Introduction to functional neuroimaging

Didem Gkay

Imaging modalitiesLesion maps - ~5 mm -

Where do we stand historicallyBrain Mapping: The systems (Toga & Mazziotta, Chap.2)

Introduction to functional MRI

Outline of fMRI topics1. The basis of the fMRI signal: hemodynamic response

2. Imaging the function: fMRI experimental setup fMRI paradigms fMRI problems

3. Data analysis techniques fMRI Preprocessing fMRI Block design data analysis fMRI Event related data analysis

4. Aggregation of activity maps from multiple people Individual ROIs Blurring

1. Basis of the fMRI signal: hemodynamic response

Changes in the active brainAs long as we eat and breathe we can continue to think

The working brain requires a continuous supply of glucose and oxygen

This is delivered through cerebral blood flow (cbf)

Human brain accounts for 2% of body weight but 15% of cardiac output (700 ml/min)ArteriesVeinsArteries containoxygenated blood(oxyhemoglobin)

Veins containdeoxygenated blood(deoxyhemoglobin)

Local blood flow varies 18-fold between different brain regions(the number of capillaries in the tissue is dissimilar)

The ratio of capillary density in GM:WM is 2-3:1

The CBF ratio of GM:WM is 4:1, The CBV ratio of GM:WM is 2

Neuronal activity is associated with an increase in metabolic activityand hence, blood flow

Arterioles (10 - 300 microns) precapillary sphincters Capillaries (5-10 microns) Venules (8-50 microns)

The change in diameter of arterioles following sciatic stimulation.

BEFORE ACTIVITYAFTER ACTIVITYvenous flow

Obtaining the fMRI signal (intensity)

T2*: The transverse relaxation time actually decays faster than T2, due to field inhomogeneity (the spinning tops gets out of phase, so we observe a rapid destruction of the alignment with the field)

deoxyhaemoglobin: is contained in blood and paramagnetic, so introduces field inhomogeneity

fMRI process: mainly measures the field inhomogeneity

- upon stimulus, the capillary and venous blood are moreoxygenated, so there is less deoxyhemoglobin

- the capillaries susceptibility is reflected on the surrounding tissue, so the surrounding field gradients are reduced.

- T2* becomes longer so the signal measured via the T2*-weightedpulse sequence increases by a few percent

animal studyanimal studyhumanHRF(HemRespFunc)BOLD: Blood oxygenated level dependent (hemodynamic response)

SUMMARY

Krimer, Muly, Williams, Goldman-Rakic, Nature Neuroscience, 1998Pial Arteries10 mNoradrenergicDopamineSub-corticalCONFOUNDSNot only neuronal activity but noradrenergic or dopamine activity affects BOLD !!

Features of hemodynamic activity

Percent Signal ChangePeak / mean(baseline)Often used as a basic measure of amount of processingAmplitude variable across subjects, age groups, etc.Amplitude increases with increasing field strength: 1.5T < 3T

500505200205

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Variability of hemodynamic response

Calcarine SulciFusiform GyrifMRI Hemodynamic Response1500ms500ms100msStimulus durationMagnitude increaseswith stimulus duration

Correlation of Electrical and BOLDactivities in monkey (Logothetis)

Dale & Buckner, 1997Responses to consecutive presentations of a stimulus add in a roughly linear fashionSubtle departures from linearity are evident

Linear SystemsScalingThe ratio of inputs determines the ratio of outputsExample: if Input1 is twice as large as Input2, Output1 will be twice as large as Output2

SuperpositionThe response to a sum of inputs is equivalent to the sum of the response to individual inputsExample: Output1+2+3 = Output1+Output2+Output3

Scaling (A) and Superposition (B)BA

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Refractory PeriodsDefinition: a change in the responsiveness to an event based upon the presence or absence of a similar preceding eventNeuronal refractory periodVascular refractory period

Refractory Effects in the fMRI Hemodynamic ResponseHuettel & McCarthy, 2000Time since onset of second stimulus (sec)Signal Change over Baseline(%)Stimulus latencyafter initial stimulus

Variability in the Hemodynamic ResponsefMRI measurements are of amount of deoxyhemoglobin per voxelWe assume that amount of deoxygenated hemoglobin is predictive of neuronal activity

SUMMARYAcross SubjectsAcross Sessions in a Single SubjectAcross Brain RegionsAcross StimuliRelative measuresfMRI provides relative change over timeSignal measured in arbitrary MR unitsPercent signal change over baseline

2. Imaging the function(change in blood flow)

fMRI experimental setup

fMRI experimentsThe environment

2. Imaging the function: experimental setupSubject lies in the scanner awaiting for commands from the scanneroperator:

a 3d high-resolution MRI is collected for high precision localization

multiple runs of an experimental protocol is performed next.

At this phase, the subject is presented with auditory, visual or tactile stimulation.

Stimulus presentation is achieved through headphones, goggles/screen, air pumps

As the subject performs the experiment behavioral/physiological data is collected through voice recording, push-buttons, electrodes on the head/feet (either for eeg or for heart rate, skin conductance)

Stimulus presentation and recording of subject response is done via a pc synchronized to the rf pulses of the scanner3 msec 100 msec

fMRI experimentsData acquisition

How large are anatomical voxels? .9375mm 5.0mm .9375mm = ~.004cm3Within a typical brain (~1300cm3), there may be about 300,000+ anatomical voxels.

How large are functional voxels? 3.75mm 5.0mm 3.75mm = ~.08cm3Within a typical brain (~1300cm3), there may be about 20,000 functional voxels.

sample 6 slice T2* functional acquisition

Partial Volume EffectsA single voxel may contain multiple tissue componentsMany gray matter voxels will contain other tissue typesLarge vessels are often presentThe signal recorded from a voxel is a combination of all components

fMRI experimental paradigms

Trial Averaging: Does it work?Static signal, variable noiseAssumes that the MR data recorded on each trial are composed of a signal + (random) noise

Effects of averagingSignal is present on every trial, so it remains constant when averagedNoise randomly varies across trials, so it decreases with averagingThus, SNR increases with averaging

CaveatsSignal averaging is based on assumptionsData = signal + temporally invariant noiseNoise is uncorrelated over time

If assumptions are violated, then averaging ignores potentially valuable informationAmount of noise varies over timeSome noise is temporally correlated (physiology)Response latency may vary

This is why averaging methods are useless in fMRI

fMRI Paradigms

fMRI paradigmsThere are 2 major paradigms for acquisition of fMRI:

block design

event related design

fMRI block designTask waveformt5-6 samplesMeasures cumulative activity in the ON blockSignal amplitude is about 1.5-3% in 1.5T scannersignalamplitude

fMRI event-related designTask Impulserapid designstandard designtMeasures single event activitySignal amplitude is about 1% in 3TTask ImpulseSignalAmplitude

What temporal resolution do we want?10,000-30,000ms: Arousal or emotional state1000-10,000ms: Decisions, recall from memory500-1000ms: Response time250ms: Reaction time10-100ms: Difference between response timesInitial visual processing10ms: Neuronal activity in one areafMRI

Basic Sampling TheoryNyquist Sampling TheoremTo be able to identify changes at frequency X, one must sample the data at (least) 2X.For example, if your task causes brain changes at 1 Hz (every second), you must take two images per second.

AliasingMismapping of high frequencies (above the Nyquist limit) to lower frequenciesResults from insufficient samplingPotential problem for long TRs and/or fast stimulus changesAlso problem when physiological variability is present

Sampling Rate in Event-related fMRI

Costs of Increased Temporal ResolutionReduced signal amplitudeShorter flip angles must be used (to allow reaching of steady state), reducing signal

Fewer slices acquiredUsually, throughput expressed as slices per unit time

fMRI problems

experimental problemsSome important problems that get in the way for better data acquisition in fMRI:

- venous flow artifacts Any signal larger than 5% change is probably due to venous activity so it should be discarded

- head motionCould be correlated with the task. May be avoidedwith bite bars or head-stabilization devices

- scanner noiseCreates problems with the auditory tasks during the rest period. Also distracts the subject

small SNRThe fMRI signal is on the range of 1-3%

fMRI data analysis techniques

The fMRI Linear TransformSchematic of the data obtained

fMRI Preprocessing

preprocessing

What is preprocessing?Correcting for non-task-related variability in experimental dataUsually done without consideration of experimental design; thus, pre-analysisOccasionally called post-processing, in reference to being after acquisition

Attempts to remove, rather than model, data variability

Quality assurance

Preprocessing

Alignment of slice timingsIt takes about 2 sec to finish one functional 3d acquisition. During this time, there will be a time difference between the hemodynomic responses sampled from slice 1 versusthe last slice, slice n. This needs to be corrected for, by shiftingthe individual intensity data in each slicet (sec)t=0t=1.6 sec

Preprocessing

Head Motion correctionAll 3d functional images (samples) should be aligned with the single anatomic image collected at the beginning or end of the session

t (sec)

Head Motion: Good, Bad,

Why does head motion introduce problems?ABCWhen you look at the time course of a single voxel, this is a specific voxel in the data matrix, not a specific voxelin the brain. When head moves, the data matrix stays samebut the voxel assignment in the brain changes.You are no longer looking at the same voxel

Correcting Head MotionRigid body transformation6 parameters: 3 translation, 3 rotation

Minimization of some cost functionE.g., sum of squared differencesMutual information

3dVolreg in AFNI

Prevention of head motion !!!

fMRI Block design data analysis

What are Blocked Designs?Blocked designs segregate different cognitive processes into distinct time periods

Task ATask BTask ATask BTask ATask BTask ATask BTask ATask BRESTRESTTask ATask BRESTREST

What baseline should you choose?Task A vs. Task BExample: Squeezing Right Hand vs. Left HandAllows you to distinguish differential activation between conditionsDoes not allow identification of activity common to both tasksCan control for uninteresting activity

Task A vs. No-taskExample: Squeezing Right Hand vs. RestShows you activity associated with taskMay introduce unwanted results

Choosing Length of BlocksLonger block lengths allow for stability of extended responsesHemodynamic response saturates following extended stimulationAfter about 10s, activation reaches maxMany tasks require extended intervalsProcessing may differ throughout the task period

Shorter block lengths allow for more transitionsTask-related variability increases (relative to non-task) with increasing numbers of transitions

Periodic blocks may result in aliasing of other variance in the dataExample: if the person breathes at a regular rate of 1 breath/5sec, and the blocks occur every 10s

Non-Task ProcessingIn many experiments, activation is greater in baseline conditions than in task conditions!Requires interpretations of significant activation

Suggests the idea of baseline/resting mental processesEmotional processesGathering/evaluation about the world around youAwareness (of self)Online monitoring of sensory informationDaydreaming

Data analysis techniques: block designMethods:

Subtraction

Correlation

t-test

frequency analysis

Block design Signal-Noise-Ratio (SNR)Task-Related VariabilityNon-task-related Variability

Data analysis techniques: block design - subtractionintensity samplesactive if : Threshold (average(Yi) - average(Xi)) > aThis method is outdatedcolor code

The Hemodynamic Response Lags Neural ActivityExperimental Design

Data analysis techniques: block design - correlationSinusoidal waves: Xi, Yi, Zi Square wave (ideal fmri signal): Ti (in reality, we observe t)

Find: sum( (Xi-avg(X)) (ti-avg(t))) / stdev(X)*stdev(t)*(N-1)sum( (Yi-avg(Y)) (ti-avg(t))) / stdev(Y)*stdev(t)*(N-1)sum( (Zi-avg(Z)) (ti-avg(t))) / stdev(Z)*stdev(t)*(N-1)

chooseMAX

Data analysis techniques: block design - t_testSamples: Xi , Yi (N samples each)

Find: (Xi-avg(X)) (Yi-avg(Y))) / SQRT(stdev(X)2*stdev(Y)2)

Look-up table for probability value wrt degrees of freedom: (number of points -1 which is 2N-2 here)

if prob

Block design: frequency analysisMcCarthy et al., 1996

Filtering ApproachesIdentify unwanted frequency variationDrift (low-frequency)Physiology (high-frequency)Task overlap (high-frequency)

Reduce power around those frequencies through application of filters

Potential problem: removal of frequencies composing response of interest

Linear DriftAFNI polort removes this

Power SpectraWe want the changes evoked by the task to be at different parts of the frequency spectrum than non-task-evoked changes.

Limitations of Blocked DesignsVery sensitive to signal drift Sensitive to head motion, especially when only a few blocks are used.

Poor choice of baseline may preclude meaningful conclusions

Many tasks cannot be conducted repeatedly

Difficult to estimate the HDR

fMRI event related design data analysis

What are Event-Related Designs?Event-related designs associate brain processes with discrete events, which may occur at any point in the scanning session.

Why use event-related designs?Some experimental tasks are naturally event-relatedAllows studying of trial effectsImproves relation to behavioral factorsSimple analysesSelective averagingGeneral linear models

Impulse-Response SystemsImpulse: single event that evokes changes in a systemAssumed to be of infinitely short duration

Response: Resulting change in system =ImpulsesConvolution with HRFResponseOutputplus noisef(t)

y(t)

Z(t)

HRF: h(t)

Event-related design data analysisimpulseimpulse response1. Assume that the observed signal yi at voxel i is a convolution of impulse responses

2. Given Zi and impulse times, f, try to estimate the impulse response hi for each voxel.

3. If estimated impulse response is similar to the hemodynamic response, then voxel i is active

OR If max amplitude of impulse response is above a threshold, voxel i is 'active' Zihiactive voxel iinactive voxel jZjhjestimated impulseresponsesystemwith IR h(t)f(t)Z(t)ffHRF(t)y(t)

Obtaining the impulse response by deconvolution

Possible Sources of NonlinearityStimulus time course neural activityActivity not uniform across stimulus (for any stimulus)

Neural activity Vascular changesDifferent activity durations may lead to different blood flow or oxygen extractionMinimum bolus size?Minimum activity necessary to trigger?

Vascular changes BOLD measurementSaturation of BOLD response necessitates nonlinearityVascular measures combining to generate BOLD have different time coursesFrom Buxton, 2001

Buckner et al., (1996)Variability across subjects

Buckner et al., (1996)Word-stem completion task. Blocked design: 30s on/off. Event-related design: 15s ISI.

Limitations of Event-Related DesignsDifferential effects of interstimulus intervalLong intervals do not optimally increase stimulus varianceShort intervals may result in refractory effects

Detection ability dependent on form of HDR

Length of event may not be known

Data driven approaches

Individual localization: ICAMckeown, SejnowskiICAtt1t2tnBell, Sejnowski

Mixed Designs

3a. Combination Blocked/EventBoth blocked and event-related design aspects are used (for different purposes)Blocked design is used to evaluate state-dependent effects Event-related design is used to evaluate item-related effects

Analyses are conducted largely independently between the two measuresCognitive processes are assumed to be independent

Mixed Blocked/Event-related Design

4. Aggregation of activity maps from multiple people

Aggregation of activity maps from multiple peopleMethods:

1. Individual ROI traces

2. Blurring

Individual ROI traces:Definition of anatomic structures and landmarks Definition of landmark pointsDefinition of structural shapes

Individual ROI traces:Generation of ROI partitions

Individual ROI traces: Extraction of function

Aggregation of activity maps: blurringStep 1: Intersubject registration (for ex: Talairach)

Step 2: Blur individual fMRI for all subjects

Step 3: Merge all subjects in a population (for ex: merge subjects in the Normal group as group1 and merge subjects in the schizophrenic group as group 2)

Step 4: Compare fMRI of group1 and fMRI of group2 via t-test or ANOVA

Step 1: Intersubject registration into Talairach coordinate system- Manual or automatic alignment is possible- Goals: 1. put AC in the origin 2. make AC-PC line horizontal 3. make AC-PC line vertical 4. scale extremities to fit into the Talairach atlas boxside viewtop viewbeforeregistrationafterregistration

The atlas problem: Homology in individual activations is hard to predict for group analysis of fMRIStep 2: Blur individual fMRI for all subjects Central Sulcus 20 hemispheresSylvian Fissure (R) 15 hemispheresSylvian Fissure (L) 15 hemispheresCalossal, Parietooccipital, Marginal sulci, 30 hemispheresLeftover variability after Talairach transformation

Similar example on facesBefore affine registrationAfter affine registration(red is for activity)

fMRI group averagingindividual28 people (blurred)

Remedy for the atlas problem: Blur activation statistics using a Gaussian kernel so they overlap in multiple subjectsStep 2: Blur individual fMRI for all subjects End result: Coarse anatomic map(about 2 cm resolution)merged activity on average anatomy

In reality, what determines Spatial Resolution?Voxel SizeIn-plane ResolutionSlice thicknessSpatial noiseHead motionArtifactsSpatial blurringSmoothing (within subject)Coregistration (within subject)Normalization (within subject)Averaging (across subjects)Functional resolution

fmri-fig-06-15-0.jpg fmri-fig-06-01-0.jpg fmri-fig-07-17-2.jpg The independent contribution of the second stimulus is shown on this plot.The yellow line shows the response to a single stimulus.Readily apparent are the significant refractory effects. At 1 second intervals, the response to the second stimulus is attenuated in amplitude by about 45% and is increased in latency by about a second. Both amplitude and latency values recover to near single-stimulus values by about six seconds.fmri-fig-08-01-0.jpg fmri-fig-09-15-0.jpg fmri-fig-10-01-0.jpg fmri-fig-10-02-0.jpg fmri-fig-10-04-0.jpg fmri-fig-10-07-0.jpg fmri-fig-11-15-2.jpg fmri-fig-11-15-1.jpg fmri-fig-11-21-0.jpg