2008 IEEE Nuclear Science Symposium Conference Record M10-28

Comparison of 3D SPECT Imaging with a RotatingSlat Collimator and a Parallel Hole Collimator

Roe} Van Holen, Stefaan Vandenberghe, Steven Staelens and Ignace Lemahieu

(1)

Fig. 1. The geometry used for the calculation of the sensitivity.

Fig. 2. Sensitivity gain of a RS collimator with respect to a PH collimatorin a plane parallel to the slats.

so

40

60

1.

80

70

200

d(mm)

100"" .

with respect to a PH collimator is given in a 40 cm by 40 cmplane parallel to the slats. For both the RS and PH collimator,

a slat collimator is characterized by a different sensItivityfunction. Because the number of slits seen (slits seen "'-J d)

only partly compensates for the decreased photon flux (r-v -b)at larger distance, the sensitivity of a slat collimated systemdecreases proportional to the distance to the collimator d:

Wsg WgSRS = 41fhe(he + de) = 41fh(h + d) cos

3Q (2)

Furthermore, sensitivity drops with increasing incidence angledue to the smaller detector width 'seen' under an angle a(W" = W cos a), the larger effective collimator distance (de ~_d_) and the higher effective collimator height (he = _h_),;~~ttiting in a cos3 a weighting. A more detailed analy~i~Qofthe sensitivity and spatial resolution - which is equal for RSand PH - of a rotating slat collimator can be found in [1]and [2]. In figure 2, the sensitivity gain of a RS collimator

R. Van Holen, S. Vandenberghe, S. Staelens and I. Lemahieu are with ME­DISIP, Department of Electronics and Infonnation Systems, Ghent University,B-9000 Ghent, Belgium e-mail: (RoeI.VanHolen@UGent.be).

This work was supported in part by the Institute for the Promotion ofInnovation by Science and Technology, Flanders, IWT, Belgium.

Abstract-Besides parallel and converging hole collimatorswhich are frequently used in nuclear medicine, slat collimatorscan be used for Single Photon Emission Computed Tomography(SPECT). The higher photon collection efficiency, inherent tothe geometry of rotating slat collimators results in much lowernoise in the data. However, reconstruction of the plane integraldata measured by a slat collimator is much more sensitive tonoise accumulation compared to traditional SPECT reconstruc­tion from line integrals. It is not a straightforward questionwhether the initial gain in efficiency will compensate for thelarger noise accumulation during reconstruction. Therefore, acomparison of the performance of parallel hole and rotating slatcollimation is needed. This study compares SPECT with rotatingslat and parallel hole collimation in combination with MLEMreconstruction with accurate system modeling and correction forscatter and attenuation. A contrast-to-noise study revealed animprovement of a factor 3 to 4 for hot lesions and more than afactor of 4 for cold lesion. Rotating slat collimators are thus avaluable alternative for parallel hole collimators.

Index Terms-SPECT, rotating slat.

I. INTRODUCTION

H Uman SPECT imaging is most often performed usingParallel Hole (PH) collimators. The trade-off between

spatial resolution and sensitivity however limits the optimiza­tion of SPECT scanners equipped with PH collimators. At thecost of a decreased Field Of View (FOV), converging beamcollimators and pinholes offer an enhanced spatial resolutionfor equal sensitivity and vice versa and therefore are thecollimators of choice for organ imaging. Rotating Slat (RS)collimators (figure 1) have the potential for a better trade-offwithout decreasing the Field Of View (FOV) and can thereforebe used as an alternative for PH collimators.

For a parallel hole collimator, the sensitivity is spatiallyinvariant since the decreased photon flux for larger collimatordistance d (photon flux r-v eft) is compensated by the largernumber of holes seen (holes seen "'-J d2 ). Parallel hole sensi­tivity SPH is generally described by:

g2

41fh2

It can be appreciated that the sensitivity throughout the FOVis only defined by the height of the collimator h and the holesize g. A more detailed analysis of the sensitivity, taking intoaccount the finite septa thickness and hole shape, can be foundin [1]. Since parallel slats only collimate in one direction,

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Fig. 3. Transaxial slice through a reconstructed volume from (a) PH dataand (b) RS data with an equal number of counts in both datasets.

9 and h respectivily are 1.5 mm and 40 mm. The detectorwidth W equals 34.6 cm. By integrating the sensitivity gainprofile over the object boundaries for all rotation angles ofthe camera, one obtains the sensitivity gain for the object ofinterest. For a cylinder (H=20 cm and radius= 10 cm) centeredin the FOV and a detector rotation radius of 15 cm, oneobtains a sensitivity gain of 36. This gain factor agrees withthe findings of Webb [3] who reported a typical sensitivitygain of about a factor 30 to 40.At first sight. this better photon collection efficiency wouldlead to better noise characteristics. Unfortunately, plane in­tegral data measured by this device can not be interpreteddirectly and even for planar images, image reconstruction isneeded. For tomographic imaging, all image points in a planecontribute to one measurement in a certain detection bin. Thenoise in this bin is the added noise over the whole plane andis much higher compared to only the added noise for a lineintegral in PH collimation. During the backprojection opera­tion of image reconstruction, the higher noise is backprojectedto a lot more image points in the case of RS, which finallyresults in higher noise accumulation. Figure 3(a) illustratesthe effect of the higher noise accumulation by starting froman equal number of counts in the measured data for both aPH and a RS collimator. This mimics the hypothetical case ofno gain in geometric sensitivity for the RS collimator. It canbe cleary seen that the RS image is deteriorated a lot moreby noise compared to the PH image when both images areconverged to equal contrast. The noise accumulation induced

Parallel Hole

••

Mean contrast recovery =40%

(a)

Rotating Slat

Mean contrast recovery =40%

(b)

contrast-to-noise for the RS for both cold and hot lesions [7].However, in this study a solid state strip detector [8] wasused and the image quality improvement was not only due tocollimation with slats but was also subject to the combinedeffect of small detector width, better collimator resolutionand solid state detector. Moreover, in this comparison, nomodel for depth dependent detector blurring was used duringreconstruction.To investigate the impact on image quality of only the RScollimator in combination with iterative reconstruction, a faircomparison is needed. This study compares fully 3D SPECTwith RS and PH collimation in combination with MLEM re­construction with scatter compensation, attenuation correctionand accurate system modeling.

II. METHODS

A. Phantom simulation

The Monte Carlo simulated data used in this study aregenerated using GATE [9]. The image quality phantom (Stan­dard Jaszczak PhantomTAf ), shown in figure 4 is simulatedcontaining 4 hot spheres (diameters: 9.9 mm, 12.4 mm,15.4 mm, 19.8 mm) and two cold spheres (diameters: 24.8 mmand 31.3 mm). The activity concentration is set in order tohave a sphere-to-background activity ratio of 8: 1 in the hotspheres. The total activity in the phantom was 37.6 Mbq.The phantom is simulated to be filled with water with anattenuation coefficient Jl of 0.154 cm- 1 at 140 keY. Figure 4(a)shows the three headed rotating slat camera that was modeledwhile in figure 4(b) the three headed parallel hole systemis shown. Both the PH and the RS camera consist of anidentical detector modeled as 192 x 192 individual pixels of1.8 x 1.8 mm. 193 parallel slats of height 40mm and 0.3mmthickness model the RS collimator. This design is based onthe SOLSTICE design proposed by Gagnon [8] but uses acomplete detector instead of only a strip of detection material.The PH collimator is implemented as a square hole collimatorwith height 40 mm and 0.3 mm septal thickness. The hole pitchis 1.8 mm and matches the slat pitch of the RS collimator. Thecollimator resolution is thus matched for both collimators andis 5 mm at 10 cm collimator distance. The rotation radius

of the detector was 15 cm and the acquisition time was setto 8 minutes. 10 realizations of the same acquisition were

Fig. 4. The geometry of the simulated SPECT camera equipped with (a) aPH collimator and (b) an RS collimator. Next to the SPECT rotation, a RSacquisition also needs a spin rotation of each detector.

(b)(a)

by the reconstruction compromises the gain in geometricefficiency and thus leads to a lower effective efficiency afterreconstruction.Planar RS imaging with Filtered Back-Projection (FBP) re­construction has previously been studied by Lodge et al. [4].Their work shows an advantage in SNR over a PH collimatorfor small activity distributions and enhanced contrast for smallhot spots. A comparison by our group uses accurate systemmodeling in an iterative reconstruction and indicates improvedcontrast-to-noise ratios up to a factor 3, even in large objectsapproaching the size of the FOV of the camera [5].In the tomographic case, FBP reconstructed SPECT imageswith a RS collimator again confirmed improved noise charac­teristics for small objects (smaller than 10 cm) and showedimproved contrast only for small regions of high tracer up­take [6]. An iterative reconstruction approach found better

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oo0סס1

simulated. For all events recorded, a flag was enabled in casea Compton scatter interaction occurred in the water phantom.

Fig. 5. Tc-99m spectrum measured on a RS camera with indication of thescattered photons and the estimated scatter. Also the energy windows aredrawn.

(4)c(x,y,z~()) i 'L;=o exp(-(ML)¢i)'

with (ML) ¢i the mean attenuation length product for spinangle <Pi. The calculation of (ML)¢i was done by tracing100 paths connecting the voxel of interest with equidistantpoints, sampling the detector. In figure 6 (a) one of such pathsis displayed. The ray tracing, using Siddon's algorithm [15],

D. Attenuation correction

1) Implementation: Since the data are affected by attenua­tion, we need a method to compensate for the loss of photonsat larger depths. An attenuation correction method which fullymodels the attenuation along each possible ray of projectionas used by Zeng et al. [13] is used for the reconstruction of thePH data. However, for RS data, this method is only possible ina fully 3D reconstruction algorithm which directly maps imageto the plane integrals using one single system matrix . Sinceour fast reconstruction method splits the system matrix in twoseparate ones, the original paths of detection are lost and thismethod can not be applied. Therefore, we base ourselves onChang's attenuation correction method [14] which calculatesan average attenuation factor at each voxel. However, whereChang calculates the mean attenuation value over all SPECTangles for every voxel, our method will calculate an averageattenuation coefficient c over all spin angles ¢ for every voxel(x, y, z) and for every SPECT angle ():

A t

fk '"' '"' 9j~ B.~ A .. LJBkiLJAij At·L..Ji b L..Jj ~J i j Li A ij Lk Bkifk

The following iterative process is followed by this algorithm:

in a first step, an initial image estimate lk t is forwardprojected with system matrix B to a sinogram estimate. Next,this sinogram estimate is forward projected using A andcompared with the scatter corrected plane integral data gj'

The resulting plane integral update is projected backwardusing A and immediately projected backward with B to imagespace where it serves as an update image. After updating andnormalizing the original image estimate, the next iterationcan start.In the first part of the system matrix (B), which transformsimage space to sinogram space, we model the depth dependentsensitivity as the mean sensitivity in a plane parallel to thedetector. Furthermore, depth dependent resolution is alsomodeled in B. System matrix A involves a mapping fromsinogram to plane integral space. At this point, we do notinclude any sensitivity modeling nor resolution modeling.

split-matrix method for accelerated image reconstruction [11],[12]. This method does not model the process to go from planeintegrals to image in one single step, but splits the process intwo separate steps, the first is a model A to go from planeintegral data to sinograms and the second models the step togo from sinograms to image (B). The resulting system matrixAB is used in an MLEM algorithm:

A t+lfk =

150145130 135 140

Energy [keV]125

-PRIMARY -SCATIER ··"DEW k=O.S" -TOTAL

C. Image reconstruction

For the purpose of reconstruction of the plane integral datacollected by the RS collimator, we used a previously proposed

true scatter is plotted and it can be seen from the energyspectrum of the scatters that there is indeed a good agreementbetween the estimate and the true scattered photons, whichwere flagged during simulation. For validation, the numberof counts, estimated with the DEW technique and the truenumber of scattered detections were compared for the tenrealizations of the data using the mean absolute error (MAE).The MAE between estimated and true number of scatters overthe different realizations was 0.6%. For comparison, also theMAE for the PH data was calculated resulting in a value of1.4%. This indicates the DEW scatter correction method isvalid for data collected with a RS collimator, although noattempt is made to make a spatial validation at the level ofthe projections.

gsc = gPvIW - k (9SW Wl\,fW) , (3)Wsw

with gSC, gNIW and gsw respectively the scatter correcteddata, the data measured in the main energy window and thedata measured in the scatter window. The width of our mainenergy window WAIW was chosen 14 keV around 140keVand WSW, the width of the scatter window was chosen10 keV and located around 125 keV. Both energy windowsare shown in figure 5 where also the estimate of the scatterwith the above formula is given for k = 0.5. Next, also the

B. Scatter correction

In the GATE simulations, a realistic phantom was modeledand consequently the datasets are contaminated by scatter.In order to correct for scatter in the data, the Dual EnergyWindow (DEW) scatter estimation technique [10] was used tocorrect the data acquired with a rotating slat collimator. Thescatter corrected data is calculated using the DEW techniqueas follows:

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returned the intersection lengths of these rays with the atten­uation image voxels. Sensitivity weighting of the intersectionlengths with cos3 ex yielded a map of weighted intersectionlengths for a certain voxel (figure 6 (b)). Finally, multiplicationwith the J.-l value of the intersected voxel and averaging overall possible paths resulted in (ML) cPi •

Since our system matrix B rotates (Gaussian rotator) the im-(a)

DIStance along X

l/atlenuationcoefficienl

DislancealongY

(b)

~~~:tion~i One possible path of

Current voxelr;;, i detection

Fig. 7. Comparison of simulation based attenuation values and calculatedvalues of c. (a) shows the values along x for y = 0 and (b) shows the valuesalong y for x = o.

Fig. 6. (a) One of the possible paths along attenuation has to be calculated. (b)The sensitivity weighted intersection lengths for all possible paths of detectionfor one voxel at one spin angle.

(a)

VI

(b)

WITHOUT AC WITH AC

t; should thus be equal to the reciprocal of the attenuationvalues c. The calculations of c were based on an attenuationmap derived from the cylindrical phantom. In figure 7 theresults of the simulation and calculation are summarized as aline profile through the reciprocal of the calculated attenuationvalues c for respectively y = 0 and x = 0 in figures 7(a) and (b) and as the ratio of respectively Ix and Ix,oand Iy and Iy,o in figures 7 (a) and (b). These profilesshow very good agreement and suggest the proposed analyticcalculation method for the attenuation values is suitable forattenuation compensation during our iterative reconstruction.Transaxial slices through reconstructed images of a uniformcylindrical source are shown in figure 8 (a) and (b) in thecase of respectively no attenuation correction and attenuationcorrection with the calculated correction factors c.

(b)(a)

CRC hot lesion (%)

o 20 40 60 80 100 120 140 160 180 200

Noise (%)

Fig. 9. Contrast-to-noise plot for both collimators for the 19.8 mm hot lesion.

Fig. 8. Transaxial slices through reconstruction of uniform cylindrical source.In (a), no attenuation correction was used during reconstruction while in (b)attenuation correction based on attenuation factors c was used.

III. RESULTS

A. Contrast-fo-noise

Figure 9 shows the contrast-to-noise plot for the 19.8 romhot spot. The hot spot shows a better contrast recovery forRS compared to the PH collimator. To have an idea aboutthe quantitative improvement, the imaging time was increasedfor the PH collimator. The results for a 2, 3 and 4 timeslonger PH acquisition are also plotted in figure 9. From theseplots, it can be seen that, to obtain the same contrast-to­noise, the PH collimator needs about a 3 to 4 times longermeasurement compared RS collimator. The results for the31.3 mm cold spot are shown in figure 10. This plot showsthat the RS collimator needs less than 4 times the imaging

(5)I =

age according to the appropriate SPECT angle before applyingsensitivity and resolution modeling, we can use the factors cto compensate the rotated image for attenuation. In this way, asemi-average attenuation compensation is performed in systemmatrix B, being calculated with every SPECT angles as anaverage over all spin angles.

2) Validation: GATE was used to validate the correctnessof the attenuation values c of our analytic calculation method.Four high count simulations (noise<0.8%) were performed,resulting in four datasets Ix, Ix,o, Iy and Iy,o, For thegeneration of Ix and Iy, line sources aligned with respectivelythe X and Y axis of the scanner (Fig. 1) were simulated witha cylindrical water phantom present. The camera was spunover 360 degrees. Binning the recorded data according to thesource position resulted in the datasets Ix and Iy. Ix,o andIy,o were generated in a similar way with the only differenceof the absence of the water cylinder. Since the detector wasrotated over all spin angles there exists the following relationbetween datasets 1 and 10 :

1 <I>

Io~ L exp( -(J\1L),pJ,i=O

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20 40 60 80 100 120 140 160 180 200

Noise (%)

Rotating slat

transverse original

•

sagittal

••

coronal

CRC cold lesion (%)100

90

80 '

70

60

SO '

40

30

20

10

o...,..e:::.-~----~-----~------'

o

Fig. 10. Contrast-to-noise plot for both collimators for the 31.3 mm coldlesion.

Fig. 12. Reconstructed images from the RS collimator at 380 herlons.

time of a PH collimator in order to obtain similar contrast­to-noise characteristics. Compared at an equal noise level of50%, contrast recovery is 28% higher for the hot lesion whileit is 30% higher for the cold lesion. For the RS collimator 40iterations are needed to obtain 50% noise while the PH onlyneeds 10 iterations to achieve this noise level.

B. Tomographic images

A transverse, coronal and sagittal slice through the imagesat equal noise (40%) is shown in figure 11 and in figure 12for respectively the PH and the RS collimator. It can be seenfrom the images already that the RS collimator improves thecontrast. The profile drawn through the lesions in figure 13confirms the better contrast recovery with the RS collimator.

Parallel Hole

Arbitrary Counts0.018

0.016

0.014

0.012

0.01

0.008

0.006

0.004

0.002

o

o

transverse original o 100 200 300 400 500

Position

•• Fig. 13. Circular profiles through the lesions are drawn, normalized to thetotal number of counts under the profile. Noise is 40%.

IV. DISCUSSION AND CONCLUSION

coronal

Fig. 11. Reconstructed images from the PH collimator at 10 iterations. Noiseis 40%.

Scatter correction was used and found at least equally ac­curate compared to DEW scatter correction for PH collimatedacquisitions. Furthermore, an analytic method for calculatingattenuation factors for every voxel at every SPECT anglewas proposed and validated. This enabled us to correct forattenuation in a previously proposed reconstruction methodfor plane integral data. With these tools available, a realisticMonte Carlo simulation of an image quality phantom could bereconstructed. The results show that SPECT images obtainedwith a rotating slat collimator in combination with iterativereconstruction and accurate modeling provide a much bettercontrast-to-noise trade-off compared to images obtained withan equivalent PH collimator. This study not only shows betterhot spot contrast recovery, which was also found by Lodge,but also proves better cold spot contrast recovery. This result

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already had been obtained by Wang with a slat collimatedsolid-state strip detector, but in that study, no depth dependentresolution was modeled. Also, it was unclear whether theimproved contrast-to-noise was due to the better solid statedetector or due to the slat collimator. Recently, it was shownby Defrise in a technical note [16] that the optimal collimatorresolution for a RS collimator has to be better by a factorV2 relative to the optimal PH collimator resolution. Thesefindings could be in favor of the RS collimator and should beinvestigated in more detail in the future.The better cold spot contrast recovery confirms that in thetomographic case, a PH collimator also suffers from noise ac­cumulation during reconstruction. This concludes that rotatingslat collimators can be a valuable alternative for parallel holecollimators, with shortening of the imaging time by a factorof 3 to 4.

REFERENCES

[1] H. Wieczorek en A. Goedicke, "Analytical model for SPECT detectorconcepts," IEEE Transactions on Nuclear Science, vol. 53, no. 3, pp.1102-1112, June 2006.

[2] S. Vandenberghe, R. Van Holen. S. Staelens, en I. Lemahieu, "Systemcharacteristics of SPECT with a slat collimated strip detector," Physicsin Medicine and Biology, vol. 51, no. 2, pp. 391-405, Jan 2006.

[3] S. Webb, D. Binnie, M. Flower, en R. Ott, "Monte Carlo modeling ofthe performace of a rotating slit collimator for improved planar gammacamera imaging," Physics in Medicine and Biology, vol. 37, pp. 1095­1108, 1992.

[4] M. A. Lodge, D. M. Binnie, M. A. Flower, en S. Webb, "Theexperimental evaluation of a prototype rotating slat collimator for planargamma camera imaging," Physics in Medicine and Biology. vol. 40, no.3, pp. 427-448, Mar 1995.

[5] R. Van Holen, S. Vandenberghe, S. Staelens, en I. Lemahieu, "Compar­ing planar image quality of rotating slat and parallel hole collimation:influence of system modeling," Physics in Medicine and Biology, vol.53. no. 7, pp. 1989-2002, Apr 2008.

[6] M.A. Lodge, S. Webb, M.A. Flower, en D.M. Binnie, "A prototype rotat­ing slat collimator for single photon emission computed tomography,"IEEE Transactions on Medical Imaging, vol. 15, no. 4, pp. 500-511,1996.

[7] W. Wang, W. Hawkins, en D. Gagnon, "3D RBI-EM reconstruction withspherically-symmetric basis function for SPECT rotating slat collima­tor," Physics in Medicine and Biology, vol. 49, no. II, pp. 2273-2292,2004.

[81 D. Gagnon, G. Zeng, M. Links, J. Griesmer, en C. Valentino, "Designconsiderations for a new solid state gammacamera: SOLSTICE." inNuclear Science Symposium Conference Record, 2001, vol. 2, pp. 1156­1160.

[9] S. Jan en et aI., "GATE - a simulation toolkit for PET and SPECT,"Physics in Medicine and Biology, vol. 49, no. 19, pp. 1-19, 2004.

[10] K. F. Koral, F. M. Swailem, S. Buchbinder, N. H. Clinthome, W. L.Rogers, en B. M. Tsui, "Spect dual-energy-window compton correction:scatter multiplier required for quantification,," Journal of NuclearMedicine, vol. 31, no. 1, pp. 90-98, Jan 1990.

[11] R. Van Holen, S. Vandenberghe, S. Staelens, en I. Lemahieu, "Fast3D image reconstruction for rotating slat collimated gamma cameras.,"Proceedings 9th International Meeting on Fully Three-DimensionalImage Reconstruction in Radiology and Nuclear Medicine, pp. 390-392,2007.

[12] G. L. Zeng en D. Gagnon, "Image reconstruction algorithm for aSPECTsystem with a convergent rotating slat collimator," IEEE Transactionson Nuclear Science, vol. 51, no. I, pp. 142-148,2004.

[13] G.L. Zeng, G.T. Gullberg, B.M.W. Tsui, en lA. Terry, "Three­dimensional iterative reconstruction algorithms with attenuation andgeometric point response correction," IEEE Transactions 011 NuclearScience, vol. 38, no. 2, pp. 693-702, 1991.

[14] L. Chang, "A method for attenuation correction in radionuclide com­puted tomography," IEEE Transactions on Nuclear Science, vol. 25, no.1, pp. 638-643, 1978.

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[15] R. L. Siddon, "Fast calculation of the exact radiological path for a three­dimensional CT array.," Medical Physics, vol. 12, no. 2, pp. 252-255,1985.

[16] M. Defrise, "Optimal collimator aperture for a fixed target resolution:gaussian modeL," Personal communication.

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