IEEE Transactions on Nuclear Science, Vol. NS-30, No. 1, February 1983
A HEXAGONAL BAR POSITRON CAMERA: PROBLEMS AND SOLUTIONS
G. Muehllehner, J.G. Colsher*, R.M. Lewitt
Hospital of the University of Pennsylvania, Department of Radiology3400 Spruce Street, Philadelphia, PA 19104
Introduction
As the ability of positron imaging devices toobtain many transverse sections simultaneously withimproved spatial resolution has increased, so has thenumber of scintillation crystals and photomultipliersrequired. While the PETT III (1) built around 1975used only 48 crystals and photomultipliers, currentstate of the art systems under development use 280 (2)or 512 (3) crystals per ring and may have severalthousand (4) crystal/photomultiplier assemblies in acomplete system. The cost of these complex systemsprecludes their use in routine diagnostic medicine,restricting their availability to a few research cen-ters. A continuous position-sensitive detector pro-vides a method of avoiding the costly one-resolution-element-per-detector design. We have investigatedposition-sensitive one-dimensional scintillationdetectors for positron imaging to assess the problemsencountered in their use and potential solutions.Special emphasis was placed on avoiding solutionswhich increased the complexity of the device.
System Description and Design Philosophy
The positron camera currently under constructionconsists of a hexagonal arrangement of six position-sensitive detectors (see Fig. 1). Each detector incor-porates a crystal of NaI(Tl) which is 500 mm long,50 mm wide and 25 mm thick. The crystal is coupled toten photomultipliers of 2-inch diameter via a suitablyshaped lightpipe. The photomultipliers are connectedto a resistive divider network to provide a position-dependent signal as will be described in detail below.Only a single ring is currently being investigated -the extension to multiple rings is straightforward ifone wishes to use a brute-force technique of simplyduplicating a single ring as is done in most positronsystems now in existence.
Continuous Detectors
Continuous detectors have two principal advantagesin positron systems: 1) They provide continuous samp-ling thereby eliminating the need for moving the detec-tors, and 2) they avoid count losses at the edge ofdiscrete detectors which increase as discrete detectorsare made smaller to improve spatial resolution.
Practically all positron systems incorporate somekind of motion in order to achieve sufficient linearand angular sampling. Considerable ingenuity has beendisplayed to arrive at simple mechanical movementssuch as "wobbling" (5,6), continuous rotation (7),dichotomic (8), "clam-shell" (9), and translate androtate (1) motion. The basic problem is illustratedin Fig. 2, which shows two pairs of opposing detectorsin coincidence. Detector pairs 1-3 and 2-4 havecounting profiles as shown by solid curves leaving anunsampled gap between the pairs. This gap is sampledby coincidence pairs 1-4 and 2-3; however, thesesamples are at a different angle from projections 1-3and 2-4. If a small source is moved along a horizontalline between detector pair 1-3, the recorded positionwill not change, but the intensity will changedepending on the exact location. Thus, the inherentassumption in stationary discrete detector systems is
*Present address: General Electric Medical SystemsOperations, P.O. Box 414, Milwaukee, WI 53201
that the source is as large as a detector; if thesource is smaller, the recorded intensity becomes afunction of position. This sampling problem wasencountered in the Donner ring (9), and it was shownthat sharp edges of objects are distorted even if 280detectors are used in a ring. The problem can bereduced by either using one of the above-mentionedmotions or increasing the number of detectors stillfurther (3). However, no matter how many detectorsare used, if discrete detectors are held stationary,the system is undersampled relative to the size of thedetectors used even if adjacent angular projectionsare summed (10). A continuous detector avoids thisproblem; the digitization resolution can easily bemade a small fraction of the spatial resolution. Evenif the source is a small fraction of the spatial reso-lution, the recorded intensity is not a function ofposition, and a small lateral shift of the source caneasily be detected.
Eliminating movement of the detectors has twomajor advantages: 1) significant higher cost and morecomplicated design due to accurate mechanical motionare avoided, and 2) cardiac gating is greatly simpli-fied. Keeping the hexagonal detector system station-ary does present a problem: at the corners where thedetectors meet, gaps are introduced which result inmissing projection data. This must be taken intoaccount in the reconstruction algorithm.
As detector size is reduced in systems employingdiscrete detectors, counting losses at the edgesbetween detectors become significant. This is parti-cularly true of hygroscopic scintillators such asNaI(Tl) and CsF, if each crystal is canned individu-ally. This effect is one of the major reasons for theswitch to BGO in high resolution positron systems (9,11,12). BGO has the advantage of being non-hygro-scopic, thus avoiding the need for canning and ofhaving higher stopping power, thus minimizing theeffect of scattered radiation leaving the edge of thecrystal. In a continuous detector, radiation scat-tered within the crystal has a high probability ofbeing totally absorbed near the point of first inter-action. Loss of spatial resolution due to scatteringin the detector has been investigated theoretically(13,14) and will be discussed further below.
Position Determination
High spatial resolution can be obtained with rela-tively few photomultipliers through interpolation ofsignals from individual tubes as has been first demon-strated by Anger (15) for scintillation imaging andwhich is also widely used in other position-sensitivedetectors such as proportional counters (16). In our
approach we sum all photomultiplier tube signals withequal weight to obtain a signal which is proportionalto the total energy deposited in the crystal and alsosum all signals with different weights to obtain a sig-nal which is proportional to the position at which thescintillation occurred. Thus, the signals from thephotomultipliers (after pre-amplification) are summedinto two amplifiers (see Fig. 3), greatly simplifyingsubsequent electronics. This summing method effec-tively finds the centroid of the light emitted in the
scintillation crystal. The accuracy of position deter-mination is limited primarily by the statistical uncer-tainty in the signals from each photomultiplier andcan be a small fraction of the diameter of the photo-multiplier.
Hi gh Countrate Capabi l i ty
Since all counts from a bar detector are pro-cessed sequentially through a single chain of elec-tronics, it is necessary to process large countrates.It has previously been estimated (17) that up to700,000 counts/second (CPS) will have to be processedfrom each detector with counting losses below 20%.After a gamma ray interacts in NaI(Tl), the resultinglight is emitted with a decay time of 240 nsec and re-quires 1000 nsec for 98% light collection. Withoutspecial pulse handling techniques, this slow decaywill result in pulse pileup at high data rates andseriously limit the countrate capability achievablewith NaI(Tl). Higher countrates can be achieved withother scintillators such as CsF or pure NaI, however,the low light output makes it difficult to obtain accu-rate position determination in a continuous detector.A number of methods have been described to increasesignificantly the countrate capability of NaI(Tl)detectors at some loss of energy and position resolu-tion (17,19,20,21). We have elected to use pulseshortening to subtract the exponential tail of thepulse (Fig. 4) and a constant integration time of 120nsec. Pulse shortening uses less light output result-ing in greater statistical uncertainty and worse posi-tional resolution. Tanaka, et al (20) have describeda variable integration time technique after pulseshortening which would avoid much of the spatial reso-lution loss encountered with a fixed integration time.Implementing a variable integration time with suffi-cient accuracy is not an easy task but represents adesirable improvement over the method we have current-ly implemented. A different and ingenious method todetermine the centroid which avoids the need for veryhigh countrate capability but requires more complexelectronic circuitry is being developed by Burnham, etal (18).
Table I shows the fraction of light collected asa function of integration time. With an integrationtime of 120 nsec, more than 1/3 of the total lightemitted is collected and integrated. Using passivepulse shaping, the total deadtime can be kept to appro-ximately 250 nsec. Coincidence timing is derived fromthe unintegrated charge pulse,and the integrated pulseis peak sampled. At an input rate of 700,000 CPS,less than 20% of all pulses occur within a time inter-val of 250 nsec (22). It is unlikely that we will en-counter a clinical situation where the singles ratewill exceed 700,000 CPS.
TABLE I
Integration Time
50 nsec
100
240
400
1000
Fraction of Light Emitted
19%
34
63
81
98
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used in many positron systems and can probably be im-proved further. On the other hand, the detection effi-ciency of a 1-inch thick crystal of NaI(Tl) (58% totaldetection efficiency, 36% photopeak detection effi-ciency) is relatively low compared to the detectionefficiency achieved with thicker BGO detectors. It isof course possible to build a bar detector using athicker crystal.. Indeed, a 2-inch thick crystal hasbeen evaluated. However, a thicker crystal has poorerspatial resolution and also a higher positional uncer-tainty for oblique rays. In order to evaluate thetrade-off between spatial resolution and sensitivity,a computer simulation was undertaken.
To study the effect of resolution and count den-sity a phantom was generated analytically with dimen-sions identical to the "Derenzo" phantom (9). Projec-tion values were calculated, convolved with the desiredspatial resolution, Poisson noise was added to simulateacquisition of varying number of events, and the phan-tom was reconstructed as described elsewhere (23).This particular phantom was selected for two reasons:1) it is widely used to evaluate emission computedtomographic devices, and 2) it is approximately repre-sentative of the high contrast, highly structuredimages obtained in brain function studies. Spatialresolution was varied from 4 mm FWHM to 14 mm FWHM andtotal image counts from 50,000 to 3.2 million. Fromthis large number of images, sets were selected whichrepresented approximately equal image quality. Twosuch sets are shown in Fig. 5. Obviously, the subjec-tive judgment of image quality introduces a parameterthat is hard to describe quantitatively. Nevertheless,the results can be compared to signal-to-noise formu-lations (24,25), confirming many of the quantitativerelationships. One fact is readily apparent from theimages shown in Fig. 5: high spatial resolution imagesneed significantly fewer counts to achieve the sameimage quality as low spatial resolution images. Forexample, if system resolution is improved from 8 mm to6 mm FWHM, count density can be reduced a factor ofapproximately 4 for the same visual image quality.The often-repeated statement that high resolutionimages need more counts than low resolution images isbased on the assumption that signal-to-noise per reso-lution element must be kept constant not overall imagequality. It must be kept in mind that the images pre-sented in Fig. 5 are high contrast images with finestructure. The conclusions do not hold for low con-trast or low detail imaging situations.
Detailed Description and Results
Fig. 6 shows a photograph of the whole body posi-tron camera in its present state of construction. Itis mounted horizontally to give easy access to all thebar detectors and to facilitate placing test sourcesin the aperture. Obviously, before patients are imagedit will be raised to an upright position.
The six detectors are mounted between two massive(5-cm thick) lead shielding plates at a separation of86 cm and with a gap width of 26 mm. While it hasbeen determined (26) that 90 cm is the optimum detec-tor separation and some whole body systems use a sepa-ration of 100 cm (1), we have found that setting theenergy threshold at 200 keV instead of 100 keV (1,26)is an effective method to reduce both scattered radi-ation and random coincidences and reduces the sensiti-vity by about the same amount as increasing the detec-tor separation.
Bar Detector
A block diagram of a bar detector and its asso-ciated electronics is shown in Fig. 3. The NaI(Tl)scintillation crystal is 500 mm long, 50 mm wide, and
Influence of Resolution and Count Density on ImageQuality.
With continuous detectors of NaI(Tl), we havemeasured an intrinsic spatial resolution of 8 mm FWHM.This value is less than the physical size of detectors
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25 mm thick with a 600 beveled edge to minimize the
gap between the six detectors and to deflect light
reaching the outer edges toward the first and last
photomultipliers. The crystals were made 50 mm wide
primarily to increase the probability of total absorp-
tion within the crystal. Toward the photomultipliers
the crystal is optically coupled to a pyrex exit win-
dow (12 mm thickness) which in turn is optically
coupled to ten photomultipliers via a lightpipe. The
lightpipe, made of Plexiglass (selected to have a
high transmission at all wavelengths of the emitted
light) serves the purpose of distributing the light
between the photomultipliers in such a way that spa-
tial resolution along the bar is nearly constant. The
photomultipliers (Hamamatsu R1306-09) are speciallydesigned for use in scintillation cameras and exhibitgood energy resolution (< 10% at 122 keV) and havestable gain as a function of time which is essentialfor reliable operation in a position sensitive detec-tor.
Preamplifiers
At the input to each preamplifier the signal isshortened via a simple delay line circuit. The delayline (60 nsec, Z = 400 Q) which is connected to groundthrough a 100 Q resistor has the effect of invertingthe signal, delaying it 120 nsec, attenuating it, andsubtracting it from the input pulse. The resultingpulseshape (after linear amplification') is shown inFig. 4. After linear preamplification, a simplebiased threshold circuit allows subtraction of lowlevel signals to avoid loss of spatial resolution dueto contributions of photomultipliers far from thepoint of scintillation. This technique (27) has beenfound to be very useful in Anger scintillation camerasand is currently used by practically all manufacturers.In this application, it has the additional benefitthat noise in the tail of the pulse is eliminated,thus preventing excessive loss of spatial resolutionat high data rates.
Pulse Summing and Shaping
The output of the threshold preamplifiers are 1)summed with equal weight to give a signal which line-arly related to the total energy deposited in thecrystal and 2) summed with different weights to give a
position-dependent signal. These summing amplifiersare mounted on the gantry so that only two signals(energy and position) are routed to the processingelectronics for each bar detector. For coincidencetiming and energy discrimination, the charge pulsebefore integration is used to keep the deadtime fordetecting valid coincidences to a minimum. For coin-cidence detection the only requirement is that the
"pulse of interest" (i.e., the coincident pulse) can-
not be preceded by any other pulse in either of the
two bar detectors in coincidence. Any pulse arrivingsubsequent to the "pulse of interest" only affects the
ability to correctly position the event but not the
ability to detect coincidence. As is shown in Fig. 3,the outputs of the summing amplifiers are integratedin an amplifier using RC integration and delaylineclipping resulting in a pulse of approximately 250
nsec duration. Since this pulse is subsequently peaksampled, we have the following requirements for both
coincidence detection and accurate position determina-tion (see Fig. 7): each "pulse of interest" must be
preceded by a pulse-free interval which is approxi-mately 120 nsec for coincidence detection and to avoid
interference of a preceding pulse with accurate posi-
tion determination. Note that the integrated pulsefrom a preceding event may overlap the integrated"pulse of interest" as long as it does not overlapduring the peak sampling time, In addition, each
'pulse of interest" must be followed by a pulse-freeinterval of approximately 120 nsec to allow accuratepositioning of the event of interest. Thus, the totaldeadtime is approximately 250 nsec (120 nsec pre- andpost-pulse deadtime). This requirement for both a pre-and post-pulse deadtime is unique to position sensitivedetectors and approximately doubles the deadtime com-pared to a system using discrete detectors.
"Ratio Circui t" and Analog-to-di gital Conversion
The amplitude of the position-dependent signal isalso a function of energy and must be divided by theenergy signal to derive an energy-independent positionsignal. This division is customarily accomplished inan analog ratio circuit. To avoid the use of sample-and-hold circuits and an analog ratio circuit, we usedthe analog-to-digital converter (ADC) to perform boththe division and the conversion. This is accomplishedby using the energy signal as the "reference voltage"in a so-called flash ADC (TRW TDC1007J) which consistsof 255 parallel comparators and has a conversion speedof 40 nsec and a sampling speed of 15 nsec. The use ofthis ADC as a ratio circuit has been described prev-iously (28) and has sufficient accuracy and dynamicrange for this application. The digital output of theADC together with the output of the coincident detectoris routed to the input port of an Intel (29) single-board computer (SBC 86/12) which stores the data event-by-event in an associated memory.
Single Detector Performance
The above-described configuration was arrived atafter evaluating many alternatives. Throughout thedevelopment process the main objectives were: averageintrinsic spatial resolution below 10 mm FWHM, dead-time below 300 nsec with countrate capability up to700,000 CPS at a data loss of less than 20%. The firstscintillation crystal which was evaluated had a thick-ness of 50 mm. Unfortunately, we were never able toachieve a spatial resolution of better than 14 mm FWHMand finally switched to a crystal of 25 mm thickness,thereby sacrificing a factor of 3 in coincidence sensi-tivity. Since we had previously used a 25-mm thickcrystal in a two-dimensionally position-sensitivedetector (30), we had a higher degree of confidencethat we would be able to achieve good spatial resolu-tion. At this time, we have measured the averagespatial resolution of three 25-mm thick crystals whichwere identical except for slight variations in crystalsurface preparation and have found that the intrinsicspatial resolution varied from 7.6 mm to 8.3 mm FWHM.The values represent averages of measurements performedevery 25 mm along 90% of the length of the detector.Resolution generally is about 10% better near the cen-
ter of the detector; the final 10 mm at either endshow severe positional distortions due to the proximityof the edge and are not useful for event localization.Thus, the effective gap between adjacent detectors isapproximately 25 mm (10 mm at the ends of both detec-tors and 5 mm physical gap). The simulations to studythe effect of these missing data described below assume
a 25-mm gap in the projection data.
In the design of the detector, little emphasis was
placed on achieving good spatial linearity, i.e., a
linear relationship between source position and theaverage location of the recorded scintillation events.As has now become commonplace in Anger scintillationcameras, spatial distortion removal (31) can and willbe used to achieve good spatial linearity before rebin-ning the data and reconstructing the transverse section.
To achieve the design goal of 700,000 CPS count-rate capability, we found it necessary to connect thelast two dynodes of the photomultipliers to independent
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high current power supplies in order to avoid currentlimitations in the dynode resistor chain and signalamplitude changes as a function of input rate. Wehave tested the detector up to 900,000 CPS outputrates and have found that count losses due to deadtimeare almost exactly equal to count "gain" due to pileupof lower amplitude signals. Unfortunately, we have sofar not been able to measure intrinsic spatial resolu-tion above 200,000 CPS because it is difficult to getsufficient activity into a small volume and also get asufficient number of gamma rays through a narrow slitso that only a small (1-2 mm) segment of the crystalis irradiated.
Two Detectors in Coincidence
In order to assess the system spatial resolutionwhich we are likely to achieve, some preliminary datawere taken with two of the six detectors in coinci-dence. Line sources filled with Ga-68 were placed inseveral locations midway between the detectors. Theaverage spatial resolution measured in the raw projec-tion data was 6.5 mm FWHM. This is approximately theexpected value: for a Gaussian detector response, theintrinsic resolution (RI) contributes (l/f2M) - RI to
the system resolution. Other sources of loss of spa-tial resolution include the deviation from 180° be-tween the two gamma rays following positron annihila-tion and effects due to the depth of interaction forgamma rays hitting the crystal at angles other thannormal (32).
Data Acquisition
The data system necessary to acquire, store, andprocess the data from the complete ring of six detec-tors was selected to suit our particular objectives.While it would have been possible to design and imple-ment a dedicated, on-line, realtime data acquisitionand reconstruction system as is commonly employed onx-ray CT scanners, such an effort would have beenexpensive in terms of required manpower and would havereduced flexibility. Since the single-ring system isintended primarily to show feasibility of the conceptand to explore fundamental instrumentation questions,the data system was designed for maximum flexibilityin data analysis and to minimize the effort necessaryto implement it.
The data acquisition system consists of an Intelsingle-board computer (SBC 86/12) connected via theIntel "Multibus" to 576 K bytes of semiconductor mem-ory and an Input/Output module (SBC534) which allowsit to communicate to a terminal and to a VAX 11/780(Digital Equipment Corp.) computer which is used fordata processing. The VAX computer is connected to aDeAnza (33) display system to display both interme-diate results and the final transverse section image.
Each detector is in coincidence with three oppos-ing detectors through a total of nine coincidence cir-cuits. Since each detector output consists of an8-bit word from the ADC, the data from a coincidentevent forms a 16-bit word (8 bits from each detector).In addition, the detector pair which generated thecoincident event must be identified. To connect theoutputs of all six ADC's to the data system, a dual8-bit bus was implemented in such a way that each ADCcan address either bus via three-state line drivers.This is shown schematically in Fig. 8. When a coinci-dent event occurs, the two appropriate ADC's digitizethe event position, and the digital event coordinatesare switched onto buses A and B. A coded interruptsignal tells the data system which detector pair gen-erated the event and the outputs of both buses areread into the data system. We expect a maximum coin-
cident countrate of 50,000 CPS in a single ring. Sincedata transfer on the buses takes less than 100 nsec,data losses due to simultaneous events is below 1%.
Data Storage
Each of nine detector pairs generates events with256 x 256 possible addresses since we use 8-bit ADC's.If the raw data are accumulated, 576 K bytes of randomaccess memory are necessary. Before an image can bereconstructed, these data must be corrected for posi-tion nonlinearities as mentioned above and must be reor-ganized into parallel projections. If they are reorgan-ized into 2-mm intervals in each projection and 180angles which is sufficient without undersampling ineither position or angle, then the data will occupyless then 64 K words of storage after reorganization.On-line reorganization thus reduces the memory require-ments significantly, albeit at a loss of flexibility.At the present time we store the raw data and leavedistortion removal and data reorganization as a task tobe performed subsequent to data acquisition. Before wecan implement gated cardiac data acquisition, on-linedistortion removal and rebinning will be necessary.
After acquisition, the data are transferred on-line to the VAX computer. Much of the software toremove distortions, reorganize and normalize the data,correct for missing projections and attenuation, andreconstruct the transverse section still needs to bewritten.
Compensation for Missing Projection Data
If the ring of six detectors is to be kept totallystationary, then it will be necessary to compensatefor the data which are missing due to the gaps betweenthe detectors. It is possible to minimize the physicalspace between the scintillation crystals. However, thelast 10 mm at either end of the crystal have large spa-tial distortions and are not useful for gamma raylocalization. Thus, the effective gap between detec-tors is 25 mm.
The gaps in the data are similar to those encoun-tered in both emission and transmission CT when adetector is defective. Often it is impractical to dis-continue use of the system until the defective detectoris repaired and the use of algorithms to "bridge thegap" are commonly employed. For example, in the PETT Veach detector samples a distance of 40 mm through wob-bling; if the detector fails just before a scan, thescan is completed, and the missing data are taken intoaccount in the reconstruction. In our system, theintrinsic spatial detector resolution is 8 mm; themissing data gap is 25 mm and thus corresponds to threeneighboring missing detectors.
The effect of the missing data and methods of com-pensation were investigated by simulating data from aDerenzo phantom which consists of a 20-cm diametercylinder divided into six sectors. Each sector hasdiscs of varying diameter and spacing as shown in Fig.9. The projection data was computed for 180 views at1° angular intervals with 1280 samples per view spaced0.2 mm apart. The projections were then convolved witha Gaussian function of 8 mm FWHM to simulate the effectof the detector spatial resolution and were subsequent-ly summed into projections of 128 samples per viewspaced 2 mm apart. Noise was added to the data tocorrespond to an accumulation of 2 million events.The transverse sections were reconstructed using aconvolution-backprojection algorithm into an imagematrix with 2 mm pixel spacing (127 x 127). TheFourier transform of the convolving function has theform of a ramp multiplied by a raised-cosine windowfunction (Hann window) whose cutoff frequency is 1/n
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of the Nyquist frequency where n is a parameter chosenfor best image quality.
The effect of the missing data was simulated bytaking the full data set (180 projections and 128samples/projection) and masking out those values whichcorrespond to coincidence lines which pass through thegap between two detector bars. Fig. 10 shows the pro-jection data for the Derenzo phantom both with andwithout the effect of the gaps.
The missing data are estimated using the follow-ing method. A ray is specified by the pair of para-meters (s,e), where s represents the distance from theray to the center of the ring and e represents theangular orientation of the ray relative to the ring.For the convolution/backprojection algorithm, we re-quire data corresponding to a set of rays (mAs, nAG),where m,n are integers, such that the rays cover theentire source distribution from a complete range ofdirections. We define H to be the set of rays whichare available from the hexagonal ring (see Fig. 10B,where s and e are plotted across and down the page,respectively), and we define f to be the set of rayswhich are not available, but which we desire to esti-mate from the ring data (these rays are in the criss-cross "gaps" evident in Fig. lOB, when compared withFig. IOA).
For those (mAs, nAe) in R we estimate the missingdata P(mAs, nAe) by linear interpolation in the 0-dir-ection. For each mAs, the interpolation is donebetween a local average of the data on one side of thegap and a local average of the data on the oppositeside of the gap. In order to specify the interpola-tion operation more precisely, we need to introduceadditional notation: the index p is used to specifythe angle on one side of the gap and the index u isused to specify the angle on the opposite side of thegap for which data are available at the particularvalue of mAs being considered. For each (mAs, nAG) inH, the interpolation algorithm determines this pair ofintegers vi,u according to the following criteria:
1) p < n < u
2) (mAs, pAe) and (mAs, uAe) are in H
3) (mAs, (p +1)AG) and (mAs, (u - 1)Ae) are in H
Next, the algorithm computes the local averages of thedata on each side of the gap, in neighborhoods of(mAs, PA) and (mAs, uAG), respectively. We defineA(m,vi) to be the average of the data associated with(mAs, MAe) and those of its eight immediate neighbor-ing rays which are in H, i.e., those of (mAs, (, + 1)AG), ((m t 1)As, pAG) and ((m + 1)As, (p + 1)AO) forwhich data are available. For the opposite side ofthe gap, we define A(m,u) in a similar way. Then theestimate PA(mAs, nAe) of the missing data is computed
by linear interpolation:
PA(mAs, nAG) = A(m,) + -n (A(m,u) - A(m,))Images reconstructed from data compensated in
this manner are shown in Fig. 9 together with imagesin which no data are missing and images in which themissing data are not compensated for. Particularlywhen noise is included, the effect of the gaps is seento be well compensated for with this technique. Theseresults, however, are only preliminary, and other com-pensation techniques are being investigated to furtherminimize artifacts due to the gaps between detectors.
Discussion
The overall design goal is to build a high resolu-tion, totally stationary, whole-body positron tomographusing continuous position-sensitive detectors toachieve simplicity of design. This has presented someunique problems, particularly: 1) achieving highsingles data rates with tolerable counting losses, 2)achieving high spatial resolution in a thick scintilla-tion detector, and 3) compensating for the gaps betweendetectors.
High countrate capability is achieved throughpulse shortening, passive integration and peak sampling.While it would have been better to implement the vari-able-integration-time method proposed by Tanaka, et al(20), we chose a constant integration time after en-countering numerous technical problems in our attemptsto build a variable sampling-time integrator whichfulfilled all the necessary requirements. At the pre-sent time we have achieved an intrinsic detector reso-lution of 8 mm FWHM, but only by using a 25-mm thickscintillation crystal. Originally, we had hoped to beable to use 50-mm thick crystals. The one 50-mm crys-tal which we evaluated never gave a spatial resolutionbetter than 14 mm. The reason for the large differencebetween the 25-mm and 50-mm thick crystals is not fullyunderstood. It is partly due to the fact that thethicker crystal had significantly lower total lightoutput than the 25-mm crystals. Reducing crystalthickness from 50 to 25 mm resulted in a reduction ofcoincidence sensitivity by a factor of 3.
Simulations of the effects of gaps between thedetectors indicate that a simple interpolation proce-dure reduces image artifacts significantly. In imageswith 2 million counts and 8-mm spatial resolution theeffect is barely visible. More sophisticated proce-dures such as iterative algorithms are likely tofurther improve image quality.
As is apparent from Fig. 6, all major componentsare assembled. While most of the hardware is func-tioning, a major effort is yet required to compensatefor positional nonlinearities in the detectors, rebinthe raw data into projections, and integrate the soft-ware to produce section images. While this is alaborious task, no major difficulties are anticipatedin completing the system.
Acknowl edgment
We are grateful to Cleg Gritsenko who assembled,debugged, and tested the positron camera. Thisresearch is supported by DOE grant DE-AC02-80EV10402and in part by USPHS grants CA31843 and HL28438.
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FIG. 1: Diagram of hexagonal arrangement of six posi-tion-sensitive detectors to form a single ring positroncamera.
658
DET DET1 2
J \\ IJ/
/\\CDET
34
FIG. 2: Two stationary opposing pairs of discretedetectors sample a projection with nonuniform sensi-tivity leaving an undersampled gap between detectors.
PHOTOMULTIPLIERS
V~~~~FILTER
\EhNERGY SIGNAL
NAI CRYSTAL LIGHTPIPE
FROM 2nd RARCAMERA
FIG. 3: Block diagram of processing electronics. FIG. 5: Two sets of images from computer simulation.In each set image quality was judged approximatelyequal.
FIG. 6: The whole body positron camera. Visible are the lead shielding, six barcameras with associated preamplifiers, the rack of electronics containing powersupplies, amplifiers, discriminators, analog-to-digital converters, and acqui-sition memory. The system is operated from the terminal which controls all dataacquisition, display and transfer to an on-line VAX computer. The system ismounted horizontally for ease of testing only.
PRE-PULSE' IDEAD TIME I INTEGRATION
150 nsec 1TIME=150 nsec
A B NEXT PULSECAN START HERE
30 nsec PEAK~~~+ SAMPLING
A B NEXT PULSECAN START HERE
BUS A BUS B
FIG. 8: Diagram showing six analog-to-digital conver-ters connected to dual bus which is interfaced toparallel input port of the data acquisition system.
FIG. 7: Diagram showing timing of charge pulses (A) andintegrated pulses (B) for minimum separation consider-ing both coincidence timing and position determination.
A
B
660
A B C
D E F
FIG. 9: Derenzo phantom has discs of 2.5, 3.0, 3.5, 4.0, 5.0, 6.25 mm diameter spaced10, 12, 14, 16, 20, 25 mm apart respectively in each of six detectors. Top row showssimulated transverse sections with no statistical noise added; images in bottom row have2 million counts each. First column (A and D) shows reconstructions without any datamissing, second column (B and E) shows the effect of 25 mm gaps in data corresponding togaps between detectors and the third column (C and F) shows images after interpolationto compensate for the missing data.
A B
FIG. 10: "Sinogram" display of simulated projectionsthrough Derenzo phantom before (A) and after (B) gapsare simulated. Vertical axis is angle e of projection,horizontal axis is distance s along projection.
