Introduction to Positron Emission Tomography

Transcription

1 Planar and SPECT Cameras Summary Introduction to Positron Emission Tomography, Ph.D. Nuclear Medicine Basic Science Lectures System components: Collimator Detector Electronics Collimator Types: Parallel, Converging, Diverging, Pinhole, Multi-pinhole Performance: Penetration, Resolution, Efficiency Detector: Components: Scintillator crystal, Optical spacer, PMTs Performance: Efficiency, Intrinsic (spatial) resolution, Energy resolution Acquisition modes: Frame vs List mode Static (time-averaged), Dynamic (TAC), Gated (cardiac / respiration) Camera QA corrections: Uniformity, Linearity, Photo-peak window, Multi-energy registration SPECT QA/QC: Center-of-rotation, Head tilt, uniformity PET Definition Positron Uses positron ( + ) emitting radio-isotopes to label physiologic tracers (e.g. glucose metabolism, cell proliferation, hypoxia) Positrons are unstable in that they annihilate with electrons, resulting in two anti-parallel photons each with energy 511 kev PET scanners measure coincident annihilation photons and collimate the source of the decay via coincidence detection Emission The source of the signal is emission of annihilation photons from within the patient, as opposed to photons transmitted through the patient in x-ray imaging Tomography Three-dimensional volume image reconstruction through collection of projection data from all angles around the patient Positron Annihilation Parent nucleus: unstable due to excessive P/N ratio ( 18 F, 11 C, 13 N, 15 O, 14 I) ( 18 O, 11 B, 13 C, 15 N, 14 Te) proton decays to neutron neutrino also emitted (inconsequential to PET) P N P N N P P N P N N P e+ positron emission positron may scatter ~ 1 mm e- e+ positron annihilates with an electron: mass energy is converted to electromagnetic energy resulting in two anti-parallel annihilation photons 1

2 Emission Coincidence Detection Tomographic Data Acquisition i time detector i detector j Random rate determined from i, j singles rates All coincidence events acquired over time allows dynamic imaging Group coincidence data into parallel projections (LOR) for tomographic reconstruction j coincidence events detector i-j coincidence Sort LOR into sinograms and/or save list-mode data LOR Projection Angle Coincidence Events: Signal and Noise PET detectors seek simultaneous gamma ray absorptions (simultaneous within ~ 5-1 ns) PET signal components Measured Projections P = T + S + R True Signal Noise from Scatter Noise from Random T! "t # r ij! activity R! "t # r i # r j! activity r ij = photon pair detection rate in detector pixels i,j r i = single photon detection rate in pixel i Scattered coincidence: one or both photons change direction from a scatter before detection True coincidence: anti-parallel photons travel directly to and are absorbed by detectors Random coincidence: photons from different nuclear decays are detected simultaneously NOTE: scattered and random coincidence lines-of-response need not pass through object! S and R has to be estimated and removed Estimation challenges R estimation accurate and efficient (singles method) S estimation can have significant errors (e.g. lung)

3 PET Acquisition: D vs. 3D Mode Form of collimation (septa) that separate axial slices in D PET - reduces scattered and random events (also reduces trues!) blocked septa & end shielding detector crystals scatter & randoms PET Contrast and Quantitation Noise from Scattered Coincidence Predominantly Compton scatter. Gamma rays scatter off of electrons, change direction and lose energy. results in misplaced events due to change in photon direction (loss of contrast) energy discrimination can eliminate scatter (but not all) correction based on scatter equations, scatter object (CT), measured data Noise from Random Coincidence Random events proportional to singles rates squared Mean random events estimated in two ways: measured with delayed coincidence window (direct measure, high noise due to random rate) calculated based on system singles rates (low noise singles-based calculation) D PET uses axial septa 3D PET uses no septa Attenuation of Signal Gamma rays are absorbed in the patient Variability due to heterogeneity of attenuating tissue Correctable with properly aligned attenuation map Signal and Noise Estimates PET Contrast: D vs. 3D mode Scatter Fraction (SF) SF = S T + S 4 SF = S T + S D = % 3D = 34% DSTE Count Rates: NEMA Cylinder Phantom 1 T NEC = T + S +!R DSTE Measured NEC Signal to Noise Ratio (SNR) SNR = T! P ( )! T T + S +!R depends on randoms estimation method Count rate (kcps) 3 1 3D R 3D S 3D T D R D T NEC rate (kcps) D NEC 3D NEC Noise Equivalent Counts (NEC) T NEC = T + S +!R D S Phantom activity (mci) FDG oncology patient activity: Phantom activity (mci) A scan = A inj! e "! ( t scan"t inj ) A scan = ( 1 "15mCi)! 1 6min 11min # 7 "1mCi 3

4 Annihilation Photon Attenuation PET/CT Attenuation Correction (AC) Anti-parallel gamma ray coincidence detection means that attenuation is independent of position along any line of response. detector 1 detector x µ ( x)dx Attn. of photon 1: P 1 = e Attn. of photon : x a x a x P = e µ ( x)dx CT (diagnostic) PET/CT Scanners" CT scan used for PET AC" CT image is downsampled to PET resolution" Advantages" Fast acquisition" Low image noise" Disadvantages" Higher dose" Attn. coeff. measured with poly-energetic photons < 14 kev" Total attn. of coincidence pair: P C = P 1 P = e a µ ( x)dx same CT, re- sampled to PET resolution Consequences of CTAC! More accurate quantitation" P c is independent of annihilation position x PET/CT Scanners PET Detector Block Clinical PET/CT Micro PET/CT PET scanners are assembled in block modules Each block uses a limited number of PMTs to decode an array of scintillation crystals signal out to processing Two dual photocathode PMTs Reflective light sealing tape gamma rays scintillation light 4

5 Inside GE Discovery STE PET/CT PET Spatial Resolution Positron Physics Positron Range Photon Non-colinearity Block matrix: BGO crystals" "6 x 8 crystals (axial by transaxial)" "Each crystal:" " "6.3 mm axial" " "4.7 mm transaxial" " Scanner construction" "Axial:" " "4 blocks axially = 4 rings" " "15.7 cm axial extent" "Transaxial:" " "7 blocks around = 56 xtals" " "88 cm BGO ring diameter" " "7 cm patient port" 13,44 individual crystals" Detectors Response function Ring Geometry Non-uniform LOR sampling Depth-of-interaction Reconstruction Filters Resolution components add in quadrature R system = R pos. phys. + R det + R sampl + R recon Positron Physics Resolution Detector Signal Decoding Positron range maximum energy of isotope scatter medium Positron rms range (mm) F 11 C 13 N 68 Ga 15 O 8 Rb Maximum positron kinetic energy (MeV) data from Derenzo, et al. IEEE TNS 33: , 1986 Light Sharing Relative PMTs signal heights depend on crystal of interaction Axial Radial Signal Decoding Energy, E = A + B + C + D Axial position, Z = (C +D) / E Transverse position, X = (B + D) / E Radial position: not determined (no DOI) Transverse Axial A C Photon non-colinearity Non-colinearity: R non-colin =. x Ring Diameter Clinical scanner: Diam. ~ 8-9 cm; R non-col. ~ mm Small animal scanner ~ 15 - cm; R non-col. ~.4 mm A PMTs C B D 5

6 Detector Resolution PET Ring Geometry Effect on Resolution Data Sampling Error: Coincidence lines-of-response are not uniformly spaced across a ring detector Interpolate to uniform spacing, or account for non-uniformity in reconstruction w center Depth-of-Interaction error: entrance position and true line-of-response w/ edge photon penetration Peaks for different crystals at different positions" Window center and width adjusted for each crystal" detection position and assigned line-of-response Resolution Effect of Smoothing vs. Noise with FBP Human abdomen simulation with cm diam. lesion :1 contrast PET Sensitivity 1. Absorption efficiency of detectors scintillation crystal attenuation coefficient scintillation crystal thickness detector response uniformity more counts (less noise) less smoothing (more noise). Solid angle coverage of object by detectors PET ring diameter smaller diameter pro: increases solid angle and sensitivity, reduces system cost con: leads to DOI resolution degradation con: limits patient size PET ring axial length larger axial extent pro: increases solid angle and sensitivity con: increases system cost 6

7 Detector Sensitivity vs. Resolution Tradeoff Inorganic scintillation crystals relevant PET scanner property sensitivity Geometric Efficiency vs. Sensitivity PET scanner sensitivity scales with the number of detectable coincidence events, which in turn scales as max. This results in lower sensitivity at the end of any PET scanner axial center plane m ax scanner axis axial end plane edg e source energy & spatial resolution counting speed (randoms rate, dead- time sensitivity max Full max photo- sensor matching, manufacturing cost Limited edge = o *crystal thickness, t: typically BGO scanners use t = 3cm, LSO scanners use t = cm for cost reasons. PET scanners are not made from NaI(Tl) or BaF due to low sensitivity, despite other advantages Graph from Emission Tomography, Eds. Wernick, Aarsvold, pg.186 PET scanner axis QA for PET Scanners: Evaluation of Performance Metrics PET Image Formation Workflow Current specifications based on National Electrical Manufacturers Association (NEMA) Standard Sensitivity - both system and per transaxial slice (measured with a line source) Primary Detection Decoding Detector corrections Spatial resolution - measured with a point source and an analytical image reconstruction algorithm at several positions in the scanner FOV (x,y,z resolution) Uniformity - measured with a uniform cylinder of activity Count rate - measured with a decaying line source in a solid, cold cylinder Coincidence Processing Data Binning Data Corrections Dead time correction accuracy - measured from the count rate data Scatter fraction - measured from the count rate data Attenuation correction accuracy, contrast performance - from a non-cylindrical phantom with hot and cold spheres. Image Reconstruction 7

8 October 18, 11 Nuclear Medicine Basic Science Lectures Stephen Bowen Analytic Reconstruction Backprojection Iterative Reconstruction Filtered Backprojection f ( ) f ( k) initial image estimate measured data p(k) = Hf (k) + n compute estimated projection data From WikiBooks Basic Physics of Digital Radiography FBP assumes linear projections and does not account for many sources of variability in LOR Backprojection leads to streak artifacts in PET images Reconstructed PET/CT images p p p ( k) compare measured and estimated projection data f (k) f (k+1) update image estimate based on ratio or difference There are many ways to: model the system (and the noise) compare measured and estimated projection data update the image estimate based on the differences between measured and estimated projection data decide when to stop iterating Modern Times: Time-of-Flight Time-of-flight capability is now offered in many new PET scanners" Measure time difference of detection of coincidence gammas" No AC kvct AC-CT Defines a line segment in space, shorter than distance between detectors" Improves image signal to noise that is a function of the object size." Conventional LOR OS-EM FBP TOF Gaussian SOR fused segment length!x = cdt/!x c = speed of light Dt = timing resolution AC: Attenuation Correction OS-EM: Ordered Subsets Expectation Maximization FBP: Filtered Back-Projection!x = 7.5 cm for the Dt ~.5 ns typical of TOF PET scanners 8

9 PET Introduction Summary PET concept Physics of positron emission, photon annihilation, coincidence detection PET components D collimated vs. 3D acquisition mode, detector block PET resolution Positron range, detector response, line-of-response sampling, depth-of-interaction Take home 1: clinical PET resolution ~ 5 mm, small animal PET ~ 1 mm PET quantitation CT attenuation correction Take home : separable attenuation correction makes PET more quantitative than SPECT or MRI PET sensitivity Absorption efficiency, geometric efficiency Take home 3: PET sensitivity 1 3 greater than SPECT, 1 6 greater than MRI PET image formation Acquisition Reconstruction 9