Sensor & Source Space Statistics Sensor & Source Space Statistics Rik Henson (MRC CBU, Cambridge) With thanks to Jason Taylor, Vladimir Litvak, Guillaume Flandin, James Kilner & Karl Friston Sensor & Source Space Statistics Sensor & Source Space Statistics Rik Henson (MRC CBU, Cambridge) With thanks to Jason Taylor, Vladimir Litvak, Guillaume Flandin, James Kilner & Karl Friston 8

OverviewOverview A mass-univariate statistical approach to localising effects in space/time/frequency (using replications across trials/subjects)…

OverviewOverview Sensor Space:Sensor Space: 1.Random Field Theory (RFT) 2.2D Time-Freq (within-subject) 3.3D Scalp-Time (within-subject) 4.3D Scalp-Time (between-subjects) Source Space:Source Space: 1.3D “time-freq” contrast images 2.SPM vs SnPM vs PPM vs FDR 3.Other issues & Future directions 4.Multivariate Sensor Space:Sensor Space: 1.Random Field Theory (RFT) 2.2D Time-Freq (within-subject) 3.3D Scalp-Time (within-subject) 4.3D Scalp-Time (between-subjects) Source Space:Source Space: 1.3D “time-freq” contrast images 2.SPM vs SnPM vs PPM vs FDR 3.Other issues & Future directions 4.Multivariate

1. Random Field Theory (RFT) RFT is a method for correcting for multiple statistical comparisons with N-dimensional spaces (for parametric statistics, eg Z-, T-, F- statistics)… 1. When is there an effect in time, eg GFP (1D)? 2. Where is there an effect in time-frequency space (2D)? 3. Where is there an effect in time-sensor space (3D)? 4. Where is there an effect in time-source space (4D)? RFT is a method for correcting for multiple statistical comparisons with N-dimensional spaces (for parametric statistics, eg Z-, T-, F- statistics)… 1. When is there an effect in time, eg GFP (1D)? 2. Where is there an effect in time-frequency space (2D)? 3. Where is there an effect in time-sensor space (3D)? 4. Where is there an effect in time-source space (4D)? Worsley Et Al (1996). Human Brain Mapping, 4:58-73

“Multimodal” Dataset in SPM8 manual (and website)“Multimodal” Dataset in SPM8 manual (and website) Single subject:Single subject: 128 EEG 275 MEG 3T fMRI (with nulls) 1mm 3 sMRI Two sessionsTwo sessions ~160 face trials and ~160 scrambled trials per session~160 face trials and ~160 scrambled trials per session (N=12 subjects soon, as in Henson et al, 2009 a, b, c)(N=12 subjects soon, as in Henson et al, 2009 a, b, c) “Multimodal” Dataset in SPM8 manual (and website)“Multimodal” Dataset in SPM8 manual (and website) Single subject:Single subject: 128 EEG 275 MEG 3T fMRI (with nulls) 1mm 3 sMRI Two sessionsTwo sessions ~160 face trials and ~160 scrambled trials per session~160 face trials and ~160 scrambled trials per session (N=12 subjects soon, as in Henson et al, 2009 a, b, c)(N=12 subjects soon, as in Henson et al, 2009 a, b, c) 2. Single-subject Example Chapter 33, SPM8 Manual

Faces Scrambled Faces > Scrambled 2. Where is an effect in time-frequency (2D)? Single MEG channelSingle MEG channel Mean over trials of Morlet Wavelet projection (i.e, induced + evoked)Mean over trials of Morlet Wavelet projection (i.e, induced + evoked) Write as t x f x 1 image per trialWrite as t x f x 1 image per trial SPM, correct on extent / heightSPM, correct on extent / height Single MEG channelSingle MEG channel Mean over trials of Morlet Wavelet projection (i.e, induced + evoked)Mean over trials of Morlet Wavelet projection (i.e, induced + evoked) Write as t x f x 1 image per trialWrite as t x f x 1 image per trial SPM, correct on extent / heightSPM, correct on extent / height Chapter 33, SPM8 Manual Kilner Et Al (2005) Neurosci. Letters

3. Where is an effect in scalp-time space (3D)? 2D sensor positions specified or projected from 3D digitised positions2D sensor positions specified or projected from 3D digitised positions Each sample projected to a 32x32 grid using linear interpolationEach sample projected to a 32x32 grid using linear interpolation Samples tiled to created a 3D volumeSamples tiled to created a 3D volume 2D sensor positions specified or projected from 3D digitised positions2D sensor positions specified or projected from 3D digitised positions Each sample projected to a 32x32 grid using linear interpolationEach sample projected to a 32x32 grid using linear interpolation Samples tiled to created a 3D volumeSamples tiled to created a 3D volume Chapter 33, SPM8 Manual Note: location of EEG maxima depends on referenceNote: location of EEG maxima depends on reference Note: location of MEG radial flux maxima (Mags or Axial Grads) doesn’t correspond to location of sourceNote: location of MEG radial flux maxima (Mags or Axial Grads) doesn’t correspond to location of source Note: cluster-level inference less useful in both cases (where sensor extent not related to source extent)Note: cluster-level inference less useful in both cases (where sensor extent not related to source extent) Note: location of EEG maxima depends on referenceNote: location of EEG maxima depends on reference Note: location of MEG radial flux maxima (Mags or Axial Grads) doesn’t correspond to location of sourceNote: location of MEG radial flux maxima (Mags or Axial Grads) doesn’t correspond to location of source Note: cluster-level inference less useful in both cases (where sensor extent not related to source extent)Note: cluster-level inference less useful in both cases (where sensor extent not related to source extent) y x t F-test of means of ~150 EEG trials of each typeF-test of means of ~150 EEG trials of each type

More sophisticated 1 st -level design matrices, e.g, to remove trial-by-trial confounds within each subject, and create mean adjusted ERP for 2 nd –level analysis across subjects Each trial Each trial-type (6) Henson Et Al (2008) Neuroimage 3. Where is an effect in scalp-time space (3D)? beta_00* images reflect mean (adjusted) 3D scalp-time volume for each condition Within-subject (1 st -level) Within-subject Across-subjects (2 nd -level) Across-subjects Confounds (4)

Taylor & Henson (2008) Biomag 4. Where is an effect in scalp-time space (3D)? Mean ERP/ERF images can also be tested between-subjects. Note however for MEG, some alignment of sensors may be necessary (e.g, SSS, Taulu et al, 2005) Without transformation to Device Space Stats over 18 subjects on RMS of 102 planar gradiometers With transformation to Device Space

OverviewOverview Sensor Space:Sensor Space: 1.Random Field Theory (RFT) 2.2D Time-Freq (within-subject) 3.3D Scalp-Time (within-subject) 4.3D Scalp-Time (between-subjects) Source Space:Source Space: 1.3D contrast images 2.SPM vs SnPM vs PPM (vs FDR) 3.Other issues & Future directions 4.Multivariate Sensor Space:Sensor Space: 1.Random Field Theory (RFT) 2.2D Time-Freq (within-subject) 3.3D Scalp-Time (within-subject) 4.3D Scalp-Time (between-subjects) Source Space:Source Space: 1.3D contrast images 2.SPM vs SnPM vs PPM (vs FDR) 3.Other issues & Future directions 4.Multivariate

Henson Et Al (2007) Neuroimage 1. Estimate evoked/induced energy (RMS) at each dipole for a certain time-frequency contrast (e.g, from sensor stats, e.g 0-20Hz, ms), for each condition (e.g, faces & scrambled) and subject 2. Smooth along the 2D surface 3. Write these data into a 3D image in MNI space (if canonical / template mesh used) 4. Smooth by 8-12mm in 3D (to allow for normalisation errors) 1. Estimate evoked/induced energy (RMS) at each dipole for a certain time-frequency contrast (e.g, from sensor stats, e.g 0-20Hz, ms), for each condition (e.g, faces & scrambled) and subject 2. Smooth along the 2D surface 3. Write these data into a 3D image in MNI space (if canonical / template mesh used) 4. Smooth by 8-12mm in 3D (to allow for normalisation errors) Where is an effect in source space (3D)? Source analysis of N=12 subjects; 102 magnetometers; MSP; evoked; RMS; smooth 12mm Note sparseness of MSP inversions…. Analysis Mask

Where is an effect in source space (3D)? Source analysis of N=12 subjects; 102 magnetometers; MSP; evoked; RMS; smooth 12mm 1. Classical SPM approach Caveats: Inverse operator induces long-range error correlations (e.g, similar gain vectors from non-adjacent dipoles with similar orientation), making RFT conservativeInverse operator induces long-range error correlations (e.g, similar gain vectors from non-adjacent dipoles with similar orientation), making RFT conservative Need a cortical mask, else activity “smoothed” outsideNeed a cortical mask, else activity “smoothed” outside Distributions over subjects may not be Gaussian (eg MSP unless smooth a lot)…Distributions over subjects may not be Gaussian (eg MSP unless smooth a lot)… 1. Classical SPM approach Caveats: Inverse operator induces long-range error correlations (e.g, similar gain vectors from non-adjacent dipoles with similar orientation), making RFT conservativeInverse operator induces long-range error correlations (e.g, similar gain vectors from non-adjacent dipoles with similar orientation), making RFT conservative Need a cortical mask, else activity “smoothed” outsideNeed a cortical mask, else activity “smoothed” outside Distributions over subjects may not be Gaussian (eg MSP unless smooth a lot)…Distributions over subjects may not be Gaussian (eg MSP unless smooth a lot)… SPM p<.05 FWE Taylor & Henson (210) Biomag

Where is an effect in source space (3D)? Source analysis of N=12 subjects; 102 magnetometers; MSP; evoked; RMS; smooth 12mm 2. Nonparametric, SnPM Robust to non-Gaussian distributionsRobust to non-Gaussian distributions Less conservative than RFT when dfs<20Less conservative than RFT when dfs<20Caveats: No idea of effect size (e.g, for future experiments)No idea of effect size (e.g, for future experiments) Exchangeability difficult for more complex designsExchangeability difficult for more complex designs 2. Nonparametric, SnPM Robust to non-Gaussian distributionsRobust to non-Gaussian distributions Less conservative than RFT when dfs<20Less conservative than RFT when dfs<20Caveats: No idea of effect size (e.g, for future experiments)No idea of effect size (e.g, for future experiments) Exchangeability difficult for more complex designsExchangeability difficult for more complex designs SnPM p<.05 FWE Taylor & Henson (2010) Biomag

Where is an effect in source space (3D)? Source analysis of N=12 subjects; 102 magnetometers; MSP; evoked; RMS; smooth 12mm 3. PPMs No need for RFT (no MCP!?)No need for RFT (no MCP!?) Threshold on posterior probability of an effect (greater than some size)Threshold on posterior probability of an effect (greater than some size) Can show effect size after thresholding…Can show effect size after thresholding…Caveats: Assume normal distributions (e.g, of mean over voxels); sometimes not met for MSP (though usually fine for IID)Assume normal distributions (e.g, of mean over voxels); sometimes not met for MSP (though usually fine for IID) 3. PPMs No need for RFT (no MCP!?)No need for RFT (no MCP!?) Threshold on posterior probability of an effect (greater than some size)Threshold on posterior probability of an effect (greater than some size) Can show effect size after thresholding…Can show effect size after thresholding…Caveats: Assume normal distributions (e.g, of mean over voxels); sometimes not met for MSP (though usually fine for IID)Assume normal distributions (e.g, of mean over voxels); sometimes not met for MSP (though usually fine for IID) PPM p>.95 (γ>1SD) Grayscale= Effect Size Taylor & Henson (2010) Biomag

Where is an effect in source space (3D)? Source analysis of N=12 subjects; 102 magnetometers; MSP; evoked; RMS; smooth 12mm 4. FDR? Choose an uncorrected threshold (e.g, p<.001) to define topological features, e.g, peak and cluster sizeChoose an uncorrected threshold (e.g, p<.001) to define topological features, e.g, peak and cluster size Topological FDR actually produces higher corrected p-values (i.e, fewer suprathreshold voxels) than FWE in the data used hereTopological FDR actually produces higher corrected p-values (i.e, fewer suprathreshold voxels) than FWE in the data used here If sources are constrained to a graymatter cortical surface, are topological features as meaningful?If sources are constrained to a graymatter cortical surface, are topological features as meaningful? 4. FDR? Choose an uncorrected threshold (e.g, p<.001) to define topological features, e.g, peak and cluster sizeChoose an uncorrected threshold (e.g, p<.001) to define topological features, e.g, peak and cluster size Topological FDR actually produces higher corrected p-values (i.e, fewer suprathreshold voxels) than FWE in the data used hereTopological FDR actually produces higher corrected p-values (i.e, fewer suprathreshold voxels) than FWE in the data used here If sources are constrained to a graymatter cortical surface, are topological features as meaningful?If sources are constrained to a graymatter cortical surface, are topological features as meaningful? SPM p<.001 unc Taylor & Henson (2010) Biomag

Some further thoughts: Since data live in sensor space, why not perform stats there, and just report some mean localisation (e.g, across subjects)?Since data live in sensor space, why not perform stats there, and just report some mean localisation (e.g, across subjects)? True but: What if sensor data not aligned (e.g, MEG)? (Taylor & Henson, 2008)? What if want to fuse modalities (e.g, MEG+EEG) (Henson et al, 2009)? What if want to use source priors (e.g, fMRI) (Henson et al, in press)? What if one wants to make an inference about a specific cortical region? Contrast localisations of conditions, or localise contrast of conditions?Contrast localisations of conditions, or localise contrast of conditions? “DoL” or “LoD” (Henson et al, 2007, Neuroimage) LoD has higher SNR (though difference only lives in trial-average, i.e evoked)? But how then test localised energy of a difference (versus baseline?) Construct inverse operator (MAP) from a difference, but then apply that operator to individual conditions (Taylor & Henson, in prep) Some further thoughts: Since data live in sensor space, why not perform stats there, and just report some mean localisation (e.g, across subjects)?Since data live in sensor space, why not perform stats there, and just report some mean localisation (e.g, across subjects)? True but: What if sensor data not aligned (e.g, MEG)? (Taylor & Henson, 2008)? What if want to fuse modalities (e.g, MEG+EEG) (Henson et al, 2009)? What if want to use source priors (e.g, fMRI) (Henson et al, in press)? What if one wants to make an inference about a specific cortical region? Contrast localisations of conditions, or localise contrast of conditions?Contrast localisations of conditions, or localise contrast of conditions? “DoL” or “LoD” (Henson et al, 2007, Neuroimage) LoD has higher SNR (though difference only lives in trial-average, i.e evoked)? But how then test localised energy of a difference (versus baseline?) Construct inverse operator (MAP) from a difference, but then apply that operator to individual conditions (Taylor & Henson, in prep) Where is an effect in source space (3D)?

Future Directions Extend RFT to 2D cortical surfaces (“surfstat”)Extend RFT to 2D cortical surfaces (“surfstat”) Go multivariate…Go multivariate… – To localise (linear combinations) of spatial (sensor or source) effects in time, using Hotelling-T 2 and RFT – To detect spatiotemporal patterns in 3D images (MLM / PLS) Extend RFT to 2D cortical surfaces (“surfstat”)Extend RFT to 2D cortical surfaces (“surfstat”) Go multivariate…Go multivariate… – To localise (linear combinations) of spatial (sensor or source) effects in time, using Hotelling-T 2 and RFT – To detect spatiotemporal patterns in 3D images (MLM / PLS) Pantazis Et Al (2005) NeuroImage Carbonell Et Al (2004) NeuroImage Barnes & Litvak (2010) Biomag Carbonell Et Al (2004) NeuroImage Barnes & Litvak (2010) Biomag Duzel Et Al (2003) Neuroimage Kherif Et Al (2004) NeuroImage Duzel Et Al (2003) Neuroimage Kherif Et Al (2004) NeuroImage

Multivariate Model (MM) toolbox Famous Novel Scrambled “M170”? Multivariate Linear Model (MLM) across subjects on MEG Scalp-Time volumes (now with 3 conditions) X Famous Novel Scrambled Sensitive (and suggestive of spatiotemporal dynamic networks), but “imprecise”

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Taylor & Henson (2010) Biomag