Justin Dauwels LIDS, MIT LMI, Harvard Medical School

1. Machine learning techniques for quantifying neural synchrony:application to the diagnosis of Alzheimer's diseasefrom EEG Justin Dauwels LIDS, MIT LMI, Harvard Medical School Amari Research Unit, Brain Science Institute, RIKEN June 9, 2008

2. RIKEN Brain Science Institute • RIKEN Wako Campus (near Tokyo) • about 400 researchers and staff (20% foreign) • 300 research fellows and visiting scientists • about 60 laboratories • research covers most aspects of brain science Collaborators François Vialatte*, Theo Weber+, Shun-ichiAmari*, AndrzejCichocki* (*RIKEN, +MIT) Project Early diagnosis of Alzheimer’s disease based on EEG Financial Support

3. Research Overview Machine learning & signal processing for applications in NEUROSCIENCE = development of ALGORITHMS to analyze brain signals • EEG (RIKEN, MIT, MGH) • diagnosis of Alzheimer’s disease • detection/prediction of epileptic seizures • analysis of EEG evoked by visual/auditory stimuli • EEG during meditation • projects related to brain-computer interface (BMI) • Calcium imaging (RIKEN, NAIST, MIT) • effect of calcium on neural growth • role of calcium propagation in gliacells and neurons • Diffusion MRI (Brigham&Women’s Hospital, Harvard Medical School, MIT) • estimation and clustering of tracts (future project) subject of this talk

4. Overview • Alzheimer’s Disease (AD) • EEG of AD patients: decrease in synchrony • Synchrony measure in time-frequency domain • Pairs of EEG signals • Collections of EEG signals • Numerical Results • Outlook

5. Alzheimer's disease Outside glimpse: clinical perspective Evolution of the disease (stages) One disease, many symptoms EEG data • 2 to 5 years before • mild cognitive impairment (often unnoticed) • 6 to 25 % progress to Alzheimer's per year memory, language, executive functions, apraxia, apathy, agnosia, etc… • Mild (early stage) • becomes less energetic or spontaneous • noticeable cognitive deficits • still independent (able to compensate) Memory (forgetting relatives) • Moderate (middle stage) • Mental abilities decline • personality changes • become dependent on caregivers Apathy • Severe (late stage) • complete deterioration of the personality • loss of control over bodily functions • total dependence on caregivers Loss of Self-control • 2% to 5% of people over 65 years old • up to 20% of people over 80 • Jeong 2004 (Nature) Video sources: Alzheimer society

6. Alzheimer's disease Inside glimpse: brain atrophy amyloid plaques and neurofibrillary tangles Video source: Alzheimer society Images: Jannis Productions. (R. Fredenburg; S. Jannis) Video source: P. Thompson, J.Neuroscience, 2003

7. Overview • Alzheimer’s Disease (AD) • EEG of AD patients: decrease in synchrony • Synchrony measure in time-frequency domain • Pairs of EEG signals • Collections of EEG signals • Numerical Results • Outlook

8. Alzheimer's disease Inside glimpse: abnormal EEG EEG system: inexpensive, mobile, useful for screening Brain “slow-down” slow rhythms (0.5-8 Hz) fast rhythms (8-30 Hz) (Babiloni et al., 2004; Besthorn et al., 1997; Jelic et al. 1996, Jeong 2004; Dierks et al., 1993). focus of this project Decrease of synchrony • AD vs. MCI (Hogan et al. 203; Jiang et al., 2005) • AD vs. Control (Hermann, Demilrap, 2005, Yagyu et al. 1997; Stam et al., 2002; Babiloni et al. 2006) • MCI vs. mildAD(Babiloni et al., 2006). Images: www.cerebromente.org.br

9. Spontaneous (scalp) EEG Time-frequency |X(t,f)|2 (wavelet transform) f (Hz) Time-frequency patterns (“bumps”) Fourier |X(f)|2 Fourier power t (sec) amplitude EEG x(t)

10. Fourier transform 2 3 1 3 2 1 Frequency High frequency Low frequency

11. Windowed Fourier transform = * Fourier basis functions Window function windowed basis functions f Windowed Fourier Transform t

12. Spontaneous EEG Time-frequency |X(t,f)|2 (wavelet transform) f (Hz) Time-frequency patterns (“bumps”) Fourier |X(f)|2 Fourier power t (sec) amplitude EEG x(t)

13. Signatures of local synchrony f (Hz) Time-frequency patterns (“bumps”) EEG stems from thousands of neurons bump if neurons are phase-locked = local synchrony t (sec)

14. Alzheimer's disease Inside glimpse: abnormal EEG EEG system: inexpensive, mobile, useful for screening Brain “slow-down” slow rhythms (0.5-8 Hz) fast rhythms (8-30 Hz) (Babiloni et al., 2004; Besthorn et al., 1997; Jelic et al. 1996, Jeong 2004; Dierks et al., 1993). focus of this project Decrease of synchrony • AD vs. MCI (Hogan et al. 203; Jiang et al., 2005) • AD vs. Control (Hermann, Demilrap, 2005, Yagyu et al. 1997; Stam et al., 2002; Babiloni et al. 2006) • MCI vs. mildAD(Babiloni et al., 2006). Images: www.cerebromente.org.br

15. Overview • Alzheimer’s Disease (AD) • EEG of AD patients: decrease in synchrony • Synchrony measure in time-frequency domain • Pairs of EEG signals • Collections of EEG signals • Numerical Results • Outlook

16. Comparing EEG signal rhythms ? 2 signals PROBLEM I: Signals of 3 seconds sampled at 100 Hz ( 300 samples) Time-frequency representation of one signal = about 25 000 coefficients

17. One pixel Numerous neighboringpixels Comparing EEG signal rhythms ?(2) PROBLEM II: Shifts in time-frequency!

18. Sparse representation: bump model f(Hz) f(Hz) Bumps Sparse representation t (sec) f(Hz) t (sec) 104- 105 coefficients • Assumptions: • time-frequency map is suitable representation • oscillatory bursts (“bumps”) convey key information t (sec) about 102 parameters Normalization: F. Vialatte et al. “A machine learning approach to the analysis of time-frequency maps and its application to neural dynamics”, Neural Networks (2007).

19. Similarity of bump models... How “similar”or “synchronous”are two bump models? = GLOBAL synchrony Reminder: bumps due to LOCAL synchrony = MULTI-SCALE approach

20. ... by matching bumps y2 y1 Some bumps match Offset between matched bumps SIMILAR bump models if: Many matches Strongly overlapping matches

21. ... by matching bumps (2) • Bumps in one model, but NOT in other • → fraction of “spurious” bumps ρspur • Bumps in both models, but with offset • → Average time offset δt(delay) • → Timing jitter with variance st • → Average frequency offset δf • → Frequencyjitter with variance sf • Synchrony: only st and ρspur relevant Stochastic Event Synchrony (SES) =(ρspur,δt,st, δf, sf) PROBLEM: Given two bump models, compute (ρspur,δt,st, δf, sf)

22. Overview • Alzheimer’s Disease (AD) • EEG of AD patients: decrease in synchrony • Synchrony measure in time-frequency domain • Pairs of EEG signals • Collections of EEG signals • Numerical Results • Outlook

23. Average synchrony 3. SES for each pair of models 4. Average the SES parameters Group electrodes in regions Bump model for each region

24. Beyond pairwise interactions... Multi-variate similarity Pairwise similarity

25. ...by clustering HARD combinatorial problem! y2 y1 y3 y4 y5 • Models similar if • few deletions/large clusters • little jitter y2 y1 y3 y4 y5 Constraint: in each cluster at most one bump from each signal

26. Overview • Alzheimer’s Disease (AD) • EEG of AD patients: decrease in synchrony • Synchrony measure in time-frequency domain • Pairs of EEG signals • Collections of EEG signals • Numerical Results • Outlook

27. EEG Data • EEG of 22 Mild Cognitive Impairment (MCI) patients and 38 age-matched • control subjects (CTR) recorded while in rest with closed eyes • →spontaneous EEG • All 22 MCI patients suffered from Alzheimer’s disease (AD) later on • Electrodes located on 21 sites according to 10-20 international system • Electrodes grouped into 5 zones (reduces number of pairs) • 1 bump model per zone • Used continuous “artifact-free” intervals of 20s • Band pass filtered between 4 and 30 Hz EEG data provided by Prof. T. Musha

28. Similarity measures • Correlation and coherence • Granger causality (linear system): DTF, ffDTF, dDTF, PDC, PC, ... • Phase Synchrony: compareinstantaneous phases (wavelet/Hilbert transform) • State space based measures • sync likelihood, S-estimator, S-H-N-indices, ... • Information-theoretic measures • KL divergence, Jensen-Shannon divergence, ... FREQUENCY TIME No Phase Locking Phase Locking

30. Sensitivity (average synchrony) Corr/Coh Granger Info. Theor. State Space Phase SES Mann-Whitney test: small p value suggests large difference in statistics of both groups Significant differences for ffDTF and ρ!

31. Classification ffDTF • Clearseparation, but not yet useful as diagnostic tool • Additionalindicators needed (fMRI, MEG, DTI, ...) • Can be used for screening population (inexpensive, simple, fast)

32. Correlations Strong (anti-) correlations „families“ of sync measures

33. Overview • Alzheimer’s Disease (AD) • EEG of AD patients: decrease in synchrony • Synchrony measure in time-frequency domain • Pairs of EEG signals • Collections of EEG signals • Numerical Results • Outlook

34. Ongoing work no stimulus no stimulus stimulus high st low st high st high st low st high st Time-varying similarity parameters st

35. Future work f(Hz) coupling between frequency bands t (sec) Matching event patterns instead of single events = allows us to extract patterns in time-frequency map of EEG! HYPOTHESIS: Perhaps specific patterns occur in time-frequency EEG maps of AD patients before onset of epileptic seizures REMARK: Such patterns are ignored by classical approaches: STATIONARITY/AVERAGING!

36. Conclusions Measure for similarity of point processes („stochastic event synchrony“) Key idea: alignment of events Solved by statistical inference Application: EEG synchrony of MCI patients About 85% correctly classified; perhaps useful for screening population Ongoing/future work: time-varying SES, extracting patterns of bumps

37. References + software Software MATLAB implementation of the synchrony measures References Quantifying Statistical Interdependence by Message Passing on Graphs: Algorithms and Application to Neural Signals, Neural Computation (under revision) A Comparative Study of Synchrony Measures for the Early Diagnosis of Alzheimer's Disease Based on EEG, NeuroImage (under revision) Measuring Neural Synchrony by Message Passing, NIPS 2007 Quantifying the Similarity of Multiple Multi-Dimensional Point Processes by Integer Programming with Application to Early Diagnosis of Alzheimer's Disease from EEG, EMBC 2008 (submitted)

38. Machine learning techniques for quantifying neural synchrony:application to the diagnosis of Alzheimer's diseasefrom EEG Justin Dauwels LIDS, MIT LMI, Harvard Medical School Amari Research Unit, Brain Science Institute, RIKEN June 9, 2008

39. Machine learning for neuroscience Multi-scale in time and space Data fusion: EEG, fMRI, spike data, bio-imaging, ... Large-scale inference Visualization Behavior ↔ Brain ↔ Brain Regions ↔ Neural Assemblies ↔ Single neurons ↔ Synapses ↔ Ion channels

40. Estimation Simple closed form expressions Deltas: average offset Sigmas: var of offset artificial observations (conjugate prior) ...where

41. Large-scale synchrony Apparently, all brain regions affected...

42. Alzheimer's disease Outside glimpse: the future (prevalence) USA (Hebert et al. 2003) • 2% to 5% of people over 65 years old • Up to 20% of people over 80 • Jeong 2004 (Nature) Million of sufferers World (Wimo et al. 2003) Million of sufferers

43. Ongoing and future work Applications • Fluctuations of EEG synchrony • Caused by auditory stimuli and music (T. Rutkowski) • Caused by visual stimuli (F. Vialatte) • Yoga professionals (F. Vialatte) • Professional shogi players (RIKEN & Fujitsu) • Brain-Computer Interfaces (T. Rutkowski) • Spike data from interacting monkeys (N. Fujii) • Calcium propagation in gliacells (N. Nakata) • Neural growth (Y. Tsukada & Y. Sakumura) • ... Algorithms • alternative inference techniques (e.g., MCMC, linear programming) • time dependent (Gaussian processes) • multivariate (T.Weber)

44. Adaptation After adaptation Initialisation Bump Fitting bump models  Signal gradient method F. Vialatte et al. “A machine learning approach to the analysis of time-frequency maps and its application to neural dynamics”, Neural Networks (2007).

45. Boxplots • SURPRISE! • No increase in jitter, but significantly lessmatched activity! • Physiological interpretation • neural assemblies more localized? • harder to establish large-scale synchrony?

46. Similarity of bump models... How “similar”or “synchronous”are two bump models?

47. Probabilistic inference POINT ESTIMATION: θ(i+1) = argmaxx log p(y, y’, c(i+1),θ) Uniform prior p(θ): δt, δf= average offset, st, sf= variance of offset Conjugate prior p(θ): still closed-form expression Other kind of prior p(θ): numerical optimization (gradient method)

48. Probabilistic inference MATCHING: c(i+1)= argmaxc log p(y, y’, c, θ(i)) EQUIVALENT to (imperfect) bipartite max-weight matching problem c(i+1) = argmaxc log p(y, y’, c, θ(i)) = argmaxc Σkk’wkk’(i)ckk’ s.t. Σk’ ckk’ ≤ 1and Σk ckk’ ≤ 1 and ckk’ 2{0,1} find heaviest set of disjoint edges not necessarily perfect • ALGORITHMS • Polynomial-time algorithms gives optimal solution(s) (Edmond-Karp and Auction algorithm) • Linear programming relaxation: extreme points of LP polytope are integral • Max-product algorithmgives optimal solution if unique [Bayati et al. (2005), Sanghavi (2007)]

49. Max-product algorithm MATCHING: c(i+1)= argmaxc log p(y, y’, c, θ(i)) Generative model p(y, y’, c, θ) /I(c) pθ(θ) Πkk’(N(t k’ – tk ;δt ,st,kk’)N(f k’ – fk ;δf ,sf, kk’)β-2)ckk’

50. Max-product algorithm MATCHING: c(i+1)= argmaxc log p(y, y’, c, θ(i)) Conditioning on θ μ↓ μ↓ μ↑ μ↑