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PET Basics Outline PET Overview Slide Outline PET Basics • Positron Emission • Basics of PET Scanner Design Frederic H. Fahey DSc • Data Acquisition Children’s Hospital Boston • Review of Scintillation Materials Harvard Medical School • PET/CT [email protected] • Time-of-Flight (TOF) PET • Special PET devices Radionuclides PET Overview Slide Used in Nuclear Medicine Single Photon Positron Isotope T1/2 Examples Isotope T1/2 Examples 99m 15 Tc 6 hrs MDP, O2 minH2O HMPAO CO MAA O2 DTPA CO2 201Tl 72 hrs Chloride 13N 10 min NH3 131I 192 hrs Thyroid 18F 109.8 min FDG (Tx, Dx) 11C 20.4 min methionine 82Rb 1.3 min cardiac 64Cu 12.7 hrs MoAB 1 Positron Decay Positron Decay • Have an excess number of protons • Lie below the line of stability • Require accelerator for production Note: It takes about 8 MeV for a particle to overcome the nuclear binding energy Cyclotron Annihilation Reaction • Provides energetic charged particles (p, d, α) • 10 – 20 MeV • For example, 18O (p,n) 18F Two 511 keV annihilation photons are emitted 180o + sd 2 Annihilation Reaction Electron Capture Conversion of mass to energy (Einstein) For lower transition energies, electron capture E(erg) = mc2 is an alternative decay mode for proton-rich = 9.1091e-28g x (2.997e10cm/sec)2 isotopes. 2 2 = 8.18e-10 gcm /cm A X + e- AY = 8.18e-10 erg ZN Z-1 N+1 E(MeV) = 8.18e-10 gcm2/cm2 x (1 Mev/1.6e-06 erg) p + e- n + γ = 0.511 MeV Positron Decay Positron Decay • Requires 1.022 MeV transition energy (creation of β+ and difference in number of orbital electrons). Electron capture results if the transition energy is below 1.022 MeV. • Transformations with transition energies of greater than 1.022 MeV can decay via electron capture or positron decay. • The greater the energy over the required 1.022 MeV the more likely positron decay will occur (rather than electron capture) and higher the kinetic energy of the emitted β+. 3 Examples 4 Energy of the Positron (β+) Energy of the Positron (β+) • Transition energy that is used during the annihilation process is shared by the β+ and the neutrino (ν). • If the β+ were to receive all of the energy it would have the maximum energy ET – 1.022 MeV = Eβmax • Positron shares excess energy with neutrino. Average energy of β+ is 1/3 Eβmax Range of the Positron (β+) Positron Emission •The range of the positron is determined empirically. •Unlike larger/heavier charged particles the positron does not travel is a straight path. 511 keV •Bounces around like a billiard ball . positron range 511 keV alpha beta In water 5 Absorber Method for Range of the Positron (β+) Determining Range of Positrons Absorber Incident Material Transmitted β particle β particle beam beam Io IT Monoenergetic Continuous spectrum Transmission = IT/Io Range of the Positron (e+) Positron Range Isotope Emax (MeV) Rmax (mm) Ga-68 1.9 8.2 O-15 1.7 7.3 N-13 1.2 5.1 C-11 0.97 4.1 F-18 0.64 2.4 Note: Average range is about 1/3 the maximum. The rms range is proportional to positron energy. 6 Positron Range Non-Colinearity The same level of non-colinearity The distribution of rms range is exponential leads to a bigger uncertainty with a and not well characterized by FWHM. larger ring diameter. R180 ≈ 0.002 x DR Limit on PET Spatial Resolution (in mm, regardless of detector size) Summary Scanner β+ Range Non-Colin Total • PET images the annihilation photons that result from β+ Whole Body (100 cm) decay. • The annihilation photons are collinear + sd. 18F 020.2 202.0 ~222.2 • The transition energy must be at least 1.022 MeV. 82Rb 2.6 2.0 ~4.6 • Excess energy of the β+ must be used before annihilation Animal (20 cm) can occur • PET spatial resolution is ultimately limited by the positron 18F 0.2 0.4 ~0.6 range and the non-colinearity of the annihilation 82Rb 2.6 0.4 ~3.0 7 Annihilation Coincidence Detection Positron Emission 511 keV positron range 511 keV Detector Blocks (GE Advance NXi) Detector Ring 8 PET Sinograms PET Sinograms Point Source Brain Sinogram Projection View 45o ngle A -5o Image for Each Angle -90o Note: Sinograms and projection Image for Each Slice views are different ways or showing the same data. 9 Blank Scan Sinograms Raw Normalized Detector Out Daily PET QC PET Sinograms • Point in transverse slice maps to sine wave • Displacement (x) vs Angle (y) • Each row is a projection through the object at the co rrespo nd ing a ng le • Each detector is mapped along a diagonal • Each pixel in the sinogram corresponds to a particular “line of response” (LOR) i.e. detector pair 10 True, Scatter and Random Randoms Estimation Coincidence Detections • Background Subtraction True • Singles Rate Calculation R=2R = 2 τ N1 N2 Scatter • Delay Window Method Random (R = 2 τ N1 N2) Delay Window Method B Noise Equivalent Counts (NEC) A C •Not all coincidences are created equal. We must Trues + Randoms correct for random and scatter coincidences. Prompts = Delays = Randoms Only •The “Noise Equivalent Count ” is the number of AB C counts from a Poisson distribution (SD estimated by SQRT{N}) that will yield the same noise level Time 0 10 20 30 40 50 (ns) as in the data at hand. •This allows one to compare counts acquired on Estimated Trues = Prompts - Delays different machines or using different acquisition schemes. 11 Scatter Fraction, Count Rate and Noise Equivalent Counts (NEC) Randoms Measurement NEC = _________T_______ 1200000.0 Total 1 + k R/T + S/T 1000000.0 800000.0 s 600000. 0 True Where TiT is True counts cp R is Random counts 400000.0 Random S is Scattered counts 200000.0 0.0 NEC k = 1 if singles rates calculation and 051015 Act Conc (uCi/mL) 2 if delayed subtraction method Direct 18 **** 17 ***** 16 ****** Cross 15 ******* 14 ******* 13 ******* 12 ******* 11 ******* 10 ******* 9 ******* 8 ******* 7 ******* 6 ******* 5 ******* 4 ******* 3 ****** 2 ***** 1 **** 123456789101112131415161718 Span of 3 Michelogram Span of 7 Michelogram 12 Set of 2D PET Sinograms 2D Detector Span of 7 Scintillator End Crystals Shields PMTs Septa n o 511 kev photon Axial Directi Courtesy of M. Graham, M. Madsen, U Iowa Direct Crossed Acquisition Modes 2D Crossed & Direct 3D 3D septa are removed 13 3D 3D RD* = 11 RD = 15 Slice Slice Orientation Orientation *RD is Ring Difference 18 16 14 12 10 2D, span=7 3D, rd=11 8 Segment 2 (Relative Unites) 3D, rd=15 6 4 Sensitivity Sensitivity 2 0 Segment 1 0 10203040 Axial Position (Plane Number) Segment 3 14 GE 3D Projection view and Michelogram 3D vs 2D in Brain PET NEC Rate: 2D vs 3D 3D PET 80000 • Sensitivity drops off towards edges 3D 70000 • 4-5X increased sensitivity overall 60000 2D • Increased scatter (15% to 40%) 50000 r Second e • Increased randoms from out-of-field activity 40000 Counts p 30000 • Rebinning algorithms to apply 2D 20000 reconstruction 10000 • Some devices can acquire in 2D or 3D whereas 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 some can only acquire in 3D Activity Concentration in 20 cm Phantom (MBq/ml) • 3D in Brain, 2D (or 3D) in Whole Body 15 3D Data – How much? 3D Data Reduction (values in parentheses are for GE Advance NXi) •Nd is # of detectors in a ring (672) • Combine angular samples or “mashing” -m •Nr is # of detector rings (18) – Samples reduced by 2 where m is the • Assume FOV is ½ the ring diameter “mashing factor” • Max ring difference • Combine axial samples (span of 7) 2 2 2 •Ns = (Nr) (Nd/2) (Nd/2) = ¼ Nr Nd • Limit ring difference (11 vs 15) • For GE NXi, – 3.66 x 107 samples – 73 MB per bed position (for 2 bytes/pixel) Arc Correction Angular Sampling 16 Criteria for Scintillation Material Angular Sampling • Detection Efficiency (Stopping Power) – High Effective Z – High Density • Interleaved rows combined •Liggpht Output into one row X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X • Doubles transverse sampling – Good energy resolution • Halves angular sampling – Good crystal identification • Slight angular error • Decay Time – Reduction of random coincidences – Time-of-Flight PET Interleaved Sinogram New Detector Materials Crystal Identification SCINTILLATOR NaI(Tl) BGO LSO GSO Rel. Light Output 100 15-20 75 20-25 Peak Wavelength (nm) 410 480 420 440 Decay Constant (ns) 230 300 12,42 30-60 Density (g/mL) 3.67 7.13 7.40 6.71 Effective Z 51 75 66 59 Index of Refraction 1.85 2.15 1.82 1.85 Hygroscopic ? Yes No No No 17 PET Attenuation Correction PET Attenuation Correction Methods -μ(L-x) P2 = e • Calculated – No noise but possibly inaccurate X • Measured -μx L – Accurate but noisy P1 = e • Segmented, Measured – Less noise => less time PTOT = P1 x P2 • Singles = e-μL •CT-Based Measured Attenuation Correction Measured Attenuation Correction 100 20 C Blank Transmission Emission Corrected Emission = (Blank/Transmission) * Emission = (100/20) * C 18 Segmented, Measured Attenuation Correction PET-CT Attenuation Correction •Noise added from measured attenuation correction •RlRel err in un ifhif phan tom (10 mi n EM) •9% with calc atten Measured •16% with 10 min TR •18% with 5 min TR •Segmentation classifies by tissue type •Smoothes lung areas •Substantial reduction in noise added Segmented PET-CT Attenuation Correction PET-CT Attenuation Correction • Acquire CT Scan and reconstruct • Apply energy transformation • Reproject to generate correction matrix • Smooth to resolution of PET • Apply during reconstruction 19 GE Advance NXi GE Discovery ST GE Discovery ST PET-CT Scanners GE Discovery STE GE Discovery ST Philips Gemini Detector Dimension (mm) 4.7 x 6.3 x 30 6.2 x 6.2 x 30 4 x 6 x 20 # of PET Detectors 13,440 10,080 17,864 PET Detector Material BGO BGO GSO Spatial Resolution 5.0 6.1 4.9 2D/3D 2D/3D 2D/3D 3D Atten Corr CT CT CT&Cs-137 Siemens Biograph LSO Siemens Hi-Rez LSO Detector Dimension (mm) 6.5 x 6.5 x 25 4 x 4 x 20 # of PET Detectors 9,216 23,336 PET Detector Material LSO LSO Spatial Resolution 6.3 4.6 CT PET 2D/3D 3D 3D Atten Corr CT CT 20 Time-of-Flight PET Time-of-Flight PET Δx = c Δt/2 Where Δx is the time-of-flight spatial uncertittainty and Δt is the ti mi ng resol uti on.
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