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 Measured 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 AB C E (50-45)/45 D

Differences in SNR

Voxel 3 Voxel 2 Voxel

t = 16 t = 8 t = 5 A BC

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

SNR = 4.0SNR = 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: –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 T 1 and T 2 * both change with field strength –T 1 increases, reducing signal recovery –T 2 * 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 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)?

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 AB

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 B A C D E F

Variability Across Subjects D’Esposito et al., 1999

Young Adults

Elderly Adults

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? AB 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)

Low Frequency Noise

High Frequency Noise

III. Methods for Improving SNR

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

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

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

Increasing Power increases Spatial Extent Subject 1Subject 2 Trials Averaged ms s 500 ms …

AB

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

Active Voxel Simulation Signal + Noise (SNR = 1.0) Noise 1000 Voxels, 100 Active 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 SNR = 0.10 SNR = 0.15 SNR = 0.25 SNR = 1.00 SNR = 0.52 (Young) SNR = 0.35 (Old) Number of Trials Averaged Number of Activated Voxels

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

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

Accurate Spatial Sampling

Partial Volume Effects

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

Activation Profiles White Matter Gray / White 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 AB