SPECT: Physics Principles and Equipment Design

Transcription

1 SPECT: Physics Principles and Equipment Design Eric C. Frey, Ph.D., Professor Division of Medical Imaging Physics Russell H. Morgan Department of Radiology and Radiological Science

2 Disclosures Johns Hopkins University Licenses an iterative reconstruction code for SPECT to GE Healthcare. Dr. Frey is entitled to a share of royalty received on sales by GE Healthcare of this reconstruction code. The terms of this arrangement are being managed by the Johns Hopkins University in accordance with its conflict of interest policies

3 Learning Objectives Describe basic principles of generating SPECT images including the instrumentation and reconstruction Review the components of a gamma camera and describe how they affect image quality Understand the major image degrading factors Understand the concept of iterative reconstruction and how it can compensate for image degrading factors

4 Outline Basic Principles Instrumentation Image Reconstruction

5 Basic Principles Goal: obtain physiological, functional, or metabolic information about patient. Method: Estimate 3D distribution of radionuclidelabeled imaging agent in body at a point in time or for multiple times. Implementation: Measure 2D projections of radioactivity distribution at a set of projection views using a gamma camera. Use computed tomography methods to estimate activity distribution from the set of 2D projection images.

6 Basic Principles: Data Acquisition Gamma Camera γ-rays Imaging Agent Gamma Camera Gamma Camera

7 Computed Tomography pt, ax m x tdx Sometimes referred to as 2D Radon transform of a Recover function a(x) from projections p(t,θ)

8 Basic Principles: Computed Tomography pt, ax m x tdx Sometimes referred to as 2D Radon transform of a Recover function a(x) from projections p(t,θ)

9 Outline Basic Principles Instrumentation Image Reconstruction

10 Instrumentation: Gamma Camera

11 Collimator: Basic Principle Establishes relationship between direction in space and point in image

12 Resolution and Efficiency Fundamental tradeoff between resolution and efficiency/sensitivity For parallel hole collimators: (FWHM resolution) 2 efficiency Fundamental limitation for nuclear medicine

13 Components of CDR dx, r i( x, x ) gx, r dx; D i intrinsic response g=geometric response p=penetration response s=septal scatter response px, r sx, r Assuming CDR is constant in planes parallel to the collimator face: i( x) g x ; D p x, D s x, D D distance to face of collimator dx

14 Components of Collimator Response Geometric: photons passing through holes Septal penetration: photons pass through septa w/o interacting and are detected Septal scatter: photons scattering from septa then detected Total response: sum of above Images of I-131 Point Source LEHR MEGP HEGP

15 Components of Collimator Response 364 kev photons Total Geometric Penetration Scatter HEGP MEGP 10 cm from collimator Intensity (arbitrary units) TRF GRF PRF SSRF MEGP Intensity (arbitrary units) TRF GRF PRF SSRF Distance from Face of Collimator (cm) Distance from Face of Collimator (cm)

16 Collimators: Fabrication Hole Shapes Round Hexagonal Square Manufacturing techniques Cast (HE, ME) Foil (Many LE)

17 Collimator Geometries Parallel-Hole Converging-Hole Diverging-Hole Pinhole-Hole

18 Parallel Hole FOV equal to collimator size Resolution: Sensitivity constant E a open 4 L 2 a open a total FWHM d Z L B L

19 Converging Hole Magnification (intrinsic resolution not as important) FOV proportional to distance to focal point Resolution in source plane: FWHM Z Sensitivity increases w/ (distance to focal point) -1

20 Diverging Hole Focal point behind detector Minification (intrinsic resolution has large effect) FOV increases w/distance from focal point Sensitvity increases decreases w/distance to face of collimator Resolution in source plane proportional to collimator distance Rarely used

21 Pinhole Collimators Resolution: determined by aperture diameter, proportional to distance FOV: increases w/distance Sensitivity: decreases w/distance 2 and pinhole diameter Very useful for small animal imaging (no fundamental resolution limit): requires very high space-bandwidth product (# of resolution elements) Future of nuclear medicine?

22 Collimator-Detector Response Combination of intrinsic and collimator response FWHM total FWHM 2 2 intrinsic FWHM collimator FWHM (cm) GRF GRF Fit GRF*IRF GRF*IRF Fit FWHM (cm) GRF GRF Fit GRF*IRF GRF*IRF Fit Distance from Face of Collimator (cm) Distance from Face of Collimator (cm)

23 Scintillation Detectors Gamma ray -> visible light proportional to energy Advantages High density available Large area detectors readily and inexpensively available Disadvantages Indirect (conversion needed, light loss, affects spatial and energy resolution) Relatively few photons created Low energy resolution Low spatial resolution

24 Scintillation Detectors Desirable Properties High sensitivity (counts/activity/time) High Z High Density Thick High light output (better energy/spatial resolution) Compatible w/photodetector Wavelength of output Index of refraction Decay time fast compared to count rate 100s of ns acceptable for conventional NM Nanoseconds for PET

25 Properties of Common Scintillators PMT SSPD Older PET Newer PET Specific Gravity Max nm Index of Refraction Decay Time (µs) Light Yield (photons/mev) Rel Yield w/pmt NaI(Tl) , CsI(Tl) , , CsI(Na) , , LaBr3(Ce) , BGO , GSO /90% 9, /10% LSO ,

26 Scintillator Thickness Sensitivity Intrinsic Resolution: Optimal Thickness: 3/8 (9.53 mm) for 140 kev 5/8 (15.87 mm) or 1 (25.4 mm) for In-111 or I-131

27 Light Guide/Pipe Protect crystal from air Transmit photons to detector Provide uniform light response Modern cameras use plate of glass rather than shaped light pipes

28 Photomuliplier Tube (PMT)

29 PMTs High gain (10 5 to 10 7 ) Gain proportional to voltage (tightly controlled) Very sensitive to magnetic fields per camera Multi-anode/position-sensitive PMTs for small animal systems Arranged in hexagonal close-packed array

30 Detection Electronics Preamplifier (Q to V) Amplifier (Pulse Shaping) PHA (pulse-height-analyzer-measure pulse height)

31 Positioning (Anger) Electronics Goals: Resolution << PMT diameter Minimize amount of electronics Estimate interaction position based on distribution of scintillation photons

32 Position Estimation (Continued) Analog position estimation Resistive charge division network E X X Y Y x X X E y Y Y E

33 Digital Position Estimation Digitize Pulse height from each Waveform from preamp Estimate energy and position using DSP or microprocessor Allows More sophisticated position/energy estimation Pulse pileup detection/rejection

34 Need for Corrections Light collection is spatially varying Spatially varying energy estimate Anger equations are approximate -> nonlinear estimates of position Crystal may have spatially varying light output, PMTs have varying gain, Edge Packing Artifact Tube Pattern Artifact

35 Energy Correction Measured signal depends on amount of light collected and turned into charge Collection of scintillation photons depends on position (poorer in between PMTs than directly under one) Results in spatial shift of energy spectrum Depends on photon energy Energy windowing results in spatially varying sensitivity Counts Average 2% lower 2% higher Energy (kev)

36 Spatial Linearity Corrections Estimates of position are inaccurate Lines tend to bend away from tube center Acquire image of flood source through mask with holes at known positions Obtain relating measured x and y positions to true ones

37 Intrinsic Uniformity Correction Energy and spatial corrections greatly improve this Some residual nonuniformity remains Function of energy and energy window Should use isotope-specific uniformity correction w/o uniformity correction w uniformity correction

38 Performance Characteristics Linearity: degree to which lines are not straight Measured w/line mask or bar phantom

39 Energy Resolution Typically get pulse w/ near Gaussian shape Full-width at half-maximum (FWHM) is common summary measure (9-10% for typical gamma cameras, 5% for CZT) Express as % of incident photon energy Measuring energy spectrum using source in air Co-57, NaI: 9%

40 Energy Resolution Results from statistical variations in number of photoelectrons: ~3 ev per scintillation photon ~11% scintillation conversion efficiency ~50% of scintillation photons collected ~10% of scintillation photons produce photoelectron For 140 kev photon we have # photoelectrons= ev 3eV Energy resolution: E E 2.35 E E % electrons 38 photons per kev

41 Intrinsic Spatial Resolution X+, X-, Y+ and Y- signals are imprecise (# photoelectrons produced on each PMT is random) Imprecision affects position estimate Approximately proportional to E -1/2 Worse for thicker crystals (variations in light spread as a function of depth of interaction) Measured using narrow well-collimated beam Expressed in terms of FWHM Typically mm for modern cameras Is spatially varying Depends on photon energy

42 Intrinsic Spatial Resolution Bar Phantom

43 Count Rate Performance Typical max count rates kcps Typical 20% loss count rates of kcps Paralyzable: new event reset deadtime n Ne N Nonparalyzable: new event does not reset deadtime n n=measured count rate N=true count rate τ= dead time 1 1 N

44 Counting System Types 1 n=1/ 0.8 Ideal Nonparalyzable n n=1/e 0.2 N=1/ Paralyzable N

45 Computed Tomography pt, ax m x tdx Sometimes referred to as Radon transform of a Recover function a(x) from projections p(t,θ)

46 Outline Basic Principles Instrumentation Image Reconstruction

47 Convolution (Filtered)Backprojection Reconstructed Image a x ht Reconstruction Kernel 0 ht pt, f e 2ift df Backprojection x m tdt d Filtered Projections

48 This image cannot currently be displayed. AAPM 2012 Summer School on Medical Imaging using Ionizing Radiation Ideal Projection from Point Source Ideal Collimator Source 48

49 Reconstruction from Ideal Projections Ideal projections produce near-ideal reconstructions using FBP even from finite # of projections True Activity Distribution FPB Reconstruction from near-ideal projections 49

50 Image Degrading Factors Attenuation in patient Scatter in patient Collimator-detector response Poisson noise Patient Motion 50

51 This image cannot currently be displayed. AAPM 2012 Summer School on Medical Imaging using Ionizing Radiation Attenuation in Patient Ideal Collimator Absorbed Scattered Source 51

52 Attenuated Projections p t, a x m x t e 0 xln dl dx

53 Effects of Attenuation Without attenuation compensation, sources at depth appear dimmer Reduces quantitative accuracy Phantom FBP Reconstruction 53

54 This image cannot currently be displayed. AAPM 2012 Summer School on Medical Imaging using Ionizing Radiation Scatter in Patient Scatter Response Unscattered Collimator Absorbed Source Multiply Scattered Scattered 54

55 Effect of Source Position on SRF Intensity Intensity (arbitrary units) Detector Detector Projection Bin Number Intensity Intensity (arbitrary units) Detector Detector Projection Bin Number

56 Effects of Scatter Amount of scatter increases with depth More scatter for isotopes emitting lower energy photons # Scattered Tc-99m Photons # Unscattered Photons Tc-99m Tl Source depth (cm) 56

57 Effects of Scatter Primarily affects low spatial frequencies Primary Primary+Scatter MTF Spatial Frequency (cm -1 ) 57

58 Use of Energy Discrimination to Reduce Scatter True Energy Photon Energy (kev) Measured Energy 20% Photon Energy (kev) Scatter

59 Effects of Scatter on Energy Spectrum Tc-99m Tl-201 Counts Primary Scatter Total Energy (kev) Counts Primary Scatter Total Energy (kev)

60 Effects of Scatter Reduces contrast, especially important for cold lesions Phantom Reconstructed From Unscattered Photons Reconstructed From Unscattered & Scattered Photons 60

61 Quantitative Effects of Scatter Degrades quantitation: if used with attenuation compensation, results in activity estimates that are too high Effect on quantitation is spatially varying Phantom Unscattered Scatter + Unscattered Reconstructed Intensity Phantom Primary Primary+Scatter Pixel Number 61

62 This image cannot currently be displayed. AAPM 2012 Summer School on Medical Imaging using Ionizing Radiation Collimator-Detector Response: Geometrically Collimated Photons Real Collimator Source 62

63 This image cannot currently be displayed. AAPM 2012 Summer School on Medical Imaging using Ionizing Radiation Collimator-Detector Response: Septal Penetration and Scatter Septal Penetration Septal Scatter Real Collimator Source 63

64 Characteristics of CDR Width increases with distance Star-shaped for poorly-designed collimator I-131 Point Source 30 cm MEGP Collimator HEGP Collimator Distance from Collimator Face 5 cm 10 cm 15 cm 20 cm Logarithmic Gray Scale 64

65 Effect of Geometric CDR on SPECT Images Loss of resolution Spatially varying resolution Point Source Phantom FBP Reconstruction from Projections with LEHR Collimator 65

66 Effect of CDR on Spatial Frequencies Fourier transform of geometric CDR is geometric transfer function (GTF) GTF acts like a filter on the image At some frequencies GTF is zero or small Some information will be essentially lost Cannot completely recover resolution 66

67 Effects of CDR on Spatial Frequencies Analagous to spatially varying low-pass filter GTF LEHR LEGP Relative Magnitude Hann, m =0.5 Rectangular, m =0.5 Butterworth, m =0.23, n= Spatial Frquency (cm -1 ) Frequency (cycle/pixel)

68 Geometric Response Function G; A D L B L D A 0 G Fourier Transform of geometric response 2D spatial frequency 2 efficiency of collimator A=Aperture function for collimator holes D=distance to face of collimator L=collimator thickness B=distance from back face of collimator to image plane For round holes (or approximately for hex holes having same open area) gr; D r 2cos1 T 2R r T R 1 r 2 T 4R 2 R Collimator hole radius r distance from perpendicular in image plane r T r L D L B a open 4 L 2 a open a total a open Area of collimator hole a total Area of unit cell (hole + septa)

69 Shape of Geometric Response LEHR collimator, D=10 cm, R=0.7mm, L=3.15 cm, B=0.5 cm GRF=geometric response function PRF=pixel response function (0.3 cm pixels) IRF=intrinsic response function (0.4 cm FWHM)

70 Distance Dependence of GRF FWHM GRF*IRF D ad b 2 c 2

71 Poisson Noise Projection data corrupted by Poisson noise: variance = mean counts in pixel Noise is spatially varying Once added, noise is irreversible, but effects can be controlled (regularization) 71

72 Computed Tomography: A Better Approach p Cx p j Mean detected counts in projection bin j x i Mean decays in image voxel i C ij Probability that decay in voxel i gives rise to detected photon in projectin bin j

73 Poisson Distribution 0.2 Pnm mn e m n! m Mean counts (not necessarily integer) n Recorded counts (integer) Px Probability of recording x counts 2 variance of n=m P N m=5 m=10 m=20 m= N

74 Poisson Noise Counts in pixels are independent random variables Noise has equal power at all frequencies Image has less information at high frequencies due to CDR GTF LEHR LEGP Noise power Spectrum: level depends on counts in image Spatial Frquency (cm -1 )

75 Effect of Poisson Noise on SPECT Images Ramp filter used in FBP amplifies high frequencies Combine with low-pass to reduce high this effect Relative Magnitude Ramp-Butterworth, m =0.23, n=6 Rectangular, m =0.5 Ramp-Hann, m = Frequency (cycle/pixel)

76 Effect of Poisson Noise: FBP Reconstruction Ramp filter amplifies high frequencies Use low pass filter to reduce high frequency noise Noise Free FBP Ramp FBP w/ Ramp & Butterworth

77 Computed Tomography: A Better Approach p Cx p j Mean detected counts in projection bin j x i Mean decays in image voxel i C ij Probability that decay in voxel i gives rise to detected photon in projectin bin j

78 Statistical Reconstruction arg max x Px p P p xp x Pp xpxdx P x p a posteriori probabiliy of the activity distribution x given the measured data p Pp x Likelihood of the activity distribution x given the measured data p Px Prior probability of activity distribution x Maximum a Posteriori (MAP) Reconstruction Px p argmax Pp xpx x Pp xpxdx argmax x Pp xpx Maximum Likelihood Reconstruction arg max x if Px constant Px p argmax x Pp x

79 Maximum Likelihood Reconstruction Poisson Likelihood Pnm mn e m n! m Mean counts (not necessarily integer) n Recorded counts (integer) p Cx p j Mean detected counts in projection bin j x i Mean decays in image voxel i C ij Probability that decay in voxel i gives rise to detected photon in projectin bin j arg max x Pp x j Cx p j j e Cx j p j! ln Pp x Lp x p j ln Cx Pp x argmax x j j Lp x argmax x Cx j ln p j! j p j lncx j Cx j

80 ML-EM Can maximize log-likelihood using Expectation- Maximization (EM) algorithm n1 x n 1 i x i x i n [1] j 1 r j j 1 C ij j C ij C T 1 CT r i i p j n C ij x i p j [Cx] j Ratio of measured to projection of current estimate (error)

81 Practical Problems Matrix C is very big (>64 billion elements) Calculate Cx and C T p on the fly (projector/backprojector) Convergence is very slow (many hundreds of iterations Use subsets of projection data (OS-EM): multiple updates per iteration 1 p j n1,m1 x n,m i x i js k Choice of subsets is important Typically use >4 angles per subset Speedup approximately equal to # subsets Not provably convergent Problematic for very low noise data C ij js k C ij i n,m C ij x i

82 Reconstruction-Based Compensation Initial Estimate Project Each Angle Computed Projections Compare Computed & Measured Measured Projections Model Cost Function New Estimate Update Estimate

83 IR Based Attenuation Compensation Iterative reconstruction allows accurate modeling of attenuation Modeling attenuation requires accurate, wellregistered attenuation map CT-based attenuation maps are generally excellent

84 Reconstruction Matrix CDRFs AAPM 2012 Summer School on Medical Imaging using Ionizing Radiation Implementing Models in Projector/Backprojector Rotated Reconstruction Matrix Rotate Projection Array Projection Array

85 Triple Energy Window (TEW) Acquire data in scatter windows above and below photopeak Estimate scatter using trapezoidal approximation Counts Window 1 Photopeak Window Window 2 Scatter Scatter Estimate Energy (kev)

86 Improved Scatter Compensation Model-based Fast Monte Carlo Limited commercial availability

87 Effective Scatter Source Estimation (ESSE)

88 Reconstruction-Based CDR Compensation Model CDR in projection and backprojection operations Convolution in planes parallel to detector Various methods for accelerating Allows modeling spatial variance of CDR Projection Array Reconstruction Matrix Rotate Rotated Reconstruction Matrix Projection Array CDRFs

89 Efficacy of Attenuation and Scatter Compensation No Comp Atten Comp Atten & Scatter Comp From Unscattered Photons From Unscattered+ Scattered Photons Reconstructed Pixel Value Unscattered-NC Scattered+Unscattered-NC Unscattered-AC Scattered+Unscattered-AC Scattered+Unscattered-ASC Pixel Number

90 Efficacy of CDR Compensation Resolution improves with iteration but remains limited: cannot totally recover resolution Resolution remains spatially varying Resolution for LEHR better than for LEGP OS-EM w/cdr compensation FBP Updates Phantom LEGP LEHR

91 Effect of Poisson Noise on OS-EM Reconstruction Noise increases with # updates Post-filter needed to control noise Updates No Post-filter 3D Butterworth Post-filter order=8 cutoff=0.24 pixel -1 Updates= # iterations x # subsets

92 Effect of Compensation on Image Noise Noise increases w/ iteration Attenuation Comp has larger noise where attenuation is greatest CDR comp results in lumpy noise Texture of noise w/cdr comp varies spatially depends on collimator Updates No Comp Atten CDR LEGP CDR LEHR

93 Review SPECT is combination of Radio-labeled pharmaceutical Gamma camera to measure 2D projection image Reconstruction method to estimate 3D activity distribution Image quality is fundamentally limited by Poisson noise and tradeoff between resolution and noise Modeling image formation process in reconstruction produces better estimates of the activity distribution