Partial Least Squares Analysis of Functional Neuroimaging Data Cheryl L. Grady Senior Scientist Rotman Research Institute at Baycrest Toronto, Ontario

Statistical Map superimposed on anatomical MRI image Time Condition 1 Condition 2... ~ 5 min fMRI Signal (% change) Condition Typical fMRI Analysis- “Pure Insertion” & Subtraction Region of interest (ROI) Source: Jody Culham’s fMRI for Dummies web sitefMRI for Dummies

However, Brain Areas are Connected! Although brain regions may activate selectively for different types of stimulus features or processing, this does not mean that activity in these individual areas is solely responsible for cognition Brain areas are heavily interconnected anatomically, so it follows that they also are interconnected functionally Our analytic approaches should be sensitive to covarying brain activity and functional connections between brain regions Multivariate analysis - when brain region “A” is active during a task, what is the rest of the brain doing?

Why use PLS? Computationally efficient – simultaneously dentifies similarities among conditions/groups as well as differences Is quite flexible and can handle “multi-table” questions easily Can be data-driven or hypothesis-driven (task contrasts can be pre-specified) Because the whole brain is assessed in a single computational step, there is no need to correct for multiple comparisons Can be applied to either functional or structural MRI data, or to ERPs For more details see Krishnan et al, Neuroimage, 2011, 56, For a step-by-step manual go to  Support + Services  Labs  PLS Software  Support + ServicesLabsPLS Software

Task-related changes Brain/Behaviour Correlations Functional Connectivity Brain TaskBrain Behaviour PLS Options for fMRI Analysis Task PLS Behaviour PLS Seed PLS

PLS Task Analysis Experimental Design Contrasts Brain Images C o n t r a s t C o n t r a s t Covariance between Design and Brain SVD Set of Latent Variables Extracted in order of amount of covariance explained

Composition of the LV Singular Image: each voxel has a weight (salience) that indicates how it relates to task contrast (positively or negatively) Singular Value (S): amount of covariance explained by each LV (1)(2)(3) Contrast across experimental conditions Sum of all voxel saliences

How do we determine the significance of our result? Permutation test to determine probability of each LV Use resampling to determine robustness of each voxel’s contribution to the spatial pattern (bootstrap)

Permutation Test X 1 is task 1 X 2 is task 2 X 3 is task 3 Subject (i 1 =1 of 3) Voxels/VOIs (1,…,j,…J=12) Run some large number of analyses with permuted data and calculate the number of times that the obtained S value for each LV is larger than the original – that is the probability Shuffle the condition labels

How Robust are the voxel contributions? We need to estimate the variance of the weight for each voxel We do this by creating a set of “new” samples by resampling the original set of participants o Sample repeatedly from finite sample o Make sure that probabilities do not change by sampling with replacement

Sampling with Replacement A B C D EF

A Get the first observation

A A Put it in the box

A A Put the original back in the hat

A B Take out another

A B B Put the second one in the box

A B B B Put it back in the hat

A BB EEF And so on, until you get the full Sample Some observations are repeated Some are not repeated

Bootstrap Use a large number of resampled datasets to calculate an estimate of the variance of the salience for each voxel Divide the salience of each voxel by it’s SD This is the bootstrap ratio (BSR), which is analogous to a Z score and can be thresholded to get a robust spatial pattern

Task PLS

Two of the Major Brain Networks Fox et al, PNAS, 2005 Default Network Task Network

19 younger (20-30 yrs, m = 25 yrs); 28 older (56-84 yrs, m = 66 yrs) Healthy, community-dwelling, cognitively normal fMRI at 3T, block design 4 tasks, with stimulus parameters set for 80% accuracy Experiment details

Tasks Detection Perceptual Matching Attentional Cueing Delayed Match to Sample Alternated with Fixation Baseline Grady et al., Cerebral Cortex, 2010

a. LV1b. LV2 Brain Score FixDETPMTATTDMS Young Old FixDETPMTATTDMS

DMN, Young only DMN, Both TPN, Young only TPN, Old only TPN, Both DMN, Old only The Default Network “Shrinks” and the Task Network “Expands” with Age

Functional Connectivity with Seed PLS

Functional Connectivity - Seed PLS Extracted Seed Values Brain Images Within-task Correlation of Seed Activity and Brain Images Singular Image Correlations of Total Brain Activity SVD and Seed Activity Across 3 Tasks

Age Reduction in Correlation between Two DN Hubs What about the rest of the network? Andrews-Hanna et al, Neuron 2007

Default Network Young Both Old Grady et al., Cerebral Cortex, 2010 Default Seed

Reduced Functional Connectivity of the DN in Older Adults Correlation YoungOld Grady et al., Cerebral Cortex, 2010 FC during fixation baseline – correlation of vmPFC activity with whole brain pattern p < Older Adults Young Adults

Task Network Young Both Old Task Seed

Maintained FC of the TN in older adults Correlation Older Adults Young Adults Grady et al., Cerebral Cortex, 2010 Correlation of right IPL activity with whole brain pattern p < 0.002

Summary Both young and old adults show DN activity during baseline and TN activity during the tasks in expected areas Young have more extensive DN activity during fixation and old have more extensive TN activity during all tasks Functional connectivity in the DN is more vulnerable to age than in the TN

Behaviour PLS

Relating Behaviour to Brain Activity Behavioural Measure (s) Brain Images Within-task Correlation of Behaviour and Brain Images Singular Image Correlations of Total Brain Activity SVD and Behaviour Across 3 Tasks

Behaviour Analysis – Across 3 Tasks PMT, ATT, DMS Brain Factor ISD S1 S2 S3 Mean RT Age

Correlations with Behaviour p <.001 Garrett et al, J Neurosci, 2011

But.... Brain’s natural state is a variable one

Younger Older Within-subject RT variability Reflects neural inefficiency Random lapses in attention or executive control Behavioural variability increases with age Macdonald et al., (2006;2009); Dixon et al. (2007)

Correlations with SD Measures p <.001 Garrett et al, J Neurosci, 2011

Correlation Strength Mean Brain ActivitySD of Brain Activity

Comparison of SD and mean Spatial Patterns Regions with both effects SD+ Beh +Mean + Beh -

Summary PLS is a useful tool for examining the many aspects of functional neuroimaging data within the same general framework Using PLS we have shown that there are age differences in DN and TN, with the former showing reduced functional connectivity and the latter showing maintained connectivity BOLD variability measures show promise for understanding aging of the brain and cognition