Workshop on Quantitative SPECT and PET Brain Studies January, 2013 PUCRS, Porto Alegre, Brasil Corrections in SPECT and PET

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1 Workshop on Quantitative SPECT and PET Brain Studies January, 2013 PUCRS, Porto Alegre, Brasil Corrections in SPECT and PET Físico João Alfredo Borges, Me.

2 Corrections in SPECT and PET SPECT and PET hold the promise to exactly quantify the concentration of radioactivity within a given volume of tissue in absolute units, e.g. as kilobecquerels per cubic centimeter. This process is compromised by photon scatter, photon attenuation, and partial volume artifacts.* *Ritt, P., Vija, H., Hornegger, J., Kuwert, T. Absolute quantification in SPECT. Eur J Nucl Med Mol Imaging (2011) 38 (Suppl 1):S69 S77.

3 Corrections in SPECT and PET In PET, options to correct for these confounding variables were developed and validated several decades ago owing to the technical advantages offered by positron decay and coincidence detection. In SPECT, technical progress in that regard has been considerably slower with various reports emphasizing the lack of quantitative ability.

4 Corrections in SPECT and PET

5 Tomographic Reconstruction Two approaches: Analytical : Simple, no modelling, fast Filtered Back Projection Direct Fourier Transform Iterative : More realistic with modelling, lengthy Algebraic Statistical

6 Analytical Formulation Radon Transform

7 Analytical Formulation Direct inversion of Radon Transform Activity slice Continuous formulation X Discrete implementation Assumes noiseless data and real projections of object No modelling included ideally, corrections should be performed before reconstruction, needs noise smoothing Biggest advantage = speed Most widely used = FILTERED BACKPROJECTION = FBP

8 Analytical Formulation

9 Analytical Formulation

10 Iterative Methods Successive estimation of the projections iterative inversion of the system of equations Discrete and matrix formulation of the reconstruction problem object and measured sinograms are discrete Very large system of equations Modelling of the detection process: geometry and physics Statistical modelling and treatment of acquisition noise Inclusion of a priori knowledge of the object or regularization Lengthy and noise increases with number of iterations

11 Iterative Methods s = R a* s = acquired projections R = projection operator a* = object to be reconstructed Given s and R, search for a solution a* that minimizes a cost function d(p,ra*) Modelling of operator R Geometry detection geometry: parallel, conical pixel intensity distribution: section, segment Physics detector: resolution, sensitivity interactions: attenuation, scattering

12 Iterative Methods

13 Iterative Methods Statistical Assumption of statistical model for the noise probability distribution for the measurements * ML-EM - Maximum Likelihood - Expectation Maximization - projections follow the Poisson distribution - solution a* maximizes the likelihood - conservation of total number of detected events - solutions 0 - slow convergence and noise increases with iterations - fast alternatives: OSEM (Ordered Subsets Expectation Maximization) RAMLA (Row Action Maximum Likelihood Algorithm)

14 Iterative x Analytical FDG distribution FBP FDG distribution OSEM

15 SPECT Corrections

16 SPECT Attenuation Correction Chang Transmission map: External source CT image

17 SPECT Chang

18 SPECT External source

19 SPECT External source

20 SPECT CT image

21 SPECT CT image

22 SPECT Scatter correction

23 SPECT Scatter correction

24 SPECT Scatter correction Options for scatter correction. either subtract measured or modelled scatter directly from projections prior to reconstruction add measured or modelled scatter as constant distribution in the projection step of the reconstruction directly incorporate a scatter model in both the forward and backprojection steps of the reconstruction include the modelled scatter only in the forward projection step

25 SPECT Scatter correction

26 SPECT Scatter correction Dual and triple energy window corrections

27 SPECT Scatter correction Dual and triple energy window corrections

28 SPECT Partial Volume Effect

29 SPECT Partial Volume Effect

30 SPECT Partial Volume Correction

31 SPECT Partial Volume Correction

32 PET/CT Correction

33 PET/CT Correction Registered Events A B C D Event A = True coincidences Event B = Scattered coincidences Event C = Randoms or false coincidences Events D = Singles

34 PET/CT Basic Correction A = AC + ScC + RandC B = AC + RandC C = RandC

35 PET/CT Random coincidence Correction Delayed Coincidence Channel Method By delaying one coincidence channel a loss of true coincidences a estimate randoms Single Rates Estimation Estimates the random rate from the relation: R ij = 2t r i r j, where t is the system temporal resolution, r i is the single rate at channel i, and r j is the rate at channel j

36 PET/CT Random coincidence Correction

37 PET/CT Random coincidence Correction Image with high number of random and scatter events Same image changing the random- scatter ratio

38 PET/CT Normalization Correction Crystals with different properties PMT gain changes on time Average efficiency varies with position in the block Sinogram of an uniform cylinder, without efficiency normalization

39 PET/CT Normalization Correction Cylinder of Ge-68

40 PET/CT Geometric Correction Geometrical Effects The probability of interaction depends on the incidence angle (radial position) and block position in the detector Cylinder - Without geometrical correction Cylinder - With geometrical correction

41 PET/CT Dead Time correction Cylinder with F18

42 PET/CT Scatter Correction Convolution subtraction (most 2D mode systems) Adjust scattering functions in linear source profiles Convolutes emission data with scattering functions and subtracts the result

43 PET/CT Scatter Correction Klein-Nischina Equation (3D mode) Extracts the scattering information from emission data and transmission data, using Klein-Nishina model Better results if scattering factor is high Residual errors are still high (15-20%)

44 PET/CT Attenuation Correction P1 = e µl1 P2 = e µl2 P1 * P2 = e µl Attenuation is dependent on the path length and not the depth of the source of activity

45 PET/CT Attenuation Correction With attenuation correction Without attenuation correction

46 PET/CT Attenuation Correction Attenuation Correction Inherent Image Registration

47 PET/CT Attenuation Correction Attenuation Values are Energy Dependent Water (Soft Tissue) and Bone are Different Solution is to Segment Image into Tissue and Bone and Scale Separately

48 PET/CT Attenuation Correction For CT values < 0, materials are assumed to have an energy dependence similar to water For CT values > 0, material is assumed to have an energy dependence similar to a mixture of bone and water The green line shows the effect of using water scaling for all materials

49 PET/CT Attenuation Correction

50 PET/CT Attenuation Correction CT PET Fused RACT PET Fused No AC

51 PET/CT Corrections Conventional Iterative Reconstruction Randoms Correction Deadtime/ Normalization Correction Radial Repositioning Quadrant Scatter Correction Attenuation Correction VUE Point Deadtime/ Normalization Correction Radial Repositioning Randoms Correction Iterative Reconstruction w/ Distance Driven Projectors Quadrant Scatter Correction Attenuation Correction VUE Point HD (mid-2007 update) Iterative Reconstruction w/ Distance Driven Projectors Deadtime/ Normalization Correction Detector Geometry Modeling Randoms Correction Volume Scatter Correction Attenuation Correction

52 Bibliography BADAWI, Ramsey (1999) Introduction to PET Physics. ZAIDI, Habib (2007) Optimisation of whole-body PET/CT scanning protocols. Biomed. Imaging Interv. J, v. 3, n.2, e36. H. Zaidi and B.H. Hasegawa. Quantitative Analysis in Nuclear Medicine Imaging. Springer. Ritt, P., Vija, H., Hornegger, J., Kuwert, T. Absolute quantification in SPECT. Eur J Nucl Med Mol Imaging (2011) 38 (Suppl 1):S69 S77. Simon R. Cherry and Magnus Dahlbom. PET: Physics, Instrumentation, and Scanners. Springer. Brian F Hutton, Irene Buvat and Freek J Beekman. Review and current status of SPECT scatter correction. Phys. Med. Biol. 56 (2011) R85 R112.

53 Thank You

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