[ieee 1999 ieee nuclear science symposium. conference record. 1999 ieee nuclear science symposium...

5
Effects of Axial Transmission Resolution in PET] C.M. Laymon and T.G. Turkington Department of Radiology, Duke University Medical Center, Durham, NC 27710 Abstract The effects of the axial resolution of transmission projection data for use in PET attenuation correction is an important consideration for developing smoothing schemes for noise reduction and for the design of transmission systems. PET transmission data from five patient scans were used in conjunction with simulated uniform emission data to quantify some effects and to compare them to the effects of transaxial transmission smoothing. PET patient emission data were also corrected for attenuation using transmission projection data that had been smoothed axially or transaxially by various amounts. Results from the uniform emission studies show that the effects of axial transmission smoothing are always less than are those of transaxial smoothing. For example, within a volume that included the lungs, 50% of the voxels are inaccurate by more than 20% with a transmission axial filtering width of about 7 cm. For transaxial smoothing, the same level of inaccuracy is reached with a filter width of about 3 cm. I. INTRODUCTION In positron emission tomography (PET), an exact correction for attenuation can be made by multiplying the emission count rate measured along each projection line of response (LOR) by an attenuation correction factor (ACF). The ACF is the inverse of the total attenuation factor along that line of response. Attenuation factors are often determined by transmission measurements using an external radiation source. Application of measured ACF's can degrade the final corrected image through the introduction of noise and because of imperfect system resolution. Additionally amelioration of transmission noise through filtering further degrades the resolution of transmission data. To avoid resolution artifacts, it is desirable to match transmission and emission resolution [l], [2]. An exception to this is the case where the object being scanned exhibits some symmetry that can be exploited. For example, the image of a uniformly attenuating cylinder oriented parallel to the scanner axis is invariant with respect to the axial resolution scale. In such a case, transmission data can be smoothed axially to an arbitrary degree and applied to emission data without degrading the final image. In this case, the exploited symmetry is the cylinder's invariance under axial translation. Given that the human body exhibits relatively large local regions that exhibit this same symmetry, the question arises as to what level of axial resolution, unmatched in the emission data, can be tolerated in transmission data used for lFunded by ElGems Inc, Haifa, Israel and in part by The Whitaker Foundation. attenuation correction. Such information is valuable for deciding on the acceptable noise levels in transmission data so that the total time available for a complete patient scan can be used optimally. Additionally, it is important for optimizing the design of a transmission system. The details of the design of a transmission system can affect its axial resolution much more severely than the transaxial resolution. For example, a transmission system for gamma-camera based PET using multiple point sources has recently been described [3]. Its transaxial resolution is determined by the gamma camera while the axial resolution depends on the point-source collimation. While the axial resolution of the system is easily adjustable, less stringent axial resolution requirements allow a more efficient use of radioactivity resulting in lower total system cost and possibly less exposure to personnel. In this work we present simulated and patient data with the goal of determining some of the effects of axial smoothing. In some cases the results are compared with the effects of smoothing transmission data transaxially. Although we present patient data containing lesions, this is not a study of lesion detectability. 11. METHODS Transmission axial resolution effects were evaluated by using existing clinical PET data [4]. Five studies representing a variety of body types were selected. Each PET data set consisted of an attenuation corrected emission image and an attenuation map from transmission data. The pixel size was 3.5 mm transaxially and 4.25 mm axially and 140 slices were used in each case. A. Simulated Transmission Data The 140 transaxial slices from each patient attenuation coefficient map were forward projected (2D) into 128 transaxial bins at each of 90 angles spanning the 180" domain appropriate for use with coincidence data. These values were converted to attenuation factors, which represent the reduction of coincidence events due to attenuation. Various degrees of resolution were simulated by smoothing the attenuation factors. Gaussian filters with full widths at half maximum (FWHMs) ranging from 0.5 to 16 cm were used in this procedure. The filters were applied in the axial (z) direction and, separately, in the transaxial (x) direction for comparison. Each attenuation factor from the smoothed data was inverted to form a set of smoothed attenuation correction factors. Finally, for each case, the ratios F= [G(ACF-'$ ACF 0-7803-5696-9/00/$10.00 (c) 2000 IEEE 1245

Upload: tg

Post on 01-Mar-2017

212 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: [IEEE 1999 IEEE Nuclear Science Symposium. Conference Record. 1999 IEEE Nuclear Science Symposium and Medical Imaging Conference - Seattle, WA, USA (24-30 Oct. 1999)] 1999 IEEE Nuclear

Effects of Axial Transmission Resolution in PET]

C.M. Laymon and T.G. Turkington Department of Radiology, Duke University Medical Center, Durham, NC 27710

Abstract The effects of the axial resolution of transmission

projection data for use in PET attenuation correction is an important consideration for developing smoothing schemes for noise reduction and for the design of transmission systems. PET transmission data from five patient scans were used in conjunction with simulated uniform emission data to quantify some effects and to compare them to the effects of transaxial transmission smoothing. PET patient emission data were also corrected for attenuation using transmission projection data that had been smoothed axially or transaxially by various amounts. Results from the uniform emission studies show that the effects of axial transmission smoothing are always less than are those of transaxial smoothing. For example, within a volume that included the lungs, 50% of the voxels are inaccurate by more than 20% with a transmission axial filtering width of about 7 cm. For transaxial smoothing, the same level of inaccuracy is reached with a filter width of about 3 cm.

I. INTRODUCTION In positron emission tomography (PET), an exact

correction for attenuation can be made by multiplying the emission count rate measured along each projection line of response (LOR) by an attenuation correction factor (ACF). The ACF is the inverse of the total attenuation factor along that line of response. Attenuation factors are often determined by transmission measurements using an external radiation source. Application of measured ACF's can degrade the final corrected image through the introduction of noise and because of imperfect system resolution. Additionally amelioration of transmission noise through filtering further degrades the resolution of transmission data.

To avoid resolution artifacts, it is desirable to match transmission and emission resolution [l], [2]. An exception to this is the case where the object being scanned exhibits some symmetry that can be exploited. For example, the image of a uniformly attenuating cylinder oriented parallel to the scanner axis is invariant with respect to the axial resolution scale. In such a case, transmission data can be smoothed axially to an arbitrary degree and applied to emission data without degrading the final image. In this case, the exploited symmetry is the cylinder's invariance under axial translation.

Given that the human body exhibits relatively large local regions that exhibit this same symmetry, the question arises as to what level of axial resolution, unmatched in the emission data, can be tolerated in transmission data used for

lFunded by ElGems Inc, Haifa, Israel and in part by The Whitaker Foundation.

attenuation correction. Such information is valuable for deciding on the acceptable noise levels in transmission data so that the total time available for a complete patient scan can be used optimally. Additionally, it is important for optimizing the design of a transmission system.

The details of the design of a transmission system can affect its axial resolution much more severely than the transaxial resolution. For example, a transmission system for gamma-camera based PET using multiple point sources has recently been described [3]. Its transaxial resolution is determined by the gamma camera while the axial resolution depends on the point-source collimation. While the axial resolution of the system is easily adjustable, less stringent axial resolution requirements allow a more efficient use of radioactivity resulting in lower total system cost and possibly less exposure to personnel.

In this work we present simulated and patient data with the goal of determining some of the effects of axial smoothing. In some cases the results are compared with the effects of smoothing transmission data transaxially. Although we present patient data containing lesions, this is not a study of lesion detectability.

11. METHODS Transmission axial resolution effects were evaluated by

using existing clinical PET data [4]. Five studies representing a variety of body types were selected. Each PET data set consisted of an attenuation corrected emission image and an attenuation map from transmission data. The pixel size was 3.5 mm transaxially and 4.25 mm axially and 140 slices were used in each case.

A. Simulated Transmission Data The 140 transaxial slices from each patient attenuation

coefficient map were forward projected (2D) into 128 transaxial bins at each of 90 angles spanning the 180" domain appropriate for use with coincidence data. These values were converted to attenuation factors, which represent the reduction of coincidence events due to attenuation. Various degrees of resolution were simulated by smoothing the attenuation factors. Gaussian filters with full widths at half maximum (FWHMs) ranging from 0.5 to 16 cm were used in this procedure. The filters were applied in the axial (z) direction and, separately, in the transaxial (x) direction for comparison. Each attenuation factor from the smoothed data was inverted to form a set of smoothed attenuation correction factors. Finally, for each case, the ratios

F = [G(ACF-'$ ACF

0-7803-5696-9/00/$10.00 (c) 2000 IEEE 1245

Page 2: [IEEE 1999 IEEE Nuclear Science Symposium. Conference Record. 1999 IEEE Nuclear Science Symposium and Medical Imaging Conference - Seattle, WA, USA (24-30 Oct. 1999)] 1999 IEEE Nuclear

were calculated for all projection pixels. In Equation (1) G represents the Gaussian filtering operation. Smoothing is performed on the inverse of the ACF’s (the AF’s) since it is those values that are proportional to the physically measured quantities. The object F can be considered an operator that, when applied (via multiplication) to the corresponding bin from forward projected emission data, removes the ideal attenuation correction based on the starting attenuation map and replaces it with the attenuation correction generated from the smoothing procedure.

Since the starting point for this procedure was clinical patient data, the attenuation maps contained transmission noise and differences between smoothed and unsmoothed projections show the effects of noise reduction as well as resolution degradation. Therefore, another set of F-values was calculated similarly but using segmented attenuation maps as a starting point. These were produced by assigning each voxel one of three values corresponding to no attenuation, lung tissue, or soft tissue. The lung and soft tissue values were obtained by taking average values from regions within the PET images. The voxel-value assignments in the segmented images were made by a simple mapping of voxel values in the original PET attenuation image to the new values. All voxels falling outside of an empirically determined body boundary were forced to have values of zero.

B. Uniform Emission Studies Uniform emission maps were generated for each of the

PET studies by assigning a constant value to each voxel within the body boundary determined from the transmission data. Voxels external to the boundary were assigned values of zero. The images were forward projected into bins that matched those used to process the transmission data. The values of F for various degrees of axial or transaxial resolution were used to multiply the uniform emission projection data. The results were reconstructed by filtered backprojection (FBP), producing a series of images simulating the effects of various transmission scenarios on attenuation correction in images of uniform objects.

The uniform emission studies employing F-values from the segmented attenuation maps were used to extract quantitative results. The corrected images were first normalized by dividing each voxel in the image by the corresponding voxel in an image formed by forward projecting and reconstructing the original uniform emission object, without application of the F-values. This procedure was followed to diminish the importance of artifacts of the projection and reconstruction procedure. Three volumetric regions of interest (ROI’s) were defined for each of the patient studies: a box shaped region within the abdomen that was the same in all five studies, a region that included all of the lungs and was similar but not identical among the five patients, and a whole-body region bounded by each patient’s outer contour. The RMS deviation of the voxel values within each ROI from the true values was calculated for each ROI for each transmission-smoothing scenario. In addition, for the lung ROI, the number of voxels that differed by more

than 2%, 5%, IO%, 20%, and 50% from the expected value of 1 were tallied.

C. Patient Emission Studies The PET attenuation corrected emission data were also

used in this work. Six artificial lesions were added to one patient’s PET image. The lesions were added by producing an image with spheres at the desired locations, each with a 2 pixel radius. This was used as a mask to extract small pieces of the PET emission image that were then smoothed by a 3D Gaussian filter with a 2-voxel FWHM. The resulting lesions were multiplied by a factor of 4 and added to the original image so that the lesions have a lesion-to-background contrast of approximately 4.

The effects of various degrees of axial and transaxial transmission resolution on an attenuation corrected patient emission image were simulated by forward projecting the emission data and multiplying by the various sets of F from the segmented transmission data. The resulting projections were reconstructed by FBP.

111. RESULTS The effects of smoothing transmission data can by seen

directly by examination of the F-images, which show the ratio of the ACF from smoothed transmission data to the true ACF. Figure 1 shows such images for anterior-posterior and for lateral lines of response for the cases of axial and transaxial filtering with a Gaussian of 4 cm FWHM. The top row contains F-images generated directly with PET data while the bottom row shows similar images but generated with the segmented transmission data. The effect of segmenting the image can be seen from the figure and is generally small. Less high-frequency structure can be seen in the segmented images due to the reduction of noise effects. The image segmentation also sharpens boundaries between regions.

Axial Transaxial

Figure 1: F values showing smoothing effect. Image pixel values are the ratio of ACF’s from smoothed transmission projection data to ACF’s from unsmoothed data. Images are shown for anterior poster and lateral LOR’S for axial and transaxial smoothing. Values for unsegmented (top row) and segmented (bottom row) data are shown.

Figure 1 illustrates some other points including the considerably different effects of axial versus transaxial

0-7803-5696-9/00/$10.00 (c) 2000 IEEE 1246

Page 3: [IEEE 1999 IEEE Nuclear Science Symposium. Conference Record. 1999 IEEE Nuclear Science Symposium and Medical Imaging Conference - Seattle, WA, USA (24-30 Oct. 1999)] 1999 IEEE Nuclear

transmission smoothing. The axially smoothed images exhibit less gross and fine structure. They also tend to have a smaller magnitude of pixel variation when crossing boundaries in the x-direction but greater in the axial direction. In both the axial and transaxial cases more structure and nonuniformity can be seen in F-values along the lateral LOR'S. This is a result of the greater attenuation and consequently, the greater differences in the attenuation factors along that direction.

produced with axially rather than transaxially smoothed transmission data.

We examine the effects of transmission smoothing on the lung ROI in more detail in Figure 4, which shows the fraction of voxels for all five patients that deviate from their correct values by more than various amounts. Results are displayed for axially (A) and transaxially (B) smoothed transmission data. The use of transaxially smoothed data produces images with a greater fraction of voxels exceeding

t 0 cn cn .-

.-

E C

I- 2

0.5 1 2 4 8 16

Figure 2: Uniform emission data corrected with axial (top row) and transaxial (bottom row) smoothed transmission data. The Gaussian filter width used for the filtering is shown below each column.

The results of applying the F-factors from segmented transmission data to simulated uniform emission data are shown in Figure 2. Results are presented for the six Gaussian-filter widths ranging form 0.5 to 16 cm. The top row was produced from axially smoothed transmission data whilst the bottom is from transaxial smoothing. The use of the 0.5 cm filter leads to almost unobservable effects in the axial case and only small ones in the transaxial case. In the axial case the effect of transmission smoothing on the lungs is mainly to outline them to varying degrees up through the 2-cm image. In the 4-cm image variations are starting to expand away from the boundaries. The effects become more pronounced with increasing filter width. The transaxially filtered images in Figure 2 appear significantly different than the axial images. In particular, the lung area deteriorates more rapidly with increasing filter width. In general, at any given filter width, the images from the transaxially filtered data appear to deviate more from the ideal uniform image. The strong structure seen in the middle right of the images of Figure 2 is from intestinal gas bubbles.

Some properties of the images shown in Figure 2 are summarized by the plots displayed in Figure 3 that show the RMS voxel deviation from the ideal value for the combined set of data from 5 patients. Plots are shown for axially and transaxially smoothed transmission data for the lung, abdomen, and whole body ROI's. A comparison of the plots shows that the deviation is much smaller in the case of the abdomen than the lungs. For each ROI it is always the case that the RMS deviation is less for the uniformity images

any given error limit than does the use of axially smoothed data. For example, with 4 cm filter applied to the transmission data in the axial direction, about 1/3 of the counts in the corrected emission image of a uniform object are incorrect by more than 20%. In the results from transaxial smoothing, about 62% of the counts exceed this limit.

Figure 5 shows the reference coronal emission image from patient data from which the images shown in Figure 6 were obtained by application of different transmission smoothing scenarios. Figure 6 shows images from axially (top row) and transaxially (bottom row) smoothed data. Little degradation of the images is observed for small filter widths although some outlining of the lungs can be seen. Some increased distortion can be seen starting at about 2 to 4 cm in both images. These include increased size of the boundary region of the lung and brightening of regions within the lung.

One of the artificial lesions, indicated by the arrow in Figure 5 was placed near the intersection of a horizontal and vertical boundary surface in the lung. The lesion merges into the lung walls with increasing filter width (Figure 6). In this particular case there appears to be faster degradation in the case of the transaxially applied transmission' smoothing.

0-7803-5696-9/00/$10.00 (c) 2000 IEEE 1247

Page 4: [IEEE 1999 IEEE Nuclear Science Symposium. Conference Record. 1999 IEEE Nuclear Science Symposium and Medical Imaging Conference - Seattle, WA, USA (24-30 Oct. 1999)] 1999 IEEE Nuclear

0.8 1 I

0.7

.- 5 0.6

E 0.5 p 0.4 03

0.2

0 1

0

0 .- 5 p:

0.8

0.7

'0 0.6 5 8 3 0.4 f 03 E = 0.2

0.1

0 0 5 10 15

Filter FWHM [cm]

Figure 3: Plots of emission image voxel deviation within the lung and abdomen ROI's (a) and for the whole body (b) for all 5 patients as a function of axial or transaxial transmission filter width

IV. DISCUSSION We have observed a rough scaling phenomenon in this

work. Filtering transmission data transaxially degrades the corrected emission images about the same amount as axially filtering with a width of somewhat greater than twice the axial width. This can be observed in the RMS deviation plots for the lung and whole body. If the FWHM values for the axially filtered results were to be replaced by twice their values and the results plotted, the curve would lie much closer to the transaxial plot than does the original. Although the nature of the effects of the two transmission smoothing scenarios is different, this result can be observed qualitatively in the lung region and the gas bubble artifacts of the uniform reconstructions of Figure 2.

The scaling phenomenon is not apparent in the more complicated patient data shown in Figure 6. In fact, it is difficult to say, especially for the smaller filter widths, if one smoothing scenario results in better images than the other. While some aspects of the images degrade more slowly with axial' transmission smoothing than transaxial, a counterexample is the dome of the liver on the left side of the patient images. Because this is a large horizontal surface bordering on a region of much lower attenuation, it tends to be strongly affected by axial smoothing.

An attenuation feature that can cause potentially serious artifacts in both the axial and transaxial smoothing cases is gas bubbles as can be observed in the uniform activity

studies. Such artifacts may be troublesome because they appear as compact hot spots that resemble lesions. The segmentation method that we employed to produce noisefree attenuation maps tends to exaggerate this effect.

1

0 9

O B

4 0 7 p 0 6

5 0 5

0.2

0.1

- 0.5 :::;k 0.2 0 1 0 0 5 10 15

FWHM (em]

Figure 4: Fraction of emission image voxels in the lung ROI for all 5 patients with errors exceeding specified limits as a function of filter width for axially (a) and transaxially (b) smoothed

Figure 5: Reference patient emission image with no transmission smoothing. Coronal slice thickness for this image is 1.8 cm. The arrow points to on of the artificial lesions.

Determination of the amount of axial transmission blurring that is acceptable is beyond the scope of this work and is likely to depend on several factors, including the statistical and resolution properties of the emission data and the goals of a particular study. Results from the current study can provide some guidance. Any smoothing of the transmission data immediately causes some degradation of the reconstructed voxel-value accuracy at some level. For example, in the axial case, about 50% of the voxels have inaccuracies of more than 5% with 1 cm smoothing. Obviously, less stringent tolerances allow greater smoothing. For example, 50% of the voxels are inaccurate by more than 20% with a filtering of about 7 cm, interpolated from this work. For transaxial smoothing, the same tolerances allow much less blurring in the cases studied here (about '/z cm or 3 cm for the two tolerances defined above).

0-7803-5696-9/00/$10.00 (c) 2000 IEEE 1248

Page 5: [IEEE 1999 IEEE Nuclear Science Symposium. Conference Record. 1999 IEEE Nuclear Science Symposium and Medical Imaging Conference - Seattle, WA, USA (24-30 Oct. 1999)] 1999 IEEE Nuclear

0.5 1 2 4 8 16 FWHM [cm]

Figure 6: Reconstruction of patient data using axial or transaxially smoothed transmission data. The value underneath each column is the FWHM value of the Gaussian filter used to smooth the transmission projection data. The reference image obtained without smoothing the transmission data is shown in Figure 5.

V. CONCLUSION Axially smoothed transmission data has a less deleterious

effect than transaxially smoothed data on attenuation corrected emission images as measured by the RMS voxel deviation and by the total number of voxels exceeding various error tolerances for the uniform activity distributions used in this work. The difference is observable in the uniform activity reconstructions themselves but is not readily apparent for small smoothing filter widths in the more complicated patient data. Results suggest that axial resolution requirements for transmission systems for attenuation correction of PET data may be substantially less stringent than the requirements for transaxial resolution. Alternatively, it may be possible to improve the noise properties of transmission data by smoothing in the axial direction.

REFERENCES [ l ] S.C. Huang, E.J, Hoffman, M.E. Phelps, D.E. Kuhl,

“Quantitaition in Positron Emission Tomography: 2. Effects of Inaccurate Attenuation Correction, ” J . Comput. Assist. Tomogr, vol. 3, pp. 804-814, 1979

[2] A. Chatziioannou and M. Dahlbom, “Detailed Investigation of Transmission and Emission Data Smoothing Protocols and Their Effects on Emission Images,” IEEE Trans. Nucl. Sci., vol. 43, pp. 290-294, 1996.

[3] C.M. Laymon, T.G. Turkington, D.R. Gilland, R.E. Coleman. “Transmission Scanning System fo a Gamma- Camera Coincidence Scanner,” J. Nucl. Med., in press.

.[4] Advance PET scanner is manufactured by General Electric Inc., Milwaukee, WI.

0-7803-5696-9/00/$10.00 (c) 2000 IEEE 1249