Single Photon Emission Computed Tomography Lindsey Appenzoller w/ Kevin Oliver University of Pennsylvania Medical Physics http://www.medical.siemens.com/

Introduction - SPECT Detect single photons emitted by radionuclide tracers 99mTc emits 140.5 keV gamma rays as it decays Determine the origin and direction of emitted gamma Reconstruct 3D images of the source or anatomy Used as a diagnostic tool to image tumors, disease, and perform bone scans

99mTc Source and Phantom Aqueous solution of 99mTc with initial activity ~ 318 μCi placed in a cylindrical phantom Two positions for source: Axis of phantom ~ 9 cm above the axis Decay detected by triple-headed gamma camera

Detector Schematic

Data collection Four scans performed: Center in air Off-center in air Center in water Off-center in water Each scan acquires data over 360 ° Steps of 3 ° 120 ° rotation of the scanner Data collected for 15 seconds at each detector angle Collected data is in the form of counts

Detector Coordinate System Detector rotates around the coordinate system of the source and phantom Interested in the x’ coordinate in the detector reference frame Coordinate system of detector: x’: 256 bins z’: 128 bins Bin dimensions => 1.78 x 1.78 mm

Centroid Determination Source projections at 0° and 90° Determine centroid of projection for each detector angle using: where , Uncertainty in centroid position: where Plot centroid position vs. angle to determine initial source positions Traces out sine curve

Example of Sinogram Fit: r = -98.9 ± 0.05 mm ϕ0 = 2.5 ± 0.02 ° Position:

Initial Position of Source Scan 1: Scan 2: Position of Center Source in Air Position of Off-Center Source in Air   Position (mm) σ (mm) σ (mm) x1 -4.45 0.03 x2 -4.31 0.04 y1 10.31 y2 98.81 0.05 Scan 3: Scan 4: Position of Center Source in Water Position of Off-Center Source in Water   Position (mm) σ (mm) x3 -4.74 0.05 x4 -7.47 0.20 y3 6.28 y4 91.25 0.23

Backprojection Our projections represent the source distribution in the phantom for a single slice at every angle of the acquisition Transform sinogram into the frequency domain to filter noise Backproject counts (from centroid position) to get information about the spatial distribution of the source Regions where backprojection lines from different angles intersect represent areas which contain a higher concentration of 99mTc

Image Reconstruction Use inverse radon transform on our total number of counts at each detector angle to reconstruct an image of the point source Inverse radon transform filters noise from back projection Example image reconstructions for source in water:

Determine Path Length in Water Emitted gamma travels a certain distance (L) through water to reach the detector at normal incidence Use geometry to determine this path length (varies with angle) Plot path length as a function of detector angle Linear attenuation in water is governed by: Account for continuous decay of source activity (Half life = 6.01 hrs)

Plot of Path Length in Water Min: ϕ = 180° - Source closest to detector Max: ϕ = 0° - Source furthest from detector

Linear Attenuation Coefficient Plot attenuation (N/N0) vs. path length (L) to determine μ Fit to linear curve: Uncertainty in the attenuation is given by: μ = 0.128 ± 0.001 cm-1 Accepted value: μ = 0.15 cm-1 Constant attributed to scatter in Lucite shell of phantom

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