1. Signal and Noise in fMRI
fMRI Graduate Course
October 16, 2002

2. What is signal? What is noise?
Signal, literally defined
Amount of current in receiver coil
What can we control?
Scanner properties (e.g., field strength)
Experimental task timing
Subject compliance (through training)
Head motion (to some degree)
What can’t we control?
Scanner-related noise
Physiologic variation (e.g., heart rate)
Some head motion
Differences across subjects

3. Signal, noise, and the General Linear Model
Amplitude (solve for)
Measured Data
Noise
Design Model
Cf. Boynton et al., 1996

4. Signal-Noise-Ratio (SNR)
Task-Related Variability
Non-task-related Variability

7. 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

8. SNR = 2.0

9. SNR = 1.0

10. SNR = 0.5

11. SNR = 0.25

12. SNR = 0.125

13. 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

14. Is noise constant through time?

16. Is fMRI noise Gaussian (over time)?

17. Is Signal Gaussian (over voxels)?

18. What does this mean for fMRI experiments?

19. Trial Averaging Static signal, variable noise Effects of averaging
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 through averaging
Noise randomly varies across trials, so it decreases with averaging
Thus, SNR increases with averaging

21. Example of Trial Averaging
Average of 16 trials with SNR = 0.6

23. Fundamental Rule of SNR
For Gaussian noise, experimental power increases with the square root of the number of observations

24. Increasing Power increases Spatial Extent
Subject 1
Subject 2
Trials Averaged 4
500 ms
500 ms … 16 36
16-20 s 64
100
144

25. Effects of Signal-Noise Ratio on extent of activation: Empirical Data
Subject 1
Subject 2
Number of Significant Voxels
VN = Vmax[1 - e( * N)]
Number of Trials Averaged

26. 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

27. 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

28. Subject Averaging

29. Variability Across Subjects
D’Esposito et al., 1999

30. Young Adults

31. Elderly Adults

34. 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)

35. Effects of Suboptimal Sampling

36. Visual HDR sampled with a 1-sec TR

37. Visual HDR sampled with a 2-sec TR

38. Visual HDR sampled with a 3-sec TR

39. Comparison of Visual HDR sampled with 1,2, and 3-sec TR

40. Visual HDRs with 10% diff sampled with a 1-sec TR

41. Visual HDR with 10% diff sampled with a 3-sec TR

42. Partial Volume Effects

43. Partial Volume Effects

44. Partial Volume Effects

45. Partial Volume Effects

46. Partial Volume Effects

47. Where are partial volume effects most problematic?
Ventricles
Grey / white boundary
Blood vessels

48. Activation Profiles Gray / White Ventricle Gray / White White Matter

49. Sources of Noise

50. What causes variation in MR signal?
Field strength
Excitation vs. Inhibition
Large vessel effects
Differences across the brain
Timing of cognitive processes

51. Excitation vs. Inhibition
M SMA
M SMA
Waldvogel, et al., 2000

52. Types of Noise Thermal noise Power fluctuations
Responsible for variation in background
Eddy currents, scanner heating
Power fluctuations
Typically caused by scanner problems
Variation in subject cognition
Head motion effects
Physiological changes
Artifact-induced problems

53. Standard Deviation Image

54. Low Frequency Noise

55. High Frequency Noise

56. 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

57. 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?

58. Physiology
Head Motion
Respiration
Motion
Shadowing
Heart Rate

59. Motion Effects Motion within an image acquisition
Results in blurring
Especially noticeable in 3D high-res images
Motion across acquisitions
More of a problem for fMRI
Significant if ½ voxel or greater (>2mm)
Increases with subject fatigue
Potential confound for subject studies
Minimized through use of restraints
Padding, vacuum pack (BIAC)
Head masks, bite bars/mouthpieces, etc. (other centers)
Tape indicators
Usually corrected in preprocessing

60. Head Motion Effects

61. Head Motion: Good and Bad

62. Image Artifacts

65. 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