I.Signal and Noise II. Preprocessing BIAC Graduate fMRI Course October 19, 2005

1. Signal and Noise in fMRI

What is signal? What is noise? Signal, literally defined –Amount of current in receiver coil How can we control the amount of received signal? –Scanner properties (e.g., field strength) –Experimental task timing –Subject compliance (through training) –Head motion (to some degree) What can’t we control? –NOISE

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 Size in fMRI AB C E (50-45)/45 D

Differences in SNR

Voxel 3 Voxel 2 Voxel

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

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 –If X 1 … X n are a set of independent random variables, each with an arbitary probability distribution, then the sum of the set of variables (probability density function) will be distributed normally.

Is noise constant through time?

Is fMRI noise Gaussian (over space)?

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 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!).

Young 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)

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 and High Frequency Noise

III. Methods for Improving SNR

Increasing Field Strength

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

Adapted from Turner, et al. (1993)

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

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 when averaged –Noise randomly varies across trials, so it decreases with averaging –Thus, SNR increases with averaging

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

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

II. Preprocessing of FMRI Data

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

Quality Assurance

Tools for Preprocessing SPM Brain Voyager VoxBo AFNI Custom BIAC scripts

Slice Timing Correction

Motion Correction

Head Motion: Good, Bad,…

… and catastrophically bad

Why does head motion introduce problems? ABC

Simulated Head Motion

Severe Head Motion: Simulation Two 4s movements of 8mm in -Y direction (during task epochs) Motion

Severe Head Motion: Real Data Two 4s movements of 8mm in -Y direction (during task epochs) Motion

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

Effects of Head Motion Correction

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

What is the best approach for minimizing the influence of head motion on your data?

Coregistration

Should you Coregister? Advantages –Aids in normalization –Allows display of activation on anatomical images –Allows comparison across modalities –Necessary if no coplanar anatomical images Disadvantages –May severely distort functional data –May reduce correspondence between functional and anatomical images

Normalization

Standardized Spaces Talairach space (proportional grid system) –From atlas of Talairach and Tournoux (1988) –Based on single subject (60y, Female, Cadaver) –Single hemisphere –Related to Brodmann coordinates Montreal Neurological Institute (MNI) space –Combination of many MRI scans on normal controls All right-handed subjects –Approximated to Talaraich space Slightly larger Taller from AC to top by 5mm; deeper from AC to bottom by 10mm –Used by SPM, fMRI Data Center, International Consortium for Brain Mapping

Normalization to Template Normalization TemplateNormalized Data

Anterior and Posterior Commissures Anterior Commissure Posterior Commissure

Should 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 Disadvantages –Reduces spatial resolution –May reduce activation strength by subject averaging –Time consuming, potentially problematic Doing bad normalization is much worse than not normalizing (and using another approach)

Slice-Based Normalization Before Adjustment (15 Subjects) After Adjustment to Reference Image Registration courtesy Dr. Martin McKeown (BIAC)

Spatial Smoothing

Techniques for Smoothing Application of Gaussian kernel –Usually expressed in #mm FWHM –“Full Width – Half Maximum” –Typically ~2 times voxel size

Effects of Smoothing on Activity Unsmoothed Data Smoothed Data (kernel width 5 voxels)

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

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

Segmentation Classifies voxels within an image into different anatomical divisions –Gray Matter –White Matter –Cerebro-spinal Fluid (CSF) Image courtesy J. Bizzell & A. Belger

Histogram of Voxel Intensities

Bias Field Correction

Region-of-Interest (ROI) drawing Allows direct, unbiased measurement of activity in an anatomical region –Assumes functional divisions tend to follow anatomical divisions Improves ability to identify topographic changes –Motor mapping (central sulcus) –Social perception mapping (superior temporal sulcus) Complements voxel-based analyses

Resources Drawing Tools –BIAC software (e.g., Overlay2) –Analyze –IRIS/SNAP (G. Gerig from UNC) Reference Works –Print atlases –Online atlases Analysis Tools –roi_analysis_script.m

ROI Examples

BIAC is studying biological motion and social perception – here by determining how context modulates brain activity in elicited when a subject watches a character shift gaze toward or away from a target.

Additional Resources SPM website – –SPM Manual Brain viewers –

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

t = 16 t = 8 t = 5 A BC

BOLD may reflect predominantly excitatory activity M1 SMA Waldvogel, et al., 2000 Solid = go ; dashed = no-go TMS results had indicated that M1 is inhibited in no-go condition.

Parrish et al., % change2% change