Zurich SPM Course 2011 Spatial Preprocessing

Course

Zurich SPM Course 2011

Spatial PreprocessingGed RidgwayWith thanks to John Ashburnerand the FIL Methods Group1fMRI time-series movie

Auditory example data2Preprocessing overviewREALIGNCOREGSEGMENTNORM WRITESMOOTHANALYSISPreprocessing overviewfMRI time-seriesMotion correctedMean functionalREALIGN

COREGAnatomical MRISEGMENTNORM WRITESMOOTH

TPMs

ANALYSISInputOutputSegmentationTransformation(seg_sn.mat)

Kernel(Headers changed)

MNI Space

ContentsRegistration basicsMotion and realignmentInter-modal coregistrationSpatial normalisationUnified segmentationGaussian smoothingRepresentation of imaging dataThree dimensional images are made up of voxelsVoxel intensities are stored on disk as lists of numbersThe image headers contain information onThe image dimensionsAllowing conversion from list -> 3D arrayThe voxel-world mappingmatrix subscripts -> world/physical/mm coordinatesCan rigidly reorient images by changing their (affine) voxel-world mappingTypes of registration in SPMManual reorientationRigid intra-modal realignmentMotion correction of fMRI time-seriesRigid inter-modal coregistrationAligning structural and (mean) functional imagesAffine inter-subject registrationFirst stage of non-linear spatial normalisationApproximate alignment of tissue probability mapsTypes of registration in SPM NonlinearSpatial normalisation using basis functionsRegistering different subjects to a standard templateUnified segmentation and normalisationWarping standard-space tissue probability maps to a particular subject (can normalise using the inverse)DARTELHigh-dimensional large-deformation warps from smooth flowsNormalisation to groups average shape template

Image headers contain information that lets us map from voxel indices to world coordinates in mmModifying this mapping lets us reorient (and realign or coregister) the image(s)Manual reorientation

Manual reorientation

(Bi)linearManual reorientation

Interpolation

(Bi)linear

Nearest Neighbour

SincInterpolationApplying the transformation parameters, and re-sampling the data onto the same grid of voxels as the target imageAKA reslicing, regridding, transformation, and writing (as in normalise - write)Nearest neighbour gives the new voxel the value of the closest corresponding voxel in the sourceLinear interpolation uses information from all immediate neighbours (2 in 1D, 4 in 2D, 8 in 3D)NN and linear interp. correspond to zeroth and first order B-spline interpolation, higher orders use more information in the hope of improving results(Sinc interpolation is an alternative to B-spline)f(x)?

Linear interpolation 1Dabxf(a)f(b)

xfLinear interpolation 1D01xf(0)f(1)f(x)

x0x1Nearest neighbourTake the value of the closest voxelTri-linearJust a weighted average of the neighbouring voxelsf5 = f1 x2 + f2 x1f6 = f3 x2 + f4 x1f7 = f5 y2 + f6 y1

Linear interpolation 2DB-spline Interpolation

B-splines are piecewise polynomialsA continuous function is represented by a linear combination of basis functions2D B-spline basis functions of degrees 0, 1, 2 and 3Nearest neighbour and trilinear interpolation are the same as B-spline interpolation with degrees 0 and 1.Manual reorientation Reslicing

Reoriented

(1x1x3 mm voxel size)Resliced

(to 2 mm cubic)Quantifying image alignmentRegistration intuitively relies on the concept of aligning images to increase their similarityThis needs to be mathematically formalisedWe need practical way(s) of measuring similarityUsing interpolation we can find the intensity at equivalent voxels(equivalent according to the current estimates of the transformation parameters)

Voxel similarity measuresMean-squared differenceCorrelation coefficientJoint histogram measures

Pairs of voxel intensitiesIntra-modal similarity measuresMean squared error (minimise)AKA sum-squared error, RMS error, etc. Assumes simple relationship between intensitiesOptimal (only) if differences are i.i.d. GaussianOkay for fMRI realignment or sMRI-sMRI coregCorrelation-coefficient (maximise)AKA Normalised Cross-Correlation, Zero-NCCSlightly more general, e.g. T1-T1 inter-scannerInvariant under affine transformation of intensitiesAutomatic image registrationQuantifying the quality of the alignment with a measure of image similarity allows computational estimation of transformation parametersThis is the basis of both realignment and coregistration in SPMAllowing more complex geometric transformations or warps leads to more flexible spatial normalisationAutomating registration requires optimisation...OptimisationFind the best parameters according to an objective function (minimised or maximised)Objective functions can often be related to a probabilistic model (Bayes -> MAP -> ML -> LSQ)

Value of parameterObjective functionGlobal optimum(most probable)Local optimumLocal optimumContentsRegistration basicsMotion and realignmentInter-modal coregistrationSpatial normalisationUnified segmentationGaussian smoothingMotion in fMRICan be a major problemIncrease residual variance and reduce sensitivityData may get completely lost with sudden movementsMovements may be correlated with the taskTry to minimise movement (dont scan for too long!)Motion correction using realignmentEach volume rigidly registered to referenceLeast squares objective functionRealigned images must be resliced for analysisNot necessary if they will be normalised anyway24Even tiny head movements can induce major artefacts in your data, so motion correction is very important.-The t-test that is used by SPM (and that will be discussed in the next lecture) is based on the signal change relative to the residual variance. This signal is computed from the sum of squared differences between the data and the linear model to which it is fitted. Movement artefacts will add up to the residual variance and therefore reduce the sensitivity of your test.- -A lot of fMRI studies have paradigms in which the subject could be moving in a way that is correlated to the different experimental conditions, for example, when you would move your head each time you press a button. If you do not correct for this, these systematic differences might appear as activations in your data. Residual Errors from aligned fMRISlices are not acquired simultaneouslyrapid movements not accounted for by rigid body modelImage artefacts may not move according to a rigid body modelimage distortion, image dropout, Nyquist ghostGaps between slices can cause aliasing artefactsRe-sampling can introduce interpolation errorsespecially tri-linear interpolation

Functions of the estimated motion parameters can be modelled as confounds in subsequent analysesfMRI movement by distortion interactionSubject disrupts B0 field, rendering it inhomogeneousdistortions occur along the phase-encoding directionSubject moves during EPI time seriesDistortions vary with subject positionshape varies (non-rigidly)

Correcting for distortion changes using UnwarpEstimate movement parameters.

Estimate new distortion fields for each image:estimate rate of change of field with respect to the current estimate of movement parameters in pitch and roll.Estimate reference from mean of all scans.Unwarp time series.

+Andersson et al, 2001ContentsRegistration basicsMotion and realignmentInter-modal coregistrationSpatial normalisationUnified segmentationGaussian smoothingMatch images from same subject but different modalities:anatomical localisation of single subject activationsachieve more precise spatial normalisation of functional image using anatomical image.Inter-modal coregistration

Inter-modal similarity measuresSeek to measure shared information in some senseFor example Mutual Information and related metricsStatistical measure of information entropyEntropy is a property of a probability distributionProbabilities can be estimated from histogramsMutual information considers both images histograms and their joint histogramJoint and marginal histograms

Joint histogram sharpness correlates with image alignmentMutual information and related measures attempt to quantify thisInitially registered T1 and T2 templatesAfter deliberate misregistration(10mm relative x-translation)Joint histogram based registration

ContentsRegistration basicsMotion and realignmentInter-modal coregistrationSpatial normalisationUnified segmentationGaussian smoothingSpatial Normalisation

Spatial Normalisation - ReasonsInter-subject averagingIncrease sensitivity with more subjectsFixed-effects analysisExtrapolate findings to the population as a wholeMixed-effects analysis

Make results from different studies comparable by aligning them to standard spacee.g. The T&T convention, using the MNI templateSeek to match functionally homologous regions, but...No exact match between structure and functionDifferent cortices can have different folding patternsChallenging high-dimensional optimisationMany local optimaCompromiseCorrect relatively large-scale variability (sizes of structures)Smooth over finer-scale residual differencesSpatial Normalisation Limitations37Standard spaces

The MNI template follows the convention of T&T, but doesnt match the particular brain

Recommended reading: http://imaging.mrc-cbu.cam.ac.uk/imaging/MniTalairach The Talairach AtlasThe MNI/ICBM AVG152 Template

38Also DICOM scanner-based voxel-world mappingCoordinate system senseAnalyze files are stored in a left-handed systemTalairach space has the opposite (right-handed) senseMapping between them requires a reflection or flipAffine transform with a negative determinantxyzxyzzxyRotated example39On the left, the x-axis has been flipped. Note that we cant rotate between the resulting coordinate systems, whereas we can between the right-hand one and the boxed one.Spatial Normalisation ProcedureStart with a 12 DF affineregistration3 translations, 3 rotations3 zooms, 3 shearsFits overall shape and sizeRefine the registration withnon-linear deformationsAlgorithm simultaneously minimisesMean-squared difference (Gaussian likelihood)Squared distance between parameters and their expected values (regularisation with Gaussian prior)

Spatial Normalisation Warping

Deformations are modelled with a linear combination of non-linear basis functions41

Spatial Normalisation DCT basisThe lowest frequencies of a 3D discrete cosine transform (DCT) provide a smooth basisplot(spm_dctmtx(50, 5))spm_dctmtx(5,5)ans = 0.447 0.602 0.512 0.372 0.195 0.447 0.372 -0.195 -0.602 -0.512 0.447 0.000 -0.633 -0.000 0.633 0.447 -0.372 -0.195 0.602 -0.512 0.447 -0.601 0.512 -0.372 0.195% Note, pinv(x)=x, projection P=x*x P{n} = x(:,1:n)*x(:,1:n) P{N} == eye(N) P{n