sensor & source space statistics sensor & source space statistics rik henson (mrc cbu,...

Sensor & Source Space StatisticsSensor & Source Space Statistics

Rik Henson(MRC CBU, Cambridge)

With thanks to Jason Taylor, Vladimir Litvak, Guillaume Flandin, James Kilner & Karl Friston

Sensor & Source Space StatisticsSensor & Source Space Statistics

Rik Henson(MRC CBU, Cambridge)

With thanks to Jason Taylor, Vladimir Litvak, Guillaume Flandin, James Kilner & Karl Friston

8 8

OverviewOverviewOverviewOverview

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

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


• Sensor Space:Sensor Space:

1.1. Random Field Theory (RFT)Random Field Theory (RFT)

2.2. 2D Time-Freq (within-subject)2D Time-Freq (within-subject)

3.3. 3D Scalp-Time (within-subject)3D Scalp-Time (within-subject)

4.4. 3D Scalp-Time (between-subjects)3D Scalp-Time (between-subjects)

• Source Space:Source Space:

1.1. 3D “time-freq” contrast images3D “time-freq” contrast images

2.2. SPM vs SnPM vs PPM vs FDRSPM vs SnPM vs PPM vs FDR

3.3. Other issues & Future directionsOther issues & Future directions

4.4. MultivariateMultivariate







1.1. 3D “time-freq” contrast images3D “time-freq” contrast images

2.2. SPM vs SnPM vs PPM vs FDRSPM vs SnPM vs PPM vs FDR



1. Random Field Theory (RFT)1. Random Field Theory (RFT)1. Random Field Theory (RFT)1. Random Field Theory (RFT)

RFT is a method for correcting for multiple statistical RFT is a method for correcting for multiple statistical comparisons with N-dimensional spaces (for parametric comparisons with N-dimensional spaces (for parametric statistics, eg Z-, T-, F- statistics)…statistics, eg Z-, T-, F- statistics)…

1.1. When is there an effect in time, eg GFP (1D)? When is there an effect in time, eg GFP (1D)?

2.2. Where is there an effect in time-frequency space (2D)?Where is there an effect in time-frequency space (2D)?

3.3. Where is there an effect in time-sensor space (3D)?Where is there an effect in time-sensor space (3D)?

4.4. Where is there an effect in time-source space (4D)? Where is there an effect in time-source space (4D)?

RFT is a method for correcting for multiple statistical RFT is a method for correcting for multiple statistical comparisons with N-dimensional spaces (for parametric comparisons with N-dimensional spaces (for parametric statistics, eg Z-, T-, F- statistics)…statistics, eg Z-, T-, F- statistics)…

1.1. When is there an effect in time, eg GFP (1D)? When is there an effect in time, eg GFP (1D)?

2.2. Where is there an effect in time-frequency space (2D)?Where is there an effect in time-frequency space (2D)?

3.3. Where is there an effect in time-sensor space (3D)?Where is there an effect in time-sensor space (3D)?

4.4. Where is there an effect in time-source space (4D)? Where is there an effect in time-source space (4D)?

Worsley Et Al (1996). Human Brain Mapping, 4:58-73Worsley Et Al (1996). Human Brain Mapping, 4:58-73Worsley Et Al (1996). Human Brain Mapping, 4:58-73Worsley Et Al (1996). Human Brain Mapping, 4:58-73

• ““Multimodal” Dataset in SPM8 Multimodal” Dataset in SPM8 manual (and website)manual (and website)

• Single subject:Single subject:128 EEG128 EEG275 MEG275 MEG3T fMRI (with nulls)3T fMRI (with nulls)1mm1mm33 sMRI sMRI

• Two sessionsTwo sessions

• ~160 face trials and ~160 ~160 face trials and ~160 scrambled trials per sessionscrambled trials per session

• (N=12 subjects soon, as in (N=12 subjects soon, as in Henson et al, 2009 a, b, c)Henson et al, 2009 a, b, c)

• ““Multimodal” Dataset in SPM8 Multimodal” Dataset in SPM8 manual (and website)manual (and website)

• Single subject:Single subject:128 EEG128 EEG275 MEG275 MEG3T fMRI (with nulls)3T fMRI (with nulls)1mm1mm33 sMRI sMRI

• Two sessionsTwo sessions

• ~160 face trials and ~160 ~160 face trials and ~160 scrambled trials per sessionscrambled trials per session

• (N=12 subjects soon, as in (N=12 subjects soon, as in Henson et al, 2009 a, b, c)Henson et al, 2009 a, b, c)

2. Single-subject Example2. Single-subject Example2. Single-subject Example2. Single-subject Example

Chapter 33, SPM8 ManualChapter 33, SPM8 ManualChapter 33, SPM8 ManualChapter 33, SPM8 Manual

Faces

Scrambled

Faces > Scrambled

2. Where is an effect in time-frequency (2D)?2. Where is an effect in time-frequency (2D)?2. Where is an effect in time-frequency (2D)?2. Where is an effect in time-frequency (2D)?

• Single MEG channelSingle MEG channel• Mean over trials of Morlet Wavelet Mean over trials of Morlet Wavelet

projection (i.e, induced + evoked)projection (i.e, induced + evoked)• Write as Write as t x f x 1t x f x 1 image per trial image per trial• SPM, correct on extent / heightSPM, correct on extent / height

• Single MEG channelSingle MEG channel• Mean over trials of Morlet Wavelet Mean over trials of Morlet Wavelet

projection (i.e, induced + evoked)projection (i.e, induced + evoked)• Write as Write as t x f x 1t x f x 1 image per trial image per trial• SPM, correct on extent / heightSPM, correct on extent / height

Chapter 33, SPM8 ManualChapter 33, SPM8 ManualChapter 33, SPM8 ManualChapter 33, SPM8 ManualKilner Et Al (2005) Kilner Et Al (2005) Neurosci. LettersNeurosci. LettersKilner Et Al (2005) Kilner Et Al (2005) Neurosci. LettersNeurosci. Letters

3. Where is an effect in scalp-time space (3D)?3. Where is an effect in scalp-time space (3D)?3. Where is an effect in scalp-time space (3D)?3. Where is an effect in scalp-time space (3D)?• 2D sensor positions specified or 2D sensor positions specified or

projected from 3D digitised positionsprojected from 3D digitised positions• Each sample projected to a 32x32 Each sample projected to a 32x32

grid using linear interpolationgrid using linear interpolation• Samples tiled to created a 3D volumeSamples tiled to created a 3D volume

• 2D sensor positions specified or 2D sensor positions specified or projected from 3D digitised positionsprojected from 3D digitised positions

• Each sample projected to a 32x32 Each sample projected to a 32x32 grid using linear interpolationgrid using linear interpolation

• Samples tiled to created a 3D volumeSamples tiled to created a 3D volume

Chapter 33, SPM8 ManualChapter 33, SPM8 ManualChapter 33, SPM8 ManualChapter 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 Note: location of MEG radial flux maxima (Mags or

Axial Grads) doesn’t correspond to location of sourceAxial Grads) doesn’t correspond to location of source• Note: cluster-level inference less useful in both cases Note: cluster-level inference less useful in both cases

(where sensor extent not related to source extent)(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 Note: location of MEG radial flux maxima (Mags or

Axial Grads) doesn’t correspond to location of sourceAxial Grads) doesn’t correspond to location of source• Note: cluster-level inference less useful in both cases Note: cluster-level inference less useful in both cases

(where sensor extent not related to source extent)(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• F-test of means of ~150 EEG trials of each typeF-test of means of ~150 EEG trials of each type

More sophisticated 1More sophisticated 1stst-level design matrices, e.g, to remove trial-by-trial confounds within -level design matrices, e.g, to remove trial-by-trial confounds within each subject, and create mean adjusted ERP for 2each subject, and create mean adjusted ERP for 2ndnd–level analysis across subjects–level analysis across subjects

More sophisticated 1More sophisticated 1stst-level design matrices, e.g, to remove trial-by-trial confounds within -level design matrices, e.g, to remove trial-by-trial confounds within each subject, and create mean adjusted ERP for 2each subject, and create mean adjusted ERP for 2ndnd–level analysis across subjects–level analysis across subjects

Each trial

Each trial-type (6)

Henson Et Al (2008) NeuroimageHenson Et Al (2008) NeuroimageHenson Et Al (2008) NeuroimageHenson Et Al (2008) Neuroimage

3. Where is an effect in scalp-time space (3D)?3. Where is an effect in scalp-time space (3D)?3. Where is an effect in scalp-time space (3D)?3. Where is an effect in scalp-time space (3D)?

beta_00* images reflect mean (adjusted) 3D scalp-time volume for each condition

Within-subjectWithin-subject(1(1stst-level)-level)

Within-subjectWithin-subject(1(1stst-level)-level)

Across-subjectsAcross-subjects(2(2ndnd-level)-level)

Across-subjectsAcross-subjects(2(2ndnd-level)-level)

Confounds (4)

Taylor & Henson (2008) BiomagTaylor & Henson (2008) BiomagTaylor & Henson (2008) BiomagTaylor & Henson (2008) Biomag

4. Where is an effect in scalp-time space (3D)?4. Where is an effect in scalp-time space (3D)?4. Where is an effect in scalp-time space (3D)?4. Where is an effect in scalp-time space (3D)?

Mean ERP/ERF images can also be tested between-subjects. Note however for 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)MEG, some alignment of sensors may be necessary (e.g, SSS, Taulu et al, 2005)Mean ERP/ERF images can also be tested between-subjects. Note however for 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)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 Stats over 18 subjects on RMSRMS of 102 of 102 planar gradiometersplanar gradiometersStats over 18 subjects on Stats over 18 subjects on RMSRMS of 102 of 102 planar gradiometersplanar gradiometers

With transformation to Device Space








1.1. 3D contrast images3D contrast images

2.2. SPM vs SnPM vs PPM (vs FDR)SPM vs SnPM vs PPM (vs FDR)









1.1. 3D contrast images3D contrast images

2.2. SPM vs SnPM vs PPM (vs FDR)SPM vs SnPM vs PPM (vs FDR)



Henson Et Al (2007) NeuroimageHenson Et Al (2007) NeuroimageHenson Et Al (2007) NeuroimageHenson Et Al (2007) Neuroimage

1. Estimate evoked/induced energy 1. Estimate evoked/induced energy (RMS) at each dipole for a certain (RMS) at each dipole for a certain time-frequency contrasttime-frequency contrast (e.g, from (e.g, from sensor stats, e.g sensor stats, e.g 0-20Hz, 150-0-20Hz, 150-200ms200ms), for each condition (e.g, ), for each condition (e.g, faces & scrambledfaces & scrambled) and subject ) and subject

2. Smooth along the 2D surface2. Smooth along the 2D surface

3. Write these data into a 3D image 3. Write these data into a 3D image in MNI space (if canonical / in MNI space (if canonical / template mesh used)template mesh used)

4. Smooth by 8-12mm in 3D (to 4. Smooth by 8-12mm in 3D (to allow for normalisation errors)allow for normalisation errors)

1. Estimate evoked/induced energy 1. Estimate evoked/induced energy (RMS) at each dipole for a certain (RMS) at each dipole for a certain time-frequency contrasttime-frequency contrast (e.g, from (e.g, from sensor stats, e.g sensor stats, e.g 0-20Hz, 150-0-20Hz, 150-200ms200ms), for each condition (e.g, ), for each condition (e.g, faces & scrambledfaces & scrambled) and subject ) and subject

2. Smooth along the 2D surface2. Smooth along the 2D surface

3. Write these data into a 3D image 3. Write these data into a 3D image in MNI space (if canonical / in MNI space (if canonical / template mesh used)template mesh used)

4. Smooth by 8-12mm in 3D (to 4. Smooth by 8-12mm in 3D (to allow for normalisation errors)allow for normalisation errors)

Where is an effect in source space (3D)?Where is an effect in source space (3D)?Where is an effect in source space (3D)?Where is an effect in source space (3D)?Source analysis of N=12 subjects; 102 magnetometers; MSP; evoked; RMS; smooth 12mmSource analysis of N=12 subjects; 102 magnetometers; MSP; evoked; RMS; smooth 12mmSource analysis of N=12 subjects; 102 magnetometers; MSP; evoked; RMS; smooth 12mmSource 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)?Where is an effect in source space (3D)?Where is an effect in source space (3D)?Where is an effect in source space (3D)?

Source analysis of N=12 subjects; 102 magnetometers; MSP; evoked; RMS; smooth 12mmSource analysis of N=12 subjects; 102 magnetometers; MSP; evoked; RMS; smooth 12mmSource analysis of N=12 subjects; 102 magnetometers; MSP; evoked; RMS; smooth 12mmSource analysis of N=12 subjects; 102 magnetometers; MSP; evoked; RMS; smooth 12mm

1. Classical SPM approach1. Classical SPM approach

Caveats:Caveats:

• Inverse operator induces Inverse operator induces long-range error correlations long-range error correlations (e.g, similar gain vectors from (e.g, similar gain vectors from non-adjacent dipoles with non-adjacent dipoles with similar orientation), making similar orientation), making RFT RFT conservativeconservative

• Need a cortical mask, else Need a cortical mask, else activity “smoothed” outsideactivity “smoothed” outside

• Distributions over subjects Distributions over subjects maymay not be Gaussian (eg not be Gaussian (eg MSP unless smooth a lot)…MSP unless smooth a lot)…

1. Classical SPM approach1. Classical SPM approach

Caveats:Caveats:

• Inverse operator induces Inverse operator induces long-range error correlations long-range error correlations (e.g, similar gain vectors from (e.g, similar gain vectors from non-adjacent dipoles with non-adjacent dipoles with similar orientation), making similar orientation), making RFT RFT conservativeconservative

• Need a cortical mask, else Need a cortical mask, else activity “smoothed” outsideactivity “smoothed” outside

• Distributions over subjects Distributions over subjects maymay not be Gaussian (eg not be Gaussian (eg MSP unless smooth a lot)…MSP unless smooth a lot)…

SPM p<.05 FWE




2. Nonparametric, SnPM2. Nonparametric, SnPM

• Robust to non-Gaussian Robust to non-Gaussian distributionsdistributions

• Less conservative than RFT Less conservative than RFT when dfs<20when dfs<20

Caveats:Caveats:

• No idea of effect size (e.g, for No idea of effect size (e.g, for future experiments)future experiments)

• Exchangeability difficult for Exchangeability difficult for more complex designsmore complex designs

2. Nonparametric, SnPM2. Nonparametric, SnPM

• Robust to non-Gaussian Robust to non-Gaussian distributionsdistributions

• Less conservative than RFT Less conservative than RFT when dfs<20when dfs<20

Caveats:Caveats:

• No idea of effect size (e.g, for No idea of effect size (e.g, for future experiments)future experiments)

• Exchangeability difficult for Exchangeability difficult for more complex designsmore complex designs

SnPM p<.05 FWE




3. PPMs3. PPMs

• No need for RFT (no MCP!?)No need for RFT (no MCP!?)

• Threshold on posterior Threshold on posterior probability of an effect probability of an effect (greater than some size)(greater than some size)

• Can show effect size after Can show effect size after thresholding…thresholding…

Caveats:Caveats:

• Assume normal distributions Assume normal distributions (e.g, of mean over voxels); (e.g, of mean over voxels); sometimes not met for MSP sometimes not met for MSP (though usually fine for IID)(though usually fine for IID)

3. PPMs3. PPMs

• No need for RFT (no MCP!?)No need for RFT (no MCP!?)

• Threshold on posterior Threshold on posterior probability of an effect probability of an effect (greater than some size)(greater than some size)

• Can show effect size after Can show effect size after thresholding…thresholding…

Caveats:Caveats:

• Assume normal distributions Assume normal distributions (e.g, of mean over voxels); (e.g, of mean over voxels); sometimes not met for MSP sometimes not met for MSP (though usually fine for IID)(though usually fine for IID)

PPM p>.95 (γ>1SD)

Grayscale=Effect Size




4. FDR?4. FDR?

• Choose an uncorrected Choose an uncorrected threshold (e.g, p<.001) to threshold (e.g, p<.001) to define topological features, define topological features, e.g, peak and cluster sizee.g, peak and cluster size

• Topological FDR actually Topological FDR actually produces higher corrected produces higher corrected p-values (i.e, fewer p-values (i.e, fewer suprathreshold voxels) than suprathreshold voxels) than FWE in the data used hereFWE in the data used here

• If sources are constrained to If sources are constrained to a graymatter cortical surface, a graymatter cortical surface, are topological features as are topological features as meaningful?meaningful?

4. FDR?4. FDR?

• Choose an uncorrected Choose an uncorrected threshold (e.g, p<.001) to threshold (e.g, p<.001) to define topological features, define topological features, e.g, peak and cluster sizee.g, peak and cluster size

• Topological FDR actually Topological FDR actually produces higher corrected produces higher corrected p-values (i.e, fewer p-values (i.e, fewer suprathreshold voxels) than suprathreshold voxels) than FWE in the data used hereFWE in the data used here

• If sources are constrained to If sources are constrained to a graymatter cortical surface, a graymatter cortical surface, are topological features as are topological features as meaningful?meaningful?

SPM p<.001 unc


Some further thoughts:Some further thoughts:

• Since data live in sensor space, why not perform stats there, and just report Since data live in sensor space, why not perform stats there, and just report some mean localisation (e.g, across subjects)?some mean localisation (e.g, across subjects)?

True but:True but:

What if sensor data not What if sensor data not alignedaligned (e.g, MEG)? (Taylor & Henson, 2008)? (e.g, MEG)? (Taylor & Henson, 2008)?

What if want to What if want to fusefuse modalities (e.g, MEG+EEG) (Henson et al, 2009)? modalities (e.g, MEG+EEG) (Henson et al, 2009)?

What if want to use source priors (e.g, What if want to use source priors (e.g, fMRIfMRI) (Henson et al, in press)?) (Henson et al, in press)?

What if one wants to make an inference about a specific cortical region?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)DoL” or “LoD” (Henson et al, 2007, Neuroimage)

LoD has higher SNRLoD has higher SNR (though difference only lives in trial-average, i.e evoked)? (though difference only lives in trial-average, i.e evoked)?

But how then test localised energy of a difference (versus baseline?)But how then test localised energy of a difference (versus baseline?)

Construct inverse operator (Construct inverse operator (MAPMAP) from a difference, but then apply that ) from a difference, but then apply that operator to individual conditions (Taylor & Henson, in prep)operator to individual conditions (Taylor & Henson, in prep)

Some further thoughts:Some further thoughts:

• Since data live in sensor space, why not perform stats there, and just report Since data live in sensor space, why not perform stats there, and just report some mean localisation (e.g, across subjects)?some mean localisation (e.g, across subjects)?

True but:True but:

What if sensor data not What if sensor data not alignedaligned (e.g, MEG)? (Taylor & Henson, 2008)? (e.g, MEG)? (Taylor & Henson, 2008)?

What if want to What if want to fusefuse modalities (e.g, MEG+EEG) (Henson et al, 2009)? modalities (e.g, MEG+EEG) (Henson et al, 2009)?

What if want to use source priors (e.g, What if want to use source priors (e.g, fMRIfMRI) (Henson et al, in press)?) (Henson et al, in press)?

What if one wants to make an inference about a specific cortical region?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)DoL” or “LoD” (Henson et al, 2007, Neuroimage)

LoD has higher SNRLoD has higher SNR (though difference only lives in trial-average, i.e evoked)? (though difference only lives in trial-average, i.e evoked)?

But how then test localised energy of a difference (versus baseline?)But how then test localised energy of a difference (versus baseline?)

Construct inverse operator (Construct inverse operator (MAPMAP) from a difference, but then apply that ) from a difference, but then apply that operator to individual conditions (Taylor & Henson, in prep)operator to individual conditions (Taylor & Henson, in prep)


Future DirectionsFuture DirectionsFuture DirectionsFuture 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) To localise (linear combinations) of spatial (sensor or source)

effects effects in timein time, using Hotelling-T, using Hotelling-T22 and RFT and RFT

– To To detectdetect spatiotemporal patterns in 3D images spatiotemporal patterns in 3D images (MLM / PLS)(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) To localise (linear combinations) of spatial (sensor or source)

effects effects in timein time, using Hotelling-T, using Hotelling-T22 and RFT and RFT

– To To detectdetect spatiotemporal patterns in 3D images spatiotemporal patterns in 3D images (MLM / PLS)(MLM / PLS)

Pantazis Et Al (2005) NeuroImagePantazis Et Al (2005) NeuroImagePantazis Et Al (2005) NeuroImagePantazis Et Al (2005) NeuroImage

Carbonell Et Al (2004) NeuroImageCarbonell Et Al (2004) NeuroImageBarnes & Litvak (2010) BiomagBarnes & Litvak (2010) Biomag

Carbonell Et Al (2004) NeuroImageCarbonell Et Al (2004) NeuroImageBarnes & Litvak (2010) BiomagBarnes & Litvak (2010) Biomag

Duzel Et Al (2003) NeuroimageDuzel Et Al (2003) NeuroimageKherif Et Al (2004) NeuroImageKherif Et Al (2004) NeuroImage

Duzel Et Al (2003) NeuroimageDuzel Et Al (2003) NeuroimageKherif Et Al (2004) NeuroImageKherif Et Al (2004) NeuroImage

Kherif Et Al (2004) NeuroImageKherif Et Al (2004) NeuroImageKherif Et Al (2004) NeuroImageKherif Et Al (2004) NeuroImage

Multivariate Model (MM) toolboxMultivariate Model (MM) toolboxMultivariate Model (MM) toolboxMultivariate Model (MM) toolbox

Famous

Novel

Scrambled

“M170”?

Multivariate Linear Model Multivariate Linear Model (MLM) across subjects on (MLM) across subjects on MEG Scalp-Time volumes MEG Scalp-Time volumes (now with 3 conditions)(now with 3 conditions)

Multivariate Linear Model Multivariate Linear Model (MLM) across subjects on (MLM) across subjects on MEG Scalp-Time volumes MEG Scalp-Time volumes (now with 3 conditions)(now with 3 conditions)

X

Famous

Novel

Scrambled

Sensitive (and suggestive Sensitive (and suggestive of spatiotemporal dynamic of spatiotemporal dynamic networks), but “imprecise”networks), but “imprecise”

Sensitive (and suggestive Sensitive (and suggestive of spatiotemporal dynamic of spatiotemporal dynamic networks), but “imprecise”networks), but “imprecise”

The End

sensor & source space statistics sensor & source space statistics rik henson (mrc cbu,...

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