1st level analysis - Design matrix, contrasts & inference

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1st level analysis - Design matrix, contrasts & inference
Nico Bunzeck, Katya Woollett

1st level data analysis in SPM5
(i) Specification of the GLM design matrix, fMRI data files and filtering (ii) estimation of GLM parameters using classical or Bayesian approaches (iii) interrogation of results using contrast vectors to produce Statistical Parametric Maps (SPMs) or Posterior Probability Maps (PPMs)

(i) fMRI model specification

(i) fMRI model specification
Timing parameters: to construct the design matrix Units for design: onset of the events or blocks (in sec or scans) Interscan interval: TR in sec; = time between acquiring a plane for one volume and the same plane in the next volume; constant Microtime resolution: (t) the number of time-bins per scan used when building the regressors (default = 16) Microtime onset: (t0) the first time-bin at which the regressors are resampled to coincide with data acquisition (default = 1) MTR: Do not change this parameter unless you have a long TR and wish to shift regressors so that they are aligned to a particular slice. acquisition. If t0 = 1 then the regressors will be appropriate for the first slice. If you want to temporally realign the regressors so that they match responses in the middle slice then make t0 = t/2 (assuming there is a negligible gap between volume acquisitions). Do not change the default setting unless you have a long TR.

(i) fMRI model specification
Data & Design matrix: defines the experimental design and the nature of the hypothesis testing matrix: organized in rows (each scans) and columns (for each effect of explanatory variable = regressor or stimulus function) can be replicated and/or manipulated for each subject/session The design matrix has one row for each scan and one column for each effect or explanatory variable. (e.g. regressor or stimulus function).

(i) fMRI model specification
Subjects/Session: Scans: select the images for the model that has to be estimated

(i) fMRI model specification
Condition: can be event-related, blocked design or a combination of both – they are modelled in the same way -> they are later convolved with a basis set - Name: be creative Onset: specify the onsets for this condition Durations: default for events = 0; single number: SPM assumes that all trails have this duration (block) for mix of blocks and events: number must match the number of onset times

(i) fMRI model specification
Multiple conditions: load all the conditions defined as *.mat it contains cell arrays: names, onsets and duration eg. Names{2}=‘finger tapping’, onsets{2}=[ ], duration{2}=[0 0 0] If you have multiple conditions you can add them by adding a new ‘condition’ branch. But you can also define them as

(i) fMRI model specification
Regressors: additional columns in the design matrix that may not be convolved with the HR, eg. movement parameters Name Value Multiple regressors: either *.mat or *.txt file that contains details of the multiple regressors; they will be named: R1, R2 … Rn

(i) fMRI model specification
High-pass filter cutoff: default = 128s slow signal drifts with a period longer than 128 will be removed removes confounds without estimating their parameters explicitly

(i) fMRI model specification
Factorial design: if you have a factorial design SPM automatically generate the contrasts that are necessary to test the main effects of interaction: F-contrasts: at within-subject level contrasts for second level analysis create as many factors as you need – name, levels (for each factor) for example: ‘Stimulus-Repetition’ – 3 levels

(i) fMRI model specification
Basis Functions: SPM uses basis functions to model the hemodynamic response; either 1 function or a set Canonical HRF: most common choice, default, easiest way to interpret the data Model derivatives: = ‘informed’ basis set -> covers variations in subject-to-subject and voxel-to-voxel responses: peak and width

(i) fMRI model specification
Model interactions: inputs (RT) convolved with the basis set Directory: where the SPM.mat file will be written

(i) fMRI model specification
Global normalization: estimating the ‘average within-brain fMRI signal’ (gns) over scans (n) and sessions (s) ‘Scaling’: SPM multiplies each value in scan and session by 100/(gns) eg. scaling over all sessions ‘none’: default, estimation of a ‘session specific grand mean value’ (gs) = fMRI signal over all voxels in a session; each fMRI data point in the session is multiplied by 100/(gs); eg. Session specific scaling

(i) fMRI model specification
Explicit masking: only those voxels in the brain mask will be analyzed speeds up the estimation restricts SPMs to within-mask voxels Serial correlations: due to aliased biorhythms and unmodelled neural activity SPM uses an autoregressive AR(1) model during Classical (ReML) parameter estimation but they can be ignored (‘none’) - Bayesion estimation Chose a mask: whole brain or just a region such as the hippocampus, amygdala

(i) fMRI model specification
What should be included in the model? Think about contrast/comparisons before the experiment The more information you have the better: the model represents the a priori ideas about how the experimental paradigm influences the measured signal

(i) Review a specified model

(i) Review a specified model
Design matrix: 24 conditions/session last 2 columns model average activity in each session -> total of 50 regressors 191 fMRI scans/session -> 382 rows and 50 columns

(i) Review a specified model
Explore Sessions and regressors: time domain corresponding to the regressor (4 events) frequency domain corresponding to the regressor: experimental variance is not removed by high-pass filtering bottom: basis function = HRF

(ii) fMRI model estimation
for which voxel does the model (or a explanatory variable) explain the observed variance?? parameters are estimated for each voxel so that the error is minimized there are more than 1 variables -> it is unlikely that the betas exactly fit: SPM calculates different parameter-sets each parameter-set determines a fitted response: Y = observed data (voxel timecourse of 1 voxel) Y differs slightly from the observed Yj the algorithm minimizes the residuals

(ii) fMRI model estimation
Fitting X to Y gives you one  (parameter estimate) for each column of X and e. Betas provide information about the fit of the regressor X to the data, Y, in each voxel

(ii) fMRI model estimation

(ii) fMRI model estimation
Select SPM.mat: - Method: “Classical”: applies Restricted Maximum Likelihood (ReML); for spatially smoothed images after estimation effects of parameters are tested by T and F-statistic -> SPM(T), SPM(F) “Bayesian 1st-level”: applies Variational Bayes (VB); images do not need to be spatially smoothed; takes long; results: contrasts identify regions with effects larger than a user-specified size, eg 1% of the global mean signal (Posterior Probability Map – PPM) 3 methods to estimate the data: classica + bayesian 1st level = 1st level analyses, bayesian 2nd level = 2nd level. Run 1 first…

(iii) Results Testing hypothesis
T-test: is there a significant increase or is there a significant decrease in a specific contrast (between conditions) – directional F-test: is there a significant difference between conditions in the contrast - nondirectional

(iii) Results Contrast-vector: c‘ = [-1 1 0 0 0 0 ] T-Contrast:
H0: no difference between condition 1 and 2 in the 1st block H1: there is a difference between condition 2 and 1 in the 1st block (condition 2 > condition 1) Parameters: Design matrix: T-statistics in the usual way: Comparison of betas to variance

(iii) Results Contrast-vector: c‘ = [-1 1 -1 1 0 0 ] T-Contrast:
H0: no difference between condition 1 and 2 in the 1st and 2nd block H1: there is a difference between condition 2 and 1 in the 1st and 2nd block (condition 2 > condition 1) T-Contrast: Parameters: Design matrix: T-statistics in the usual way: Comparison of betas to variance

(iii) Results Contrast-vector: c‘ = [1 0 0 0 0 0 0; F-Contrast:
; ; ; ] H0: the factors 1, 2, 3 and 4 do not explain a significant amount of variance H1:the factors 1, 2, 3 and 4 do explain a significant amount of variance: F-Contrast: Parameters: Design matrix:

(iii) Results Contrast-vector: c‘ = [1 0 0 0 0 0 0; F-Contrast:
; ] H0: the factor 1 does not explain a significant amount of variance H1:the factor 1 does explain a significant amount of variance: F-Contrast: Parameters: Design matrix:

(iii) Results Results: Glas-brain List of activated voxel
(maximum intensity projection (MIP)) List of activated voxel

(iii) Results The multiple comparison problem Results:
Voxel-level P: chance of finding a voxel with this or a greater height (T or Z), corrected or uncorrected for search volume Uncorrected: Default: > voxels = 50 false positives FWE: ‘family wise error’ is a false positive anywhere in the SPM controls any false positives FDR: ‘false discovery rate’ – controls the expected proportion of false positives among suprathresholded voxels -> it adapts to the amount of signal in the data Results: Glas-brain (maximum intensity projection (MIP)) List of activated voxel

(iii) Results Results: Glas-brain List of activated clusters corrected
(maximum intensity projection (MIP)) List of activated clusters corrected uncorrected

(iii) Results Cluster level (P): chance of finding a cluster with this many (ke) or a greater number of voxel, corrected or uncorrected for search volume Set-level (P): the chance of finding this (c) or a greater number of clusters in the search volume Results: Glas-brain (maximum intensity projection (MIP)) List of activated clusters corrected uncorrected

(iii) Results Plotting responses Estimated effect sizes
Fitted responses

(iii) Results Overlaying the data Slices Sections

(iii) Results Overlaying the data Render

(ii) fMRI model estimation
Bayesian 1st-level: applies Variational Bayes (VB); allows to specify spatial priors for regression coefficients and regularised voxel-wise AR(P) modelsfor fMRI noise prcesses images do not need to be spatially smoothed takes 5x longer than the classical approach results: contrasts identify regions with effects larger than a user-specified size, eg 1% of the global mean signal (Posterior Probability Map – PPM)

(ii) fMRI model estimation
Matrix design Graphical design