Antonio Giuliano Zippo Neuronal Ensemble Modeling and Analysis with Variable Order Markov ...

157 Pages·2011·5.59 MB·English

Antonio Giuliano Zippo

Neuronal Ensemble Modeling and
Analysis with Variable Order Markov
Models

Ledizioni LediPublishing
Antonio Giuliano Zippo
Department of Mathematics
University of Milan
Via C. Saldini n.50
20133 Milan - Italy

Advisors:
Bruno Apolloni
Department of Computer Science
University of Milan
Via Comelico 39, Milan, Italy

Simone Bassis
Department of Computer Science
University of Milan
Via Comelico 39, Milan, Italy

Gabriele E. M. Biella
Institute of Bioimaging and Molecular Physiology
National Research Council
Via Fratelli Cervi, Segrate, 20090 Milan, Italy

Series Editors:
Vincenzo Capasso,
Coordinator of the PhD Program in Mathematics and Statistics for Computational
Sciences;
Alfredo Lorenzi,
Coordinator of the PhD Program in Mathematics;
Bernhard Ruf,
Director of the Graduate School.

Editorial Assistant: Stefania Leonardi

© 2011 Antonio Giuliano Zippo
Open Access copy available at air.unimi.it
First Edition: April 2011
ISBN 978-88-95994-57-4
All rights reserved for the print copy.
For the digital copy rights please refer to air.unimi.it

Ledizioni LediPublishing
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Antonio Giuliano Zippo
Neuronal Ensemble Modeling
and Analysis with
Variable Order Markov Models
2
Contents
1 Biological Background 19
1.1 The Central Nervous System: a survey . . . . . . . . 20
1.2 The Neurons . . . . . . . . . . . . . . . . . . . . . . 20
1.2.1 Elements of Neuronal Anatomy . . . . . . . . 20
1.2.2 Action Potentials and Signal Transmission . . 22
1.3 The Somatosensory System . . . . . . . . . . . . . . 28
1.3.1 A brief introduction to Thalamus Anatomy . 28
1.3.2 A brief introduction to Cortex Anatomy . . . 31
1.3.3 The Thalamo-cortico-thalamic loop. . . . . . 32
1.4 State of Consciousness . . . . . . . . . . . . . . . . . 34
1.4.1 Human Disorders of Consciousness . . . . . . 35
2 Computational Neuroscience Modeling 39
2.1 Multielectrode thalamocortical recordings . . . . . . 40
2.1.1 Spike Sorting . . . . . . . . . . . . . . . . . . 41
2.2 Neural Code. . . . . . . . . . . . . . . . . . . . . . . 46
2.2.1 Firing rate . . . . . . . . . . . . . . . . . . . 47
2.2.2 Spiking timing . . . . . . . . . . . . . . . . . 47
2.2.3 Population coding . . . . . . . . . . . . . . . 48
2.2.4 Stationarity issues . . . . . . . . . . . . . . . 48
2.3 Neuronal analytical Modeling . . . . . . . . . . . . . 49
2.3.1 Integrate-and-fire . . . . . . . . . . . . . . . . 50
2.3.2 Hodgkin-Huxley . . . . . . . . . . . . . . . . 50
3
4 CONTENTS
2.3.3 Izhikevich . . . . . . . . . . . . . . . . . . . . 52
3 Mathematical Modeling Methods 53
3.1 Symbol Sources . . . . . . . . . . . . . . . . . . . . . 54
3.1.1 Finite Markov Process . . . . . . . . . . . . . 56
3.1.2 Variable Order Markov Models . . . . . . . . 59
3.2 Lossless Compressor Codes . . . . . . . . . . . . . . 62
3.2.1 Prediction by Partial Matching . . . . . . . . 64
3.2.2 Context-Tree Weighting . . . . . . . . . . . . 65
3.2.3 Probabilistic Suffix Trees . . . . . . . . . . . 68
3.3 Estimation Framework . . . . . . . . . . . . . . . . . 70
3.4 VOMM’s model similarities . . . . . . . . . . . . . . 71
3.4.1 Average Log-Loss. . . . . . . . . . . . . . . . 72
3.4.2 Compressor-based similarity function . . . . . 73
3.4.3 Stationary Phase Detection . . . . . . . . . . 74
3.5 Neuronal Groups Discovery . . . . . . . . . . . . . . 75
3.5.1 Small-World Networks . . . . . . . . . . . . . 75
3.6 Graphs, Trees and Statistics . . . . . . . . . . . . . . 80
3.7 Modeling Intermittent Chaos . . . . . . . . . . . . . 81
3.7.1 Class Extraction . . . . . . . . . . . . . . . . 82
3.7.2 Information Analysis . . . . . . . . . . . . . . 82
3.7.3 Logistic Modeling . . . . . . . . . . . . . . . 83
3.7.4 Parameter Optimization . . . . . . . . . . . . 84
4 Experiments 85
4.1 Neuropathic Animal models . . . . . . . . . . . . . . 86
4.2 Patients with disorders of consciousness . . . . . . . 89
5 Implementations 91
5.1 Average Log-Loss Similarity . . . . . . . . . . . . . . 91
5.2 NCD Similarity . . . . . . . . . . . . . . . . . . . . . 92
5.2.1 NGD routine . . . . . . . . . . . . . . . . . . 93
CONTENTS 5
6 Results 95
6.1 Chronic Pain . . . . . . . . . . . . . . . . . . . . . . 98
6.1.1 Single Cell Analyses . . . . . . . . . . . . . . 102
6.1.2 Multiunit Analyses . . . . . . . . . . . . . . . 106
6.1.3 Discussion . . . . . . . . . . . . . . . . . . . . 108
6.2 Cortical Ongoing Activity . . . . . . . . . . . . . . . 111
6.2.1 Drifts . . . . . . . . . . . . . . . . . . . . . . 112
6.2.2 Intermittent Chaos in Spontaneous Cortical
Activity . . . . . . . . . . . . . . . . . . . . . 115
6.2.3 Predictability of Higher order Synchrony. . . 121
6.3 Human Disorders of Consciousness . . . . . . . . . . 122
7 Conclusions 133
7.1 Future developments . . . . . . . . . . . . . . . . . . 136
6 CONTENTS
List of Figures
1.1 A representation of neuron anatomy. . . . . . . . . . 22
1.2 A schematic representation of synapse. . . . . . . . . 23
1.3 A protein that functioning as ion channel. . . . . . . 24
1.4 The action potential and its ionic current components. 27
1.5 Cortical areas of human brain. . . . . . . . . . . . . 29
1.6 Thalamus within the human brain (left). Thalamus
nuclei and their cortical projections (right). . . . . . 30
1.7 Thalamocortical loop. We can observe the involved
neuronslikeTCneurons(relaycells)andgranular/pyramidal
cortical neurons. The thalamic cells in red are RT
neurons. . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.8 Thebrainsascendingreticularactivatingsystem(ARAS)
isresponsibleforarousalandsubstainsthewakefulness. 36
2.1 Anelectrodethatrecordstheelectricalactivitywithin
a micro-column. The dark blue circle represents the
detectable region that vary with the electrode impe-
dence. . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2 An example of the electrical activity recordings with
microelectrodes.. . . . . . . . . . . . . . . . . . . . . 43
2.3 100 spike waveforms each of them with 64 samples . 44
7
8 LIST OF FIGURES
3.1 Atipicalbehaviouralpatternofathalamiccellduring
tonic-bursting phases . . . . . . . . . . . . . . . . . . 58
3.2 The respective symbolic sequence where black cells
represent spikes. . . . . . . . . . . . . . . . . . . . . 58
3.3 The estimation framework for VOMM with lossless
compression algorithms. . . . . . . . . . . . . . . . . 70
3.4 InthepanelabovetheLogisticMapwithintheInter-
mittent Chaos Region (α ∈ [3.8284,3.8287145]). In
the central panel the average log-loss computed on
slidingwindows of500units at50units. Inthepanel
below the peaks of the derivative of average log-loss
follow the chaotic region while the periodic phases
represent low values of average log-loss. . . . . . . . 76
3.5 AnexampleofNCDmatrixfromathalamusofanex-
perimentalchronicpainanimalmodel. Therecording
gathers 33 neurons. . . . . . . . . . . . . . . . . . . . 77
3.6 AnexampleofNGDprocedurecomputedontheNCD
matrix in Fig 3.5 with the 33x33 matrix. . . . . . . . 78
3.7 AnexampleofNGDprocedurecomputedontheNCD
matrix in Fig 3.5. with an extract of 20 cells. . . . . 79
3.8 An example of small-world network . . . . . . . . . . 80
3.9 Another example of small-world network . . . . . . . 81
6.1 Preliminary evidences: Firing rate (above) and Cor-
relation (below) throughout the experimental classes
(CR, PI, SC, SL) and the recording sites (VPL and
SS-I). . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2 EEG power spectra for four different CPAs . . . . . 102
6.3 Rasterplotsfrom(respectively)SC,CRandSLanimals.103