Introduction to functional
neuroimaging
Didem Gökçay
Imaging modalities
Lesion maps
-
~5 mm
-
Where do we stand historically
Brain Mapping: The systems (Toga & Mazziotta, Chap.2)
Introduction to functional MRI
Outline of fMRI topics
•1. 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’ brain
As 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)
Arteries
Arteries contain
oxygenated blood
(oxyhemoglobin)
Veins
Veins contain
deoxygenated 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 activity
and 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.
after activity
BEFORE ACTIVITY
venous flow
AFTER ACTIVITY
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 more
oxygenated, 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*-weighted
pulse sequence increases by a few percent
BOLD: Blood oxygenated level dependent
(hemodynamic response)
animal study
animal study
human
HRF
(HemRespFunc)
SUMMARY
CONFOUNDS
Pial Arteries
Noradrenergic
Sub-cortical
Dopamine
10 m
Not only neuronal activity but noradrenergic or dopamine activity affects BOLD !!
Krimer, Muly, Williams, Goldman-Rakic, Nature Neuroscience, 1998
Features of hemodynamic activity
Percent Signal Change
505
1%
500
5
5
0
5
10
15
10
15
205
1%
200
0
5
• Peak / mean(baseline)
• Often used as a basic
measure of “amount of
processing”
• Amplitude variable across
subjects, age groups, etc.
• Amplitude increases with
increasing field strength:
1.5T < 3T
20
25
20
25
Variability of hemodynamic response
fMRI Hemodynamic
Response
7
100ms
6
Stimulus duration
500ms
1500ms
1500ms
500ms
100ms
5
4
3
Calcarine
Sulci
2
1
0
-6
-4
-2
0
2
4
6
8
10
12
-1
Magnitude increases
with stimulus duration
7
100ms
6
500ms
1500ms
5
4
Fusiform
Gyri
3
2
1
0
-6
-4
-2
0
-1
2
4
6
8
10
12
Correlation of Electrical and BOLD
activities in monkey (Logothetis)
Dale & Buckner, 1997
• Responses to consecutive presentations of a
stimulus add in a “roughly linear” fashion
• Subtle departures from linearity are evident
Linear Systems
• Scaling
– The ratio of inputs determines the ratio of outputs
– Example: if Input1 is twice as large as Input2, Output1
will be twice as large as Output2
• Superposition
– The response to a sum of inputs is equivalent to the
sum of the response to individual inputs
– Example: Output1+2+3 = Output1+Output2+Output3
Scaling (A) and Superposition (B)
A
-5
0
5
10
15
-5
20
0
5
10
15
20
-5
0
5
10
15
20
B
-5
0
5
10
15
20
25
30
-5
0
5
10
15
20
25
30
-5
0
5
10
15
20
25
30
Linear additivity
A
B
-5
-5
0
5
10
15
20
C
-5
0
5
10
15
20
25
0
5
10
15
20
25
25
D
0
5
10
15
20
25
-5
Refractory Periods
• Definition: a change in the responsiveness
to an event based upon the presence or
absence of a similar preceding event
– Neuronal refractory period
– Vascular refractory period
Refractory Effects in the fMRI
Hemodynamic Response
0
6
4
2
1
1.40
Signal Change over Baseline(%)
1.20
1.00
0.80
Stimulus latency
after initial stimulus
0.60
0.40
0.20
0.00
-0.20
-0.40
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Time since onset of second stimulus (sec)
Huettel & McCarthy, 2000
SUMMARY
• fMRI measurements are of amount of deoxyhemoglobin
per voxel
• We assume that amount of deoxygenated hemoglobin is
predictive of neuronal activity
Variability in the Hemodynamic Response
• Across Subjects
• Across Sessions in a Single Subject
• Across Brain Regions
• Across Stimuli
Relative measures
• fMRI provides relative change over time
– Signal measured in “arbitrary MR units”
– Percent signal change over baseline
2. Imaging the function
(change in blood flow)
fMRI experimental setup
fMRI experiments
MR console
MR scanner
response
buttons
goggle
synchronization box
subject
experiment PC
MR ROOM
OPERATOR ROOM
The environment
headphone
RF/TTL
pulse
2. Imaging the function: experimental setup
Subject lies in the scanner awaiting for commands from the scanner
operator:
- 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)
3 msec 100 msec
Stimulus presentation and recording of subject response is done via
a pc synchronized to the rf pulses of the scanner
fMRI experiments
fMR experiment
responses and images
impulse
slice j
..........
t (sec)
0
2
5
8
11
14
..........
I
I
2
2
5
5
8
8
11
11
14
14
I: Change of intensity
of an active voxel in time
t
I: Change of intensity
of a passive voxel in time t
Data acquisition
300
How large are anatomical voxels?
 5.0mm 
=
3
~.004cm
 .9375mm 
Within a typical brain (~1300cm3), there may be about 300,000+
anatomical voxels.
How large are functional voxels?
 5.0mm 
=
3
~.08cm
 3.75mm 
Within a typical brain (~1300cm3), there may be about 20,000
functional voxels.
sample 6 slice T2* functional acquisition
Partial Volume Effects
• A single voxel may contain
multiple tissue components
– Many “gray matter” voxels will
contain other tissue types
– Large vessels are often
present
• The signal recorded from a
voxel is a combination of all
components
fMRI experimental paradigms
Trial Averaging: Does it work?
• Static signal, variable noise
– Assumes that the MR data recorded on each trial are composed
of a signal + (random) noise
• Effects of averaging
– Signal is present on every trial,
so it remains constant when averaged
– Noise randomly varies across trials,
so it decreases with averaging
– Thus, SNR increases with averaging
Caveats
• Signal averaging is based on assumptions
– Data = signal + temporally invariant noise
– Noise is uncorrelated over time
• If assumptions are violated, then averaging
ignores potentially valuable information
– Amount of noise varies over time
– Some noise is temporally correlated (physiology)
– Response latency may vary
• This is why averaging methods are useless in
fMRI
fMRI Paradigms
fMRI paradigms
There are 2 major paradigms for acquisition of fMRI:
- block design
- event related design
fMRI block design
signal
amplitude
Task waveform
5-6
samples
t
Measures cumulative activity in the ON block
Signal amplitude is about 1.5-3% in 1.5T scanner
fMRI event-related design
Measures single event activity
Signal amplitude is about 1% in 3T
OVERALL
Signal
Amplitude
t
Task
Impulse
Task Impulse
standard design
rapid design
What temporal resolution do we want?
fMRI
•
•
•
•
•
10,000-30,000ms: Arousal or emotional state
1000-10,000ms: Decisions, recall from memory
500-1000ms: Response time
250ms: Reaction time
10-100ms:
– Difference between response times
– Initial visual processing
• 10ms: Neuronal activity in one area
Basic Sampling Theory
• Nyquist Sampling Theorem
– To 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.
Aliasing
• Mismapping of high frequencies (above the Nyquist limit)
to lower frequencies
– Results from insufficient sampling
– Potential problem for long TRs and/or fast stimulus changes
– Also problem when physiological variability is present
Sampling Rate in Event-related
fMRI
Costs of Increased Temporal Resolution
• Reduced signal amplitude
– Shorter flip angles must be used (to allow reaching of
steady state), reducing signal
• Fewer slices acquired
– Usually, throughput expressed as slices per unit time
fMRI problems
experimental problems
Some 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 motion
Could be correlated with the task. May be avoided
with bite bars or head-stabilization devices
- scanner noise
Creates problems with the auditory tasks during the
rest period. Also distracts the subject
- small SNR
The fMRI signal is on the range of 1-3%
fMRI data analysis techniques
The fMRI Linear Transform
Schematic of the data obtained
fMRI Preprocessing
preprocessing
What is preprocessing?
• Correcting for non-task-related variability
in experimental data
– Usually done without consideration of
experimental design; thus, pre-analysis
– Occasionally called post-processing, in
reference to being after acquisition
• Attempts to remove, rather than model,
data variability
Quality assurance
Preprocessing
Alignment of slice timings
It 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 versus
the last slice, slice n. This needs to be corrected for, by shifting
the individual intensity data in each slice
t=1.6 sec
t=0
Preprocessing
Head Motion correction
All 3d functional images (samples) should be aligned with
the single anatomic image collected at the beginning or
end of the session
Head Motion: Good, Bad,…
Why does head motion introduce
problems?
A
B
C
507
89
154
663
507
89
119
171
83
520
119
171
179
117
53
137
179
117
When you look at the time course of a single voxel, this
is a specific voxel in the data matrix, not a specific voxel
in the brain. When head moves, the data matrix stays same
but the voxel assignment in the brain changes.
You are no longer looking at the same voxel
Correcting Head Motion
• Rigid body transformation
– 6 parameters: 3 translation, 3 rotation
• Minimization of some cost function
– E.g., sum of squared differences
– Mutual 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 A
Task B
Task A
Task B
Task A
Task B
Task A
Task B
Task A
REST
Task B
REST
Task A
REST
Task B
REST
What baseline should you choose?
• Task A vs. Task B
– Example: Squeezing Right Hand vs. Left Hand
– Allows you to distinguish differential activation
between conditions
– Does not allow identification of activity common to
both tasks
• Can control for uninteresting activity
• Task A vs. No-task
– Example: Squeezing Right Hand vs. Rest
– Shows you activity associated with task
– May introduce unwanted results
Choosing Length of Blocks
• Longer block lengths allow for stability of extended responses
– Hemodynamic response saturates following extended stimulation
• After about 10s, activation reaches max
– Many tasks require extended intervals
• Processing may differ throughout the task period
• Shorter block lengths allow for more transitions
– Task-related variability increases (relative to non-task) with increasing
numbers of transitions
• Periodic blocks may result in aliasing of other variance in the data
– Example: if the person breathes at a regular rate of 1 breath/5sec, and
the blocks occur every 10s
Non-Task Processing
• In many experiments, activation is greater in
baseline conditions than in task conditions!
– Requires interpretations of significant activation
• Suggests the idea of baseline/resting mental
processes
–
–
–
–
–
Emotional processes
Gathering/evaluation about the world around you
Awareness (of self)
Online monitoring of sensory information
Daydreaming
Data analysis techniques: block design
Methods:
1. Subtraction
2. Correlation
3. t-test
4. frequency analysis
Block design Signal-Noise-Ratio (SNR)
Task-Related
Variability
Non-task-related
Variability
Data analysis techniques: block design - subtraction
y1 y2 y3
X1 X2 X3
yi yj yk
Xi Xj Xk
intensity samples
active if : Threshold (average(Yi) - average(Xi)) > a
color code
This method is outdated
The Hemodynamic Response
Lags Neural Activity
Experimental
Design
Convolving
HDR
Time-shifted
Epochs
Introduction
of Gaps
Data analysis techniques: block design - correlation
Sinusoidal 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)
choose
MAX
Data analysis techniques: block design - t_test
Xi
Yi
Xi
Yi
Samples: 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 <0.05, significant difference in means
Block design: frequency analysis
McCarthy et al., 1996
Filtering Approaches
• Identify unwanted frequency variation
– Drift (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
-0.5
-1
-1.5
AFNI polort removes this
97
10
0
94
91
88
85
82
79
76
73
70
67
64
61
58
55
52
49
46
43
40
37
34
31
28
25
22
19
16
13
10
7
4
1
Linear Drift
2.5
2
1.5
1
0.5
0
Power Spectra
We want the changes evoked by the task to be at different parts
of the frequency spectrum than non-task-evoked changes.
Limitations of Blocked Designs
• Very 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-related
• Allows studying of trial effects
• Improves relation to behavioral factors
• Simple analyses
– Selective averaging
– General linear models
Impulse-Response Systems
• Impulse: single event that evokes changes in a system
– Assumed to be of infinitely short duration
• Response: Resulting change in system
f(t)
Impulses
y(t)
Convolution
with HRF
Response
ε
plus noise
Z(t)
Output
HRF: h(t)
=
ε(t)
Event-related design data analysis
impulse response
HRF
f(t)
y(t)
system
with IR h(t)
Z(t)
1. 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.
impulse
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'
active voxel i
f
Zi
estimated
impulse
response
inactive voxel j
Zj
f
hi
hj
Obtaining the impulse response by deconvolution
Possible Sources of Nonlinearity
• Stimulus time course  neural activity
– Activity not uniform across stimulus (for any stimulus)
• Neural activity  Vascular changes
– Different activity durations may lead to different blood flow or
oxygen extraction
• Minimum bolus size?
• Minimum activity necessary to trigger?
• Vascular changes  BOLD measurement
– Saturation of BOLD response necessitates nonlinearity
– Vascular measures combining to generate BOLD have different
time courses
From Buxton, 2001
Variability across subjects
Buckner et al., (1996)
Word-stem completion task. Blocked design: 30s on/off.
Event-related design: 15s ISI.
Buckner et al., (1996)
Limitations of Event-Related Designs
• Differential effects of interstimulus interval
– Long intervals do not optimally increase
stimulus variance
– Short 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: ICA
t
Bell, Sejnowski
t1
ICA
t2
tn
Mckeown, Sejnowski
Mixed Designs
3a. Combination Blocked/Event
• Both 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 measures
– Cognitive processes are assumed to be independent
Mixed Blocked/Event-related Design
…
Target-related Activity (Phasic)
Blocked-related Activity (Tonic)
Task-Initiation Activity (Tonic)
Task-Offset Activity (Tonic)
…
4. Aggregation of activity maps
from multiple people
Aggregation of activity maps from multiple people
Methods:
1. Individual ROI traces
2. Blurring
Individual ROI traces:
Definition of anatomic structures and landmarks
Definition of landmark points
Anterior commissure
Anatomic images
Definition of structural shapes
Posterior commissure
Cingulate sulcus
Sagittal View
Sagittal View
Individual ROI traces:
Generation of ROI partitions
Sagittal View
Sagittal
Sagittal View
Coronal
Axial
Individual ROI traces: Extraction of function
Sagittal
Coronal
Axial
ROI
Selection
Functional images
Localized activation
Repetitive localization
(optional)
Aggregation of activity maps: blurring
Step 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 box
Shift AC PC vertically and side-to-side
side view
Align extreme points
top view
AC
PC
AC
PC
before
registration
after
registration
Step 2: Blur individual fMRI for all subjects
The atlas problem: Homology in individual activations is hard to predict for group analysis of fMRI
Calossal, Parietooccipital,
Marginal sulci, 30 hemispheres
Central Sulcus
20 hemispheres
Leftover variability after Talairach transformation
Sylvian Fissure (L)
15 hemispheres
Sylvian Fissure (R)
15 hemispheres
Similar example on faces
After affine registration
Before affine registration (red is for activity)
fMRI group averaging
individual
28 people (blurred)
Step 2: Blur individual fMRI for all subjects
Remedy for the atlas problem:
Blur activation statistics using a Gaussian kernel so they overlap in multiple subjects
convolve
individual activ.: subj1, subj2
merged activ after blurring
merged activity on average anatomy
End result: Coarse anatomic map
(about 2 cm resolution)
In reality, what determines Spatial Resolution?
• Voxel Size
– In-plane Resolution
– Slice thickness
• Spatial noise
– Head motion
– Artifacts
• Spatial blurring
–
–
–
–
Smoothing (within subject)
Coregistration (within subject)
Normalization (within subject)
Averaging (across subjects)
• Functional resolution