Ming-Wei Lee 1, Wei-Tso Lin 1, Yu-Ching Ni 2, Meei-Ling Jan 2, Yi-Chun Chen 1 * National Central University

Transcription

1 Rapid Constructions of Circular-Orbit Pinhole SPECT Iaging Syste Matrices by Gaussian Interpolation Method Cobined with Geoetric Paraeter Estiations (GIMGPE Ming-Wei Lee, Wei-Tso Lin, Yu-Ching Ni, Meei-Ling Jan, Yi-Chun Chen *., National Central University, Taiwan.. Institute of Nuclear Energy Research, Taiwan.

2 Outline Interpolation of Iaging Syste Matrices Procedures of GIMGPE Siplified Grid-Scan Experient Iage Paraeterization Iaging Properties Database Projection Centroids Model Gaussian Coefficients Estiation Results OSEM Reconstructions of a Derenzo Phanto Detectability of SKE/BKE Tasks Conclusion

3 Iaging Syste Matrix Linear Digital-Iaging Syste: g Iage, Discrete, pixel g = Hf + n. H Iaging Syste Matrix, Discrete, voxel-into-pixel f Object, Discrete, voxel n Noise Vector. 3. Cobination. Measureent. Siulation H = [H detector H geo ] A 3

4 Interpolation of Iaging Syste Matrices The interpolation of H atrix was firstly proposed by Rowe et al. []. Coarse-Grid point-source caera pinhole H = R + B R: Total counts & centroid locations B: Blur functions on the caera A finer-grid H atrix can be interpolated. R is a slowly varying function of point-source locations. B is a function of centroid locations. [] R. K. Rowe et al., Journal of Nuclear Medicine, vol. 34, no. 3, pp ,

5 Fro Stationary to Circular Orbit Previously, the proposed GIMGPE has tested with FASTSPECT II []. X-SPECT Syste:. Dual- Headed Gaa Caera, Caera # Discrete NaI(Tl Crystal Array. Caera # Spherical FOV (Dia f: 9 Pinhole Diaeter:.5 d: 33.5 d: 33.5 [] M.-W. Lee and Y.-C. Chen, 0 IEEE NSS/MIC Conference Record, pp , 0. 5

6 Siplified Grid-Scan Experient A siplified grid-scan pattern contains The boundary of Field-of-View, and Three inner planes that are parallel to the caera plane. Reducing ~75% voxels of a full 3D grid-scan pattern at 0 projection angle 6

7 Iage Paraeterization Circular Gaussian Function A ( uuc ( vvc hi ( u, v exp[ ], A:Aplitude, u c and v c : Centroid coordinates, :Standard deviation. Photon Counts: ~ 6000 (counts Projection of a point source stepped on a voxel within the FOV of a pinhole SPECT syste. 7

8 Circular Orbit Pinhole SPECT Syste d (x p - x o (y p - y o (z p - z o (, f (x p - u c (y - v (z - z D = f + d and M = f / d. p c p i (, Pinhole Projection Iage Object Space y z: rotation axis (x o, y o, z o x θ d Pinhole (x p, y p, z p f (u c, v c pixels Iage Plane (u c, v c, z i 8

9 Aplitude (D around the sae pixel Ap x Iage Plane (x-pixel, y-pixel (0, D (5,5 (9, (9, (0,50 (43, Ap. (/ Distance

10 σ(m around the sae pixel.5. σ Iage Plane (x-pixel, y-pixel (0, M.3.. (5,5 (9, (9, (0,50 (43, Magnificat ion

11 Iaging Properties Database Fitting the iaging property curves: 4th-order Laurent polynoial for Aplitude(D. Linear function for σ(m. Aplitude( D a b 3 c d, D D D ( M a M b, where denotes the -th pixel.

12 Iaging Properties Database A full iaging properties database has [58 58 (4+] eleents: fitting coefficients of Ap.(D and σ(m curves..5 x 04 Aplitude (counts Experient Data Estiation Data Ap.(D Standard Deviation (pixels Experient Data Estiation Data σ(m Distance (D, d+f Magnification (M, f/d

13 Projection Centroids Model ig ig Projection centroids are calculated as ( u, v, where is the projection angle. ig cos x(,, u f cos e d y(,, ig sin z(,, v f sin e d y(,, u v Geoetry of a pinhole SPECT iaging syste [3]. This projection odel is proposed by D. Beque et al [3]. [3] D. Beque et al, IEEE Trans. Med. Iag., vol. 4, pp ,

14 Procedure of GIMGPE Geoetrical Calibration Projection Centroids Model Siplified Grid-Scan Experient Iage Paraeterization Iaging Properties Database: Ap.(D and σ(m 6 projection angles θ: 0 ~ Rotate the Object Space at θ projection angle H θ Estiate the Projection Centroids of each voxel Calculate the Blur Functions with the corresponding projection centroids, D and M of each voxel 4

15 Configuration of Derenzo Phanto Rod diaeter:.7,.3, and 3.4 ( Caera # 7.4 f: 9 Rod length: 5. Caera # d: 33.5 pinhole Derenzo Phanto Spherical FOV (Dia

16 OSEM Reconstruction of a Derenzo Phanto - grid spacing Display scale: [0% ax - 90% ax] st -9 th Slice Full 3D Grid-Scan Experient GIMGPE 6

17 OSEM Reconstruction of a Derenzo Phanto - grid spacing GIM[4] Display scale: [0-90% ax] 3 th -7 th Slice GIMGPE [4] Y. C. Chen et al, in Sall-Anial SPECT Iaging, M. A. Kupinski and H. H. Barrett eds., Springer New York, pp. 95-0, June

18 Line Profile of One Slice grid spacing 4 Full 3D Grid-Scan Experient GIMGPE th Slice Aplitude (counts The voxel on the cross line 8

19 Line Profile of One Slice grid spacing GIM GIMGPE 0th Slice Aplitude (counts The voxel on the cross line 9

20 0 Detectability M A M M g s d SNR g g g g g g g g SNR ( low - contrast signal, consider a If. ln ( ln (, ] ( ( [ present : (signal H, ( absent : H (signal n s b n r f r H f g n b n r Hf g s b b Ideal Observer

21 SKE/BKE Tasks Detectability Estiation: 7 Unifor Sphere Phanto Against a Flat Background Noise, 8 Contrast (A S /A B : [0.0; 0.0; 0.05; 0.0; 0.0; 0.50;.00;.00]. R+R/4 y y R R R = 8 R/ R x R R+R/ R z

22 Detectability Perforance : Full 3D Grid-Scan Experient SNR ax( *: GIMGPE - grid spacing GIMGPE SNR -SNR Grid-Scan Grid-Scan 00.6% SNR Contrast (A S /A B, 5 4, 7 3, 6 SNR Contrast (A S /A B, 5 4, 7 3, 6

23 Detectability Perforance : GIM *: GIMGPE SNR ax( - grid spacing GIMGPE SNR -SNR GIM GIM % 80 70, , 5 SNR Contrast (A S /A B 4, 7 3, 6 SNR Contrast (A S /A B 4, 7 3, 6 3

24 Conclusion The preliinary evaluation of GIMGPE ethod shortens the easureent tie of a full.0- grid H atrix about 64 ties and a full.0- grid H atrix about 5 ties. The OSEM reconstructed iages of a Derenzo phanto with the interpolated H atrices show coparable resolution and siilar line profiles as that reconstructed with the full 3D grid-scan H atrix and the GIM finer-grid H atrix. The SKE/BKE detection tasks deonstrate the interpolated H atrices have the sae detectability level as the full 3D grid-scan H atrix and the finer-grid GIM H atrix. Based on the GIMGPE ethod, further interpolations of the H atrix to uch finer spacing and ore projection angles could be easily done. 4

25 Acknowledgeent This work was supported in part by National Science Council Grant NSC 0--E and Institute of Nuclear Energy Research, Taiwan.