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

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

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

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

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

SNR = 1.0

SNR = 0.5

SNR = 0.25

SNR = 0.125

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

Is noise constant through time?

Is fMRI noise Gaussian (over time)?

Is Signal Gaussian (over voxels)?

What does this mean for fMRI experiments?

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

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

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

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

Effects of Signal-Noise Ratio on extent of activation: Empirical Data Subject 1 Subject 2 Number of Significant Voxels VN = Vmax[1 - e(-0.016 * N)] Number of Trials Averaged

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

Effects of Signal-Noise Ratio on extent of activation: Simulation Data SNR = 1.00 SNR = 0.52 (Young) Number of Activated Voxels SNR = 0.35 (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

Subject Averaging

Variability Across Subjects D’Esposito et al., 1999

Young Adults

Elderly Adults

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)

Effects of Suboptimal Sampling

Visual HDR sampled with a 1-sec TR

Visual HDR sampled with a 2-sec TR

Visual HDR sampled with a 3-sec TR

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

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

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

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

Activation Profiles Gray / White Ventricle Gray / White White Matter

Sources of Noise

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

Excitation vs. Inhibition M1 SMA M1 SMA Waldvogel, et al., 2000

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

Standard Deviation Image

Low Frequency Noise

High Frequency Noise

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

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?

Physiology Head Motion Respiration Motion Shadowing Heart Rate

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

Head Motion Effects

Head Motion: Good and Bad

Image Artifacts

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