Signal and Noise in fMRI fMRI Graduate Course October 15, 2003
Jan 21, 2016
Signal and Noise in fMRI
fMRI Graduate Course
October 15, 2003
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?– Electrical variability in scanner– Physiologic variation (e.g., heart rate)– Some head motion– Differences across subjects
I. Introduction to SNR
Signal, noise, and the General Linear Model
MYMeasured Data
Amplitude (solve for)
Design Model
Noise
Cf. Boynton et al., 1996
Signal-Noise-Ratio (SNR)
Task-Related Variability
Non-task-related Variability
Signal Size in fMRI
45 50
50 - 45
A B
C
E
(50-45)/45D
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1 51 101 151 201 251
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1 51 101 151 201 251
Differences in SNR
Voxel 3
Voxel 2
Voxel 1
690 730 770
790 830 870
770 810 850
t = 16
t = 8 t = 5
A
B C
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– 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
Effects of Field Strength on SNR
Turner et al., 1993
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
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
Excitation vs. Inhibition
M1 SMA M1 SMA
Waldvogel, et al., 2000
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
Is noise constant through time?
Is fMRI noise Gaussian (over time)?
Outside Brain
Edge of Brain
Boundary of Brain
Middle of Brain
Is Signal Gaussian (over voxels)?
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: 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
Variability Across Subjects
D’Esposito et al., 1999
Young Adults
Elderly Adults
-5 -3 -1 1 3 5 7 9 11
-5 -3 -1 1 3 5 7 9 11
Effects of Intersubject Variability
Parrish et al., 2000
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)
960
970
980
990
1000
1010
1020
1030
1040
1050
1 51 101 151 201 251
Low Frequency Noise
650
660
670
680
690
700
710
720
730
740
750
1 51 101 151 201
High Frequency Noise
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
III. Methods for Improving SNR
Fundamental Rule of SNR
For Gaussian noise, experimental power increases with the square root of the
number of observations
SD
SD/2
SD/4
SD/8
SD/16
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
through averaging– Noise randomly varies across trials, so it decreases
with averaging– Thus, SNR increases with averaging
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Example of Trial Averaging-1.5
-1
-0.5
0
0.5
1
1.5
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
-1
-0.5
0
0.5
1
1.5
2
2.5
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
-1.5
-1
-0.5
0
0.5
1
1.5
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
-1.5
-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
Average of 16 trials with SNR = 0.6
1
2
3
4
5
6
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
Peak latency of reference HDR
4 sec 5 sec 6 sec 4 sec 5 sec 6 sec
Vmax 89 96 72 25 80 98
Correlation of data with prediction
0.997 0.995 0.993 0.960 0.994 0.998
Subject1 Subject 2
Number of Trials Averaged
Num
ber
of S
igni
fica
nt V
oxel
s 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
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
-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
Num
ber
of A
ctiv
ated
Vox
els
Old (66 trials) Young (70 trials) Ratio (Y/O)Observed 26 53 2.0Predicted 57% 97% 1.7
Explicit and Implicit Signal Averaging
r =.42; t(129) = 5.3; p < .0001
r =.82; t(10) = 4.3; p < .001
A
B
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
Accurate Temporal Sampling
Visual HDR sampled with a 1-sec TR
0.13%
0.01%-0.02%
-0.08%
-0.04%
-0.18%
-0.12%
-0.18%
0.29%
0.53%
0.71%
0.60%
0.44%
0.34%
0.24%
0.16%
0.02%
-0.04%-0.07%
-0.20%
-0.10%
0.00%
0.10%
0.20%
0.30%
0.40%
0.50%
0.60%
0.70%
0.80%
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
Visual HDR sampled with a 2-sec TR
0.01%
-0.08%
-0.18% -0.18%
0.53%
0.60%
0.34%
0.16%
-0.04%
-0.20%
-0.10%
0.00%
0.10%
0.20%
0.30%
0.40%
0.50%
0.60%
0.70%
0.80%
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
Visual HDR sampled with a 3-sec TR
0.13%
-0.08%
-0.12%
0.53%
0.44%
0.16%
-0.07%
-0.20%
-0.10%
0.00%
0.10%
0.20%
0.30%
0.40%
0.50%
0.60%
0.70%
0.80%
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
Comparison of Visual HDR sampled with 1,2, and 3-sec TR
-0.20%
-0.10%
0.00%
0.10%
0.20%
0.30%
0.40%
0.50%
0.60%
0.70%
0.80%
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
Visual HDRs with 10% diff sampled with a 1-sec TR
-0.20%
-0.10%
0.00%
0.10%
0.20%
0.30%
0.40%
0.50%
0.60%
0.70%
0.80%
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
Visual HDR with 10% diff sampled with a 3-sec TR
-0.20%
-0.10%
0.00%
0.10%
0.20%
0.30%
0.40%
0.50%
0.60%
0.70%
0.80%
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
Accurate Spatial Sampling
Partial Volume Effects
Partial Volume Effects
Partial Volume Effects
Partial Volume Effects
Partial Volume Effects
Where are partial volume effects most problematic?
• Ventricles
• Grey / white boundary
• Blood vessels
55
60
65
70
75
0
20
40
60
60
65
70
75
80
50
55
60
65
70
40
45
50
55
60 Activation Profiles
White Matter
Gray / White
Gray / WhiteVentricle
Ventricle
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
A B