Spatial & Temporal Properties (cont.) Signal and Noise BIAC Graduate fMRI Course October 5, 2004

Temporal Resolution

What temporal resolution do we want? 10,000-30,000ms: Arousal or emotional state ,000ms: Decisions, recall from memory ms: Response time 250ms: Reaction time ms: –Difference between response times –Initial visual processing 10ms: Neuronal activity in one area

Basic Sampling Theory Nyquist Sampling Theorem –To be able to identify changes at frequency X, one must sample the data at 2X. –For example, if your task causes brain changes at 1 Hz (every second), you must take two images per second.

Aliasing Mismapping of high frequencies (above the Nyquist limit) to lower frequencies –Results from insufficient sampling –Potential problem for designs with long TRs and fast stimulus changes –Also problem when physiological variability is present

Sampling Rate in Event-related fMRI

Costs of Increased Temporal Resolution Reduced signal amplitude –Shorter flip angles must be used (to allow reaching of steady state), leading to reduced signal Fewer slices acquired –Usually, throughput expressible as slices per unit time

Frequency Analyses t < -1.96t < McCarthy et al., 1996

Phase Analyses Design –Left/right alternating flashes –6.4s for each Task frequency: –1 / 12.8 = McCarthy et al., 1996

Why do we want to measure differences in timing within a brain region? Determine relative ordering of activity Make inferences about connectivity –Anatomical –Functional Relate activity timing to other measures –Stimulus presentation –Reaction time –Relative amplitude

Timing Differences across Regions Menon et al., 1998 Presented left hemifield before right hemifield (0-1000ms delays) Plot of LH signal as function of RH signal fMRI vs RT (LH) fMRI vs. Stimulus

Menon et al., 1998 Activation maps Relative onset time differences

Timing of mental events measured by fMRI Miezin et al., 2000 Subjects pressed button with one hand at onset of 1.5s stimulus Then, pressed another button at offset of stimulus

V1 FFG Huettel et al., 2001

Subject 1 4.0s 5.5s Subject 2 Primary Visual Cortex (V1) Secondary Visual Cortex (FFG) Huettel et al., 2001

Width of fMRI response increases with duration of mental activity From Menon and Kim, 1999; after Richter et al, 1997

Independence of Timing and Amplitude Adapted from Miezin et al. (2000)

Linearity of the Hemodynamic Response

Linear Systems Scaling –The ratio of inputs determines the ratio of outputs –Example: if Input 1 is twice as large as Input 2, Output 1 will be twice as large as Output 2 Superposition –The response to a sum of inputs is equivalent to the sum of the response to individual inputs –Example: Output = Output 1 +Output 2 +Output 3

Scaling (A) and Superposition (B) B A

Linear and Non-linear Systems AB CD

Possible Sources of Nonlinearity Stimulus time course  neural activity –Activity not uniform across stimulus (for any stimulus) Neural activity  Vascular changes –Different activity durations may lead to different blood flow or oxygen extraction Minimum bolus size? Minimum activity necessary to trigger? Vascular changes  BOLD measurement –Saturation of BOLD response necessitates nonlinearity –Vascular measures combining to generate BOLD have different time courses From Buxton, 2001

Effects of Stimulus Duration Short stimulus durations evoke BOLD responses –Amplitude of BOLD response often depends on duration –Stimuli < 100ms evoke measurable BOLD responses Form of response changes with duration –Latency to peak increases with increasing duration –Onset of rise does not change with duration –Rate of rise increases with duration Key issue: deconfounding duration of stimulus with duration of neuronal activity

The fMRI Linear Transform

Boynton et al., 1996 Varied contrast of checkerboard bars as well as their interval (B) and duration (C).

Boynton, et al, 1996

Differences in Nonlinearity across Brain Regions Birn, et al, 2001

SMA vs. M1 Birn, et al, 2001

Caveat: Stimulus Duration ≠ Neuronal Activity Duration

Refractory Periods Definition: a change in the responsiveness to an event based upon the presence or absence of a similar preceding event –Neuronal refractory period –Vascular refractory period

Dale & Buckner, 1997 Responses to consecutive presentations of a stimulus add in a “roughly linear” fashion Subtle departures from linearity are evident

Intra-Pair Interval (IPI) Inter-Trial Interval (16-20 seconds) 6 sec IPI 4 sec IPI 2 sec IPI 1 sec IPI Single- Stimulus Huettel & McCarthy, ms duration

Methods and Analysis 16 male subjects (mean age: 27y) GE 1.5T scanner –CAMRD Gradient-echo EPI –TR : 1 sec –TE : 50 msec –Resolution: * * 7 mm Analysis –Voxel-based analyses –Waveforms derived from active voxels within anatomical ROI Huettel & McCarthy, 2000

Hemodynamic Responses to Closely Spaced Stimuli Huettel & McCarthy, 2000

Refractory Effects in the fMRI Hemodynamic Response Huettel & McCarthy, 2000 Time since onset of second stimulus (sec) Signal Change over Baseline(%)

Refractory Effects across Visual Regions HDRs to 1 st and 2 nd stimuli in a pair (calcarine cortex) Relative amplitude of 2 nd stimulus in pair across regions

Intra-Pair Interval (IPI) Inter-Trial Interval (16-20 seconds) 6 sec IPI 1 sec IPI Single- Stimulus

L R Figure 2 Mean HDRs Single 6s IPI 1s IPI Time since stimulus onset (sec) Signal Change over baseline (%)

Refractory Effect Summary Duration –HDR evoked by a long-duration stimulus is less than predicted by convolution of short-duration stimuli –Present for durations < ~6s Interstimulus interval –HDR evoked by a stimulus is reduced by a preceding similar stimulus –Present for intervals < ~6s Differences across brain regions –Some regions show considerable departures from linearity –May result from differences in processing Source of non-linearity not well understood –Neuronal effects comprise at least part of the overall effect –Vascular differences may also contribute

Using refractory effects to study cognition: fMRI Adaptation Studies

Neuronal Adaptation Several neuronal populations vs. homogeneous population Adaptation If neurons are insensitive to the feature being varied, then their activity will adapt. Viewpoint SensitiveViewpoint Invariant Grill-Spector & Malach, 2001

Lateral OccipitalPosterior Fusiform

Is the refractory effect attribute specific? Boynton et al., 2003

Lateral Temporal-Occipital Peri-Calcarine AB CD Long Short Huettel, Obembe, Song, Woldorff, in preparation

Overall Summary Spatial resolution –Advantages (of increasing) Smaller voxels allow distinction among areas –Disadvantages Require more slices, thus longer TR Reduces signal per voxel Temporal resolution –Advantages (of increasing) Improves sampling of hemodynamic response –Disadvantages Reduces # of slices per TR May not be necessary for some designs Non-linearity of hemodynamic response –Advantages (of phenomenon for design) May be used to study adaptation –Disadvantages Reduces power of short interval designs Must be accounted for in analyses

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 (i.e., noise)? –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

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.

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 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., % change2% change

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

Increasing Field Strength

Adapted from Turner, et al. (1993)

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

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

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