PET/SPECT PhantomPET/SPECT Phantom

Side View of PhantomSide View of Phantom

Image ResolutionImage Resolution

• Intrinsic resolution FWHMIntrinsic resolution FWHM

• Field of view Field of view

• Measurement:Measurement:A thin line source with F-18 is placed in a 20 cm phantom containing water as a scattering medium. The A thin line source with F-18 is placed in a 20 cm phantom containing water as a scattering medium. The source is scanned and the images are reconstructed. A two dimensional Gaussian is filtered to the points source is scanned and the images are reconstructed. A two dimensional Gaussian is filtered to the points surrounding the location of the source. The resolution at full width half maximum will be about 2.4 times surrounding the location of the source. The resolution at full width half maximum will be about 2.4 times the standard deviation parameter of the Gaussian distribution. The procedure is repeated with the source at the standard deviation parameter of the Gaussian distribution. The procedure is repeated with the source at different positions in the field of view. different positions in the field of view.

• Axial resolution Axial resolution

• Measurement:Measurement:A small point source is stepped through the imaging volume in small increments. For each step a scan of A small point source is stepped through the imaging volume in small increments. For each step a scan of the source is made. The images are reconstructed, and a small region of interest is drawn around the the source is made. The images are reconstructed, and a small region of interest is drawn around the location of the source. The measured activities in the ROI as a function of z-position is extracted from the location of the source. The measured activities in the ROI as a function of z-position is extracted from the series of images. Gaussians are fitted the points. The resolution in full width half maximum will be about series of images. Gaussians are fitted the points. The resolution in full width half maximum will be about 2.4 times the standard deviation parameter of the Gaussian distribution. The procedure is repeated with the 2.4 times the standard deviation parameter of the Gaussian distribution. The procedure is repeated with the source in different locations in the field of view. source in different locations in the field of view.

SensitivitySensitivity

• A 20 cm cylinder phantom is filled with a A 20 cm cylinder phantom is filled with a water solution with an activity concentration water solution with an activity concentration of 0.1 µCurie per cc and placed in the center of of 0.1 µCurie per cc and placed in the center of the field of view. The sensitivity is defined as the field of view. The sensitivity is defined as the true coincidence rate (i.e. scatter and the true coincidence rate (i.e. scatter and randoms subtracted) divided by the activity randoms subtracted) divided by the activity concentrationconcentration..

Timing ResolutionTiming Resolution

• Timing resolution FWHM:Timing resolution FWHM: 5 ns 5 ns

• The coincidence window is the time interval in which one event has to appear in order to The coincidence window is the time interval in which one event has to appear in order to be accepted in coincidence with another event. be accepted in coincidence with another event.

• The coincidence window is operator selector selectable to 8, 12 or 16 nanoseconds. 12 The coincidence window is operator selector selectable to 8, 12 or 16 nanoseconds. 12 nanoseconds will give full efficiency. nanoseconds will give full efficiency.

• 1.7 Linearity and random coincidences 1.7 Linearity and random coincidences

• The dead time is attributed to three components: detector dead time, the triple The dead time is attributed to three components: detector dead time, the triple coincidence rate and the system dead time, the latter being of less importance. coincidence rate and the system dead time, the latter being of less importance.

• The sources of the dead time are identified and measured with high precision. The sources of the dead time are identified and measured with high precision.

• The dead times are calculated with high accuracy, based on count rates, and corrections The dead times are calculated with high accuracy, based on count rates, and corrections are made based on these calculations. The dead times do not impose limitations in usable are made based on these calculations. The dead times do not impose limitations in usable count rates in our system. count rates in our system.

• The correction for the contribution of accidental coincidences is based on a high The correction for the contribution of accidental coincidences is based on a high precision measurement of the coincidence time window. The accidental counts are then precision measurement of the coincidence time window. The accidental counts are then calculated with high accuracy and subtracted from the total coincidence counts. calculated with high accuracy and subtracted from the total coincidence counts.

PET Phantom ImagesPET Phantom Images

The SINOGRAMThe SINOGRAM Gamma Camera Example Gamma Camera Example

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Sinogram Formation in PETSinogram Formation in PET

• Coincidence events in PET scanner are categorized by Coincidence events in PET scanner are categorized by plotting each LOR as function of its angular orientation plotting each LOR as function of its angular orientation versus its displacement from center of gantry. (A) Center of versus its displacement from center of gantry. (A) Center of gantry is noted by cross (X), and locus of interest (e.g., gantry is noted by cross (X), and locus of interest (e.g., tumor) is noted by ellipse. Four LORs passing through locus tumor) is noted by ellipse. Four LORs passing through locus of interest are labeled A, B, C, and D. (B) These 4 LORs are of interest are labeled A, B, C, and D. (B) These 4 LORs are plotted on this sinogram where angular orientation is on plotted on this sinogram where angular orientation is on yy--axis and displacement from center of gantry is on axis and displacement from center of gantry is on xx-axis. If -axis. If all possible LORs that pass through this point are plotted, it all possible LORs that pass through this point are plotted, it maps out half of sine wave turned on its side as shown here. maps out half of sine wave turned on its side as shown here. (C) Sinograms of more complicated objects, such as (C) Sinograms of more complicated objects, such as sinogram of brain scan shown, are composed of many sinogram of brain scan shown, are composed of many overlapping sine waves. (D) Reconstructed brain image overlapping sine waves. (D) Reconstructed brain image corresponding to sinogram in (C) is shown. corresponding to sinogram in (C) is shown.

Sinogram Formation in PETSinogram Formation in PET

Image ProcessingImage Processing

• Digital Signal ProcessingDigital Signal Processing

• Direct Image Reconstruction Direct Image Reconstruction

• Sampling TheorySampling Theory

• Fourier AnalysisFourier Analysis

• Image FiltersImage Filters

• Mathematical Image ReconstructionMathematical Image Reconstruction

Image ReconstructionImage Reconstruction

Direct Image ReconstructionDirect Image Reconstruction BackProjectionBackProjectionAlgebraic ReconstructionAlgebraic Reconstruction

Time of Flight SystemsTime of Flight SystemsDirect Image ReconstructionDirect Image Reconstruction

BackprojectionBackprojection

BackprojectionBackprojectionAnimationAnimation

Sampling TheorySampling Theory

• A discrete “digital” image is a sampled image. A discrete “digital” image is a sampled image.

• Samples are taken from specific locations, Samples are taken from specific locations, usually a square (2-dimensional) array of usually a square (2-dimensional) array of elements, called pixels. elements, called pixels.

Sampling Theory continued,Sampling Theory continued,

• The idea is to obtain enough samples so that The idea is to obtain enough samples so that the essential information contained in the the essential information contained in the image is not lost.image is not lost.

• This can be proven mathematically, and is This can be proven mathematically, and is fundamental in communications theory, fundamental in communications theory, signal processing, electrical engineering, signal processing, electrical engineering, and other fields.and other fields.

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Discrete function “Approximates” Discrete function “Approximates” Continuous FunctionContinuous Function

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Sampling The Information From Sampling The Information From The Heart BeatThe Heart Beat

More complicated samplingMore complicated sampling