Three-Dimensional SPECT Simulations of a Complex Three ...

Three-Dimensional SPECT Simulations of a Complex Three-Dimensional Mathematical Brain Model and Measurements of the Three Dimensional Physical Brain Phantom Hee-Joung

Kim, Barry R. Zeeberg, Frederic H. Fahey, Alden N. Bice, Edward J. Hoffman,

and Richard C. Reba

Department ofRadiology, George Washington University, Washington, DC.; Georgetown University, Washington, DC.; University of Washington, Seattle, Washington; and UCLA Medical School, Los Angeles, California

We havedevelopeda three-dimensionalcomputersimulation

2). These apparent deficits may be due to altered radio activity localization or to imaging/reconstruction artifacts.

ofSPECTimaging. Wehaveappliedthesimulation procedure The quantitative potential of SPECT or PET for esti to the realistic mathematical Hoffmanthree-dimensional brain mating the regional concentration of neuroreceptors or model to generate the projection data (in the absence of blood flow can be degraded by inaccuracies in kinetic attenuation, scatter, or noise) of both a parallel-hole and a multidetector SPECT system with point-focusing collimators. The simulatedprojectiondata were then reconstructedusing standard software. The projection data resulting from the distribution of grey matter alone, or grey and white matter,

were simulated. The results of these simulations indicate the

modeling ofradiotracerlocalization. as well as inaccuracies in image reconstruction. In particular, a shape- and size

dependent recovery coefficient (3) could cause two regions with identical radioactivity concentration artifactually to appear

to have significantly

different

radioactivity

concen

trations. For example, this phenomenon would be trouble some in the case of the muscarinic cholinergic receptor, reconstructed human brain images. For example, the recon structed values for grey matter along a cortical circumferential which is distributed uniformly throughout the grey matter profilein a transverseslicethroughthe basalgangliavaried of the cerebral cortex (4). In this case, there may be an by a factor of 2.40 (parallel-hole)and 2.99 (point-focusing), apparent regional difference of radioligand localization although the original grey matter values were identical in all caused by differing regional thicknesses of cortical grey cortical regions in the model. We have compared the simu matter. lated reconstructed images with those obtained by imaging We have previously reported the results of computer

existence of significant qualitative and quantitative artifacts in

the physicalthree-dimensionalHoffmanbrainphantom,which was constructedbaseduponthe sameset of data fromwhich the mathematicalthree-dimensionalHoffmanbrainmodelwas derived. Althoughthe simulationdid not include all of the

simulation studies using a multi-detector point-focusing SPECT instrument and the grey matter distribution within

images were in good agreement, indicating the applicability

a brain slice cylinder (5,6). We now extend those studies by: (a) including simulations using an ultra high-resolution parallel-hole SPECT instrument; (b) using the mathemat

of thesimulation to a realisticsituationandtheimportance of

ical three-dimensional

the detectorresolutioneffect.

ulating grey and white matter in addition to grey matter alone; and (d) imaging the physical three-dimensional Hoffman brain phantom that was constructed based upon the same set of data from which the mathematical three dimensional Hoffman brain model was derived (7).

degradingfactors presentin the physicalimaging,the two

J NucI Med 1991; 32:1923—1930

sing the muscarinic acetyicholinergic receptor (mAChR) binding radioligand (R,R)-['231]4IQNB and a multidetector point-focusing SPECT instrument, we have found apparent deficits in the posterior parietal cortex in normal volunteers and in Alzheimer's disease patients (1,

Hoffman brain model ( 7); (c) sim

MATERIALS AND METHODS Imaging Physical Phantom A physical Hoffman three-dimensional brain phantom with a grey-to-white matter ratio of5: 1 (7) was filled with approximately 15 mCi (555 MBq) of 99mTc in 1400 ml of water,

avoid introducing

air bubbles. The phantom

taking

care to

was scanned 4 hr

after filling using the Trionix Triad three-headed camera with a ReceivedJan. 2, 1991; revision accepted Apr. 2, 1991. For reprints contact: Barry Zeeberg, PhD, Department of Radiology, Radio pharmaceuticalChemistry, Room 662 Ross Hall, 2300 I St. NW, Washington

after filling using the Strichman 8 10 with a set of 572 hole point

DC 20037.

focusing collimators. A description of the physics of point-focus

Three-DimensionalSimulations of SPECT Imaging • Kim et al

set of ultra high-resolution

parallel-hole

collimators,

and 7 hr

1923

@

ing instrumentation

has been given previously (5,6,8). The ac

quisition parameters for parallel-hole collimators are I3.6 cm rotational radius, 15% energy window, 120 angular views, ap proximately 0.23 x 106counts/slice, 64 x 64 array with 3.56 mm pixer' for the projection data. Those for point-focusing colli

@

mators are 20% energy window, 2.5 x 106 counts/slice, 12 lines, and 6 mm slice spacing.

20 slices,

Gaussian A = 8.57 counts, and = 10.24 mm; and for the third Gaussian A = 1.75 counts, and i = 49.86 mm. The sigmas for both the response from the line source and from the point source would theoretically be the same; however A for the response for

the point source must be computed from the formula: APSF= A@F/(qrt(2@r)@F)(see Appendix).

These formulas for A and

For the parallel-holecollimators,the measuredprojectiondata were reconstructedby filteredbackprojectionin the spatial do

are derived from measurements

main using a Hamming filter with cutoff frequency 0.43 pixer'

of a I-mm line source and can be used in simulations in which the object resolution is 1 mm (see Results, section 1). For simu lations in which the object resolution is 3 mm, the appropriate

and correctedfor attenuation with Chang's first-ordercorrection method (9) by usingthe circularboundary of the physicalHoff man three-dimensionalphantom. For point-focusingcollimators, the measuredprojectiondata were reconstructedwith the man

data resulting from simulations ofa 3-mm cube: a mathematical model ofa 3-mm cube was prepared by packing together twenty seven 1-mm voxels. The projection data were simulated at a series

formulas for A and a were derived by analysis of the projection

ufacturer's reconstruction software (version 2.5 1) using the rela tively high-resolution filter which we previously determined to be

of distancesbetweenthe cube and the detector, as done for the

optimal for human imaging systems(6). These filters are pro

view was simulated. The projection data at the different distances were analyzed in a manner identical to that described above for the 1-mm diameter line source, except that APSFwas determined directly rather than using the formula: APSF= A,@F/(sqrt(2i)@F).

prietary, and no information is available about their design. Attenuation correction was applied using the manufacturer's software with an “absorptionlength―equal to 60 pixels (10).

brain simulation shown in Figure 2, except only one fixed angular

In order to facilitatecomparison with the formulasgiven above Detector Response Characteristics @ @

@

For point-focusingcollimators, the three-dimensionalpoint spread function (3DPSF) was experimentally measured as previ ously described (6). The 3DPSF represented the projection data, not the reconstructed image, and was normalized so that the integrated volume was equal to unity.

for the 1-mm line source, however, we present the formula for A@ using the inverse relationship A@ = Ap@{sqrt(2@r)a@): A 51071 counts —111.23 counts/mm D; forO mm d < 39 mm, =

1.5596

105D),

mm

and

+

0.01261

for 39 mm

1 D

+

d(—l.0987

d < 250

mm,

x

iO@

=

+

4.1941

1.5156

mm

X

+

0.014289 D.

For parallel-holecollimators,the 3DPSF was experimentally measured using a line source: polyethylene tubing (1 mm i.d., 28

Imaging Simulation Studies

cm length) was filled with a 99mTcsolution (15 mCi (555 MBq) in 0.2 ml) and the ends ofthe tubing thermally sealed. The tubing

brain model is 1 mm x I mm with 6-mm interslice spacing. We

wassecuredon top of a flat surfaceas a straightline source.The camera face was positioned at several distances from the source,

were able to represent the model using cubic voxels of 1 x 1 x 1 mm, so that a slice in the original model would be 6 voxels in

zero to eight plexiglassheets(1.3 x 23 x 23 cm) werepositioned

thickness.

between the line source and the detector, and the source was

of 1 voxel thickness. In order to represent the three-dimensional brain model at a voxel resolution of 3 mm x 3 mm x 3 mm, we sampled every third voxel within the transaxial slice, and then duplicated and extended each transaxial slice to an axial length

imaged for 2 mm. The line source was imaged using the Triad SPECT

system.

The

acquisition

parameters

were:

15% energy

window, 128 x 128 array with 1.11 mm pixer' for the projection data. The acquired data were decay- and attenuation-corrected.

The averaged profile perpendicular to the line source was analyzed as the sum of three Gaussians using an iterative nonlin ear least squares curve fitting program. Relative, rather than

absolute,residualerrors were used in the curve fittingprocedure in order to fit adequately the low amplitude tails. The parameters

to be fit were the amplitude (A), sigma (r), and center of each Gaussian.The first Gaussian representedthe geometricdetector response, and the second and third Gaussians represent the components due to scatter within the plexiglas, septal penetration, and scatter within the crystal. A and a for all three Gaussians could be modeled as functions of the distance between the line source and the detector face and the depth of the plexiglas scattering medium. Only the first Gaussian, which represented

@ @ @

The in-sliceresolutionofthe digitizedmathematicalHoffman

For all the isolated

slice simulations,

we utilized

a slice

of 2 voxels.

The simulated projection data are built up as the successive summation of projection data for each nonzero voxel: for each

nonzero voxel,the measured 3DPSF is multiplied by the voxel value, translated accordingto the voxel position, and summed into an array containing the accumulated simulated projection data. Symbolically, a nonzero voxel at position (ij,k) contributes OBJ(ij,k)3DPSF(i'-ij'-j,k'-k) to PROJ(i'j',k'), where PROJ is the simulated projection data and OBJ is the mathematical radioactive object. This computation is object-driven. For paral Id-hole simulations, we used a modification in which an analy tical expression for the 3DPSF was used in place of tabulated

measurednumerical data. For simulationswhich included both

grey and white mauer, two separate simulations were performed, the geometricdetector response,is used in the simulations pre and the projection data added together in a ratio of5: 1to simulate sented here, and A and a for this component could be modeled the 5: 1 ratio in the physical phantom. (7). as a function ofthe distance(D) betweenthe line sourceand the For point-focusing collimators, the simulated projection data detector face and the depth (d) of the line source within the were converted to the format required by the manufacturer's scattering medium (A = 2,094 counts —4.957 counts/mm D; for reconstruction software. The simulated projection data were re 0 mm d < 39 mm, a 1.407mm + 0.01298D + d (—9.667 constructed. The same filter used for the physical phantom was x l0@ + 4.312 x l05D), and for 39 mm d < 250 mm, a = applied in the simulations. The reconstruction algorithm auto I .369 mm + 0.0 1466 D), for D 250 mm, where D and d are matically performs a background subtraction based upon the given in mm. For comparison, at D = 130 mm, for the second radioactivity detected in certain positions of the projection data.

1924

The Journal of Nuclear Medicine • Vol.32 • No. 10 • October1991

For parallel-hole collimators, we applied the same filter used for the physical phantom.

@

Since the simulation

studies did not

TABLE1 R•glon of Interest Analysis for th• Simulated and Physically MeasUred

include the effect ofattenuation, we did not apply an attenuation

HoffmanThree-Dimensional Brain Phantom

correction to any of the simulated projection data.

I

2

5

4

5

S

7

Ph

Data Analysis Regions of interest (ROls) were drawn using the theoretical maps ofgrey matter (Fig. lB), white matter (Fig. lC) or ventricles (not shown). Circumferential cortical profiles were determined as described previously (5,6,11), using the circumferential path drawn on the theoretical map ofgrey matter (Fig. 1D). A circum ferential profile was obtained by tabulating the counts in pixels along a circumferential path chosen manually so as to lie entirely within cortical grey matter pixels, approximately parallel to the

exterior outline of the cortex. Approximately30 control points are interactively selected, and these are automatically connected by straight line segments. Approximately 85 pixels along the straight line segments are sampled programmatically and the

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were scaled by the same scale factor used for column 1. The same procedure was repeated for columns 8—10. 2. Data in individual columns 5 and 6 were normalized that the maximum value was equal to 100.

so

3. Data in columns 7 and I 1 were normalized so that the mean values for the grey matter regions were equal to the mean values for the grey matter regions in columns 4 and 10, respectively, for the purpose of comparison with the simulated data in those columns.

RESULTS Resolution of Brain Model Representation and of Sampling Visual comparison of the brain model grey matter (Fig.

FIGURE 1. Digitizedtransverseslicesthroughthe basalgan

gliachosen fromthethree-dimensional Hoffman brainmodel(7),

lA), with a simulated isolated slice parallel-hole recon struction of this same grey matter with 1-mm resolution for the projection data and 64 angular views, in the absence of attenuation, scatter, or noise (Fig. 2), indicates the high degree of performance

of this system. In order to decrease

indicating ROls or circumferential path. Grey matter with I -mm

the computational requirements for subsequent three-di

voxels (A), grey matter with 3-mm voxels with ROIs used in analysissuperimposedas greyish regions(B), white matter with 3-mmvoxelswith ROlsusedin analysissuperimposedas greyish regions (C), and grey matter with 3-mm voxels with black dots indicatingthe location of the circumferentialpath (D). For ROls, two grey levelsare used in order to facilitatevisuallydistinguish ing adjacentregionsof interest.

at 3 x 3 x 3 mm resolution (Fig. 1B),with 3-mm resolution for the projection data and 64 angular views. Visual com parison of the reconstruction of the grey matter with 3mm resolution for the projection data and 64 angular

Three-DimensionalSimulations of SPECT Imaging • Kim et al

mensional

simulations,

the brain model was represented

views (Fig. 3) with that obtained at the higher resolution

1925

$‘@V U) I-

FIGURE2. Simulatedrecon structed image of grey matter

@

in an isolated 1-mm thick basal

ganglia slice imaged with par allel-holecollimators. One-mil limeterresolutionwas usedfor the objectand projectiondata samplingand 64 angularviews

z

0 C 0

? @‘ Lu N

-I

0

z

wereutilized. 20

(Fig. 2) indicates a slight blurring effect. Quantitative comparison

using ROIs (Table 1; columns

CIRCUMFERENTIAL PROFILE

FIGURE4. Circumferential profilesfor parallel-hole recon structed imagesin Figures2 and 3.

distribution. On the other hand, the absolute values were significantly different (Table 1; columns

There is some spillover of reconstructed counts into the white matter and ventricular structures, for both the high est resolution (Table 1; column 5) or the lower resolution (Table 1;column 1) simulations. The circumferential pro files for the simulated image (Fig. 4) show that an apparent approximately two-fold variation in cortical radioactivity concentration can arise from regions that are theoretically of identical radioactivity concentration.

Simulation of Grey and White Matter in a Basal Ganglia Slice Within a Three-Dimensional Brain Using Parallel-Hole Collimators: Imaging of the Three Dimensional Hoffman Physical Brain Phantom structed brain slice (Fig. 7B) is approximately 2.5: 1 (Table 1; column 4) in comparison with the theoretical ratio of 5:1. For the physically imaged brain phantom (Fig. 8), the

grey-to-white matter ratio is approximately 2: 1 (Table 1; column 7), in comparison with the theoretical ratio of 5:1. Comparison of the shapes of the circumferential profiles (Fig. 9) and the tabulated ROI data (Table 1; columns 4, 7) for the simulated

and physically

imaged phantoms

indicates the correspondence between the two images.

Simulation of Grey Matter in a Basal Ganglia Slice Within a Three-Dimensional Brain Using Parallel-Hole Collimators

Simulation of Grey Matter in an Isolated Basal Ganglia Slice Using Point-Focusing Collimators

Circumferential profiles (Fig. 6) for an isolated brain slice (Fig. 3) and a brain slice within a three-dimensional brain (Fig. 7A) indicate that the out-of-slice contribution

has little effect on the shape of the cortical radioactivity

For the reconstructed image of the grey matter distri bution in an isolated slice using point-focusing

collimators

(Fig. 10), there is some spillover of counts into the white matter and ventricular structures (Table 1; column 8). The

FIGURE3. Simulatedrecon structed image of grey matter

FIGURE5. Simulatedrecon structed image of grey matter in an isolated3-mmthick basal

inanisolated3-mmthickbasal imaged

1, 3), indicating

a quantitatively large out-of-slice contribution. This large contribution is not surprising, since a thin (3 mm) slice was simulated.

The grey-to-white matter ratio in the simulated recon

Slice Using Parallel-Hole Collimators

slice

60

1, 5) indicates

good agreement for grey matter structures and slight de viations for some white matter and ventricular structures. The good agreement for the grey matter structures is also indicated in the circumferential profiles (Fig. 4). The mod est deviations are due to both the resolution of the object representation (Table 1, columns 5, 6) and to the resolu tion of the projection sampling (Table 1; columns 1, 6). There is a negligible effect of increased angular sampling (Figs. 3, 5; Table 1; columns 1, 2). For all parallel-hole simulations described below, we used 3 x 3 x 3 mm brain model resolution with 3-mm resolution for the projection data and 64 angular views. Simulationof Grey Matter in an Isolated Basal Ganglia

ganglia

40

SAMPUNG POINT ALONG

with

parallel-hole collimators.

ganglia slice imaged with par aIIeI-hOIe collimators. Three

Three-millimeterresolutionwas usedfor the object and projec

for the object and projection

millimeterresolutionwasused

boil data samplingand 64 an gular views were utilized.

1926

@—

data samplingand 120 angular views were utilized.

The Journalof NuclearMedicine• Vol. 32 • No. 10 • October1991

@

1@

@$

P. U) I-

z

0 C 0 Lu N

FIGURE8. Physically meas

-I .(

ured reconstructedimageof a basal ganglia slice within the physicalbrainphantomimaged withparallel-hole collimators.

0

z

20

40

60

SAMPLING POINT ALONG

CIRCUMFERENTIAL PROFILE

0.06 and 0. 12 for parallel-hole

FIGURE6. Circumferential profilesfor parallel-hole recon structedimagesin Figures3 and7A. circumferential profile (Fig. 11) for the simulated image shows that an apparent approximately three-fold variation in cortical radioactivity concentration can arise from re gions that are theoretically of identical radioactivity con centration. Simulation of Grey Matter in a Basal Ganglia Slice Within a Three-Dimensional Brain Using Point

FocusingCollimators Comparison of circumferential profiles (Fig. 11) for an isolated brain slice (Fig. 10) and a brain slice within a three-dimensional brain (Fig. l2A) indicate that the out of-slice contribution

has little effect on the shape of the

cortical radioactivity distribution, but this effect is some what larger than that for parallel-hole simulations (Fig. 6). This effect with parallel-hole and point-focusing collima tors can be compared quantitatively by computing the

RMSerrorsbetweenthe isolatedsliceandthe slicewithin the three-dimensional model. RMS errors, computed using profiles that all have an identical number of sampling points and whose means are all normalized to unity, are

A

and point-focusing

colli

mators, respectively. The absolute values were significantly different for point-focusing collimators (Table 1; columns 8, 9), mdi cating a quantitatively large out-of-slice contribution. This out-of-slice contribution (approximately six-fold) is larger

than that for parallel-hole collimators (Table 1; columns 1, 3; approximately

three-fold).

Simulation of Grey and White Matter in a Basal Ganglia Slice Within a Three-Dimensional Brain Using Point-Focusing Collimators: Imaging of the Three Dimensional Hoffman Physical Brain Phantom

The grey-to-white matter ratio in the simulated recon structed brain slice (Fig. l2B) is approximately 2.5: 1(Table 1; column 10) in comparison with the theoretical ratio of 5: 1. For the physically imaged brain phantom (Fig. 13),

the grey-to-white matter ratio is approximately 2.5:1 (Table 1; column 11) in comparison with the theoretical ratio of 5:1. The circumferential profiles (Fig. 14) and the tabulated ROl data (Table 1; columns 10, 11) for the simulated and physically imaged phantoms permits a quantitative comparison between the two images.

B U) 0

C

t

0 Lu N @1

ft 0

z

0

20

40

60

80

FIGURE 7. Simulatedreconstructed imageof greymatter(A) and grey and white matter in a 5:1 ratio (B) in a basal ganglia slice within a full three-dimensionalbrain model imaged with parallel-holecollimators.Three-millimeterresolutionwas usedfor the object and projection data sampling and 64 angular views wereutilized.

FIGURE 9. Circumferentialprofilesfor parallel-holerecon structed imagesin Figures7B and 8.

Three-Dimensional Simulationsof SPECTImaging• Kimet al

1927

SAMPLING POINT ALONG

CIRCUMFERENTIAL PROFILE

@

1

I

FIGURE 10. Simulated re constructedimageofgrey mat ter in an isolatedbasalganglia slice imaged with point-focus ing collimators. @

‘1@

I

DISCUSSION

The simulated reconstructed images of the Hoffman three-dimensional

FIGURE 12. Sir@iuiated reconstructed mage of qrey matter (A) and qrey ond ,@hjt@r@atter in 5 1 atio B@in a bas@I gang(ia s'ice @ithina fu@thre-d@meri@ior a@bron mode@ maoed ;ith point focusaig coIlimator@

brain model (Figs. 7B, l2B) demon

strate the qualitative degradations that might be expected in the reconstructed images of radioactivity distributed within a real brain. The simulation omitted several factors

(attenuation, scatter, and noise), which degrade a real reconstruction, since one of the advantages of using sim ulation studies is that factors that normally act in combi nation in the physical process can be separately studied and each individual effect evaluated. Thus, we present these results as a baseline for future comparison with the results when attenuation, scatter, and noise will be in eluded. This approach

will allow us to develop methods

for compensating for these factors and to evaluate these methods by comparison of the compensated image with the image obtained in the absence of the degrading factor. In spite of the omission of these factors, we still report substantial deviations from the theoretical image for the simulations of neuroreceptor imaging, and it may only be of theoretical interest to determine how much further degradation occurs when these factors are included. Al though the simulation (Figs. 7B, 12B) omitted these fac tors, there are qualitative similarities with a reconstructed image of the physically measured brain phantom (Figs. 8, 13). The circumferential profiles (Figs. 9, 14) and the ROI

data (Table 1; columns 4, 7, 10, 11) derived from the simulated and physically measured brains provide a quan

titative estimate of the contribution of imaging artifact to the apparent cortical deficits, particularly in the posterior parietal region. The circumferential profiles (Fig. 9, 14) show that an apparent two- to three-fold variation in regional radioactivity concentration can artifactually arise

from regions that are oftheoretically identical radioactivity concentration. There are significant deficits in the recon structed image of the simulated data, although the math ematical model had no deficit. The same types of artifacts

which we have demonstrated in the simulated images may also occur in the physically measured images of human subjects (2,5,6). The high frequency variation in the simulated high resolution circumferential profiles (Figs. 9, 14) is not the result of noise or statistical fluctuation, since the simula tions were noise-free. As shown previously for point-fo cusing collimators (5,6), these variations are completely deterministic, and are a function of the angular position ofthe detectors relative to the brain slice, the three-dimen sional spatial dependence ofthe cortical thickness, and the

position and orientation of the cortical regions. Both parallel-hole and point-focusing collimators ex hibit qualitatively similar artifactual variations along the cortical circumferential

profiles (Figs. 9, 14), indicating

that this artifact may be a general property of SPECT U)

I-

z

0 C 0

Lu N -J

0

z

20 40 60 SAMPUNGPOINTALONG CIRCUMFERENTIAL PROFILE

FIGURE 11. Circumferential profilesfor point-focusing recon

FIGURE 13. Physically meas ured reconstructedimage of a basal ganglia slice within the physicalbrainphantomimaged

structed images in Figures 10 and 12A.

with point-focusing collimators.

1928

The Journalof NuclearMedicine• Vol. 32 • No. 10 • October1991

Possible applications .

dude:

(a)

aiding

in

of the simulation

reducing

mistakes

in

procedure

in

interpreting

an

apparent deficit as representing a physiologic variation, and (b) utilization in a quantitatively accurate iterative reconstruction algorithm. The importance of incorporat ing a realistic three-dimensional model of the imaging procedure can be understood by a quotation from Parker (12):

U) 5-

z

0 C 0 Lu N .J

0

z

“The most important part of the iterative reconstruction is the model of the data collection 20

40

important

SAMPLING POINT ALONG

CIRCUMFERENTIAL PROFILE

FIGURE 14. Circumferential profilesfor point-focusing recon structed images in Figures 12B and 13.

imaging,

not a property

of a particular

of anatomy

and function,

imaging

device.

@

@

@

into the image in a complex nonlinear

We have demonstrated that the quantitative potential of SPECT for estimating the regional concentration of neuroreceptors or blood flow can be degraded as a result of finite detector resolution and inaccuracies in image

collection determines how accurate the reconstruction

COMPUTATION OF PSF FROM LSF Assume that the PSF is given as: PSF(x,y,z) =

@:AMP

(i)e_@2@2W2@@s1A) ,

where AMP@(i) = AMPps,(i@z,d), a@(i)

Eq.l

aps,(i@z,d): z =

distance, d = depth.

LSF(y,z) is defined as: LSF(y,z)

=

PSF(x,y,z)dx.

Eq.2

By substituting Equation I into Equation 2: LSF(y,z) = @:s:

dioactivity concentration artifactually to appear to have significantly different radioactivity concentrations. The major difference between parallel-hole and point

=

@: s:

=

@: AMP@F(i)e@2/20@sF(@

=

@: AMP,@F(i)

is the nature of the out-of-slice con

tribution. This distortion is both qualitative (Figs. 6, 11) and quantitative (Table 1; columns 1, 3, 8, 9). This effect will tend to diminish our ability to detect variations due to a disease state if that variation is localized within a single slice. @

will

APPENDIX

reconstruction. In particular, a shape- and size-dependent recovery coefficient causes two regions with identical ra

focusing collimators

H. Generally speaking,

but not function

alone. The finite resolution ofthe imaging system imposes a limitation on our ability to measure pure function. This couples anatomy way.

than the reconstructor,

the reconstructor affects how rapidly the estimate ap proaches the correct answer, but the model of the data be.―

The circumferential variation is slightly greater for point focusing than for parallel-hole collimators, but this differ ence is small compared to the magnitude of the overall variation. Thus, it is clear that SPECT images represent a combination

operation. . . . The

model, A, of the data collection process is much more

60

Comparison of the simulated reconstructed brain slice (Fig. 7B) to the physically measured phantom (Fig. 8)

‘J@

J.i:e_72/24sF(I)dx

aPSF(i)@@12@@.

Eq. 3

Equation 3 suggests that LSF(y,z) can be modeled as:

LSF(y,z) =

AMP

indicate the degree of realism ofthe simulation procedure.

@

@

Inclusion ofadditional degrading factors in the simulation procedure, such as attenuation, scatter, and noise, would be expected to further improve the correspondence of the

where

simulated image with the physically measured image.

and

The major limitations of the simulation procedure are: (a) the low resolution representation of the brain model that we used in order to decrease the time required for computation, and (b) the omission ofadditional degrading factors such as attenuation, scatter, and noise. Future studies are planned that will overcome these limitations.

Three-DimensionalSimulations of SPECT Imaging • Kim et al

Eq. 4

‘@LsF(j) =

AMP,@(i) = AMPJ@F(i)

aPSF(@

Eq. 5

Therefore AMP@F(i) AMP@(i) = ..n;

Eq. 6

1929

By replacingEquations4 and 6 into Equation 1, PSF can be computed from LSF as: @

PSF(x,y,z)

@

=

AMP,@F(t) _( @+‘?)f' (•)

@: ,—

. e

- isr

V2@r o@sF(1)

Eq. 7

normals [Abstract]. J NucI Med 1990:31:729.

3. Hoffman El, Huang SC, Phelps ME. Quantitation in positron emission computed tomography: I. Effect of object size. J Compul Assist Tomogr 1979:3:299—308.

4. DaviesP. VerthAH.Regionaldistribution of muscarinic acetyicholine receptor in normal and Alzheimer's-type dementia brains. Brain Res 1978:138:385—392.

5. Kim Hi, ZeebergBR, LoewMH, Reba RC. 3D simulationsof multidetec

ACKNOWLEDGMENTS The authors thank Drs. Frank B. Atkins and Murray H. Loew for useful discussions and suggestions. This work was supported by a grant from the National Institutes of Health (N5222l5)

and,

in part, by a grant from the Department of Energy (DE FGO5 88ER60649). REFERENCES I. Holman BL Gibson RE. Hill TC, Eckelman WC, Albert M, Reba RC. Muscarinic acetyicholine receptors in Alzheimer's disease in vivo imaging with iodine-l23-labeled 3-quinuclidinyl-4-iodobenzilate and emission to mography. JAMA 1985:254:3063—3066. 2. Kim Hi, Zeeberg BR, Gibson RE, Hosain P. Wesley R, Reba RC. SPEC1 study of the localization of R,R-['23IJIQNB in Alzheimer's patients and

1930

tor point-focusing SPECT imaging. J Nuc/Med 1991:32:333—338. 6. Kim Hi, Zeeberg BR, Loew MH, Reba RC. 3D computer simulations of resolution effects of multidetector point focusing SPECT imaging. IEEE Trans Med Imag l99l:in press. 7. Hoffman Ei, Cutler PD, Digby WM, Mazziotta iC. 3-D phantom to simulate cerebral blood flow and metabolic images for PET. IEEE Trans

NuciSci 1990;37:616—620. 8. Moore SC, Mueller SP. Inversion of the 3D Radon transform for a multidetector, point-focused SPECT brain scanner. Phys Med Biol 1986:3 1:207—22 1. 9. Chang LT. A method for attenuation correction in radionuclide computed tomography. IEEE Trans Nuc/Sci 1978;NS-25:638—643. 10. SME Multi-X 810 B preliminary user's guide. Strichman Medical Equip. ment, Inc., Massachusetts, 1989.

I 1. Links iM, Loats HL, Holcomb HH, Loats SE, Stumpf Mi, Wagner HN ir. Cortical circumferential profiling: an objective approach to cortical quantification in emission tomography [Abstract]. J Nuci Med 1989:30:816.

12. Parker iA. Image reconstructionin radiology. Boca Raton: CRC Press; 1990:480.

The Journalof NuclearMedicine• Vol. 32 • No. 10 • October1991