Resampling strategies for inference on spatiotemporal test statistics estimated by multiresolutional

1
Resampling strategies for inference on
spatiotemporal test statistics estimated by
multiresolutional analysis of fMRI data in the
wavelet domain
John Suckling, Mick Brammer, Ed Bullmore Brain
Mapping Unit and Wolfson Brain Imaging Center,
Institute of Psychiatry, Kings College, London
HBM2002 Sendai, Japan June 2002
2
Motivations and strategies for spatially-informed
analysis of time series statistics
Motivations

• Greater sensitivity to distributed effects on
  physiology
• Smaller search volume - less multiple
  comparisons problem
• Often more independence of tests

Strategies

• Spatial smoothing prior to voxel-wise testing -
  what filter?
• Cluster-level testing on thresholded voxel maps
  - what threshold?
• Multiresolutional approaches
• Gaussian scale-space (Poline, Worsley)
• wavelets (Ruttimann, Brammer)

3
y
x
xy
y
2D (i)DWT
x
spatial map of GLM coefficients b
increased scale j, fewer wavelet coefficients wj

• 2D Discrete Wavelet Transform (DWT)
• multiresolutional spatial filtering of time
  series statistic maps
• spatially extended signals are losslessly
  described by wavelet coefficients at mutually
  orthogonal scales and orientations

4
Multiresolutional brain mapping in wavelet domain
Ruttimann et al (1998), Brammer (1998)
If b iid N(0, Is2) then w iid N(0, Is2) -
so assuming b maps are white Gaussian fields
under the null hypothesis
Then 1) Do an omnibus c2 test for significance
at each scale 2) ...test each standardised
coefficient wi,j/s2 at surviving scales
against Normal Z approximation 3) take inverse
wavelet transform (iDWT) of remaining
coefficients to reconstitute activation map in
space
Two questions b maps arent generally white
does that matter? can we use data resampling to
estimate the 2D wavelet variance s2 ?
5
Wavelet-resampling or wavestrappingwhitening
confers exchangeability
DWT
observed
GLM
iDWT
resampled
TIME
WAVELETS
Resample time series data using 1D-DWT to
estimate spatial statistics, including variance
of 2D-DWT coefficients, under null hypothesis of
no activation.
SPACE
6
The algorithm...
obs
ran
7
Nominal type 1 control demonstrated empirically
by analysis of null data
Observed number of (false) positive coefficients
less than or equal to number expected under the
null hypothesis Independence of coefficients
allows simple estimation of confidence interval
for expected number of false positive tests
E(FP)10
8
Mapping of simulated activations
9
Some generic activation maps from 3D-DWT MRA
Visual stimulation
Object-location learning
3 / 35 (fine-detail) scales rejected by c2
test 45 / 112,192 coefficients survived
permutation test, E(FP) 10 95CI 4,16
10
Conclusions
Wavelets are optimal decorrelating filters for
1/f-like spatial and temporal processes, which
are widespread in fMRI
Wavelets achieve a multiresolutional analysis
(MRA) which can be used for testing fMRI time
series statistics at several scales of spatial
resolution

• We have presented a novel, resampling based
  strategy for 2D (and 3D) multiresolutional
  analysis of fMRI statistic maps
• good type 1 error control
• promising sensitivity