fmri methods lecture7 – review: analyses & statistics

fMRI Methods

Lecture7 – Review: analyses & statistics

Neurons

Neural computation

Neural selectivity

Hierarchy of neural processing

Integration of information

Retinal ganglion cell receptive fields

V1 neuron receptive field(Hubel & Wiesel)

Integrate

Cortical columns

Neighboring neurons often share the same selectivity and are strongly connected.

“units of computation”

At least in the visual system

Many columns in a voxel.

Hemodynamic changes

Birth of the HRF

Boynton et. al. 1996

Linear shift invariant system

Stimulus

HRFHRF

Scaling

Time Invariance

Measured Response: Additivity

Convolution

Multiply each timepoint of the neural activity by a copy of the HRF

Estimating neural activity

We actually want to go the other way around.

So we assume that neuro-vascular coupling is constant across brain areas, tasks, and states

Estimating neural activity

If we find a reduced/increased hemodynamic response in one experimental condition versus another, what can we deduce about the neural activity generating it?

Faces Objects

Experiment designsPresent stimuli or tasks in a particular temporal structure and see where responses are related/correlated with this

temporal structure.

Sparse event related design:

Rapid event related design:

Block design:

Time

Experiment designs

Experiment designs

Experiment designs

AnalysesWe have 4 ways of analyzing the data:

1.Correlation with an HRF convolved model

2.Regression with an HRF convolved model

3.Regression with an un-convolved model (deconvolution)

4.Trigger averaging

General linear modelA mathematical model describing the expected response

predictor 1 predictor 2 predictor 1 predictor 2

1001000110010

0110010100100

Design matrix

General linear modelPredictors as vectors

Dimensions = time-points in data

Direction = temporal structure

Length = variability of structure

If predictors have the same number of “trials”/”blocks”, they will have the same length

General linear modelThe time-course of a voxel is also a vector

What is the relationship between the data and the model?

How do we best scale the predictors/model to fit the data?

data

HRF convolved modelOur data contains hemodynamic changes, not neural responses. Assume a canonical HRF and convolve the predictors/model:

1. CorrelationCorrelate each predictor with the data (voxel time-course):

data predictor 1

data

predictor 2

2. Regression (take 1)Use linear regression to determine scaling factor for each predictor:

= * + errora1 a2

data

design matrix

beta

residuals

Unconvolved modelEstimate the amplitude and shape of the response at the same time:

1001000110010

3. Regression (take 2)Use regression to determine scaling of each predictor:

= * a1 a2 … an

Randomization/JitterIt’s important to randomize trial timing:

4. Trial triggered averageCut out the trials from your time-course:

Normalize each trial to its first two samples

The idea is that you expect the same relative response in each trial.

Trial triggered average

Inspired by ERP

Jitter and randomness very important

Error bars are simply the standard error of the mean

StatisticsHow do we know whether the beta values are significantly different from zero or from one another?

In a single subject analysis and a multi subject fixed effects analysis this depends on the beta value’s variability:

Contrast vector

StatisticsTranslate the t-value to a p-value according to the number of “degrees of freedom”

T distribution (100 DOF)

Fixed effects analysisCommonly done by building a long GLM; stacking the data

= * + errora1 a2

Diff1.11.1-0.3

20.51.2

Random effects analysisWhen comparing responses in the same subjects, perform

paired “repeated measure” t-test on beta values

Beta 21.21.40.42.20.81

Beta 10.10.30.70.20.3-0.2

Random effects analysisWhen comparing responses across different subjects,

perform regular “two sample” t-test on beta values

Group 21.21.40.42.20.81

Group 10.10.30.70.20.3-0.2

Statistical parameter mapsPerform the analysis for each voxel separately and color the voxels by their statistical significance (p values)

Around 64,000 voxels in a standard fMRI scan….

BonferroniRandom field theoryCluster thresholdingFalse discovery rate

Beware of statistical thresholding

Threshold is always arbitrary!From looking at these maps you don’t know how big the difference between betas really is or anything about the actual responses…

“Strong” response?

Comparing statistical “maps”

P values are a function of the average response strength and its variability:

Do not compare response strength across subjects, conditions, experiments, using SPM maps!

ExampleA real example from an experiment with autistic individuals:

ExampleWhen estimating the response within each ROI:

Response variability

What could cause differences in response variability?

Signal and noise

System noiseCan we compare responses across different scanners?

Static field inhomogeneities Scanner drift

Head motionWere subjects moving differently during the scan?

Head motionIn the lab we’ll try different methods of correcting for head

motion.

Inclusion in the GLM, projecting out, cutting the data

Physiological noiseHemodynamic changes caused by heart rate, blood

pressure, and respiration.

Neural variabilityThe brain is never at “rest”, spontaneous neural activity fluctuations are as large as stimulus evoked responses.

Behavioral/Cognitive variabilityComplex experiment = variable behavioral responses

1.Subjects can choose different strategies.2.Changes in attention/arousal (caffeine).

Response times Effects of caffeine.

To the lab!

Open a folder for your code on the local computer. Try to keep the path name simple (e.g. “C:\Your_name”).

Download code and MRI data from:http://www.weizmann.ac.il/neurobiology/labs/malach/ilan/lecture_notes.html

Save Lab6.zip in the folder you’ve created and unzip.

Open Matlab. Change the “current directory” to the directory you’ve created.

Open: “Lab6_ProjectingOutNoise.m”

Lab #7

ScansCreate experiments to test the following questions:

1.What is the subject’s real HIRF and how similar is it to a canonical HIRF?

2.How should one arrange the stimuli in a rapid event related experiment? Test different ways of arranging the stimuli (jitter, randomization). What is the minimal inter-stimulus interval that enables accurate separation of responses?

You can do the experiments in the visual or auditory domains.