(this printout in Nov. 97, article is to appear in proc 1997 NSS/MIC). Computerized Biological Brain Phantom for Evaluation of. PET and SPECT Reconstruction.
(this printout in Nov. 97, article is to appear in proc 1997 NSS/MIC)
Computerized Biological Brain Phantom for Evaluation of PET and SPECT Reconstruction D. A. Dougherty1, I. T. Hsiao2 , W. Wang2 and G. R. Gindi2 3 ;
1 Department of Anatomy
2 Department of
Electrical Engineering Radiology SUNY at Stony Brook, Stony Brook, NY 11794 3 Department of
Abstract–A digital brain phantom was created from available primate autoradiographic (AR) data for use in emission computed tomography studies. The tissue was radio-labelled with a functional analogue of the PET agent [18 F]-fluoro-deoxyglucose (FDG). Following sacrifice of the animal, film records from serial m thickness sections were digitized and calibrated to obtain ground truth 2D spatial distributions of relative radionuclide density. A 3D version was constructed by using a video subtraction method to align consecutive slices. In order to assess the effects of accurate modelling of activity, the AR data, containing cortical and basal ganglia structures, was used as a phantom in the context of a partial- volume correction method for obtaining accurate regional quantitation. A second phantom, less realistic in terms of activity assignment, was constructed and also tested. The results indicate that quantitation errors due to effects of nonuniform activity in the AR phantom are significant and comparable in magnitude to errors due to non-phantom effects.
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I. I NTRODUCTION Digital phantoms, along with elaborate digital simulations of image formation, are utilized extensively in emission computer tomography (ECT) as a first stage in validating improvements in reconstruction algorithms and compensation schemes. Since trust in the conclusions of such testing increases with increasing verisimilitude of the digital simulation, one often strives to model noise, scatter, attenuation, and camera characteristics with as much realistic detail as possible. Less attention has been devoted to the modelling of the patient via digital phantom, however, and it is possible that significant improvements might result by using highly realistic phantoms. Three desirable aspects of a realistic 3D brain phantom are: (a) realistic assignment of possibly nonuniform activity (radionuclide density) within the tissue (b) accurate representation of the 3D anatomy with tissue labels delineating major anatomical compartments and ROI’s of interest, and (c) a measure of the statistical variation of these quantities in the target population, i.e. the statistics of biodistribution and anatomical shape variation. Cargill [1] addressed aspects of all three considerations in a digital SPECT phantom for imaging cirrhotic liver. For brain phantoms used for SPECT blood flow and PET metabolism studies, one approach has been to use 3D segmented MR brain scans [2, 3] or 2D segmentations of stained human brain tissue [4]. Here, radionuclide activity assignment is accomplished typically by setting constant activities in
all gray, white, and cerebro-spinal fluid (csf) regions, respectively. Interestingly, values for these ratios (typ. 8:2:1 ratios in gray, white, csf) have been derived from research on primate animal AR data [4, 5]. Though capturing considerable detail, such phantoms are limited by finite MR resolution, segmentation error, and the incorrect piecewise-constant assignment of activity. As PET and SPECT resolution improves, these limitations may become increasingly significant. It would be interesting to remove these limitations from SPECT and PET simulations to investigate their effects on test results. Unfortunately, there is no way to easily obtain ground-truth activity in humans. For animal studies, however, one can use autoradiography to obtain both exquisitely precise activity assignment and accurate segmentation. Such a study could be directly useful, for example, in testing the data processing associated with small-animal PET and SPECT scanners. In autoradiography, a radioagent is introduced into an animal, allowed to biodistribute, after which the animal is sacrificed. For brain studies, the brain is removed, often frozen, embedded in a rigid medium, then physically sliced via a microtome into thin (typ. 20m) tissue sections. As seen in Fig. 1, the tissue slices are apposed to film, which is exposed by short range + or ? particles to obtain a low-noise, highresolution (typ. 50m) two-dimensional (2D) record of activity. (Note that many PET and SPECT radiopharmaceuticals can also be used for autoradiography, since a emission in SPECT is often accompanied by emission of suitable energy, and PET agents emit +.) The film optical density (O.D.) is digitally recorded by densitometer, and O.D. values then converted to absolute activities (nCi/g per pixel) with the aid of a calibration curve obtained by recording and digitizing activity standards on each film sheet. The result is a series of 2D recordings of activity at effectively infinite spatial and activity resolution relative to that obtainable by ECT. Figure 2 shows one AR slice, along with profile plots, of a typical primate brain. The appealing idea of utilizing AR data for an ECT phantom is conceptually simple, but presents technical challenges in practice. Initial work in this area, utilizing animal data, has appeared in [6, 7, 8]. It is not clear, however, how this approach might apply for a human phantom. For some advanced primates, it turns out that brain structure is qualitatively similar to that of humans. Figure 3 displays a coronal section of human brain along with a corresponding slice (from an autora-
In ths work, we describe construction of an AR-based primate phantom, and use this phantom to see whether knowledge of precise anatomy and activity within a human-like geometry might affect conclusions in digital testing. Our test, in the context of a quantitation task for PET, is used to compare results obtained with the AR phantom to those from a less realistic version of this phantom. For convenience, we shall refer to the biologically correct AR phantom as B (Biological) and the Artificial phantom as A. II. M ETHODS Fig. 1 A simplified view of autoradiography image formation.
A. Phantom Construction
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Fig. 2 (a) One slice of the AR stack, (b) the vertical profile shown in (a), (c) the horizontal profile shown in (a).
diograph) of a rhesus monkey. Aside from a gross scale factor of about 2.5, the similarities are intriguing. Homology for interior gray structures is evident, and the degree of cortical gyrification is comparable in both, albeit less in rhesus. Absolute cortical thickness, however, is about the same in both species. When scaled to human dimensions, such a primate phantom would represent, approximately, a human brain phantom suffering an overall geometrical warping, and a proportionately thicker, less convoluted cortex. However, the activity assignment and segmentation would be practically perfect.
Fig. 3 Gross brain homology between human and rhesus monkey shown in the coronal sections.
We obtained autoradiographic data of the brain of a rhesus monkey (macacca mulatta) sacrificed as part of an unrelated neuroscience experiment involving regional glucose metabolic changes resulting from memory tasks [9]. The slices, from a single hemisphere, were cut coronally rather than transversely, and there exist gaps of unusable data. However, this limitation did not affect our testing. The neuroscience experiment utilized the common glucose-analog AR agent [14 C]-2-deoxyglucose (2DG), whose biochemistry is similar to that of the PET metabolic agent [18 F]-fluoro-deoxyglucose (FDG). Animal studies [10] using both agents as AR tracers demonstrated quantitatively the nearly equal spatial distribution of 2DG and FDG. Thus, to a good approximation, our AR data serves as a PET-FDG brain phantom. The tissue was sliced at 20m thickness, apposed to film and exposed along with methacrylate activity calibration standards, and developed. We digitized 60 left-hemisphere coronal slices, spaced at 200m, from the region indicated in Fig. 4b. When scaled to human dimensions (factor of 2.5) this slab was equivalent to a tissue block of about 10cm10cm3cm, with equivalent voxel size of 250m 250m 500m. (Here, the 3rd dimension is in a direction perpendicular to the coronal plane.) Each slice was digitized to 1280960 pixels and corrected by mapping O.D. through a standards calibration curve obtained by interpolating a 3rd-degree polynomial through the 8 calibration measurements on each film sheet. Figure 2 illustrates an AR slice post calibration along with profile plots. To place the slices into a 3D volume, we displayed overlapped pairs of successive slices using digital transparency mode on a display, with one of the pair displayed in real time. By manually rotating and translating the film sheet and viewing the overlap image (Fig. 4a), we could obtain good alignment. The alignment accuracy was limited by tissue irregularity; the worst of these involved relatively large displacements of the anterior temporal lobe from slice to slice. The final alignment quality was adequate, as can be seen in the display (Fig. 4c) of the slab resliced in the transverse plane. This data thus represents an accurate activity assignment placed into 3D, as depicted in Fig. 4d. This autorad data was then used to generate tissue segmentation labels. Note that the autorad, though a measure of activity, can be used as well to display ground-truth segmentation into various gray and white matter ROI’s. Note that the 2DG autorad is visibly nearly identical to a cresyl violet stained tissue
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(d) Fig. 4 Three-dimensional phantom construction, (a) alignment between two slices, (b) region of brain from which phantom is derived, (c) horizontal reslice demonstrating good alignment, (d) the representative set of four slices from the aligned stack.
image in its gray-white boundaries. Cresyl violet is used for stainning cell bodies and provides ground segmentation. The segmentation from AR is thus effectively ground truth relative to that obtained from an MR segmentation. Each of the 60 AR slices was carefully hand segmented into gray and white matter, and five ROI’s: amygdala, caudate, putamen, globus pallidus, and a cortical region were outlined as depicted in Fig. 5. Note that regions of csf, unavailable in this set, would normally have zero, or very low, activity.
In [11], data from a coregistered (to PET) and segmented MR scan is used to correct the underestimation of quantitation in cortical and deep gray ROI’s. The accuracy of this method for quantitation correction depends on the degree to which the observed PET reconstruction results from an underlying object that consists of spatially uniform activities in gray matter and in white matter, with zero activity in csf. PET image formation is assumed to be modelled solely by convolution with a system point-spread function, since this blurring is the dominant source of partial-volume errors. The effects of noise and other factors are ignored. mr and X mr To describe our adaptation of the method, let XG W be (0; 1) indicator functions for gray (G) and white (W) matter obtained from an MR segmentation. Denote the (observed) PET reconstruction by Iobs , and the corrected PET image by Icorr . (For clarity, we drop any notation indicating the spatial dependencies of these 2 quantities.) Denote the system pointspread function (psf), accounting for the net effects of image formation and reconstruction, by h, and convolution with h by h. The first step in the partial-volume (PV) correction is to subtract from Iobs the contribution due to white matter. For the mr h]. The assumptions here, this quantity is simply IW [XW scalar IW is the value of the presumed constant activity of white matter obtained by sampling a region of Iobs deemed mr h] to lie well within white matter. Since the quantity [XW is at MR resolution, it must be downsampled to PET resolution before subtraction from Iobs . We denote this process of integrating MR voxel quantities to those of PET size by the clumsy but descriptive notation [()mr ]pet . The correction for mr h]pet . This white matter is then given by Iobs ? IW [XW quantity represents the blurred image due to gray matter only, and one further correction, to deblur gray matter, is needed. With the assumption of constant gray matter activity, this is mr h]pet . Putting these steps accomplished by dividing by [XG together, the PV correction formula is summarized as:
mr h]pet I ? IW [XW Icorr = obs (1) mr [XG h]pet Note that the correction Icorr applies in gray regions only. If gray matter activity is nearly uniform, then the 3D quantity
Fig. 5
One slice of the AR stack and its segmentation map with 5 ROIs. 1=caudate, 2=globus pallidus, 3=putamen, 4=amygdala, 5=region of insular cortex.
We created a less realistic, phantom (A). It differed from Phantom B in the segmentation of gray and white regions, and activity was assigned as a constant value of 4.0 in all gray matter, including the 5 ROI’s, and 1.0 in all white matter. Note that the ROI’s selected on the basis of anatomy only, were not unusually hot or cold in activity. B. Partial-Volume Correction Method We attempted to assess the errors stemming from the use of a realistic (B) phantom as compared with a less realistic phantom (A). To do this, we used a modification of a partialvolume correction method for brain PET as proposed in [11].
Icorr will be nearly correct.
For an underlying artificial object, such as phantom A, that is perfectly consistent with these two assumptions, the PV correction, termed “recovery”, should be perfect. To the extent that the underlying object violates these assumptions, the recovery is in error. Our phantom B violates the assumption of uniform activity. Thus, by comparing regional quantitation accuracy obtained from phantom A with that from B, we estimate the error due to using an unrealistic (in an activity sense) phantom. By using an appropriately shifted version of B, we can compare these errors to those from a realistic non-phantom effect, such as a misregistration of MR to PET. A third important source of inaccuracy is segmentation error. The real object has an underlying “true” segmentation as seen in Fig. 5. (At a histological scale, tissue boundaries are still ambiguous, but at the millimeter scale of MR, this uncer-
tainty is, for all practical purposes, inconsequential.) Any MR segmentation algorithm results in a label field X mr that is in error due to simple missegmentation and to the effects of finite MR resolution. As discussed below, our biological phantom B offers an opportunity to study the effects of missegmentation, but we defer this for future work. In this study, labels are in error due only to misregistration effects. C. Testing Procedure
now carried out at MR resolution, is performed to obtain Iobs , and white voxel regions again sampled to obtain IW . The MR labels are downsampled to PET as before, and Eq. 1 evaluated. ROI quantitations are evaluated, as for phantom B, with the exception that for true quantitation, the values are now given mr . by Itrue Xroi Finally, to simulate the effects of misregistration for phanmr and X mr are shifted a distance of tom B, the label arrays XG W two MR voxels, thus simulating a realistic misregistration of 2 mm. The shifts are done in two directions, left and right. Equation 1 is again evaluated, but with the misregistered labels, and with Iobs not shifted.
To implement the PV correction with phantom B, we begin with the high-resolution ground-truth AR segmentation, a ar and X ar denote the slice of which is shown in Fig. 5. Let XG W high-resolution binary indicator arrays for gray and white segmentation, respectively. Furthermore, represent the five gray TABLE 1 ar , matter ROI’s at AR resolution by the binary label fields Xroi R ESULTS OF ROI Q UANTITAION FOR A RTIFICIAL P HANTOM A where roi represents any of the five regions depicted in Fig. 5. Cortical Caudate Putamen Globus Amygdala Average Next, downsample the AR label fields to MR resolution by avROI Pallidus Error eraging every 882 pixels into one MR pixel to obtain the mr mr mr MR label fields XG ; XW and Xroi . The analog values in True 3319 1311 2460 827 1238 the arrays X mr reflect accurate partial-voxel labels at the MR Iobs -9.4% -19.8% -13.1% -15.6% -9.2% 13.4% voxel size of 1 mm3 and array size 10010030. The segI 0 % 0 % 0 % 0 % 0 % 0% corr mr and X mr are then convolved with h at mentation labels XG W the MR resolution, and then downsampled to PET resolution mr h]pet and [X mr h]pet . to form the terms [XW W III. RESULTS To simulate the formation of Iobs , we simply convolve the original AR intensity data Itrue (an 80080060 array) with The first row of Table 1 shows, for phantom A, the true quanthe system psf h. Note that this convolution represents an ap- titation, in arbitrary units, in the five gray ROI’s. The second proximation to image formation that should ordinarily be mod- row shows the quantitation values, obtained by applying ROI elled as a digital projection of a high-resolution phantom fol- templates to Iobs , expressed as percentage error relative to the lowed by resampling at the detector resolution, followed by true value. The last column expresses average error as the simfiltering, then backprojection. We model the kernel h as a 3D ple arithmetic average of the absolute values of entries in the isotropic Gaussian with FWHM of 6mm, and sample h at the corresponding row. As expected, regional quantitation is unresolution of the AR data. To avoid artifactual errors in quan- derestimated due to the spread of counts to adjacent white mattitation due to edge effects in the convolution, evaluations are ter. The third row verifies the perfect recovery as expected with done within a border excluding the edge region of the array. the idealized phantom A. Following the convolution, each block of 16164 AR pixels is summed into one PET voxel (equivalent size 2mm2mm2mm) TABLE 2 to form Iobs . The array size for Iobs is 505015. For a refR ESULTS OF ROI Q UANTITAION FOR B IOLOGICAL P HANTOM B erence location in the array for Iobs , the values of 16 pixels are Cortical Caudate Putamen Globus Amygdala Average averaged to form IW . Finally, the operation in Eq. 1 is carried ROI Pallidus Error out to form the final 505015 PET array for gray-corrected activity, Icorr . True 1.55e8 7.99e7 1.47e8 2.70e7 4.78e7 We then obtain ROI quantitation values for the true object I -16.4 % -18.8% -12.8% -1.7% -9.2% 11.8% obs Itrue , as well as for the reconstruction Iobs and correction Icorr . ar , car- Icorr 4.1% -1.4% -2.9% 7.3% 1.9% 3.5% For the true object, the ROI value is simply Itrue Xroi ried out at the high AR resolution. For the PET images, the pet and I X pet . Here, the ROI values are given by Iobs Xroi In Table 2, for phantom B, true quantitation values differ corr roi masks X pet are obtained by averaging each block of 222 significantly from those in Table 1 since the activity values, MR segmentation labels. derived for B from a calibration of radioactive standards, are in The entire procedure is repeated for phantom A simply as a units of nCi/g. Again, quantitation is underestimated in the five check to ensure that recovery is perfect, as predicted. Here, the regions with about the same percentage error as for phantom A. original AR data are segmented, and labels are downsampled As seen in the third row, the recovery is no longer perfect, and to MR resolution by a “voting” process in which the majority the 3.5% average error can be attributed to the nonuniformity label in each block of 882 AR labels is assigned to the MR of activity in phantom B. label. Activities of 4.0 and 1.0 units are assigned to each gray In itself, the magnitude of these errors in the regions of and white pixel, respectively. For phantom A, the true image, Icorr are not meaningful, but by comparing these to errors obItrue , thus exists at MR resolution. A 3D convolution with h, tained for the misregistered version of phantom B, we may see
TABLE 3 R ESULTS OF ROI Q UANTITAION FOR B IOLOGICAL P HANTOM B F OLLOWING S HIFT
Cortical Caudate Putamen Globus Amygdala Average ROI Pallidus Error True
1.55e8 7.99e7
Iobs Icorr
-16.4
Right
Icorr
% -2.3% %
10.7
% 0.9%
-18.8
%
5.1
1.47e8 2.70e7
4.78e7
-12.8
-9.2
% -2.9% %
-0.2
% 10.7% -1.7
%
5.0
% 6.5% %
4.1
%
11.8
4.9
%
Left
whether errors due to nonuniform activity are comparable to errors due to a non-phantom effect, namely realistic misregistration. Table 3 shows results for the misregistered version of B. By definition, the first two rows remain unchanged, and the errors with left and right shifts are listed in the third row. The average error for this case, 4.9%, represents an increment of 1.4% from the corresponding figure in Table 2, and is attributable to registration effects. The effects due to nonuniform phantom activity are thus at least comparable to those for misregistration for this test. IV. S UMMARY
AND
C ONCLUSIONS
As our main contribution, we described an autoradiographbased primate phantom for ECT and its 3D construction. We tested the use of the phantom in a partial-volume correction scheme in a setting where the physics simulation was limited to 6 mm detector blur, but the effects of misregistration and of activity assignment in the phantom itself were realistically modeled. We demonstrated, for this anecdotal study, that the the conclusions of such a quantitation test depend on the realism of the phantom. One important aspect that we did not test is segmentation error. One needs both a true segmentation and a model of realistic segmentation error that is dependent on the particular algorithm used to obtain it. Phantom B provides the former, but the non-rigid registration of MR segmented values to AR coordinates, needed for the second step, is a formidable project we leave for later work. ACKNOWLEDGEMENTS We thank Anand Rangarajan and Haili Chui for assistance with autoradiograph digitization and alignment. We also thank Patricia Goldman-Rakic for access to the rhesus data, and members of her lab, especially Lila Davachi, for assistance with the data. Useful discussions with George Zubal, Jonathan Nissanov, Cliff Patlak, Prantika Som, and Zvi Oster are appreciated. This work has been supported by grant R01-NS32879 from NIH-NINDS. R EFERENCES [1] E. B. Cargill, A Mathematical Liver Model and its Application to System Optimization and Texture Analysis, PhD thesis, The University of
Arizona, Tucson, AZ, 1989. [2] I.G. Zubal, C.R. Harrell, E.O. Smith, A.L. Smith, and P. Krischlunas, “Two Dedicated Software Voxel-Based Anthropomorphic (Torso and Head) Phantoms”, In P.J. Dimbylow, editor, “Proceeding of the International Conference at the National Radiological Protection Board”, pp. 105–111, 1995. [3] E. J. Hoffman, P. D. Cutler, W. M. Digby, and J. C. Mazziotta, “3-D Phantom To Simulate Cerebral Blood Flow and Metabolic Images for PET”, IEEE Trans. Nuclear Sci, 37, pp. 616–620, 1990. [4] D. Mahoney, S. Huang, A. Ricci, J. Mazziotta, R. Carson, E. Hoffman, and M. Phelps, “A Realistic Computer-Simulated Brain Phantom for Evaluation of PET Characteristics”, IEEE Transactions on Medical Imaging, vol. 6, pp. 250–257, 1987. [5] C. Kennedy, O. Sakurada, M. Shinohara, J. Jehle, and L. Sokoloff, “Local Cerebral Glucose Utilization in the Normal Conscious Macaque Monkey”, Annals of Neurology, 4(4), pp. 293–301, Oct. 1978. [6] Q. Ramsby, “Evaluation of SPECT Neuroreceptor Imaging Utilizing Quantitative Autoradiography”, Master’s thesis, Biological Engineering, Department of Electrical and Systems Engineering, University of Connecticut, 1993. [7] G. Gindi and A. Rangarajan, “What Can SPECT Reconstruction Learn from Autoradiography”, In Proc. of IEEE Nuclear Science Symposium and Medical Imaging Conference, volume 4, pp. 1715–1719, November 1994. [8] G. R. Gindi, D. Dougherty, I. H. Hsiao, and A. Rangarajan, “Autoradiograph-Based Phantoms for Emission Tomography”, In K. Hanson, editor, SPIE Medical Imaging 1997: Image Processing, volume 3034, pp. 403–414, SPIE, 1997. [9] H.R. Friedman and P.S. Goldman-Rakic, “Coactivation of Prefrontal Cortex and Inferior Parietal Cortex in Working Memory Tasks Revealed by 2DG Functional Mapping in the Rhesus Monkey”, J. of Neuroscience, 14(5), pp. 2775–2788, May 1994. [10] P. Som, Y. Yonekura, Z. Oster, M. Meyer, M. Pelleteri, J. Fowler, R. MacGregor, J. Russell, A. Wolf, I. Fand, W. McNally, and A. Brill, “Quantitative Autoradiography with Radiopharmaceuticals, Part 2: Applications in Radiophamaceutical Research: Concise Communication”, J. Nucl. Med., 24, pp. 238–244, 1982. [11] H.W. M¨uller-G¨artner, J.M. Links, J.L. Prince, R.N. Bryan, E. McVeigh, J.P. Leal, C. Davatzikos, and J.J. Frost, “Measurement of Radiotracer Concentration in Brain Gray Matter Using Positron Emission Tomography: MRI-Based Correction for Partial Volume Effects”, J. of Cerebral Blood Flow and Metabolism, 12(4), pp. 571–583, 1992.
