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An Attenuation Correction Method for RespiratoryGated PET CT Image by jmeltzer


									   An Attenuation Correction Method for Respiratory-
                 Gated PET/CT Image
       Tomohiro Yamazaki, Hidenori Ue, Hideaki Haneishi, Akira Hirayama, Takashi Sato and Shigeru Nawano

    Abstract– Previously we have proposed a motion correction                    Recently, a system combining PET and CT has commercially
method for avoiding both motion blur and image noise in                        been available. Such a system is called PET/CT system and is
respiratory-gated lung SPECT images [1][2]. In a PET/CT                        coming into wide use. The first advantage of the PET/CT is
system, attenuation correction can be achieved by making an                    that it provides a fused image of anatomical information given
attenuation map from a CT image. In PET/CT system using                        by CT and physiological information given by PET with ease.
respiratory-gated PET, however, when a CT image acquired
                                                                               The second advantage is that an attenuation coefficient map
under a breath-hold condition is used for attenuation correction
of PET in different respiratory phase, voxel values of the                     obtained from CT image can be used in the attenuation
reconstructed PET image may be incorrect, especially in a region               correction (AC) of PET through a proper transformation of
that has large respiratory motion. In this paper, we propose an                attenuation coefficient. It results in the omission of the
attenuation correction method for this case. The effectiveness of              conventional transmission scan for PET. Furthermore the use
the proposed method was tested using the 4D-NCAT phantoms                      of the CT image with less static noise can reduce noise of
[3] and a marked stability in the voxel values around the                      reconstructed PET image [6].
diaphragm was observed. The proposed method was also applied                     In this paper, we consider the case that the RGPET imaging
to clinical data.                                                              is carried out in a PET/CT system. In a normal PET/CT
                                                                               system a breath-hold CT image is used for AC of PET. Since
                          I. INTRODUCTION                                      the normal PET yields an averaged image during many

Anormal PET scan takesmany respiratory cycles in time
 than CT and includes
                       much longer acquisition
                                                                               respiration cycles, a breath hold CT image does not
                                                                               necessarily correspond to the averaged PET data. Especially
scan data. The motion of organs during the PET scan makes                      in the region of large motion a large error can occur [7][8]. An
reconstructed image blurred. To overcome this problem,                         attenuation correction in PET with high accuracy requires a
respiratory-gated (RG) PET is under study. In a RGPET                          set of respiratory-gated CT corresponding to a set of RGPET.
system, patient’s respiration cycles are monitored by a proper                 However, introduction of respiratory-gated CT image
sensor and each cycle is segmented into some respiratory                       acquisition would increase the radiation dose to patient.
phases. Coincidence gamma counts acquired in each segment                        In this paper, we propose to generate a set of respiratory-
are used to reconstruct a PET image in the corresponding                       gated CT images artificially from a single phase CT by the
respiratory phase. As a result, those reconstructed images have                nonlinear motion correction method that we have previously
less motion-blur [4][5]. However, because detected counts of                   proposed. We applied the proposed method to a computer
gamma rays are distributed into each phase image, a long                       phantom and clinical data.
acquisition time is required for accumulating sufficient counts
at each phase image. Unless the acquisition time is sufficiently
long, detected counts become inadequately small; hence, the                                             II. METHOD
reconstructed image becomes noisy.                                             A. Processing flow
 To prevent this problem, previously we proposed a nonlinear                    Our strategy for obtaining a high quality PET image
motion correction method to sum up a set of images of                          including the proposed AC method is shown in Fig. 1. Let us
respiratory-gated SPECT. Summed image with motion                              assume that we obtain a set of RGPET raw data and a breath-
correction can reduce both blur due to respiratory motion and                  hold CT image in a certain phase (e.g., end-expiration). Those
noise due to lack of detected counts. The proposed method                      given data and the image are indicated by squares with round
                                                                               corners and the processing is indicated by square with angular
can directly be applied to RGPET.
                                                                               corners in Fig. 1. Data processing is performed according to
                                                                               the following steps.
   Manuscript received November 17, 2006. This research was partially          Step 1: The CT image corresponds to the phase #i PET image.
supported by the Ministry of Education, Science, Sports and Culture, Grant-    At first, PET images are reconstructed without attenuation
in-Aid for Scientific Research on Priority Areas, No. 16035203 in 2004 and
No. 17032002 in 2005-2006.
   T. Yamazaki and H. Ue are with Graduate School of Science and               Step 2: The motion of each phase PET image from the PET
Technology, Chiba University, Chiba, 263-8522, Japan.                          image in the same phase as the CT acquisition timing is
   H. Haneishi is with the Research Center for Frontier Medical Engineering,   estimated by the motion correction.
Chiba University, Chiba, 263-8522, Japan. He is also with Graduate School of   Step 3: A CT image corresponding to each respiration phase is
Science and Technology, Chiba University, Chiba, 263-8522, Japan (e-mail:      generated from the original CT image by deforming according
                                                                               to the motion vector field (MVF).
   A. Hirayama is with GE Yokogawa medical systems.
   T. Sato and S. Nawano are with the National Cancer Center Hospital East,
              Step1                                               Step2                                                                       Step3

                                                                              Motion        Motion vector
              PET                                                             correction     field (MVF)                                                             Attenuation
                                                                PET image                                                                  CT image
            raw data                                                                        Ph. i →Ph. 1                                                                 map
                                                                 phase #1                                                                  phase #1

                             (without attenuation correction)
            phase #1                                                                                                                                                  phase #1

               PET                                                                                                                           original                Attenuation
                                                                PET image
             raw data                                                                                                                       CT image                     map
                                                                 phase #i
             phase #i                                                                                                                     (Breath-hold)               phase #i

              PET                                                                                                                                                   Attenuation
                                                                PET image                                                                  CT image
            raw data                                                                                                                                                    map
                                                                 phase #N                   Motion vector                                  phase #N
            phase #N                                                         Motion                                                                                  phase #N
                                                                             correction      field (MVF)
                                                                                            Ph. i →Ph. N

                                                                                     Attenuation correction

                                                                PET image                    PET image                         PET image
                                                                 phase #1                     phase #i                          phase #N

                                                                 Motion                                                          Motion
                                                                correction                                                      correction

                                                                                              PET final

Fig. 1. Processing flow of RGPET images in PET/CT system. In this figure, squares with round corner represent data and squares with angular corners represent
                                                                                                             E1 = ∑ { f ref (ri ) − f def (ri + Δri )}2                                   (1)
Step 4: Attenuation correction is applied to RGPET raw data                                               where R and Δri denotes the region of deformation and the
using the AC maps obtained in Step 3. Then RGPET images
are reconstructed.                                                                                        motion vector at position ri . The smoothness of deformation,
Step 5: The motion correction and summation technique is                                                  E2, is given by
applied to the reconstructed RGPET images and a final high                                                   E2 = ∑ ∑ uij + ∑ ∑ vij + ∑ ∑ wij
                                                                                                                            2              2            2
quality PET image is obtained.                                                                                     i=x, y ,z j= x, y ,z    i= x, y ,z j=x, y,z   i= x, y ,z j = x, y ,z

                                                                                                          where u , v and w denote the amount of movements in x, y
B. Motion correction
 The motion correction technique is shortly reviewed in this                                              and z directions at each location of the motion field,
subsection [2]. In this method, the motion correction is                                                  respectively. In this equation, simple notations such as
accomplished by fitting one phase image to another phase                                                   ∂ 2u / ∂x 2 = u xx are used.
image. The image to be deformed is called floating image and                                                  While E1 works so as to make the floating image agree
another image is called reference image. The MVF is defined                                               with the reference image, E2 works so that a smoother motion
by a rectangular parallelepiped that contains the extracted                                               is selected preferably. By combining E1 and E2, the total
lung region of each phase image and motion vectors are                                                    objective function is given by
given at many control points inside the rectangular                                                           Etotal = αE1 + E2            (3)
parallelepiped. By moving every control points, the floating
image is deformed. The objective function consisting of both                                              where α is a constant for adjusting the balance of two
the degree of similarity between a reference and a deformed                                               objective functions, and is determined empirically. The
image, and the smoothness of deformation is defined and                                                   objective function is optimized using a simulated annealing
optimized.                                                                                                algorithm and the floating image is deformed. Simulated
   Denoting the reference image by f ref (r ) and the deformed                                            annealing is a robust optimization algorithm and it cannot be
                                                                                                          easily affected by local minima. Moreover, the
image by f def (r ) where r = ( x, y, z ) , the degree of similarity                                      implementation of the algorithm is relatively easy.
between a reference and a deformed image, E1, is given by
A. Way of simulation
   The four-dimensional NURBS-based cardiac-torso
(NCAT) phantom was used [3]. The NCAT phantom was
developed to provide a realistic model of the human anatomy
and physiology to be used for nuclear imaging research. Fig.
2 shows a coronal slice image of the NCAT phantom. The                                                              (a)                (b)
voxel size of this data is 6.4 x 6.4 x 6.4 mm. In the section D,
some lesions were added to the original noise-free image as
indicated by arrows. The size of the lesions is one voxel. In
this experiment, the heartbeat motion was not included in the
phantom data. NCAT phantom images in eight different
respiratory phases were generated in the above described
manner and regarded as ideal RGPET images. On the other
hand, as a breath-hold CT image acquisition, a CT image                                                             (c)                (d)
was generated under end-expiration. We added noise onto
                                                                             Fig. 3 Examples of images with different noise levels. (a) is the original
the PET projection data based on clinical data.
                                                                             image. (b), (c) and (d) represent the images with 0.098, 0.300, and 0.503 of
   PET and CT images are reconstructed by the filtered back
                                                                             coefficient of variation, respectively.
projection (FBP). A ramp filter was used in the FBP.

                                                                                correlation coefficient

                                                                                                                    No motion correction



                                                                                                                0    0.1   0.2   0.3         0.4   0.5   0.6
 Fig. 2. The NCAT phantom with radio activities used for computer                                                                CV
simulation. White dots indicated by arrows represent simulated hot lesions
                                                                             Fig. 4 Correlation coefficient between the original image and the motion-
used in the section D.
                                                                             corrected images. In a wide range of noise level, high values of correlation
                                                                             coefficient are obtained.
B. Accuracy of motion correction
  The accuracy of motion correction from RGPET images
without attenuation correction was first validated. Although                 C. Quantitative evaluation of the proposed method
the direct evaluation of the estimated MVF is ideal, the true                   In this paper, we compare three cases of the attenuation
MVF generated from the NCAT phantom was not available.                       correction. The reconstruction of end-inspiration PET image
Thus, the following alternative way of evaluation was used.                  was evaluated. Case 1 is that respiratory-gated CT images are
Using the estimated MVF, the noise-free activity distribution                obtained perfectly corresponding to RGPET data and those
is deformed. The degree of similarity of such a deformed                     CT images are used for AC of the corresponding RGPET
distribution and the target distribution (noise-free activity                data. We call this case “ideal”. Case 2 is that a breath-hold
distribution in the target respiratory phase) is evaluated by a              CT image is acquired under end-expiration and that CT
correlation coefficient (CC) between those two images. When                  image is used for AC for RGPET data without motion
those two images match perfectly, the CC becomes unity and                   correction. We call this case “mismatch”. Case 3 is that a
when the matching becomes worse, the correlation                             breath-hold CT image is acquired under end-expiration as
coefficient becomes smaller. This measure approximately                      Case 2 but that CT image is first deformed using MVF
gives the similarity between the true MVF and the estimated                  derived from RGPET images reconstructed without AC so as
MVF.                                                                         to match to end-inspiration phase image and used for AC for
  In order to see the robustness of the motion correction                    RGPET data. We call this case “proposed”.
technique, a wide range of noise was examined. Noise level                       The results of attenuation correction are shown in Fig. 5.
was indicated by coefficient of variation (CV) in the liver.                 In the mismatch case, large error was seen. This error was
CV is defined by the standard deviation divided by mean.                     brought by misalignment between the PET image and the CT
Four images with different noise levels are shown in Fig. 3.                 image. On the other hand, this error disappears in the
Fig. 4 shows calculated CC, which includes an arrow                          proposed case. To compare quantitatively, relative error was
indicating CC (0.833) without motion correction. From the                    calculated in the ROI (Region of interest) of the axial image.
result, we find the proposed method performs successfully                    Relative error was defined by
and is highly robust.
                             f −f
   Relative error [%] =               × 100                 (4)
                              f max
where f max , f and f denote the maximum value in the
true image, the mean of the reconstructed image in the ROI
and the mean of true image in the ROI. From Table I, the                                          (a) Image in a single phase
proposed method was effective quantitatively. Especially in
the top region of the liver (ROI B), the effectiveness of the
proposed method is marked.

                                                                                         (b) Summed image without motion correction



                                                                                           (c) Summed image with motion correction
                                              Large error
                                                                              Fig. 6. Images of colonal (left column) and sugittal slice (right column). (a)
                                                                              represents images in a single phase. (b) represents summed images without
                                                                              motion correction. (c) represents the images after motion correction and
                       B                                                      summation

                                                                                        IV. APPLICATION TO CLINICAL DATA
                                                                                The proposed method was applied to three sets of clinical
                                                                              data obtained by a PET/CT (GE, Discovery-SL). PET data
                                                                              were obtained under quiet breathing using respiratory-gated
                                                                              system. The matrix size of these data was 128 x 128 x 35
                       B                                                      voxels, with a voxel size of 3.91 x 3.91 x 4.25 mm. The
                                                                              radiolabeled reagent used is fluorine deoxyglucose (FDG).
                                      (c)                                     The breath-hold CT image was obtained under end-expiration
                                                                              condition. The matrix size was 512 x 512 x 35 voxels, with a
Fig. 5. Images of axial (left column) and coronal slice (right column). (a)   voxel size of 0.98 x 0.98 x 4.25. CT image was rescaled to
represents the ideally attenuation-corrected image. (b) represents the        the size same as PET.
mismatch case. (c) represents the proposed method.
                                                                               We examined the effect of the attenuation correction of end-
                                                                              inspiration PET image as the computer simulation described
                                                                              in III C. Fig.7 shows coronal slice of reconstructed PET
Relative error evaluated in ROIs.
                                                                              images. Fig. 7(a) represents the mismatch case where the
  ROI                           Relative error[%]                             original CT image was used for AC of end-inspiration PET as
                   Case 1             Case 2        Case 3                    it was. Fig. 7(b) represents the result of the proposed method.
                   (ideal)          (mismatch     (proposed)                  It can be observed that the edge of the liver becomes sharper
                                          )                                   in (b).
    A                 7.1               10.7         10.0                       Fig. 8 shows the profile along the line shown in Fig. 7. In
    B                 0.8               31.6          2.6                     this figure, the proposed method is drawn by a solid line and
                                                                              the mismatched case is drawn by a dashed line. The proposed
                                                                              method shows clearer density change in the region from lung
D. Effect of motion correction and summation                                  to liver.
 All eight phase images after applying the proposed AC were
motion-corrected and summed. The result is shown in Fig.
6(c). For comparison, images in a single phase and summed
images without motion correction are also presented in (a)
and (b) in the same figure. It is observed that noise is reduced                            (a)                                   (b)
in (b) and (c), and motion blur is further reduced in (c).                    Fig. 7. Result of attenuation correction. (a) represents mismatch case. (b) is
                                                                              applied proposed attenuation correction.
                                                                                                                   Hokins University for permitting the use of NCAT phantom
                                                                                                                   and for fruitful discussion.
       Voxel value

                                                                                                                   [1] Ue H, Haneishi H, Iwanaga H et al: Motion correction
                                                                                                                       for synthesis and analysis of respiratory-gated lung
                     1   3   5   7   9   11    13    15    17    19    21    23      25   27   29   31   33   35       SPECT image Proc. of SPIE. 5747: 1173-1180, 2005
                                              Head <-- Projection [voxel] --> Foot
                                                                                                                   [2] Ue H, Haneishi H, Iwanaga H et al: Nonlinear motion
                                                                                                                       correction of respiratory-gated lung SPECT images.
                                                                                                                       IEEE Trans Med Imaging 25: 486-495, 2006
Fig. 8. Intensity profile along the line in Fig. 7. The solid line and dashed                                      [3] Segars WP: Development and application of the new
line are corresponding to the proposed method and the mismatched case,                                                 dynamic NURBS-based cardiac-torso (NCAT) phantom,
respectively.                                                                                                          Ph D dissertation, The University of North Carolina,
   Finally we examined the effect of summation of all phase                                                        [4] Suga K. Technical and analytical advances in pulmonary
images. The proposed attenuation correction method was                                                                 ventilation SPECT with xenon-133 gas and Tc-99m-
applied to RGPET images. Two cases were tested same as III                                                             Technegas. Ann Nucl Med 2002; 16:303-10.
D, namely those images were summed up with motion                                                                  [5] Suga K, Kawakami Y, Zaki M, Yamashita T, Matsumoto
correction and without motion correction. The results are                                                              T, Matsunaga N. Pulmonary perfusion assessment with
shown in Fig. 9. By summing RGPET images, the resulting                                                                respiratory gated 99mTc macroaggregated albumin
image becomes less noisy as shown in (b) and (c).                                                                      SPECT: preliminary results.
Furthermore, by the motion correction the motion blur is                                                           [6] Kinahan PE, Townsend DW, Beyer T et al: Attenuation
reduced, which can be observed especially near the                                                                     correction for a combined 3D PET/CT scanner. Med
diaphragm.                                                                                                             phys 25:2046-2053 1998
                                                                                                                   [7] Osman MM, Cohade C, Nakamoto Y et al: Respiratory
                                                                                                                       motion artifacts on PET emission images obtained using
 (a)                                                                                                                   CT attenuation correction on PET-CT. Eur J Nucl Med
                                                                                                                       Mol Imaging 30:603-606
                                                                                                                   [8] Beyer T, Antoch G, Blodgett T et al: Dual-modality
                                                                                                                       PET/CT imaging: the effect of respiratory motion on
 (b)                                                                                                                   combined image quality in clinical oncology. Eur J Nucl
                                                                                                                       Med Mol Imaging 30:588-596, 2003.


Fig.9. Result of summation. (a) is image in a single phase. (b) is summed
image without motion correction. (c) is summed image with motion

                      V. CONCLUSION
 In this paper, we have proposed an attenuation correction
method for respiratory gated PET in which respiratory-gated
CT images were artificially generated from a real breath-hold
CT image using the previously proposed motion correction
technique. The proposed method was applied to both NCAT
phantom and clinical data and its effectiveness was proven.
Furthermore, it was also demonstrated that the respiratory
gated PET images with attenuation correction were motion-
corrected and summed to yield PET images with reduced
noise as well as less motion blur.

  Authors thank Suga and Iwanaga in Yamaguchi University
School of Medicine for helpful discussion. They also thank
WP Segars, BMW Tsui and their research group in Johns

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