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.