PowerPoint-Prsentation

Signal, Noise and PreprocessingLars Kasper, PhDTNU & MR-Technology GroupInstitute for Biomedical Engineering, UZH & ETHZGenerous slide support:Guillaume FlandinGed RidgwayKlaas Enno StephanJohn Ashburner

*Huettel et al.*Methods and Models for fMRI AnalysisSeptember 25th, 2015Translational Neuromodeling UnitSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialAfter Andreeas practical intro, this will be the first theoretical talk of the morning. start with what measuring in fMRIThis is why I want to start not with preprocessing itself, but instead on a perspective of what we measure in fMRI which is, mainly noise; and what we want to measure in fMRI, which is: BOLDThis will then motivate preprocessing.The title, by the way, is borrowed from a chapter in Scott Huettels fabulous book. Functional Magnetic Resonance Imaging, which I can heartily recommend for reading. Especially, since we start right with the acquired data in this talk and do not shed light on the question how an MR scanner works or what is the brain physiology allowing us to do fMRI.1Overview of SPM for fMRILars Kasper2fMRI Preprocessing

RealignmentSmoothingNormalisationGeneral linear modelStatistical parametric map (SPM)Image time-seriesParameter estimates

Design matrix

TemplateKernelRandomfield theoryp 5 %event-related: for normal TRs (2s+) improves estimates > 5 %Lars Kasper13fMRI PreprocessingSladky et al, NeuroImage 2011

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialAs I mentioned, MR images of a whole vol take about 3 seconds, but they are typically not acquired simultaneously, but slice by slice. This creates a shift of true acq time for some voxels of up to 1 TR, i.e. 2-3 seconds. Now, if we leave it at that, and assume they all stem from the same time-point, we would lose sensitivity for time-locked effects.13Interpolation - IntuitionLars Kasper14fMRI PreprocessingSupport Point SummingMoving AverageWolfram Mathworld, Convolution

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialSTC Results: SimulationLars Kasper15fMRI PreprocessingSladky et al, NeuroImage 2011Slice-timing Correction

BlockStimulation

Temporal-Derivative Modelling

TR1s4sTR1s4sTR1s4sTR1s4s10s blocks15s blocksEvent-RelatedStimulation

event/42 sevent/63sSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatial

STC Results: ExperimentLars Kasper16fMRI PreprocessingSladky et al, NeuroImage 2011SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialSTC was considered obsolete for a couple of years, since informed basis function modelling (see GLM lecture) provides an alternative, but a recent paper convincingly showed that it actually is better to do it.

in particular, only SMA visible in finger tapping with STC16Sources of Noise in fMRILars Kasper17fMRI PreprocessingAcquisition TimingSubject MotionAnatomical IdentityInter-subject variabilityThermal NoisePhysiological NoiseSpatial PreprocSpatial PreprocSpatial PreprocSpatial PreprocSlice-TimingRealignmentCo-registrationSegmentationSmoothingPhysIO ToolboxSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialLets have a look at the large block of spatial preprocI already mentioned the question of spatial identity of a voxel. This is addressed in one way or the other by all these steps.

17

Finite Resolution and Voxel IdentityLars Kasper18fMRI Preprocessing

voxel = volume element (3D pixel)

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialQ: What is the same voxelin the same session (realignment) .in which region(coreg) .between subjects(normalize)18Preproc = Correct Voxel MismatchLars Kasper19fMRI PreprocessingVoxel Mismatch BetweenFunctional Scans/RunsFunctional/Structural Images SubjectsRealignmentInter-Modal CoregistrationNormalisation/SegmentationSmoothingSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialTo summariseSmoothing, on the other hand, is our last resort. If we are not too far off, we smear out remaining voxel mismatches at the end. The order of these steps is importantand somehow also reflects the generalisability and complexity of the respective problems19REALIGNCOREGSEGMENTNORM WRITESMOOTHGLMSpatial PreprocessingLars Kasper20fMRI PreprocessingSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialfMRI time-seriesMotion correctedMean functionalREALIGN

COREGStructural MRISEGMENTNORM WRITESMOOTH

TPMs

GLMInputOutputSegmentationDeformation Fields(y_struct.nii)

Kernel(Headers changed)

MNI Space

Spatial PreprocessingLars Kasper21fMRI PreprocessingSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialStart with realignthen coregthen segment, and use this for normalize. Finally smoothing and off we go to the GLM (stat. analysis).21General Remarks: Image RegistrationRealignment, Co-Registration and Normalisation (via Unified Segmentation) are all image registration methodsGoal: Manipulate one set of images to arrive in same coordinate system as a reference imageKey ingredients for image registrationVoxel-to-world mappingTransformationSimilarity MeasureOptimisationInterpolation

Lars Kasper22fMRI PreprocessingSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialAll but smoothing part of spatial preproc steps belong to the class of image registration algorithms. Thats why, before turning to the individual algorithms, I want to give the following remarks on image registrationImage reg aims at manipulating one set of images to arrive in the same coordinate system as another, ref imageKey ingredients to accomplish this arean understand how voxel data represents data in the world, a set of allowed trafos to manipulate images, a measure to quantify similarity, an algorithm to optimise this similarity, and finally, a way to interpolate, to get back voxels from the world.22A. Voxel-to-World Mapping3D images are made up of voxels.Voxel intensities are stored on disk as lists of numbers.Meta-information about the data:image dimensions conversion from list to 3D array

voxel-to-world mappingSpatial transformation that maps from: data coordinates (voxel column i, row j, slice k) to: a real-world position (x,y,z mm) in a coordinate system e.g.:Scanner coordinatesT&T/MNI coordinatesLars Kasper23fMRI Preprocessing

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialA. Voxel-to-World: Standard SpacesLars Kasper24fMRI PreprocessingTalairach Atlas

MNI/ICBM AVG152 Template

Definition of coordinate system:Origin (0,0,0): anterior commissureRight = +X; Anterior = +Y; Superior = +ZActual brain dimensions European brains, a bit dilated (bug)SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatial24Also DICOM scanner-based voxel-world mappingB. TransformationsTransformations describe the mapping of all image voxels from one coordinate system into anotherTypes of transformationsrigid body = translation + rotationaffine = rigid body + scaling + shearnon-linear = any mapping(x,y,z) to new values (x,y, z) described by deformation fieldsLars Kasper25fMRI Preprocessing

TranslationRotationScalingShear

non-lineardeformationSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialC. Similarity & D. OptimisationSimilarity measure summarizes resemblance of (transformed) image and reference into 1 numbermean-squared differencecorrelation-coefficientmutual informationAutomatic image registration uses an optimisation algorithm to maximise/minimise an objective functionSimilarity measure is part of objective functionAlgorithm searches for transformation that maximises similarity of transformed image to referenceAlso includes constraints on allowed transformations (priors)Lars Kasper26fMRI Preprocessingintra-modality (same contrast)inter-modality (different contrasts possible)

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialREALIGNCOREGSEGMENTNORM WRITEPreprocessing Step CategorisationLars Kasper27fMRI PreprocessingB. Allowed TransformationsRigid-BodyAffineNon-linearC. Similarity MeasureMean-squared DifferenceMutual InformationTissue Class ProbabilityD. OptimisationExact Linearized SolutionConjugate Direction Line SearchIterated Conditional Modes (EM/Levenberg-Marquardt)SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatial

1x1x3 mm voxel size2x2x2 mmvoxel size E. Reslicing/InterpolationFinally, images have to be saved as voxel intensity list on disk againAfter applying transformation parameters, data is re-sampled onto same grid of voxels as reference imageLars Kasper28fMRI PreprocessingReorientedResliced

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialE. B-spline InterpolationLars Kasper29fMRI Preprocessing

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialfMRI time-seriesMotion correctedMean functionalREALIGN

COREGStructural MRISEGMENTNORM WRITESMOOTH

TPMs

GLMInputOutputSegmentationDeformation Fields(y_struct.nii)

Kernel(Headers changed)

MNI Space

Spatial PreprocessingLars Kasper30fMRI PreprocessingSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialThis might have been a lengthy intro, but it helps to understand and classify the following algorithms very simply as different image registrations.

So, lets see how the individual image registration flavours work in the SPM preproc pipeline30fMRI time-seriesMotion correctedMean functionalREALIGN

RealignmentAligns all volumes of all runs spatiallyRigid-body transformation: three translations, three rotationsObjective function: mean squared error of corresponding voxel intensitiesVoxel correspondence via Interpolation

Lars Kasper31fMRI PreprocessingSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialRealignment Output: ParametersLars Kasper32fMRI Preprocessing

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialfMRI Run after RealignmentLars Kasper33fMRI Preprocessing

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialslice 21after warpingslice 34 before33Motion correctedMean functional

COREGStructural MRI

(Headers changed)

Co-RegistrationAligns structural image to mean functional imageAffine transformation: translations, rotations, scaling, shearingObjective function: mutual information, since contrast differentOptimisation via Powells method: conjugate directions, line seach along parametersTypically only trafo matrix (header) changed

Lars Kasper34fMRI PreprocessingSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialOptimisation via Powells method: initialisation with 12 (i.e. number of parameters of function) search direction long each parameter; best parameter weighting of all parameters combined to a new search direction; Search direction with maximum contribution to new search direction is removed from search direction list34

intensity bins structural

Marginal Histogramintensity bins functional

Joint Histogram

Anatomical MRICo-Registration: OutputJoint and marginal HistogramQuantify how well one image predicts the otherhow much shared informationJoint probability distribution estimated from joint histogram

Lars Kasper35fMRI PreprocessingMean functional

Joint Histogram: h(if,is)Count of voxels who have intensity if in functional and is in structural imageSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialCo-Registration: OutputVoxels of same tissue identity should have same intensity in an MR-contrastIn a second MR contrast, this intensity might be different, but still the same among all voxels of the same tissue typeTherefore, aligned voxels in 2 images induce crisp peaks in joint histogram

Lars Kasper36fMRI PreprocessingSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialSources of Noise in fMRILars Kasper37fMRI PreprocessingAcquisition TimingSubject MotionAnatomical IdentityInter-subject variabilityThermal NoisePhysiological NoiseSpatial PreprocSlice-TimingRealignmentCo-registrationSegmentationSmoothingPhysIO ToolboxSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialSpatial Normalisation: ReasonsInter-Subject VariabilityInter-Subject AveragingIncrease sensitivity with more subjects (fixed-effects)Generalise findings to population as a whole (mixed-effects)Ensure Comparability between studies (alignment to standard space)Talairach and Tournoux (T&T) convention using the Montreal Neurological Institute (MNI) spaceTemplates from 152/305 subjects

Lars Kasper38fMRI Preprocessing

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialWhy Is this a problem?38Warps structural image to standard space (MNI)Non-linear transformation: discrete cosine transforms (~1000)Objective function: Bayes probability of voxel intensityMotion corrected

Structural MRISEGMENTNORM WRITE

TPMs

Segmented ImagesDeformation Fields(Headers changed)

MNI SpaceUnified SegmentationLars Kasper39fMRI PreprocessingMotion corrected

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialEven though its called unified segmentation, it is a 2-step procedure in the SPM pipelinefirst estimation, then writing out images39Theory: Segmentation/NormalisationWhy is normalisation difficult?No simple similarity measure, a lot of possible transformationsDifferent Imaging Sequences (Contrasts, geometry distortion)Noise, artefacts, partial volume effectsIntensity inhomogeneity (bias field)Normalisation of segmented tissues is more robust and precise than of original imageTissue segmentation benefits from spatially aligned tissue probability maps (of prior segmentation data)Motivates a unified model of segmentation/normalisationLars Kasper40fMRI PreprocessingSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialThe rationale behind this method is that normalisation is harder than coreg and realign, since we deal with different brains, sessions, even scanners. It would be easier to break down the problem a bit by using a similarity measure that is robust to all these imperfectionsand the anwer is: tissue probability maps402015-06-14An SPM Perspective on fMRI PreprocessingLars KasperTheory: Unified Model SegmentationLars Kasper41fMRI Preprocessing[1] Ashburner & Friston (2005), Neuroimage

Bias FieldRawBias FieldCorrectedcoil inhomo-geneities

Deformation Fields ~1000discrete cosine transforms

Prior: Tissue probability maps TPMs in MNI spacepixel count

Gaussian Mixture Modelprobability of intensity in given voxel fortissue classCSFWM

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialWhat is the probability of a given pixel to be of tissue class gray matter, white matter/csf

Model has different ingredients

Output: Deformation fields that can be applied to both structural and functional imagesAn SPM Perspective on fMRI Preprocessing2015-06-14Lars Kasper41Summary of the unified modelSPM12 implements a generative model of voxel intensity from tissue class probabilitiesPrincipled Bayesian probabilistic formulationGaussian mixture model: segmentation by tissue-class dependent Gaussian intensity distributionsvoxel-wise prior mixture proportions given by tissue probabilities mapsDeformations of prior tissue probability maps also modeledNon-linear deformations are constrained by regularisation factorsinverse of estimated transformation for TPMs normalises the original imageBias field correction is included within the model

Lars Kasper42fMRI PreprocessingSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialsegmentation works irrespective of image contrast

Estimated Tissue probability maps (TPMs)Spatially normalised BrainWeb phantomsCocosco, Kollokian, Kwan & Evans. BrainWeb: Online Interface to a 3D MRI Simulated Brain Database. NeuroImage 5(4):S425 (1997)Segmentation resultsLars Kasper43fMRI PreprocessingT1T2PDSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatial

Benefits of Unified SegmentationLars Kasper44fMRI PreprocessingAffine registration

Non-linear registration

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialSpatial normalisation LimitationsSeek to match functionally homologous regions, but...Challenging high-dimensional optimisationmany local optimaDifferent cortices can have different folding patternsNo exact match between structure and functionInteresting recent paper Amiez et al. (2013), PMID:23365257CompromiseCorrect relatively large-scale variability Smooth over finer-scale residual differences

Lars Kasper45fMRI PreprocessingSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatial45

SMOOTHGLM

Kernel

MNI SpaceSmoothing Why blurring the data?Intra-subject signal qualitySuppresses thermal noise (averaging)Increases sensitivity to effects of similar scale to kernel (matched filter theorem)Single-subject statistical analysisMakes data more Gaussian (central limit theorem)Reduces the number of multiple comparisonsSecond-level statistical analysisImproves spatial overlap by blurring anatomical differences

Lars Kasper46fMRI PreprocessingSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialSmoothing How is it implemented?

Convolution with a 3D Gaussian kernel, of specified full-width at half-maximum (FWHM) in mmmathematically equivalent to slice-timing operation or reslicing, but different kernels there (Sinc, b-spline)Gaussian kernel is separable, and we can smooth 2D data with 2 separate 1D convolutions

Lars Kasper47fMRI Preprocessing

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialfMRI Run after SmoothingLars Kasper48fMRI Preprocessing

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialslice 21after warpingslice 34 before48fMRI time-seriesMotion correctedMean functionalREALIGN

COREGStructural MRISEGMENTNORM WRITESMOOTH

TPMs

GLMInputOutputSegmentationDeformation Field(y_struct.nii)

Kernel(Headers changed)

MNI Space

Spatial PreprocessingLars Kasper49fMRI PreprocessingSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialSources of Noise in fMRILars Kasper50fMRI PreprocessingAcquisition TimingSubject MotionAnatomical IdentityInter-subject variabilityThermal NoisePhysiological NoiseSpatial PreprocTemporal PreprocNoise ModelingSpatial PreprocSpatial PreprocSpatial PreprocSlice-TimingRealignmentCo-registrationSegmentationSmoothingPhysIO ToolboxSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialTo do so, we tackle different sources of noise in different preprocessing step. A lot of them fall in the category of spatial preproc, which will be the lion share of this talk. It will be framed by remarks on temporal preprocessing and noise modelling, i.e. what to do with the noise you cannot preprocess away.

50Thank youand:TNU Zurich, in particular: KlaasMR-technology Group IBT, in particular: KlaasEveryone I borrowed slides from Lars Kasper51fMRI Preprocessing

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialMixture of GaussiansClassification is based on a Mixture of Gaussians model, which represents the intensity probability density by a number of Gaussian distributions.Multiple Gaussians per tissue class allow non-Gaussian intensity distributions to be modelled e.g. partial volume effects

Lars Kasper52fMRI Preprocessing

Image IntensityFrequency(number of pixels) SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialTissue Probability MapsTissue probability maps (TPMs) are used as the prior, instead of the proportion of voxels in each class

Lars Kasper53fMRI Preprocessing

ICBM Tissue Probabilistic Atlases. These tissue probability maps were kindly provided by the International Consortium for Brain MappingSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialDeforming the Tissue Probability MapsTissue probability maps images are warped to match the subjectThe inverse transform warps to the TPMs

Lars Kasper54fMRI Preprocessing

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatial

TemplateimageAffine registration(error = 472.1)Non-linearregistrationwithoutregularisation(error = 287.3)Non-linearregistrationusingregularisation(error = 302.7)Why regularisation? OverfittingRegularisation constrains deformations to realistic range (implemented as priors)

Lars Kasper55fMRI PreprocessingSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialModelling inhomogeneityA multiplicative bias field is modelled as a linear combination of basis functions.

Lars Kasper56fMRI Preprocessing

Corrupted imageCorrected imageBias Field

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialUnified segmentation: The mathsLars Kasper57fMRI Preprocessing

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialUS Maths: Bias FieldLars Kasper58fMRI Preprocessing

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialUS Maths: Spatial Priors by TPMsLars Kasper59fMRI PreprocessingSNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialUS Maths: Deformation FieldsLars Kasper60fMRI Preprocessing

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatialUS Maths: RegularisationLars Kasper61fMRI Preprocessing

SNR & PreprocTemporalRealignNormaliseGeneralCoregSmoothSpatial