Yliopiston tukisaatio and Tekniikan Edistamissiatio.The authors are with the Department of Electrical Engineering, Univer-

sity of Oulu, Linnanmaa, 90570 Oulu 57, Finland.

Fig. 1. Pulse rate versus time output of ACD circuits.

between the two detectors. One disadvantage of thismethod, however, is the noise signal caused by randomcoincidences. If the two pulse rate distributions in Fig. 1 areused as timing signals, the slope (dr/dt) of the function r(t) isimportant. The statistical fluctuation of the measurement isinversely proportional to the slope of the timing signal. Thefunction r(s) can be constructed by measuring the ACDpulse rate in respect to the position (s) ofa point source, andthe slope of r(s) is dr/ds and the velocity of the source isv = ds/dt. The dependence between the slopes dr/dt anddr/ds is, therefore,

dr dr ds drt dt ds = v ds = vk.dt dt ds ds

(1)

Several parameters can be calculated from the functionr(t) to describe the flow of radioactivity [2], [4], althoughuncertainty in the position ofthe point on the recorded tracechosen to represent the mean velocity of the tracer in thefluid may give rise to statistical errors which vary accordingto the parameter used. In this paper, the following para-meters are discussed as timing signals: a certain frequencyvalue and a certain integral value on the rising edge of thesignal r(t), the first moment of the distribution r(t), andthe total pulse count of one distribution r(t). In the presentcase digital data storage and digital data processing wereused for transit time determination. Four timing techniquesused for the tracer methods are discussed in the followingand first the expected deviation of transit times in every caseare calculated.

0018-9456/79/1200-0321$00.75 © 1979 IEEE

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-28, NO. 4, DECEMBER 1979

nt

to

Fig. 2. Content of pulse counter versus time in the frequency countingmethod.

A. Frequency Counting MethodThe ACD pulse frequency can be measured by a digital

counter which is cleared every T seconds. The counterreading before clearing divided by counting period T givesthe recent pulse frequency value. The timing signal isproduced when the counter reaches the value No. If theperiod T is chosen to be so long that the timing occurs withgreat probability during a certain period, the content of thecounter versus time function is of the shape shown in Fig. 2.

Using the definitions in Fig. 2 and making a geometricalapproximation one can write

,N(T) Na0to T

START STOP

Fig. 3. The integrated pulse rate function used for measuring the transittime of the radioactive source.

C. First Moment MethodWhen the function r(t) is stored digitally in a data memory

several estimates for transit time can be calculated. A goodtiming point is the first moment, the center of gravity, of thepulse rate distribution. A straightforward way of resolvingthe first moment is to store the data, calculate the momentsofboth distributions, and then to determine the time intervalbetween them.

If the rate distribution consists of N,01 pulses, the firstmoment is really the mean value of N,01 time values. Thestandard deviation of the time between two first moments is,therefore,

(2)

where a,O is the standard deviation ofthe time measurementstart due to the statistical fluctuation (,N) of the meanpulse count (N). If a°O is solved from (2) and the fluctuationin the start and stop moments is summed, the standarddeviation (aLT) of the measured mean transit time (T) in thefrequency counting method can be resolved to

CF /2 N(T)(3)arT = N_()

B. Integral MethodThe integral of the pulse rate time function

N(t) = r(t) dt (4)

can be found readily by increasing the counting period (T) ofthe previous method ofinfinity, and N(t) is the content of thecounter at the time t. Fig. 3 shows the integrated pulse ratefunction N(t) used for the timing of the radioactive source.The timing uncertainty ato at No = N(to) is inversely pro-portional to the slope of the N(t) signal to its derivative r(t).The amplitude fluctuation is proportional to N(t0). Thusthe timing jitter is as shown in Fig. 3

ar = __ v rN(t0) (S)rN-= 2 r(t0)(5

(6)tot

where a, is dependent on the shape of the function r(t).

D. Total Count MethodThe total count method for liquid flow measurement

using radioactive isotopes is described in [2]. Here the totalpulse count (N,1t) from pulses caused by an activity passing adetector is chosen to represent the velocity of the source.Using the total count method andACD technique followingcalculations can be made in the manner shown in Fig. 4

Ntot = r(t) dt = wN101=~~~ (7)

The positron active source remains between the two coin-cidence detectors for the time w, and rmax is the maximumpulse frequency due to the activity used. The diameter ofthedetectors, being in face to face geometry, is d, v is the velocityof the source, and the time w = dlv. Now the velocity may beobtained from

drmax 1v= = c (8

2Ntot NtotThe constant c can be determined by measuring the knownvelocities. The main error in this method is, therefore, causedby the randomness of the counted pulse rate. The derivativeof v due to N1to is

dv r d (9)dNtot 2NtOt

;p

322

t

(8)

HEUSALA AND MYLLYLA: MICROPROCESSOR-BASED FLOW MEASUREMENT

(a) (b) (c)Fig. 4. (a) Detector setup. (b) Triangular approximation of function r(t). (c) Prespective function r(s).

which yields, for the relative uncertainty r., of the velocity,

2oX, 2'-v tot = -

-

The total pulse count of one distribution r(t) can be cal-culated by substituting (11) and (13) into (7)

(10)

In (10) it is expected that Nt,t will be normally distributed,having a standard deviation of N/4

E. Other MethodsThe correlation function between two digitally stored

frequency distributions may also be calculated, and then thetime delay in respect of the maximum or first moment ofthecorrelation function, for instance, can be chosen as estimatesof the transit time. The properties ofthe correlation functionare especially useful if the original signal is very noisy,activity is low, and back radiation is strong.Once a positron active tracer has been injected into a flow

and its dispersion is complete, the concentration of activitycan be detected by the positron camera technique used inmedicine. Three-dimensional images of the activity at twolocations can be constructed and the velocity profile of theflowing liquid determined from the difference between theimages.

III. COMPARISON OF THE FOUR VELOCITY DETERMINATIONMETHODS IN THE CASE OF ACD TECHNIQUE

The detector setup and the functions r(t) and r(s) in thecase ofACD technique are shown in Fig. 4. The ACD signalis shown to be approximately triangular when a positronactive point racer is detected by cylindrical scintillators [3].Some general equations describing this signal have beendeveloped first for helping the following comparison of thediscussed methods.The transit time z and the base ofthe triangle r(t) are given

by

So=

Vand w=

d

v

The terms w/T and 1/JlNott needed in the following expan-sion become, by substitution of (11) and (14),

The relative uncertainty £, of the velocity at the 95-percentlevel of significance is given by

-V = 100 " = 100 2orv I

if the main error in velocity determination is proportionalonly to the timing error r7-.The relative uncertainty of velocity measurement in four

cases discussed have been developed in the following bymeans of the common parameters s0, k, and v.

A. Error FVT in the Frequency Counting MethodSubstituting (3) into (17) yields

(18)EvTl-100 * 2V zr N(TIf the timing point is a half of maximum and there are hcounting periods during the time interval w, the period Tand the total count N101 are given by

(11) Substituting (19), (20), (15), and (16) into (18) yields

where So is the distance between the timing points.The maximum pulse rate rmaxcan be written in the manner

shown in Fig. 4

dir rmak=dr -=max (12)ds d/2

kdI-,

rmax- 2

£vT = 100 oX ' (21)

B. Error FrN in the Integral MethodI Recalling that the rising edge of the function r(t) is linear,

(5) becomes1

(13) arN= (22)

kd2Ntot = --4 (14)

w d/E:_ dT So /V So

1N_2d\/NIO d ik

(15)

(16)

(17)

T = w/h

Ntot= hN(T).

(19)

(20)

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IEEE TRANSAC1IONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-28, NO. 4, DECEMBER 1979

F--- - - - - . -

I~AC/DC 220V/5VIr

*TL [....9 DISPLAYINTEGRATOR T

Fig. 5. Schematic diagram of the positron activity monitoring system.

Substituting z = so/v and (22) into (17) yields

vN = 100 2 - (23)sO v

C. Error Ev,, in the First Moment Method

The velocity uncertainty in the case of first moments is

H=1002,2-T N-. (24)

The effect of noise pulses is reduced by using a certain ratediscrimination level. If the discrimination level is one halfofmaximum in the case of triangular approximation, the totalpulse count is reduced to 3/4 of original and the timedeviation (u,) ofdata values is approximately w/4. Equation(24) becomes

£~= 10022 /2* w/4 I(25)

TV (3/4~). Ntot(25

Substituting (15) and (16) into (25) yields

= 100 22

(26)

D. £, tot in the Total Count Method

The inaccuracy ofvelocity determination in the case ofthetotal count method is given by substituting (16) into (10)

Evtot= 100 - 4 1k (27)

E. Comparisonoff;vT, fEvNq 6,, and eVtot

From (21), (23). (26). and (27) we can obtain the differ-ences between r0T, EvNi Ev and v tot that are characterized bythe factors 4 /2/ /h, 2, 1.6, 4so /d, respectively. It is shown

that, in theory, the first moment method is the most accuratein respect to the randomness ofthe detected pulse rate. Theaccuracy of the frequency counting method is stronglydependent on the value ofw/Tand the advantage of the totalcount method is that only one detecting location is needed.In practice, the integral method is the most suitable,however, since the selection of optimal sampling period T isnot needed. If h > 12 yields CvT < Er, and if h > 8 yields6vT < EvN. Equation (3) is not valid, if too great value of h isused in the measurement.The total count method is always the most inaccurate

compared to other methods discussed if the same activityand detector setup geometry is used. The value of k can beincreased by increasing the activity. If one wants Pv tot =f;vNand so /d = 10, the activity have to be 400 times stronger inthe total count method.The accuracy differences between methods discussed,

except the total count method, are not significant. Theimplementation of the first moment method needs the mostcomplicated electronics compared to the frequency count-ing and integral method. The authors feel that the integralmethod is the most suitable technique in general.

IV. INSTRUMENT CONSTRUCTIONFig. 5 shows a schematic diagram of the microprocessor-

based instrument used for monitoring and analyzing thetransit times (mean velocities) of positron active sources.

The pulse rate is fed to the system from four scintillationdetectors. ACD electronics are used to detect the annihila-tion quanta and the pulse rate time function is storeddigitally in the data RAM. The system produces printedlistings of information on pulse rate and transit time esti-mates. An audio cassette recorder can also be used forstoring the necessary information and, instead of printout,the data are read out on a calculator-plotter system.

There are two ACD circuits for each detector group, a

AUDIOCASSETTERECORDER

324

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ACDI jx I NoI I -L 1-

i

HEUSALA AND MYLLYLA: MICROPROCESSOR-BASED FLOW MEASUREMENT

-3423asd>- 7Sms

- 3A253sd7? 6.Oms

- 3.424Os6,=6.9ms

- 34239s6r z 7.6ms

10-

Fig. 6. Four distributions of a hundred transit times measured by the integrator unit changing the timing threshold. The meanvelocity of the source was 0.5 m/s.

TTL-counter with capacity of 16 bits, a microprocessorsystem and interface units for data display. The ACDcircuits are designed for Nal detectors, which have a deadtime of about 1-2 his.The instrument has a 4K byte NMOS RAM for 2048

16-bit length rate values. The shortest counting period is 100ps, and the counter can follow a pulse rate (r(t)) of up to 30MHz. A plastic scintillator can also be used. The system hasa 6K bytes program memory for data analysis and 2K bytesfor the operating system. The first prototype of the instru-ment, without the peripherals, was mounted in a case 17in x 17 in x 12 in.

In parallel with this processor system is a TTL integratorunit, which enables the frequency counting, integral, andtotal count methods to be studied. This unit does not have adata memory. It consist of a simple digital counter, clock,and transit time display.

V. EXPERIMENTAL RESULTS

The constant velocity of a 1-mm diameter point source(Na 22) of 111 kBq (3 yCi) activity inside a metal pipe (4 42mm) was measured by the methods presented above. First,the optimal timing threshold and the deviation of transittimes measured by the integral method at different velocitieswere studied by the TTL integrator unit. Second, theaccuracy of all the methods discussed was studied by themicroprocessor unit calculating the transit times fromthe digitally stored data.The following parameter values were valid for the detec-

tor setup used: k = 70 kHz/m, rmax= 1.75 kHz, detectordiameter d = 50 mm, and pipe diameter 42 mm.

A. Study on the Integral Method by the TTL IntegratorFig. 6 shows the distributions of a hundred transit times

measured by the integrator unit with four different timingthresholds. The point corresponding to 1/4 ofthe amplitudewas found to be the best for timing purposes.

Equation (22) was tested by measuring the transit timedistributions for velocities 0.1, 0.5, and 1 m/s. The standard

v- l.Om/sd -4.Orrra

10

6, 15n-sv- 0.5rrysd =6.Oms

(Fiq.7 )

5

r00n

r-,

Fig. 7. Two distributions of a hundred transit times measured by theintegrator unit at velocities 0.1 and 1 m/s.

deviations (a,N) calculated from the measured distributions(Figs. 6 and 7) give results 15 ms, 6 ms, and 4 ms, comparedwith the theoretical values calculated by (22) of 12 ms, 5 ms,and 3.8 ms, respectively.

B. Measurements by Microprocessor UnitThe Table I consists of the results of measurements in

which the functions r(t) were stored digitally and then thedifferent transit time estimates were calculated. It is shownthat the integral method is the best in respect to randomtiming error. The measured inaccuracies are: ev7 = 0.21percent, 0VN = 0.20 percent and ev = 0.21 percent. Thecalculations by (21), (23), and (26) give results 0.19,0.24, and0.195 percent, respectively, for the velocity 0.1 m/s. Thedifferences between results are not significant. The actualaccuracy of the integral method is better than the theoreticalvalue since the actual curve r(t) is not exactly linear at timingpoint.Taking the velocity dependence of Pv into account we

obtained inaccuracy of 0.2, 0.5, and 0.7 percent, respectively,for velocities of 0.1, 0.5, and 1 m/s at the 95-percent level ofsignificance with the detectors 1 m apart can be achieved by

III Ib

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IEEE [RANSACLrioNS ON INSTRI-MENIATION AND MEASUREMENT, VOL. IM-28, NO. 4, DECEMBER 1979

COMPARISON BETWEENTABLE I

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Ev is normallsed standard error at 95 9 confidence for velocity of 0.1 m/s, when the distance between detectors Is 1 m- source of radiation: 1-mm diameter Na22, 111 kBq (3 pCi)

ACD technique with a 3-1Ci source activity. Greateraccuracy can be achieved by increasing the distance ofdetectors and the activity of the source.

VI. CONCLUSIONS

The transit time of a positron active source between twolocations can be measured accurately without lead collima-tors using ACD technique and microprocessor electronics.The total count method enables the velocity at one detectionpoint to be measured. The theoretical background of thelimitations and accuracy of the ACD technique presentedis shown to be correct.The disadvantage of random coincidences can be reduced

and the accuracy of the ACD increased by employing fastplastic scintillators. These fast effective detectors open up a

wide range of industrial applications for positron activityand other isotopes.The randomness of the counted pulse rate in the absorp-

tion measurements can be reduced using coincidence detec-

tion, thus permitting more accurate thickness and density'measurements by ACD.Many possible industrial applications are available for

the positron gamma camera, since many liquid-flow prob-lems and various industrial dispersion and absorption phen-omena may be solved using three-dimensional imaging ofpositron activity.

REFERENCES[1] M. E. Phelps, E. J. Hoffman, et al., Application of annihilation coin-

cidence detection to transaxial reconstruction tomography, J. Nucl.Med., vol. 3, 1975.

[2] C. G. Clayton, R. Spackman, and A. M. Ball, "The accuracy andprecision of liquid flow measurement by radioactive isotopes," in Proc.

Symp. Radioisotope Tracers in Industry and Geophysics, (Prague,Czechoslovakia), 1966.

[3] H. H. Heusala, and R. A. Myllyla, "A design of a velocimeter using a

radioactive positron emitting source without lead collimators," Nucl.Instrum. Methods, vol. 135, 1976.

[4] K. Ljunggren, "Review of the use of radioactive tracers for evaluatingparameters pertaining to the flow of material in plant and naturalsystems," in Proc. Symp. Radioisotope Tracers in Industry and Geophy-sics (Prague, Czechoslovakia), 1966.

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