IEEE Transactions on Nuclear Science, Vol. NS-27, No. 1, February 1980
SCINTILTATION CAMERA FTFIL UNIF)RMITY: VISUAL OR QUANTITATIVE?
P.T. Cahill, R.J.R. Knowles, and D.V. Becker
New York Hospital-Cornell University Medical Center, New York, N.Y. 10021
Polytechnic Institute of New York, Brooklyn, N.Y. 11201
Long Island College Hospital, Brooklyn, N.Y. 11201
SUMRY
Global and local scintillation camera uniformitywere studied phencnenolgically with emphasis on statis-tical features. A system parameter (the systematicerror) was developed to quantitate global field unifor-mity. (The systematic error also appears to predictthe maximum variation in response resulting fron localirradiation of the detector.) Uniformity correctionby a statistically weighted rmatrix renormalizationprocedure was demonstrated to improve the global fre-quency distribution of the counts per pixel. Such arenormalization procedure also slightly improved localresponse if the systematic error was smali but not ifthe systemiatic error was large. The failure of thisrenormalization procedure appeared to correlate withlong range interactions in the detector. The exis-tence of such long range interactions casts doubt onthe efficacy (and even the desirability) of manycarnmnly used uniformity corrections.
INTFRODUCTION
Traditionally, uniformity of detector responsefor scintillation cameras has been judged visually.Such visual evaluation is accomplished by observingthe density uniformity of polaroid or of film trans-parencies when the camera is used to image either auniform sheet source or a distant point source. Formost films, the mnimiumm detectable visual variationis eight to ten percent.
More recently, camera manufacturers have offeredquantitative specifications for field uniformity.A typical standard is that variations shall be fivepercent or less over any one- (or sanetimes two-)inchstrip across the detector. For the operationalimplementation of such standards, one or two millioncounts is usually accumulated in the form of a 64X64matrix representing the entire camera field. Statis-tical analysis, however, indicates that the 4.5% (onesigma level on two millioxn counts) to 12.8% (two sigmalevel on one million counts) Poisson error per pixelmay overshadow the 5% uniformity specification as thesystem resolution limit is approached. Moreover,specification in terms of strips may not adequatelylimit uniformity variations throughout the total camerafield. Thus there exists a critical need for a param-eter to specify total field uniformity independentlyof the counting statistics.1
With advances in technology, camera uniformityhas been enhanced by optical and/or electronic methodsof analog preprocessing at various stages during theformation of the image. Recently, digital systems foruniformity correction have been introduced into thedetection chain. Some systems subtract counts fram(and, in at least one case, add counts to) selectedareas of the field on the theory that nonuniformitiesresult fran local variations in the sensitivity of thedetector. Other systems use adjustable functionalenergy windows for each pixel of the image on the theorythat nonuniformities result fram local variations inthe energy signal of the camera. In addition, point
shifting corrections based on the theory that localnonlinearities in the position signals cause nonuni-formities are being developed. Although lack of auniversally accepted quantitative measure has hinderedinterccrparisons, all of these methods of field cor-rection have demonstrated at least visual improvementin field uniformity under conditions of global irradi-ation.
Such attention to global detector response isjustified in so far as it provides a useful tool forscintillation camera quality control; however, clinicalnuclear medicine is more often concerned with cameraresponse to multiple sources arrayed three-dimension-ally. A major question is whether global response isan adequate predictor of local response.213 If, forexample, point shifting is an iwportant entity innonuniformities, then the global response will not bea good predictor of local response because only in thecase of local irradiation are there demonstrable boun-dary effects. Therefore uniformity corrections thatimprove global response may or may not improve localresponse. Such considerations are of critical impor-tance to quantitative nuclear medicine where the goalis to infer source activity (percent of dose) fromlocal detector response.
In principle, the local transfer functions couldbe measured for a given system of optical and elec-tronic preprocessing, and the response of the camerato various arrays of sources could be calculated. Inpractice, cameras differ substantially in their detec-tion logic, and proprietary information is ofteninvolved. Furthermore, each camera includes a verylarge set of tunable parameters that are regularlyadjusted by service personnel using far more art thanscience. Hence the study of camera uniformity isultimately reduced to a phenomenological study. Funda-mental to quantitative nuclear medicine is the statis-tical nature inherent in its basic data set (radio-active decay processes). Thus statistical analysisaffords a natural methodology for the phenomenologicalexamination of scintillation camera uniformity.
METHODS
Four different cameras (three different manufac-turers) were studied. These cameras were subjectedto both global and local irradiations by various Tc-99msources. For the global irradiations, collimators wererEmrved, and point sources of eighty microcuries wereplaced at least four feet fram the detector. For thelocal irradiations, flasks of several sizes with activ-ities less than one hundred microcuries were placeddirectly on the appropriate general purpose collimator.First, a single flask was sequentially rmved to manydifferent positions on the collimator, and the decay-corrected counts were compared. Second, variousarrays of flasks were positioned on the collimator,and their effects on the count rate of one flask weremeasured.
In all of these irradiations, the total count rate
of the system (< 6 KHz) fell well below the count ratepreviously determined to produce a ten percent deadtimeloss (60 KHz). (Deadtime was determined by using cal-ibrated attenuators with a distant collimated pointsource irradiating the uncollimated detector. Theequivalent decay method was also employed, and theresults of the two methods were in agreement.) Ingeneral, the deadtimes involved in the following mea-surements were no more than one percent.
Both global and local responses were digitizedand subjected to ccputer analyses, including a matrixrenormalization procedure (Figure 1). This renormali-zation methodology was used as an analytic tool onlyand should not be construed as an a priori ccmnitmentto any particular theory concerning the origin ofscintillation camera nonuniformities.
Information about field uniformity is presentedin terms of alphanumeric coded images (Figure 2). Thiscode may be either a simple percent code (percent ofmean counts per pixel) or a statistical code (numberof standard deviations from the mean). Informationabout field uniformity is dramatically presented bymeans of frequency distributions (number of pixelsversus counts per pixel) (Figure 3). The size of thebins used for the counts per pixel can be determinedeither by a percent of the mean (Gaussian distribution)or by a fraction of the standard deviation from themean (Poisson distribution).
RESULTS AND DISCUSSICN
1. Global Irradiation
If the detector is uniformly irradiated and ifthe detector response is unifonm, then the frequencydistribution should be Poisson in nature. Experimentaldata, however, deviate from the Poisson distributionin a systematic manner that depends on the averagenumber of counts per pixel (Figure 4). In the lowcount domain, the data are somewhat Poisson in theirdistribution; in the high count domain, there islittle resemblence to the supposed parent distribution.This indicates that there must be at least tw compon-ents to the standard deviation of the set frcm theaverage counts per pixel:
6 =6 + 6isAccording to statistical theory, a cross correlationterm may also be present:
+ 26p6SySTrhis continency can be examined by considering
6S = 62 _- = 6 2 _ NA
as a function of the average counts per pixel (NA).Results in Table 1 demnstrate that, within the over-all statistical error, the systematic error is inde-pendent of the average number of counts per pixel.Therefore there is no detectable cross correlationbetween the Poisson and systematic error terms. (Forvery small NA, variations in the systematic error maybe accounted for by the skewness of the Poisson dis-tribution.)
At this point, we noteparenthetically that thesystematic error term is characteristic of the systemand correlates with other visual and quantitativeestimates of field uniformity: a large systematicerror implies a nonuniform field, and a small system-atic error implies a uniform detector response.Moreover, the systematic error appears to form theupper bound for variations between counts obtainedby locally irradiating various areas of the detector
with identical small sources (several different physi-cal sizes were used). Thus the systematic error isa most useful parameter characteristic of the camerasystem.
2. Global Response Renormalized
To further our analysis of field nonunifonmities,we next considered renormalization of the digitalizedimage of a uniformly irradiated field by a correctionmatrix derived from another uniformly irradiated field.Such matrix corrections have traditionally been of thegeneral form indicated in the upper part of Figure 1.In view of our previous observations about two distinctstatistical dcmains, such a simple expression mustobviously be inadequate: scme allowance must be madefor the count level of both the observed field O(I,J)and the normalizing flood field F(I,J). A more real-istic expression is presented in the lower part ofFigure 1. (In most cases, a = b.) Tllhe later correc-tion recognizes that the observed image cannot becorrected for its random (Poisson) component but onlyfor its systematic (structural) camponent and that itmay be overcorrected by a high count flood (large sys-tematic component and small random component) actingon a low count image (large random component and smallsystematic component).
Application of such a correction does, in fact,rmprove the frequency distribution of other uniformlyirradiated images (Figures 5a,b,c). Tfhis qualitativeimpression is born out by a detailed analysis of thevariations between pixels as a function of the averagecounts per pixel (Figure 6).
3. Local Irradiation by a Single Source with and with-out Renormalization
When such renormalization procedures were appliedto equivalent local irradiations of the detector, theresults fell into two catagories (Table 2). For sys-tems with small systematic errors, such renormalizationprocedures produced a small improvement in the agree-ment between the counts collected from different areasof the detector. For systems with large systematicerror, however, such renormalization procedures actu-ally reduced the agreement significantly.
This result could be consistent with the spatialnonlinearity theory of nonuniformity since the shift-ing of points only becomes apparent when local irradi-ation creates boundaries across which shifting mayoccur (i.e., there is no operational distinction be-tween variations in local sensitivity and variationsin local spatial linearity when the entire detectoris uniformly irradiated). It is important to note,though, that such experimental results are only a nec-essary condition for the spatial nonlinearity theoryand not a sufficient condition.
4. Local Irradiation by an Array of Sources
In order to investigate this disparity betweenlocal and global response to renormalization, severalpatterns of local irradiation were produced. Results,Table 3, indicate that in systems with large systematicerror, local count rate was significantly reduced (12%)by the presence of other sources anywhere in thedetector field even though the total count rate of thedetector (6kHz.) was well below the measured count rate(60kHz.) with a ten percent deadtime loss. It is diffic-ult to reconcile such long range interactions with anysimple point shifting mechanism.
CONCUSIONS
Systematic error is a useful parameter to charact-erize both global and local uniformity for scintillation
510
cameras. Matrix renormalization should not be carriedout in systeis with large systeuLutlc error. Failureof matrix renornalizaticn in cases of large systamticerror appears to result from previously unreportedlcng range interactions that would appear to render alloCmmn uniformity corrections useless.
Ackniowledgemets
This research was supported in part by CbntractNO]-HV-52985 and Grant RO] Hl 2]684 from the NationalHeart, Lung and Blood Institute, by a Grant from theRosenfeld Heart FOundation, Inc., N.Y., and TheInstitute of Imaging Sciences, Polytechnic Instituteof New York. Part of this research wms taken from thedissertaticn sumiitted by R.J.R. Knowles to the facultyof the Polytechnic Institute of New York in partialfulfillment of the requirefents for the degree of Ph.D.(]979).
Referenoes
]. Cox NJ, and Diffey EL, Brit. J. of Radiology, 49:735 (1976)
2. Wicks, R and Blau, M.,J. Nucl. Med. 20:252 (]979)3. Tcdd-Pokrvpek, A, et al., IAA-S4-210/]54,67-84
GLOBAL RESPONSE RENORMALIZED
1. TRADITIONAL FORM:
C(I,J) - O(l,J) N
F(l,J)C(I.J) = CORRECTED FIELD PIXELO(l,J) = OBSERVED FIELDF(l.J) - FLOOD FIELDT - NORMALIZATION FACTOR (OFTEN = NA
2. MORE REALISTIC EXPRESSION WEIGHTED FOR SYSTEMATIC ERROR
A - PERCENT SYSTEMATIC ERROR IN OBSERVED IMAGEs = PERCENT SYSTEMATIC ERROR IN FLOOD
Figure 1. Flood renormalizaticn equaticns.
- CI'
am.a:
II
ml
2~~~~~~~2
B I/' '-
_.. ..' -1-ll C UII 3Pi Ii
Figure 3. Fyequency distributicns of unifonraly irradi-ated field (curves are theoretical, boxes are data).Left: Poisson distributicn. Right: Guassian distri-buticn of perent of the average counts per pixel.
-._K:*0~03
Figure 4. Frequency distributions of uniformay irradi-ated fields with different average oonts per pixel.Clocwie fran uEer left: 258, 1229, 2380, and 10518omots per pixel.
Figure 5a. Effects of renormalization on uniformlyirradiated fields presented in six-percent oode.left: raw data. Right: renonmlized field.
Figure 2. Digital image of uniformly irradiated field.left: percent oode ($ is within, - is below, and +is above 6% of the nean). Right: Poisson statisticalcode (two standard deviations per syxbol).
511
SYSTEYATIC ERROR (I AS A FUNCTION OF TIE ANERA)E rER OF EMBEDS PER P1XELKY-1- -l i: '' I-:"li" ---~- -- i--' igib
Table 2. Renomalization may either worsen (large sys-tematic error systerTs) or inporve (doll systaeatic er-ror systems) local unifonriity of response.
PERCENT DECREASE IN COUNT RATE OF ONE SMALL SOURCE WHEN
SURROUNDED BY VARIOUS CONFIGURATIONS OF SIX OTHER IDENTICAL SOURCES
CAMERA A B C D
SIX NEARESTNEIGHBORS
SIX NEARESTNEIGHBORS(ROTATED 300)SIX FARNEIGHBORS
SIX NEARESTNEIGHBORS(OFF CENTER)
13.7 6.8 4.4 15.2
12.8 6.7 3.8 13.8
13.5 6.8 3.5 14.7
11.8 6.6 2.6 13.5
M TA" Table 3. Interactions of arrays of small sources.
STArlSrICPLWE
S 1O 15
EFFECT OlF IW00NALl9I2O POISO ERROR
Figure 6. Ilir tion of unifonmly irradiatedfields causes the standard deviation of the countsper pixel to exhibit Poisson behavior.
