1.Stroke Detection Based on the Scaling Properties of Human EEG Rudolph C. Hwa University of Oregon Frontier Science 2003 Pavia, Italy September 2003

2. Outline Electroencelphalogram (EEG) Detrended fluctuation analysis (DFA) Moment analysis Stroke index Global properties Origin of scaling behavior 3. My collaborator Thomas Ferree Dept of Radiology University of California at San Francisco PhD in nuclear theory Now, an Assistant Prof. in Neuroscience Our goal: to learn about the Human Brain from physicists perspective 4. A cross section of the human brain 5. Usual method of studying stroke Radiological Imaging: MRI Massive, immobile, expensive, limited access Static properties of damaged tissues Often wait 10-24 hr for MRI report, yet only 3hr window for drug treatment. Takes an expert to interpret 6. normal stroke Luu et al, J.Clinical Neurophy. (01)Hornak, textbook on MRI 7. Our proposal: Hwa & Ferree, PRE (02); Ferree & Hwa, Neurocomputing (02); Hwa, He & Ferree, J. Int. Neuroscience (03); Ferree & Hwa, J. Clin. Neurophysiology (03) EEG Light, portable, inexpensive, rapid Can be used in hospital room, ambulance, home Spatial-temporal properties An index can be read by non-experts (like a thermometer) 8. Acquiring the Scalp EEG 129 electrodes, including reference at vertex Good enough resolution for study of spatial variability 9. Approximately 107 aligned pyramidal neurons per cm2 . Each electrode integrates over 10-100 cm3 of electrical activities. 10. EEG signals are mainly from the cortex which are strongly affected by the subcortical fibers 11. Electroencephalogram (EEG) = Scalp Potential 12. Human EEG time series 13. Resting EEG: Fourier Analysis 14. Detrended Fluctuation Analysis (DFA) DNA, Peng,Buldyrev,Havlin,Simons,Stanley,Goldberger, PRE(94). Heartbeat, Peng,Havlin,Stanley,Golberger, Chaos (95). Many, many other fields. Study fluctuations from the semi-local trends Divide a time series y(t) into bins Y(t) t k 2k 3k 15. 0 20 40 60 80 100 120 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 Local Linear Fits for Channel 2 V(V) Time Index Perform linear fit of y(t) in each bin trend Calculate variance from the trend Fb 2 (k) Average over all bins RMS fluctuation F(k) k 2k 3k 4k 16. How does F(k) depend on k? If there is no scale of significance, we expect scaling. F(k) k But there are regularities in some channels. 10 Hz No obvious regularity Underlying oscillation in the band 8-13 Hz 17. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -20 0 20 40 60 80 100 t (sec) y(V) Ch 1 Ch 2 Ch 3 Scaling behavior in human EEG F k Power law behavior: in two regions 1 , 2 Frequency in the band 18. Although the scaling behaviors are not over large ranges, these are properties that characterize the human EEG. Usual DFA treats integrated time series. Our time series are not integrated first. Since y(t) is bounded, F(k) will saturate at asymptotic k, thus 2 eventually becomes 0. But our time series is only 10 s long. So k never gets to be very large: k < 1.25 s. Our result: {1 , 2} for each channel. 19. 0 0.5 1 1.5 2 2.5 x 10 4 -40 -20 0 20 40 60 80 100 Time Index V(V) 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 -1 -0.5 0 0.5 1 1.5 ln k lnF Random walk = 0.5 EEG scaling behavior: > 0.5 (positive correlations) < 0.5 (anti-correlation) 20. Subject A 128 channels Scatter plot Summary of temporal fluctuations 21. We have 128 pairs of {1, 2} for each subject. Extracted from time series of each channel Spatially distributed over the scalp We can make topographical plots to see the spatial distribution. But unless we know what {1, 2} means, they only raise other questions. Spatial Distribution 22. 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 2 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Scalp topography of scaling exponents 1 2 What do the peaks and valleys mean? How to compare different topographies efficiently? How to define/quantify global brain state? 23. Distributions of Scaling Exponents Gq = 1 N j q j=1 N = Pmm q m=1 M Mq = Gq G1( ) q Define moments of distributions Normalize each moment by the mean 24. Mq (i) e iq q 5 q dependences of the moments Comparison across subjects 18 normal subjects 10 stroke subjects 25. = 2 1 Nq e q Correlation between 1 & 2 Define slope of scatter plot: Determine distribution Calculate moments of 26. = 2 / 1( ) 27. Stroke subjects have, on average, larger and 28. Stroke subjects have smaller relative fluctuations 29. Define stroke index S S = 1 2 1 2 + 0.156 2 2 2 2 S=1.3 Normal subjects have S>1.3 30. S can serve as a stroke index 31. EEG of a subject in sleep 0 40 min 32. In MRI one sees the effect of a stroke to be local. In EEG: S is smaller for stroke subjects, but makes no reference to the spatial distribution. Our claim is that the electrical responses to a stroke are global. We need another measure A to quantify 1 and 2 collectively: A = 1 + 52 Then study P(A) across channels, and across subjects. 33. =1.19 Distributions in A How does become large for the stroke subjects? It is not due to larger 1 and 2 in a few channels. The effect is global. for stroke is roughly twice the for normal. Across subjects acrosssubjects across channels 34. What do the scaling exponents mean? Origin of the scaling behavior Dynamical models of the brain Mathematical models of the time series Short time series (10 s) with 2 scaling regions Model x(t) = sint + a(t) y(t) = d t x( t )t R t (t) fluctuations: correlated to previous steps 1 > 0.5 anti-correlated to previous steps 1 < 0.5 35. R>100 (large A) 36. The time series must involve an integration of a few previous steps (R1/4 sec) in order to develop significant . Stroke subjects generally have larger . What we have here is a quantification of the familiar phenomenon of a slow-down. Does the integration correspond to some slurring of the brain activity for the stroke subjects? 37. Conclusion EEG is a simple and inexpensive way to collect data. Scaling analysis yields a stroke index S. use S to detect or monitor stroke. Stroke effect is global. contrary to conventional wisdom. A possible way to define a brain state. a major unexplored area. Need effective communication to neuroscientists.