1. Cartography and Chronometry
fMRI Graduate Course
October 9, 2002

2. 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

3. Spatial Resolution

4. 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

5. 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)

6. 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.

7. 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.

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

9. 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 (1.5T): 14 sl/s
Duke Inverse Spiral (4.0T): 21 sl/s
Reduced signal per voxel
What is our dependent measure?

10. Effects of Stimulus Duration on Spatial Extent of Activity

11. Example: Ocular Dominance
Goodyear & Menon, 2001

12. 4sec 
10sec 
Goodyear & Menon, 2001

13. Example: Visual System
100ms
500ms
1500 ms

14. 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.

15. Temporal Resolution

16. What temporal resolution do we want?
10,000ms: Change in arousal or emotional state
1000ms: Decisions, recall from memory
ms: Response time
250ms: Reaction time
10-100ms:
Difference between response times
Initial visual processing
10ms: Neuronal activity in one area

17. 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.

19. 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

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

21. Phase Analyses Design Task frequency: Left/right alternating flashes
6.4s for each
Task frequency:
1 / 12.8 = 0.078
McCarthy et al., 1996

22. 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

23. 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

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

25. 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

26. 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

27. Linearity of the Hemodynamic Response

28. 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

29. 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

30. 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

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

32. Boynton, et al, 1996

33. Boynton, et al, 1996

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

35. SMA vs. M1
Birn, et al, 2001

36. Caveat: Stimulus Duration ≠ Neuronal Activity Duration

37. fMRI Hemodynamic Response
1500ms
500ms
100ms
Calcarine Sulci
Fusiform Gyri

38. Calcarine
1500ms
500ms *
Fusiform
100ms

39. 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

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

41. 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

42. 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
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

43. 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

44. 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

45. 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

46. 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

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

48. 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

49. Using refractory effects to study cognition: fMRI Adaptation Studies

50. 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

51. Lateral Occipital
Posterior Fusiform

52. 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