1. Spatial and Temporal Limits of fMRI
Jody Culham
Department of Psychology
University of Western Ontario
Spatial and Temporal Limits of fMRI
Last Update: November 29, 2008
fMRI Course, Louvain, Belgium

2. Spatial Limits of fMRI

3. fMRI in the Big Picture

4. What Limits Spatial Resolution
noise
smaller voxels have lower SNR
head motion
the smaller your voxels, the more contamination head motion induces
temporal resolution
the smaller your voxels, the longer it takes to acquire the same volume
4 mm x 4 mm at 16 slices/sec
OR 1 mm x 1 mm at 1 slice/sec
vasculature
depends on pulse sequences
e.g., spin echo sequences reduce contributions from large vessels
some preprocessing techniques may reduce contribution of large vessels (Menon, 2002, MRM)

5. Ocular Dominance Columns
Columns on the order of ~0.5 mm have been observed with fMRI

6. Submillimeter Resolution
vein
Stria of Gennari
(Layer IV)
Spin Echo
Functional
(activation
localized to
Layer IV)
Gradient Echo
Functional
(superficial activation
includes vessels)
Spin Echo
Anatomical
Gradient Echo
Anatomical
Goenze, Zappe & Logothetis, 2007, Magnetic Resonance Imaging
anaesthetized monkey; 4.7 T; contrast agent (MION)
~0.3 x 0.3 x 2 mm

7. Temporal Limits of fMRI AND Event-Related Averaging

8. Sampling Rate
Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging

9. BOLD Time Course

10. Evolution of BOLD Response
Hu et al., 1997, MRM

11. Event-Related Averaging
In this example an “event” is the start of a block

12. Event-Related Averaging

13. Event-Related Averaging

14. Event-Related Averaging
“Zero” = average signal intensity in first volume of all 8 events

15. Event-Related Averaging
RAW
Not particularly useful
No baseline, just averaged values
Error bars may be huge (esp. if multiple runs)
FILE-BASED
Zero = average across all events at specified volume(s)
Safest procedure to use
Most similar to GLM stats
EPOCH-BASED
Zero = starting point of each curve at specified volume(s)
Sometimes useful if well-justified
May look very different than GLM stats

16. Event-related Averaging
File-based
zero is based on average starting point of all curves
works best when low frequencies have been filtered out of your data
similar to what your GLM stats are testing
Epoch-based
each curve starts at zero
can be risky with noisy data
only use it if you are fairly certain your pre-stim baselines are valid (e.g., you have a long ITI or your trial orders are counterbalanced)
can give very different results from GLM stats

17. Convolution of Single Trials
Neuronal Activity
BOLD Signal
Haemodynamic Function
Time
Time
Slide from Matt Brown

18. BOLD Summates
Neuronal Activity
BOLD Signal
Slide from Matt Brown

19. BOLD Overlap and Jittering
Closely-spaced haemodynamic impulses summate.
Constant ITI causes tetanus.
Burock et al

20. Design Types Block Design Slow ER Design Rapid Counterbalanced
= trial of one type
(e.g., face image)
= null trial
(nothing happens)
Design Types
= trial of another type
(e.g., place image)
Block
Design
Slow ER
Design
Rapid
Counterbalanced
ER Design
Rapid
Jittered ER
Design
Jody
Mixed
Design

21. Block Designs
= trial of one type
(e.g., face image)
= trial of another type
(e.g., place image)
Block
Design
Early Assumption: Because the hemodynamic response delays and blurs the response to activation, the temporal resolution of fMRI is limited.
WRONG!!!!!
Jody

22. What are the temporal limits?
What is the briefest stimulus that fMRI can detect?
Blamire et al. (1992): 2 sec
Bandettini (1993): 0.5 sec
Savoy et al (1995): 34 msec
2 s stimuli
single events
Data: Blamire et al., 1992, PNAS
Figure: Huettel, Song & McCarthy, 2004
Data: Robert Savoy & Kathy O’Craven
Figure: Rosen et al., 1998, PNAS
Jody
Although the shape of the HRF delayed and blurred, it is predictable.
Event-related potentials (ERPs) are based on averaging small responses over many trials.
Can we do the same thing with fMRI?

23. Detection vs. Estimation
detection: determination of whether activity of a given voxel (or region) changes in response to the experimental manipulation 1
estimation: measurement of the time course within an active voxel in response to the experimental manipulation
% Signal Change
Jody 4 8 12
Time (sec)
Definitions modified from: Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging

24. Block Designs: Poor Estimation
Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging

25. Pros & Cons of Block Designs
high detection power
has been the most widely used approach for fMRI studies
accurate estimation of hemodynamic response function is not as critical as with event-related designs
Cons
poor estimation power
subjects get into a mental set for a block
very predictable for subject
can’t look at effects of single events (e.g., correct vs. incorrect trials, remembered vs. forgotten items)
becomes unmanagable with too many conditions (4 conditions + baseline is about the max I will use in one run)
Jody

26. Slow Event-Related Designs
Slow ER
Design
Jody

27. Spaced Mixed Trial: Constant ITI
Bandettini et al. (2000)
What is the optimal trial spacing (duration + intertrial interval, ITI) for a Spaced Mixed Trial design with constant stimulus duration?
2 s stim
vary ISI
Block
Sync with trial onset and average
Jody
Source: Bandettini et al., 2000

28. Optimal Constant ITI Brief (< 2 sec) stimuli:
Source: Bandettini et al., 2000
Brief (< 2 sec) stimuli:
optimal trial spacing = 12 sec
For longer stimuli:
optimal trial spacing = 8 + 2*stimulus duration
Effective loss in power of event related design:
= -35%
i.e., for 6 minutes of block design, run ~9 min ER design
Jody

29. Trial to Trial Variability
Huettel, Song & McCarthy, 2004,
Functional Magnetic Resonance Imaging

30. How Many Trials Do You Need?
Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging
standard error of the mean varies with square root of number of trials
Number of trials needed will vary with effect size
Function begins to asymptote around 15 trials

31. Effect of Adding Trials
Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging

32. Pros & Cons of Slow ER Designs
good estimation power
allows accurate estimate of baseline activation and deviations from it
useful for studies with delay periods
very useful for designs with motion artifacts (grasping, swallowing, speech) because you can tease out artifacts
analysis is straightforward 
Hand motion
artifact
% signal change
Time
Activation 
Cons
poor detection power because you get very few trials per condition by spending most of your sampling power on estimating the baseline
subjects can get VERY bored and sleepy with long inter-trial intervals
Jody

33. Can we go faster?!
Yes, but we have to test assumptions regarding linearity of BOLD signal first
Rapid
Counterbalanced
ER Design
Rapid
Jittered ER
Design
Tzvi
Mixed
Design

34. Linearity of BOLD response
“Do things add up?”
red = 2 - 1
green = 3 - 2
Sync each trial response to start of trial
Tzvi
Not quite linear
but good enough!
Source: Dale & Buckner, 1997

35. Optimal Rapid ITI Rapid Mixed Trial Designs
Source: Dale & Buckner, 1997
Tzvi
Rapid Mixed Trial Designs
Short ITIs (~2 sec) are best for detection power
Do you know why?

36. Design Types Rapid Counterbalanced ER Design Jody = trial of one type
(e.g., face image)
Design Types
= trial of another type
(e.g., place image)
Rapid
Counterbalanced
ER Design
Jody

37. Detection with Rapid ER Designs
Figure: Huettel, Song & McCarthy, 2004
To detect activation differences between conditions in a rapid ER design, you can create HRF-convolved reference time courses
You can perform contrasts between beta weights as usual
Jody

38. Variability of HRF Between Subjects
Aguirre, Zarahn & D’Esposito, 1998
HRF shows considerable variability between subjects
different subjects
Within subjects, responses are more consistent, although there is still some variability between sessions
same subject, same session
same subject, different session

39. Variability of HRF Between Areas
Possible caveat: HRF may also vary between areas, not just subjects
Buckner et al., 1996:
noted a delay of .5-1 sec between visual and prefrontal regions
vasculature difference?
processing latency?
Bug or feature?
Menon & Kim – mental chronometry
Buckner et al., 1996

40. Variability Between Subjects/Areas
greater variability between subjects than between regions
deviations from canonical HRF cause false negatives (Type II errors)
Consider including a run to establish subject-specific HRFs from robust area like M1
Handwerker et al., 2004, Neuroimage

41. The Problem of Trial History
Activation
Activation
WARNING: This slide is confusing, needs to be redone. Supposed to show that yellow>red>white, not just because of trial summation
Time
Time
Event-related average is wonky because trial types differ in the history of preceding trials
Estimation does not work well if trial history differs between trial types
Two options
Control trial history by making it the same for all trial types
Model the trial history by deconvolving the signal (requires jittered timing)

42. One Approach to Estimation: Counterbalanced Trial Orders
Each condition must have the same history for preceding trials so that trial history subtracts out in comparisons
For example if you have a sequence of Face, Place and Object trials (e.g., FPFOPPOF…), with 30 trials for each condition, you could make sure that the breakdown of trials (yellow) with respect to the preceding trial (blue) was as follows:
…Face  Face x 10
…Place  Face x 10
…Object  Face x 10
…Face  Place x 10
…Place  Place x 10
…Object  Place x 10
…Face  Object x 10
…Place  Object x 10
…Object  Object x 10
Most counterbalancing algorithms do not control for trial history beyond the preceding one or two items

43. Analysis of Single Trials with Counterbalanced Orders
Approach used by Kourtzi & Kanwisher (2001, Science) for pre-defined ROI’s:
for each trial type, compute averaged time courses synced to trial onset; then subtract differences
Event-related average
with control period factored out
A signal change = (A – F)/F
B signal change = (B – F)/F …
Raw data
Event-related average
sync to trial onset A B F

44. Pros & Cons of Counterbalanced Rapid ER Designs
high detection power with advantages of ER designs (e.g., can have many trial types in an unpredictable order)
Cons and Caveats
reduced detection compared to block designs
estimation power is better than block designs but not great
accurate detection requires accurate HRF modelling
counterbalancing only considers one or two trials preceding each stimulus; have to assume that higher-order history is random enough not to matter
what do you do with the trials at the beginning of the run… just throw them out?
you can’t exclude error trials and keep counterbalanced trial history
you can’t use this approach when you can’t control trial status (e.g., items that are later remembered vs. forgotten)

45. Design Types Rapid Jittered ER Design Jody = trial of one type
(e.g., face image)
Design Types
= trial of another type
(e.g., place image)
Rapid
Jittered ER
Design
Jody

46. BOLD Overlap With Regular Trial Spacing
Neuronal activity from TWO event types with constant ITI
Partial tetanus BOLD activity from two event types
Slide from Matt Brown

47. BOLD Overlap with Jittering
Neuronal activity from closely-spaced, jittered events
BOLD activity from closely-spaced, jittered events
Slide from Matt Brown

48. BOLD Overlap with Jittering
Neuronal activity from closely-spaced, jittered events
BOLD activity from closely-spaced, jittered events
Slide from Matt Brown

49. Fast fMRI Detection A) BOLD Signal
B) Individual Haemodynamic Components
C) 2 Predictor Curves for use with GLM (summation of B)
Slide from Matt Brown

50. Post Hoc Trial Sorting Example
Wagner et al., 1998, Science

51. Fast fMRI Detection Pros:
Incorporates prior knowledge of BOLD signal form
affords some protection against noise
Easy to implement
Can do post hoc sorting of trial type
Cons:
Vulnerable to inaccurate hemodyamic model
No time course produced independent of assumed haemodynamic shape

52. Fast fMRI Estimation
We can detect fMRI activation in rapid event related designs in the same way that we do for other designs (block design, slow event related design
For any kind of event-related designs, it is very important to have a resonably accurate model of the HRF
In addition, with rapid event related designs, we can also estimate time courses using a technique called deconvolution

53. Convolution of Single Trials
Neuronal Activity
BOLD Signal
Haemodynamic Function
Time
Time
Slide from Matt Brown

54. DEconvolution of Single Trials
Neuronal Activity
BOLD Signal
Haemodynamic Function
Time
Time
Slide from Matt Brown

55. Deconvolution Example
time course from 4 trials of two types (pink, blue) in a “jittered” design

56. Summed Activation

57. Single Stick Predictor
single predictor for first volume of pink trial type

58. Predictors for Pink Trial Type
set of 12 predictors for subsequent volumes of pink trial type
need enough predictors to cover unfolding of HRF (depends on TR)

59. Predictor Matrix
Diagonal filled with 1’s .

60. Predictors for the Blue Trial Type
set of 12 predictors for subsequent volumes of blue trial type

61. Linear Deconvolution
Miezen et al.
2000
Jittering ITI also preserves linear independence among the hemodynamic components comprising the BOLD signal.

62. Predictor x Beta Weights for Pink Trial Type
sequence of beta weights for one trial type yields an estimate of the average activation (including HRF)

63. Predictor x Beta Weights for Blue Trial Type
height of beta weights indicates amplitude of response (higher betas = larger response)

64. Fast fMRI: Estimation Pros: Produces time course
Does not assume specific shape for hemodynamic function
Can use narrow jitter window
Robust against trial history biases (though not immune to it)
Compound trial types possible
Cons:
Complicated
Unrealistic assumptions about maintenance activity
BOLD is non-linear with inter-event intervals < 6 sec.
Nonlinearity becomes severe under 2 sec.
Sensitive to noise

65. Design Types Mixed Design Jody = trial of one type (e.g., face image)
= trial of another type
(e.g., place image)
Jody
Mixed
Design

66. Example of Mixed Design
Otten, Henson, & Rugg, 2002, Nature Neuroscience
used short task blocks in which subjects encoded words into memory
In some areas, mean level of activity for a block predicted retrieval success

67. Pros and Cons of Mixed Designs
allow researchers to distinguish between state-related and item-related activation
Cons
sensitive to errors in HRF modelling

68. A Variant of Mixed Designs: Semirandom Designs
a type of event-related design in which the probability of an event will occur within a given time interval changes systematically over the course of an experiment
First period:
P of event: 25%
Middle period:
P of event: 75%
Last period:
P of event: 25%
probability as a function of time can be sinusoidal rather than square wave

69. Pros and Cons of Semirandom Designs
good tradeoff between detection and estimation
simulations by Liu et al. (2001) suggest that semirandom designs have slightly less detection power than block designs but much better estimation power
Cons
relies on assumptions of linearity
complex analysis
“However, if the process of interest differs across ISIs, then the basic assumption of the semirandom design is violated. Known causes of ISI-related differences include hemodynamic refractory effects, especially at very short intervals, and changes in cognitive processes based on rate of presentation (i.e., a task may be simpler at slow rates than at fast rates).”
-- Huettel, Song & McCarthy, 2004

70. EXTRA SLIDES

71. Voxel Size non-isotropic non-isotropic
EXCEPT when the activated region does not fill the voxel (partial voluming)
isotropic
3 x 3 x 6
= 54 mm3
e.g., SNR = 100
3 x 3 x 3
= 27 mm3
e.g., SNR = 71
2.1 x 2.1 x 6
= 27 mm3
e.g., SNR = 71
In general, larger voxels buy you more SNR.

72. Partial Voluming
The fMRI signal occurs in gray matter (where the synapses and dendrites are)
If your voxel includes white matter (where the axons are), fluid, or space outside the brain, you effectively water down your signal
fMRI for Dummies

73. Partial Voluming
Partial volume effects: The combination, within a single voxel, of signal contributions from two or more distinct tissue types or functional regions (Huettel, Song & McCarthy, 2004)
This voxel contains mostly gray matter
This voxel contains mostly white matter
This voxel contains both gray and white matter. Even if neurons within the voxel are strongly activated, the signal may be washed out by the absence of activation in white matter.
Partial voluming becomes more of a problem with larger voxel sizes
Worst case scenario: A 22 cm x 22 cm x 22 cm voxel would contain the whole brain

74. The Initial Dip
The initial dip seems to have better spatial specificity
However, it’s often called the “elusive initial dip” for a reason

75. Initial Dip (Hypo-oxic Phase)
Transient increase in oxygen consumption, before change in blood flow
Menon et al., 1995; Hu, et al., 1997
Smaller amplitude than main BOLD signal
10% of peak amplitude (e.g., 0.1% signal change)
Potentially more spatially specific
Oxygen utilization may be more closely associated with neuronal activity than positive response
Slide modified from Duke course

76. Rise (Hyperoxic Phase)
Results from vasodilation of arterioles, resulting in a large increase in cerebral blood flow
Inflection point can be used to index onset of processing
Slide modified from Duke course

77. Slide modified from Duke course
Peak – Overshoot
Over-compensatory response
More pronounced in BOLD signal measures than flow measures
Overshoot found in blocked designs with extended intervals
Signal saturates after ~10s of stimulation
Slide modified from Duke course

78. Slide modified from Duke course
Sustained Response
Blocked design analyses rest upon presence of sustained response
Comparison of sustained activity vs. baseline
Statistically simple, powerful
Problems
Difficulty in identifying magnitude of activation
Little ability to describe form of hemodynamic response
May require detrending of raw time course
Slide modified from Duke course

79. Slide modified from Duke course
Undershoot
Cerebral blood flow more locked to stimuli than cerebral blood volume
Increased blood volume with baseline flow leads to decrease in MR signal
More frequently observed for longer-duration stimuli (>10s)
Short duration stimuli may not evidence
May remain for 10s of seconds
Slide modified from Duke course

80. Implications Aguirre, Zarahn & D’Esposito, 1998
Generic HRF models (gamma functions) account for 70% of variance
Subject-specific models account for 92% of the variance (22% more!)
Poor modelling reduces statistical power
Less of a problem for block designs than event-related
Biggest problem with delay tasks where an inappropriate estimate of the initial and final components contaminates the delay component

81. Blocked vs. Event-related
Source: Buckner 1998

82. Advantages of Event-Related
Flexibility and randomization
eliminate predictability of block designs
avoid practice effects
Post hoc sorting
(e.g., correct vs. incorrect, aware vs. unaware, remembered vs. forgotten items, fast vs. slow RTs)
Can look at novelty and priming
Rare or unpredictable events can be measured
e.g., P300
Can look at temporal dynamics of response
Dissociation of motion artifacts from activation
Dissociate components of delay tasks
Mental chronometry
Source: Buckner & Braver, 1999

83. Exponential Distribution of ITIs
Flat Distribution
Exponential
Distribution
Frequency
Frequency 2 3 4 5 6 7 2 3 4 5 6 7
Intertrial Interval
Intertrial Interval
An exponential distribution of ITIs is recommended
WARNING: I’ve been getting conflicting advice on whether it’s better to have an exponential distribtuion… need to find out more

84. NEW SLIDES