... In vivo imaging in Nuclear Medicine. 1957: Anger camera (X;Y) X Y

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1 József Varga, PhD EMISSION IMAGING BASICS OF QUANTIFICATION Imaging devices Aims of image processing Reconstruction University of Debrecen Department of Nuclear Medicine. In vivo imaging in Nuclear Medicine 1957: Anger camera Principle: many photomultiplier tubes see the same large scintillation crystal; an electronic circuit decodes the coordinates of each event Hal Anger (Berkeley) with his positron camera Developer of the scintillation camera 2 Scintillation counter Parts of an analogue gamma camera 3 1. Collimator 2. Crystal: NaI (Tl) 3. Photomultiplier tubes 4. Impulses 5. Anger circuit 6. X, Y coordinates 7. Good events 8. Memory scope 9. Analog-digital converters 10. Computer Matrix circuit Differential discriminator 4 Event Positioning Acquisition with an analogue camera Signal level * Coordinates Y Data block +1 Image + y - x + Slide 5 Camera X (X;Y) Analogdigital converter "FRAME" X Y Acquisition memory "LIST" Counts Time? Counter Storage 6 Full digital gamma camera Gamma cameras 7 8

2 Camera types The role of a collimator Analogue: Anger matrix circuit for decoding coordinates (may be interfaced to computer) (Semi) digital: digital corrections (energy, linearity, sensitivity) Full digital: separate ADC to each PMT coordinates and corrections calculated digitally Detector tor IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII Chrystal Photomultipliers + preamplifiers Lead collimator To form an image from the detected photons, the direction of movements should be known The collimator lets through only the photons that move perpendicularly to its plane 9 Source: Freek Beekman et al., Utrecht 10 Septal penetration Effects of septal penetration Image of an I-131 point source with low energy, high resolution (LEHR) collimator Hexagonal holes of a LEHR collimator septal penetration Decreased resolution Increased background Narrow-beam and effective attenuation coefficients are significantly different Collimators for SPECT systems: Beam forms Effect of collimator on resolution Acquired with a general purpose collimator 3-detector camera, fan beam collimator Pinhole collimator Source: Meikle S., Sydney 15 16

3 Spatial resolution of clinical SPECT: ~ 15 mm How to measure resolution: Image of a line source Current small animal SPECT and PET: spatial resolution around mm Micro-SPECT = special small animal SPECT, with mm resolution Effect of resolution demonstrated on a rat brain phantom: Full Width at Half Maximum (FWHM) 2 mm 1 mm 0.5 mm 0.25 mm 0 mm Source: Freek Beekman et al., Utrecht Point / line spread function Point spread function degrades with distance Example: Gray matter Imaging positron emitters From MRI (segmentation) Spread by the resolution of PET PET: Concept Coincidence detection: Advantages Coincidence detection at 180 : (no collimator) - higher sensitivity - better signal/noise ratio Easier attenuation correction (sum of the two paths inside = body thickness) * More physiological radiopharmaceuticals (C-11, N-13, O-15, F-18) Dynamic tomography is possible (simultaneous acquisition in all directions) 23 24

4 Latent Digital Image A Digital Image Slide 25 Slide 26 Colour palette Effect of matrix size Pixel count usually 255 increments This is linear but could be logarithmic or exponential 512 Slide 27 Slide 28 Resolution and noise Choice of matrix size interpolated to 128 from 64 x 64 (coarse) up to 512 x 512 (fine) some non-square matrices e.g x 256 Restoration filter the pixel size should be less than a half of the best resolution in the image. this will depend on the camera/collimator attenuation and distance from the patient but usually taken as extrinsic FWHM 29 Slide 30 Emission imaging: Study types Static: Imaging an equilibrium distribution Dynamic: Series of images following the accumulation / metabolic pathways / secretion of a radiopharmaceutical Whole body: Static images connected Tomographic: Single photon emission computed tomography (SPECT) Positron emission tomography (PET) Whole body bone scintigram Spot images 31 32

5 Dynamic study Examples: Dynamic studies Following a process - from a single view - at various times Kidney Esophagus Gated blood pool Aims of image processing in nuclear medicine Aims of image processing in nuclear medicine Enhanced image display Image filtering Quantification Analysis of changes Palettes Normalisation, thresholding Interpolating Enhanced image display Image filtering Quantification Analysis of changes Noise reduction Decay (Poisson distribution) Scatter Preservation and recovery of details Linking images Linking images Spatial distribution Spatial distribution Aims of image processing in nuclear medicine Aims of image processing in nuclear medicine Enhanced image display Enhanced image display Image filtering Quantification Analysis of changes Linking images Spatial distribution From regions From curves Of changes Comparison to normal range Normalised / scaled to: injected dose and body size (SUV) blood concentration reference area Image filtering Quantification Analysis of changes Linking images Spatial distribution Time-activity curves and their parameters Parametric images and averages in subregions Difference, change image Aims of image processing in nuclear medicine Aims of image processing in nuclear medicine Enhanced image display Image filtering Quantification Analysis of changes Enhanced image display Image filtering Quantification Analysis of changes Linking images Spatial distribution Whole body images Hybrid imaging devices Spatial registration Joint display (fusion) Linking images Spatial distribution Reconstruction with corrections Reslicing Slices Slices through a 3D point ( browser view) 39 40

6 Smoothing 9 point smooth New value inserted: The nine point smooth weights each pixel with a part of the value of all those around Helps compensate for the artificial effects of digitisation statistical noise But may lose genuine detail x Sum of weights: = 16 Weighted sum of counts: 1x1+4x2+6x1+2x2+2x4+4x2+2x1+1x2+6x1 = 45 Weighted average: 45 / 16 = 2.8 > 2.8 The process is repeated for each pixel Slide 41 Slide 42 Interpolation Initial matrix The opposite of smoothing An image is transposed into a finer matrix Average values are slotted into the pixels between original values Slide 43 Slide 44 Finer matrix Regions of Interest (4 + 8) 2 = 6 Real Pixelated Slide 45 Slide 46 Information from dynamic studies How to analyze changes (dynamics) Time-activity curves from regions Parametric images Calculate a parameter of the time-activity curve for each pixel Curve fitting and parameters Deconvolution followed by curve fitting Gamma-variate function Image series Outline Regions of Interest Display with pseudo-colors Compartmental kinetic model Graphical methods Create timeactivity curves from the ROIs 47 48

7 Information compression: Dynamic studies Based on Result Temporal resolution ROI time curve of each pixel time-activity curve parametric image Information content Spatial resolution 49 full single characteristic subregion full T max Curve parameters (examples) Kidney Cardiac wall motion Oesophagus expon. fit T 1/2 V d V s peak ejection rate diast. EF = syst. peak filling rate V d -V s V d *100% max max 10 T max T max/10 disappearance time 50 Parametric images Deconvolution Right kidney Left kidney C max 100% 50% Amplitude cos-fn. Backgroundcorrected curves: Heart deconvolution T max half time transit time time of emptying phase angle Residual impulse response function What happens in SPECT? SPECT Single Photon Emission Computed Tomography The principles of SPECT are similar to those found in traditional Computed Tomography. The main difference is in how the data is acquired. Slide 53 Slide 54 Why use Tomography? Steps of SPECT In planar imaging, contrast is often low because of radioactivity in front of and behind the area of interest. Data Acquisition Matrix Size, Arc of Rotation, Angular Samples, Orbit, Acquisition Mode Emission CT removes this superimposition, thus vastly improving the detectability of abnormal areas. Reconstruction & Filtering Sinogram, Back Projection, Spatial Frequency, the Fourier Transform, Filtering, Iterative Methods Thus there can be up to a 6-fold improvement in the image contrast. Reslicing Slice orientation as determined by the organ Slide 55 Slide 56

8 Data Acquisition (Arc of Rotation) 10,000 Counts Matrix size and noise For a 64x64 matrix Noise per Pixel = 10,000 = = 1% 10,000 In theory we only need to collect view over 180o of arc why? Percentage Noise = 64x64 Matrix This is not the case in SPECT, because 2500 Counts 1. Spatial resolution degrades with distance between the camera and the object 2. A certain percentage of the total counts comprise of scattered photons For a 128x128 matrix Noise per Pixel = 10,000 = 2500 = Percentage Noise = 100 = 2% x128 Matrix 3. Attenuation is not uniform in the patient Slide 57 Data Acquisition (Arc of Rotation) Data Acquisition (Angular Slide 58 Samples) How many samples should we take? Exception to this rule is Cardiac Imaging Why? For accurate reconstruction, the number of views taken over the 360o arc should equal the image matrix. When the number of samples is less than the minimum, streak artefacts will appear in the reconstructed slices. Taken from Groch et al, 2000 Slide 59 Backprojection Slide 60 Process of filtered backprojection Projections utilized: 1 3 Real section 4 Reconstructed Forrás: 61 Projections and sinogram Filtered back projection Projection: sum along parallel projection lines Back projection without filtering blurred image Sinogram: all projections of a single slice 62 Ramp (=increasing with frequency) filter on a sinogram 63 64

9 Impact of filter on back projection Spatial Frequency: simplest example Lead Blocks 1cm 1cm 1cm The spatial frequency of this scenario is constant, i.e. 1 line pair per cm, or 1 lp cm Slide 66 Question: spatial frequency 1st pattern: spatial frequency Lead Blocks The frequency content of this object is a constant. This may be represented in frequency space as shown below : 1cm 1cm 1cm 1cm 1cm What is the spatial frequency of this object? 1 cm -1 Spatial Frequency Slide 67 Slide 68 2nd pattern: spatial frequency 3rd pattern: mixed The frequency content of this object is also a constant. This may be represented in frequency space as shown below : 1cm 1cm 1cm How would we represent this object in frequency space? 1cm 1cm 1cm 1cm 1cm 1cm 2 cm -1 Spatial Frequency 1 cm -1 2 cm -1 Spatial Frequency Slide 69 Slide 70 3rd (mixed) pattern Fourier Transform: Image Frequency components How would we represent this object in frequency space? 1cm 1cm 1cm 1cm 1cm -1 2cm -1 Spatial Frequency Fourier Transform 1cm 1cm 1cm 2 cm -1 Spatial Frequency i 2π u x F( u) = f( x) e dx Slide 71 Slide 72

10 Frequency transfer Spectrum of a planar gamma camera image power spectrum 1.E+09 1.E+06 Sum Image spectrum Diff. Noise spectrum More components: Closer approximation 1.E Spatial frequency Spectrum of a PET slice (after Hann-filtered backprojection) Typical spatial frequency content of SPECT data 1E+14 e d 1E+11 litu p m A Power spectrum Image Noise Most of the image is made up of low frequency data i.e. data that is changing very slowly in space. There is no spatial detail in this data. The contribution of high frequency data to the image is low. i.e. data that is changing rapidly is swamped by data that is changing slowly Spatial frequency 75 Slide 76 Reconstruction (Filtered Back Projection) Reconstruction (Filtered Back Projection) Typical steps in Filtered Back Projection 1. Acquire raw data and transform to frequency space. 2. Pass raw data through a Ramp Filter. How? 3. Back Project in the usual manner. 4. Filter the back projected data using a Low Pass Filter (may be done before, during or after back projection). Depending on the system, the order in which these tasks are performed can be different. Slide 77 Slide 78 Reconstruction (Filtered Back Projection) Reconstruction (Filtered Back Projection) The function of the ramp filter is to - Suppress low frequencies Amplify high frequencies This will increase the contribution of high frequency data to the image thus resulting in - improved contrast and - spatial resolution. Ramp Filter The number if counts acquired per projection will greatly influence the contribution of noise to the image. Which noise level is a result of a high number of counts per projection? Slide 79 Slide 80

11 Reconstruction with filtering Example: Butterworth-filter Image Data in frequency space Low Pass Filter Ideally we would like to keep as much of the data as possible and only remove those frequencies that are in the noise. Low Pass Filter We can change the shape of the low pass filter to achieve this by adjusting the order and cut-off. Noise Level Slide 81 From: M. Nowak Lonsdale, Bispebjerg Hospital 82 Reconstruction with filtering - example Brain SPECT: Filter selection Raw data has been put through a ramp filter and back projected factory default optimized The above data has been passed through a low pass (Butterworth) filter. Slide Can blurring be corrected for? Filters Deconvolution Raw image Adaptive Wiener filter Window functions specify which frequencies to let through. In Fourier space: multiplication of components Suppression of high frequencies Hann, Hamming, Butterworth, Shepp- Logan, Parzen Restoration filters: window fn. may be >1 (Metz, Wiener) Ramp filter amplifies NOISE multiplication by a window function Window functions 1.0 Hanning Metz Frequency (1/cm) Reconstruction filters 1.0 RAMP Hanning Metz 2 Deconvolution Raw image Adaptive Wiener filter Frequency (1/cm) 86 Effect of restoration filter on thyroid image High count images Which filter is optimal? Hann Low count images Referencia Raw METZ-filtered 87 Hann Hann+Metz 88

12 ITERATIVE RECONSTRUCTION Number of iterations: myocardial SPECT Principle: estimate distribution calculate projections from estimated distribution subtract estimated from measured projections modify distribution by the difference Methods: EM: expectation maximization ML-EM: maximum likelihood EM OS-EM: ordered subsets EM Source: J.R. Halama, Loyola Univ Reconstruction (Iterative Methods) COMPARISON: Methods for reconstruction Iterative Reconstruction Methods Replacing filtered back projection as the reconstruction method of choice. Less efficient than FBP but is better at handling projection noise in low count density projections. Parameters that degrade the image can be incorporated into the reconstruction, including attenuation effects, scatter, and geometry. Filtered backprojection (FBP): Single step (fast) Filter can be chosen (at least ramp) Attenuation correction: afterward Scatter: using effective attenuation coefficient Iterative reconstruction: Time consuming Filter not necessary (post-reconstruction filter?) Attenuation correction can be included (with measured attenuation map) Scatter correction can be included (3D!) Slide Main difficulties with emission imaging Artefact (Attenuation Correction) Noise: Poisson approximation: Gaussian, Attenuation: exponential in homogeneous medium Scatter: decreases resolution SD( count) count Tc-99m, 20% window: radiation scattered at up to 60 o angle included! Activity Distribution in Object Projection The reconstructed activity in each slice is reduced in an exponential fashion from the edges of the patient toward the centre. This results in a cupping artefact. 93 Slide 94 Artefact (Attenuation Correction) Artefact (Centre of Rotation) No Correction Corrected Centre of Projection Centre of Rotation = Centre of Projection Centre of Projection Count Density Count Density Centre of Rotation Centre of Projection = COR Error Slide 95 Slide 96

13 Artefact (Centre of Rotation) Artefact (Motion) Taken from Halama Slide 97 Slide 98 Quality Assurance Quality Assurance Uniformity Analysis Centre of Rotation Analysis In order to evaluate uniformity and COR corrections, it is necessary to be able to generate high quality projections and reconstructions to see the effect on contrast and spatial resolution. Slide 99 Slide dimensional cine display Automatic contour detection Circular versus Non-Circular Source: J.R. Halama, Loyola Univ Scatter Effect of scattering medium Tc F-18 with scatter without scatter

14 Possibilities for scatter correction Triple window scatter correction Simulated scatter 3 window estimate from noiseless projection Decreased effective attenuation coefficient used in Chang s attenuation correction Two (Jaszczak), three or more energy windows Inclusion into iterative reconstruction (preferably 3D) 3 window estimate from noisy projection Filtered noisy estimate Effect of triple energy window scatter correction Without corr. With corr. Source: Eur J Nucl Med (1997) 24: Myocardial perfusion study with Tl