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

Anger Gamma Camera X Y Positional Circuit Z Gate Output Collimator

Collimators

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

Single Photon Emission Computed Tomography SPECT Acquire multiple planar views

SPECT Acquisition Linear Sampling Angular Sampling d  1 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

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

SPECT Acquisition

SPECT Acquisition Angular sampling Minimum acquisition: 1800

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

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

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

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

Spatial Frequency Spatial Domain Frequency Domain Amplitude Counts pixel

Spatial Frequency Frequency Domain Amplitude Frequency

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

Reconstruction Algorithms f1 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

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

Transverse Image 60 60 60 60

Backprojection 120 120 120 60 60 120 120 60 60 120 120 120 counts

Backprojection 120 120 counts 20 20 20 20 20 20 20 20 20 20 20 20

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

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

Backprojection 80 80 80

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

Filter High Freq Noise Resultant freq Low Freq

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.

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

Filter Backprojection

Filter Backprojection

Filter Backprojection standard 0.5 mCi 1.0 mCi 6.0 mCi

Iterative Reconstruction  x  x  x Recon Image Initial

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

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

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

standard 6mCi/FBP 6mCi/Iterative

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

Reconstruction Algorithms Filtered Backprojection Iterative Reconstruction

Reconstruction Algorithms

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

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

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

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

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

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

Attenuation Correction Segmented Attenuation Correction Measured Segmented

Attenuation Correction Segmented Attenuation Correction MEASURED SEGMENTED 3 Minutes 2 Minutes 1 Minute

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

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

SPECT Corrections Center-of-Rotation

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