Three-dimensional coded aperture techniques in diagnostic nuclearmedicine imaging

Li Zhang a Richard C. Lanza, Berthold K. P. Horn a dRobert E. Zimmennanb

aMsach Institute ofTechnology, Cambridge, MA 02139bBrigham and Women's Hospital, Harvard Medical School, Boston, MA 02115

ABSTRACT

Coded aperture techniques based on a cyclic difference set uniformly redundant array (URA) can increase sensitivity of animaging system without degrading the spatial resolution. In this paper, we discuss the pattern design and present itsapplication for diagnostic nuclear medicine imaging with experimiital results. Point-like, p1anai and three-diinisiona1 140keV gaimna-ray sources are used in our experiments. We have experimaitally demonstrated a three-dimensional codedaperture technique for nuclear medicine imaging and have compared it with convaitional collimator systems.

Keywords: coded aperture, nuclear medicine, imaging

1. INTRODUCTION

Positron emission tomography (PET), single photon emission computed tomography (SPECT), and planar gamma imagingare standard in diagnostic nuclear medicine imaging. All these techniques use photon collimation; PET with electroniccollimation, and the latter two with lead collimation and thus suff from very low efficiicy or saisitivity. Conventionalcollimator systems trade offspatial resolution for sensitivity; A typical collimator system has sensitivity ofonly 0.1% or less.Coded apcture techniques use a coded patteni (spatial multiplexing) instead of a collimator to encode the photon sourceinformation (strength and location), thus each detector resolution element sees the entire field of view and every photonsource contributes to the signal in all detector resolution elements. This significantly improves the system sensitivity withoutdegrading the spatial resolution of the reconstructed images thus decreases the radiation dose needed to gen&ate the imagesof a certain quality.

Coded aperture imaging is a technique for producing images ofphoton emitting objects (20 keV - 10MeV) by using a mask(coded aperture) with spatially varying degrees of photon opacity distributed according to some mathematical algorithm. AnX-ray or gamma-ray source will then cast a shadow onto a position sensitive photon detector, thus encoding the spatialinformation contained in the source. The resulting shadowgram can be deconvolved with a suitable decoding algorithm toreconstruct the original source distribution (object).' The signal-to-noise improvement for a coded aperture system over asame-size pin-hole camca is in principle proportional to the square root ofthe number ofholes in the pattn. The choice ofaperture patterns detainines the spatial resolution as well as the system response function. We have used a cyclic differenceset uniformly redundant array as the coded aperture pattern; the system point spread function is a delta function and thus nospurious sidelobes are introduced.

Further author information -Li. (correspondence): Email: lizhanginit.edu; Telephone: 617-258-6522; Fax: 617-253-2343R.C.L.: Email: lanza@mit.edu; Telephone: 617-253-2399; Fax: 617-253-2343B.K.P.H.: Email: bkphai.mit.edu; Telephone: 617-253-5863R.E.Z.: Email: zimmer@bwh.harvard.edu; Telephone: 617-732-7196

Partof the SPIE Conference on Physics of Medical Imaging • San Diego, California • February 1998364 SP1E Vol. 3336 • 0277-786X198/$lO.OO

2. THEORY

Coded apaure techniques appiy to 1-D coding and 2-D coding by using 1-D and 2-D specially arranged apertures,respectively. The patterns have the property such that the system point-spread function (PSF) is a delta function, thus nodistortion is iniroduced by the spatial multiplexing process. The system PSF can be obtained by cross-correlation,deconvolution, and other decoding techniques such as maximum iUropy or iterative annealing methods. The general designrule for a cyclic difference set uniformly redundant array coded aperture pattern is that the auto-correlation function has onepeak and perfectly flat sidelobes.

There is no complete theoiy for designing coded aperture patterns with the above mentioned properties. We have used twoapproaches: the first is exhaustive search method, which searches all possible combinations to find out the complete list ofsatisfactory patterns for a specific matrix dimension; the second method uses some existing equation to design a subset ofpatterns with such properties, such as the classical URA or its variations MURA and HURA.2

Our exhaustive search approach has found more possible patterns with the desired property, which can not be calculatedfrom any exisling equation. The results for 1-D and 2-D situations are shown below, and do not include the shifted (orrotated), reflected, and complementary patterns, nor all 0 (or 1) and single 0 (or 1) patterns.

1-D cyclic set URAAn exhaustive search for a complete list of n element 1-D cyclic difference set URA has yielded the following results(n1...31):

n=70010111

n=11

I 1011010001

n=13

00000010100110000010110001

n=15

000111101011001

n=19

0000110110011110101

n=21

001001100001010000000

n=23

00001111101011001100101

n=31

00000000000001000010100000100110000000000000100010100100000011000000000000011000000100101000100000000000010000010001000010110000000000010000110100000010001000000000100000001000001010011000001000111010100101111001101100000100110001111001010110111010000011001011011110101000100111

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For the unlisted values of n among n=1.3 1, the cyclic differaice s URA does not exist.

2-D cyclic set URAAn exhaustive search for a complete list of2-D m by n element cyclic thffence set URA has yielded the following results:

3 by 5 (1 pattern) (half-occupied pattern)011110100100110

2 by 8 (6 patterns) (no half-occupied patterns)01010110 01100101 0011011000000011 00000011 00000101

10011100 00111010 0101110000000101 00001001 00001001

4by4 (6 patterns) (no half-occupied patterns)0110 1110 01110101 0001 01000011 0001 00100000 0001 0001

1011 1110 00100001 0100 00010100 0100 1101

0001 0001 0001

3 by 7 (1 pattern) (no half-occupied patterns)001011000000010000001

5 by 7 (1 pattern) (half-occupied pattern)01101000111111011010000010110001011

11 by 13 (1 pattern) (half-occupiedpattern)01111111111110101100001101001001111001001011000011010101100001101010110000110100100111100100010011110010001001111001001011000011010010011110010

For the unlisted values ofmbyn, the cyclic difference set URA patterns do not exist, wherem by n includes the following:

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m2,n2...12m3,n3...9m-4, n=4. . .8m5,n5...7m11, n13

Many patterns found above cannot be calculated from any existing equation, for example, the 3 by 7, all 2 by 8 and all 4 by 4patteins in the 2-D case.

The most often used decoding methods for URA include cross-coffelation, Fourier transform, deconvolution, maximumentropy, and itaaiive annealing.3'4 Fourier iransform and cross-correlalion methods are fast, but iteration methods maygenerate cleaner reconstructed images. In all decoding methods, the object plane being focused on is reconsiructed, and otherplanes are blurred.

The counting sensitivity (CS) is defined as the counting rate for signals. The improvement of CS for a coded aperture systemover a collimator system such as a pin-hole camera depends on the number of open apertures. For a 41 by 43 URA pattern,the CS improvement is (41*43+1)/2=882 for a point source. The signal-to-noise ratio (SNR) improvement for such a case is

jii = 2 1 , where statistical noise in the data is considered.

The sensitivity advantages which are realized in coded aperture imaging depend also on the background which is present. Asan example, consider case where the object, 5k consists ofa "bright spot" on a diffuse background ofmany other objects, S,encoded in the field of view in addition to the desired one. This is of course the practical case where there is other materialin the field of view which contributes to the detected signal. There may also be a non-icoded background B present due tosignals passing around the aperture or to other detector noise. The sensitivity improvement as compared to a pinhole orcollimator would be proportional to the number of open holes and thus the SNR would be proportional to the square root ofthis ratio, IL It is important to note that even under circumstances where the background is large compared to the signal, thecoded aperture system always has an improved SNR as compared to a collimated or pinhole imaging system. Jupp, et.al.(1997 IEEE Nuclear Science Symposium, in press) have derived a simple relationship for this:

rI I

SNRCIJ tPBJI (1)

SNRpJJJ ____[ tCAl (1_tc)j

where

Sk flux from point source of interest: sum of all other field ofview source componentsB = unmodulated detector backgroundtrill

= open aperture area fraction for pinhole imager= open aperture area fraction for coded aperture imager

R = 1Ltpffj

Figure 1, from Jupp, et.ai shows this for a particular mask design with approximately 425 open holes. The SNR gain isnormalized to R"2, i.e. 1 represents a SNR improvement of 4251/2 or 20.6. The background represeats the case where thereare background points spread over the field of view. Even with a diffuse aperture flux background of 100 limes the signal,the coded aperture still is better than the single pinhole with respect to SNR by a factor of more than two.

367

I

O.80.6

o 0.4

0.2

1 10 100

3. EXPERIMENTS

We have conducted coded aperture imaging experiments with a 1 1 by 13 and a 41 by 43 cyclic difference set IJRA patternand have compared results with collimator systems including pm-hole caina, and planar gamma imag. Experimeiits havebeen conducted using Siemens ORBITOR and E.CAM gammaISPECT camas. The above experiniaits are for Tc-99m (140keV gamma rays) radiopharmaceuticals used routinely in nuclear medicine, such as MDP for bone imaging. The objects(gamma-ray sources) we used include point source, 2-D source (sources in a plane with arbitrary disiribution), and 3-Dsource (sources in 3-D with arbilrary disiribulion) composed of phantoms and small animals, whae the phantoms usedinclude simple ones and standard phantoms used in nuclear medicine.

Our 11 by 13 URA pattern is composed of a mosaic version of the basic pattern. The photon shield is made of 5 mm x5 mmx 1.5 mm lead (square apertures), supported by a 1 mm aluminum backing plate. Our 41 by 43 URA pattern is composed ofa single basic pattern. The photon shield is made of 4 mm x 4 mm x 3.17 mm lead (square apertures), supported by a 1.25mm aluminum backing plate.

• -' '.••!1, -1' ...--

0.8.0.6 -

00.4 . 1,=O-ES,02

o %...,, I I

0.01 0.1 1 10 IC

Detector Background. B * + ES,)

00.01 0.1 1 10

Diffuse Aperture Flux. ES, * (k B)

1

08*

0.610

0.4

0.2

100

•1

— — — — —ES, = 1, B = 0ZS,=0,B=1ES, — B

00.01 Oi

Point Source Flux, 5k (ES + B)Figure 1. SNR for various background conditions compared to pin-hole.

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We experiniita11y demonstrated 3-D coded aperture imaging for nudear medicine by first using phantoms from one to threediinaisions, then using a thyroid phantom, and finally a mouse injected with Tc-99m.

Our experimental set-up geometry is similar to Figure 2, where the detector is a gamma camera, and the source is a 140 keVgamnia-ray emitter from one to three dimensions. We used a Siemens ORBITOR gamma camera for the mouse experimentdescribed, and a Siemens E.CAM camera for all the rest of the experiments.

1-D, 2-D, and 3-D phantoms (11 by 13 pattern)

We have used a point source as the 1-D phantom, two line sources in a same plane as the 2-D phantom, and one point sourcewith two line sources in three different planes as the 3-D phantom. Al! sources are Tc-99m, a 140 keV gamma-ray emitter.

(1) 1-Dsource

We put a point source 12 cm away from the coded aperture pattern, and the pattern was 12 cm away from the detector. Thisanangemait was used to obtain the system PSF experimentally.

(2) 2-D source

We have put a line source in a plane 12 cm away from the coded aperture pattern, and the pattern was 12 cm away fromthedetector. This arrangement was used to simulate a 2-D planar object, whose gamma-ray emitters were distributed arbitrarilyin two-dimensions.

(3) 3-Dsource

We have used three sources in three different planes to simulate a 3-D object: a point source 12 cm away from the codedaperture pattern ("pattern"), a line source 14 cm away from the pattern, and another line source 16 cm away from the pattern,and the pattern was 12 cm away from the detector. In this geometry, we took a picture (collected data); then we move thetriple sources 2 cm closer to the pattern, and took another picture; then move the sources 2 cm further closer to the patternand took another picture. We then reconstruct the images of the object plane 12 cm away from the pattern.

We have also tried to enhance the line source image in the middle by decreasing the contributions from the nearest andfarthest sources. We used this method to test the effectiveness of enhancing the focused image plane.

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Figure 2. Coded aperture imaging geometry.

Thyroid phantom (41 by 43 pattern

The thyroid phantom we have used is a standard phantom made by Picker Nuclear (Model 3602, volume 35cc). After beingfilled with Tc-99m, it was composed of a hot lobe with a dark spot in one side, and a dark lobe with a half-activity hotspoton the other lobe. The total activity was 0.2 mCi at the thne of experiment.

We have put the phantom 10.5 cm away from the pattern, and the pattern was 17 cm away from the gamma camera. We havecollected data for 30 minutes in this geometiy. Then we installed a high resolution (1.1 mm by 1.1 mm) 140 keV leadcollimator on the gamma camera and took a 10 minute data collection, with the phantom in contact with the collimator.

Mouse (1 1 by 13 pattern)

We have injected 0.2 mCi Tc-99m MDP agent (bone agent) into a mouse and left the agent circulating for three hours beforeimaging the immobilized mouse. At the time of experiment, the mouse had 0.1 mCi activity for 140 keV photons. We put themouse 10 cm away from the pattern, and the pattern was 10 cm away from the gamma camera. We first collected the data for10 minutes, then used a pin-hole plane to replace the pattern and collected data for 10 minutes, then installed a high-resolulion (1.1 mm by 1.1 mm) 140 keV lead collimator on the gamma camera and took a 10 minute data collection, with themouse in contact with the collimator.

In this paper, we have used a Fourier transform correlation algorithm for decoding, which can generate images in seconds.Iterative algorithms such as maximum entropy may give cleaner images, but the process is slow and the results may dependon the particular algorithm instead ofthe imaging system itself.

4. RESULTS

1-D, 2-D, and 3-Dphantoms (11 by 13 pattern)

The reconstructed images for coded aperture methods in this set of experiments are shown in Figure 3. The pixel size for allimagesis l.2nunx 1.2mm.

In the figure, (a) shows the reconstructed image for a point source. The data collected have 20 million counts, and thecollection time is 210 seconds. This image is the actual system PSF obtained experimentally, where Statistical noise in datawas naturally included. We can see the point image is very clean. This implies a clean delta-function-like system PSF. (b)shows the reconsiructed image for a line source. The data collected has 20 million counts. We can see the line source is veryclear. This demonstrates the performance for imaging two-dimensional planar sources. (c) -(f) show the results of iriplesources. The data collected for (c), (d), (e) has 30 million counts for each of them. In (c), the point source is focused indecoding; in (d), the upper line source is focused in decoding; and in (e), the lower line source is focused in decoding. Wecan see when the plane being focused was changed, the sources in that plane stood out. It should be noticed that the upperline source is longer than the lower line source, as shown in the reconstructed images. (f) shows the results of suppressingcontributions from (c) and (e) in order to enhance the object plane (d). By comparing (d) and (f), we can see that the upperline source did stand out more predominantly.

370

-n.:

'JU

' .bas

Figure 3. Coded aperture imaging: reconstructed images for (a) point source; (b) line source; (c) - (1) triple sources, where(c) point source being focused, (d) the upper line source being focused, (c) the lower line source being focused, (1) the upperIrne source in (d) being enhanced by suppressing the contributions from sources m two adjacent planes in data processing.

Thyroid phantom (41 by 43 pattern)

The reconstructed images for coded aperture methods and the mrngc from planar gamma imager are shown in Figure 4. Thepixel size for all images is 2.14 mm x 2.14 mm.

In Figure 4, the reconstructed image from coded aperture mhods is shown in (a), and the image from the planar gammairnagcr is shown in (b). In (a), the data collected has 198 million counts, and the collection time is 30 minutes. In (b), thedata collecied has 200 thousand counts, and the collection time is 10 minutes. In this experiment, the counting sensitivity fora coded aperture imager is 990 times as large as a collimator imager. This number is close to our calculated result 882.

Both images have given the major characteristics of the phantom: the lower lobe has higher activity with dark spots, and theupper lobe has a half-activity hot spot. By comparing these two images, we see the collimator image (b) has cleanerbackground. It should be noted that the collimator used has 1.1 mm by 1.1 mm high resolution, while the coded aperture sizeis 4 mm x 4 mm. Thus comparing the resolution is not really a !tir thing because the apertures were not designed to have aresolution of 1 to 2 mm.

t71

(e)

Figure 4. Images for a thyroid phantom filled with Tc-99m. (a) reconstructed image from coded aperture method, (b) imagefrom planar gamma imager.

Mouse (11 by 13 pattern)

The reconstructed images for coded aperture methods and the images from collimator systems are shown in Figure 5. Thepixel size for all images is 1.51 mm x 1.51 mm.

(a) shows the image from a pin-hole camera. The aperture is a 5 mm by 5 mm square pin-hole. The data coil ecte. Aas 1.04million counts, and the collection time is 10 minutes. (b) shows the image from a planar gamma imager with a highresolution 1.1 mm by 1.1 mm lead collimator. The data collected has 25 thousand counts, and the data collection time is i 0minutes. (c) shows the reconstructed image for coded aperture methods. The data collected has 5.6 million counts, and thedata collection time is 10 minutes.

In this set of experiments, the counting sensitivity for coded aperture method is more than 5 times as large as the same-sizepin-hole camera, and is 224 times as large as the planar collimator gamma imager. The mouse bone image in (a) is veryblurred and can not he discrmimated. The image in (c) is much clearer than (a), although details can not be shown very muchdue to the aperture size 5 mm by 5 mm, which determines the spatial resolution. The image in (b) has very low sensitivity.It has shown a fmcr resolution because of its fmer collimator size.

Figure 5. Images for a mouse injected with Tc-99m hone agent. (a) image from a pm-hole camera, (h) image from planargamma imager, (c) reconstructed image from coded aperture method.

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(a) (b)

5. DISCUSSIONS

Results from our experimts have shown significantly improved sensitivity for a coded aperture imaging system ovacollimator systems, especially for small sources, which are realistic in nuclear medicine imaging such as for tumors. Thesignal-to-noise ratio is 20 times higher for a coded apture imaging system with a 41 by 43 pal1n ov a pin-hole camera,and the counting sensitivity is 880 times higher for such a pattern.

In real diagnostic nuclear medicine imaging applications, an object with point-like sources is more realistic because tumorsin patients are usually point-like. For this case, coded aperture techniques are especially well suited as a high sensitivityimaging tecimique because its SNR improvement is best for small sources.

The results presented in this paper have shown that planar collimator gamma imager has higher resolution. However, wemust note that the comparison for resolution is not veiy fair, because we have used coded aperture with sizes of 4 or 5 mm ineach dimension, but the collimator we used is a commercial one with an aperture size of 1.1 nun in each dimension. Thisdifference can result in an inherent resolution difference of four folds.

In addition, planar collimator gamma imager can image only 2-D objects, but coded aperture mthod is a focusing technique,thus has some tomographic capability, which can be used for generating 3-D images.

6. ACKNOWLEDGMENT

This research was supported in part by the Federal Aviation Agency through grant number 93-G-053.

7. REFERENCES

1. II. H. Barrett and W. Swindell, Radiologicallmaging, Academic Press, New York, 1981.2. E. E. Femmore and T. M. Cannon, "Coded aperture imaging with uniformly redundant arrays," Applied Optics, 17 (3),

337-347, February, 1978.3. L. Zhang, Coded Aperture Imagingfor Fast Neutron Activation Analysis, SM thesis, Massachusetts Institute of

Technology, February, 1996.4. S. F. Gull, "Developments in maximum eniropy data analysis," in J. Skilhing, editor, Maximum Enfropy and Bayesian

Methods, Kiuwer Academic Publishers, London, 1988.

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