- Email: [email protected]
Developments in particle tracking using the Birmingham Positron Camera
Nuclear
Instruments
and Methods
in Physics
Research
A 392 (1997) 421-426
NUCLEAR INSTRUMENTS 8 METHODS IN PHVSICS RESEARCH Secllon
ELSEWIER
A
Developments in particle tracking using the Birmingham Positron Camera D. J. Parke?*,
D.A. Allen”, D.M. Benton=, P. Fowlesb, P.A. McNeil”, Min Tan”, T.D. Beynona
“Positron Imaging Centre. School of Ph.vsics and Space Research. UninersiQ of Birmir~gham, Birmingham bSchool of Chemistty Unioersity of Birmingham, Birmingham B15 ZTT UK
BI5 ZTT. UK
Abstract The RAL/Birmingham Positron Camera consists of a pair of MWPCs for detecting the pairs of back-to-back 511 keV photons arising from positron-electron annihilation. It was constructed in 1984 for the purpose of applying PET to engineering situations, and has been widely used for the non-invasive imaging of flow. including extensive studies on geological samples. The technique of Positron Emission Particle Tracking (PEPT), whereby a single positron-emitting tracer particle can be tracked at high speed, was developed at Birmingham and has proved a very powerful tool for studying the behaviour of granular materials in systems such as mixers and fluidised beds. In order to extend its effective field of view, the camera has recently been mounted on a motorised translation stage under computer control so that the motion of a tracer particle can be followed over a length of up to 1.5 m. A preliminary investigation into the feasibility of enhancing the PEPT technique using the singles count rates in the two detectors has also been undertaken.
1. Introduction The Birmingham positron camera was constructed at the Rutherford Appleton Laboratory in 1984 with the aim of using the technique of positron emission tomography (PET) to study engineering systems. The first application was to observe the lubricant distribution in operating aero-engines and gearboxes. but in recent years the range of applications has widened enormously. The camera continues to perform reliably, and is used intensively. The camera. which has been fully described elsewhere [ 1.21. consists of a pair of multi-wire proportional chambers, each having a sensitive area 600 x 300 mm*, operated in coincidence. The cathode planes are made of lead, 50 urn thick, which also serves as the principal photon convertor. Each plane is divided into parallel strips which are read out via a delay-line so as to provide positional information with a spatial resolution of around 8 mm. Timing signals are taken from the anode wires and enable coincidence recognition with a 25 ns resolving time (2~). In order to improve sensitivity, each detector contains a stack of 20 detector sections one
*Corresponding
author.
E-mail: parker @ pet. ph.bham.ac.uk.
016%9002/97/$17.00 Copyright PII SO168-9002(97)00301-X
behind the other, but, even so, the total efficiency for detecting incident 511 keV y-rays is only around 7%. The data are recorded in list mode. A major weakness of the camera is that the useful data logging rate is limited to around 3000 events/s. This is due in the first instance to dead-time in the read-out system, but a more fundamental limit is imposed by the high rate of random coincidences which occurs as the activity present is increased (a consequence of the low efficiency, which means that the singles rates in the two detectors are high relative to the coincidence rate). The detectors and read-out electronics are identical to those used in the MUPPET system belonging to the Royal Marsden Hospital [3], but because of the greater range of geometries encountered in engineering as opposed to medical studies a versatile mount is used, on which the two detectors can be positioned at separations from 300 to 600mm and with their long axes either horizontal or vertical. For tomographic imaging. this mount rocks backwards and forwards, rotating through 180- in about 40 s. However, the limited data rate means that it takes around an hour to acquire sufficient data for reconstruction of a 3D tomographic image, and applications are effectively restricted to steady-state situations, where the ability to label and observe the distribution of a single component in a multi-phase environment can give unique information on certain engineering systems.
$:m 1997 Elsevier Science B.V. All rights reserved XII. MEDICAL
IMAGING/PET
422
D.J. Parker et al. fNuc1. Imtr. and Meth. irl Phys. Res. A 392 (1997) 421-426
A limited programme of medical studies has also been carried out. Alternatively. 2D projection images can be obtained in a few minutes with the camera stationary, and an extensive series of geological studies of water flow through specimens of fractured rock has been performed in this way. However, the majority of the studies currently under way using the camera rely on the technique of Positron Emission Particle Tracking (PEPT) which was developed at Birmingham [2,4]. This paper describes some recent extensions to this technique.
2. Positron Emission Particle Tracking In Positron Emission Particle Tracking (PEPT) a single positron-emitting tracer particle is introduced into the field of view of the camera and can be tracked at high speed. Using the a-priori knowledge that only a single positron-emitting source is present, its location can be accurately determined from triangulation of only a few detected coincidence events, each of which should in principle serve to define a line passing close to the tracer (to within the resolution of the camera). In practice, however, some of the detected events are “corrupt”, for example due to scattering of one or both of the photons before detection, and this makes it necessary to detect sufficient events that the useful ones, which do approximately meet at a point in space, can be distinguished from the broadcast background due to corrupt events. An iterative algorithm has been developed whereby the point in space closest to which the initial set of events all pass is calculated and the events lying furthest from this point are discarded. The calculation is repeated using the remaining events, and this process continues until only a predefined fractionfof events remains. The fractionfof useful events depends on the amount of scattering material present, and also on the position of the tracer in the field of view, reaching a maximum of around 0.33 for a bare point source at the centre of the field of view (this is considerably lower than expected theoretically due to scattering in the detectors themselves, indicating that the algorithm is not perfect at discriminating corrupt from useful events). A stationary particle can be located arbitrarily well by taking a sufficiently large sample of events, but for a moving tracer there is an optimum sample size. large enough to provide good statistics but not so large that the particle moves too far during the location process. In practice this optimum is found to correspond to the tracer moving approximately 20 mm during location. In the standard approach [2], overlapping samples are used so that the tracer is located on average every 4 mm along its path. The precision of location decreases with tracer speed - a particle moving at 1 m/s inside a typical piece of equipment can be located to within 5 mm in 3D approx-
imately 250 times per second, whereas one moving at 0.1 m/s would be located to better than 2 mm 25 times per second. The uncertainty in location is principally in the z-coordinate, normal to the detector faces, and increases as the separation of the two detectors increases. For this reason, the majority of early PEPT measurements were carried out at a separation of 300 mm. For a detector separation of 300 mm, the optimum data rate of around 2500 events/s is achieved with a tracer activity of around 4 MBq, assuming negligible attenuation of the y-rays in the surrounding material. For larger separations or when the y-rays have to penetrate a considerable mass of material, correspondingly higher activities are used. Positron-emitting tracer particles are made in two ways. Particles down to about 1 mm in diameter and made of radiation resistant material can be directly irradiated using the beam from a cyclotron: irradiation with a 33 MeV ‘He beam yields glass beads containing the radionuclide 18F (half-life 110 min) or copper beads containing 61Cu (3.4 h). Alternatively, the radionuclide may be produced in solution and then transferred into a bead of an ion-exchange medium resin beads 600 pm in diameter containing “F are currently made in this way [S], and only the practical difficulty of handling small particles is restricting the production of even smaller tracers. PEPT is currently being used to study particulate motion in a variety of mixers and fluidised beds. One of the key questions in such studies is that of “scale-up” from the laboratory scale to full sized plant. To address this question, it is desirable to study somewhat larger systems than would normally fit within the field of view of the camera. This paper describes two extensions to the PEPT technique which are intended to address this issue. Firstly, the camera has recently been mounted on rails, effectively extending its axial field of view for many types of study. Secondly, attempts are being made to obtain additional information on the z-coordinate by comparison of the singles rates in the two detectors, which it is hoped may complement the PEPT data for large detector separations.
3. PEPT using a moving camera In order to extend the axial (horizontal) field of view of the positron camera, its entire structure has been mounted on a pair of straight rails providing a travel of up to 120 cm. When the detectors are mounted with their long axes vertical the axial length over which PEPT can be performed with the camera stationary is at most 25 cm, but introducing translation of the camera increases this to 145 cm. The camera is driven by a motor through a rack and pinion. An absolute shaft encoder is connected via a reducing gear to the shaft of the pinion so as to read out the
D.J. Parker et al. /Nucl. Instr. and M&h. in Phys, Res. A 392 (1997) 421-426
position of the translation stage with a precision of 0.4mm. When the translation stage is in use, the shaft encoder data is recorded for every stored event. A simplified version of the PEPT algorithm has been incorporated in the data logging program, which currently runs on a VAX 4000/200 computer. Data are recorded in buffers which contain between 500 and 2500 events (operator selectable). When a buffer is transferred to the computer, a PEPT estimate of the axial position of the tracer particle is calculated from the last few events. The number of events used is such that after discarding the appropriate fraction of corrupt events exactly 12 remain, giving an estimate which should be accurate to better than 5 mm (provided the tracer is not moving faster than 1 m/s). If this estimate indicates that the tracer is more than 15 mm from the horizontal centre of the detector, the computer causes the motor to move the translation stage so as to follow the tracer. The stage drives at a speed of approximately 60 mm/s; it moves approximately 15 mm if the tracer is between 15 and 30 mm offcentre, and approximately 30 mm if the tracer is further off-centre. Note that it is not important to control the movement accurately since the shaft encoder provides the definitive record of what move actually occurred. Using this approach automatic tracking of the tracer particle can be reliably performed provided the axial movement is not too violent. In the subsequent PEPT processing of data recorded using the moving camera, the shaft encoder value for each event is used to correct for the instantaneous position of the translation stage so as to transform its coordinates into the laboratory frame of reference. The standard PEPT algorithm is then used on the transformed data (but the value of ,f is based on the position of the tracer within the instantaneous field of view). Inevitably, movement of the translation stage introduces additional errors into the PEPT location data. In particular, there was concern that the relatively rapid acceleration and deceleration involved might introduce distortions. This was investigated by comparing measurements on a stationary source made (i) with the camera stationary and (ii) with the camera oscillating backwards and forwards, a move of 30 mm being performed as each buffer of data was received, with each move in the opposite direction to the previous one. When the second dataset was processed as described above, correcting for the changing position of the translation stage, the uncertainty in location (given by the standard deviation of the set of estimates of the location of the stationary source) was found to be only slightly larger than that from the first dataset. Subtracting the two values in quadrature indicated that the motion of the stage was contributing around 0.4 mm to the uncertainty in the x-coordinate. Such a contribution is negligible in the context of the type of study for which the translation stage is likely to be used.
423
In general, using the moving stage will actually improve the quality of PEPT data (provided the tracer does not move too fast for the stage to follow), since it ensures that the tracer particle remains close to the centre of the field of view where PEPT is most accurate. Fig. 1 shows data from such a study [6]. In this case the diameter of the mixing vessel was 28 cm and it was fitted with a central shaft 8 cm in diameter. 30% of the volume between the shaft and the outer wall was occupied by powder, which was stirred by a single flat paddle extending the entire length of the vessel. The shaft and paddle rotated at 38 rpm. A single 600 urn tracer particle (made by ion exchange) was introduced and data were recorded over a period of an hour; for every event the instantaneous angle of the paddle was determined, using a clock which was reset once per revolution by an optical switch, and this information was recorded along with the other camera data. The PEPT data could then be related to the position of the paddle. In Fig. l(a) the transverse view of the vessel has been divided into 5 x 5 mm” pixels and the grey scale shows the fraction of the total run-time during which the tracer was found in each pixel at the same time as the paddle was within a specified 30 range of angles (the approximate position of the paddle at the mid-point of each interval is indicated). This method of presenting the data is equivalent to plotting the number of particles at each point in the bed; the way in which the bed of powder was lifted by each passage of the paddle is apparent. In Fig. l(b) the arrows indicate the average velocity of the tracer when it was within each 10 x 10 mm2 pixel at the same time as the paddle was within the specified range of angles. For this particular study the value of being able to use a long vessel was that end effects could be made negligible.
4. Possible enhancement of PEPT using the singles rates The uncertainty in PEPT location is always dominated by the uncertainty in the =-coordinate linking the two detectors. As the detectors are moved further apart in order to accommodate larger systems, the precision achievable in this coordinate deteriorates. It is therefore valuable to consider what additional measurements might be made to improve the determination of Z. Using just the existing detectors, two further pieces of data are immediately available, namely the singles count rates in the two detectors, and a small study has been carried out to investigate the feasibility of using the instantaneous values of these two count rates to provide an estimate of Z. Clearly as the tracer approaches one detector the singles rate in that detector increases and that in the other detector decreases. Moreover, because of the low efficiencies of the two detectors the singles rates are large compared with the coincidence rate, so that the statistics
XII. MEDICAL
IMAGING/PET
424
D.J Parker et al. /‘Nucl. Inste and Meth. in Phw. Res. A 392 (1997) 421-426
Fig. 1. Data from a PEPT study of a single flat paddle agitating a bed of powder. The integrated data from a 60 min study have been broken down into 12 subsets on the basis of the angle of the paddle (only 8 of these 30” intervals are shown, and each is labelled with the range of angles of the paddle tip from the downward vertical which it contains): (a) fraction of total run time during which the tracer was found in each pixel, and (b) average tracer velocity within each pixel. The approximate position of the paddle mid-way through each interval is shown in (a).
may be adequate to detect a relatively small change in rate. Fig. 2 shows the singles count rate in detector 1 as a function of the z-coordinate, for a detector separation of 400 mm. Data were measured using a point source of
r8F whose position was determined using the standard PEPT technique. Two sets of measurements were performed, firstly with the source positioned at intervals along the axis of the two detectors (i.e. central in x and y) and secondly with the source positioned 100 mm
425
D.J. Parker et al. /Nucl. Instr. and Meth. in Phys. Res. A 392 (1997) 421-426
40000 35000 -~
0 l
30000 -u !! 25000 --
0 central 3
l
1OOmm off centre in y
0 l l 0
! 20000 --
0l
3 :
15000
6
10000 --
0
--
o 0
o*
9
Q
0
0
5000 ~-
I
0
0
50
100
150
200
250
300
350
400
2 (mm) Fig. 2. Singles count rate in detector 1 as a function of the z-coordinate of a “F point source positioned at intervals along the central axis (hollow symbols) and along an axis 100 mm off-centre in 4’(solid symbols), for a detector separation of 400 mm.
off-centre in 4’ (i.e. only 50mm from the edge of the detector). For comparison, it may be noted that the useful coincidence rate for a central source in this geometry is approximately 400 counts/s per MBq (decreasing with activity). Although the coincidence rate drops dramatically close to the edge of the detector, there is only a small reduction in the singles rate, and the shape of the curve relating singles rate to z appears to be approximately independent of Y or y, suggesting that the ratio of the singles rates in the two detectors can provide an estimate of z independent of the values of the other two coordinates. The curves in Fig. 2 have approximately the form of an inverse square dependence, measured from a point some distance inside the detector. In this case, it can be shown that the quantity
J SlS2 should be approximately proportional to z. In fact, the relationship is not perfectly linear, but can be better represented by a cubic polynomial. In order to assess whether the singles rates are adequate to make a useful enhancement to PEPT, data were measured for a 7 MBq point source of 18F mounted at a radius of 90 mm on a rotating turntable. Coincidence data were recorded as usual, but the singles pulses from the two detectors were also fed to a pair of scalers and each time a coincidence event was recorded the instantaneous contents of these scalers were also recorded. The upper curves in Fig. 3 show the data processed using the standard PEPT algorithm. For this source (which is less active than the optimum, giving 1200 events/s) at a speed
of 0.7 m/s (1.2 rotations/s) approximately 80 PEPT locations were obtained per second, deviating from the true trajectory with a standard deviation of 9.6 mm in 3D or 7.9 mm in z alone. The lower curve in Fig. 3 shows the estimates of z provided by Eq. (l), using in each case the singles rates measured over the same interval as used to determine a PEPT location. The scatter of the points appears less than for the PEPT values of z. When a simple linear scaling was used to convert the values of R to a z location in mm, the results deviated from the true trajectory with a standard deviation of 6.7 mm, which is slightly less than the 7.9 mm resulting from PEPT. As noted above, the use of R in this way introduces some distortion, and it was found that by using a slightly non-linear conversion to mm the standard deviation in z could be reduced below 6 mm. Thus, although further work remains to be done in order to determine the best way of deducing z accurately from a combination of the two singles rates, it appears that for the situation studied the singles rates can provide a slightly better estimate of z than the standard PEPT approach. Clearly, the best results will be obtained by combining both approaches. These measurements were performed using a “bare” system, so that the y-rays did not experience attenuation or scattering in traversing the region between source and detector. There will clearly be problems in using this approach in many real systems due to non-uniform attenuation. It is most likely to be of value for tracking in low-density systems having considerable symmetry. Indeed several groups have successfully performed tracking of radioactive tracer particles in fluidised beds purely on
XII. MEDICAL IMAGING/PET
D.J. Parker et al. / Nucl. Instr. and M&h. in Phys. Rex ‘4 392 (1997) 431-4176
426
2%
250. rzoo-
E ‘5.150 loo-
300. 250. i? g200N
150. 100. I
I
I
I
I
I
4
5
6
7
8
9
I 10
Time (s) 1
Fig. 3. The upper three plots show the PEPT data for a tracer on a turntable rotating in the pz plane at 1.2 Hz. The lower plot shows the alternative estimate of the z-coordinate obtained from comparison of the two singles rates. as described in the text.
the basis of comparing the detected array of external detectors [7,8].
count
rates in an PI
Acknowledgements c31 The authors gratefully acknowledge financial support from EPSRC. The data shown in Fig. 1 come from a study funded by Elf via a grant to the University of Cambridge.
CSI Eel c71
References [l]
M.R. Hawkesworth. M.A. O’Dwyer, J. Heritage,
M
P.A.E. Stewart,
J. Walker, P. Fowles, R.C. Witcomb, J.E. Bateman,
PI
J.F. Connolly and R. Stephenson, Nucl. Instr. and Meth. A 253 (1986) 145. D.J. Parker, M.R. Hawkesworth, C.J. Broadbent, P. Fowles, T.D. Fryer and P.A. McNeil, Nucl. Instr. and Meth. A 348 (1994) 583 P.K. Marsden, R.J. Ott, J.E. Bateman, S.R. Cherry, M.A. Flower and S. Webb, Phys. Med. Biol. 34 (1989) 1043. D.J. Parker, C.J. Broadbent, P. Fowles, M.R. Hawkesworth and P.A. McNeil, Nucl. Instr. and Meth. A 326 (1993) 592. D.M. Benton and P. Fowles, to be published. B. Laurent, J. Bridgwater and D.J. Parker, to be published. D. Moslemian, N. Devanathan and M.P. Dudukovic, Rev. Sci. Instr 63 (1992) 4361. F. Larachi, M. Cassanello, M. Marie, J. Chaouki and C. Guy, Trans. I. Chem. E. 73 A (1995) 263.
Instruments
and Methods
in Physics
Research
A 392 (1997) 421-426
NUCLEAR INSTRUMENTS 8 METHODS IN PHVSICS RESEARCH Secllon
ELSEWIER
A
Developments in particle tracking using the Birmingham Positron Camera D. J. Parke?*,
D.A. Allen”, D.M. Benton=, P. Fowlesb, P.A. McNeil”, Min Tan”, T.D. Beynona
“Positron Imaging Centre. School of Ph.vsics and Space Research. UninersiQ of Birmir~gham, Birmingham bSchool of Chemistty Unioersity of Birmingham, Birmingham B15 ZTT UK
BI5 ZTT. UK
Abstract The RAL/Birmingham Positron Camera consists of a pair of MWPCs for detecting the pairs of back-to-back 511 keV photons arising from positron-electron annihilation. It was constructed in 1984 for the purpose of applying PET to engineering situations, and has been widely used for the non-invasive imaging of flow. including extensive studies on geological samples. The technique of Positron Emission Particle Tracking (PEPT), whereby a single positron-emitting tracer particle can be tracked at high speed, was developed at Birmingham and has proved a very powerful tool for studying the behaviour of granular materials in systems such as mixers and fluidised beds. In order to extend its effective field of view, the camera has recently been mounted on a motorised translation stage under computer control so that the motion of a tracer particle can be followed over a length of up to 1.5 m. A preliminary investigation into the feasibility of enhancing the PEPT technique using the singles count rates in the two detectors has also been undertaken.
1. Introduction The Birmingham positron camera was constructed at the Rutherford Appleton Laboratory in 1984 with the aim of using the technique of positron emission tomography (PET) to study engineering systems. The first application was to observe the lubricant distribution in operating aero-engines and gearboxes. but in recent years the range of applications has widened enormously. The camera continues to perform reliably, and is used intensively. The camera. which has been fully described elsewhere [ 1.21. consists of a pair of multi-wire proportional chambers, each having a sensitive area 600 x 300 mm*, operated in coincidence. The cathode planes are made of lead, 50 urn thick, which also serves as the principal photon convertor. Each plane is divided into parallel strips which are read out via a delay-line so as to provide positional information with a spatial resolution of around 8 mm. Timing signals are taken from the anode wires and enable coincidence recognition with a 25 ns resolving time (2~). In order to improve sensitivity, each detector contains a stack of 20 detector sections one
*Corresponding
author.
E-mail: parker @ pet. ph.bham.ac.uk.
016%9002/97/$17.00 Copyright PII SO168-9002(97)00301-X
behind the other, but, even so, the total efficiency for detecting incident 511 keV y-rays is only around 7%. The data are recorded in list mode. A major weakness of the camera is that the useful data logging rate is limited to around 3000 events/s. This is due in the first instance to dead-time in the read-out system, but a more fundamental limit is imposed by the high rate of random coincidences which occurs as the activity present is increased (a consequence of the low efficiency, which means that the singles rates in the two detectors are high relative to the coincidence rate). The detectors and read-out electronics are identical to those used in the MUPPET system belonging to the Royal Marsden Hospital [3], but because of the greater range of geometries encountered in engineering as opposed to medical studies a versatile mount is used, on which the two detectors can be positioned at separations from 300 to 600mm and with their long axes either horizontal or vertical. For tomographic imaging. this mount rocks backwards and forwards, rotating through 180- in about 40 s. However, the limited data rate means that it takes around an hour to acquire sufficient data for reconstruction of a 3D tomographic image, and applications are effectively restricted to steady-state situations, where the ability to label and observe the distribution of a single component in a multi-phase environment can give unique information on certain engineering systems.
$:m 1997 Elsevier Science B.V. All rights reserved XII. MEDICAL
IMAGING/PET
422
D.J. Parker et al. fNuc1. Imtr. and Meth. irl Phys. Res. A 392 (1997) 421-426
A limited programme of medical studies has also been carried out. Alternatively. 2D projection images can be obtained in a few minutes with the camera stationary, and an extensive series of geological studies of water flow through specimens of fractured rock has been performed in this way. However, the majority of the studies currently under way using the camera rely on the technique of Positron Emission Particle Tracking (PEPT) which was developed at Birmingham [2,4]. This paper describes some recent extensions to this technique.
2. Positron Emission Particle Tracking In Positron Emission Particle Tracking (PEPT) a single positron-emitting tracer particle is introduced into the field of view of the camera and can be tracked at high speed. Using the a-priori knowledge that only a single positron-emitting source is present, its location can be accurately determined from triangulation of only a few detected coincidence events, each of which should in principle serve to define a line passing close to the tracer (to within the resolution of the camera). In practice, however, some of the detected events are “corrupt”, for example due to scattering of one or both of the photons before detection, and this makes it necessary to detect sufficient events that the useful ones, which do approximately meet at a point in space, can be distinguished from the broadcast background due to corrupt events. An iterative algorithm has been developed whereby the point in space closest to which the initial set of events all pass is calculated and the events lying furthest from this point are discarded. The calculation is repeated using the remaining events, and this process continues until only a predefined fractionfof events remains. The fractionfof useful events depends on the amount of scattering material present, and also on the position of the tracer in the field of view, reaching a maximum of around 0.33 for a bare point source at the centre of the field of view (this is considerably lower than expected theoretically due to scattering in the detectors themselves, indicating that the algorithm is not perfect at discriminating corrupt from useful events). A stationary particle can be located arbitrarily well by taking a sufficiently large sample of events, but for a moving tracer there is an optimum sample size. large enough to provide good statistics but not so large that the particle moves too far during the location process. In practice this optimum is found to correspond to the tracer moving approximately 20 mm during location. In the standard approach [2], overlapping samples are used so that the tracer is located on average every 4 mm along its path. The precision of location decreases with tracer speed - a particle moving at 1 m/s inside a typical piece of equipment can be located to within 5 mm in 3D approx-
imately 250 times per second, whereas one moving at 0.1 m/s would be located to better than 2 mm 25 times per second. The uncertainty in location is principally in the z-coordinate, normal to the detector faces, and increases as the separation of the two detectors increases. For this reason, the majority of early PEPT measurements were carried out at a separation of 300 mm. For a detector separation of 300 mm, the optimum data rate of around 2500 events/s is achieved with a tracer activity of around 4 MBq, assuming negligible attenuation of the y-rays in the surrounding material. For larger separations or when the y-rays have to penetrate a considerable mass of material, correspondingly higher activities are used. Positron-emitting tracer particles are made in two ways. Particles down to about 1 mm in diameter and made of radiation resistant material can be directly irradiated using the beam from a cyclotron: irradiation with a 33 MeV ‘He beam yields glass beads containing the radionuclide 18F (half-life 110 min) or copper beads containing 61Cu (3.4 h). Alternatively, the radionuclide may be produced in solution and then transferred into a bead of an ion-exchange medium resin beads 600 pm in diameter containing “F are currently made in this way [S], and only the practical difficulty of handling small particles is restricting the production of even smaller tracers. PEPT is currently being used to study particulate motion in a variety of mixers and fluidised beds. One of the key questions in such studies is that of “scale-up” from the laboratory scale to full sized plant. To address this question, it is desirable to study somewhat larger systems than would normally fit within the field of view of the camera. This paper describes two extensions to the PEPT technique which are intended to address this issue. Firstly, the camera has recently been mounted on rails, effectively extending its axial field of view for many types of study. Secondly, attempts are being made to obtain additional information on the z-coordinate by comparison of the singles rates in the two detectors, which it is hoped may complement the PEPT data for large detector separations.
3. PEPT using a moving camera In order to extend the axial (horizontal) field of view of the positron camera, its entire structure has been mounted on a pair of straight rails providing a travel of up to 120 cm. When the detectors are mounted with their long axes vertical the axial length over which PEPT can be performed with the camera stationary is at most 25 cm, but introducing translation of the camera increases this to 145 cm. The camera is driven by a motor through a rack and pinion. An absolute shaft encoder is connected via a reducing gear to the shaft of the pinion so as to read out the
D.J. Parker et al. /Nucl. Instr. and M&h. in Phys, Res. A 392 (1997) 421-426
position of the translation stage with a precision of 0.4mm. When the translation stage is in use, the shaft encoder data is recorded for every stored event. A simplified version of the PEPT algorithm has been incorporated in the data logging program, which currently runs on a VAX 4000/200 computer. Data are recorded in buffers which contain between 500 and 2500 events (operator selectable). When a buffer is transferred to the computer, a PEPT estimate of the axial position of the tracer particle is calculated from the last few events. The number of events used is such that after discarding the appropriate fraction of corrupt events exactly 12 remain, giving an estimate which should be accurate to better than 5 mm (provided the tracer is not moving faster than 1 m/s). If this estimate indicates that the tracer is more than 15 mm from the horizontal centre of the detector, the computer causes the motor to move the translation stage so as to follow the tracer. The stage drives at a speed of approximately 60 mm/s; it moves approximately 15 mm if the tracer is between 15 and 30 mm offcentre, and approximately 30 mm if the tracer is further off-centre. Note that it is not important to control the movement accurately since the shaft encoder provides the definitive record of what move actually occurred. Using this approach automatic tracking of the tracer particle can be reliably performed provided the axial movement is not too violent. In the subsequent PEPT processing of data recorded using the moving camera, the shaft encoder value for each event is used to correct for the instantaneous position of the translation stage so as to transform its coordinates into the laboratory frame of reference. The standard PEPT algorithm is then used on the transformed data (but the value of ,f is based on the position of the tracer within the instantaneous field of view). Inevitably, movement of the translation stage introduces additional errors into the PEPT location data. In particular, there was concern that the relatively rapid acceleration and deceleration involved might introduce distortions. This was investigated by comparing measurements on a stationary source made (i) with the camera stationary and (ii) with the camera oscillating backwards and forwards, a move of 30 mm being performed as each buffer of data was received, with each move in the opposite direction to the previous one. When the second dataset was processed as described above, correcting for the changing position of the translation stage, the uncertainty in location (given by the standard deviation of the set of estimates of the location of the stationary source) was found to be only slightly larger than that from the first dataset. Subtracting the two values in quadrature indicated that the motion of the stage was contributing around 0.4 mm to the uncertainty in the x-coordinate. Such a contribution is negligible in the context of the type of study for which the translation stage is likely to be used.
423
In general, using the moving stage will actually improve the quality of PEPT data (provided the tracer does not move too fast for the stage to follow), since it ensures that the tracer particle remains close to the centre of the field of view where PEPT is most accurate. Fig. 1 shows data from such a study [6]. In this case the diameter of the mixing vessel was 28 cm and it was fitted with a central shaft 8 cm in diameter. 30% of the volume between the shaft and the outer wall was occupied by powder, which was stirred by a single flat paddle extending the entire length of the vessel. The shaft and paddle rotated at 38 rpm. A single 600 urn tracer particle (made by ion exchange) was introduced and data were recorded over a period of an hour; for every event the instantaneous angle of the paddle was determined, using a clock which was reset once per revolution by an optical switch, and this information was recorded along with the other camera data. The PEPT data could then be related to the position of the paddle. In Fig. l(a) the transverse view of the vessel has been divided into 5 x 5 mm” pixels and the grey scale shows the fraction of the total run-time during which the tracer was found in each pixel at the same time as the paddle was within a specified 30 range of angles (the approximate position of the paddle at the mid-point of each interval is indicated). This method of presenting the data is equivalent to plotting the number of particles at each point in the bed; the way in which the bed of powder was lifted by each passage of the paddle is apparent. In Fig. l(b) the arrows indicate the average velocity of the tracer when it was within each 10 x 10 mm2 pixel at the same time as the paddle was within the specified range of angles. For this particular study the value of being able to use a long vessel was that end effects could be made negligible.
4. Possible enhancement of PEPT using the singles rates The uncertainty in PEPT location is always dominated by the uncertainty in the =-coordinate linking the two detectors. As the detectors are moved further apart in order to accommodate larger systems, the precision achievable in this coordinate deteriorates. It is therefore valuable to consider what additional measurements might be made to improve the determination of Z. Using just the existing detectors, two further pieces of data are immediately available, namely the singles count rates in the two detectors, and a small study has been carried out to investigate the feasibility of using the instantaneous values of these two count rates to provide an estimate of Z. Clearly as the tracer approaches one detector the singles rate in that detector increases and that in the other detector decreases. Moreover, because of the low efficiencies of the two detectors the singles rates are large compared with the coincidence rate, so that the statistics
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Fig. 1. Data from a PEPT study of a single flat paddle agitating a bed of powder. The integrated data from a 60 min study have been broken down into 12 subsets on the basis of the angle of the paddle (only 8 of these 30” intervals are shown, and each is labelled with the range of angles of the paddle tip from the downward vertical which it contains): (a) fraction of total run time during which the tracer was found in each pixel, and (b) average tracer velocity within each pixel. The approximate position of the paddle mid-way through each interval is shown in (a).
may be adequate to detect a relatively small change in rate. Fig. 2 shows the singles count rate in detector 1 as a function of the z-coordinate, for a detector separation of 400 mm. Data were measured using a point source of
r8F whose position was determined using the standard PEPT technique. Two sets of measurements were performed, firstly with the source positioned at intervals along the axis of the two detectors (i.e. central in x and y) and secondly with the source positioned 100 mm
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off-centre in 4’ (i.e. only 50mm from the edge of the detector). For comparison, it may be noted that the useful coincidence rate for a central source in this geometry is approximately 400 counts/s per MBq (decreasing with activity). Although the coincidence rate drops dramatically close to the edge of the detector, there is only a small reduction in the singles rate, and the shape of the curve relating singles rate to z appears to be approximately independent of Y or y, suggesting that the ratio of the singles rates in the two detectors can provide an estimate of z independent of the values of the other two coordinates. The curves in Fig. 2 have approximately the form of an inverse square dependence, measured from a point some distance inside the detector. In this case, it can be shown that the quantity
J SlS2 should be approximately proportional to z. In fact, the relationship is not perfectly linear, but can be better represented by a cubic polynomial. In order to assess whether the singles rates are adequate to make a useful enhancement to PEPT, data were measured for a 7 MBq point source of 18F mounted at a radius of 90 mm on a rotating turntable. Coincidence data were recorded as usual, but the singles pulses from the two detectors were also fed to a pair of scalers and each time a coincidence event was recorded the instantaneous contents of these scalers were also recorded. The upper curves in Fig. 3 show the data processed using the standard PEPT algorithm. For this source (which is less active than the optimum, giving 1200 events/s) at a speed
of 0.7 m/s (1.2 rotations/s) approximately 80 PEPT locations were obtained per second, deviating from the true trajectory with a standard deviation of 9.6 mm in 3D or 7.9 mm in z alone. The lower curve in Fig. 3 shows the estimates of z provided by Eq. (l), using in each case the singles rates measured over the same interval as used to determine a PEPT location. The scatter of the points appears less than for the PEPT values of z. When a simple linear scaling was used to convert the values of R to a z location in mm, the results deviated from the true trajectory with a standard deviation of 6.7 mm, which is slightly less than the 7.9 mm resulting from PEPT. As noted above, the use of R in this way introduces some distortion, and it was found that by using a slightly non-linear conversion to mm the standard deviation in z could be reduced below 6 mm. Thus, although further work remains to be done in order to determine the best way of deducing z accurately from a combination of the two singles rates, it appears that for the situation studied the singles rates can provide a slightly better estimate of z than the standard PEPT approach. Clearly, the best results will be obtained by combining both approaches. These measurements were performed using a “bare” system, so that the y-rays did not experience attenuation or scattering in traversing the region between source and detector. There will clearly be problems in using this approach in many real systems due to non-uniform attenuation. It is most likely to be of value for tracking in low-density systems having considerable symmetry. Indeed several groups have successfully performed tracking of radioactive tracer particles in fluidised beds purely on
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the basis of comparing the detected array of external detectors [7,8].
count
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Acknowledgements c31 The authors gratefully acknowledge financial support from EPSRC. The data shown in Fig. 1 come from a study funded by Elf via a grant to the University of Cambridge.
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References [l]
M.R. Hawkesworth. M.A. O’Dwyer, J. Heritage,
M
P.A.E. Stewart,
J. Walker, P. Fowles, R.C. Witcomb, J.E. Bateman,
PI
J.F. Connolly and R. Stephenson, Nucl. Instr. and Meth. A 253 (1986) 145. D.J. Parker, M.R. Hawkesworth, C.J. Broadbent, P. Fowles, T.D. Fryer and P.A. McNeil, Nucl. Instr. and Meth. A 348 (1994) 583 P.K. Marsden, R.J. Ott, J.E. Bateman, S.R. Cherry, M.A. Flower and S. Webb, Phys. Med. Biol. 34 (1989) 1043. D.J. Parker, C.J. Broadbent, P. Fowles, M.R. Hawkesworth and P.A. McNeil, Nucl. Instr. and Meth. A 326 (1993) 592. D.M. Benton and P. Fowles, to be published. B. Laurent, J. Bridgwater and D.J. Parker, to be published. D. Moslemian, N. Devanathan and M.P. Dudukovic, Rev. Sci. Instr 63 (1992) 4361. F. Larachi, M. Cassanello, M. Marie, J. Chaouki and C. Guy, Trans. I. Chem. E. 73 A (1995) 263.