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!