Lecture series: Data analysis

Lectures: Each Tuesday at 16:00

(First lecture: May 21, last lecture: June 25)

Thomas Kreuz, ISC, CNR thomas.kreuz@cnr.it

http://www.fi.isc.cnr.it/users/thomas.kreuz/

• Stefano Luccioli: Neuronal models (February/March 2013)

• Roberto Livi / Alessandro Torcini: Dynamical systems theory (March-May 2013)

• Thomas Kreuz: Data analysis (May/June 2013)

• Simona Olmi: Synchronization & Collective dynamics (September/October 2013)

Other 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”

This lecture series

• 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

Schedule

• 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

[ Literature ]

• Example: Epileptic seizure prediction

• Data acquisition

• Introduction to dynamical systems

• Linear measures

Today’s lecture

Example:Epileptic seizure prediction

Aim of time series analysis

Knowledge

detail

expand Future(Prediction)

Past(Analysis)

- 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)

Data (especially time series)• Meteorology

• Astronomy

• Seismology

• Economy

• …

• Medicine - Cardiology - … - Neurology

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

Medical measurement techniquesMethod Measurement device Principle What is actually measured? Temporal resolution Spatial resolution Pros Cons

Surface EEG (Scalp) Scalp electrodes Extracellular potential mostly EPSPs and IPSPs, smaller excellent, 1 ms poor (spatially smoothed non-invasive Distortion

in amplitude but long-lasting average behavior) Artefacts

spikes cancel out (very short, ~10 cm^2 surface

lowpass-filtered) ~r^4 (no depth)

ECoG (Brain surface) Subdural grid electrodes Extracellular potential Exception: Population spikes in excellent, 1 ms much better localization invasive (epilepsy)

epileptic seiures (high synchrony)

Intracranial EEG Depth electrodes Extracellular potential same as above excellent, 1 ms even better localization very invasive (epilepsy)

brain damage

MEG SQUID (at ~ 3 K) Magnetic fields Intracellular currents excellent, 1 ms < 1 cm, up to 1 mm non-invasive source localization

superconductive loop + (complementary to EEG) better than EEG no contact still not very accurate

2 Josephson junctions no distortion

MRI Receiver coil Disturbance of magnetic Structure (different tissue, almost none (anatomy) vastly improved non-invasive unspecific

Hydrogen dipoles via different amount of water) expensive

short RF energy pulses No neuronal activity inconvenient

fMRI Receiver coil BOLD-effect Metabolism (Energy Production) very slow, delay 0.5 s vastly improved non-invasive unspecific

(Blood Oxygenation Level) Indirect: neuronal activity no temporal sequencing (brain mapping possible) localization expensive

but very unspecific of information flow of cognition inconvenient

PET PET scanner (Sensor ring) Radioactive compound Metabolism (Energy Production) inferior to fMRI inferior to fMRI non-invasive unspecific

accumulates, positrions expensive

annihilate emitting 2 photons inconvenient

in 180deg

Optical Imaging Microscope, photo detector Voltage-sensitive dyes unspecific improved very high, ~0.1 mm minimal damage only surfaces

input/output ?

multi-photon laser scanning Fluorescence photons (mostly intracellular calcium improved very high, ~0.1 mm 3D mostly surfaces

microscopy after laser pulses changes) minimal damage

Patch-clamp direct junction through pipette Current waveforms can be active properties of ion channels excellent, < 1 ms excellent controlled compromises

applied environment brain circuits

Single-unit recordings Brain slice preparations Slices alive for some hours Membrane potential excellent, < 1 ms maximum pharmacological compromises

in vitro specificity brain circuits

Extracellular recordings voltage-sensitive microelectrode Cell isolation multi-unit activity (theoretically up excellent, < 1 ms great, tetrode electrodes parallel very invasive (epilepsy)

sharp-tip or wire tetrode Localization via Triangulation to 1000, in practice <20) (Triangulation) in vivo possible brain damage

Multisite recordings Multi-Electrode-Array (MEA) many recording sites but multi-unit activity (> 100) excellent, < 1 ms excellent parallel even more damaging

Silicon chip small electrode volume in vivo possible

• 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)

Medical time series

• 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

Causes of brain disease

• 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.

Brain diseases

~ 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

Epilepsy

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

Epilepsy surgery

Implanted electrodes

Epilepsy (inter-ictal EEG)

L

R

Epilepsy (ictal EEG)

L

R

Movie:Absence

Movie:Seizure

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

Epileptic seizure prediction

Microwire recordings in humans

– 64 microwires (40 μm diameter) able torecord single-neuron-activity and LFPs

– Effective recording bandwidth 1 Hz - 10 kHz

Clinical contacts

Setup:

Intracranial spike train data

Motivation: Spike train synchronySynchronization 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

Movie:SPIKE-Distance

Data acquisition

• 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]

Levels of measurement

Levels of measurement II

[Trochim, 2006]

[Wharrad, 2004]

• Profiles (samples) / Images (pixels) / Volumes

(voxels)

• Continuous data (time series) – Discrete data (sequence of events)

• Univariate / bivariate / multivariate data

• …

Types of data

Measurement

System / Object Instrument

Environment

Signal

Beware: Interactions !

Data acquisition

Sensor

System / Object

Amplifier AD-Converter

Computer

Filter

Sampling

Sampling• Process of converting a signal (a function of continuous

time) into a numeric sequence (a function of discrete time).

• Time series

equally sampled

• Example: sufficient sampling of sine wave (2 sampling values per cycle)

Sampling interval

Sampling frequency

Aliasing

• Solution for bandlimited signals: Sampling frequency should at least be twice the highest frequency ().

(Nyquist–Shannon sampling theorem)

Effect that causes different signals to become indistinguishable (or aliases of one another) when sampled.Math. reason: Folding at Nyquist frequency

Filtering

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:

- Lowpass filter Local field potential (LFP) - Highpass filter Multi-unit activity

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

Introduction to dynamical systems

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

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

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)

Non-linear systems

Violation of strong causality

Similar causes can have different effects

Sensitive dependence on initial conditions

(Deterministic chaos)

Linearity / Non-linearity

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!

Linear systems- have simple solutions- Changes of parameters and initial

conditions lead to proportional effects

• Example: Epileptic seizure prediction

• Data acquisition

• Introduction to dynamical systems

Today’s lecture

Linear measures

Nonlinear measures

- Introduction: State space reconstruction

- Lyapunov exponent

- Dimensions

- Entropies

- …

Next lecture