Nuclear Medicine Imaging

Transcription

1 Introduction to Medical Engineering (Medical Imaging) Suetens 5 Nuclear Medicine Imaging Ho Kyung Kim Pusan National University Introduction Use of radioactive isotopes for medical purposes since 1920 Imaging radionuclide concentration in the human body since 1940 Projection image of the radionuclide concentration in the body by Ben Cassenin the early 1950s (scanning method) The first "true" gamma cameraby Hal Anger in the late 1950s (aka, Anger scintillation camera) SPECT (Single Photon Emission Computed Tomography) PET (Positron Emission Tomography) Detect photon pairs originating after positron emission Based on Anger's demonstration with two scintillation cameras The first dedicated PET system by Ter-Pogossianet al. in the 1970s The first PET scanner for human studies by Phelps, Hoffman et al. 2

2 Radionuclides Administration of a tracer molecule to the patient in NM (usually by intravenous injection) Particular molecule carrying an unstable isotope a radionuclide Being involved in a metabolic process Measurement of the concentration of the tracer molecule as a function of position & time by detecting gamma rays produced from the unstable isotopes Measurement of the function or metabolism NM with an SNR that is orders of magnitude higher than that of any other modality (CT, MRI, US) 3 Radioactive decay β emission n p + + e (β particle) Daughterproduct in an excitedstate rapidly decays to a more stable nuclear arrangement + one or more γphotons Daughter product in a metasbleor isomericstate releases γphotons with a delay 99m Tc Metastable daughter product of 99 Mo (T 1/2 = 66 h) 99m Tc 99 Tc (T 1/2 = 6 h) kev γ-photon Electron capture (EC) p + + e (orbital electron) n Daughter product in an excitedstate promptly decays toward a state w/ lower energy + one or more γ photons 123 I (T 1/2 = 13 h) 4

3 Positron emission (β + decay) p + n + e + (anti-electron) Positron hits an electron and annihilatesafter a very short time (~ 10-9 s) & within a few mm of the site of its origin The mass of two particles is converted into energy (each 511 kev) as two photons in opposite directions 18 F (T 1/2 = 109 min) (the daughter nucleus may further emit γ photons) 5 Statistics Much smaller the number of detected photons in NM imaging than in x-ray imaging Noise plays a more important role The decay per time unit: () = () () = the number of radioactive isotopes at time = decay probability per time unit (an isotope-dependent decay constant) The expected value is: = = ( ) / Half-life / = Source strength units Curie (Ci) = Bq(1 mci= 37 MBq) Becquerel (Bq) = one expected event per second (disintegration per second) Typical dose in NM imaging ~ 10 2 MBq Probability of measuring photons when photons are expected (Poisson distribution) = SNR=! 6

4 Interaction of photons with matter Ideally, the emitted photon would notinteract with the patient's tissue, but Compton scatter & photoelectric absorption attenuate the emitted γ rays. For (%)photons emitted in point & = %along the &-axis, then the number of photons in the detector at position & = %: ' = (%) ( +, ) * * For (%)photon pairs emitted in point & = % along the &-axis, the number of detected pairs at positions in & = ' 1 & & = ' 2 : ',' = %, ( ) * * +1 ( +2 ) * *, = % ( ) * * Contrary to SPECT, the attenuation in PET is identical for each point along the projection line 7 Detector Unlike CT, a very small number of photons is acquired in a longer time interval. Consequently, emission tomography detectors are optimized for sensitivity. Scintillation crystal + PMTs Scintillation crystals High 3because 4 56 ~3 Gamma camera performance in single-photon imaging should be optimized for 140 kev( 99m Tc) PET camera should be optimized for 511 kev NaI(Tl) for single photons (140 kev) in gamma camera & SPECT BGO (bismuth germanate) for annihilation photon (511 kev) in PET Photomultiplier tube Photocathode + cascade of dynodes Glued to crystal 8

5 Collimation The source is an unknown distribution in NM, unlike the x-ray imaging (e.g., projection line) W/o collimation, the detected photons do not contain information about the spatial distribution Collimation in single photon detection (SPECT) Mechanical collimator: a thick lead plate with cylindrical holes Suffering from sensitivity Collimation in PET Coincidence detection or electronic collimation Detected both photons with an electronic coincidence circuit Higher sensitivity rather than in SPECT 9 10

6 Photon position & detected number of photons A single giant crystal ( cm) + a dense matrix (30 to 70) of PMTs (a few cm each) Energy = the sum of all PMT outputs, 9 : : Position: ;= = < => =,?= => = = > = = > = A = PMT index; (; :,? : )= PMT position The spatial resolution is limited by the fluctuations in the PMT-output Detected number of photons: for tracer activity λ(&) along the &-axis; F F SPECT: ' =( & ( +2 ) * * ( + D ) C C d& F PET: ',' = +1 ( & d& F In PET, the attenuation is identical for each point along the projection line The measured projections are a simple scaling of the unattenuated projections In SPECT, attenuation is position-dependent No simple relation b/w attenuated & unattenuated projections (more difficult image recon.) 11 Energy resolution & count rate Energy resolution Statistical noise coupled to estimating energy The number of electrons activated in scintillation events Time delay after which each electron releases the scintillation photons Unpredictable directions in which scintillation photons are emitted FWHM of the photopeak in the energy distribution NaI(Tl) ~ 10% 14 kevfor 140-keV photon BGO ~ 20 % Count rate A wrong single position may occur when the probability that two or more photons arrive at the same time increases (with increasing activity) A photon can only be successfully detected if no other photon arrives while the first one is being detected Probability that no other photon arrives: 0 I J = K I = the overall sensitivity; = the activity (Bq); J= detection time (s) Detection probability decreases exponentially with increasing activity in front of camera!! Important to keep Jas low as possible because a higher value for I is preferred A bottleneck in count rate performance for true 3D PET 12

7 Planar imaging Simply the raw single-photon projection data Each pixel corresponds to the projection along a line & 13 2D Fourier reconstruction & FBP To apply the projection theorem, the attenuation effect must be corrected An attenuation factor in the number of detected photons (see previous eqs') prevents straightforward application of Fourier reconstruction or FBP e.g., at 140 kev, every 5 cm of tissue absorbs about 50% of the photons Attenuation correction in PET Estimation of the attenuation factor by transmission measurements with the external source (L 2) = ( ) * * ' = the position of external source, ' = the detection position at the other side of the patient Exactly same as the attenuation factor for PET In SPECT Iterative reconstruction Straightforward FBP with the attenuation correction severe artifacts but still provide very valuable diagnostic information for an experienced physician 14

8 ML-EM algorithm Iterative methods in SPECT The attenuation problem A significant Poisson noise (streak artifacts in the reconstructed images) Maximum-likelihood expectation-maximization (ML-EM) algorithm Most popular method Based on a Bayesiandescription of the problem Bayesian approach Assuming that a reconstructed image Λ is computed from the measurement N, Bayes' rule states: O P Q O(Q) Λ N = O(P) Λ N = the posterior probability (Λ) = the prior probability (N) = the likelihood For a given measurement N, the most likely solutionis obtained when maximizing Λ N, called the maximum-a-posteriori probability (MAP) approach Assuming that the probability (N)& the prior probability (Λ)are constants, maximizing Λ N maximizing the likelihood N Λ (easier to calculate!) called the maximumlikelihood(ml) approach 15 The likelihood function for emission tomography The measurements N are measurements R : of the attenuated projection : in detector position A The reconstructed image Λis the regional activity S in each pixel T V : = SW U :S S, A=1,X U :S = the attenuation coefficient Representing the sensitivity of detector A for activity in T With a perfect collimation, U :S is zero everywhere except for the pixels Tthat are intersected by projection line A, yielding a sparse matrix Y The likelihood of measure R : if : photons on average are expected: R : : = = = Z = The overall probability (independent histories among photons): N Λ = = = Z = Obviously a very small value! e.g., the max. R : : value of = 0.1 for : = 15 for a single slice with 10,000 detector positions A, then the maximum likelihood N Λ ~10 : [ =! [ =! 16

9 Because (N)& (Λ)are constants; Λ N ~ N Λ = = = Z = : [ =! When maximizing N Λ, the data R :!are constant and can be ignored; Λ N ~ N Λ = = : [ = : Because the logarithm is monotonically increasing, maximization of the resulting log-likehood function also maximizes Λ N ; ] N Λ = : R : ln( : ) : = : R : ln( S U :S S ) S U :S S Hessian(the matrix of second derivatives) is negative definite if the matrix U :S has max rank the likelihood function has a single maximum if a sufficient number of different detector positions A are used 17 Maximizing the likelihood function To maximize ] N Λ ; `a ` b = U :S [ = : b c =b b 1 =0, T=1,e Involving the inversion of a matrix of X eelements (~ 10 8 ) undesirable! Alternatively, iterative optimization (e.g., a gradient ascent algorithm) is suitable slow Expectation-maximization (EM) algorithm "Complete" variables f= ; :S, ; :S = the (unknown) number of photons detected in A coming from position T; g ; :S hλ =U :S S Log-likelihood function for the complete variable f; ] < f,λ = : S ; :S ln U :S S U :S S A two-stage procedure yielding the max of ] < and ]: E-step: compute the expectation function g ] < f,λ N,Λ ijl M-step: calculate a new estimate of Λthat maximizes this expectation function derived in the first step 18

10 E-step: g ] < f,λ N,Λ ijl = : S :S ln U :S S U :S S :S =U :S S ijl [ = c =b b kl+ b M-step: ` g ] ` < f,λ N,Λ ijl = =b : =0 S = = =b b b U :S = c =b Then, the ML-EM algorithm: S n = b kl+ U = c :S =b [ = : kl+ bc =b b or n S = ijl S + b kl+ `a = c kl+ =b ` b A gradient descent method 19 20

11 21 22

12 Noise reduction Low radioactivity low # detected photons Poisson noise deteriorated projection data Most likelysolution from ML-EM algorithm (considering Poisson noise) yields an image as similar as possible to the measured projections a noisy reconstructed image To suppress noise; Smoothen the reconstructed image (instead of smoothening the measured projections) Interrupt the iterations before convergence Low frequencies converge faster than high ones in ML-EM Terminating early has an effect comparable to low-pass filtering Define some prior probability function that encourages smooth solutions 23 3D reconstruction FBP Only possible if the sequence of projection & backprojection results in shift-invariant PSF Not true at near the edge of the FOV where is intersected by fewer measured projection lines The data may be completed by computing the missing projections Select a subset of projection that meets the requirement and reconstruct to compute an initial, relatively noisy, reconstruction image Forwardly project the reconstruction along the missing projection lines to compute an estimate of the missing data Combine the computed & measured data into a single set of data that now meets the requirement of shift-invariance Reconstruct the completed dataset with true 3D FBP ML-ME reconstruction Fourier rebinning Convert a set of 3D data into a set of 2D projections based on a property of the Fourier transform of the sinograms Reconstruct 2D set with the 2D ML-EM algorithm 24

13 Image quality Contrast Mainly determined by the characteristics of the tracer & the amount of scatter Background tracer uptake due to not-zero concentration in blood during metabolic process Background radiation due to scattered photons Spatial resolution Mostly expressed in FWHM of the PSF In PET (~ 4 5 mm) Positron range: a positron travels over a certain distance before annihilation (~ mm) Deviation from 180 : a deviation (~ 0.3 ) of annihilation-photon directions, corresponding to 2.5 mm for a camera of 1 m diameter Detector resolution: called "intrinsic" resolution ~ 2 3 mm for a small crystal array (4 mm 2 ) ~ 4 mm for a single large crystal In SPECT (~ cm) Detector resolution: comparable to PET Collimator resolution: dominant factor 25 Noise Poisson noise Compton scatter May be suppressed by collimator & energy windowing Before & after attenuation correction Artifacts Attenuation: streak artifacts Compton scatter: yielding a relatively smooth but nonuniformbackground uptake Poisson noise: streak artifacts Patient motion 26

14 27 Gamma camera & SPECT scanner Collimator + large NaI(Tl) crystal + PMT array Front-end electronics (Anger logic) calculate position coordinates (x, y), energy z, and the detection time t 28

15 PET scanner Large ring (diameter 1 m) of BGO crystals; no detector rotation; table motion small (about 4 mm 4 mm) scintillation crystals + PMTs detection time is determined with an accuracy of about 10 ns (in 10 ns light travels about 3 m), which is very short as compared to the scintillation of BGO (300 Randoms: ns) photon pairs that do not originate from the same atom but nevertheless are considered as a coincidence the probability of a random ~ (radioactivity) 2 Schematical representation of a PET detector ring cut in half. (a) When septa are in the field of view, the camera can be regarded as a series of separate 2D systems. Coincidences along oblique projection lines between neighboring rings can be treated as parallel projection lines from an intermediate plane. This doubles the axial sampling, i.e. 15 planes can be reconstructed from 8 rings. (b) Retracting the septa, increases the number of projection lines and hence the sensitivity of the system, but fully 3D reconstruction is required. (a) (b) 29 Clinical use Small amount of radioactive-labeled molecules are administered to selectively measure functional parameters of different organs (e.g., perfusion, metabolism, innervation) Single photon emitting atoms short half-life; continuously available parent; γ-ray energy high enough to leave the body but not too high to penetrate the crystal 99m Tc (T 1/2 = 6 h), 123 I (13 h), 131 I (8 d), 111 In (3 d), 201 Tl (3 d), 67 Ga (3 d) Positron emitting tracers produced by a cyclotron 11 C (T 1/2 = 20 min), 13 N (10 min), 15 O (2 min), 18 F (109 mind) Clinical applications bone metabolism 99m Tc labeled phosphonate accumulating in proportion to bone turnover, which is increased by several pathologies, such as tumors, fractures, inflammations, & infections 30

16 Bone metabolism 99m Tc labeled phosphonate Accumulating in proportion to bone turnover, which is increased by several pathologies, such as tumors, fractures, inflammations, & infections Left: whole-body scintigraphy after injection of 25 mci 99m Tclabeled methylene diphosponate. This patient suffers from a stress fracture of the right foot. Right: control scans show an increased uptake in the metatarsal bone II compatible with a local stress fracture. 31 Myocardial perfusion & viability Using tracers accumulated in the myocardium in proportion to the blood flow gamma-emitting tracers: 201 Tl, 99m Tc-Mibi PET-tracers: 13 NH 3, H 2 15 O the imaging process is repeated after several hours to compare the tracer distribution after stress & rest if there is a transient ischemia during stress by comparing myocardial perfusion with glucose metabolism, PET is the gold standard to evaluate myocardial viability Myocardial perfusion SPECT scan. Rows 1, 3 and 5 show the myocardial perfusion during a typical stress test. Rows 2, 4 and 6 show the rest images acquired three hours later. The first two rows are horizontal long axis slices, the middle two rows are vertical long axis slices and the bottom two rows are short axis slices. This study shows a typical example of transient hypoperfusion of the anterior wall. On the stress images there is a clear perfusion defect on the anterior wall (horizontal axis slice 9, vertical long axis 16 to 18, short axis slice 13 to 18). The perfusion normalizes on the corresponding rest images. 32

17 Lung embolism 99mTc-labeled human serum albumin is intravenously injected, and it sticks in the first capillaries (i.e., in the lungs) areas of decreased or absent tracer deposit correspond to a pathological perfusion, which is compatible with a lung embolism Lung perfusion (Q) and ventilation (V) scan. The upper row shows four planar projections of a ventilation scan after the inhalation of radioactive pertechnegas. The second and third row show the corresponding lung perfusion images obtained after injection of 99mTclabeled macroaggregates. Several triangular defects are visible in the perfusion scan with a normal ventilation at the same site. This mismatch between perfusion and ventilation is typical for lung embolism. 33 Tumors 18FDG(fluoro-deoxy-glucose) measures (glucose) metabolic activity. The PET scan shows the uptake of the glucose analogue fluoro-deoxy-glucose in the body of the patient. Dark areas correspond to a high FDG uptake. This patient suffers from Hodgkin disease with involvement of multiple lymph nodes in the neck, axilla, retroperitoneal, groins, etc. Pathological lymph nodes are characterized by a high FDG uptake. 34

18 Thyroid function Captation of 99m Tc pertechnetate or 123 I iodide shows the tracer distribution within the thyroid, which is a measure of the metabolic function. 123 I iodide with a T1/2 of 8 days is mainly used for treatment of hyperthyroidism (thyroid hyperfunction) or thyroid cancer. 99m Tc thyroid scan of a patient with a multinodular goiter. Several zones of normal and decreased uptake are visualized. A large cold nodule without any tracer uptake is seen in the lower part of the left lobe. Hypoactive zones are seen in the upper part of the left lobe and central part of the right lobe. 35 Biological effects & safety Accumulated tracer molecules in the liver, the kidneys and the bladder. radioactive decay biologic excretion the equivalent dose of an 18 FDG PET scan = 44.4 msv for the bladder, whereas the patient's effective dose = 3.8 msv Typical doses by ICRP (effective dose) lung = msv thyroid = msv bone = 1.3 msv myocardium = ~ 5 msv tumor = ~ 6 msv (FDG); 13 msv (Ga) 36

19 Future expectations New scintillators for the development of combined PET & SPECT systems Dual modality PET-CT SPECT-CT Growing interests in PET FDG PET scan evaluation of tumor patients for diagnosis, staging, & tumor recurrence becoming the gold standard for therapy monitoring in daily practice & for treatment evaluation with new drugs in the early stages (Phase I & II) Labeling new compounds with PET tracers Therapy with radioactive tracers, especially for the treatment of hematological diseases by means of radioimmunotherapy with labeled antibodies 37