Signal, Noise and Preprocessing*

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Denis Cooper
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MR-Technology Group Institute for Bioedical Engineering, UZH & ETHZ Generous

1 Translational Neuroodeling Unit Signal, Noise and Preprocessing* Methods and Models for fmri Analysis Septeber 27 th, 2016 Lars Kasper, PhD TNU & MR-Technology Group Institute for Bioedical Engineering, UZH & ETHZ Generous slide support: Guillaue Flandin Ged Ridgway Klaas Enno Stephan John Ashburner *Huettel et al.

2 Overview of SPM for fmri Preprocessing Iage tie-series Kernel Design atrix Statistical paraetric ap (SPM) Realignent Soothing General linear odel Noralisation Statistical inference Rando field theory Teplate Paraeter estiates p <0.05 2

3 fmri = Acquiring Movies z y of threediensional Blood Oxygen-Level Dependent (BOLD) contrast iages x typically echoplanar iages (EPI) Run/Session: Tie Series of Iages Task No Task Task scan 1 tie scan N 3

4 fmri = Acquiring Movies The Localized Tie-series is the Fundaental Inforation Unit of fmri Signal: Fluctuation through Blood oxygen level dependent (BOLD) contrast Noise: All other fluctuations Run/Session: Tie Series of Iages scan 1 tie scan N 4

5 fmri Movie: An exaple 5

6 fmri Movie: Subtract the Mean interest in fluctuations only 6

7 The Goal of Preprocessing Before After Preprocessing 8

8 Sources of Noise in fmri Acquisition Tiing Subject Motion Anatoical Identity Inter-subject variability Theral Noise Physiological Noise Teporal Preproc Spatial Preproc Spatial Preproc Spatial Preproc Spatial Preproc Noise Modeling Slice-Tiing Realignent Co-registration Segentation Soothing PhysIO Toolbox 9

9 fmri Movie: Noise Sources interest in fluctuations only 10

The SPM Graphical User Interface Preprocessing 1.

10 The SPM Graphical User Interface Preprocessing Realignent Slice-Tiing Correction Co-registration Unified Segentation & Noralisation Soothing Noise Modeling Physiological Confound Regressors 11

11 Sources of Noise in fmri Acquisition Tiing Subject Motion Anatoical Identity Inter-subject variability Theral Noise Physiological Noise Teporal Preproc Slice-Tiing Realignent Co-registration Segentation Soothing PhysIO Toolbox 12

12 Slice-tiing correction (STC) Slices of 1 scan volue are not acquired siultaneously (60 s per slice) Creates shifts of up to 1 volue repetition tie (TR), i.e. several seconds Reduces sensitivity for tie-locked effects (saller correlation) True 2D Acquisition Sae-Tiepoint Assuption z tie 13

13 Slice-tiing correction (STC) Slice-tiing correction: All voxel tie series are aligned to acquisition tie of 1 slice Missing data is sinc-interpolated (band-liited signal) Sladky et al, NeuroIage

14 Interpolation Interpolation: Estiate issing data between existing data via certain regularity assuptions Signal at issing point is weighted average of neighbors Weighting function = interpolation kernel Here: assuption of liited frequency range of signal: sinc-interpolation 15

15 Slice-tiing correction (STC) Slice-tiing correction: All voxel tie series are aligned to acquisition tie of 1 slice Missing data is sinc-interpolated (band-liited signal) Before or after realignent? before: doinant through-slice otion after: doinant within-slice otion At all? Sladky et al, NeuroIage

16 STC Results: Siulation Slice-tiing Correction Teporal-Derivative Modelling Block Stiulation 10s blocks 15s blocks Event-Related Stiulation 1s TR 4s 1s TR 4s 1s TR 4s 1s TR 4s true beta = 100 % uncorrected event/ 4±2 s event/ 6±3s corrected Sladky et al, NeuroIage

17 Slice-tiing correction (STC) Slice-tiing correction: All voxel tie series are aligned to acquisition tie of 1 slice Missing data is sinc-interpolated (band-liited signal) Before or after realignent? before: doinant through-slice otion after: doinant within-slice otion At all? block design: for long TR (3s+) & short blocks (10s) iproves estiates > 5 % event-related: for noral TRs (2s+) iproves estiates > 5 % Sladky et al, NeuroIage

18 STC Results: Experient Sladky et al, NeuroIage

19 Sources of Noise in fmri Acquisition Tiing Subject Motion Anatoical Identity Inter-subject variability Theral Noise Physiological Noise Spatial Preproc Spatial Preproc Spatial Preproc Spatial Preproc Slice-Tiing Realignent Co-registration Segentation Soothing PhysIO Toolbox 20

20 Finite Resolution and Voxel Identity voxel = volue eleent (3D pixel) 21

21 Preproc = Correct Voxel Misatch Voxel Misatch Between Functional Scans/Runs Functional/Structural Iages Subjects Realignent Inter-Modal Coregistration Noralisation/ Segentation Soothing 22

22 Spatial Preprocessing REALIGN COREG SEGMENT NORM WRITE SMOOTH GLM 23

Spatial Preprocessing Input SNR & Preproc Teporal Spatial General Realign Coreg Output Noralise Sooth fmri tie-series Structural MRI TPMs Segentation Deforation Fields

23 Spatial Preprocessing Input SNR & Preproc Teporal Spatial General Realign Coreg Output Noralise Sooth fmri tie-series Structural MRI TPMs Segentation Deforation Fields (y_struct.nii) Kernel REALIGN COREG SEGMENT NORM WRITE SMOOTH Motion corrected Mean functional (Headers changed) MNI Space GLM 24

24 General Rearks: Iage Registration Realignent, Co-Registration and Noralisation (via Unified Segentation) are all iage registration ethods Goal: Manipulate one set of iages to arrive in sae coordinate syste as a reference iage Key ingredients for iage registration A. Voxel-to-world apping B. Transforation C. Siilarity Measure D. Optiisation E. Interpolation 25

25 A. Voxel-to-World Mapping 3D iages are ade up of voxels. Voxel intensities are stored on disk as lists of nubers. Meta-inforation about the data: iage diensions conversion fro list to 3D array voxel-to-world apping Spatial transforation that aps fro: data coordinates (voxel colun i, row j, slice k) to: a real-world position (x,y,z ) in a coordinate syste e.g.: Scanner coordinates T&T/MNI coordinates 26

brain diensions Origin (0,0,0): anterior coissure Right = +X;

26 A. Voxel-to-World: Standard Spaces Talairach Atlas MNI/ICBM AVG152 Teplate z y Definition of coordinate syste: x Actual brain diensions Origin (0,0,0): anterior coissure Right = +X; Anterior = +Y; Superior = +Z European brains, a bit dilated (bug) 27

rotation Translation Rotation affine = rigid body + scaling + shear non-linear = any

27 B. Transforations Transforations describe the apping of all iage voxels fro one coordinate syste into another Types of transforations rigid body = translation + rotation Translation Rotation affine = rigid body + scaling + shear non-linear = any apping (x,y,z) to new values (x,y, z ) described by deforation fields Scaling non-linear deforation Shear 28

28 Spatial Preproc: SPM vocabulary SPM uses different naes for different odes of iage registration depending on input iages and allowed transforations Realignent Intra-odal iage registration e.g. functional iages rigid body transforations translation/rotation Co-Registration Inter-odal registration e.g. T1/T2 contrast functional to structural iage affine transforations rigid body stretching/shearing Noralisation Multi-odal registration e.g. T1 and/or T2 structural iage(s) to teplate non-linear transforations voxel-wise apping (deforation fields) 29

29 C. Siilarity & D. Optiisation Siilarity easure suarizes reseblance of (transfored) iage and reference into 1 nuber ean-squared difference correlation-coefficient utual inforation intra-odality (sae contrast) inter-odality (different contrasts possible) Autoatic iage registration uses an optiisation algorith to axiise/iniise an objective function Siilarity easure is part of objective function Algorith searches for transforation that axiises siilarity of transfored iage to reference Also includes constraints on allowed transforations (priors) 30

30 Preprocessing Step Categorisation B. Allowed Transforations Rigid-Body Affine Non-linear REALIGN COREG SEGMENT NORM WRITE C. Siilarity Measure Mean-squared Difference Exact Linearized Solution Mutual Inforation Conjugate Direction Line Search D. Optiisation Tissue Class Probability Iterated Conditional Modes (EM/Levenberg-Marquardt) 31

paraeters, data is re-sapled onto sae grid of voxels as

31 E. Reslicing/Interpolation Finally, iages have to be saved as voxel intensity list on disk again After applying transforation paraeters, data is re-sapled onto sae grid of voxels as reference iage Reoriented Resliced 1x1x3 voxel size 2x2x2 voxel size 32

32 E. B-spline Interpolation 33

33 Spatial Preprocessing Input SNR & Preproc Teporal Spatial General Realign Coreg Output Noralise Sooth fmri tie-series Structural MRI TPMs Segentation Deforation Fields (y_struct.nii) Kernel REALIGN COREG SEGMENT NORM WRITE SMOOTH Motion corrected Mean functional (Headers changed) MNI Space GLM 34

34 Realignent fmri tie-series Aligns all volues of all runs spatially Rigid-body transforation: three translations, three rotations REALIGN Objective function: ean squared error of corresponding voxel intensities Voxel correspondence via Interpolation Motion corrected Mean functional 35

35 Realignent Output: Paraeters 36

36 fmri Run after Realignent 37

37 Co-Registration Structural MRI Aligns structural iage to ean functional iage Affine transforation: translations, rotations, scaling, shearing Motion corrected COREG Mean functional (Headers changed) Objective function: utual inforation (diff. contrast!) Optiisation via Powell s ethod: conjugate directions, line seach along paraeters Typically only trafo atrix ( header ) changed 38

the sae tissue type Therefore, aligned voxels in 2 iages induce crisp peaks in joint histogra intensity bins structural

38 Co-Registration: Mutual Inforation Joint Histogra Marginal Histogra Mean functional Anatoical MRI Voxels of sae tissue identity have sae intensity in an MR-contrast In a 2 nd MR contrast, intensity ight be different, but still the sae aong all voxels of the sae tissue type Therefore, aligned voxels in 2 iages induce crisp peaks in joint histogra intensity bins structural intensity bins functional Joint Histogra: h(i f,i s ) Count of voxels who have intensity i f in functional and i s in structural iage 39

voxel intensity in one iage predicts the intensity in the other how uch

39 Co-Registration: Output Aligned voxels in 2 iages induce crisp peaks in joint histogra Optiization criterion: Joint histoga: Quantify how well voxel intensity in one iage predicts the intensity in the other how uch shared (=utual) inforation Joint histogra: proxy to joint probability distribution 40

40 Sources of Noise in fmri Acquisition Tiing Subject Motion Anatoical Identity Inter-subject variability Theral Noise Physiological Noise Spatial Preproc Slice-Tiing Realignent Co-registration Segentation Soothing PhysIO Toolbox 41

41 Spatial Noralisation: Reasons Inter-Subject Variability Inter-Subject Averaging Increase sensitivity with ore subjects (fixed-effects) Generalise findings to population as a whole (ixed-effects) Ensure Coparability between studies (alignent to standard space) Talairach and Tournoux (T&T) convention using the Montreal Neurological Institute (MNI) space Teplates fro 152/305 subjects 42

42 Unified Segentation Structural MRI TPMs Deforation Fields Segented Iages Warps structural iage to standard space (MNI) SEGMENT NORM WRITE Non-linear transforation: discrete cosine transfors (~1000) Objective function: Bayes probability of voxel intensity Motion corrected (Headers changed) MNI Space 43

43 Theory: Segentation/Noralisation Why is noralisation difficult? No siple siilarity easure, a lot of possible transforations Different Iaging Sequences (Contrasts, geoetry distortion) Noise, artefacts, partial volue effects Intensity inhoogeneity (bias field) Noralisation of segented tissues is ore robust and precise than of original iage Tissue segentation benefits fro spatially aligned tissue probability aps (of prior segentation data) Motivates a unified odel of segentation/noralisation 44

44 Suary of the unified odel SPM12 ipleents a generative odel of voxel intensity fro tissue class probabilities Principled Bayesian probabilistic forulation Gaussian ixture odel: segentation by tissue-class dependent Gaussian intensity distributions voxel-wise prior ixture proportions given by tissue probability aps Deforations of prior tissue probability aps also odelled Non-linear deforations are constrained by regularisation factors inverse of estiated transforation for TPMs noralises the original iage Bias field correction is included within the odel 45

Theory: Unified Model Segentation Bayesian generative odel 1 of voxel intensities yy ii fro tissue class

intensities yy Gaussian Mixture Model probability of intensity in given voxel for tissue class coil

ii cc ii = kk kk=1 σσ kk Bias Field Corrected pixel count iage Intensity yy [1] Ashburner & Friston (2005),

45 Theory: Unified Model Segentation Bayesian generative odel 1 of voxel intensities yy ii fro tissue class probabilities, deforation fields and bias fields Objective function: log joint probability of all voxel intensities yy Gaussian Mixture Model probability of intensity in given voxel for tissue class coil inhoogeneities CSF μμ kk Bias Field Raw KK ρρ(ββ) E = log PP(yy μμ, σσ, γγ, bb 11 KK, αα, ββ) WM γγ kk PP yy ii cc ii = kk kk=1 σσ kk Bias Field Corrected pixel count iage Intensity yy [1] Ashburner & Friston (2005), Neuroiage Prior: Tissue probability aps bb 11 bb 22 bb 33 Deforation Fields bb kk (αα) TPMs in MNI space ~1000 discrete cosine transfors 46

46 Segentation results segentation works irrespective of iage contrast Spatially noralised BrainWeb phantos T1 T2 PD Estiated Tissue probability aps (TPMs) Cocosco, Kollokian, Kwan & Evans. BrainWeb: Online Interface to a 3D MRI Siulated Brain Database. NeuroIage 5(4):S425 (1997) 47

47 Benefits of Unified Segentation Affine registration Non-linear registration 48

48 Spatial noralisation Liitations Seek to atch functionally hoologous regions, but... Challenging high-diensional optiisation any local optia Different cortices can have different folding patterns No exact atch between structure and function Interesting recent paper Aiez et al. (2013), PMID: Coproise Correct relatively large-scale variability Sooth over finer-scale residual differences 49

49 Soothing Why blurring the data? Intra-subject signal quality Suppresses theral noise (averaging) Increases sensitivity to effects of siilar scale to kernel (atched filter theore) Kernel Single-subject statistical analysis Makes data ore Gaussian (central liit theore) SMOOTH Reduces the nuber of ultiple coparisons Second-level statistical analysis Iproves spatial overlap by blurring anatoical differences MNI Space GLM 50

50 Soothing How is it ipleented? Convolution with a 3D Gaussian kernel, of specified full-width at half-axiu (FWHM) in atheatically equivalent to slice-tiing operation or reslicing, but different kernels there (Sinc, b-spline) Gaussian kernel is separable, and we can sooth 2D data with 2 separate 1D convolutions 51

51 fmri Run after Soothing 52

52 Spatial Preprocessing Input SNR & Preproc Teporal Spatial General Realign Coreg Output Noralise Sooth fmri tie-series Structural MRI TPMs Segentation Deforation Field (y_struct.nii) Kernel REALIGN COREG SEGMENT NORM WRITE SMOOTH Motion corrected Mean functional (Headers changed) MNI Space GLM 53

53 Sources of Noise in fmri Acquisition Tiing Subject Motion Anatoical Identity Inter-subject variability Theral Noise Physiological Noise Teporal Preproc Spatial Preproc Spatial Preproc Spatial Preproc Spatial Preproc Noise Modeling Slice-Tiing Realignent Co-registration Segentation Soothing PhysIO Toolbox 54

Teaser: PhysIO Noise Modelling We can odel tie series of non-bold physiological fluctuations fro prior knowledge (locations, doinant frequencies) or peripheral recordings (ECG, breathing belt) Filter

54 Teaser: PhysIO Noise Modelling We can odel tie series of non-bold physiological fluctuations fro prior knowledge (locations, doinant frequencies) or peripheral recordings (ECG, breathing belt) Filter these out via incorporation into general linear odel See next talk! Result: Cardiac (red), respiratory (blue) physiological tie courses, and their interaction (green) contribute severely to reaining non-gaussian voxel fluctuations For ore details: See you again on Nov. 8 55

55 Thank you and: TNU Zurich, in particular: Klaas MR-technology Group IBT, in particular: Klaas Everyone I borrowed slides fro 56

56 Further Reading Good Textbook: Karl Friston, J.A., Willia Penny (Eds.), Statistical Paraetric Mapping, Acadeic Press, London, in particular Ashburner, J., Friston, K., 2007a. Chapter 4 - Rigid Body Registration, pp Ashburner, J., Friston, K., 2007b. Chapter 5 - Non-linear Registration, pp Ashburner, J., Friston, K., 2007c. Chapter 6 - Segentation, pp For atheatical/engineering connoisseurs: (see also extra slides here): Ashburner, J., Friston, K.J., Unified segentation. NeuroIage 26, doi: /j.neuroiage

57 Mixture of Gaussians Classification is based on a Mixture of Gaussians odel, which represents the intensity probability density by a nuber of Gaussian distributions. Multiple Gaussians per tissue class allow non-gaussian intensity distributions to be odelled e.g. partial volue effects Frequency (nuber of pixels) Iage Intensity 58

58 Tissue Probability Maps Tissue probability aps (TPMs) are used as the prior, instead of the proportion of voxels in each class ICBM Tissue Probabilistic Atlases. These tissue probability aps were kindly provided by the International Consortiu for Brain Mapping 59

59 Deforing the Tissue Probability Maps Tissue probability aps iages are warped to atch the subject The inverse transfor warps to the TPMs 60

60 Why regularisation? Overfitting Regularisation constrains deforations to realistic range (ipleented as priors) Non-linear registration using regularisation (error = 302.7) Teplate iage Affine registration (error = 472.1) Non-linear registration without regularisation (error = 287.3) 61

61 Modelling inhoogeneity A ultiplicative bias field is odelled as a linear cobination of basis functions. Corrupted iage Bias Field Corrected iage 62

62 Unified segentation: The aths Mixture of Gaussians: probability of voxel i having intensity y i, given it is fro a specific cluster k (e.g. tissue class gray atter) Prior probability of voxel s tissue class (e.g. voxel proportion) γγ kk Joint Probability: Marginal probability of voxel intensity: Joint probability all voxels intensity: 63

63 US Maths: Bias Field Ipleented by adjusting the Means and Variances of the Gaussians on a pixel-by-pixel basis by a function soothly varying in space, ρρ ii ββ : μμ kk μμ kk ρρ ii ββ, σσ kk 2 σσ kk ρρ ii ββ 2 ρρ ii is the exponential of a linear cobination of low frequency basis functions Paraeters to be estiated: vector ββ intensity probability conditioned on cluster identity: 64

64 US Maths: Spatial Priors by TPMs Replacing stationary ixing proportions γγ kk by voxel-dependent proportions which are infored by the prior tissue probabilities bb iiii for this voxel ii and different tissue types kk γγ kk γγ kk ii = γγ kk bb iiii KK jj=1 γγ jj bb iiii Note: KK can be larger than the nuber of tissue classes, since each class can be reflected by a ixture of Gaussians, e.g. 3 Gaussians for gray atter (to allow for non-gaussian distributions per tissue class) E.g. partial volue effects 65

65 US Maths: Deforation Fields Deforation (and thereby noralisation) is ipleented by allowing the prior TPMs (which are in MNI-space) to be spatially transfored by a paraeterised apping b iiii b iiii αα PP cc ii = kk γγ, αα = γγ kkbb iiii (αα) KK jj=0 γγ jj bb iiii (αα) Paraeter vector to be estiated: αα about 1000 discrete cosine transfors 66

66 US Maths: Regularisation Linear Regularisation of Bias Field and Deforation Field Estiates By including prior distributions for αα and ββ as zero-ean ultivariate Gaussians Covariance: αα TT CC αα αα = bbbbbbbbbbbbbb eeeeeeeeeeee; ρρ ββ = exp(kk 70 NN(0, ββ)) Thus, the final objective function to be axiised is the log-joint probability of intensity, bias and deforation field paraeters: Equivalently, the negative free energy is iniised: 67

Signal, Noise and Preprocessing*

Translational Neuroodeling Unit SNR & Preproc Teporal Spatial General Realign Coreg Noralise Sooth Signal, Noise and Preprocessing* Methods and Models for fmri Analysis Septeber 25 th, 2015 Lars Kasper,