# Signal and Noise II. Preprocessing

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```					I.Signal and Noise

II. Preprocessing

BIAC Graduate fMRI Course
October 19, 2005
1. Signal and Noise in
fMRI
What is signal? What is noise?
• Signal, literally defined
– Amount of current in receiver coil
• How can we control the amount of received
signal?
–   Scanner properties (e.g., field strength)
–   Experimental task timing
–   Subject compliance (through training)
–   Head motion (to some degree)
• What can’t we control?
– NOISE
I. Introduction to SNR
Signal, noise, and the General
Linear Model

Y  M  
Amplitude (solve for)
Measured Data                                      Noise
Design Model

Cf. Boynton et al., 1996
Signal Size in fMRI
A      45     B         50

E

C   50 - 45   D   (50-45)/45
Differences in SNR
Voxel 1

790   830   870

Voxel 2

690   730    770

Voxel 3

770   810    850
Effects of SNR: Simulation Data
• Hemodynamic response
– Unit amplitude
– Flat prestimulus baseline
• Gaussian Noise
– Temporally uncorrelated (white)
– Noise assumed to be constant over epoch
• SNR varied across simulations
– Max: 2.0, Min: 0.125
SNR = 2.0
2

1.5

1

0.5

0
-5 -4 -3 -2 -1       0   1   2   3   4   5   6   7   8   9 10 11 12 13 14 15

-0.5

-1
SNR = 1.0
2

1.5

1

0.5

0
-5 -4 -3 -2 -1       0   1   2   3   4   5   6   7   8   9 10 11 12 13 14 15

-0.5

-1
SNR = 0.5
2

1.5

1

0.5

0
-5 -4 -3 -2 -1       0   1   2   3   4   5   6   7   8   9 10 11 12 13 14 15

-0.5

-1
SNR = 0.25
4

3

2

1

0
-5 -4 -3 -2 -1       0   1   2   3   4   5   6   7   8   9 10 11 12 13 14 15
-1

-2

-3
SNR = 0.125
6

5

4

3

2

1

0
-5 -4 -3 -2 -1 0   1   2   3   4   5   6   7   8   9 10 11 12 13 14 15
-1

-2

-3

-4

-5
SNR = 4.0   SNR = 2.0

SNR = 1.0    SNR = .5
What are typical SNRs for fMRI
data?
• Signal amplitude
– MR units: 5-10 units (baseline: ~700)
– Percent signal change: 0.5-2%
• Noise amplitude
– MR units: 10-50
– Percent signal change: 0.5-5%
• SNR range
– Total range: 0.1 to 4.0
– Typical: 0.2 – 0.5
II. Properties of Noise in fMRI

Can we assume Gaussian noise?
Types of Noise
• Thermal noise
– Responsible for variation in background
– Eddy currents, scanner heating
• Power fluctuations
– Typically caused by scanner problems
• Variation in subject cognition
– Timing of processes
• Head motion effects
• Physiological changes
• Differences across brain regions
– Functional differences
– Large vessel effects
• Artifact-induced problems
Why is noise assumed to be
Gaussian?

• Central limit theorem
– If X1 … Xn are a set of independent random
variables, each with an arbitary probability
distribution, then the sum of the set of
variables (probability density function) will be
distributed normally.
Is noise constant through time?
0.40%             Young

0.35%
Standard Deviation at Time Point (%)

Old

0.30%

0.25%

0.20%

0.15%

0.10%

0.05%

0.00%
-5 -4 -3 -2 -1 0    1   2   3   4   5    6   7     8   9 10 11 12 13
Time since stimulus onset (s)
Is fMRI noise Gaussian (over space)?

Outside Brain
Edge of Brain
Boundary of Brain
Middle of Brain
Is Signal Gaussian (over voxels)?
18%

16%                     Young
14%
Percentage of All Active Voxels

12%
Old

10%

8%

6%

4%

2%

0%
0   0.5    1                  1.5                   2   2.5
Peak Amplitude (% change over baseline)
Variability
Variability in Subject Behavior: Issues

• Cognitive processes are not static
– May take time to engage
– Often variable across trials
– Subjects’ attention/arousal wax and wane
• Subjects adopt different strategies
– Feedback- or sequence-based
– Problem-solving methods
• Subjects engage in non-task cognition
– Non-task periods do not have the absence of thinking

What can we do about these problems?
Response Time Variability

A                  B
Intersubject Variability
A       B

A & B: Responses across
subjects for 2 sessions
C & D: Responses within
single subjects across
C       D         days
E & F: Responses within
single subjects within a
session

E        F
- Aguirre et al., 1998
620
1.50%            617
595
Signal Change over Pre-stimulus Baseline (%)

1.30%            566
560
1.10%            559
555
0.90%            551
549
0.70%            520
383
0.50%

0.30%

0.10%

-0.10% -5 -4 -3 -2 -1   0    1   2   3   4   5    6   7     8   9 10 11 12 13

-0.30%
Time since stimulus onset (s)
Implications of Inter-Subject Variability
• Use of individual subject’s hemodynamic responses
– Corrects for differences in latency/shape

• Suggests iterative HDR analysis
– Initial analyses use canonical HDR
– Functional ROIs drawn, interrogated for new HDR
– Repeat until convergence

• Requires appropriate statistical measures
– Random effects analyses
– Use statistical tests across subjects as dependent measure
(rather than averaged data)
Spatial Variability?
A              B

McGonigle et al., 2000
Standard
Deviation Image
Spatial Distribution of Noise
A: Anatomical Image
B: Noise image
C: Physiological noise
D: Motion-related noise
E: Phantom (all noise)
F: Phantom (Physiological)

- Kruger & Glover (2001)
Low and High Frequency Noise
750

740

730

720

710

700
2

690                  1.5

1

680                  0.5

0

670                  -0.5

-1

660                  -1.5

-2

650
1   51   101          151   201
III. Methods for Improving
SNR
Increasing Field Strength
Theoretical Effects of Field
Strength
• SNR = signal / noise
• SNR increases linearly with field strength
– Signal increases with square of field strength
– Noise increases linearly with field strength
– A 4.0T scanner should have 2.7x SNR of 1.5T
scanner
• T1 and T2* both change with field strength
– T1 increases, reducing signal recovery
– T2* decreases, increasing BOLD contrast
Adapted from Turner, et al. (1993)
Measured Effects of Field Strength
• SNR usually increases by less than theoretical
prediction
– Sub-linear increases in SNR; large vessel effects may
be independent of field strength
• Where tested, clear advantages of higher field
have been demonstrated
– But, physiological noise may counteract gains at high
field ( > ~4.0T)
• Spatial extent increases with field strength
• Increased susceptibility artifacts
Trial Averaging
• 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
Increasing Power increases Spatial
Extent
Trials    Subject 1   Subject 2
Averaged

4
500 ms             500 ms
…      16

36
16-20 s
64

100

144
A   B
0.00   0.00   0.00   0.00   0.00   0.00   0.00   0.00   0.00   0.00   3.85

0.00   0.00   0.00   0.00   0.00   0.00   0.00   0.00   0.00   2.44   2.41

0.00   0.00   0.00   0.00   0.00   0.00   3.36   3.68   2.79   1.78   1.84

0.00   0.00   0.00   0.00   5.88   6.79   8.36   2.09 -0.50 -3.08 -0.96

0.00   0.00   3.20   5.46   2.00   6.50   6.13   5.67 -0.06 -3.41 -1.56

2.66   2.42   0.01   5.81   5.88   5.86   6.84   5.63   3.71 -1.76 -2.25

3.74   3.42   1.43   0.68   2.13   6.47   8.05   8.96 10.27 2.45      0.29

4.60   2.27   0.77   1.41   0.80   1.71   9.65   9.91 12.19 3.17      1.75

0.94   1.38   1.22   2.96   0.30 -1.58 2.19      4.10   5.84   3.06   0.53

-0.46 -1.11 -0.31 1.27 -0.94 -4.97 -3.26 -1.93 -1.07 0.28 -1.21

-4.05 -2.33 -2.67 -2.17 -1.64 -7.44 -7.22 -4.83 -3.93 0.00            0.55
Effects of Signal-Noise Ratio on extent of
activation: Empirical Data
100
Subject 1
90
Number of Significant Voxels

80

70
Subject 2
60

50

40
VN = Vmax[1 - e(-0.016 * N)]
30
Subject1                       Subject 2
Peak latency of
4 sec    5 sec         6 sec   4 sec    5 sec      6 sec
20                   reference HDR

Vmax             89       96            72      25        80        98
10                  Correlation of data
0.997    0.995         0.993   0.960    0.994      0.998
with prediction

0
0    25   50         75              100              125           150         175             200
Number of Trials Averaged
Active Voxel Simulation
Signal + Noise (SNR = 1.0)
2
1.5
1
0.5
0                                                         2

1

3

5

7

9

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17

19
-0.5                                                       1.5
-1                                                        1
-1.5                                                       0.5
-2                                                        0

1

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-0.5
2
-1
1.5
-1.5
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-0.5
-1
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1000 Voxels, 100 Active                                                       • Signal waveform taken from
Noise                                    observed data.
2
1.5                                                 • Signal amplitude distribution:
1
0.5                                                 Gamma (observed).
0
1

3

5

7

9

11

13

15

17

19

• Assumed Gaussian white noise.
-0.5
-1
-1.5
-2
Effects of Signal-Noise Ratio on extent of
activation:
Simulation Data
Number of Activated Voxels   120

SNR = 1.00
100

80                    SNR = 0.52
(Young)

60                                 SNR = 0.35
(Old)

40                                              SNR = 0.25

SNR = 0.15
20
SNR = 0.10
0
0                50                100                  150                  200
Number of Trials Averaged

Old (66 trials)           Young (70 trials)            Ratio (Y/O)
Observed            26                        53                         2.0
Predicted          57%                       97%                         1.7
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)
• Nevertheless, averaging provides robust,
reliable method for determining brain activity
II. Preprocessing of
FMRI Data
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
Tools for Preprocessing
•   SPM
•   Brain Voyager
•   VoxBo
•   AFNI
•   Custom BIAC scripts
Slice Timing Correction
Motion Correction
… and catastrophically 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
Severe Head Motion: Simulation

Two 4s movements of
8mm in -Y direction         Motion
Severe Head Motion: Real Data

Two 4s movements of
8mm in -Y direction         Motion
• Rigid body transformation
– 6 parameters: 3 translation, 3 rotation
• Minimization of some cost function
– E.g., sum of squared differences
– Mutual information
Effects of Head Motion Correction
Limitations of Motion Correction
• Artifact-related limitations
– Loss of data at edges of imaging volume
– Ghosts in image do not change in same manner as
real data

• Distortions in fMRI images
– Distortions may be dependent on position in field, not

• Intrinsic problems with correction of both slice
timing and head motion
What is the best approach for minimizing the
influence of head motion on your data?
Coregistration
Should you Coregister?
–   Aids in normalization
–   Allows display of activation on anatomical images
–   Allows comparison across modalities
–   Necessary if no coplanar anatomical images

– May severely distort functional data
– May reduce correspondence between functional and
anatomical images
Normalization
Standardized Spaces
• Talairach space (proportional grid system)
–   From atlas of Talairach and Tournoux (1988)
–   Based on single subject (60y, Female, Cadaver)
–   Single hemisphere
–   Related to Brodmann coordinates

• Montreal Neurological Institute (MNI) space
– Combination of many MRI scans on normal controls
• All right-handed subjects
– Approximated to Talaraich space
• Slightly larger
• Taller from AC to top by 5mm; deeper from AC to bottom by 10mm
– Used by SPM, fMRI Data Center, International Consortium for
Brain Mapping
Normalization to Template
Normalization Template   Normalized Data
Anterior and Posterior Commissures

Posterior
Anterior     Commissure
Commissure
Should you normalize?
–   Allows generalization of results to larger population
–   Improves comparison with other studies
–   Provides coordinate space for reporting results
–   Enables averaging across subjects
– Reduces spatial resolution
– May reduce activation strength by subject averaging
– Time consuming, potentially problematic
• Doing bad normalization is much worse than not normalizing
(and using another approach)
Slice-Based Normalization
Before Adjustment (15 Subjects)

After Adjustment to Reference Image

Registration courtesy Dr. Martin McKeown (BIAC)
Spatial Smoothing
Techniques for Smoothing
• Application of
Gaussian kernel
– Usually expressed in
#mm FWHM
– “Full Width – Half
Maximum”
– Typically ~2 times
voxel size
Effects of Smoothing on Activity
Unsmoothed Data

Smoothed Data (kernel width 5 voxels)
Should you spatially smooth?
– Increases Signal to Noise Ratio (SNR)
• Matched Filter Theorem: Maximum increase in SNR by filter with
same shape/size as signal
– Reduces number of comparisons
• Allows application of Gaussian Field Theory
– May improve comparisons across subjects
• Signal may be spread widely across cortex, due to intersubject
variability

– Reduces spatial resolution
– Challenging to smooth accurately if size/shape of signal is not
known
Temporal Filtering
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
Power Spectra
Segmentation
• Classifies voxels within an image into different
anatomical divisions
– Gray Matter
– White Matter
– Cerebro-spinal Fluid (CSF)

Image courtesy J. Bizzell & A. Belger
Histogram of Voxel Intensities
0.04

0.035

Anatomical
0.03
Functional
0.025

0.02

0.015

0.01

0.005

0
Bias Field Correction
Region-of-Interest (ROI) drawing
• Allows direct, unbiased measurement of activity
in an anatomical region
– Assumes functional divisions tend to follow
anatomical divisions
• Improves ability to identify topographic changes
– Motor mapping (central sulcus)
– Social perception mapping (superior temporal sulcus)
• Complements voxel-based analyses
Resources
• Drawing Tools
– BIAC software (e.g., Overlay2)
– Analyze
– IRIS/SNAP (G. Gerig from UNC)
• Reference Works
– Print atlases
– Online atlases
• Analysis Tools
– roi_analysis_script.m
ROI Examples
-2
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Left Hemisphere - Gaze Shifts

0
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in elicited when a subject watches a character shift gaze toward or away from a target.

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Distance Posterior from the Anterior Commissure (in mm)
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BIAC is studying biological motion and social perception – here by determining how context modulates brain activity

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Right Hemisphere - Gaze Shifts

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• SPM website
– http://www.fil.ion.ucl.ac.uk/spm/course/notes01.html
– SPM Manual
• Brain viewers
– http://www.bic.mni.mcgill.ca/cgi/icbm_view/
Signal-Noise-Ratio (SNR)

Variability

Variability
A
t = 16

B             C
t=8                t=5
BOLD may reflect predominantly
excitatory activity

TMS results had indicated
that M1 is inhibited in no-go
condition.

M1                             SMA      M1                SMA

Solid = go ; dashed = no-go        Waldvogel, et al., 2000
1% change         2% change

Parrish et al., 2000

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