Cartography and Chronometry Dr. Scott Huettel fMRI Graduate Course October 8, 2003

Why do you need to know? Spatial resolution Temporal resolution Tradeoffs between coverage and spatial resolution Influences viability of preprocessing steps Temporal resolution Tradeoffs between number of slices and TR Needed resolution depends upon design Non-linearity of the hemodynamic response Limits experimental designs Affects subsequent analyses Reduces power

Spatial Resolution

What spatial resolution do we want? Hemispheric Lateralization studies Selective attention studies Systems / lobic Relation to lesion data Centimeter Identification of active regions Millimeter Topographic mapping (e.g., motor, vision) Sub-millimeter Ocular Dominance Columns Cortical Layers

What determines Spatial Resolution? Voxel Size In-plane Resolution Slice thickness Spatial noise Head motion Artifacts Spatial blurring Smoothing (within subject) Coregistration (within subject) Normalization (within subject) Averaging (across subjects)

Why can’t we just collect data from more/smaller voxels?

K – Space Revisited . . . . . . . . . . . . . . . . . . . . A B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FOV: 10cm, Pixel Size: 2 cm FOV: 10 cm, Pixel Size: 1 cm To increase spatial resolution we need to sample at higher spatial frequencies.

How large are functional voxels? = ~.08cm3  5.0mm   3.75mm   3.75mm  Within a typical brain (~1300cm3), there may be about 20,000 functional voxels.

How large are anatomical voxels? = ~.004cm3  5.0mm   .9375mm   .9375mm  Within a typical brain (~1300cm3), there may be about 300,000+ anatomical voxels.

Costs of Increased Spatial Resolution Acquisition Time In-plane Higher resolution takes more time to fill K-space (resolution ~ size of K-space) #Slices/second Sample rates for 64*64 images Early Duke fMRI: 2-4 sl/s GE EPI: 12 sl/s Duke Spiral: 14 sl/s Duke Inverse Spiral: 21+ sl/s Reduced signal per voxel What is our dependent measure?

T2* Blurring Signal decays over time needed for collection of an image For standard resolution images, this is not a critical issue However, for high-resolution (in-plane) images, the time to acquire an image may be a significant fraction of T2* Under these conditions, multi-shot imaging may be necessary.

Partial Volume Effects A single voxel may contain multiple tissue components Many “gray matter” voxels will contain other tissue types Large vessels are often present The signal recorded from a voxel is a combination of all components

Matching fMRI and electrophysiology Disbrow et al, 2000

High Spatial Resolution fMRI: Ocular Dominance Columns

Early examples of ocular dominance Red = Left eye Blue = Right eye Pixel size 0.5mm2 Menon et al., 1997

Reliability of Ocular Dominance Measurements Cheng et al., 2001 Same subject participated in two sessions Raw data at left Boundaries of dominance columns match well across sessions

Effects of Stimulus Duration on Spatial Extent of Activity

Example: Ocular Dominance Goodyear & Menon, 2001

4sec  10sec  Goodyear & Menon, 2001

Example: Visual System 100ms 500ms 1500 ms

Temporal Resolution

What temporal resolution do we want? 10,000-30,000ms: Change in arousal or emotional state 1000-10,000ms: Decisions, recall from memory 500-1000ms: Response time 250ms: Reaction time 10-100ms: 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 TR = 4s TR = 2s TR = 1s

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 < -1.96 t < +1.96 McCarthy et al., 1996

Phase Analyses Design Task frequency: Left/right alternating flashes 6.4s for each Task frequency: 1 / 12.8 = 0.078 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 Presented left hemifield before right hemifield (0-1000ms delays) fMRI vs RT (LH) Plot of LH signal as function of RH signal fMRI vs. Stimulus Menon et al., 1998

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

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 We also investigated the latency of the hemodynamic response across brain regions. We found, in both elderly and young adults, that the hemodynamic response in primary visual cortex anticipates that in fusiform cortex by about 300 ms. This result has since been replicated using face stimuli. Huettel et al., 2001

Subject 1 Subject 2 5.5s 4.0s Secondary Visual Cortex (FFG) Primary Visual Cortex (V1) These figures demonstrate this effect on an individual voxel level. The overlaid color maps are not traditional significance maps; they are maps of latency to hemodynamic peak, with earliest responses in blue and latest responses in yellow. As can be seen, on the left image, activation in the fusiform gyri generally has a much later peak than that in calcarine cortex, shown at right. Huettel et al., 2001

Width of fMRI response increases with duration of mental activity Menon and Kim, 1999

Linearity of the Hemodynamic Response

Linear Systems Scaling Superposition The ratio of inputs determines the ratio of outputs Example: if Input1 is twice as large as Input2, Output1 will be twice as large as Output2 Superposition The response to a sum of inputs is equivalent to the sum of the response to individual inputs Example: Output1+2+3 = Output1+Output2+Output3

Scaling (A) and Superposition (B)

Linear and Non-linear Systems B C D

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

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

Boynton, et al, 1996

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 Our basic design was derived from electrophysiological studies of refractory periods. We presented either a single short duration visual checkerboard, or a pair of checkerboards separated by an intra-pair interval of either 1, 2, 4, or 6 seconds. A long inter-trial interval ensured that the hemodynamic response returned to baseline before the onset of the next trial. Our hypothesis was that the second stimulus in the pair would have relatively little effect upon the composite waveform at short intervals, like 1 or 2 seconds, but would have a large effect at long intervals. That is, the hemodynamic response would be relatively linearly additive at long-intervals, but non-linear at short intervals. 500 ms duration Huettel & McCarthy, 2000

Methods and Analysis 16 male subjects (mean age: 27y) GE 1.5T scanner CAMRD Gradient-echo EPI TR : 1 sec TE : 50 msec Resolution: 3.125 * 3.125 * 7 mm Analysis Voxel-based analyses Waveforms derived from active voxels within anatomical ROI The study was conducted at 1.5T in the center for advanced magnetic resonance development at Duke. We took two echo-planar slices chosen to bracket the calcarine sulcus in each subject, and sampled those slices with repetition time of 1 sec. In each subject we identified a functional ROI consisting of contiguous active voxels in calcarine cortex. Huettel & McCarthy, 2000

Hemodynamic Responses to Closely Spaced Stimuli These graphs show the time courses of fMRI activation in calcarine cortex. The yellow line that is repeated in each graph shows the response to a single stimulus. The colored lines show the response to pairs of stimuli. Readily apparent is the contribution of the second stimulus above that of the single stimulus condition. To determine how large of a hemodynamic response was evoked by the second stimulus, we took the residual area between the two curves (the additive effect of the second stimulus), and we time-locked that difference to the onset of the second stimulus. Huettel & McCarthy, 2000

Refractory Effects in the fMRI Hemodynamic Response Signal Change over Baseline(%) The independent contribution of the second stimulus is shown on this plot. The yellow line shows the response to a single stimulus. Readily apparent are the significant refractory effects. At 1 second intervals, the response to the second stimulus is attenuated in amplitude by about 45% and is increased in latency by about a second. Both amplitude and latency values recover to near single-stimulus values by about six seconds. Time since onset of second stimulus (sec) Huettel & McCarthy, 2000

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

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

L R Figure 2 Single 6s IPI 1s IPI Mean HDRs 05 10 15 20 25 30 35 40 45 50 55 60 Mean HDRs L Single 6s IPI 1s IPI Signal Change over baseline (%) R Time since stimulus onset (sec)

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

Lateral Occipital Posterior Fusiform

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

Lateral Temporal-Occipital B Long Short Lateral Temporal-Occipital C D Peri-Calcarine Huettel, Obembe, Song, Woldorff, in preparation

Overall Summary Spatial resolution Temporal resolution Advantages (of increasing) Smaller voxels allow distinction among areas Disadvantages Require more slices, thus longer TR Reduces signal per voxel Temporal resolution Improves sampling of hemodynamic response 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 Reduces power of short interval designs Must be accounted for in analyses