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Fundamentals of Positron Emission Tomography (PET)

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Fundamentals of Positron Emission Tomography (PET) Fundamentals of Positron Emission Tomography (PET) NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2019 Content • Fundamentals of PET • Camera & Detector Design • Real World Considerations • Performance Evaluation • Clinical Uses NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2019 PET Fundamentals NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2019 Image Formation NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2019 Annihilation Radiation following Positron Emission Beta - plus decay or positron decay : A A 0 Z X Z1Y 1 NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2019 Radiation Sources and Interactions Ideal Tracer Isotope • Tracers contain elements of life – perfect for providing the functional information such as metabolism rate. • Electronic collimation – high sensitivity. • Easier attenuation correction. Detect Radioactive Decays Ring of Photon Detectors • Radionuclide decays, emitting +. • + annihilates with e– from tissue, forming back-to-back 511 keV photon pair. • 511 keV photon pairs detected via time coincidence. • Positron lies on line defined by detector pair (known as a chord or a line of response or a LOR). Detect Pair of Back-to Back 511 keV Photons The Tracer Principle Again • Drug is labeled with positron (+, anti-particle of an electron) emitting radionuclide. • Drug localizes in patient according to metabolic properties of that drug. • Trace (pico-molar) quantities of drug are sufficient. • Radiation dose fairly small (<1 rem). PET data acquisition Organization of data True counts in LORs are accumulated In some cases, groups of nearby LORs are grouped into one average LOR (“mashing”) LORs are organized into projections etc… Multi-Layer PET Cameras Scintillator Tungsten Septum Lead Shield • Can image several slices simultaneously. • Can image cross-plane slices. • Can remove septa to increase efficiency (“3-D PET”) Planar Images “Stacked” to Form 3-D Image PET data acquisition 2D mode vs. 3D mode 2D mode 3D mode (= with septa) (= no septa) True True not detected (septa block detected photons) PET data acquisition 2D and 3D acquisition modes 2D mode 3D mode (= with septa) (= no septa) In the 3D mode there are no septa: photons from a larger number of incident angles are accepted, increasing the sensitivity. septa Note that despite the name, the 2D mode provides three-dimensional reconstructed images (a collection of transaxial, sagittal and transaxial slices), just like the 3D mode! Line Impulse Signal (2) × x’ The value of the projection function p(x’) at this point is the integral of the function 2-D integral of f(x,y) along the straight line: x’=xcos+ysin The integral of a line impulse function and a given 2-D signal gives the projection data from a given view … p(, x) f (x, y) (x cos y sin x)dxdy NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2019 Signals and Systems 2D Reconstruction PET image reconstruction 2D Reconstruction Each parallel slice is reconstructed independently (a 2D sinogram originates a 2D slice) Slices are stacked to form a 3D volume f(x,y,z) etc Slice 5 etc Slice 4 Plane 5 Slice 3 Plane 4 Slice 2 Plane 3 Slice 1 Plane 2 Plane 1 2D reconstruction 2D reconstruction 2D reconstruction 2D reconstruction 2D reconstruction PET data acquisition Organization of data In 3D, there are extra LORs relative to 2D ... + ... 3D mode same planes as 2D + oblique planes Simple and Filtered Back-projection From Computed Tomography, Kalender, 2000. Filtered Back-projection The Ram-Lak filter in spatial domain Statistical Description of the Projection Data The probability of a given projection data g=(g1,g2,g3,…, gM)is Measured no. of M M gm counts on detector g g m m pixel m. p(g) p(gm ) e m1 m1 gm! where gm is the expected value for the number of counts on detector pixel #m N gm fn pnm In the context of emission n1 tomography, pnm is the Remember that probability of a gamma ray generated at a source pixel n is detected by detector element m. g p p p L p f 1 11 12 13 1N 1 g2 p21 p22 p23 L p2N f2 g p p p L p f 3 31 32 33 3N 3 M M M M O M M gM pM1 pM 2 pM 3 L pMN f N NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2019 The Maximum Likelihood Reconstruction Recall that the likelihood function, L(f,g), of a possible source function f is L(f,g) p(g | f ) So that the maximum likelihood solution (the image that maximizing the likelihood function) can be found as ˆ fML argmax L(f,g) f or equivalently ˆ fML arg max logL(f,g) argmax l(f,g) f f where l(f,g) is the log - likelihood function l(f,g) logL(f,g) NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2019 Methods to Estimate the Underlying Image The Maximum Likelihood Expectation Maximization (MLEM) Algorithm (old ) M (new) fn gm fn M N pnm , n 1,2,...,N m1 (old ) pnm pnm fn m1 n1 NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2019 Early PET Imaging 1951: Gordon L. Brownell and colleagues at the Massachusetts General Hospital PET Cameras • Patient port ~60 cm diameter. • 24 to 48 layers, covering 15 cm axially. • 4–5 mm fwhm spatial resolution. • ~2% solid angle coverage. • $1 – $2 million dollars. Images courtesy of GE Medical Systems and Siemens / CTI PET Systems Modern PET Cameras GE Discovery II PET/CT Scanner Control room Separated from scanners microPET Focus microCT microPET Focus Positron Emission Tomography (PET) Functional Brain Imaging with Fluorodeoxyglucose (FDG) http://www.osti.gov/accomplishments/pet.h PET Scan tml Clinical Applications of PET I‐124 study: bone or soft tissue? FDG study: lung or ribs? Clinical Applications of PET Treatment planning for radiation therapy PET Isotopes and Production NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2019 Chapter 3: Radioactivity Beta Emission • Beta particle is an ordinary electron. Many atomic and nuclear processes result in the emission of beta particles. • One of the most common source of beta particles is the beta decay of nuclides, in which Beta decay A A 0 Z X Z1Y 1 Beta-plus decay A A 0 Z X Z1Y 1 Electron capture A A Z X e Z1Y 160 Production of PET Isotopes • +emitting isotopes are proton rich • For use in imaging we typically would like short lived isotopes (minutes to hours) • Produced by proton induced reactions: (p,n), (p,a), ( p,2n).. Medical Cyclotrons • 11-24 MeV Protons • 10-500 A • Several hundred in operation in the US Target for cyclotron-produced radionuclides CS-15 Cyclotron and Target Station Commonly Used PET Isotopes NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2019 Radiation Sources and Interactions Characteristics of non-standard PET Radionuclides *Qaim et al. Radiochimica Acta 2007; 95:67-73 Why PET Imaging? NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2019 Element of Life • Interesting Chemistry Easily incorporated into biologically active drugs. • 1 Hour Half-Life Maximum study duration is 2 hours. Gives enough time to do the chemistry. • Easily produced Short half life local production. 18F 2 hour half-life 15O, 11C, 13N 2–20 minute half-life glucose, H2O, NH 3, CO2, O2, etc. PET against SPECT PET: Impaired Image Quality in Larger Patients Slim Patient Large Patient • For an equivalent data signal to noise ratio, a 120 kg person would have to be scanned 2.3 times longer than a 60 kg person 1) 1) Optimizing Injected Dose in Clinical PET by Accurately Modeling the Counting-Rate Response Functions Specific to Individual Patient Scans. Charles C. Watson, PhD et al Siemens Medical Solutions Molecular Imaging, Knoxville, Tennessee, JNM Vol. 46 No. 11, 1825-1834, 2005 Attenuation Correction Quantitation Transverse Volume Rendered Corrected Uncorrected *Data courtesy of Duffy Cutler, Washington University + Accurate Quantitation (µCi/cc) Possible – Doubles Image Acquisition Time Attenuation of Internal Source P e(d1d2) d2 d1 Event detection probability is product of individual photon detection probabilities. Clinical Applications NPRE 435, Principles of Imaging with Ionizing Radiation, Fall 2019 PET In Oncology • diagnosis - location and extent of disease - general (FDG) or tumour-specific probes • prognosis - size, stage, grade of disease - proliferation (FLT) and/or hypoxia (EF5, etc) • "real-time" therapy evaluation - customizing treatment could increase efficacy, decrease toxicity, and improve economics What is [18F]FDG?c Fluorodeoxyglucose Glucose (FDG) CH2OH CH2OH O OH O OH OH OH OH OH OH F* Why [18F]FDG-PET in tumors? Elevated glucose metabolism in tumor [18F]FDG is a glucose analog [18F]FDG uptake into viable neoplastic cells PET Imaging for Lung Cancer • Differentiating benign from malignant lesions • Staging and re-staging for therapy planning • Predicting and monitoring response to therapy METABOLICALLY AIMED RADIOTHERAPY (MART) CT PET TREATMENT PLAN CT BASED PET/CT BASED Cancer / Oncology Brain Heart Metastases Normal Uptake in Shown with Other Organs Arrows Shown in Blue Bladder • Many tumors have higher than normal uptake. • Image the whole body to find metastases. Other Clinical Uses • Brain Dysfunction Tumor vs. Necrosis Alzheimer’s Disease Epilepsy • Heart Tissue Viability Why Combine PET/SPECT with MRI FIGURE 1. First simultaneous PET/MRI study in 66-y-old healthy volunteer. MRI sequences included T2-weighted turbo spin echo, echo planar, time-of-flight MR angiog- raphy, and MR spectroscopy. PET image displayed was reconstructed from 20-min emission data recorded at steady state after injection of 370 MBq of 18F-FDG. Data were acquired on BrainPET prototype (Siemens). MPRAGE 5 magnetization-prepared rapid gradient echo; MRS 5 MR scintigraphy; TSE 5 turbo spin echo. (Ciprian Catana et al, Journal of Nuclear Medicine, 2012) Why Combine PET with MRI FIGURE 5.
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