fmri – week 7 – snr & preprocessing scott huettel, duke university signal-to-noise ratio...

FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

Signal-to-Noise Ratio & Preprocessing

FMRI Undergraduate Course (PSY 181F) FMRI Graduate Course (NBIO 381, PSY

362)

Dr. Scott Huettel, Course Director


What is signal? What is noise?

• Signal, literally: Amount of current in receiver coil• Signal, practically: Task-related variability

• Noise, literally and practically: Non-task-related variability

• How can we control the amount of signal?– Scanner properties (e.g., field strength)– Experimental task timing: efficient design– Subject compliance with task: through training

• How can we reduce the noise? – Choose good pulse sequences and have stable scanner – Minimize head motion, to some degree, with restrictors– Effectively preprocess our data


I. Introduction to SNR (Signal to Noise Ratio)


Signal, Noise, and the General Linear Model

MYMeasured Data

Amplitude (solve for)

Design Model

Noise

Cf. Boynton et al., 1996


Signal Size in fMRI

45A 50B

50 - 45C

E(50-45)/45D

Let’s look at two TRs (#s 45 and

50) of one dataset.


Voxel 3

Voxel 2

Voxel 1

690 730 770

790 830 870

770 810 850


Signal-Noise-Ratio (SNR)

Task-Related Variability

Non-task-related Variability


Differences in SNR


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

-1

-0.5

0

0.5

1

1.5

2

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


SNR = 1.0

-1

-0.5

0

0.5

1

1.5

2

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


SNR = 0.5

-1

-0.5

0

0.5

1

1.5

2

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


SNR = 0.25

-3

-2

-1

0

1

2

3

4

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


SNR = 0.125

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

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


SNR = 4.0 SNR = 2.0

SNR = 1.0 SNR = .5


What are typical SNRs for fMRI data?

• Signal amplitude– Percent signal change: 0.2-2%

• Noise amplitude– 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


Types of Noise• Thermal noise

– Responsible for variation in background of image– Eddy currents, scanner heating

• Power fluctuations– Typically caused by scanner problems

• Artifact-induced problems

• Variation in subject cognition– Timing of processes

• Head motion• Physiological fluctuations

– Respiration– Cardiac pulsation

• Differences across brain regions– Functional differences– Large vessel effects


Why is noise assumed to be Gaussian?

• Central limit theorem– If X1 … Xn are a set of independent random

variables, each with an arbitrary probability distribution, then the sum of the set of variables (probability density function) will be distributed normally.

Note: Gaussian refers to the normal, bell-curve distribution.


Task-related noise?


Standard Deviation

Image


Spatial Distribution of Noise

A: Anatomical ImageB: Noise imageC: Physiological noiseD: Motion-related noiseE: Phantom (all noise)F: Phantom

(Physiological)

- Kruger & Glover (2001)


650

660

670

680

690

700

710

720

730

740

750

1 51 101 151 201

Low and High Frequency Noise

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2


Noise vs. 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


Intersubject Variability

A & B: Responses across subjects for 2 sessions

C & D: Responses within single subjects across days

E & F: Responses within single subjects within a session

- Aguirre et al., 1998

BA

C D

E F

Note: These data were collected using a periodic

design that allowed timing of stimulus presentation.

This served to exacerbate differences in HDR onset

(e.g., some, but not all, subjects timed!).


Consistency in the HDR


Potential Corrections for Inter-Subject Variability

• Use of individual subject’s hemodynamic responses– Corrects for differences in latency/shape

• HDR-free analysis methods– Finite-impulse response (FIR) techniques– Use of basis functions to look for task-evoked changes– Other measures (e.g., area under the curve)

• Corrections across subjects– Random-effects analyses – Use statistical tests across subjects as dependent

measure (rather than averaged data)


Spatial Variability?Visual Paradigm

McGonigle et al., 2000

Cognitive Paradigm

“The following precautions were taken: the same operators always controlled the scanner, ambient light and sound levels were similar

between sessions, and spoken instructions to the subject were always exactly the same.

One obvious factor that we could not control was that our subject was always aware that he had performed the task before in the scanner, only

under slightly different circumstances. We called this the “Groundhog Day” effect.”


“A reanalysis…”

Smith et al., 2005 Reducing the threshold gives much less apparent

variability.


III. Methods for Improving SNR


Increasing 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 incr. field strength– T1 increases, reducing signal recovery (bad)– T2* decreases, increasing BOLD contrast (good)


Adapted from Turner, et al. (1993)


Measured Effects of Field Strength

• SNR 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 ??, > ~7.0T ??)






field ( > ~4.0T ??, > ~7.0T ??)

• High-field scanning may provide better data from capillaries and small veins






field ( > ~4.0T ??, > ~7.0T ??)

• High-field scanning may provide better data from capillaries and small veins

• Increased susceptibility artifacts – Some regions (e.g., ventral frontal lobe) may be more

distorted at high field


1.5T

4.0T


Collect more data?

• Static signal, variable noise– Assumes that the MR data recorded (on each trial) are

composed of a signal + (random) noise

• Effects of trial averaging (simplest case)– 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

Subject 1 Subject 2Trials Averaged

4

16

36

64

100

144

500 ms

16-20 s

500 ms

…


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

A B


0

10

20

30

40

50

60

70

80

90

100

0 25 50 75 100 125 150 175 200

Number of Trials Averaged (N)

Nu

mb

er

of

Sig

nifi

can

t V

oxels

(V

n)

Subject 1

Subject 2

VN = Vmax[1 - e(-0.016 * N)]

Effects of Signal-Noise Ratio on extent of activation: Empirical Data


Active Voxel Simulation

Signal + Noise (SNR = 1.0)

Noise1000 Voxels, 100 Active

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

1 3 5 7 9

11

13

15

17

19

-2

-1.5

-1

-0.5

0

0.5

1

1.5

21 3 5 7 9

11

13

15

17

19

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

1 3 5 7 9

11

13

15

17

19

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

1 3 5 7 9

11

13

15

17

19

• Signal waveform taken from observed data.

• Signal amplitude distribution: Gamma (observed).

• Assumed Gaussian white noise.


Effects of Signal-Noise Ratio on extent of activation:

Simulation Data

0

20

40

60

80

100

120

0 50 100 150 200

SNR = 0.10

SNR = 0.15

SNR = 0.25

SNR = 1.00

SNR = 0.52 (Young)

SNR = 0.35 (Old)

Number of Trials Averaged

Nu

mb

er

of

Act

ivate

d V

oxels

Old (66 trials) Young (70 trials) Ratio (Y/O)Observed 26 53 2.0Predicted 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 pure averaging ignores potentially valuable information– Amount of noise varies over time– Some noise is temporally correlated (physiology)

• Same principle holds for more complex analyses: increasing the quantity of data improves SNR


IV. 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


A. Quality Assurance


B. Slice Timing Correction


C. Motion Correction: Good, Bad,…


… and catastrophically bad


Why does head motion introduce problems?

507 89 154

119 171 83

179 117 53

663 507 89

520 119 171

137 179 117

A B C


Simulated Head Motion

Motion


Severe Head Motion: Real Data

Two 4s movements of 8mm in -Y direction (during task epochs)

Motion


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


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 position in head

• Intrinsic problems with correction of both slice timing and head motion


What are the best approaches for minimizing the influence of head

motion?


Prevention…


… and training!


D. Co-Registration and Normalization

Matching two images of the same subject’s brain

collected using different pulse sequences.

Matching an image from a single subject, typically a

high-resolution anatomical, to a template in a standardized

space.


Standardized Spaces

• Talairach space (proportional grid system)– From atlas of Talairach and Tournoux (1988)– Based on single subject (60y, Female, Cadaver)– Single hemisphere– First commonly used system

• Montreal Neurological Institute (MNI) space– Combination of many MRI scans on normal controls

• All right-handed subjects– Approximated to Talairach space

• Slightly larger• Taller from AC by 5mm; deeper from AC by 10mm

– Used by FSL, SPM, fMRI Data Center, International Consortium for Brain Mapping, many others


Comparing Talairach and MNI

Images from Cambridge Brain Imaging Unit

http://imaging.mrc-cbu.cam.ac.uk/imaging/MniTalairach


Normalization to TemplateNormalization Template Normalized Data

SPM

FSL


Anterior and Posterior Commissures

Anterior Commissure

Posterior Commissure


When wouldn’t you normalize?

• Advantages– Allows generalization of results to larger

population– Improves comparison with other studies– Provides coordinate space for reporting results– Enables averaging across subjects

• Other options?– Anatomical region-of-interest approach– Functional mapping within subjects


E. Spatial 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 ~12mm)


Before smoothing

(hypothetical data)

After smoothing (hypothetical

data)


Should you spatially smooth?

• Advantages– 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

• Disadvantages– Reduces spatial resolution – Challenging to smooth accurately if size/shape of signal

is not known


F. Temporal Filtering

• 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: Frequencies to Eliminate


Summary

• There is sometimes signal in your data.– Try to maximize it!

• There is always noise in your data.– Try to prevent it! …via design,

precautions– Try to minimize it! …via preprocessing

fmri – week 7 – snr & preprocessing scott huettel, duke university signal-to-noise ratio...

Documents

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snreffects of snr

properties of noise

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signal size

snr rangetotal range

taskrelated variabilitynoise