TSINGHUA SCIENCE AND TECHNOLOGY IS SN l l 1 0 0 7 - 0 2 1 4 l l 0 8 / 2 0 l l p p 5 0 - 5 5 Volume 15, Number 1, February 2010

Partial Volume Correction in SPECT Using Anatomical Information and Iterative FBP

Kjell Erlandsson**, Brian F Hutton

The Institute of Nuclear Medicine, University College London, London, NW12BU, United Kingdom

Abstract: The ability to correctly quantify activity concentration with single photon emission computed tomo-

graphy (SPECT) is limited by its spatial resolution. Blurring of data between adjacent structures, which is

known as partial volume effects, can be compensated for by utilizing high resolution structural information

from other imaging modalities such as CT or MRI. Previously developed partial volume correction (PVC)

methods normally assume a spatially invariant point spread function. In SPECT this is not a good approxi-

mation, since the resolution varies with the distance from the collimator. A new method, p-PVC, was devel-

oped in this paper, which takes into account the distance dependent blurring. The method operates in pro-

jection space and is combined with filtered back-projection (FBP) reconstruction. Results from simulations

show that similar quantitative results could be obtained with p-PVC+FBP as with OSEM with resolution re-

covery, although with better structural definition and an order of magnitude faster.

Key words: partial volume effect (PVE); partial volume correction (PVC); SPECT

Introduction

The ability to correctly quantify single photon emis-sion computed tomography (SPECT) activity concen-trations in small structures is limited by the spatial res-olution of the imaging system. The limited resolution results in blurring of data between adjacent structures, which is known as partial volume effects (PVE). Quantification of brain studies in particular will be degraded due to the presence of different components such as gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF). It is possible to compensate for these effects by utilizing high resolution structural information from other imaging modalities such as CT or MRI.

The purpose of partial volume correction (PVC) in PET and SPECT is two-fold: (1) provide quantitatively

accurate values of tracer binding in individual studies; and (2) eliminate variations in PVE across subjects. A number of PVC methods have been developed in the past utilizing anatomical information, which are either voxel-based[1-4] or volume-of-interest (VOI)-based[4-6]. PVC methods that do not depend on anatomical data have also been developed[7], although these can also be classified as resolution-recovery methods. These me-thods were developed mainly for PET, but have also been applied in SPECT[8,9]. The main difference be-tween PET and SPECT in relation to PVE is the spatial variation of the point spread function (PSF). While in PET it is often assumed that the PSF is symmetric and spatially invariant, in SPECT this is not generally a good approximation, since the resolution varies with the distance from the gamma-camera. This variation can be taken into account with an analytical restoration filter[10,11], or by using an iterative reconstruction tech-nique that includes resolution-recovery[12,13]. Iterative reconstruction algorithms have also been developed that incorporate anatomical information[14-16], but these

Received: 2009-10-18; revised: 2009-12-20

** To whom correspondence should be addressed. E-mail: k.erlandsson@ucl.ac.uk

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methods just use the anatomical data for smoothing within regions, not for PVC.

We have developed a new PVC method that takes into account the distance dependent blurring in SPECT. The method operates in projection space and works in combination with filtered back-projection (FBP) re-construction, and is therefore faster than standard itera-tive algorithms. We have evaluated this new method, p-PVC, using simulated SPECT data corresponding to a simple geometrical phantom as well as an anthropo-morphic brain phantom. The results were compared with OSEM reconstruction[17] with resolution recovery.

1 Methods 1.1 p-PVC method

The basis for the p-PVC method is the availability of a structural image (CT or MRI) that is co-registered with the SPECT data. The structural image is segmented into regions corresponding to different anatomical structures. The number and size of the regions used depend on each application. For the purpose of the correction, it is assumed that each region contains a uniform activity distribution. The p-PVC algorithm can be described as follows:

10

AR 1

{ { }}FBP

{ { }}n

nn

F A II p

F A I (1)

where p0 is the measured projection data, In is the im-age estimate after the n-th iteration. FBP{·} represents reconstruction by filtered back-projection, A{·} the operation of averaging an image over a set of pre- de-fined anatomical regions, generating a piece-wise con-stant image, F{·} simple forward-projection, and FAR{·} forward-projection with non-uniform attenuation and distance-dependent resolution.

p-PVC is an iterative algorithm, which converges after just a few (3-4) iterations. (Here we use the term “convergence” in the sense that a relatively small changes in image values were observed empirically.) In each iteration, a multiplicative correction is applied to the original projection data, compensating for the effects of resolution-blurring, based on a simplified image, as well as for attenuation. The simplified image consists of piece-wise constant regions with image values that are updated in each iteration. New image estimates are obtained by FBP reconstruction. The al-gorithm is initialized with a uniform image, I0.

The correction factors in Eq. (1) are similar to those used in Ref. [4], although in that case the correction is applied in the object domain, while in our method the correction is applied in the projection domain in order to take into account the distance dependent PSF. The algorithm is similar to the iterative refinement ap-proach[18], and is based on iterative FBP, which has long been used for attenuation correction[19].

For comparative purposes, FBP reconstructions were also performed without p-PVC. In this case attenuation correction (AC) was applied using a procedure similar to Eq. (1) but without including resolution modeling in the forward projection. In OSEM, attenuation was in-cluded in the system matrix.

1.2 Simulations

The p-PVC method was evaluated with simulated SPECT data including the effects of distance- depend-ent resolution blurring in 3-D and non-uniform at-tenuation, but not Compton scattering (assuming this can be accurately corrected for). Two different digital phantoms were used (see below), and projection data was generated using a layer-by-layer blurring tech-nique[20]. In this algorithm, a 3-D distance-dependent PSF is modelled using an incremental blurring proce-dure, in which a series of planes parallel to the detector, starting furthest away, are convolved with a small ker-nel and added to the next plane.

The assumed geometry was that of a dual-headed rotating gamma-camera SPECT system, equipped with parallel-hole low-energy-high-resolution (LEHR) col-limators. The radius of rotation was 150 mm (corre-sponding to a typical brain scan), the number of pro-jection angles 120 over 360 degrees, and the pixel size 2×2 mm. Poisson noise was added according to as-sumed activity concentration and scanning time.

1.3 Elliptical phantom

The first phantom consisted of an ellipsoid with half-axis dimensions of 80, 100, and 60 mm in the x-, y- and z-directions, respectively. It contained 6 hot spheres with 8 mm radius, placed centrally in axial direction and at different radial distances from the cen-tre of the phantom: 10, 25, 40, 55, 70, and 85 mm, re-spectively. The activity concentration in the spheres was 4 times that of the background. The total activity in the phantom was 100 MBq and the total scanning

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time 60 min. Projection data were generated assuming uniform attenuation within the phantom. Six noise re-alizations were performed and the data were recon-structed with FBP without resolution compensation as well as with 1-5 iterations of p-PVC. Eight regions were used for PVC: the outside-of-the-phantom region, the phantom background, and the 6 spheres. Recon-struction was also done with 1-24 iterations of OSEM (10 sub-sets) with resolution modeling (OSEM-R) for comparison. Mean and standard deviation (SD) images were generated across the 6 noise realizations.

The data were analyzed by looking at the recovery value for each sphere, calculated as the mean value within the sphere divided by the mean background value, normalized to the true ratio (4). Mean values and SD were then calculated across the 6 spheres. The mean recovery values were plotted versus the mean background coefficient-of-variation (COV=SD/mean) at each iteration. We also looked at the max-values in the spheres, processed in a similar manner.

1.4 Brain phantom

We also simulated SPECT data using an anthropo-morphic brain phantom[21] with an activity distribution corresponding to a dopamine receptor or transporter scan. The relative activity concentrations in CSF, WM, GM, and striatum (caudate and putamen) were 0, 1, 4, and 16, respectively. This corresponds to a striatal binding potential (BP) of 3. The total activity in the brain was 37 MBq and the total scanning time 40 min. Projection data were generated with non-uniform at-tenuation. The data were reconstructed with FBP without resolution compensation as well as with 3 it-erations of p-PVC. Eight regions were used for PVC: the outside region, CSF, WM, GM, and left and right caudate and putamen. Reconstruction was also done with 12 iterations of OSEM-R (10 sub-sets) for com-parison. The images were analyzed by calculating stri-atal BP relative to GM (BP=striatum/GM 1) as well as by visual inspection.

2 Results 2.1 Elliptical phantom

Figure 1 shows images of the elliptical phantom recon-structed with FBP with and without p-PVC and with OSEM-R as well as the original phantom. It can be

seen that p-PVC improves the contrast in the spheres as compared to FBP without PVC. There is also less variability between the spheres. The OSEM-R image shows high contrast and low background variability, however the spheres appear too small compared to the original. In Fig. 2 it can be seen that the noise distribu-tions for p-PVC+FBP is relatively uniform over the field-of-view (FOV), while that for OSEM-R mimics the activity distribution.

Fig. 1 One central slice through the elliptical phan-tom (top left), and images reconstructed with FBP (top right), p-PVC+FBP, 3 iterations (bottom left), and OSEM-R, 12/10 iterations/sub-sets (bottom right)

Fig. 2 Noise distribution (SD) in images recon-structed with p-PVC+FBP, 3 iterations (left) and OSEM-R, 12/10 iterations/sub-sets (right)

The mean sphere recovery vs. background COV is shown in Fig. 3. This graph shows that the p-PVC+ FBP data converge towards a point close to the OSEM-R curve, meaning that similar quantitative values can be obtained with the two algorithms at the same noise level. The p-PVC+FBP curve is practi-cally vertical – the contrast increases in each iteration without an increase in noise. This is because the pseudo-images, used in the calculation of the

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correction factors, are noise-free. The max-recovery values are plotted in Fig. 4. While OSEM-R overshoots the true max-value, p-PVC+FBP converges to a value just above the true one.

Fig. 3 The mean value to background ratio in the spheres divided by the true ratio as a function of mean background noise (COV) for OSEM-R (diamonds) and FBP with p-PVC (circles). Each point represents the mean value of the six spheres after a number of itera-tions, and the error bars represent the SD across the spheres.

Fig. 4 The max-value to mean background ratio in the spheres divided by the true ratio as a function of mean background noise (COV) for OSEM-R (dia-monds) and FBP with p-PVC (circles). Each point represents the mean value of the six spheres after a number of iterations, and the error bars represent the SD across the spheres.

2.2 Brain phantom

Reconstructed images from the brain phantom simula-tion are shown in Fig. 5. In the p-PVC+FBP image the striatal structures are more well-defined and have higher contrast as compared with FBP alone. Com-pared with OSEM-R, the shape of the striatum is closer to the true shape with p-PVC+FBP. The calculated stri-atal BP-values were 1.94, 2.67, and 2.45 for FBP, p-PVC+FBP, and OSEM-R, respectively, the true value being 3. These results show that p-PVC+FBP can produce good results even with complex-shaped

objects.

Fig. 5 A slice through the brain phantom (top left), and images reconstructed with FBP (top right), p-PVC+FBP, 3 iterations (bottom left), and OSEM-R, 12/10 iterations/sub-sets (bottom right)

3 Discussion

We have presented a novel PVC method for SPECT which utilizes anatomical information, takes into ac-count the distance dependent resolution in 3-D, oper-ates in projection space, and can be combined with FBP reconstruction. As other PVC methods based on anatomical information, the accuracy of this method can be affected by errors in a series of data processing steps, such as image realignment, segmentation, and parcelation. The sensitivity to this type of errors has been investigated by other groups for various PVC methods[8,22-24], and we would expect the effects to be similar for p-PVC. Methods for resolution recovery that do not utilize anatomical data are obviously not susceptible to this type of errors. We therefore chose to compare p-PVC+FBP with OSEM-R, with the aim of clarifying the advantages and disadvantages with each approach.

Our simulation results show that our new p-PVC algorithm can take advantage of additional structural information to improve SPECT images both qualita-tively and quantitatively. Compared with OSEM-R, it resulted in similar recovery vs. noise values in the el-liptical phantom. However, while OSEM-R showed a tendency to over-estimate the image values at the cen-tre of the spheres, p-PVC+FBP gave more accurate

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results. This, of course, is due to the additional data utilized in p-PVC, which was not available with OSEM-R. The improved structural definition was also obvious in the brain phantom experiment, where also a more accurate BP value was obtained (although the OSEM-R values may have improved with more itera-tions). Anatomical data can also be incorporated in iterative reconstruction algorithms, but this is typically used for enforcing smoothness within regions but not across regions, and not for resolution compensation. A further advantage with our approach is the speed: p-PVC+FBP is an order of magnitude faster than OSEM-R, which is particularly advantageous for processing dynamic (4-D) data-sets. Furthermore p-PVC does not increase the image noise as compared to FBP without PVC. This is evident from the vertical trend of the iteration sequence in the resolution vs. noise graph.

Our PVC method is based on the assumption of uniform distribution within a number of regions. This does not mean that the final outcome is a piecewise constant image – what it means is that the correction for resolution blurring is done between different re-gions but not within each region. In the simulation ex-periments presented here, we assumed a uniform activ-ity distribution in each region, which is obviously a simplification compared with a real situation. In the future we plan to investigate the effect of non-uniform distributions on the accuracy of the algorithm.

4 Conclusions

Our new PVC method constitutes a fast and accurate method for obtaining improved reconstructed SPECT images based on additional structural information, taking into account the distance dependent resolution. Compared to OSEM with resolution recovery, our me-thod gives similar regional mean values, but with bet-ter structural definition and an order of magnitude faster.

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