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Stiliyan Kalitzin, Epilepsy Institute of The Netherlands (SEIN)

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State transitions in the epileptic brain

Stiliyan Kalitzin,

Epilepsy Institute of The Netherlands (SEIN)

Central Didactic Question 1:

Why do epileptic seizures occur ?

This question is not about :

What are epileptic seizures ?

What causes epilepsy ? (neural loss, channel protein mutations, etc)

This question is about:

Autonomous transitions to epileptic type of activity and back

- Why is this question relevant for ISPWxx ?
- Trial-and error “neuro-phenomenology” approach has its limits. To understand prediction, predictability and to be able to actually predict seizures we need to know how do they set on.
- Even more so, to avoid, stop or contain the seizure onset we need to know what are we dealing with.
- On a more “mundane” level, even the classical diagnostic challenge of finding the seizure onset site (SOS) can benefit from proper knowledge of the onset mechanism.

General Warning : all concepts that follow are (computer) model inspired.

Living brain is a system with nearly infinite number of degrees of freedom and of humongous complexity.

- Candidates:
- Attractor deformation scenario, precipitated by
- - plastic changes from sensory or other input
- - fluctuating chemical (metabolic) compounds
- B. Transitions in multi-stable (multi-attractor) systems
- - sensory input
- - stochastic fluctuations (thermal noise)
- C. Intrinsic instability – intermittency
- - no precipitating factor

Attractor: invariant, asymptotically stable manifold in the phase space of the system.

Irreducible (no sub-attractors) connected

seizure

Autonomous

normal

Fluctuations

(noise)

B. Multi-attractor scenario

Attractor1

Attractor2

Fluctuations

seizure

normal

Control

Parameter

Generic models for autonomous epileptic state transitions

A. Attractor deformation scenario

Attractor

Non-autonomous

Control

Parameter

Complex non-linear models:

Autonomous seizure generation

Example: complex Z^4 model with two deformation dimensions

Phase-space plot

HC slice, low Mg ictal data,

Hilbert-transform complex reconstruction

(courtesy: P. Carlen, H. Khosravaniand M. Derchansky)

repulsor

attractor

Topological attractors in phase-spaces.

Analytic models and reconstructions

Fixed point

Method: relative critical point sets detecting vector-field ridges and convergence manifolds

Kalitzin, S. N., Staal J., ter Haar Romeny B., Viergever MA. (2001).

"A computational method for segmenting topological point-sets and application to image analysis."

Pattern Analysis and Machine Intelligence, IEEE Transactions on 23(5): 447-459.

Modelling bistability in cortico-thalamic circuits

Bifurcation diagram

Input

distribution

Input

Normal activity - steady state

Paroxysmal activity - limit cycle

normal

and

paroxysmal

only

normal

only

paroxysmal

© SEIN, 2004

Medical Physics Department

Extra bonus from modeling: Closed-loop seizure abortion as prescribed from model simulation in bi-stable system

Closed - loop seizure control

Counter - stimulus parameters

_

+

Suffczynski, P., Kalitzin S. & Lopes da Silva, F.H., Dynamics of non - convulsive epileptic phenomena modeled by a bistable neuronal network. Neuroscience 126(2) p. 467-484, 2004

Medical Physics Department

Statistical validation of multi-attracor scenario

for ictal transitions in rats and humans

Modeling distributions of ictal and interictal durations

Suffczynski S., Lopes da Silva FH., Parra J., Velis D., Bouwman B., Clementina M., van Rijn P., van Hese P., Boon P., Houman K., Derchansky M., Carlen P., Kalitzin S., (2006),

”Dynamics of epileptic phenomena determined from statistics of ictal transitions,” IEEE Trans Biomed Eng 53(3): 524-32.

A+B combined scenario

Multi-stability (multi-homeostatic system)

involving synaptic plasticity

Kalitzin, S., van Dijk BW, Spekreijse H. (2000).

"Self-organized dynamics in plastic neural networks: bistability and coherence."

Biol Cybern 83(2): 139-50.

Ergodic

C. Intermittency in continuous deterministic systems

(dynamical billiards)

Pre-ictal?

Alternative: Discrete intermittent systems

Elan L. Ohayon, Hon C. Kwan, W. McIntyre Burnham, Piotr Suffczynski, Stiliyan Kalitzin, Emergent Complex Patterns in Autonomous Distributed Systems: Mechanisms for Attention Recovery and Relation to Models of Clinical Epilepsy, IEEE SMC’2004 Conference Proceedings, October 10-13 2004 The Hague, p. 2066-2072

The “EPI-TABLE”

Central Didactic Question 2:

When do we know that we know more than nothing ?

This question is about:

Defining (weak) predictability

“Existence of a set of retrospective measurements such that a statistically significant association between the outcomes of these measurements and the time to the first seizure following these measurements can be demonstrated”.

Statistical significance:

N surrogates obtained as random permutations of predictor’s values for the same times of measurement

Kalitzin, S. N., J. Parra, et al. (2007). "Quantification of unidirectional nonlinear associations between multidimensional signals." IEEE Trans Biomed Eng54(3): 454-61.

- Predictability association measure
- Non-linear h2 association index – favors single mode distributions
- Mutual information – weaker measure

seizure

Time to seizure

Example of stochastic parameter random walk:

Weak but statistically significant predictability based on measuring the control parameter

- Few clouds on the prediction horizon
- Brain is predominantly an open system, concepts such as “spontaneous activity” or “spontaneous seizures” are agnostic categories.
- Brain is unlikely to be in a “thermal equilibrium” state. Noise fluctuations do not spread evenly over all degrees of freedom and therefore one cannot observe everything at all times.
- Brain is seldom a stationary system, we need ample statistics in short times.

Our approach: active, stimulation based observation

Stimulus sequence

Photosensitive epilepsy (PSE) is the most common form of human reflex epilepsy which offers a highly reproducible model to investigate whether the transition to an epileptic response may be detected

Objective: To quantify the dynamical state of the brain during stimulation prior to eventual photo paroxysmal response.

J. Parra, S. Kalitzin, , J Iriarte, W. Blanes, D. Velis, F. Lopes da Silva, Gamma band phase clustering and photosensitivity. Is there an underlying mechanism common to photosensitive epilepsy and visual perception? Brain 126, p. 1164-1172, 2003

10Hz photic stimulator

(20Hz, 15Hz, ..)

MEG/EEG

recording

Triggered response

Patient/Subject

rPCI

Question: can we predict an eventual discharge from features of the triggered response ?

Observation: enhanced fast activity in the VEP

Analysis: PCI

No seizure

Seizure

MEG study

rPCI statistics per subject

rPCI in TLE seizure prediction

Averaged rPCI performance for 3 patients, 5 contacts

Localization of the Seizure Onset Sites (SOS).

Interictal (>24hrs before the leader seizure) rPCI (collective data from 6 patients, 18 contacts)

Active paradigms of seizure anticipation: Computer model evidence for necessity of stimulation

Piotr Suffczynski, Stiliyan Kalitzin , Fernando Lopes da Silva, Jaime Parra, Demetrios Velis, Fabrice Wendling

Phisical Review E 78(5), 051917(9)

Computer modeling: powerful reconstructive tool

( deformation of bi-stable dynamics realistic model of TLE)

Almost any parameter change that affects the seizure thresholdwill have some measurable appearance. The question is: how universally this appearance is related to the seizure threshold?

Seizure threshold and observables co-registration

Different paths to seizure: different “risk estimators”

S0 (energy of the background signal)

Seizure threshold

Driving

rPCI

Closed-loop stimulation: direct neuronal control (neuro-feedback)

Autonomous seizure generation Automated seizure denial

Minimum dose/effect principle

Minimum intervention policy: discrete pulse control

Reactive pulse control

Phase-space “surgery”

Peter Carlen

Fernando Lopes da Silva

Piotr Suffczynski

Fabrice Wendling

Thank You !

Demetrios Velis

Elan Ohayon

Wouter Blanes

Frank van Engelen

Erik Kuitert

Jaime Parra

Stiliyan Kalitzin

seizure

normal

Attractor1

Attractor2

seizure

normal

“Aggregate” A+B+C scenario

deformation

Control

Parameter

Stimulation scenarios:

- Provocative (reflex epilepsies)
- “Non-provocative” (no adverse clinical reactions)
- Curative – to subdue adverse clinical condition

Stimulus sequence

Provocative Photo Stimulation (Visual Sensitivity)

Photosensitive epilepsy (PSE) is the most common form of human reflex epilepsy which offers a highly reproducible model to investigate whether the transition to an epileptic response may be detected

Objective: To quantify the dynamical state of the brain during stimulation prior to eventual photo paroxysmal response.

J. Parra, S. Kalitzin, , J Iriarte, W. Blanes, D. Velis, F. Lopes da Silva, Gamma band phase clustering and photosensitivity. Is there an underlying mechanism common to photosensitive epilepsy and visual perception? Brain 126, p. 1164-1172, 2003

10Hz photic stimulator

(20Hz, 15Hz, ..)

MEG/EEG

recording

Triggered response

Patient/Subject

rPCI

Question: can we predict an eventual discharge from features of the triggered response ?

Simulated PCI with constant amplitudes

Analysis: PCI

No rPCI

Control

Quantification: Relative Phase Clustering Index (rPCI)

PCI

rPCI

Frequency

rPCI per group of subjects

MEG study

86 PPR , 386 control samples

AUC=91%

Mean rPCI values > 0.106, were > 85% sensitive and 80% specific.

MEG study

Is there a (rPCI) build-up phenomenon??

Direct intracranial electrical stimulation(allegedly) non-provocative

PTL

Active observation: stimulation with “carrier frequency”

Phase clustering index (PCI)

Complex amplitudes

Repetitive stimulus

S. Kalitzin, J. Parra, D. Velis, F. Lopes da Silva, Enhancement of phase clustering in the EEG/MEG gamma frequency band anticipates transition to paroxysmal epileptiform

activity in epileptic patients with known visual sensitivity, IEEE-TBME, v.49, 11 p 1279-1286, 2002

Extended definition based on q-norm, q>1

Higher q penalizes amplitude fluctuations;

q=2 is the magnitude squared coherence

(MSC) Dobie and Wilson (1994).

Extended definition based on response amplitude entropy

Penalizes singular

amplitude distributions

Simple example: perfect phase alignment

Statistical significance of PCI

Random phase generation

Critical value of PCI (amplitude dependent !)

Corresponding to a significance level p