Clustering of fMRI data for activation detection using HDR models

1. Clustering of fMRI data for activation detection using HDR models Ashish Rao, Thomas Talavage

2. Motivation • Perform fMRI data analysis at cluster level. • Retain physiological connection; not get lost in statistics. • Accept isolated voxel activation conservatively.

3. Objectives of proposed procedure • To detect cortical activity on a regional basis. • To estimate the hemodynamic response (HDR) using a model waveform. • To cluster fMRI data based on the parameters of the model fit. • To characterize a representative response for the cluster identified for activity.

4. Common HDR models • Poisson* • Gamma† • Gaussian‡ *Friston et al., 1994; †Lange et al.,1997; ‡Rajapakse et al.,1998.

5. Chosen HDR model • Model – Gamma variate function* • Parameters: • x0 = baseline • A = amplitude • = delay • = spread *Dale and Buckner, 1997.

6. The big picture X (data) Fit Clustering Y (activation) ρs (model parameters)

7. Preliminary procedure Model Parameters Initial data Average response Average across trials Weighted MMSE fit Amplitude map Thresholding Reduced data set Clusters Segmentation Algorithm (k means) Data for clustering % signal change

8. Preliminary procedure • Preprocess data (drift correct, normalize) • Average across trials voxel-by-voxel • Fit model (weighted MMSE) to obtain parameters • Reduce data set by thresholding amplitude (A) map • Calculate % signal change (A/x0) • Perform k-means clustering

9. Validation experiment • Performed at IUMC using a 1.5T scanner • Flashing checkerboard stimulus presented for 1s • right visual hemifield = stimulus 1 • left visual hemifield = stimulus 2 • Spiral EPI pulse sequence (TR=1s; TE=40ms; ISI=15s; FOV=24cm; flip angle=90o; 64×64 matrix) • 270 images of 10 slices (ST=3.8mm) • Oblique slices through primary visual cortex

10. Results – standard t-test map The t-test map was used as a standard for comparison. Stimulus 1 Stimulus 2 S I R L R L

11. Results – amplitude maps Stimulus 2 Stimulus 1

12. Results – log error of fit maps Stimulus 1 Stimulus 2

13. Results – clusters Stimulus 1; k=7 clusters Stimulus 2; k=7 clusters

14. Results – clusters Stimulus 1; k=8 clusters Stimulus 2; k=8 clusters

15. Results – clusters Stimulus 1; k=12 clusters Stimulus 2; k=12 clusters

16. Clustering – unsupervised? • Consistency of region of activation (bright red cluster) over • Prefer unsupervised clustering because suitable value of k not known a priori. • Hierarchical clustering* is an option as it merges “closest” voxels. *Filzmoser et al.,1999.

17. Summary of results • Activation maps consistent with t-test results. • Consistency over k = 7-12 clusters. • Sagittal sinus showed high amplitude fit, but was discarded due to high error of fit. • Spatial contiguity observed.

18. Discussion • Need a metric to identify activation that accounts for: • Multiple cluster activity • Co-activation • Disjoint activity • Single voxel activity • Possible solutions: • Average “distance” of voxels from cluster mean • Average error of fit Relate to prior knowledge of anatomical and functional connectivity of the brain

19. Discussion • Gamma variate model not optimal. • Alternate HDR models • Difference of two shifted Gamma variate functions* to account for initial dip† in HDR. • Family of models • Removes prior assumptions on appropriateness of model; rather choose the model that best fits the data. *Rajapakse et al., 1998; †Menon et al., 1995.

20. Future work • Structural constraints on regions of activity • Incorporate Markov Random Fields. • Poor contrast-to-noise ratio • Reduce dimensionality of data space*. • Model fitting is a non-linear (hard) problem† • Fit a single model waveform to entire cluster rather than an individual voxel basis. *Chen et al., 2004; †excruciating, likely cause of suicide in academic setting.

21. Acknowledgements • fMRI group at Purdue • Prof. Talavage • Greg • Jordan • recent additions • Greg (again!!) for experimental data

22. References • K. J. Friston, P. J. Jezzard, and R. Turner, “Analysis of functional MRI time-series,” Hum. Brain Mapp., vol. 1, pp. 153-171, 1994. • N. Lange and S. L. Zeger, “Nonlinear fourier time series analysis for human brain mapping by functional magnetic resonance imaging,” J. Roy. Statist. Soc. Appl. Stat., vol. 46, pp. 1-29, 1997. • J. C. Rajapakse, F. Kruggel, J. M. Maisog, and D. Y. von Cramon, “Modeling hemodynamic response for analysis of functional MRI time-series,” Hum. Brain Mapp., vol. 6, pp. 283-300, 1998. • A. M. Dale and R. L. Buckner, “Selective averaging of rapidly presented individual trials using fMRI,” Hum. Brain Mapp., vol. 5, pp. 329-340, 1997. • P. Filzmoser, R. Baumgartner, and E. Moser, “A hierarchical clustering method for analyzing functional MR images,” Magn. Reson. Imag., vol. 17, pp. 817-826, 1999. • R. S. Menon, S. Ogawa, X. Hu, J. P. Strupp, P. Anderson, and K. Ugurbil, “BOLD based functional MRI at 4 Tesla includes a capillary bed contribution: echo-planar imaging correlates with previous optical imaging using intrinsic signals,” Magn. Reson. Med., vol. 33, pp. 453-459, 1995. • S. Chen, C. A. Bouman, and M. J. Lowe, “Clustered Components Analysis for Functional MRI,” IEEE Trans. Med. Imag., vol. 23, pp. 85-98, 2004.