Capturing time-varying dynamics: lectures from brain dynamics Klaus Lehnertz (and many more)

Transcription

1 Capturing time-varying dynamics: lectures from brain dynamics Klaus Lehnertz (and many more) Interdisciplinary Center for Complex Systems Dept. of Epileptology Neurophysics Group University of Bonn, Germany Helmholtz-Institute for Radiation- and Nuclear Physics

2 # neurons: ~ # synapses/neuron: ~ length of all connections: ~ m (~2.5 x distance earth-moon) connectivity factor: ~ 10-6 (adult) connectivity factor: ~ 10-4 (juvenile) ion channels / neuron: ~ neurotransmitter & other active substances: ~ 50 # glia cells: ~3-fold # neurons Complex Network Brain structure fluctuations (endogenous/exogenous) function control; movement; perception; attention; learning; memory; knowledge; emotions; motivation; language; thinking; planning; personality; self-identity; consciousness; ; dysfunctions order disorder

3 Epilepsy Greek term for seizure; disease first mentioned ~ 1750 BC ~ 1 % of world population suffers from epilepsy epilepsy is a dynamical disease famous people suffering from epilepsy: Sokrates, Alexander the Great, Julius Caesar, Lenin, Flaubert, Dostojevski, Carroll, Poe, Berlioz, Paganini, Händel, van Gogh, Newton, Pascal, Helmholtz, Nobel

4 Extreme Event Epileptic Seizure frequency: ~ 3 szrs/mon (max.: several 100 szrs/day) inter-seizure seizure-intervals intervals mostly Poissonian distributed (apparently) non-predictable (exception: reflex epilepsies) duration: 1 2 min (exception: status epilepticus > 5 min) during the seizure: impaired mental functions, altered consciousness, loss of consciousness, involuntary movements, after the seizure: neurologic dysfunctions, depression, main seizure types: generalized seizure (apparently instantaneous) focal seizure (with/without generalization) Figure from E Tauboll et al. Epilepsy Res 8, 153,1991

5 Electrophysiological Recording Techniques invasiveness / locality EEG / MEG µv V / ft dc 10 2 Hz ECoG,, SEEG, LFP mv V dc 10 3 Hz SUA, MUA µv mv Hz (?) experimental

6 Epilepsy: Primary Generalized Seizure 50 µv 1s

7 Epilepsy: Focal Seizure with spreading

8 M. Stead et al., Brain 133, 2789, 2010 Epilepsy: Focal Seizure with spreading

9 Treatment of Epilepsy antiepileptic drugs; primary therapy; success: ~ 70 % side effects, long-term treatment epilepsy surgery; option for ~ 5 10 % of patients requirement: localize and delineate epileptic focus from functionally relevant brain areas success: ~ 60 % (15 % 85 %) long-term outcome, surgery-induced alterations? alternative therapies; for ~ 22 % of patients seizure prediction, seizure control success:?

10 Epilepsy --- Unsolved Issues - basic mechanisms in humans - where in the brain and when and why do seizures start? - seizure precursors? - where and why do seizures spread? consistency? - when and why do seizure end? consistency? - seizure-free interval: normal? pathologic? - interactions epilepsy normal brain functioning (cognition) - long-term (yrs) dynamics - epileptic focus vs. epileptic network

11 Epileptic Focus vs. Epileptic Network traditional concept: epileptic focus - circumscribed area of the brain - critical amount of neurons epileptic seizures recent evidence: epileptic network - functionally and anatomically connected brain structures - activity in any one part affects activity in all the others - vulnerability to seizures in any one part of the network influenced by activity everywhere else in the network - seizures may entrain large neural networks from any given part - growing evidence from imaging, electrophysiological, and modeling studies e.g. SS Spencer, Epilepsia 43, 219, 2002; AT Berg & IE Scheffer, Epilepsia 52, 1058, 2011; KL et al., Physica D 267, 7, 2014

12 Inferring Networks of the Brain - Structure small-scale: nodes neurons links synapses desirable, but hard (impossible?) to access large-scale: nodes brain regions links fiber bundles high-res. MRI, DTI, parcellation schemes,

13 Inferring Networks of the Brain - Function small-scale: nodes single neuron (glia) dynamics links synaptic (other) interactions emerging technology large-scale: nodes sensors (dynamics of networks of neuron networks) links interactions (binary, weighted, directed) EEG, ieeg, MEG, fmri,

14 Measuring Interactions probing (active) vs. observing (passive) probing (actio est reactio) system response due to perturbation (relaxation phen.) (EP/ERP) observing (if probing is not possible) time series analysis of ongoing activity characteristics of an interaction - strength } - direction + temporally and spatially resolved - coupling function

15 Capturing Time-Varying Interactions statistical approaches approaches in time-/frequency domain information theoretical approaches state-space-based approaches Fokker-Planck-formalism complexity - different aspects of dynamics / synchronization phenomena - robustness against noise/measurement errors - computing time (field data analyses) - interpretability (causality? direct vs. indirect; common sources)

16 Inferring Functional (Interaction) Brain Networks multichannel recordings of brain dynamics interaction matrix I adjacency matrix A A = f(i) sensor - thresholding - significance testing - node sensor e.g. E. Bullmore & O. Sporns, Nat. Rev. Neurosci. 10, 186, 2009 ; KL et al., Physica D 267, 7, 2014 node

17 Epileptic Networks during Seizures network sync: a mechanism for seizure termination? K Schindler et al., Brain 130, 65, patients, 100 seizures - intracranial EEG recordings (53 ± 21 sites) - cross-correlation matrix (zero-lag) - spectrum of eigenvalues

18 Epileptic Networks during Seizures functional topology from more random to more regular back to more random - 60 patients, 100 seizures - intracranial EEG recordings (53 ± 21 sites) - max. cross-correlation fct. - thresholding (A fully connected) - clustering coefficient C - average shortest path length L - synchronizability S=λ max /λ min from graph Laplacian - comparison with random networks (prescribed degree sequence) less synchronizable K Schindler et al., Chaos 18, , 2008, S Bialonski et al, PloS One 6, e22826.,2011 see also: Ponten et al., Clin. Neurophysiol. 118, 918, 2007 Kramer et al., Epilepsy Res. 79, 173, 2008 Kramer et al., J. Neurosci. 30, 1007, 2010

19 Epileptic Networks during Seizures networks are assortative - harder to synchronize - network disintegration - less vulnerable to attacks - 60 patients, 100 seizures - intracranial EEG recordings (53 ± 21 sites) - correlation coefficient - max. of cross-correlation fct - thresholding (A fully connected) - assortativity coefficient a - comparison with surrogate networks (based on IAAFT time series surrogates) S Bialonski & KL, Chaos 23, , 2013

20 Epileptic Networks during Seizures how important is the epileptic focus? - important in only 35 % of cases - neighborhood more important (>50%) - neighborhood bridge - improved prevention techniques? - 52 patients, 86 seizures - intracranial EEG recordings (53 ± 21 sites) - correlation coefficient - max. of cross-correlation fct - weighted networks (A normalized) - various centrality indices: strength (C S ), eigenvector, closeness, betweenness (C B ) - comparison with surrogate networks (based on IAAFT time series surrogates) C. Geier et al, Seizure 25, 160, 2015 similar findings with eigenvector centrality similar findings with closeness centrality focus (black), neighborhood (orange), other (green)

21 Searching for Seizure Precursors seizure precursors - best identifiable from interaction measurements - synchronization vs. de-synchronization - when: up to hours before onset - where: mostly far off epileptic focus - dependent on epilepsy type - targeted interventions f= focus, n = neighborhood, o = other unifocal epilepsies (N=20) multifocal epilepsies (N=16) F. Mormann et al., Physica D 144, 358, 2000; Clin Neurophysiol, 116, 569, 2005; Brain 130, 314, 2007; KL et al, Sci Rep 6, 24584, 2016

22 Long-Term Dynamics of Epileptic Networks mainly reflects daily rhythms, epileptic process only marginally seizures exemplary frequency distributions pat.: 13 power spectral density estimates (grand average) - 13 patients, 75 seizures - intracranial EEG recordings (> 2100 h) (56 sites, range: 24-72) - mean phase coherence (frequency-adaptive) - thresholding (fixed mean degree) - clustering coefficient C - average shortest path length L C n L n daily rhythms precursor dynamics? MT Kuhnert et al., Chaos 20, , 2010

23 Long-Term Dynamics of Epileptic Networks mainly reflects daily rhythms, easier to synchronize pre-ictally? ---- pre-ictal; - - inter-ictal - 7 patients, 16 seizures - intracranial EEG recordings (> 1000 h) (90 sites, range: 44-90) - mean phase coherence (frequency-adaptive) - thresholding (pre-def. link density) - assortativity a - comparison with surrogate networks (a pre a inter )/a inter C Geier et al., Front. Hum. Neurosci. 9, 462, 2015

24 Confounding Variables - spatial and temporal sampling, good observables - relevant scales, non-stationarity, scale-separation (delayed interactions) KL et al., Physica D 267, 7, 2014

25 Delayed Directed Interactions TL01-TL05 TR01-TR05 TLL4-TLR4-36 h ieeg recording, patient with right MTLE - averaged delayed symbolic transfer entropy - driving post. MTL -> ant. MTL - delay times: ~ ms H Dickten & KL, Phys Rev E 90, ,2014

26 Confounding Variables - spatial and temporal sampling, good observables - relevant scales, non-stationarity, scale-separation (delayed interactions) - incomplete measurements (direct/indirect interactions, common sources) KL et al., Physica D 267, 7, 2014

27 Confounding Variables: Common Sources mean phase coherence phase lag index ref-electr.: GLA1+GLA2 weighted phase lag index epileptic focus: GLA6 lesion: GLD3+GLD4-20 h ieeg recording, seizure-free interval - moving-window analysis (20,48 s; 4096 d.p.) F. Mormann et al., Physica D 144, 358, 2000 S. Porz, M. Kiel & KL Chaos 24, , 2014 C. J. Stam et al. Hum Brain Mapp 28, 1178, 2007 M. Vinck et al. NeuroImage 55, 1548, 2011

28 Confounding Variables: Common Sources TR06 TL03 TR06 TL05 equivalence (light gray) non-equivalence (dark gray) of power spectra GLB4 GLB3 GLB4 GLA3 R - P TR07 GLA3 R P TR02 GLB1 R - P W S. Porz, M. Kiel & KL Chaos 24, , 2014

29 Confounding Variables - spatial and temporal sampling, good observables - relevant scales, non-stationarity, scale-separation (delayed interactions) - incomplete measurements (direct/indirect interactions, common sources) - time series analysis techniques, surrogate approaches, network inference KL et al., Physica D 267, 7, 2014

30 Measuring Directional Interactions S D 1 0 direction D?? strength S coupling strength influencing factors: - number of data points - noise - system properties - uncoupled vs. fully coupled evaluate both strength and direction H. Osterhage et al., Phys Rev E 77, , 2008; KL & H. Dickten, Phil Trans Roy Soc A 373, , 2015

31 Conclusions - epilepsy: disorder of large-scale neuronal networks (structure & function) - paradigm shift: epileptic focus epileptic network - characterization of interactions new therapeutic options - characterization of individual network properties individualized treatment? other brain diseases? - improve methodologies!