Transcript mbi2004 3829

The linear systems model of
fMRI: Strengths and
Weaknesses
Stephen Engel
UCLA Dept. of Psychology
Talk Outline
• Linear Systems
– Definition
– Properties
• Applications in fMRI (Strengths)
• Is fMRI Linear? (Weaknesses)
• Implications
– Current practices
– Future directions
Linear systems
 System = input -> output
Stimulus or Neural activity -> fMRI responses
 System is linear if shows two properties
Homogeneity & Superposition
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Useful properties of linear systems
• Can add and subtract responses meaningfully
• Can characterize completely using impulse
response
• Can use impulse response to predict output to
arbitrary input via convolution
• Can characterize using MTF
Subtracting responses
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a
-=
b
Characterizing linear systems
1)
Impulse response
2)
MTF
Using the impulse-resp. characterization of SILS
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SILS
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Predicting block response
?
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Characterizing linear systems
1)
Impulse response
2)
MTF
Using the frequency characterization of SILS
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SILS
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Talk Outline
• Linear Systems
– Definition
– Properties
• Applications in fMRI (Strengths)
• Is fMRI Linear? (Weaknesses)
• Implications
– Current practices
– Future directions
Uses of linear systems in fMRI
• If assume fMRI signal is generated by a
linear system can:
– Create model fMRI timecourses
– Use GLM to estimate and test parameters
– Interpret estimated parameters
– Estimate temporal and spatial MTF
Simple GLM Example
Paradigm
Task a
Task b
rest
Data
rest
X
Y
=
b
*
b1
b2
Model fitting assumes homogeneity
X
Y
b1
b2
=
b
*
b1
b2
Rapid designs assume superposition
Stimulus
a b b a r r b a ...
Data
X
Y
=
b
*
b1
b2
Wagner et al. 1998, Results
Zarahn, ‘99; D’esposito et al.
MAINTENANCE > ITI
D’Esposito et al.
More on GLM
• Many other analysis types possible
– ANCOVA
– Simultaneous estimate of HRF
• Interpretation of estimated parameters
– If fMRI data are generated from linear
system w/neural activity as input
– Then estimated parameters will be
proportional to neural activity
• Allows quantitative conclusions
MTF
• Boynton et al. (1996) estimated
temporal MTF in V1
– Showed moving bars of checkerboard that
drifted at various temporal frequencies
– Generated periodic stimulation in
retinotopic cortex
– Plotted Fourier transform of MTF (which is
impulse response)
Characterizing linear systems
1)
Impulse response
2)
MTF
MTF
• Engel et al. (1997) estimated spatial
MTF in V1
– Showed moving bars of checkerboard that
varied in spatial frequency but had
constant temporal frequency
– Calculated cortical frequency of stimulus
– Plotted MTF
– Some signal at 5 mm/cyc at 1.5 T in ‘97!
Talk Outline
• Linear Systems
– Definition
– Properties
• Applications in fMRI (Strengths)
• Is fMRI Linear? (Weaknesses)
• Implications
– Current practices
– Future directions
Is fMRI really based upon a
linear system?
• Neural activity as input fMRI signal as
output
• fMRI tests of temporal superposition
• Electrophysiological tests of
homogeneity
• fMRI test of spatial superposition
Tests of temporal
superposition
• Boynton et al. (1996) measured
responses to 3, 6, 12, and 24 sec
blocks of visual stimulation
• Tested if r(6) = r(3)+r(3) etc.
• Linearity fails mildly
Dale & Buckner ‘97
• Tested superposition in rapid design
 Full field stimuli
 Groups of 1, 2, or 3
– Closely spaced in time
– Responses overlap
 Q1: 2-1 = 1?
Dale and Buckner, Design
fMRI fails temporal
superposition
• Now many studies
• Initial response is larger than later
response
• Looks OK w/3-5 second gap
• Possible sources
– Attention
– Neural adaptation
– Hemodynamic non-linearity
Test of homogeneity
• Simultaneous measurements of neural
activity and fMRI or optical signal
• Q: As neural activity increases does
fMRI response increase by same
amount?
Logothetis et al., ‘01
Optical imaging studies
• Measure electrophysiological response
in rodents
• Various components of hemodynamic
response inferred from reflectance
changes at different wavelengths
• Devor ‘03 (whisker) and Sheth ‘04
(hindpaw)
Nonlinearities
• Optical imaging overestimates large neural
responses relative to small ones
– But Logo. found opposite
• fMRI overestimates brief responses relative to
long ones
– Amplified neural adaptation?
Spatial issue
• W/in a local region does signal depend
upon sum or average activity?
• Or “is the whole garden watered for the
sake of one thirsty flower?” (Grinvald)
Spatial Properties of HRF
Thompson et al., 2003
Testing spatial superposition
• Need to measure responses of neurons
from population a, population b, and
both
• Where have intermingled populations
that can activate separately?
– LGN
– Prediction twice as much fMRI response
for two eye stimulation than for one eye
• Should be different in V1
Conclusions
• Linear model successful and useful but…
• Hemodynamic responses possibly not
proportional to neural ones
– Though could be pretty close for much of range
– Take care interpreting
• differences in fMRI amplitude
• GLM results where neural responses overlap
Conclusions
• Temporal superposition of hemodynamic
responses could still hold
– Most applications of GLM may be OK w/proper
interpretation and spacing to avoid neural
adaptation
– Run estimated fMRI amplitude through inverse of
nonlinearity relating hemodynamics to neural
activity (static nonlinearity)
Rapid designs assume superposition
Stimulus
a b b a r r b a ...
Data
X
Y
=
b
*
b1
b2
Future Directions
• Better characterization of possible nonlinearities
• Modeling of non-linearities
• Further tests of linearity
– Hemodynamic superposition
– Spatial superposition