FMRI Methods Lecture 10 – Using natural stimuli. Reductionism Reducing complex things into simpler...
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Transcript of FMRI Methods Lecture 10 – Using natural stimuli. Reductionism Reducing complex things into simpler...
fMRI Methods
Lecture 10 – Using natural stimuli
ReductionismReducing complex things into simpler components
Explaining the “whole” as a sum of its parts
Duck behavior is the sum of its automatically behaving parts.
Descartes 1662
VisionDecompose visual experience into:
Locations in visual field
Contrast
Orientation
Spatial frequency
Direction of motion
Categories – objects, faces, houses
Visual experiment
Change a stimulus attribute in a controlled manner and see how the neural response changes (easy to do!).
Repeat many times and average.
Visual system
Different neurons in different visual system areas process specific components:
Spatial receptive field
Contrast and spatial frequency sensitivity
Color sensitivity
Selectivity for orientation, direction of motion, visual category.
Temporal dependence, adaptation.
What happens in real life?
Inter-subject correlationCorrelate the responses across subjects/runs
Hasson et. al. Science 2004
Global component
General response across many areas – similar across subjects.
Due to structure of movie?
General arousal?
Reverse correlation
Reverse correlation
Natural stimulus
Despite the complexity of the stimulus:
1.Categorical visual areas maintain selectivity.
2.Responses are similar across different subjects.
3.Reverse engineering works: can go from brain to stimulus.
4.Or “map” multiple areas at once by breaking down the stimulus into visual components (e.g. retinotopic mapping).
Temporal receptive windows
Hasson et. al. J Neurosci. 2008
Temporal receptive windows
Do the neurons care about the momentary stimulus being presented, or about its context within a certain temporal history…
Temporal receptive windows
Scrambling the movie at different segment lengths.
Inter-subject correlation in some cortical areas depended on the “temporal continuity” of the movie.
In autism
Individuals with autism show weak inter-subject correlations
Hasson et. al. Aut. Res. 2009
In autismIndividual variability, but group averages were similar…
Total = Sum of components?
Data driven multivariate analyses Our variables are voxels
We assume that voxel fMRI measurements represent a sum of separate linear components (separate “brain processes”) that are mixed in some unknown way.
Find a mathematical criteria to separate the data into meaningful components:
Principle component analysis (PCA)Independent component analysis (ICA)Clustering algorithms: K means, spectral clustering, etc…
1. Normalize the data (% sig change).
2. Find the direction with largest variability (1st component). Data are most correlated along this direction….
3. Add it’s orthogonal direction (2nd component).
Principal component analysis
In two dimensions
PCA is a way of representing the data in components that are orthogonal (dot product = 0, correlation = 0), while ordering them by the amount of variability that they explain.
fMRI data has as n by m dimensions (n voxels and m time-points). Perform PCA on the temporal dimensions.
Principal component analysis
Num
vox
els
Num TRs
One way of computing a PCA is using singular value decomposition (SVD):
Computing the components
Data = U * S * VT
Eigenvectorsn by n matrix
Eigenvaluesn by n matrix
n by m matrix
n = num of trsm = num of voxels
n by m matrix
Data structure
If the data is correlated, it will have components (eigenvectors) that will explain a large part of the variability…
Reduce the dimensionality of the data?
Var
ianc
e
Spatio-temporal components
Brain areas that “work together” will be correlated in time
The “weighting” of a particular component in the different voxels:
The dot product of a voxel’s “weights” and the components matrix will give the original voxel’s timecourse
Principle component analysis
Are orthogonality and “variability explained” good criteria for separating independent brain processes?
How many simultaneous processes are there? Are they correlated in time?
Reliability across scans and subjects?
Typically more than one PCA solution….
Has mostly been used for dimensionality reduction (good for compressing data).
Independent component analysis
A different algorithm that separates components such that they are “statistically independent”.
Pr(A ∩ B) = Pr(A) * Pr(B)
Cov(X,Y) = 0
Independent variables are uncorrelated, but not all uncorrelated variables are independent…
They need to have a joint distribution fulfilling:
Good for separating audio
Two microphones:
Microphone 1 Microphone 2
Two sources:
Source 1 Source 2
Good for cleaning EEG data
Spatially consistent “sparse” processes.
Separating fMRI components
Independent component analysisAnd with fMRI “free viewing” movie data:
Independent component analysis
Things to think about:
1.You decide how many independent components to split the data into (arbitrary choice).
2.Reliability across scans and subjects.
3.How can we tell whether the components are biologically meaningful?
To the lab!