Lecture series: Data analysis

1. Lecture series: Data analysis Thomas Kreuz, ISC, CNR thomas.kreuz@cnr.it http://www.fi.isc.cnr.it/users/thomas.kreuz/ Lectures: Each Tuesday at 16:00 (First lecture: May 21, last lecture: June 25)

2. Other lecture series • Stefano Luccioli: Neuronal models (February/March 2013) • Roberto Livi / Alessandro Torcini: • Dynamical systems theory (March-May 2013) • Thomas Kreuz: Data analysis (May/June 2013) • SimonaOlmi: Synchronization & Collective dynamics • (September/October 2013)

3. This lecture series • Introduction to data / time series analysis • Univariate:Measures for individual time series • - Linear time series analysis: Autocorrelation, Fourier spectrum • - Nonlinear time series analysis: Lyapunov exponent, Dimension, Entropy • Bivariate:Measures for two time series • - Measures of synchronization for continuous data (e.g., EEG) • cross correlation, coherence, mutual information, phase synchronization, • nonlinear interdependence • - Measures of directionality: Granger causality, transfer entropy • - Measures of synchronization for discrete data (e.g., spike trains): • Victor-Purpura distance, van Rossum distance, event synchronization, • ISI-distance, SPIKE-distance • Multivariate:Measures of synchronization for multi-neuron data • Victor-Purpura and van Rossum population extensions • Applications to electrophysiological signals • (in particular single-unit data and EEG from epilepsy patients) • Epilepsy – “window to the brain”

4. Schedule • Lecture 1: Example (Epilepsy & spike train synchrony), • Data acquisition, Dynamical systems • Lecture 2: Linear measures, Introduction to non-linear • dynamics • Lecture 3: Non-linear measures • Lecture 4: Measures of continuous synchronization • Lecture 5: Measures of discrete synchronization • (spike trains) • Lecture 6: Measure comparison & Application to epileptic • seizure prediction

5. [ Literature ] • H. Kantz, T. Schreiber: • Nonlinear Time Series Analysis • Cambridge University Press, Cambridge, 2003 • H. Abarbanel: • Analysis of Observed Chaotic Data • Springer, 1997. • A. Pikovsky, M. Rosenblum, J. Kurths: • Synchronization. A Universal Concept in Nonlinear Sciences • Cambridge University Press, Cambridge, 2001 • PhD thesis Thomas Kreuz (see homepage) • http://webarchiv.fz-juelich.de/nic-series//volume21/nic-series-band21.pdf • Acknowledgements: Lecture series Klaus Lehnertz, University of Bonn • Florian Mormann, University of Bonn

6. Today’s lecture • Example: Epileptic seizure prediction • Data acquisition • Introduction to dynamical systems • Linear measures

7. Example: Epileptic seizure prediction

8. Aim of time series analysis Past (Analysis) detail Knowledge Future (Prediction) expand • - Compact description of data (Example: Simplified Model) • - Interpretation (Examples: Seasonal regularities) • - Hypothesis testing (Example: Global warming) • - Simulation (Example: Estimate probability of catastrophic events) • - Forecasting (Example: Weather, stock market) • - Control (Example: Avoid outliers)

9. Data (especially time series) • Meteorology • Astronomy • Seismology • Economy • … • Medicine • - Cardiology • - … • - Neurology

10. Prediction of extreme events • Meteorology: Storms, Tornados, … • Astronomy: Solar eruptions / sun flares • Seismology: Earth quakes • Economy: Stock market crashes, “Black Friday” • … • Medicine • - Cardiology: Heart attack • - … • - Neurology: Epileptic seizure

12. Medical measurement techniques

13. Medical time series • Electrocardiogram (ECG) - transthoracic measurement of the electrical activity of the heart • Electromyography (EMG) - electrical activity produced by skeletal muscles • Electrooculography (EOG) - measures the resting potential of the retina • Electroretinography (ERG) - electrical responses of various cell types in the retina (including the photoreceptors) to stimuli • Electronystagmography (ENG) - diagnostic test to record involuntary movements of the eye • Electrogastrogram (EGG) - electrical signals that travel through the stomach muscles • Electrocorticogram (ECoG) - electrical activity from the cerebral cortex (brain surface) • Electroencephalogram (EEG)- voltage fluctuations due to ionic current flows within the neurons of the brain (surface / intracranial)

14. Causes of brain disease • Trauma: Physiological wound caused by an external source • Infections: Disease caused by the invasion of a micro-organism or virus • Degeneration: progressive loss of structure or function of neurons, including death of neurons • Tumors: Abnormal growth of body tissue • Autoimmune disorders: Immune system attacks and destroys healthy body tissue • Stroke: Interruption of the blood supply to the brain

15. Brain diseases • Alzheimer’s: Progressive cognition deterioration, ultimate cause unknown • Attention deficit/hyperactivity disorder(ADHD): caused by structural and biochemical imbalance • Encephalitis: Inflammation of the brain • Huntington's disease: Degenerative neurological disorder that is inherited, affects muscle coordination. • Locked-in syndrome: Lesion on the brain stem (complete paralysis). • Meningitis: Inflammation of the protective membranes covering the brain and spinal cord • Multiple sclerosis: Chronic, inflammatory demyelinating disease, meaning that the myelin sheath of neurons is damaged • Parkinson's: Death of dopamine-generating cells in the substantia nigra, a region of the midbrain (cause unknown) • Tourette's syndrome: Tics (not only vocal), genetical factors, inherited • Epilepsy: Seizures, resulting from abnormal, hypersynchronous neuronal activity in the brain.

16. Epilepsy • ~ 1 % of world population suffers from epilepsy • ~ 70 % can be treated with antiepileptic drugs • ~ 22 % cannot be treated sufficiently • ~ 8 % might profit from epilepsy surgery • Epilepsy Center Bonn: • presurgical evaluations: 160 cases / year • invasive evaluations: 60 - 70 cases / year

17. Epilepsy surgery Presurgical evaluation - exact localization of seizure generating area (epileptic focus) current gold standard: EEG recording of seizure origin - exact delineation from functionally relevant areas - Estimation of post-operative status (seizure control, neuropsychological deficits, ...) Surgical intervention - Tailored resection of epileptic focus

18. Implanted electrodes

19. L R Epilepsy (inter-ictal EEG)

20. L R Epilepsy (ictal EEG)

21. Movie: Absence

22. Movie: Seizure

23. Epileptic seizure prediction • Motivation / Open questions • Does a pre-ictal state exist (ictus = seizure)? • Do characterizing measures allow a reliable detection of this state? • Goals / perspectives • Increasing the patient‘s quality of life • Therapy on demand (Medication, Prevention) • Understanding seizure generating processes

24. Clinical contacts Microwire recordings in humans • 64 microwires (40 μm diameter) able to • record single-neuron-activity and LFPs • Effective recording bandwidth 1 Hz - 10 kHz Setup:

25. Intracranial spike train data

26. Motivation: Spike train synchrony Synchronization is a key feature for establishing the communication between different regions of the brain. Epilepsy results from abnormal, hypersynchronous neuronal activity in the brain. Accessible brain time series: iEEG (standard) and neuronal spike trains (recent) EEG-Observation: Drop of synchrony before epileptic seizure (so far not clinically sufficient) Open question: What happens on the neuronal level? Needed: Real-time measure of spike train synchrony

27. Movie: SPIKE-Distance

28. Data acquisition

29. Levels of measurement • Nominal data (=/≠) Categorical • - Fixed set of categories (labels) • - Examples: Religion, favorite color, blood type • Ordinal data (=/≠, </>)Qualitative • - Rank ordering possible, but no distance defined • - Example: Academic grades • Interval(=/≠, </>, +/-) Qualitative • - Distance between attribute is defined • - Examples: Temperature in °C, calendar year • Ratio(=/≠, </>, +/-, x/÷) Quantitative • - Absolute zero exists • - Examples: Temperature in K, height, weight, age • [Stanley Smith Stevens, 1946]

30. Levels of measurement II [Trochim, 2006] [Wharrad, 2004]

31. Types of data • Profiles (samples) / Images (pixels) / Volumes (voxels) • Continuous data (time series) – • Discrete data (sequence of events) • Univariate / bivariate / multivariate data • …

32. Measurement Signal System / Object Instrument Environment Beware: Interactions !

33. Data acquisition AD-Converter Amplifier Sampling Sensor System / Object Computer Filter

34. Sampling • Process of converting a signal (a function of continuoustime) into a numeric sequence (a function of discretetime). • Time series • equally sampled • Example: sufficient sampling of sine wave (2 sampling values per cycle) Sampling interval Sampling frequency

35. Aliasing Effect that causes different signals to become indistinguishable (or aliases of one another) when sampled. Math. reason: Folding at Nyquist frequency • Solution for bandlimited signals: Sampling frequency should at least be twice the highest frequency (). • (Nyquist–Shannon sampling theorem)

36. Filtering

37. Filtering: Examples • Anti-aliasing filter (lowpass) • Anti-hum filter (notch for 50/60 Hz powerline) • [Artifact: undesired alteration in data, introduced by a • technology and/or technique] • Recording from extracellular microelectrode: • - Lowpassfilter  Local field potential (LFP) • - Highpass filter  Multi-unit activity

38. Analog-Digital-Conversion • Defines data precision • Example: 10 bit ADC • - Voltage: 0-r (range) • - Unit value: •  Quantification error = q/2 • Important: • Optimal adjustment of signal via amplifier

39. Introduction to dynamical systems

40. Dynamical system • System with force (greek ‘dynamo’: dunamio) • State of system dependent on time • Change of state dependent on current state • - deterministic: same circumstance  same evolution • - stochastic: same circumstance  random evolution • probability distribution dependent on current state

41. Dynamical system • Described by time-dependent states • Evolution of state • - continuous (flow) • - discrete (map) • can be both be linear or non-linear • Example: sufficient sampling of sine wave (2 sampling values per cycle) Control parameter

42. Linear systems • Weak causality • identical causes have the same effect • (strong idealization, not realistic in experimental situations) • Strong causality • similar causes have similar effects • (includes weak causality • applicable to experimental situations, small deviations in • initial conditions; external disturbances)

43. Non-linear systems Violation of strong causality Similar causes can have different effects Sensitive dependence on initial conditions (Deterministic chaos)

44. Linearity / Non-linearity • Linear systems • have simple solutions • Changes of parameters and initial conditions lead to proportional effects • Non-linear systems • can have complicated solutions • Changes of parameters and initial conditions lead to non-proportional effects • Nonlinear systems are the rule, linear system is special case!

45. Today’s lecture • Example: Epileptic seizure prediction • Data acquisition • Introduction to dynamical systems

46. Next lecture • Linear measures • Nonlinear measures • - Introduction: State space reconstruction • - Lyapunov exponent • - Dimensions • - Entropies • - …