1. Single Photon Emission Tomography
Physics CLRS 344
Single Photon Emission Tomography
SPECT

2. Anger Gamma Camera X Y
Positional Circuit Z
Gate
Output
Collimator

3. Collimators

4. Tomography Shows position and relationship of objects in 3D.
Planar Imaging
Resolution is depth dependent
Single Photon Emission Computed Tomography
Resolution is independent on depth
Resolution is inferior to Planar
Reconstruction magnifies noise
Signal-to-noise ratio is less than planar for the same number of acquired counts

5. Single Photon Emission Computed Tomography SPECT
Acquire multiple planar views

6. SPECT Acquisition Linear Sampling Angular Sampling
d  note: max is the max obs. frequency
(2max) Nyquist Frequency
Angular Sampling
Number of views = D/2d
D: Diameter of view
d: linear sampling distance

7. SPECT Acquisition Sampling Point Actual signal, 9 Hz
False signal, 1 Hz

8. SPECT Acquisition

9. SPECT Acquisition
Angular sampling
Minimum acquisition: 1800

10. Spatial Frequency Spacing (mm) Line pair (mm) 6 8 Freq (1/mm) 0.25
(# lines per unit distance)
Spacing (mm) 2 3 4
Line pair (mm) 6 8
Freq (1/mm)
0.25
0.167
0.125
Frequency
High
Low

11. Modulation Transfer Function
Low spatial Frequency
Counts
Pixel-distance
Counts
High spatial Frequency
Pixel-distance

12. Modulation Transfer Function
Low spatial Frequency
Counts
MTF= cout()/cin() = 1
Pixel-distance
High spatial Frequency
Counts
MTF= cout()/cin() = 0.33
Pixel-distance

13. Modulation Transfer Function
ideal
Collimator-source distance
MTF= cout()/cin()
2.5 cm
10 cm
Spatial Frequency (cm-1)

14. Spatial Frequency Spatial Domain Frequency Domain Amplitude Counts
pixel

15. Spatial Frequency
Frequency Domain
Amplitude
Frequency

16. Reconstruction Algorithms
Filter Backprojection
Easy to implement
Computational fast
Iterative reconstruction
Number of iterations: hard to determine
Computational intense

17. Reconstruction Algorithmsf1 f2 f3 f4 f5 f6 f7 f8 f9
g4=f1+f2+f3
g5=f4+f5+f6
g6=f7+f8+f9
Radon Equation
g3=f1+f4+f7
g2=f2+f5+f8
g1=f3+f6+f9

18. Reconstruction Algorithms
Radon Equation
g3+ g4 2
g2+ g4
g1+ g4
g3+ g5
g2+ g5
g1+ g5
g3+ g6
g2+ g6
g1+ g6 g4
Backprojection Operator g5
Filtered Backprojection g6 g3 g2 g1

19. Transverse Image 60 60 60 60

20. Backprojection 120 120 120 60 60 120 120 60 60 120 120 120 counts

21. Backprojection
120
120
counts 20 20 20 20 20 20 20 20 20 20 20 20

22. Backprojection
120
120
counts
counts 40 40
120 40 80 80 40 40 80 80 40
120 40 40
120 40 80 80 40 40 80 80 40
120 40 40 40 40
counts
120
120
counts

23. Backprojection 40 40 40 80 80 40 40 80 80 40 40 40 40 80 80 40 40 80 80 40 40 40 40 40

24. Backprojection 80 80 80

25. Ramp Backprojection 80 80 80 80 80 80 80
Amp
Spatial Freq.

26. Filter
High Freq
Noise
Resultant freq
Low Freq

27. Filter Cut-off frequency Nyquest Freq Spatial Freq. Smoothing function
Amp
Cut-off frequency
Nyquest Freq
Spatial Freq.
Smoothing function
Butterworth- Low Pass
Metz
Wiener
Parzen
Amp
Amp
Spatial Freq.
Spatial Freq.

28. Filter Backprojection
Amp
Amp X
Spatial Freq.
Spatial Freq.
Amp
Spatial Freq.

29. Filter Backprojection

30. Filter Backprojection

33. Filter Backprojection
standard
0.5 mCi
1.0 mCi
6.0 mCi

34. Iterative Reconstruction
 x
 x
 x
Recon Image
Initial

35. Iterative Reconstruction
 y
 y
 y
 y
 x
Recon Image
Initial

36. Iterative Reconstruction
 45
 45
 y
 45
 45
 x
Recon Image
Initial

37. Reconstruction Algorithms
Iterative Methods 10 6 5 11 7 9 8 8 3 4 7 2 5 3
3.5
4.5
6.5
1.5 8 8

38. standard
6mCi/FBP
6mCi/Iterative

39. Reconstruction Algorithms
Scan Time
7 min
5 min
3 min
Filtered
Backprojection
Iterative
Reconstruction

40. Reconstruction Algorithms
Filtered
Backprojection
Iterative
Reconstruction

41. Reconstruction Algorithms

42. Attenuation Correction
Uniform attenuation
First Order Attenuation Correction
Chang’s Method
Measured (Transmission Image)
Point source Measured Attenuation
Point source Segmented Attenuation

43. Attenuation Correction
Chang’s Method d1
Contour d2
Assume: uniform 
Transverse slice
Note: Only good for Brain imaging

44. Attenuation Correction
Transmission Method (point source)
Geometric Mean I0 I2 I1 d2 d1 D

45. Attenuation Correction
Transmission Method (Measured)
For each
Line of response (LOR)
Obtain; 1, 2, 3, etc

46. Attenuation Correction
Transmission Method (Measured)
Low statistics
Poor Image quality
Require long transmission scans

47. Attenuation Correction
Transmission Method (Segmented)
Option:
Group attenuation factors into 3 groups;
Lung, Tissue, and Bone
lung
tissue
bone

48. Attenuation Correction
Segmented Attenuation Correction
Measured
Segmented

49. Attenuation Correction
Segmented Attenuation Correction
MEASURED
SEGMENTED
3 Minutes Minutes Minute

50. SPECT Corrections
Partial Volume
Concentration:
Counts/ROI
nCi/cc

51. SPECT Corrections Partial Volume Concentration: Counts/ROI (reduced)
nCi/ROI (reduced)
Activity:
Counts/ROI (Correct)

52. SPECT Corrections
Center-of-Rotation

53. SPECT Corrections Uniform Flood Calibration Planar Image SPECT Image
Noise/Signal ratio: (N)/N
SPECT Image
Noise/Signal ratio: 1/(12N/2(D/d)3)
100 Million Count Flood (for improved statistics)
Matrix: 64 x 64
< 1% standard deviation