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

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

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

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

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 50 - 45 C (50-45)/45 D FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

Voxel 1 790 830 870 Voxel 2 690 730 770 Voxel 3 770 810 850 FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Standard Deviation Image FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

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

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

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

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

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

Intersubject Variability D 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

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

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

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

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

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

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

Adapted from Turner, et al. (1993) fmri-fig-09-12-0.jpg Adapted from Turner, et al. (1993) FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

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

fmri-fig-09-13-0.jpg FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

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

fmri-fig-09-14-0.jpg FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

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

1.5T 4.0T fmri-fig-09-15-0.jpg FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

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

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

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

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

Effects of Signal-Noise Ratio on extent of activation: Empirical Data Subject 1 Subject 2 Number of Significant Voxels (Vn) VN = Vmax[1 - e(-0.016 * N)] Number of Trials Averaged (N) FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

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

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

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

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

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

fmri-fig-10-01-0.jpg FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

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

fmri-fig-10-03-0.jpg FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

B. Slice Timing Correction fmri-fig-10-04-0.jpg FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Comparing Talairach and MNI Images from Cambridge Brain Imaging Unit http://imaging.mrc-cbu.cam.ac.uk/imaging/MniTalairach FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

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

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

fmri-fig-10-15-0.jpg FMRI – Week 7 – SNR & Preprocessing Scott Huettel, Duke University

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

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

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

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

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

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

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

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