Transcript Multi

Lecture series: Data analysis
Thomas Kreuz, ISC, CNR
[email protected]
http://www.fi.isc.cnr.it/users/thomas.kreuz/
Lectures: Each Tuesday at 16:00
(First lecture: May 21, last lecture: June 25)
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)
•
Simona Olmi: Synchronization & Collective dynamics
(September/October 2013)
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”
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
[ 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
Today’s lecture
• Example: Epileptic seizure prediction
• Data acquisition
• Introduction to dynamical systems
• Linear measures
Example:
Epileptic seizure prediction
Aim of time series analysis
detail
Past
(Analysis)
expand
Future
(Prediction)
Knowledge
- Compact description of data
- Interpretation
- Hypothesis testing
- Simulation
- Forecasting
- Control
(Example: Simplified Model)
(Examples: Seasonal regularities)
(Example: Global warming)
(Example: Estimate probability of catastrophic events)
(Example: Weather, stock market)
(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 techniques
Method
Surface EEG (Scalp)
ECoG (Brain surface)
Measurement device
Scalp electrodes
Subdural grid electrodes
Principle
Extracellular potential
Extracellular potential
What is actually measured?
mostly EPSPs and IPSPs, smaller
Temporal resolution
excellent, 1 ms
Spatial resolution
poor (spatially smoothed
in amplitude but long-lasting
average behavior)
spikes cancel out (very short,
~10 cm^2 surface
lowpass-filtered)
~r^4 (no depth)
Exception: Population spikes in
Pros
non-invasive
Cons
Distortion
Artefacts
excellent, 1 ms
much better
localization
invasive (epilepsy)
excellent, 1 ms
even better
localization
very invasive (epilepsy)
epileptic seiures (high synchrony)
Intracranial EEG
Depth electrodes
Extracellular potential
same as above
brain damage
MEG
SQUID (at ~ 3 K)
Magnetic fields
superconductive loop +
Intracellular currents
excellent, 1 ms
(complementary to EEG)
2 Josephson junctions
MRI
fMRI
PET
Receiver coil
Receiver coil
PET scanner (Sensor ring)
< 1 cm, up to 1 mm
non-invasive
source localization
better than EEG
no contact
still not very accurate
non-invasive
unspecific
no distortion
Disturbance of magnetic
Structure (different tissue,
Hydrogen dipoles via
different amount of water)
expensive
short RF energy pulses
No neuronal activity
inconvenient
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
Metabolism (Energy Production)
inferior to fMRI
non-invasive
unspecific
Radioactive compound
almost none (anatomy)
vastly improved
inferior to fMRI
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 ?
Patch-clamp
multi-photon laser scanning
Fluorescence photons
(mostly intracellular calcium
microscopy
after laser pulses
changes)
direct junction through pipette
Current waveforms can be
active properties of ion channels
improved
very high, ~0.1 mm
Brain slice preparations
Slices alive for some hours
Membrane potential
excellent, < 1 ms
excellent
controlled
compromises
environment
brain circuits
excellent, < 1 ms
pharmacological
compromises
specificity
brain circuits
great, tetrode electrodes
parallel
very invasive (epilepsy)
(Triangulation)
in vivo possible
brain damage
excellent
parallel
even more damaging
maximum
in vitro
Extracellular recordings
Multisite recordings
voltage-sensitive microelectrode
Cell isolation
multi-unit activity (theoretically up
sharp-tip or wire tetrode
Localization via Triangulation
to 1000, in practice <20)
Multi-Electrode-Array (MEA)
many recording sites but
multi-unit activity (> 100)
Silicon chip
small electrode volume
mostly surfaces
minimal damage
applied
Single-unit recordings
3D
excellent, < 1 ms
excellent, < 1 ms
in vivo possible
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)
Causes of brain disease
• Trauma: Physiological wound caused by an external
source
• Infections: Disease caused by the invasion of a microorganism 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
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.
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
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
Implanted electrodes
Epilepsy (inter-ictal EEG)
L
R
Epilepsy (ictal EEG)
L
R
Movie:
Absence
Movie:
Seizure
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
Microwire recordings in humans
Setup:
– 64 microwires (40 μm diameter) able to
record single-neuron-activity and LFPs
– Effective recording bandwidth 1 Hz - 10
kHz
Clinical contacts
Intracranial spike train data
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
Movie:
SPIKE-Distance
Data acquisition
Levels of measurement
•
Nominal data (=/≠)
- Fixed set of categories (labels)
Categorical
- Examples: Religion, favorite color, blood type
•
Ordinal data (=/≠, </>)
- Rank ordering possible, but no distance defined
Qualitative
- Example: Academic grades
•
Interval (=/≠, </>, +/-)
- Distance between attribute is defined
Qualitative
- Examples: Temperature in °C, calendar year
•
Ratio (=/≠, </>, +/-, x/÷)
- Absolute zero exists
Quantitative
- Examples: Temperature in K, height, weight, age
[Stanley Smith Stevens, 1946]
Levels of measurement II
[Trochim, 2006]
[Wharrad, 2004]
Types of data
• Profiles (samples) / Images (pixels) / Volumes
(voxels)
• Continuous data (time series) –
Discrete data (sequence of events)
• Univariate / bivariate / multivariate data
• …
Measurement
System / Object
Instrument
Environment
Beware: Interactions !
Signal
Data acquisition
System / Object
Sampling
Sensor
Amplifier
AD-Converter
Filter
Computer
Sampling
• Process of converting a signal (a function of continuous
time) into a numeric sequence (a function of discrete time).
• 𝑇 = (𝑥𝑡1 , 𝑥𝑡2 , 𝑥𝑡3 , … , 𝑥𝑡𝑁 )
• 𝑇 = (𝑥𝑖 , 𝑥𝑖+∆𝑡 , 𝑥𝑖+2∆𝑡 , … , 𝑥𝑖+
equally sampled
∆𝑡
𝑓𝑠 =
Sampling interval
1
∆𝑡
Sampling frequency
Time series
𝑁−1 ∆𝑡 )
Aliasing
Effect that causes different signals to become indistinguishable
(or aliases of one another) when sampled.
Math. reason: Folding at Nyquist frequency 𝑓𝑁 =
1
2∆𝑡
=
𝑓𝑆
2
• Solution for bandlimited signals: Sampling frequency should
𝑓𝑠
at least be twice the highest frequency ( 𝑓 < = 𝑓𝑁 ).
2
(Nyquist–Shannon sampling theorem)
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:
𝑞=
𝑟
210
 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 𝑥 ∈ ℛ 𝑛
• Evolution of state
- continuous (flow)
- discrete (map)
𝑑𝒙
𝑑𝑡
= 𝒇(𝒙, 𝑡, 𝜆)
𝒙𝑡+∆𝑡 = 𝑭(𝒙𝒕 , ∆𝑡, 𝜆)
𝜆 Control parameter
𝒇, 𝑭 can be both be linear or non-linear
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
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 nonproportional effects
Nonlinear systems are the rule, linear system is special case!
Today’s lecture
• Example: Epileptic seizure prediction
• Data acquisition
• Introduction to dynamical systems
Next lecture
Linear measures
Nonlinear measures
- Introduction: State space reconstruction
- Lyapunov exponent
- Dimensions
- Entropies
-…