1. Signal-to-Noise Ratio & Preprocessing
FMRI Undergraduate Course (PSY 181F)
FMRI Graduate Course (NBIO 381, PSY 362)
Dr. Scott Huettel, Course Director
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

2. 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
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

3. I. Introduction to SNR (Signal to Noise Ratio)
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

4. Signal, Noise, and the General Linear Model
Amplitude (solve for)
Measured Data
Noise
Design Model
Cf. Boynton et al., 1996
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

5. Let’s look at two TRs (#s 45 and 50) of one dataset.
Signal Size in fMRI A 45 50 B
Let’s look at two TRs (#s 45 and 50) of one dataset. E C
(50-45)/45 D
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

6. Voxel 1
Voxel 2
Voxel 3
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

7. Signal-Noise-Ratio (SNR)
Task-Related Variability
Non-task-related Variability
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

8. Differences in SNR
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

9. 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
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

10. SNR = 2.0
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

11. SNR = 1.0
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

12. SNR = 0.5
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

13. SNR = 0.25
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

14. SNR = 0.125
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

15. SNR = 4.0
SNR = 2.0
SNR = 1.0
SNR = .5
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

16. 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 ??
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

17. II. Properties of Noise in fMRI
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

18. Types of Noise Thermal noise Power fluctuations
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
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

19. 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.
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

20. Task-related noise?
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

21. Standard Deviation Image
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22. 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)
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

23. Low and High Frequency Noise
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

24. Noise vs. Variability
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

25. 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?
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

26. Response Time Variability
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

27. Intersubject VariabilityD E F
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
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!).
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

28. Consistency in the HDR
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

29. 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)
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

30. Spatial Variability? Visual Paradigm 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.”
McGonigle et al., 2000
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

31. Reducing the threshold gives much less apparent variability.
“A reanalysis…”
Reducing the threshold gives much less apparent variability.
Smith et al., 2005
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

32. III. Methods for Improving SNR
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

33. 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)
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

34. Adapted from Turner, et al. (1993)
fmri-fig jpg
Adapted from Turner, et al. (1993)
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

35. 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 ??)
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

36. fmri-fig jpg
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

37. 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 ??)
High-field scanning may provide better data from capillaries and small veins
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

38. fmri-fig jpg
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

39. 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 ??)
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
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

40. 1.5T
4.0T
fmri-fig jpg
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

41. 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
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

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

43. Increasing Power increases Spatial Extent
Subject 1
Subject 2
Trials Averaged 4
500 ms
500 ms … 16 36
16-20 s 64
100
144
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

44. A B
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

45. Effects of Signal-Noise Ratio on extent of activation: Empirical Data
Subject 1
Subject 2
Number of Significant Voxels (Vn)
VN = Vmax[1 - e( * N)]
Number of Trials Averaged (N)
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

46. Active Voxel Simulation
Signal + Noise (SNR = 1.0)
1000 Voxels, 100 Active
Signal waveform taken from observed data.
Signal amplitude distribution: Gamma (observed).
Assumed Gaussian white noise.
Noise
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

47. Effects of Signal-Noise Ratio on extent of activation: Simulation Data
SNR = 1.00
SNR = (Young)
Number of Activated Voxels
SNR = (Old)
SNR = 0.25
SNR = 0.15
SNR = 0.10
We conducted a simulation that tested the effects of signal to noise and number of trials averaged upon the spatial extent of activation. We created a virtual brain with 100 active voxels, with voxel amplitude drawn from a distribution modeled on our empirical data.
What we found is that, for the number of trials conducted in our study (66 for the elderly and 70 for the young, indicated by arrows), the simulation predicts that we have sufficient power to identify nearly all of the active voxels in the young subjects, but only about 57% of the active voxels in the elderly subjects.
That is, the 2 to 1 difference in spatial extent of activation that we measured between our groups appears to be nearly completely a function of the group difference in noise levels.
Although we show this for age groups, this effect will occur for any group comparison (such as with patient populations or drug studies) where the groups differ in voxelwise noise levels. Furthermore, consider what would be predicted had we run only 30 trials for each group. At those numbers, our results predict that we would have observed about a 4 to 1 difference in extent of activation. So differences in spatial extent of activation will vary according to the number of trials conducted.
Number of Trials Averaged
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

48. 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
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

49. IV. Preprocessing of FMRI Data
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

50. 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
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

51. fmri-fig jpg
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

52. A. Quality Assurance fmri-fig-10-02-0.jpg
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

53. fmri-fig jpg
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

54. B. Slice Timing Correction
fmri-fig jpg
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

55. C. Motion Correction: Good, Bad,…
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

56. … and catastrophically bad
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

57. Why does head motion introduce problems?
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

58. Simulated Head Motion Motion
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

59. Severe Head Motion: Real Data
Two 4s movements of 8mm in -Y direction (during task epochs)
Motion
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

60. 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
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

61. Effects of Head Motion Correction
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

62. 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
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

63. What are the best approaches for minimizing the influence of head motion?
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

64. Prevention… fmri-fig-10-07-0.jpg
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

65. … and training! fmri-fig-10-08-0.jpg
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

66. 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.
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

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

68. 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
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

69. Comparing Talairach and MNI
Images from Cambridge Brain Imaging Unit
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

70. Normalization to Template
Normalization Template
Normalized Data
SPM
FSL
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

71. Anterior and Posterior Commissures
Anterior Commissure
Posterior Commissure
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

72. fmri-fig jpg
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

73. 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
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

74. E. Spatial Smoothing Application of Gaussian kernel
Usually expressed in #mm FWHM
“Full Width – Half Maximum”
Typically ~2 times voxel size
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

75. Effects of Smoothing on Activity
Unsmoothed Data
Smoothed Data (kernel width ~12mm)
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

76. Before smoothing (hypothetical data)
After smoothing (hypothetical data)
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

77. 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
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

78. 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
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

79. Power Spectra: Frequencies to Eliminate
FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

80. 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