University of Toronto T-Space - A Complexity Analysis of Noise … · 2013-10-10 · Department of...

A Complexity Analysis of Noise-Like Activity in the Nervous System and its Application to Brain State

Classification and Identification in Epilepsy

by

Demitre Serletis

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Department of Physiology and the Institute of Biomaterials and Biomedical Engineering University of Toronto

© Copyright by Demitre Serletis 2010

II

A Complexity Analysis of Noise-Like Activity in the Nervous

System and its Application to Brain State Classification and

Identification in Epilepsy

Demitre Serletis

Doctor of Philosophy

Department of Physiology and the Institute of Biomaterials and Biomedical Engineering University of Toronto

2010

Abstract

Complexity lies halfway between stochasticity and determinism, suggesting that brain activity is

neither fully random nor fully predictable but lives by the rules of nonlinear high- and low-

complexity dynamics. One important aspect of brain function is noise-like activity (NLA),

defined as background, electrical potential fluctuations in the nervous system distinct from

spiking rhythms in the foreground. The objective of this thesis was to investigate the

neurodynamical complexity of NLA recorded at the cellular and local network scales in in vitro

preparations of mouse and human hippocampal tissue, under healthy and epileptiform conditions.

In particular, it was found that neuronal NLA arises out of the physiological contributions of gap

junctions and chemical synaptic channels and is characterized by a spectrum of complexity,

ranging from high- to low-complexity, that was measured using methods from nonlinear

dynamical systems theory. Importantly, the complexity of background, neuronal NLA was

shown to depend on the degree of cellular interconnectivity to the surrounding local network. In

addition, the complexity and multifractality of NLA was further studied at the cellular and local

network scales in epileptiform transitions to seizure-like events, identifying emergent low-

complexity and reduced multifractality (bordering on monofractal-type dynamics) in the

III

pathological ictal state. Finally, dual intracellular recordings of hippocampal epileptiform

activity were analyzed to measure NLA synchronicity, showing evidence for increased same-

and cross-frequency correlations and increased phase synchronization in the pathological ictal

state. Convergence towards increased phase synchrony manifested in lower frequency regions

including theta (4-10 Hz) and beta (12-30 Hz), but also in higher frequency bands (gamma, 30-

80 Hz). In summary, there is evidence to suggest that background NLA captures important

neurodynamical information pertinent to the classification and identification of brain state

transitions in healthy and epileptiform hippocampal dynamics, using sophisticated

neuroengineering analyses of these physiological signals.

IV

Acknowledgments I would like to begin by thanking my supervisors, Drs. Peter Carlen, Berj Bardakjian and

Taufik Valiante, for the tremendous role they have played in making my graduate studies a

spectacular learning experience. This dynamic triad was the key to my success in the lab, and I

am grateful to each of them for their insightful wisdom, passionate drive, infinite patience,

insatiable curiosity and incredible sense of good humor. I truly appreciate their constant

guidance, motivation and love for research – and I am honored to call them my mentors and

close personal friends.

I also wish to express a word of thanks to the two other members of my Ph.D. committee,

Dr. Hon Kwan (Department of Physiology) and Dr. Liang Zhang (Institute of Medical Science),

for their helpful advice and useful suggestions in bringing this thesis to fruition.

I am indebted to the many colleagues and friends whom I met over the years, for their

kind assistance and friendship. I am particularly grateful to the following: Damian Shin and

Shanthi Mylvaganam for technical assistance in the lab; Osbert Zalay for his invaluable help

with computer programming and related technical issues; and Marija Cotic, Eunji Kang and Josh

Dian for additional computational assistance. I am also thankful to my lab-mate and fellow Ph.D.

student, Joe El-Hayek, for his vast knowledge of all things relating to neurophysiology and for

our random discourses on literature and philosophy. Finally, I am thankful to Carlos Florez for

his generosity and ever-lasting friendship, and for taking over the battle in the trenches of the lab.

Most importantly, I would like to thank my family for their unconditional love and never-

ending encouragement to pursue the nearly-impossible. To my parents, Apostole and Aglaia,

your strength, courage and integrity are an inspiration to me. I am so fortunate to have your full

support and I dedicate this thesis to you – you are both my heroes. To my sister, Anna, and my

brother-in-law, Tony, thank you for helping me through the good and the bad; I would have

never achieved this without you there to keep me going. Last, but by no means least, I would like

to thank the light of my life, Lorraine, for always being there. Sweetheart, you mean more to me

than anything else in the world, and I am eternally thankful to God for blessing us with the purest

and happiest love imaginable. You are my angel, forever!

V

“Δεν ελπίζω τίποτα. Δεν φοβάμαι τίποτα. Είμαι λεύτερος.”

(I hope for nothing. I fear nothing. I am free.)

Nikos Kazantzakis, Greek writer and philosopher

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Contents

ACKNOWLEDGMENTS ......................................................................................................................... IV

LIST OF ABBREVIATIONS .................................................................................................................... X

LIST OF TABLES .................................................................................................................................... XI

LIST OF FIGURES ................................................................................................................................. XII

1 INTRODUCTION ............................................................................................................................. 1

2 BACKGROUND ................................................................................................................................ 3

2.1 The Brain and Epilepsy ............................................................................................................................... 3

2.2 Relevant Hippocampal Anatomy ................................................................................................................ 4

2.3 A Conceptual Shift to Studying Noise in the Nervous System ...................................................................... 5

2.4 Complexity Theory and the Brain ............................................................................................................... 6

2.4.1 A Deterministic Approach to Brain Dynamics ............................................................................................ 6

2.4.2 Stochasticity in the Brain ............................................................................................................................ 7

2.5 Fractal Theory and Brain Dynamics ............................................................................................................ 9

2.5.1 Mono‐ and Multifractal Systems ................................................................................................................ 9

2.5.2 Examples of Fractality in Real Systems ..................................................................................................... 10

2.6 Multi‐Spatial Synchronization of Brain Dynamics ..................................................................................... 11

2.6.1 Synchrony in the Brain ............................................................................................................................. 11

2.6.2 Measures of Synchrony ............................................................................................................................ 12

2.7 Research Question and Hypotheses ......................................................................................................... 13

2.8 Rationale and Clinical Relevance .............................................................................................................. 14

3 GENERAL METHODS .................................................................................................................. 15

VII

3.1 In Vitro Models of Hippocampal Tissue .................................................................................................... 15

3.1.1 Whole‐Intact Mouse Hippocampal Preparation ...................................................................................... 15

3.1.2 Human Hippocampal Slice Preparation .................................................................................................... 15

3.2 Electrophysiological Experiments ............................................................................................................. 16

3.3 Computational Analyses .......................................................................................................................... 18

3.4 Statistical Analyses .................................................................................................................................. 18

4 THE COMPLEXITY OF NEURONAL NOISELIKE ACTIVITY DEPENDS ON THE

DEGREE OF NETWORK INTERCONNECTIVITY .......................................................................... 19

4.1 Overview ................................................................................................................................................. 19

4.2 Materials and Methods ........................................................................................................................... 20

4.2.1 Animal Tissue ............................................................................................................................................ 20

4.2.2 Experimental Design ................................................................................................................................. 20

4.2.3 Chemicals.................................................................................................................................................. 21

4.2.4 Data Analysis ............................................................................................................................................ 21

4.3 Results .................................................................................................................................................... 26

4.3.1 Gap Junction and Chemical Synaptic Activity Contribute to NLA ............................................................. 26

4.3.2 Cellular Input Resistance Measurements ................................................................................................. 26

4.3.3 Continuous Wavelet Transform Analysis of NLA Dynamics...................................................................... 27

4.3.4 Power and 1 Spectral Analysis of NLA Dynamics ................................................................................. 27

4.3.5 Validation of 1 Measurements via External Noise Injection ................................................................ 28

4.3.6 Correlation Dimension Analysis of NLA Dynamics .................................................................................... 29

4.4 Discussion ............................................................................................................................................... 29

5 THE COMPLEXITY AND MULTIFRACTALITY OF NEURONAL NOISELIKE ACTIVITY

IN HIPPOCAMPAL EPILEPTIFORM DYNAMICS .......................................................................... 39

5.1 Overview ................................................................................................................................................. 39


5.2.1 Animal and Human Tissue ........................................................................................................................ 40


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5.2.3 Chemicals.................................................................................................................................................. 41

5.2.4 Data Analysis ............................................................................................................................................ 42

5.3 Results .................................................................................................................................................... 49

5.3.1 Passive Cellular Membrane Properties .................................................................................................... 49

5.3.2 Characterizing Epileptiform Activity In Vitro ............................................................................................ 49

5.3.3 Extracellular NLA Complexity during Epileptiform State Transitions ....................................................... 50

5.3.4 Intracellular NLA Complexity during Epileptiform State Transitions ........................................................ 52

5.3.5 Intracellular NLA Multifractality during Epileptiform State Transitions ................................................... 53

5.4 Discussion ............................................................................................................................................... 54

6 PHASE SYNCHRONIZATION OF NEURONAL NOISELIKE ACTIVITY IN

HIPPOCAMPAL EPILEPTIFORM DYNAMICS ............................................................................... 67

6.1 Overview ................................................................................................................................................. 67


6.2.1 Animal Tissue ............................................................................................................................................ 68


6.2.3 Chemicals.................................................................................................................................................. 69

6.2.4 Data Analysis ............................................................................................................................................ 69

6.3 Results .................................................................................................................................................... 73

6.3.1 Passive Cellular Membrane Properties .................................................................................................... 73

6.3.2 Epileptiform Activity in Dual Intracellular Recordings .............................................................................. 73

6.3.3 Nonlinear Phase Correlations of NLA in Epileptiform Dynamics .............................................................. 74

6.3.4 Phase Synchronization of NLA in Epileptiform Dynamics ......................................................................... 74

6.4 Discussion ............................................................................................................................................... 75

7 SUMMARY AND CONCLUSIONS .............................................................................................. 88

7.1 Summary of Contributions ....................................................................................................................... 88

7.2 Conclusions ............................................................................................................................................. 91

7.3 Future Directions ..................................................................................................................................... 91

IX

8 REFERENCES ................................................................................................................................ 94

X

List of Abbreviations / One-over-frequency

ACSF Artificial cerebrospinal fluid AE Approximate entropy AMPA α-Amino-3-hydroxyl-5-methyl-4-isoxazole-propionate ANOVA Analysis of variance APV DL-2-amino-5-phosphonovaleric acid AR Autoregressive ARCH Autoregressive conditional heteroscedasticity ARMA Autoregressive moving average ATP Adenosine triphosphate CA1 Cornu Ammonis region 1 CA3 Cornu Ammonis region 3 CNQX 6-Cyano-7-nitroquinoxaline-2,3-dione CWT Continuous wavelet transform

Correlation dimension DFT Discrete Fourier transform

Fractal dimension DNA Deoxyribonucleic acid EC Extracellular EE Epileptiform event EEG Electroencephalography EGTA Ethylene glycol tetraacetic acid EPSPs Excitatory post-synaptic potentials

Frequency GABAA -Aminobutyric acid type A GTP Guanosine triphosphate

Local Hurst exponent Global Hurst exponent

HEPES 4-(2-Hydroxyethyl)-1-piperazineethanesulfonic acid 95th-percentile half-width

IC Ictal IIC Interictal IPSPs Inhibitory post-synaptic potentials IR-DIC Infra-red microscopy with differential interference contrast I-V Current-voltage

Maximum Lyapunov exponent MA Moving average NLA Noise-like activity NMDA N-methyl-D-aspartic acid

Power spectrum PSI Phase synchronization index SC Subiculum S.E.M. Standard error of the mean SR 95531 Gabazine

Singularity exponent WTMM Wavelet-transform modulus-maxima

XI

List of Tables Table No. Page No.

1. Characteristics of epileptiform activity in vitro 58

XII

List of Figures Figure No. Page No.

1. Whole-cell recordings of NLA reveal its dependence on cellular 33 interconnectivity.

2. Continuous wavelet transform and power spectral analyses of NLA dynamics. 34

3. 1⁄ spectral analysis of NLA complexity. 36

4. Correlation dimension analysis of NLA complexity. 38

5. Isolation of background NLA by spike attenuation from an intracellular 59 recording of epileptiform activity.

6. Complexity measures as a function of signal length for representative interictal 60 and ictal NLA signals.

7. Representative seizure-like events recorded in mouse and human hippocampal 61 tissue.

8. Complexity analyses of local network NLA from epileptiform dynamics 62 recorded in the whole-intact mouse hippocampus.

9. Complexity analyses of intracellular NLA in epileptiform dynamics. 64

10. Altered multifractal complexity of neuronal NLA in epileptiform dynamics. 65

11. Representative dual intracellular recordings of epileptiform events in the CA3 79 region of the intact mouse hippocampus.

12. Wavelet coherence plots for representative dual NLA signals from 81 intracellular recordings of interictal (IIC) and ictal (IC) dynamics.

13. Wavelet bicoherence plots for representative dual NLA signals from 82 intracellular recordings of interictal (IIC) and ictal (IC) dynamics.

14. Wavelet-based phase synchronization index (PSI) for representative dual NLA 84 signals from intracellular recordings of interictal (IIC) and ictal (IC) dynamics.

15. Frequency-specific phase synchronization index (PSI) for dual NLA signals 86 from intracellular recordings of interictal (IIC) and ictal (IC) dynamics.

16. Statistical mean and variance analyses of the phase synchronization index (PSI). 87

1

1 Introduction The brain is a complex system under dynamical flux, constantly transitioning between

different “states.” The notion of varying brain states is an abstract reference to the various modes

of functional, spatiotemporal activity exhibited by the brain either in health or disease. In the

healthy brain, examples of possible states include different stages of sleep (e.g. rapid eye

movement sleep) or various mental tasks (e.g. cognition, memory recall, etc). In contrast, the

epileptic brain exhibits abnormal dynamics during the onset and persistent occurrence of seizure

activity; in this context, associated brain states are commonly referred to as the ictal (i.e.

seizure), preictal, interictal and postictal states. It is only due to recent developments in the field

of neurodynamics, however, that we have begun to understand the complexity inherent to both

normal and abnormal brain rhythms.

In particular, the study of background fluctuations at the cellular (i.e. neuronal), local

network and global (i.e. EEG) scales of the brain has emerged as a crucial component to

understanding brain state transitions. This activity has been previously referred to as “noise,”

“oscillations,” and “variability” to differentiate it from true stochasticity, the latter specifically

arising out of purely random processes. The concept of fluctuations, or “noise-like activity”

(NLA), is herewith used in strict reference to background activity distinct from action potential

(i.e. spiking) dynamics, manifesting as seemingly-random, time-varying deviations in electrical

potential. Fluctuating dynamics are ubiquitous throughout the nervous system but have not been

very well characterized to date. They are often regarded as the background context to more

obvious spike-related events in the foreground (i.e. action potentials, bursts and seizures), and

have been described by Llinás as “traveling […] waves that we see as gentle ripples in calm

water, [on top of whose] crests much larger electrical events known as action potentials may be

evoked.1” Importantly, the significance of these fluctuations lies in their information content

pertaining to the understanding of brain state transitions, and thus in their potential role in

improving current methods for classifying and identifying different brain states. In the context of

epilepsy, the study of background NLA from single- and multi-site recordings may offer an

enhanced means for detection and possibly anticipation of epileptiform activity.

Hence, the purpose of this thesis is to present a neuroengineering approach to the study of

the background NLA signal recorded from the cellular and local network scales of the

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hippocampus, using electrophysiological data collected from mouse and human tissue

preparations. In particular, Chapter 2 begins with a focused background review of hippocampal

anatomy and relevant neurodynamical concepts, with particular emphasis on dynamical

complexity, fractal theory and multi-spatial synchronization. Chapter 3 then provides a general

description of the experimental methods used to prepare mouse and human hippocampal tissue,

and summarizes the electrophysiological and computational protocols used for data collection

and subsequent analysis (with additional methodological details interspersed throughout the

remaining chapters). Following this, Chapters 4, 5 and 6 each present a comprehensive study of

some dynamical aspect of background NLA. Specifically, Chapter 4 investigates the

physiological contributions of gap junctions and chemical synaptic channels to neuronal NLA

complexity, and the latter’s dependence on the degree of interconnectivity in the surrounding

local network. Chapter 5 then targets the question of altered dynamical complexity and

multifractality in background NLA during the transition to seizure, with particular emphasis on

the dynamical differences between the interictal and pathological ictal states. Chapter 6 takes a

multi-spatial approach to study the possibility for synchronization between dual recordings of

neuronal NLA during the transition to seizure. Finally, Chapter 7 concludes with a summary of

findings and an outline of future research ventures, followed by a comprehensive list of relevant

references in Chapter 8. Ultimately, it is hoped that this body of work will have far-reaching

clinical implications for the treatment of epileptic patients suffering from intractable seizures –

an aspiration shared by all neuroscientists currently working in this field.

3

2 Background

2.1 The Brain and Epilepsy The brain is the most mysterious and intriguing organ of the human body, representing

the product of hundreds of thousands of years of evolution. It is a beautifully complex system

comprised of hundreds of billions of individual, interrelated neuronal cells that act in coordinated

fashion to control the important functions of the human body. Even the slightest disturbance in

normal brain function, however, can have dramatic, often times devastating, clinical results. One

of the best examples of this dysfunction is seen in epilepsy, a chronic neurological condition of

recurrent seizures with dramatic physical, psychological and social repercussions that affects

approximately 1% of adults and 2% of children.2 The term “epilepsy” is generic, in the sense that

it encompasses a spectrum of diverse seizure disorders that arise through different

pathophysiological mechanisms with partial or generalized clinical manifestations occurring as a

function of the location and extent of brain tissue affected.3 One of the most common causes of

focal (partial) epilepsy is mesial temporal sclerosis, which affects the hippocampus and related

mesial temporal lobe structures resulting in progressive neuronal loss, inflammation and chronic

gliosis.4, 5 In fact, hippocampal pathology is commonly linked to focal epileptiform activity, and

given the widespread use of animal and human hippocampal models in electrophysiological

studies,6, 7 this justifies the use of hippocampal tissue as an ideal experimental substrate for

studying seizure-like activity in the brain.

In general, however, seizures typically manifest as single, spontaneous, transient

disruptions of normal electrical brain activity resulting from the excessive and/or synchronous

firing of neuronal populations (i.e. networks), producing altered motor, sensory, behavioral

and/or autonomic functions.8-11 Present day therapy to control epilepsy includes several strategies

with associated side effects, namely pharmacotherapy, surgical resection of the epileptogenic

focus, brain stimulation, and local drug delivery.12 None of these therapies, however, directly

tackles the abnormal dynamics of dysfunctional, seizure-like activity occurring at the cellular

and local network levels. For this reason, one must turn to sophisticated mathematical analyses

and novel neuroengineering techniques to better understand the differences in neurodynamical

complexity between healthy and epileptiform brain activity.

4

2.2 Relevant Hippocampal Anatomy The hippocampus has classically been used as a model system in electrophysiological

studies due to its simple, cytoarchitectonic organization of intrinsic circuitry.13 It has been

extensively studied for its roles in memory, learning, cognition and spatial coding in the healthy

brain, in addition to its pathophysiological role in epilepsy.3 Also referred to as the hippocampal

formation, the hippocampus constitutes part of the medial surface of the temporal lobe in the

brain. Despite variations in the rodent and primate brain, it is generally an elongated “C”-shaped

structure that contains three distinct regions forming a three-layered allocortex throughout its

extent; these include the dentate gyrus, the hippocampus proper (or Cornu Ammonis, which is

itself divided into three subregions identified as CA3, CA2 and CA1), and the subiculum (SC).5,

14-16 Information courses unidirectionally in transverse hippocampal slices via a trisynaptic

circuit that has been well-characterized to date.17 In particular, afferent fibers to the hippocampus

arise primarily from the medial and lateral aspects of the entorhinal cortex, with the former

traversing the alvear pathway to enter the CA1 and SC regions, and the latter coursing along the

perforant pathway to reach the dentate gyrus.18 Granule cells in the dentate gyrus then project to

the CA3 region across their mossy fibers, and CA3 pyramidal cells subsequently relay

information to the CA1 region via the Schaffer collaterals. CA1 activity then passes to the

subiculum, the major output center of the hippocampus, sending parallel projections to different

cortical and subcortical regions including the entorhinal cortex, effectively completing the

trisynaptic circuit.14, 19 However, studies have proposed that information processing arises not

only in the transverse axis, but also across the longer septotemporal axis implying that in vitro

slices are not sufficient to capture information flow in three-dimensions.13 This has led to the

important development of an intact hippocampal preparation that preserves local, three-

dimensional circuitry while offering electrophysiological, morphological and pharmacological

advantages comparable to slices,20, 21 all the while remaining viable and resistant to hypoxia over

several hours following isolation.22 It is for these reasons that the whole-intact hippocampal

preparation was specifically used in the experiments outlined in this thesis.

5

2.3 A Conceptual Shift to Studying Noise in the Nervous System To date, the majority of research efforts into seizure detection and prediction have been

limited to the study of spiking dynamics, focusing on action potentials, epileptiform bursts and

seizures. These studies have led, for example, to the development of responsive neurostimulator

devices such as the commercially-available NeuroPace system currently under clinical

evaluation.23 In general, these devices have met with limited success in their algorithmic ability

to accurately detect, much less predict, the onset of seizures based on spiking behavior.

However, another important aspect of brain function is captured in what has been previously

referred to as “noise,” “variability,” or “oscillations.”1, 24 At the cellular level, this activity is

thought to arise out of the integrated dynamical activity of intrinsic and extrinsic sources,

including thermal noise, shot noise, ionic channel fluctuations, chemical synaptic events and gap

junctions.25-33 Amongst other functions, it is thought to enhance neuronal signal detection via

stochastic resonance.34 In this context, the term “noise-like activity” (NLA) is introduced here to

describe time-varying, background, electrical membrane potential fluctuations at the cellular

level of the nervous system. Distinct from obvious spiking rhythms in the foreground (i.e. action

potentials, bursts and seizures), this thesis postulates that neuronal NLA is characterized by a

spectrum of dynamical complexity ranging from high- to low-complexity that may be measured

for the purposes of classifying and identifying brain state transitions.

It has now become generally accepted that background NLA contains meaningful

structure, although there is ongoing debate whether its origins arise out of stochastic (i.e.

random) processes versus exceedingly-complex deterministic mechanisms that appear random.24

Of significant relevance, fluctuating background dynamics at the cellular level have been found

to contain substantial information pertaining to the activity of the rest of the network.30 For

example, tight correlations have been reported between the intracellular activity in neocortical

neurons and macroscopic EEG recordings, suggesting that these cells capture dynamical features

describing the overall activity of the network.35 In addition, the correlational structure of

neuronal noise in the brain has been implicated in population coding at the local network level.36

Finally, from a neurodynamics perspective, noise has been directly implicated in mechanisms of

seizure initiation, whereby state transitions in a bifurcation paradigm were directly found to be

induced by network noise.37, 38 These findings underscore the important role of NLA in brain

dynamics. It is for these reasons that a more comprehensive analysis of fluctuating dynamics

6

using a combination of complexity and fractal methodologies is warranted, to better describe the

changing properties of NLA during state transitions in the healthy and epileptic brain.

2.4 Complexity Theory and the Brain Many real systems are characterized by complex, network-like interactions among

underlying, constituent elements.39 One such example is the brain, in which relatively simple

units (neurons) collectively produce complex but structured global behavior. To date, this

emergent self-organized brain activity has been difficult to characterize.40 According to the

sciences of complex systems, complexity is halfway between randomness (continuously

generated by internal and external environmental effects) and determinism (due to the

nonlinearities arising from the interactions of almost infinitely many components).41 This

suggests that brain activity is neither fully random nor fully predictable, but lives by the rules of

nonlinear high-complexity (i.e. stochastic-like dynamics) and low-complexity (i.e. deterministic-

like) dynamics.42 For the purposes of this thesis, deterministic and stochastic methodologies were

applied to the study of NLA in the brain to investigate the complexity therein. For completeness

sake, a brief description of these traditional concepts is included here; however, the remainder of

this thesis focuses solely on the notion of low- and high-complexity in the background NLA

component of brain activity, in keeping with important and recent trends in the scientific

literature.

2.4.1 A Deterministic Approach to Brain Dynamics

Historically, deterministic models comprised the traditional approach to studying

dynamical activity in the brain; this was best exemplified by the development of the well-

recognized Hodgkin-Huxley model of the action potential.43, 44 In general terms, the

deterministic approach describes the view that natural phenomena are governed entirely by rules

or laws, independent of chance or randomness.45 This implies an element of predictability for a

particular system, based on knowledge of that system’s parameters and its initial (i.e. starting)

conditions. In one case of determinism, referred to as “chaos,” predictability becomes impossible

due to an extreme sensitivity to initial conditions, a fundamental property of chaotic systems

7

known as the “butterfly effect.45” In a chaotic system, long-term output is irregular and random-

like (i.e. easily confused with true randomness or “stochasticity”); however, short-term

predictions remain feasible given the assumption that the system has arisen out of a known rule

or law. It is precisely for this feature, the ability to predict the output of complex systems in the

short run, that deterministic methods have become popular in the study of brain dynamics.44

Overall, the application of deterministic nonlinear techniques to the study of brain

rhythms has given rise to the concept of “neurochaos,” reported at virtually all levels of the

central nervous system.46 Of relevance to the study of epileptiform transitions, seizures have

been described as transitions from “high-complexity, possibly chaotic electrical brain activity to

low-complexity, possibly rhythmic behavior.47” Importantly, however, this does not imply that

the brain is strictly a chaotic (i.e. deterministic) system; rather, all one can say is that the brain

exhibits some chaotic-like properties spanning the range of low- to high-complexity dynamics

that lend themselves to analysis via specific deterministic techniques. This approach is limited,

however, in that it largely ignores the stochastic properties inherent to the brain arguably

manifesting within NLA in the system. To deal with this aspect, one must also consider a

stochastic methods approach.

2.4.2 Stochasticity in the Brain

Noise is an important phenomenon that was traditionally ignored because it was regarded

as detrimental to signal detection.34 Scientists have often sought out ways to normalize, regulate,

or even abolish noise as a means of improving the output from a given system. However,

information pertaining to brain state transitions has recently been identified within “noisy”

signals, particularly synaptic activity.30, 35 In fact, synaptic noise refers to “intense subthreshold

synaptic activity” that is widely expressed in neurons, and has been found to reflect the overall

activity of a given neuronal network.48 At the cellular level, one study reported that

approximately 65% of recorded noise in CA1 stratum pyramidale neurons is synaptic in origin,

suggesting that other sources also contribute to NLA.49 Gap junctions, for example, have also

been implicated in contributing to cellular noise.22, 31, 48, 50 Furthermore, other stochastic

phenomena have also been identified, including electrical noise (i.e. thermal and shot noise),28, 51

ionic channel fluctuations,25, 29, 32, 52, 53 and one-over-frequency (1⁄ ) noise.42, 54-57 Stochasticity

8

in the brain also becomes important when considering the phenomenon of stochastic resonance,

whereby noise has been found to enhance the detection of independent, synaptic, subthreshold

stimuli (as demonstrated in hippocampal CA1 neurons).24, 34 Alternatively, stochastic properties

have additionally been identified in the context of spatiotemporal investigations into epileptiform

dynamics, based on their interdependences with deterministic rhythms.58

Methods pertaining to the study of deterministic dynamics are not suitable for analyzing

stochasticity due to their ignorance of noise and error in real systems. In fact, these features are

best analyzed and modeled using stochastic techniques that measure underlying low and high-

complexity properties.44 One such measure is the 1⁄ spectral analysis of time series data

recorded from a given system. In particular, this measure refers to the relationship between a

signal’s power spectrum, , and frequency such that an observed increase in at lower

frequencies follows the relation:56

1⁄

where denotes frequency and is approximately 1. In general, 1⁄ noise is thought to result,

to some extent, from multiple random inputs delivered over varying time scales, thereby

resulting in stochastic-based, power-law correlations.54 From a physiological standpoint, 1⁄

noise is electrical in nature, arising out of current flow in systems characterized by limited

numbers of charge carriers.28

In addition, there are several other stochastic models that may be considered (but are

beyond the scope of this thesis), including the Autoregressive model (AR), the Moving Average

model (MA), and the Autoregressive Moving Average model (ARMA), that deal with variables

of finite, constant variance (i.e. homoscedastic variables).59, 60 Although not implemented here,

these linear parametric methods have been routinely utilized in the analysis of time series data,

under the assumption that noise within the system is constant and unchanging. Alternatively,

newer stochastic models consider the system’s variables in the context of volatility and

tranquility (i.e. heteroscedasticity); one example of this is the Autoregressive Conditional

Heteroscedasticity (ARCH) model, which has recently been applied to modeling nonstationary

variance in human EEG signals.61, 62 In fact, in addition to the ARCH model, there are a number

9

of ARCH-like models (GARCH, GARCH-M, EGARCH, and Asymmetric GARCH) that have

since evolved for studying the stochastic behavior of time series data.

2.5 Fractal Theory and Brain Dynamics Fractal theory offers a means of characterizing the irregular complexity underlying many

physiological and physical processes in nature. Nowhere in physiology is this mathematical

approach more relevant than to the study of non-stationary biomedical signals, such as those

recorded from the cardiovascular or central nervous systems. More specifically, the fractal

architecture of these signals describes the extent of self-similarity therein, typical of fractal

processes, whereby approximately similar patterns emerge across varying spatial and temporal

scales.63 This “scale-invariance” is a defining property of fractal systems and has been identified

ubiquitously throughout nature, ranging from complex geometrical shapes to time series

fluctuations. In the latter recorded at the cellular, local network and global (EEG) scales of the

brain, fractality refers to the degree of long-range temporal correlations in these data, such that

fluctuations over shorter temporal intervals are proportional to those occurring over longer

intervals.42, 64-66

2.5.1 Mono- and Multifractal Systems

The application of fractal analyses to biomedical signals has been recently popularized

due to varying degrees of success reported using these methods to understand the turbulent and

extraordinary complexity of various biophysical systems. Physiological signals recorded from

living systems are characterized by a tremendous degree of nonstationarity and nonlinearity, and

it is largely due to these features that their analysis has posed a significant challenge, to date.67

However, such processes exhibit irregular, long-range, fluctuating correlations across multiple

temporal scales suggestive of fractal-like signals, making them suitable targets for study using

fractal techniques. Importantly, the dynamical aspect of the scaling relation itself is what defines

a given signal as mono- or multifractal.

10

In the frequency ( ) domain, long-memory fractal processes express complex 1⁄

spectral behavior, where denotes a scaling, power-law exponent.42, 68-73 This type of scaling

within time series data has been described in the literature as a quantifiable property that is either

static or dynamic for different systems under varying conditions.67, 74 In particular, monofractal

signals are characterized by uniformly consistent scaling throughout, quantified using a single

singularity exponent (i.e. the Hurst exponent, H); thus, they are deemed to be homogeneous.

Multifractal signals, in contrast, are inhomogeneous and hence substantially more complex.

Their dynamical characterization requires a range of singularity exponents (e.g. the local Hurst

exponent, h) to capture the intrinsic power-law scaling [corresponding to fractal dimension,

D(h)] for each moment (or singularity) within the signal. Plotting D(h) against h produces a

multifractal singularity spectrum that captures important details surrounding the complexity and

dynamical nonlinearity of a system under investigation. Aside from theoretical models and some

simple systems, most real systems encountered in the biophysical world exhibit mono- and

multifractal properties that may be explored using fractal techniques.

2.5.2 Examples of Fractality in Real Systems

Fractal properties have been identified in a number of different physiological contexts.

For example, characteristic scale-invariant, long-term correlations have been reported in DNA

nucleotide sequences, demonstrating stochastic-like fractal properties in genome organization.75

At the cellular level, fractal concepts have been used to describe electrical potential fluctuations

in biological membranes, suggesting that this noise-like activity is correlated, error-tolerant and

self-organized in the temporal domain.76 In a separate area of study, fractal methods have been

applied to investigate the biomechanical, step-to-step fluctuations in human walking rhythms and

balance as a function of age and pathology. Specifically, these signals have been identified to

express long-range correlations consistent with increased fractality that degrades both with

increasing age and in the context of neurodegenerative disease (namely, Parkinson’s disease and

Huntington’s disease).67, 77-79 From a cardiovascular perspective, human heartbeat rhythms have

also been shown to express a significant degree of multifractality in healthy patients.

Importantly, similar analyses looking at long-range correlations and fractality in certain

pathological conditions (e.g. congestive heart failure) have been linked to altered fractal scaling

11

and even loss of multifractality, with comparable results also reported in the context of aging and

different phases of sleep.67, 74, 80-82 Even more relevant to this thesis, mono- and multifractal

dynamics have been identified in central nervous system activity, including whole-night sleep

EEG recordings,66 low-frequency, endogenous brain oscillations measured using functional

magnetic resonance imaging,69 and human pallidal neuronal spike trains in patients afflicted with

Parkinson’s disease.83 Moreover, attempts have been made to analyze in vivo EEG recordings

from implanted electrodes in an epileptogenic rat model using wavelet-based fractal spectral

analysis, identifying key dynamical trends including decreased anti-persistent dynamics and

reduced fractal dimension during the transition to seizure.84

2.6 Multi-Spatial Synchronization of Brain Dynamics

2.6.1 Synchrony in the Brain

Synchronization phenomena abound in the biophysical world. Complex nonlinear

systems such as the brain are comprised of multiple levels of substructure, ranging from the

global and local network scales down to the cellular level. Governed by physiological

mechanisms, however, the activity of distinct units within and between each scale is coordinated

and organized in such a way as to produce varying brain states of diverse spatiotemporal

functionality. Biomedical recordings of electrical brain activity are able to capture transient shifts

from one state to another, each characterized by altered degrees of low- and high-complexity

dynamics that may ultimately be used to identify pathological states, both in the experimental

and clinical environments. A critical aspect of organized brain function, however, relies on the

dynamical synchronization of multiple events spanning diverse and independent brain regions.

More specifically, simultaneous recordings of spatially segregated neuronal signals are thought

to capture underlying functional interactions that would otherwise go undetected using single-

site recording techniques. This dynamical, spatiotemporal coupling has been characterized as

temporally transient and frequency-specific, necessitating the need for sophisticated, phase-based

analytical techniques to investigate this phenomenon in more detail.85 This approach is

particularly relevant to the study of certain “dynamical” diseases such as epilepsy, characterized

by chronic, recurrent seizure-like events arising out of hyperexcitable, often times

hypersynchronous, firing of diverse neuronal populations.8, 10 In this context, the functional

12

interplay between individual neurons within a local network is likely to capture the

spatiotemporal evolution of epileptiform activity, thus meriting further quantitative investigation

using computational methods targeting synchronization dynamics therein.

2.6.2 Measures of Synchrony

A number of correlation measures have been implemented to study synchronization

phenomena, including the linear cross-correlation and coherence functions, the nonlinear

correlation coefficient, Granger causality, mutual information and transfer entropy.64, 86-89

Recently, however, applications of nonlinear multivariate techniques have become increasingly

relevant to the study of noisy, non-stationary, neurophysiological recordings, with particular

emphasis on the synchronization behavior of parallel, multi-site signals. These methods have

successfully identified synchronous dynamics arising in the healthy brain (e.g. in the binding of

visual information)90, 91 and in certain neuropsychological diseases (including schizophrenia,

Alzheimer’s disease, Parkinson’s disease and epilepsy).92 Traditionally, synchronization has

been identified via correlation analyses of signal amplitude or frequency information arising in

the temporal and frequency domains.93 Synchrony of phase components, however, has recently

emerged as a promising approach suitable for studying complex and noisy signals.94, 95

Specifically, phase synchrony has been defined as a measure of transient frequency-specific

synchronization, or phase-locking, between two weakly-coupled, nonlinear oscillators,

independent of variable correlations in their respective amplitudes.85, 86, 94, 96 This phenomenon

has been extensively studied in the biological sciences, with phase synchronization effects shown

for various conditions arising in the cardiovascular, respiratory and neurological systems.86, 97-101

In fact, increased overall phase synchrony has been previously reported for in vivo extracellular

field recordings of epileptiform dynamics from the CA1 and CA3 regions of the rat

hippocampus, using a wavelet-based method that has been subsequently adapted for use in this

thesis.102, 103

13

2.7 Research Question and Hypotheses This thesis presents a neurodynamical interpretation of fluctuating background NLA

recorded in vitro from the neuronal and local network scales of mouse and human hippocampal

tissue, under healthy and epileptogenic conditions. The specific research question under

investigation is whether background NLA at the cellular and/or local network scales captures

altered dynamical properties of complexity (i.e. high- and low-complexity), multifractality and

synchrony that may be used to classify and identify state transitions in epileptiform activity,

specifically between the interictal and pathological ictal states. The answer to this question is

important as it could have significant experimental and clinical consequences by heralding

unique markers of complexity that could be tracked over time to classify and identify state

transitions in seizure-like activity, based on dynamical interpretation of the subtle, background

NLA signal in the system.

To address this question, three central hypotheses are postulated as follows:

Hypothesis 1. Background NLA arises out of the integrated activity of underlying physiological

sources, including gap junctions and chemical synaptic channels;

Hypothesis 2. NLA may be characterized by a spectrum of complexity and multifractality,

ranging from high- to low-complexity dynamics, as measured at the cellular and/or local network

scales in the healthy and epileptic brain. In this context, proper characterization of background

NLA requires complexity and multifractal measures that may then be used to classify brain states

and identify transitions therein (i.e. from the interictal to the ictal state) in the context of seizure

activity recorded in vitro;

Hypothesis 3. The dynamical complexity of multi-spatial, neuronal NLA signals within the

surrounding local network is invariably related, becoming increasingly correlated and

synchronized during transitions to epileptiform activity, with maximal synchrony in the

pathological ictal state.

14

2.8 Rationale and Clinical Relevance From a neuroscientific perspective, the rationale for conducting the research described in

this thesis is to investigate an important aspect of dynamical brain activity that often goes

unnoticed – i.e. subtle fluctuations in electrical potential (NLA) at the cellular and local network

levels of the nervous system. In contrast to more apparent spiking rhythms in the foreground, this

background variability is thought to express high- and low-complexity features arising out of

underlying physiological correlates whose identification and characterization may shed light on

the problem of brain state classification and identification. In addition to identifying these

properties at the cellular level, their detection in local network fluctuations will also support the

presence of correlations between the fluctuating dynamics of the single-cell and the network.

Overall, these efforts will allow for an improved appreciation of noise in the nervous system,

illustrating the importance of integrating complex methods from the disciplines of physiology

and neuroengineering.

From a clinical perspective, an improved characterization of brain state transitions based

on background NLA dynamics in the brain may potentially pave the way for future attempts at

seizure detection, anticipation and control. The ability to accurately classify and identify

different brain states, particularly during transitions from normal to epileptiform behavior, would

offer tremendous advantages for patients plagued by medically refractory seizures. Given recent

technological advancements, this information could potentially be incorporated into the

development of a device algorithmically capable of tracking specific features of fluctuating

dynamical activity in the brain. Upon real-time recognition of subtle dynamical changes in brain

activity, this theoretical device could perhaps deliver a warning signal to caution the patient

against that pending seizure. In fact, by triggering either a small electrical signal or chemical

injection, seizure abolition or prevention may become a realistic intervention in the future. Such

a device would revolutionize the management of epileptic patients suffering from refractory

seizures and ultimately obviate the need for aggressive (i.e. resective) surgical management.

Interestingly, similar applications could foreseeably apply this type of approach to other non-

epileptic nervous system disorders, further underscoring the importance of continued research

endeavors to merge established physiological methods with novel neuroengineering advances.

15

3 General Methods

3.1 In Vitro Models of Hippocampal Tissue

3.1.1 Whole-Intact Mouse Hippocampal Preparation

In accordance with the University Health Network Animal Care Committee, intact mouse

hippocampal tissue was prepared using a protocol adapted from previous studies.20, 21 To begin,

C57/BL mice (P10-14) were anesthetized with halothane and decapitated. The cranial vault was

opened to permit extraction of the brain. The cerebellum was quickly removed and the two

cerebral hemispheres were disconnected via surgical transection in the sagittal plane. Each

hemisphere was then immersed for 5 minutes in ice-cold (2-5°C), oxygenated (95% O2/5%

CO2) artificial cerebrospinal fluid (ACSF) containing (in mM): 123 NaCl, 2.5 KCl, 1.5 CaCl2, 2

MgSO4, 25 NaHCO3, 1.2 NaH2PO4 and 25 glucose (pH 7.4). Within each hemisphere, the

hippocampus was then exposed by medially displacing the midline structures (i.e. brainstem and

thalamus) using fine spatulas, under constant perfusion with ice-cold, oxygenated ACSF.

Dissection of the hippocampus was achieved by a cut in the septal region and ventral extension

of this transection, taking care to preserve the subiculum (SC) and entorhinal cortex.104

Following disconnection, the whole hippocampus was isolated and immersed in room-

temperature, oxygenated ACSF for at least 1 hour prior to the start of any experimental

recordings.

3.1.2 Human Hippocampal Slice Preparation

Approval to collect and use human tissue for experimental purposes was granted by the

Human Tissue Committee of the University Health Network Research Ethics Board. Patients

diagnosed with intractable epileptic seizures secondary to mesial temporal sclerosis and awaiting

elective surgical resection of lesional hippocampal tissue were identified and consented prior to

surgery. Following tissue procurement, no identifying information was recorded, thereby

ensuring full patient confidentiality.

For each case, surgical dissection of the hippocampus was performed in standard fashion

via selective hippocampectomy, by the same neurosurgeon and at the same institution. The

16

protocol for human hippocampal slice preparation was adapted from previous studies.7, 105, 106 At

the time of resection, blood supply to the hippocampus was preserved until the final moment of

disconnection, at which time approximately 1 cubic inch of hippocampal tissue was removed and

placed immediately into a chamber of ice-cold, oxygenated transport ACSF containing (in mM):

2.5 KCl, 1 CaCl2, 2 MgCl2, 25 NaHCO3, 1.2 NaH2PO4, 25 glucose and 207 sucrose (pH 7.4).

This tissue was then transported from the operating room to our laboratory within the same

institution in less than 5 minutes, at which time the hippocampal specimen was placed into a

second chamber of ice-cold, oxygenated ACSF. 600 μm-thick slices were then sectioned using a

Leica VT1200 vibratome (Leica Microsystems) and placed into oxygenated ACSF at room

temperature for at least 1 hour prior to the start of any experimental recordings.

3.2 Electrophysiological Experiments Following dissection and incubation, hippocampal tissue was transferred to an RC-26

open bath recording chamber (Warner Instruments). Each specimen was secured using fine pins

or a slice holder for either the mouse whole-hippocampus (with its concave, medial surface

facing downwards) or human hippocampal slices, respectively. Temperature in the chamber was

regulated at 33.5±0.5°C via perfusion of warmed, oxygenated (95% O2/5% CO2) ACSF flowing

at a rate of 2-3 mL/min. The solution surface in the chamber was also oxygenated (95% O2/5%

CO2) to minimize oxygen evaporation. Application of different perfusion treatments began after

at least 5 minutes of stable recording, depending on the specific experiment being performed.

Infra-red microscopy with differential interference contrast (IR-DIC) was utilized for

direct visualization under an Olympus BX51WI upright microscope (Olympus Optical Co.) at

40X magnification (using a water-immersion lens), with an OLY-150IR camera-video monitor

unit (Olympus Optical Co.). A Digidata 1322A digitizer (used for analog-to-digital conversion)

and an Axopatch 200B amplifier (Axon Instruments) were used to acquire single whole-cell

patch-clamp recordings under current–clamp conditions. Based on the specific experimental

protocol being followed, a second Axopatch 200B amplifier (Axon Instruments) was used to

capture either concomitant extracellular field recordings or a second (i.e. dual) intracellular

recording under current-clamp. Electrodes with 5-8 MΩ resistance were pulled from borosilicate

capillary tubing (World Precision Instruments) using a Narishige PP-830 vertical puller. The

17

solution in each intracellular recording pipette contained (in mM): 135 K-Gluconate, 10 NaCl, 1

MgCl2, 2 Na2ATP, 0.3 NaGTP (Tris), 10 NaHEPES, 0.5 EGTA and 0.0001 CaCl2 (pH 7.4).107

Taking into account the Donnan equilibrium principle,108 the liquid junction potential was

calculated to be 6.2 mV using Clampex 9.2 (Axon Instruments); however, no corrections were

made for the purposes of this study. In contrast, extracellular field recording electrodes were

simply filled with regular ACSF. Data visualization was achieved using Clampfit 9.2 (Axon

Instruments).

Prior to each intracellular recording, whole-cell seal resistance was determined to be 2-4

GΩ prior to breaking through the cellular membrane. The resting membrane potential was

recorded and sufficient negative current was injected to achieve a stable, subthreshold membrane

potential between -60 and -65 mV, characterized by the absence of action potentials. Current

pulses (±100 pA, 900 ms in duration at 50 pA increments) were delivered to obtain an input-

output (i.e. current-voltage, or I-V) relationship, whose slope was later measured both at the

beginning and end of each recording to be the cellular input resistance. Using Clampfit 9.2, data

was collected at a sampling rate of 10 kHz and subjected to a low-pass, 8-pole Bessel filter of 5

kHz.

Of particular relevance to Chapters 5 and 6 which focus on the study of NLA in the

context of seizure-like activity, epileptiform transitions were induced using a low-Mg2+/high-K+

ACSF solution reliably known to induce epileptiform activity containing (in mM): 123 NaCl, 5

KCl, 1.5 CaCl2, 0.25 MgSO4, 25 NaHCO3, 1.2 NaH2PO4 and 25 glucose (pH 7.4). This is a

robust model commonly used in animal and human hippocampal preparations in vitro to acutely

induce epileptiform events resembling electrographic seizures in vivo.7, 21 More specifically,

reduced Mg2+ in the perfusion solution enhances excitability and spontaneous firing by

eliminating the Mg2+ blockade of excitatory NMDA receptors, in addition to reducing surface

screening and stimulating the release of additional transmitter from presynaptic nerve terminals

(by promoting Ca2+ influx through voltage-gated channels), with increased K+ further supporting

the evolution and persistence of self-sustaining seizure activity.109 Due to the established

implementation of this pharmacological seizure model in the literature and owing to its

consistent and reliable effects in vitro, it was chosen as the seizure model of choice to be used in

the experiments outlined in this thesis.

18

3.3 Computational Analyses Computational work was performed using several commercially available software

packages, including Clampfit 9.2 (Axon Instruments) and MATLAB 7.7 (The MathWorks, Inc.),

a publicly available, Unix-based PhysioToolkit program for performing multifractal analyses,110

and several wavelet-based computational algorithms for coherence, bicoherence and phase

synchronization analyses obtained through personal correspondence with an independent

researcher.102, 103

3.4 Statistical Analyses All statistical analyses were performed using the SigmaStat 3.5 software package (Systat

Software, Inc.). Experimental data were subjected to one- or two-way analysis of variance

(ANOVA), where appropriate, using a Bonferroni post-hoc test. Specific details for each

statistical analysis are provided in the Methodology section of each experimental study.

Significance was reported for p < 0.05. All data are reported in consistent format as mean ±

S.E.M.

19

4 The Complexity of Neuronal Noise-Like Activity Depends on the Degree of Network Interconnectivity

4.1 Overview Noise-like activity (NLA) defines background electrical membrane potential fluctuations

at the cellular level of the nervous system, comprising an important aspect of brain dynamics.

Previously referred to as “noise,” “variability,” or “oscillations,”1, 24 this activity is thought to

arise at the cellular level out of the integrated dynamical activity of intrinsic and extrinsic

sources including thermal noise, shot noise, ionic channel fluctuations, chemical synaptic events

and gap junctions.25-33 Residing in the background context to spiking rhythms in the foreground

(i.e. action potentials, bursts and seizures), this chapter postulates that neuronal NLA arises out

of the integrated activity of underlying physiological sources (namely gap junctions and

chemical synaptic channels) and may be characterized by a spectrum of dynamical complexity

ranging from high- to low-complexity dynamics (Hypotheses 1 and 2).

To test this hypothesis, whole-cell voltage recordings of NLA from fast-spiking stratum

oriens interneurons and stratum pyramidale neurons located in the CA3 region of the intact

mouse hippocampus were collected in vitro. Gap junctions and chemical synaptic channels were

experimentally blocked during recording in order to study the effects of pharmacological

isolation of the cellular system from its surrounding local network. NLA recordings were then

subjected to physiological and computational analyses to identify high- and low-complexity

dynamical features. Specifically, complexity measures were implemented from dynamical

systems theory [i.e. one-over-frequency (1⁄ ) spectral and correlation dimension analyses].

Based on the results reported in this chapter, there was evidence for complexity in neuronal

NLA, ranging from high- to low-complexity dynamics. Importantly, these high- and low-

complexity signal features were largely dependent on gap junction and chemical synaptic

transmission. Progressive neuronal isolation from the surrounding local network via gap junction

blockade (abolishing gap junction-dependent spikelets) and then chemical synaptic blockade

(abolishing excitatory and inhibitory post-synaptic potentials), or the reverse order of these

treatments, resulted in the emergence of high-complexity NLA dynamics, with resolution to low-

complexity behavior following blockade washout and restoration of local network

interconnectivity. These results implicate gap junctions and chemical synaptic channels as

20

physiological contributors to the background NLA signal and show that NLA complexity is

affected by the degree of neuronal interactions (i.e. interconnectivity) in the surrounding local

network. Ultimately, these findings highlight the potential importance of the NLA signal to the

study of network state transitions arising in normal and abnormal brain dynamics (such as in

epileptiform transitions, for example).

4.2 Materials and Methods

4.2.1 Animal Tissue

Electrophysiological experiments using the whole-intact hippocampus model from

C57/BL mice (P10-14) were performed in strict adherence to the regulations and policies set

forth by the University Health Network’s Animal Care Committee. Please refer to the General

Methods (Section 3.1.1) for detailed protocols describing the animal dissection and tissue

preparation steps used.

4.2.2 Experimental Design

A relevant summary of the basic electrophysiological approach was previously outlined

in Section 3.2 of the General Methods. More specifically, whole-cell patch-clamp recordings

were collected from fast-spiking stratum oriens interneurons [selected according to specific

electrophysiological criteria111 and morphological appearance under infra-red visualization112]

and from stratum pyramidale neurons located in the CA3 hippocampal region. After 5 minutes of

stable recording under ACSF perfusion, a second set of current pulses was delivered to reassess

cellular stability, followed by the injection of a subthreshold Gaussian white noise impulse (1 nA

peak-to-peak amplitude, 2 seconds duration) generated using MATLAB 7.7 software (The

MathWorks, Inc.).

The perfusion solution was then switched from ACSF to one containing either a gap

junction blocker (1-octanol) or a mixture of chemical synaptic blockers (CNQX, APV and

gabazine), followed by both types of blockade and finally ACSF washout. Following each

change in solution, the recording interval lasted 5 minutes to ensure sufficient perfusion of the

21

tissue; it should be noted that only the final minute of each 5-minute recording interval was used

in subsequent analyses. In most cases, near-complete washout was attained largely due to the

difficulty in completely eliminating all residual pharmacological blockers from the recording

chamber. Injections of step-wise current pulses and a subthreshold Gaussian white noise impulse

(1 nA peak-to-peak amplitude, 2 seconds duration) were delivered at the end of each 5-minute

recording period prior to changing solutions. External recordings, referred to as extracellular

(EC) recordings, were collected at the end of each experiment with the electrode entirely

withdrawn from the tissue and suspended in ACSF, to allow for comparison to the physiological

whole-cell recordings. These control recordings were deemed representative of external,

environmental “noise” contaminants including those arising from equipment, thermal sources,

leakage noise, etc.

4.2.3 Chemicals

Pharmacological agents were purchased from Sigma-Aldrich, namely: 6-cyano-7-

nitroquinoxaline-2,3-dione (CNQX, a competitive AMPA/kainate receptor antagonist), DL-2-

amino-5-phosphonovaleric acid (APV, a selective NMDA receptor antagonist), SR 95531

(gabazine, a specific GABAA receptor antagonist) and 1-octanol. Each drug was dissolved in

double-distilled water (18.2 MΩ cm-1, Milli-Q system, Millipore) to produce specific final

concentrations: CNQX (10 μM), APV (60 μM), gabazine (10 μM) and 1-octanol (300 μM).

4.2.4 Data Analysis

4.2.4.1 Cellular Input Resistance

Input resistance was determined following each treatment from the slope of the relevant

I-V curve and normalized to the value under control (ACSF) conditions. Normalized data were

converted into a normal distribution via arcsine square root transformation prior to subsequent

statistical analysis.

22

4.2.4.2 Continuous Wavelet Transform

The continuous wavelet transform (CWT) decomposes a given signal, , in the

frequency-time domain and has been used extensively in the fields of geology, physics,

meteorology and engineering.102, 113-116 In principle, the CWT constructs a frequency-time

representation of a signal (for example, an intracellular recording) based on the correlation

between that signal and a set of finite, basis functions (i.e. wavelets). The latter, denoted by

, , are derived by various modifications from an original mother wavelet, , such that:114

,

| | /

where and are scaling and translation factors, respectively, used to generate the modified

wavelet, , , from the original mother wavelet, , and denotes a one-dimensional

parameter (e.g. time). Various mother wavelets have been previously used in the literature,

including the Morlet wavelet used here, referring to a popular Gaussian-modulated plane wave

function (also known as a Gabor function) defined by:102, 115, 117

⁄ ⁄

where denotes the non-dimensional wavelet central angle frequency; at the time-frequency

resolution, it is optimally determined to be ≥ 6.102, 117

Subsequent convolution of the actual signal, , with , yields a correlation

measure represented by wavelet coefficients, , , as follows:

, ,

∞

∞

with , denoting the complex conjugate of , . By varying the wavelet scaling factor,

, and the translation factor, , a graphical map of the associated changes in correlation (as

measured by , may also be generated as wavelet plots to yield the strength of specific

frequency features as a function of time. These computations were all performed using the one-

dimensional wavelet analysis function, cwt.m, in MATLAB 7.7 (The MathWorks, Inc.).

23

4.2.4.3 Power Spectral Analysis

The discrete Fourier transform (DFT) for each time series was computed using the one-

dimensional fast Fourier transform algorithm, fft.m, in MATLAB 7.7 (The MathWorks, Inc.).

The application of this transform to a given signal of observations (here, 1 minute sampled at

10 kHz, yielding 600,000 observations) yields the following:118

⁄

where / and 0, … , 1. Also, denotes the coefficient of the DFT,

is the observation in the signal, and assumes the constant, complex value of √ 1.

The power of the DFT was then determined by matrix multiplication of with its

complex conjugate, , for window lengths of 4096 data points. Averaging across these windows

and plotting against frequency (up to 1 kHz) produced the estimated power spectrum for each

NLA signal.119 For the sake of simplicity and to help with subsequent analysis, power spectra

were plotted as log-log plots. Moreover, only the final minute of recording under each perfusion

treatment was analyzed, ensuring thorough immersion in the new solution and complete removal

of the preceding one following each change in treatment.

4.2.4.4 1⁄ Spectral Analysis

1⁄ processes are described by spectral power-law correlations indicative of

randomness and stochasticity. The term specifically refers to the inverse power-law relationship

between a signal’s power spectral density, , and frequency, , such that:56

1⁄

where the exponent, , is a scaling exponent. This parameter describes the scale-invariant,

temporal relationship between frequencies for a given system with multiple time scales, property

of complex dynamics and self-organization.42, 54 Functionally, captures the temporal memory

effects in the system, or the rate at which power declines from lower to higher frequencies.

24

Although the exact origin of this 1⁄ behavior in biological systems remains unknown, it is

presumed to arise from underlying random events and is indicative of long-term power-law

correlations.40, 42, 54, 120 In the absence of any such relationship, for = 0, the power spectrum

remains constant and flat over a finite frequency range, characteristic of “white noise.” Other

types of noise include “pink noise” (for = 1) and “brown noise” (for = 2), the latter defining a

smoother, faster rate of decreasing power density with frequency than the former.

The power-law exponent, , was computed by performing linear regression on each log-

log transformed power spectrum. In other words, since:

1⁄

the application of the logarithmic operator to both sides yields:

log log log

where log is constant. After generating for each NLA signal as described above (see

Section 4.2.4.3), least squares linear regression was used to fit a line to each log-log plot of

power versus frequency to obtain the slope, . Values of were then compared and subjected

to statistical analysis to identify significant changes in NLA complexity. In this way, it was

possible to analyze the 1⁄ noise architecture of NLA as a measure of complexity for NLA

recorded from fast-spiking CA3 interneurons and pyramidal cells subjected to either gap junction

and/or chemical synaptic blockade. The 1⁄ relation was additionally determined following

injection of a subthreshold Gaussian white noise impulse (1 nA peak-to-peak amplitude, 2

seconds duration) to investigate the effect of external noise inputs into the cellular system and to

validate the protocol for computing the 1⁄ spectrum.

4.2.4.5 Correlation Dimension Analysis

The correlation dimension, , estimates the fractal dimension of a given attractor, or in

other words, the dimensionality or local structure of the state-space occupied by that attractor. It

has become particularly useful in distinguishing deterministic dynamics from stochastic activity

for attractors that correspond to measured time signals.121 Moreover, it is important to note that

25

larger values of are consistent with increased dimensionality in state-space reflective of high-

complexity signal behavior, in comparison to lower values that mark low-complexity signal

dynamics.

To compute , one begins with the correlation sum, , defined by:121, 122

21

where describes the time-delay vector reconstruction of a given time series, , analyzed as

point pairs , in state-space,122, 123 describes the Heaviside (i.e. unit-step) function, and

denotes the number of point pairs in state-space. Overall, is a measure of the fraction of

point pairs , in state-space located at distances closer than a defined length, , excluding

temporally-correlated point pairs separated in time by less than the Theiler window (i.e. the

interval corresponding to the first zero of the autocorrelation function of the time series).124 Here,

the state-space reconstruction was achieved using a minimal embedding dimension of 7 (i.e. the

lowest integer dimension containing the attractor in its entirety) and an embedding time delay of

3 seconds.125, 126 is then shown to follow a power-law distribution for small values of such

that:121, 122

~

which implies:

log ~ log

where is the correlation dimension for the attractor corresponding to the time series, .

From this, plotting log against log allows for measurement of the slope, , using a

least-squares linear regression analysis.

4.2.4.6 Statistical Analysis

Experimental data were subjected to one- and two-way analysis of variance (ANOVA)

using a Bonferroni post-hoc test against controls and between pairs (when relevant). Any

26

normalized data (e.g. input resistance values) were converted into a normal distribution via

arcsine square root conversion. Significance was derived from comparison to ACSF (control)

values or noise-injected values (when relevant), and p-values are reported where significant (i.e.

for p < 0.05). Each sample size (e.g. n = 1) equates to a single recorded cell. All data are reported

in consistent format as mean ± S.E.M.

4.3 Results

4.3.1 Gap Junction and Chemical Synaptic Activity Contribute to NLA

NLA was predominantly characterized by spontaneous activity in fast-spiking CA3

interneurons and CA3 pyramidal neurons (Fig. 1). Gap junction blockade with 1-octanol

eliminated related spikelet events127 (Fig. 1, A and C), whereas chemical synaptic blockade with

CNQX, APV and gabazine abolished excitatory- (EPSPs) and inhibitory post-synaptic potentials

(IPSPs) in the NLA signal (Fig. 1, B and D). Perfusion with both blockade treatments induced

pharmacological cellular isolation from the surrounding local network, with maximal

suppression of spontaneous activity (Fig. 1, A-D). Washout with ACSF largely restored network

function, with concomitant recovery of spontaneous NLA in each cell.

4.3.2 Cellular Input Resistance Measurements

Cellular input resistance was determined from the slope of each I-V curve and averaged

across all cells. In particular, fast-spiking CA3 interneurons (n=40) had an average input

resistance of 347.5 ± 56.6 MΩ, whereas CA3 pyramidal cells (n=24) were characterized by an

average input resistance of 237.1 ± 35.7 MΩ. Moreover, relative input resistance (normalized to

ACSF values) was significantly increased following combined blockade irrespective of which

treatment was applied first, in both interneurons [1.56 ± 0.15, p = 0.002 (Fig. 1E); 1.59 ± 0.19, p

= 0.015 (Fig. 1F)] and pyramidal cells [1.33 ± 0.17, p = 0.009 (Fig. 1E); 1.39 ± 0.12, p = 0.035

(Fig. 1F)] (results shown as mean ± S.E.M.). These findings demonstrate the physiological

effects of pharmacological blockade and confirm that the drugs successfully imposed their

intended effects on the cellular system.

27

4.3.3 Continuous Wavelet Transform Analysis of NLA Dynamics

Continuous wavelet transform (CWT) analysis qualitatively revealed the neurodynamical

complexity inherent to cellular NLA (Fig. 2A). Specifically, wavelet decomposition of NLA into

constituent frequency features plotted as a function of time identified the most dominant features

to reside in the low frequency range, below 20 Hz (Fig. 2A, ‘ACSF’). Progressive blockade

suppressed this activity, leading to maximal inhibition following cellular isolation from the

network (Fig. 2A, ‘1-Octanol + synaptic’). In this isolated state, residual activity likely revealed

intrinsic cellular conductances including ion channel fluctuations.25, 29, 32, 128 Subsequent washout

largely restored network interconnectivity with concomitant recovery of spontaneous NLA (Fig.

2A, ‘Washout’). These findings further implicate gap junctions and chemical synaptic channels

as physiological contributors to neuronal NLA. Moreover, this activity was clearly distinct from

extracellular (EC) recordings capturing external “noise” from equipment or environmental

contaminants (Fig. 2A, ‘EC’), suggestive of the cellular origin of the recorded NLA signal.

4.3.4 Power and 1⁄ Spectral Analysis of NLA Dynamics

Further confirmation of the above results was achieved by power spectral analysis of

cellular NLA (Fig. 2, B and C), revealing a negative power of frequency over the frequency

range consistent with complex 1⁄ noise.42, 54 In power spectral plots of cellular NLA

recordings, progressive pharmacological blockade with either gap junction and/or chemical

synaptic blockers reduced power spectral magnitude and slope values as compared to control

(ACSF) treatment, a trend that largely reversed upon washout of the blockers (Fig. 2, B and C).

The 1⁄ noise relation was quantified by measuring the scaling exponent, , as the slope of

fitted regression lines, revealing values exceeding 2 (i.e. near brown noise, 1⁄ ) under ACSF

perfusion (Fig. 3, B and C). Power spectral magnitude and slope values were comparable to

those reported in the literature,25, 129 and were found to be markedly higher for cellular NLA

recordings than for external noise signals. In fact, values of were significantly higher for NLA

recorded intracellularly from interneurons [2.19 ± 0.02, p < 0.001 (Fig. 3B, left); 2.16 ± 0.05, p <

0.001 (Fig. 3B, right)] and pyramidal neurons [2.15 ± 0.08, p < 0.001 (Fig. 3C, left); 2.23 ± 0.08,

p < 0.001 (Fig. 3C, right)] as compared to values for EC signals. In the latter case, estimates of

were approximately equal to 1 (approaching a more random, pink noise structure, 1⁄ ).

28

Importantly, perfusion with progressive pharmacological blockade decreased , with

significant changes arising under combined blockade in both interneurons [1.74 ± 0.07, p < 0.001

(Fig. 3B, left); 1.63 ± 0.13, p = 0.004 (Fig. 3B, right)] and pyramidal cells [1.50 ± 0.12, p < 0.001

(Fig. 3C, left); 1.70 ± 0.18, p = 0.042 (Fig. 3C, right)], as compared to control (ACSF)

conditions. These findings were consistent irrespective of which type of blockade was applied

first (i.e. gap junction or chemical synaptic blockade). Overall, the decrease in the scaling

exponent, , from ~ 2 to ~ 1.5 represents a shift towards more random pink noise ( ~ 1),

consistent with emerging high-complexity dynamics in the isolated cellular system. However,

this trend was reversed following blockade washout suggesting that low-complexity dynamics

arise in the face of increased interconnectivity with the surrounding local network.

4.3.5 Validation of 1⁄ Measurements via External Noise Injection

During recording, a stochastic Gaussian white noise (1⁄ ) impulse was also injected

into each cell (Fig. 3A) to ascertain the effects of subthreshold external noise inputs into the

cellular system and to validate 1⁄ spectral measurements. This impulse was found to average

out the brown noise-like architecture (1⁄ ) in untreated cells. This resulted in a significantly

more complex, pink noise-like structure with ~ 1 in both interneurons [0.92 ± 0.09, p < 0.001

(Fig. 3B, left); 1.18 ± 0.15, p < 0.001 (Fig. 3B, right)] and pyramidal cells [1.04 ± 0.07, p < 0.001

(Fig. 3C, left); 0.90 ± 0.04, p < 0.001 (Fig. 3C, right)], compared to pre-noise injected values of

. Within this noise-injected context, progressive pharmacological blockade further reduced in

both interneurons [0.69 ± 0.06, p = 0.089 (Fig. 3B, left); 0.83 ± 0.11, p = 0.490 (Fig. 3B, right)]

and pyramidal cells [0.58 ± 0.04, p = 0.013 (Fig. 3C, left); 0.58 ± 0.12, p = 0.496 (Fig. 3C,

right)]. Overall, these results show that the dynamical complexity of NLA was amenable to

additive effects via an external noise input, and help validate the measurement of 1⁄ noise.

Importantly, the similarity in results between different cell types also suggests that 1⁄ noise

may be a fundamental property of cellular NLA in the nervous system, with related changes in

dynamical complexity arising as a function of network interconnectivity.

29

4.3.6 Correlation Dimension Analysis of NLA Dynamics

Nonlinear, deterministic-like properties of diverse biological systems have also been

well-characterized in the literature.27, 42, 45, 46 Taking this approach, the correlation dimension

( ) of neuronal NLA was analyzed under varying degrees of pharmacological blockade as

another measure of dynamical complexity. For an attractor depicting the state-space trajectory of

a dynamical signal over time, is the quantitative measure of the fractal dimension of that

attractor.121 For low-complexity attractors, will assume relatively low, typically finite, values

in keeping with reduced state-space dimensionality required to capture their dynamical behavior.

In contrast, increasingly complex processes correspond to larger attractors described by higher,

possibly infinite, values of . Hence, is a potentially useful measure for assessing the degree

of complexity in cellular NLA.

Average values under ACSF treatment were similar between interneurons [4.76 ± 0.25

(Fig. 4A); 4.33 ± 0.30 (Fig. 4B)] and pyramidal neurons [4.44 ± 0.26 (Fig. 4A); 4.21 ± 0.23 (Fig.

4B)]. Similarity between these results suggests that cellular NLA expresses a comparable,

perhaps fundamental, degree of complexity among different cell types. Progressive cellular

isolation via gap junction and/or chemical synaptic blockade further increased , indicating that

a larger fractal dimension was required to describe an increasingly complex (i.e. high-

complexity) attractor in phase-space (representing the NLA signal). The most pronounced

increase in occurred following combined blockade in both interneurons [6.84 ± 0.16, p <

0.001 (Fig. 4A); 6.76 ± 0.10, p < 0.001 (Fig. 4B)] and pyramidal cells [6.49 ± 0.23, p < 0.001

(Fig. 4A); 6.28 ± 0.31, p < 0.001 (Fig. 4B)], compared to control (ACSF) conditions. Washout of

pharmacological blockade restored most network interconnectivity, leading to resolution of to

near-control levels and a shift back towards low-complexity behavior. Based on this analysis,

these results again confirm that cellular NLA complexity is dependent on the degree of cellular

interconnectivity within the local network.

4.4 Discussion NLA, also referred to as “noise,” “variability,” or “oscillations”,24 describes seemingly-

random, time-varying fluctuations in electrical membrane potential. It serves as the background

30

context to more obvious spike-related events in the foreground (i.e. action potentials, bursts and

seizures). At the cellular level, this activity is thought to arise out of the integrated dynamical

activity of various intrinsic and extrinsic sources, including thermal (i.e. Johnson-Nyquist) noise,

shot noise, ionic channel fluctuations, chemical synaptic events and gap junction-related

activity.25-32, 128 The importance of understanding the mechanisms underlying cellular NLA in the

nervous system, however, emerges from studies identifying the relevance of its information

content to the activity of the surrounding local network.30 Strong correlations have been reported,

for example, between the intracellular activity of neocortical neurons and comparatively

macroscopic EEG recordings, suggesting that individual cellular activity reflects that of the local

network.35 One study reported on the smoothing effect of cellular noise on the relation between

membrane potential and spike rates throughout the brain, ultimately contributing to contrast

invariance in the cat visual cortex.130 Other studies have implicated neuronal noise and its

correlational structure to population coding (namely, information encoding and decoding) at the

local network level.36, 131 Furthermore, from a neurodynamical standpoint, noise has been

directly implicated in various mechanisms of seizure initiation by inducing state transitions in a

bifurcation-type paradigm.37, 38 These studies allude to the potential for NLA to capture

meaningful dynamical content not necessarily identifiable in the more obvious spike-related

events in the foreground. Importantly, complex properties buried within the NLA signal may be

critical to solving the problem of identifying and classifying network state transitions such as

those arising in various stages of sleep or in the epileptic brain, for example.

The results obtained here are important in that they show evidence for the physiological

contributions of gap junction and chemical synaptic activity to background neuronal fluctuations,

directly implicating these physiological mediators of intercellular communication in NLA

dynamics. Moreover, pharmacological blockade of gap junction or chemical synaptic channels

respectively abolished spikelet events or excitatory- (EPSPs) and inhibitory post-synaptic

potentials (IPSPs) in the NLA signal. These latter findings are consistent with comparable

reports in the literature linking each signal feature, namely spikelets versus EPSPs and IPSPs, to

their respective channels.22, 31, 35, 127 These results also complement other studies demonstrating

the contribution of other cellular features to background NLA, with specific reference to ion

channel dynamics.25, 29, 32, 128

31

Based on the 1⁄ spectral and analyses, there is evidence for dynamical complexity

in cellular NLA in fast-spiking interneurons and pyramidal neurons of the CA3 hippocampal

region. According to the traditional concepts of randomness and determinism, this suggests that

brain dynamics, at least at the cellular level, are neither solely stochastic-like nor purely

deterministic-like in nature. Instead, it appears that cellular NLA arises within a hybrid system

that may be characterized in terms of a spectrum of dynamical complexity, ranging from high- to

low-complexity behavior. Similar ideas have been recently described in the literature, suggesting

that brain dynamics are governed by a balance between stochastic and deterministic

influences.132, 133 This notion is supported by one study that identified stochastic features and

local pockets of determinism in extracellular field recordings of rat hippocampal slices subjected

to epileptic conditions.134 Another study reported on epileptiform behavior in rat hippocampal

slices using artificial neural networks, characterizing seizure-like events by transitions from

high-complexity, possibly-chaotic dynamics towards low-complexity, possibly rhythmic

activity.47 Of further relevance to our work, it has been argued that this apparent complexity does

not just manifest in global brain dynamics but also emerges from interactions within and

amongst various hierarchical levels of organization in the brain itself.42 This self-organized

architecture produces a critical state of dynamical function that has been previously studied for

its fractal-like properties, amongst other features.40, 76

Another important facet of complexity arises from competition with synchrony, the latter

arising out of independent, coupled oscillatory systems135 and emerging at the expense of the

former within finite networks in the brain.42 This concept is supported by the findings reported in

this chapter, where cellular dynamical complexity was found to express increasingly high-

complexity behavior in the context of cellular isolation resulting from pharmacological blockade

of gap junctions and chemical synaptic channels. This increase in complexity manifested as an

overall shift in the 1⁄ spectrum towards smaller values of the scaling exponent, , and a

concomitant increase in values, consistent with increased random-like properties and a larger

state-space dimensionality. Thus, high-complexity NLA dynamics emerged at the expense of

reduced local network synchrony (synonymous here with cellular isolation). In contrast, washout

of the pharmacological blockers largely restored local network interconnectivity (i.e. synchrony),

with a simultaneous reduction in dynamical complexity manifesting as a shift in the 1⁄

32

spectrum towards larger values of (consistent with less signal randomness) and decreased

values (implying smaller dimensionality in the state-space).

In conclusion, these results show physiological and computational evidence for the

contributions of gap junctions and chemical synaptic channels to background fluctuations at the

cellular scale of the nervous system. In addition, subtle shifts in cellular complexity were found

to depend on the degree of interconnectivity in the surrounding local network, implying that

neuronal NLA is at least partially dependent on network dynamics. Specifically, high-complexity

properties emerged in isolated neurons and low-complexity dynamics were identified in the

context of increased cellular interconnectivity. Hence, background NLA is likely to contribute

further dynamical information pertaining to state transitions arising in the brain, both in health

(e.g. sleep states) and disease (e.g. epilepsy). This sets the stage for the following chapter

targeting NLA complexity and multifractality in epileptiform dynamics arising in the mouse and

human hippocampus.

33

Figure 1. Whole-cell recordings of NLA reveal its dependence on cellular interconnectivity.

A and B, NLA recorded from two representative fast-spiking CA3 interneurons. C and D, NLA

recorded from two CA3 pyramidal neurons. The current-voltage (I-V) trace for each cell is

shown (top right). EPSPs and IPSPs persisted following gap junction blockade (A and C),

whereas spikelets were more clearly visualized following chemical synaptic blockade (B and D).

Combined blockade resulted in maximal suppression of spontaneous activity, suggestive of

maximal cellular isolation from the surrounding local network (A-D). NLA largely recovered

following restoration of cellular interconnectivity via ACSF washout of the pharmacological

blockers. E, increased input resistance in fast-spiking interneurons and pyramidal neurons

initially treated with gap junction, then combined, blockade. Input resistance was normalized to

control values under ACSF (dotted horizontal line). F, as in E, but for cells initially treated with

chemical synaptic, then combined, blockade. Values are reported as mean ± S.E.M. (shown by

error bars). * p < 0.05 compared to ACSF values.

34

Figure 2. Continuous wavelet transform and power spectral analyses of NLA dynamics. A,

wavelet analysis of NLA recorded from a representative fast-spiking CA3 interneuron. For each

treatment step, a 10 second-long window of NLA is shown in the frequency-time domain, with

relative intensity denoted by the vertical color bar (right). The strongest signal features were

detected at low frequencies (< 20 Hz), becoming increasingly suppressed with progressive drug

blockade. Following combined blockade, residual activity below 5 Hz was suggestive of

remaining intrinsic conductances (e.g. ion channel dynamics) in the isolated cell. Cellular NLA

was distinct from external, extracellular activity (‘EC’) recorded with the electrode withdrawn

from the cell. B, power spectral analysis of NLA recorded from two fast-spiking CA3

interneurons. Signal power was markedly increased for cellular NLA compared to EC

recordings, suggesting that NLA is distinct from external noise, with ensuing reductions in

power magnitude following progressive pharmacological blockade of gap junctions and/or

chemical synaptic channels. Log-log plots also reveal negatively-sloping traces consistent with

1⁄ dynamics over the frequency range, capturing a degree of complexity that was quantified

35

by measuring the slopes of fitted regression lines (shown as dotted lines) for each treatment.

Slope values were then used as estimates of the power-law exponent, , revealing shifts in 1⁄

noise towards lower values of (shown by flatter regression lines) under progressive, and

especially combined, blockade. These findings are consistent with emerging high-complexity in

cellular isolation from the surrounding local network. C, similar results as in B, but for two

representative pyramidal neurons.

36

Figure 3. ⁄ spectral analysis of NLA complexity. A, injection of subthreshold Gaussian

white noise ( ~ 0) into a fast-spiking CA3 interneuron (top) elicited membrane potential

fluctuations resembling NLA (bottom). B and C, average values of the power-law exponent, ,

determined for CA3 interneuronal (B) and pyramidal NLA (C) under varying pharmacological

blockade of gap junctions and/or chemical synaptic activity (shown as grey bars). NLA recorded

from both cell types under control (ACSF) perfusion revealed 1⁄ spectra resembling brown

noise ( ~ 2), distinct from external, extracellular (EC) recordings resembling comparatively

more random pink noise ( ~ 1). Importantly, pharmacological blockade significantly shifted

each 1⁄ spectrum towards a higher complexity structure marked by increased randomness,

manifesting as decreasing values of from ~ 2 to ~ 1.5 (i.e. closer to pink noise, ~ 1); this

effect was reversed following blockade washout. Thus, these findings suggest that high-

complexity dynamics emerge in the face of cellular isolation (via blockade), with low-

complexity observed in the context of increased cellular interconnectivity with the surrounding

local network. Furthermore, external white noise ( ~ 0) injection shifted from ~ 2 (brown

37

noise) towards ~ 1 (pink noise) under control (ACSF) conditions. In this noise-injected context

(shown as white bars), pharmacological blockade of gap junctions and chemical synaptic

channels further reduced to ~ 0.5 (i.e. closer to comparatively more random white noise), again

consistent with emerging high-complexity behavior. Similar results for both cell types suggest

that 1⁄ spectra and related complexity shifts depending on the degree of local network

interconnectivity may be a fundamental property of cellular NLA dynamics. Values are reported

as mean ± S.E.M. (shown by error bars). * p < 0.05 compared to EC; #, compared to ACSF; §,

compared to raw-data values for each treatment prior to noise injection; and , compared to

post-noise injected values under ACSF.

38

Figure 4. Correlation dimension analysis of NLA complexity. A and B, average correlation

dimension ( ) values for neuronal NLA recorded from CA3 interneurons and pyramidal cells

treated firstly with gap junction (A) or chemical synaptic blockade (B), followed by both

treatments. Both cell types were characterized by increased values following progressive

pharmacological blockade, irrespective of which treatment was applied first, with maximal

values attained under combined blockade. Increased values are consistent with increased

state-space dimensionality for attractors representing the NLA signal under pharmacological

blockade, suggestive of high-complexity dynamics in the context of cellular isolation. In

contrast, this trend was reversed with ACSF washout and restoration of local network

interconnectivity. Hence, these results suggest that NLA complexity is a function of the degree

of cellular interconnectivity in the surrounding local network. Consistency of these findings for

both cell types also suggests this may be a fundamental property of cellular NLA dynamics in the

nervous system. Values are reported as mean ± S.E.M. (shown as error bars). * p < 0.05

compared to ACSF.

39

5 The Complexity and Multifractality of Neuronal Noise-Like Activity in Hippocampal Epileptiform Dynamics

5.1 Overview Fractal methods offer an invaluable means of investigating the irregular and turbulent

nonlinearity in non-stationary biomedical recordings from various living systems, including the

heart and the brain. In the previous chapter, neuronal noise-like activity (NLA) was characterized

by a range of complex behavior ranging from high- to low-complexity dynamics. This chapter,

however, extends this concept further by postulating that measures of dynamical complexity and

multifractality for background NLA vary across different brain states in epileptiform transitions

to seizure-like activity (Hypothesis 2), similar to changes identified in pathological conditions

affecting other body systems, including the heart.67, 74, 79

To test this hypothesis, interictal and ictal states were identified in intracellular

epileptiform events recorded at the cellular and local network scales from two in vitro

preparations treated with low-Mg2+/high-K+ artificial cerebrospinal fluid (ACSF), namely whole-

intact mouse hippocampal tissue and lesional human hippocampal slices. Background NLA in

these signals was isolated using a threshold-based, spike-attenuation algorithm that effectively

suppressed large-amplitude spiking dynamics, leaving behind residual NLA (Fig. 5).136

Computational analyses derived from nonlinear dynamical systems theory, including the

correlation dimension, maximum Lyapunov exponent, one-over-frequency (1⁄ ) spectral

analysis and approximate entropy measures, were then applied to the resultant interictal and ictal

NLA signals to identify shifts in dynamical complexity between different epileptiform states.

Multifractal singularity spectra were also computed to identify altered multifractal properties in

neuronal NLA between different epileptiform states during the transition to seizure-like activity.

Based on the results presented in this chapter, it was found that ictal NLA signals were

characterized by emergent low-complexity features at both the cellular and local network scales

(as measured by a decrease in the correlation dimension and maximum Lyapunov exponent

measures, a shift in the 1⁄ spectrum towards larger values, and lower approximate entropy),

compared to high-complexity properties identified in the preceding interictal state. Importantly,

reduced NLA complexity in the pathological ictal state coincided with a concomitant decrease in

fractal dimension, reduced anti-persistent (i.e. increasingly persistent) dynamics and reduced

40

overall multifractality (bordering on monofractal-type dynamics), compared to interictal NLA

dynamics. These results suggest that multifractal complexity breaks down in the pathological

ictal state, consistent with the loss of signal variability and heterogeneity therein and far from the

equilibrium of turbulent yet healthy fractal dynamics. Ultimately, these findings show evidence

for a spectrum of complexity and fractality underlying background NLA recorded in vitro, that

becomes dynamically altered during the transition to seizure-like activity. More importantly,

they support the use of neuroengineering techniques to investigate and detect subtle dynamical

system changes in background NLA that could bolster current methods of classifying and

identifying brain states, at least in the context of epileptiform activity.


5.2.1 Animal and Human Tissue

Electrophysiological experiments were performed using the whole-intact hippocampal

preparation from C57/BL mice (P10-14), in strict adherence to the regulations and policies set

forth by the University Health Network’s Animal Care Committee. Please refer to the General

Methods (Section 3.1.1) for detailed protocols describing the animal dissection and tissue

preparation steps used.

Permission to use human tissue for experimental purposes was granted by the Human

Tissue Committee of the University Health Network Research Ethics Board. Eligible patients

suffering from refractory epileptic seizures secondary to mesial temporal sclerosis and awaiting

elective surgery for hippocampal resection were identified and consented. Patient confidentiality

was adhered to throughout the entire process, and no personal information was recorded. Section

3.1.2 of the General Methods provides further details concerning the protocol for preparing

human hippocampal slices following tissue procurement from the operating room.


A thorough description of the general electrophysiological approach and related materials

was outlined earlier in Section 3.2 of the General Methods. Specific to this chapter, for

41

experiments using the intact mouse hippocampus, whole-cell voltage recordings were collected

under current-clamp from fast-spiking CA3 stratum oriens interneurons [selected according to

specific electrophysiological criteria111 and morphological appearance under infra-red

visualization112], CA3 stratum pyramidale neurons, and regular-firing subicular (SC) pyramidal

cells. For all recordings, a separate extracellular field electrode was consistently placed within

80-100 μm of the intracellular recording electrode,137 to confirm the occurrence of epileptiform

activity at the local network level. Experiments were performed on the CA3 region for its

apparent role as the driver of intra-hippocampal activity, delivering its outputs to the CA1 region

via the Schaffer collateral projection fibers,17, 42, 138, 139 and on the SC region for its role as the

primary output structure from the hippocampal circuit, initiating and sustaining epileptiform

activity in the brain.140, 141 Similar experiments recording from SC pyramidal neurons in lesional

human hippocampal slices were also performed for comparative purposes; however the CA3

region was avoided in this context due to issues of neuronal loss and extensive gliosis that would

affect recordings from the CA3 region of the hippocampus proper in mesial temporal sclerosis.5

After 5 minutes of stable recording under ACSF perfusion, a second set of current pulses

was delivered to reassess cellular stability. The perfusion solution was then switched from ACSF

to a low-Mg2+/high-K+ ACSF solution reliably known to induce epileptiform activity7, 21

containing (in mM): 123 NaCl, 5 KCl, 1.5 CaCl2, 0.25 MgSO4, 25 NaHCO3, 1.2 NaH2PO4 and

25 glucose (pH 7.4). While perfusing with low-Mg2+/high-K+ ACSF, continuous voltage

recordings of membrane potential changes at the cellular and local network levels captured the

onset and resolution of epileptiform events, up to a maximum length of 1 hour before washing

out with ACSF.

5.2.3 Chemicals

All chemicals were purchased from Sigma-Aldrich.

42

5.2.4 Data Analysis

5.2.4.1 Selection of Interictal and Ictal Epileptiform Signals

All data processing and subsequent computational analyses were performed using

MATLAB 7.7 (The MathWorks, Inc.). To increase computational efficiency, raw epileptiform

signals were down-sampled to 1 kHz. For experiments using intact mouse hippocampal tissue,

epileptiform events were identified by visual inspection of each intracellular recording and

confirmed at the local network scale in a simultaneous extracellular field recording located no

more than 100 μm away. Ictal intervals were selected from the onset of dense spiking activity

persisting beyond 5 seconds, independent of preictal events and often associated with a

paroxysmal depolarizing shift in membrane potential, lasting for 60 seconds of continuous

epileptiform activity. In contrast, the interictal signal was defined as spontaneous activity

preceding any obvious preictal events and the ictal state itself. Of note, following subsequent

isolation of the background NLA signal (Fig. 5), as described in the next section, interictal

signals were longer in length (500 seconds) compared to ictal signals in order to capture the

intrinsically more complex dynamics inherent to the former. This 500 second limit was

determined from empirical testing of selected interictal NLA signals, plotting various complexity

measures (i.e. the correlation dimension and maximum Lyapunov exponent) as a function of

time and revealing a convergence effect towards plateau values after substantially long time

periods (Fig. 6).

Alternatively, in the case of lesional human hippocampal slices, extracellular field

recordings were unable to capture epileptiform dynamics in the network. This was presumably

due to less circuitry (secondary to neuronal loss and chronic, inflammatory gliosis) and a

decreased cellular density in human tissue, thus preventing initiation and sustainability of

seizure-like events in the network. For this reason, field recordings from human hippocampal

slices were excluded from subsequent analysis. However, dramatic transitions to epileptiform

excitability were identified at the intracellular level in these experiments, with ictal intervals

defined as for comparable events in the intact mouse hippocampus. Interestingly, epileptiform

events in human hippocampal slices were quicker to induce and lasted for comparatively shorter

durations compared to those in the intact mouse hippocampus, such that 30 second-long NLA

signals for the interictal and ictal states were sufficiently long enough to demonstrate a plateau

effect of the same complexity measures as a function of time (Fig. 6).

43

5.2.4.2 Isolation of Interictal and Ictal NLA

A subsequent processing step was then performed on all raw interictal and ictal signals

using a spike attenuation algorithm originally developed as part of a neural rhythm extraction

program, to reduce overwhelming spiking dynamics and isolate the background NLA signal.136

In brief, this technique combines an automated, amplitude-threshold detection paradigm with a

spike ‘melting’ step to reduce large amplitude spikes by blending them into the surrounding

NLA, without filtering or excising them. Of note, spike identification was performed using a

global threshold value equivalent to 1.4-fold of the root mean square of the mean amplitude for

each time series to identify spikes outside the range of average baseline activity. This was

followed by a high degree of fine spike attenuation using a precise scaling factor of 0.8; further

details of the descriptive methodology are provided elsewhere.136 However, the purpose for

implementing this protocol was to effectively reduce the amplitude effect for each signal, yet

preserve all inherent frequency features for subsequent analysis using the complexity and

multifractal methods described below. A representative example of NLA isolation is shown for

an intracellular recording from the intact mouse hippocampus (Fig. 5).

5.2.4.3 Correlation Dimension

A description of the correlation dimension ( ) analysis was provided earlier; please refer

to Chapter 4 (Section 4.2.4.5) for the detailed methodology.

5.2.4.4 Maximum Lyapunov Exponent

The maximum Lyapunov exponent, , provides a measure of the exponential rate of

divergence (or convergence) of a trajectory in state-space from another nearby trajectory

differing only by its initial starting conditions.45, 125, 126, 142 Despite the fact that there exists a

spectrum of Lyapunov exponents with one exponent for each dimension in state-space,

considerable attention is often given to the largest or maximal one. For a given time series whose

reconstructed state-space trajectories remain bounded, a positive value for reveals

divergent or expansive behavior characteristic of complex and possibly chaotic dynamics. In

44

contrast, a value of zero is indicative of stable, steady-state (e.g. periodic) dynamics.

Finally, a negative value implies convergence towards a fixed attractor in state-space,

typical of dissipative systems.

A computationally efficient method found to be reliable for small data sets was used to

measure .142 As was described for (Section 4.2.4.5), the method reconstructs a state-

space attractor corresponding to a given time series, , using the method of delays,123 such

that the reconstructed trajectory, , is a matrix of rows each defining a state-space vector. For

each selected reference point on the trajectory, , the algorithm then computes the nearest

neighbor, î, with the shortest distance to that reference point. In mathematical form:142

0 î

î

where 0 is the initial distance from the point to its nearest neighboring point, and … is

the magnitude or Euclidean norm. In practice, nearest neighbor pairs were selected so that they

were temporally separated by more than the Theiler window,124 taken to be the interval

corresponding to the first zero of the autocorrelation function of the time series. Thus,

defines the approximate rate of separation of the pair of trajectories after some evolution

time, , such that:

0

where denotes the separation of the pair at time . Taking this one step further, the

application of the logarithmic function to both sides yields:

log log 0

from which is computed by finding the slope of the equation using least-squares linear

regression. By averaging over all values of , a mean estimate of is subsequently obtained.

45

5.2.4.5 1⁄ Spectral Analysis

1⁄ spectral analysis was previously described in Chapter 4 (Section 4.2.4.4). Here,

however, the method was used to investigate dynamical shifts in NLA complexity during the

transition to epileptiform activity. Specifically, this was achieved by measuring the 1⁄ noise

architecture of interictal and ictal NLA via quantification of the slope, , from their respective

log-log power spectral plots.

5.2.4.6 Approximate Entropy

Entropy is a concept first defined in thermodynamics to quantify the distribution of

available microstates for a given physical system. Adapted for use in information theory and

signal analysis, this approach may be applied to the study of complex, irregular signals and their

inherent information content.143, 144 In this context, entropy offers a measure of the uncertainty or

randomness for a given signal by quantifying the probability density function of the distribution

of that signal’s values.

Thus, an algorithm for measuring approximate entropy (AE) was adapted to quantify the

degree of irregularity and unpredictability in physiological recordings of neuronal NLA.145, 146 A

variant of the Kolmogorov-Sinai entropy measure, this statistical method was developed to

compute the predictability of future amplitude values based on knowledge of previous values.144

The approach is scale-invariant and effective in its capacity to smooth transient interferences and

suppress external noise effects.146, 147 To begin, assume there are observations, , , … , ,

in a given time series, . Taking the embedding space to be real -dimensional space, , a

sequence of vectors may be constructed, , , … , , defined by , … ,

for 1, 2, … , 1. Moreover, the maximum absolute difference between the scalar

components for two vectors and is given by:145, 146

,, ,…,

with the noise-suppression threshold, , denoting a positive, real number such that 0.1σ

with σ representing the standard deviation of the original time series signal, .146 Thus, AE

46

may be estimated for a signal of data points as a function of the parameters and , and is

written as:145, 146

,

where is defined as:

1

1 log ,

and , is the correlation sum for a given vector, , measuring the ratio of the number of vector

pairs ( , ) with , to the total number of vectors in the -dimensional state-

space, 1. Rewriting the full expression yields the following:

1

1 log2

1 , .

Consistent with the other complexity measures described above, the value of was

chosen as 7 to capture higher-dimensional neuronal dynamics; this is in contrast to lower values

(e.g. 2) reported for lower-dimensional systems in the literature.145-148

5.2.4.7 Multifractal Analysis

The multifractal singularity spectrum was computed for each interictal and ictal NLA

signal using a publicly available, Unix-based, PhysioToolkit program.110 Specifically, this tool

implements the wavelet-transform modulus-maxima (WTMM) method of generalizing the

multifractal formalism to fractal signals, an approach that has been deemed superior to other

techniques including the structure-function method.69, 74, 149 The WTMM approach was used to

generate the continuous wavelet transform of each NLA signal using derivatives of the Gaussian

function as the mother wavelet. Here, the seventh derivative of the Gaussian function was

selected as an acceptable, commonly-used, real-valued analyzing wavelet that empirically

yielded consistent and reliable multifractal results.110, 149

47

Computation of the modulus of maxima values for the wavelet transform across each

scale, , for each interictal and ictal NLA signal allowed for evaluation of the local Hurst

exponent, , at each signal moment. In particular, a scaling partition function of the order,

, , was defined at each by taking the sum of the powers of each wavelet coefficient

(the magnitude of the latter denoting the local maxima of the modulus of the wavelet transform

coefficients at scale ).72, 74, 149 In general, as → 0 (i.e. at small scales), the following relation

emerges:

, ~

with denoting the singularity exponent. Importantly, , captures the scaling of smaller

signal fluctuations and weaker singularities for negative values of , and larger signal

fluctuations and stronger singularities for positive values of .72, 74, 150, 151 Rewriting this equation

with constant, , and applying the logarithmic operator gives the following:

,

log , log log

Hence, it follows that the singularity exponent, , may be estimated from the slope of the log-

log plot of , against for each order, . For these computations using interictal and ictal

NLA recordings, the order ranged from -5, -4, …, 0, …, 4, 5, with scaling also ranging from

101 to 102.53, consistent with other reports in the literature.110, 149

The resulting singularity exponents were then plotted against their respective orders to

reveal the inherent degree of linearity (or nonlinearity) in interictal and ictal NLA. For

monofractal signals, this spectrum obeys linearity such that:

1

with the constant denoting the global Hurst exponent. In contrast, multifractal signals are

characterized by nonlinearity in that translates into a range of values in the singularity or

multifractal spectrum following the Legendre transform of , such that:

48

with slope, , defined by the slope equation:

⁄

and where represents the fractal dimension of the set of points corresponding to the local

Hurst exponent, .69, 74, 149 Accordingly, plotting against yields a singularity or

multifractal spectrum that typically takes on a parabolic shape for multifractal signals.

Hence, multifractal spectra were generated for interictal and ictal NLA signals and the

resultant parabolas were quantified for comparative and statistical purposes. This was

accomplished by measuring specific parabolic parameters, including the maximum fractal

dimension on the -axis, , its corresponding local Hurst exponent on the -axis, ,

and the left-hand, 95th-percentile half-width of the multifractal singularity spectrum, , the

latter giving an estimate of the curvature of the left-hand half of the singularity curve and serving

as an estimate of signal multifractality.79 In particular, a small value describes a steep

parabolic rise for a narrow singularity spectrum, descriptive of a more monofractal-like signal,

compared to larger values suggestive of increased nonlinearity and multifractality. It

should be noted that the right-hand half of the singularity curve is often ignored due to its

inconsistency in providing stable estimates, in keeping with other multifractal studies.79, 152


Experimental data were subjected to one-way analysis of variance (ANOVA) using a

Bonferroni post-hoc test. Significance was ascertained from comparison to interictal values

(serving as the control) in the context of perfusion with low-Mg2+/high-K+ ACSF, and p-values

are reported where significant for p < 0.05. Each sample size (e.g. n = 1) equates to a single

epileptiform event recorded from a patch-clamped cell, unless otherwise specified. All data are

reported in consistent format as mean ± S.E.M.

49

5.3 Results

5.3.1 Passive Cellular Membrane Properties

Whole-cell patch-clamp recordings were obtained from a total of 11 fast-spiking CA3

interneurons, 8 CA3 pyramidal neurons and 10 regular-firing SC pyramidal neurons in intact

mouse hippocampal tissue. Recordings were also collected from another 9 regular-firing SC

pyramidal neurons in lesional human hippocampal slices obtained from a total of 5 patients

undergoing surgical resection for intractable epilepsy. In this patient group, age ranged from 22

to 44 years old. Experimental recordings were used to compute two passive membrane properties

for each cellular group, namely input resistance and resting membrane potential. More

specifically, input resistance was determined for each cell from the slope of a current-voltage

(i.e. I-V) curve taken at the beginning and at the end of each experimental recording, and these

values were averaged for each group of cells. Fast-spiking CA3 interneurons in the mouse

whole-hippocampus were found to have an input resistance of 360.9 ± 48.7 MΩ, and a resting

membrane potential of -61.5 ± 1.9 mV (values reported as average ± S.E.M.). Input resistance

values for CA3 and regular-firing SC pyramidal cells in the mouse whole-hippocampus were

lower, reported as 158.1 ± 32.1 and 40.8 ± 10.2 MΩ, with corresponding resting membrane

potentials of -66.7 ± 0.7 and -64.6 ± 0.8 mV, respectively. Comparatively, the input resistance

for regular-firing SC pyramidal cells in human hippocampal tissue was found to be 34.1 ± 12.7

MΩ, with an average resting membrane potential of -65.9 ± 1.1 mV. These results are similar to

those reported in the literature,19, 140, 153, 154 confirming cellular viability in both tissue

preparations used in the experiments reported here.

5.3.2 Characterizing Epileptiform Activity In Vitro

Following the application of epileptogenic low-Mg2+/high-K+ ACSF, a total of 16

spontaneous, seizure-like events were recorded from fast-spiking CA3 interneurons, with 16

similar events recorded from CA3 pyramidal neurons and another 19 from regular-firing SC

pyramidal cells in the mouse whole-hippocampus. In experiments using lesional human

hippocampal tissue, another 18 epileptiform events were recorded from regular-firing SC

pyramidal neurons. Representative examples of seizure-like activity are shown for each cell type,

50

with the ictal interval consistently defined from the onset of dense spiking activity persisting

beyond 5 seconds, independent of preictal events and often associated with a paroxysmal

depolarizing shift in membrane potential, lasting for 60 seconds of continuous epileptiform

activity (Fig. 7, A-D). Table 1 outlines certain features characterizing the observed epileptiform

dynamics for each of the four cell populations. Specifically, the mean time to onset of the first

epileptiform event following perfusion with low-Mg2+/high-K+ ACSF was approximately the

same in fast-spiking CA3 interneurons (12.4 ± 1.8 min), CA3 pyramidal cells (8.1 ± 2.2 min) and

SC pyramidal cells (11.4 ± 1.7 min) in the intact mouse hippocampus. However, the mean

duration of these events was longer in fast-spiking CA3 interneurons (5.3 ± 1.0 min) than in

either CA3 pyramidal cells (2.7 ± 0.3 min) or regular-firing SC pyramidal cells (3.0 ± 0.4 min)

(p < 0.05). Moreover, when compared to the latter group, recordings of regular-firing SC

pyramidal cells in human hippocampal slices showed a considerably slower onset of epileptiform

activity (3.8 ± 0.4 min, p < 0.05) with reduced duration as well (0.8 ± 0.2 min, p < 0.05). It is

presumably due to the use of lesional human hippocampal slices affected by mesial temporal

sclerosis and limited by less local circuitry that these time estimates are shorter compared to

cellular recordings from the healthier (and denser) intact mouse hippocampus.

5.3.3 Extracellular NLA Complexity during Epileptiform State Transitions

Extracellular recordings were obtained simultaneously to intracellular recordings in

experiments using intact mouse hippocampal tissue, to confirm the occurrence of seizure-like

events at the local network level (within 80-100 μm of the patched cell).137 As described in

Sections 5.2.4.1 and 5.2.4.2, interictal and ictal signals were selected from these field recordings,

processed to isolate the background NLA component, and then subjected to various complexity

analyses to investigate whether the surrounding local network is able to capture dynamical

differences between varying epileptiform states. Complexity measures included the correlation

dimension ( ), maximum Lyapunov exponent ( ) and approximate entropy (AE) (Fig. 8).

In this context, values for interictal NLA signals were consistently elevated suggestive of

high-complexity dynamics, irrespective of where the field electrode was placed, either in the

CA3 or SC hippocampal regions (8.82 ± 0.21, in experiments patching on to fast-spiking CA3

interneurons, n = 16 epileptiform events; 8.07 ± 0.27, in experiments patching on to CA3

51

pyramidal neurons, n = 16; and 7.91 ± 0.33 in experiments patching on to regular-firing SC

pyramidal neurons, n = 19) (Fig. 8A). Similar analysis of ictal NLA signals, however, yielded

significantly reduced values across these three cell populations (4.35 ± 0.35, 3.15 ± 0.34 and

2.92 ± 0.50, respectively; p < 0.05) suggestive of a dynamical shift towards emergent low-

complexity in the ictal state.

A second measure of complexity, , further confirmed the observed shift in

complexity as a function of epileptiform brain state (Fig. 8B). This analysis showed elevated,

positive values for interictal NLA field recordings in the vicinity of patched fast-spiking

CA3 interneurons (0.196 ± 0.034, n = 16), CA3 pyramidal cells (0.194 ± 0.050, n = 16) and

regular-firing SC pyramidal cells (0.200 ± 0.035, n = 19). Following transition to the ictal state,

was significantly reduced (but remained positive) for ictal NLA field recordings obtained

from each cell group (0.006 ± 0.001, 0.011 ± 0.005 and 0.013 ± 0.010, respectively; p < 0.05).

Again, these results imply a dynamical shift towards low-complexity in the pathological ictal

state.

A third marker of complexity, AE, was also applied to interictal and ictal NLA recorded

extracellularly (Fig. 8C). Specifically, AE values were similar for field NLA signals in the

interictal state recorded adjacent to patched fast-spiking CA3 interneurons (0.54 ± 0.05, n = 16),

CA3 pyramidal cells (0.53 ± 0.06, n = 16) and regular-firing SC pyramidal cells (0.48 ± 0.04, n =

19). Ictal NLA values for AE were significantly reduced, however, reported as 0.27 ± 0.05, 0.25

± 0.03 and 0.22 ± 0.03 across the three respective cellular populations (p < 0.05). Once again,

these results show evidence for dynamical shifts in complexity, from high- to low-complexity,

during the transition to seizure-like activity (consistent with the results using and ).

Interestingly, these results are consistent with the observed dynamical changes at the intracellular

level (reported in the following section), confirming that local network transitions mirror those

recorded from individual cells within that network. Moreover, the dynamical differences

between the interictal and ictal states validate the appropriate selection of these epileptiform

intervals at the intracellular level for subsequent multifractal analysis.

52

5.3.4 Intracellular NLA Complexity during Epileptiform State Transitions

Intracellular interictal and ictal signals were selected and processed from whole-cell

recordings of seizure-like activity obtained from intact mouse hippocampi and human

hippocampal slices under perfusion with low-Mg2+/high-K+ ACSF, as discussed previously (refer

to Sections 5.2.4.1 and 5.2.4.2). Resulting interictal and ictal NLA signals were then subjected to

various complexity analyses using the , , 1⁄ and AE measures (Fig. 9).

In particular, was elevated for all recorded interictal NLA signals, including those

from fast-spiking CA3 interneurons (5.98 ± 0.56, n = 16), CA3 pyramidal cells (5.91 ± 0.48, n =

16) and regular-firing SC pyramidal cells in the intact mouse hippocampus (5.58 ± 0.29, n = 19)

(Fig. 9A). Similarly, the latter group of cells in lesional human hippocampal slices also yielded

elevated interictal values in the range of 6.21 ± 0.26 (n = 18), suggestive of high-complexity

in interictal NLA. In contrast, was significantly reduced for ictal NLA across all four groups

of cells (2.02 ± 0.31, 1.51 ± 0.20, 3.22 ± 0.25 and 3.20 ± 0.18, respectively; p < 0.05), consistent

with emerging low-complexity in the ictal state. Similar trends were observed using the

measure, with substantial reductions from higher (positive) values for interictal NLA

signals (0.400 ± 0.141, 0.188 ± 0.055, 0.210 ± 0.057 and 0.236 ± 0.040) to lower (still positive)

values in the ictal state (0.023 ± 0.014, 0.035 ± 0.019, 0.018 ± 0.013 and 0.044 ± 0.010; p

< 0.05) for each group of patched cells, respectively (Fig. 9B). 1⁄ spectral analysis further

confirmed these findings (Fig. 9C). Specifically, interictal NLA values of the exponent, , were

lower for all four cell groups (2.12 ± 0.53, 2.05 ± 0.41, 1.92 ± 0.17 and 1.89 ± 0.19), typical of

more random-like, high-complexity dynamics; in comparison, the ictal state was characterized

by significantly elevated values (4.70 ± 0.25, 5.74 ± 0.20, 3.77 ± 0.17 and 3.37 ± 0.16; p <

0.05), suggestive of increased temporal correlations and a shift towards low-complexity NLA

dynamics. Finally, implementation of AE analysis showed additional evidence of these trends,

with greater AE measured in the interictal state (0.45 ± 0.03, 0.40 ± 0.03, 0.43 ± 0.03 and 0.38 ±

0.03) than in the ictal state (0.29 ± 0.02, 0.24 ± 0.03, 0.28 ± 0.02 and 0.20 ± 0.03; p < 0.05) for

each cell group (Fig. 9D).

Overall, these results show evidence for a shift away from high-complexity during the

transition to seizure dynamics, approaching low-complexity in the pathological ictal state. These

findings are similar to those observed in extracellular epileptiform recordings of NLA at the local

53

network level (see Section 5.3.3), supporting the notion that dynamical transitions at the cellular

level, at least in part, are also detectable in the surrounding local network. Importantly, the

dynamical differences in complexity shown here for interictal and ictal NLA signals validate

their appropriate selection for subsequent multifractal analysis.

5.3.5 Intracellular NLA Multifractality during Epileptiform State Transitions

Multifractal analysis using the wavelet-transform modulus-maxima (WTMM) technique

(outlined in Section 5.2.4.7) was applied to further investigate neurodynamical changes arising

during epileptiform transitions in mouse and human hippocampal tissue, in vitro. In particular,

differences in the degree of nonlinearity underlying interictal and ictal NLA signals recorded

intracellularly were apparent, based on computation of their respective singularity

exponents. These were subsequently used to produce multifractal singularity plots of fractal

dimension, , against the local Hurst exponent, (Fig. 10). Specifically, interictal NLA

signals revealed greater nonlinearity in consistent with increased multifractality, compared

to the emergence of increased linear scaling in the ictal state suggestive of decreased

multifractality, bordering on monofractal-type dynamics (Fig. 10A).

Singularity spectrum plots of against revealed classic parabolic relations typical

of multifractal behavior in interictal and ictal NLA signals, with evident dynamical differences

between the two epileptiform states (Fig. 10B). Notably, the multifractal relation was most

dramatically suppressed in the ictal state, becoming increasingly narrower and shifting towards

greater values of . To quantify these differences, the maximum fractal dimension on the -axis,

, its corresponding local Hurst exponent on the -axis, , and the left-hand, 95th-

percentile half-width, , for each parabolic curve was measured for interictal and ictal NLA

signals from fast-spiking CA3 interneurons, CA3 pyramidal neurons and regular-firing SC

pyramidal neurons of the intact mouse hippocampus, in addition to the latter group in human

hippocampal slices. In particular, values were significantly decreased following the

transition from the interictal state (1.07 ± 0.03, 1.22 ± 0.07, 1.04 ± 0.02 and 1.10 ± 0.02) to the

ictal state (0.85 ± 0.05, 0.90 ± 0.03, 0.89 ± 0.03 and 0.94 ± 0.01; p < 0.05) across all four cell

populations (Fig. 10C). Moreover, the transition to the ictal state coincided with a shift towards

54

increased average values for each cell group, from interictal NLA values of less than

0.5 and consistent with ‘anti-persistent’ (i.e. irregular, negatively self-correlated) dynamics (0.38

± 0.02, 0.42 ± 0.02, 0.44 ± 0.02 and 0.40 ± 0.03) to significantly greater values exceeding 0.5

and characteristic of ‘persistent’ (i.e. more regular, positively self-correlated) dynamical

behavior (0.64 ± 0.04, 0.67 ± 0.04, 0.65 ± 0.03 and 0.65 ± 0.04; p < 0.05) (Fig. 10D). Finally, the

actual width of the multifractal parabolic relation was quantified and shown to decrease

following the transition to seizure-like activity, from larger interictal NLA values (0.121 ±

0.008, 0.101 ± 0.005, 0.103 ± 0.006 and 0.109 ± 0.004) to reduced values in the ictal state (0.049

± 0.008, 0.048 ± 0.007, 0.064 ± 0.009 and 0.067 ± 0.005; p < 0.05) for each cell group (Fig.

10E). In summary, these three multifractal measures as applied to background NLA show

statistical evidence for decreased multifractal dynamics with convergence towards

monofractality, consistent with reduced dynamical complexity in the pathological ictal state.

5.4 Discussion Fractal theory was initially developed to mathematically describe the intricate, non-

Euclidean geometric forms found abundantly in the natural world, offering an escape from the

limitations imposed by traditional Euclidean concepts of geometry.63 In this context, fractals

were defined as self-similar shapes comprised of subsets resembling the whole through some

underlying relation, such that this relation persists invariantly across changes in scale or

measurement resolution. Over the last twenty to thirty years, similar ideas have been applied not

only to the structural or spatial study of real systems, as in computational fractal image and data

compression, for example,155 but also to signal analyses of time series data obtained from the

realms of science and the social sciences.

The application of fractal analyses to biomedical signals, in particular, has been recently

popularized due to varying degrees of success reported using these methods to understand the

turbulent and extraordinary complexity of various biophysical systems. Physiological signals

recorded from living systems are characterized by a tremendous degree of nonstationarity and

nonlinearity, and it is largely due to these features that their analysis has posed a significant

challenge, to date.67 However, such processes exhibit irregular, long-range, fluctuating

correlations across multiple temporal scales suggestive of fractal-like signals, making them

55

suitable targets for study using fractal techniques. Importantly, the dynamical aspect of the

scaling relation itself is what defines a given signal as mono- or multifractal. Monofractal signals

are characterized by uniformly consistent scaling throughout, quantified using a single

singularity exponent (i.e. the Hurst exponent, ); thus, they are deemed to be homogeneous.

Multifractal signals, in contrast, are inhomogeneous and hence substantially more complex; their

dynamical characterization requires a range of singularity exponents (e.g. the local Hurst

exponent, ) to capture their intrinsic scaling at each moment (or singularity) within the signal.

Aside from theoretical models and some simple systems, most real systems encountered in the

biophysical world exhibit multifractal properties.

Based on the findings in this chapter, the pathological ictal state was characterized by an

emergent shift towards low-complexity cellular NLA dynamics and reduced multifractality, as

compared to high-complexity and increased multifractality in the interictal state. Decreased

dynamical complexity in intracellular, ictal NLA signals manifested as a decrease in the ,

and AE measures, with concomitant shifts in the 1⁄ spectrum towards larger values of

(denoting a less random noise architecture with increased temporal correlations). In applying

these methodologies from dynamical systems theory, it was shown that background NLA

captures important information content that may be used to classify and identify transitions from

one brain state to another. Importantly, however, these findings also helped validate the selection

and processing of appropriate interictal and ictal signals for subsequent multifractal analysis.

Other computational attempts to investigate cellular and EEG recordings of epileptiform

dynamics have used similar, as well as alternative, techniques revealing comparable results of

reduced complexity during the transition to seizure.44, 47, 125, 126, 156, 157 Also in keeping with these

reported findings, our results specific to extracellular NLA recordings from the intact mouse

hippocampus additionally confirmed a measurable decrease in complexity at the local network

level, paralleling the results shown at the cellular scale (Figs. 8 and 9). This is substantial

because it supports the notion that local field and perhaps global EEG recordings are capable of

capturing similar dynamical transitions to those arising at the cellular level,30, 35, 36 further

justifying the use of these comparatively macroscopic recording techniques in future

neurodynamical studies.

Another interesting point shown here is the similarity in results for the complexity and

multifractal measurements across different cell populations in the intact mouse hippocampus and

56

lesional human hippocampal slices. More specifically, the CA3 hippocampal region is of

particular interest for its active role in driving intra-hippocampal events, effectively delivering

network output across the Schaffer collateral projections to the CA1 region.17, 42, 138 On the other

hand, the SC was also studied here for its role as the primary output of the hippocampus,

contributing to initiation and sustainability of epileptiform events in the brain.140, 141, 158 Both

regions were studied in the whole-intact mouse hippocampus, wherein comparable complexity

and multifractal measurements were obtained for epileptiform NLA signals recorded from fast-

spiking CA3 interneurons, CA3 pyramidal neurons and regular-firing SC pyramidal cells.

Consistency in these results between all three cell types implies that neurodynamical information

in the CA3 region is potentially retained, at least in part, during signal transmission along the

outflow path of the local intra-hippocampal circuit, passing through the subsequent CA1 and SC

regions. Interestingly, intracellular, interictal NLA values for were more heterogeneous in

fast-spiking CA3 interneurons as compared to pyramidal cells (shown by more expansive error

bars for CA3 interneurons in Fig. 9B), suggesting potential variability in this cell population and

possible sensitivity of the measurement to this factor. On another note, results were

compared for regular-firing SC pyramidal cells between the intact mouse hippocampus and

lesional human hippocampal slices, since the CA3 region in the latter is typically victim to

pathological changes including chronic gliosis and marked neuronal loss, all of which could

potentially result in altered signal effects.5 However, complexity and multifractal results were

comparable between the two models, suggesting that these neurodynamical measures of

intracellular NLA may be fundamental properties ubiquitously captured at the cellular scale.

To date, no multifractal studies have been conducted on in vitro epileptogenic recordings

of background neuronal NLA from either rodent or human hippocampal tissue. The findings

reported here show evidence for varying complexity and multifractal scaling in cellular NLA,

specifically revealing that these features become altered during the transition to seizure-like

activity. In particular, measurements from parabolic multifractal singularity plots show increased

fractal dimension and anti-persistent dynamics for interictal NLA, compared to a reduced fractal

dimension and shift towards increasingly persistent dynamics in the ictal state (Fig. 10).

Concomitantly, a narrower range of multifractality was identified for ictal NLA signals,

converging towards increasingly monofractal behavior, suggesting that breakdown in

multifractal complexity coincides with loss of signal variability and heterogeneity. This is

57

consistent with an unhealthy state that is far from the equilibrium of turbulent yet healthy fractal

complexity. Similar findings of reduced fractality in pathological states, measured either by

shifting multifractal dynamical relations or even as subtle changes in monofractality, have also

been reported in vivo for seizure-like EEG recordings using implanted electrodes84 and for

various other disease-like conditions, including congestive heart failure67, 74, 80-82 and Parkinson’s

disease.83 Thus, it may be argued that the application of complexity and fractal theories is

essential to the study of neurodynamical behavior in physiological time series data.

In summary, the neurodynamical results shown here support the conclusion that ictal

NLA is characterized by reduced multifractal complexity. Moreover, this supports the hypothesis

that NLA contains complex and multifractal signal features that may, at least in part, be used to

classify and identify brain state transitions in the healthy and epileptic brain. Nevertheless,

ongoing advances in the mathematical and neuroengineering sciences, combined with

technologically-enhanced alternatives to collecting essential physiological data from the central

nervous system, are increasingly necessary to pave the way for an improved understanding of

spatiotemporal dynamics in the healthy and diseased brain. One such advance involves multi-

spatial recording techniques and synchrony analysis across multiple sites in the local network

and beyond, a concept which forms the subject for the next chapter.

58

Table 1. Characteristics of epileptiform activity in vitro

Tissue Model

Cell Type

# of Cells

# of EEs

(n)

Mean Time to EE onset (minutes)

Mean EE Duration (minutes)

Intact Mouse Hippocampus

Fast-spiking CA3 interneuron

11

16

12.4 ± 1.8

5.3 ± 1.0*

CA3 pyramidal

8

16

8.1 ± 2.2

2.7 ± 0.3

Regular-firing SC pyramidal

10

19

11.4 ± 1.7

3.0 ± 0.4

Human Hippocampal

Slices

Regular-firing SC pyramidal

9

18

3.8 ± 0.4**

0.8 ± 0.2***

Summary of the total number of patch-clamped cells and epileptiform events (EEs) recorded

from mouse and human hippocampal tissue in vitro, including the mean time to first onset and

mean duration of each EE. * p < 0.05 compared to mean EE duration in mouse CA3 and SC

pyramidal cells. ** p < 0.05 compared to mean time to EE onset in mouse SC pyramidal cells.

*** p < 0.05 compared to mean EE duration in mouse SC pyramidal cells.

59

Figure 5. Isolation of background NLA by spike attenuation from an intracellular

recording of epileptiform activity. Whole-cell (i.e. intracellular) recording of a seizure-like

event from a patch-clamped CA3 interneuron treated with low-Mg2+/high-K+ ACSF (left),

showing spiking dynamics therein. Computational, threshold-based spike detection and iterative

attenuation of large amplitude spikes yields the residual, isolated, background NLA signal (right)

used in subsequent complexity and multifractal analyses.

60

Figure 6. Complexity measures as a function of signal length for representative interictal

and ictal NLA signals. A, correlation dimension, , and maximum Lyapunov exponent, ,

plotted against signal length for interictal NLA signals recorded intracellularly from four

different representative cell types in mouse and human hippocampal tissue. B, and as a

function of signal length for ictal NLA signals recorded from the same four cells. In all cases,

both measures of complexity converged towards plateau values after some finite time interval.

These findings show that longer interictal NLA signal lengths of 500 seconds (A, columns 1-3)

and shorter ictal NLA signal lengths of 60 seconds (B, columns 1-3) were necessary to fully

capture inherent dynamical information in NLA recorded from cells in the intact mouse

hippocampus. In comparison, results from lesional human hippocampal slices revealed that

shorter interictal and ictal NLA signal lengths of 30 seconds (A and B, column 4) were sufficient

to appropriately capture the dynamical content therein. Thus, subsequent complexity and

multifractal analyses were conducted using the signal lengths identified here.

61

Figure 7. Representative seizure-like events recorded in mouse and human hippocampal

tissue. A, simultaneous intracellular (‘Intra’) and extracellular (‘Extra’) recordings of

epileptiform activity obtained from a fast-spiking CA3 interneuron in the stratum oriens layer of

the whole-intact mouse hippocampus, under perfusion with low-Mg2+/high-K+ ACSF. B, similar

recordings of seizure-like activity in a patched CA3 stratum pyramidale neuron in the intact

mouse hippocampus. C, epileptiform dynamics recorded from a regular-firing SC pyramidal

neuron in the intact mouse hippocampus. D, whole-cell recording of seizure-like activity in a

regular-firing SC pyramidal neuron in a lesional human hippocampal slice. The current-voltage

(I-V) relationship for each cell is shown (top left). Extracellular signals were only obtained in

experiments using the intact mouse hippocampus to confirm epileptiform activity in the

surrounding local network arising within 100 μm of the intracellular electrode. Ictal intervals

were defined from the onset of dense spiking activity persisting beyond 5 seconds, independent

of preictal events and often associated with a paroxysmal depolarizing shift in membrane

potential, lasting for 60 seconds of continuous epileptiform activity (shown by a horizontal line

above each intracellular trace). In contrast, the interictal signal was defined as spontaneous

activity preceding any obvious preictal events and the ictal state itself.

62

Figure 8. Complexity analyses of local network NLA from epileptiform dynamics recorded

in the whole-intact mouse hippocampus. A, average correlation dimension, , of interictal

(IIC) and ictal (IC) NLA signals from extracellular recordings of seizure-like activity captured in

the local network surrounding patch-clamped fast-spiking CA3 interneurons (n = 16), CA3

pyramidal neurons (n = 16) and regular-firing SC pyramidal neurons (n = 19). values were

highest in the interictal state, irrespective of the location of the recording field electrode in the

CA3 or SC region. was significantly decreased in the ictal state across all three groups,

consistent with a shift towards low-complexity dynamics in this pathological state. B, average

values of the maximum Lyapunov exponent, , as a function of epileptiform state. Values of

were higher (and positive) for interictal NLA signals; following transition to the ictal state,

decreased significantly to near-zero, yet still positive, values. Consistent with the

results, these findings show emerging low-complexity in the ictal state as compared to high-

complexity interictal dynamics. C, average values of approximate entropy (AE), used as another

measure of dynamical complexity, were computed for the same interictal and ictal NLA signals

as in A and B. AE values for interictal NLA signals were comparably higher across all three

63

groups compared to significantly reduced values in the ictal state, revealing a shift from high- to

low-complexity during the transition to seizure-like activity. Overall, these results show evidence

for decreased dynamical complexity in the pathological ictal state, as measured in NLA recorded

at the local network level. Values are reported as mean ± S.E.M. (shown by error bars). * p <

0.05 compared to interictal values.

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Figure 9. Complexity analyses of intracellular NLA in epileptiform dynamics. A, average

correlation dimension, , for processed interictal (IIC) and ictal (IC) NLA signals from

intracellular epileptiform recordings in the intact mouse hippocampus (fast-spiking CA3

interneurons, n = 16; CA3 pyramidal neurons, n = 16; regular-firing SC pyramidal neurons, n =

19) and lesional human hippocampal slices (regular-firing SC pyramidal neurons, n = 18).

was significantly decreased in the pathological ictal state, capturing a dynamical shift from high-

to low-complexity during the transition to seizure. B, average values of the maximum Lyapunov

exponent, , as a function of epileptiform state for each of the four cellular populations.

Large, positive values of characterized interictal NLA signals, with significant reductions

to near-zero (yet still positive) values in the ictal state; these findings again confirm reduced

complexity in the latter. Also, note the increased heterogeneity in values for fast-spiking

CA3 interneurons (shown by larger error bars), suggesting potential variability in this cell

population as compared to the other three groups of pyramidal cells. C, plots of the average

scaling exponent, , from 1⁄ spectral analysis of interictal and ictal NLA signals recorded

intracellularly. Values of were significantly elevated in ictal NLA across each cell group,

implying a shift towards a smoother, less random 1⁄ relation and emerging low-complexity

dynamics in ictal NLA. D, average values of approximate entropy (AE) as a function of

epileptiform state, showing significantly decreased values in ictal NLA; again, these findings

confirm dynamical deviation from high-complexity in the interictal state during the transition to

seizure. Values are reported as mean ± S.E.M. (shown by error bars). * p < 0.05 compared to

interictal values.

65

Figure 10. Altered multifractal complexity of neuronal NLA in epileptiform dynamics. A,

representative singularity exponents plotted as a function of order, , for interictal (IIC) and

ictal (IC) NLA signals recorded from a patch-clamped regular-firing SC pyramidal cell in a

lesional human hippocampal slice. The interictal NLA signal displayed a greater degree of

nonlinear scaling (solid line), shown by increased curvature in the plot, consistent with

increased multifractality. Conversely, ictal NLA was characterized by comparatively linear

scaling (dotted line) suggestive of reduced multifractal, almost monofractal, scaling. B,

corresponding multifractal singularity spectrum plotting fractal dimension, , as a function of

the local Hurst exponent, , for the same interictal and ictal signals as in A. Note the classic,

broad, parabolic curve typical of multifractal complexity, particularly evident for the interictal

state. In contrast, this relation was narrowed in the ictal state and displaced towards higher

values exceeding 0.5, implying reduced multifractality and decreasingly anti-persistent,

increasingly persistent, dynamics. C, D and E, averaged plots of maximum fractal dimension,

, corresponding local Hurst exponent, , and left-hand, 95th-percentile half-width,

, as a function of interictal and ictal NLA signals from the intact mouse hippocampus (fast-

spiking CA3 interneurons, n = 16; CA3 pyramidal neurons, n = 16; regular-firing SC pyramidal

neurons, n = 19) and lesional human hippocampal slices (regular-firing SC pyramidal neurons, n

= 18). Note the significant decrease in , increased , and lower values

characterizing NLA in the pathological ictal state. These findings respectively confirm reduced

fractal dimension, less anti-persistent (i.e. increasingly persistent) dynamics and decreased

66

multifractal complexity during the transition to seizure-like activity. Values are reported as mean

± S.E.M. (shown by error bars). * p < 0.05 compared to interictal values.

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6 Phase Synchronization of Neuronal Noise-Like Activity in Hippocampal Epileptiform Dynamics

6.1 Overview Organized brain activity is a function of dynamical synchronization across independent

brain regions. The interplay between individual neurons within a local network is thought to

capture the spatiotemporal evolution of healthy and pathological (e.g. epileptiform) events in the

brain. Hence, the application of sophisticated neuroengineering techniques to simultaneous

recordings of spatially segregated neuronal signals may therefore detect subtle synchronization

effects pertaining to the transition to seizure-like activity. Phase synchrony analysis, in

particular, has evolved as one such method that may be used to identify transient, frequency-

specific coupling effects across multi-site signals. Given that neuronal noise-like activity (NLA)

was characterized in the previous two chapters by a shifting spectrum of complex and

multifractal properties in healthy and epileptiform brain activity, it is foreseeable that NLA

signals from distinct cellular units within a given network may be invariably related, becoming

increasingly correlated and synchronized during transitions to the pathological ictal state. To

explore this notion further, this chapter investigates the possibility for synchronization among

dual intracellular recordings of NLA underlying epileptiform events recorded from the whole-

intact mouse hippocampus, postulating that multi-spatial NLA signals are amenable to

synchronization effects, at least within a local hippocampal network, becoming increasingly

synchronized during dynamical transitions to seizure-like activity (Hypothesis 3).

To test this hypothesis, interictal and ictal states were identified in dual intracellular

recordings of epileptiform activity from fast-spiking CA3 stratum oriens interneurons and/or

CA3 stratum pyramidale neurons in the intact mouse hippocampus, under perfusion with low-

Mg2+/high-K+ artificial cerebrospinal fluid (ACSF). Background NLA in these signals was then

isolated using a threshold-based, spike-attenuation algorithm that effectively suppressed large-

amplitude spiking dynamics, leaving behind residual NLA (Fig. 5).136 Wavelet-based methods of

coherence, bicoherence and phase synchronization analysis were adapted from previous studies

of nonlinear phase coupling across two field electrodes capturing hippocampal epileptiform

transitions in vivo,102, 103 and these were implemented here to investigate similar effects across

dual interictal and ictal NLA signals.

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Based on the results in this chapter, same- and cross-frequency phase correlations were

identified among dual NLA signals in at least three frequency bands [theta (4-10 Hz), beta (12-

30 Hz) and gamma (30-80 Hz)42], with increased phase coupling emerging during the transition

from the interictal to the ictal state. Moreover, qualitative and statistical evidence was found for

increased phase synchronization of the theta, beta and gamma frequency bands in dual

recordings of ictal NLA, as compared to interictal NLA signals. Hence, these findings validate

the use of multi-spatial recordings of background NLA in studying neurodynamical transitions to

seizure activity, showing that this otherwise unassuming signal is amenable to synchronization

effects that manifest in lower but also in higher frequency ranges, at least within the same local

network in the hippocampus.


6.2.1 Animal Tissue

Electrophysiological experiments using the whole-intact hippocampus preparation from

C57/BL mice (P10-14) were conducted in strict adherence to the regulations and policies set

forth by the University Health Network’s Animal Care Committee. The General Methods

(Section 3.1.1) provide a detailed summary of the specific dissection and tissue preparation

protocols implemented here.


The general electrophysiological approach and related materials used in these

experiments were previously described in Section 3.2 of the General Methods. Specific to this

chapter, dual whole-cell voltage recordings were simultaneously collected under current-clamp

from different paired combinations of two cell types: fast-spiking CA3 stratum oriens

interneurons [selected according to specific electrophysiological criteria111 and morphological

appearance under infra-red visualization112] and CA3 stratum pyramidale neurons. For each dual

recording, the two intracellular electrodes were consistently measured to be in near vicinity to

one another (no more than 100 μm apart), increasing the likelihood that both patched cells were

69

in the same local network.137 The CA3 location was targeted given its apparent role as the driver

of intra-hippocampal activity, delivering its outputs to the CA1 region via the Schaffer collateral

projection fibers.17, 42, 138

Following 5 minutes of stable recording under ACSF, current pulses were delivered to

ensure cellular viability. The perfusion solution was then switched from ACSF to a low-

Mg2+/high-K+ ACSF solution reliably known to induce epileptiform activity,7, 21 containing (in

mM): 123 NaCl, 5 KCl, 1.5 CaCl2, 0.25 MgSO4, 25 NaHCO3, 1.2 NaH2PO4 and 25 glucose (pH

7.4). During perfusion with the latter solution, continuous dual intracellular recordings captured

the onset and resolution of epileptiform events from two cellular sources up to a maximum

length of 1 hour before washing out with ACSF.

6.2.3 Chemicals

All chemicals were purchased from Sigma-Aldrich.

6.2.4 Data Analysis

6.2.4.1 Selection and Processing of Interictal and Ictal NLA Signals

All data processing and subsequent computational analyses were performed in MATLAB

7.7 (The MathWorks, Inc.). The protocol for selecting interictal and ictal signals, followed by

subsequent spike attenuation of large amplitude spikes to isolate residual NLA in the

background,136 has already been described in detail (refer to Chapter 5, Sections 5.2.4.1 and

5.2.4.2). These steps were applied here to dual intracellular recordings of epileptiform activity in

the intact mouse hippocampus, yielding simultaneous recordings of interictal and ictal NLA that

were then subjected to phase synchronization analysis.

70

6.2.4.2 Continuous Wavelet Transform Analysis and Wavelet Power

Continuous wavelet transforms (CWT) of spike-attenuated NLA signals in each dual set

of recordings were computed as described in Chapter 4 (Section 4.2.4.2).

6.2.4.3 Wavelet-Based Coherence

Intermittent first-order dynamical interactions in the frequency domain were quantified

for dual intracellular NLA signals, and , using a wavelet-based measure of coherence.

This measure was modified from the Fourier-based coherence function, taken as the ratio of the

cross spectrum to the product of the auto-spectrum of the two signals, such that:103

, ,

, ,

where and are the wavelet scaling and translation factors. Importantly, the localized power

spectrum, , , is given by:

, , , , ,

with wavelet power, , for the time series, , computed such that:102, 103

| , |

and with , denoting the complex conjugate of the wavelet power term, , , for the

time series, , at a desired temporal resolution, , in the subsequent coherence map. Note that

, and , are each defined by a similar equation to that shown above.

6.2.4.4 Wavelet-Based Bicoherence

The degree of nonlinear phase coupling for paired intracellular NLA signals was

computed via a wavelet-based technique for computing the bicoherence spectrum. This approach

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is comparatively better than traditional Fourier-based methods that are unable to detect nonlinear

interactions in the short-term, and is even able to identify zero bicoherence when no phase

coupling is present.159 Moreover, this method also permits the quantification of inherent phase

coupling and identification of independent sources between two signals.103, 160

At the desired temporal resolution, , the wavelet cross-bispectrum for two time series,

and , is given by:160

, , , , , ,

with:

defining the range for . Wavelet bicoherence was then calculated as:

, ,

| , , | ,

assuming values between 0 (consistent with no coupling) and 1 (for maximal phase coupling).

6.2.4.5 Measuring the Phase Synchronization Index

The phase relationship between each set of dual NLA signals recorded from two

channels, and , was quantified using a measure of phase synchronization adapted from recent

studies of epileptiform dynamics at the local network scale.94, 101-103 Assuming each wavelet

coefficient for a given set of dual NLA signals to behave as weakly-coupled periodic oscillators,

the algorithm computes the phase angle, , in 2 radian space for each coefficient as a function

of time, . It then follows that the phase difference is given by:

, ,, , ,

72

where , and , denote the time-varying phase estimates for each wavelet

coefficient, , , and and satisfy a condition of resonance:

between the two frequencies, and , of the coupled oscillators.

For computational simplicity and to be consistent with other studies using this method,

the restriction that was also imposed here.102, 103 The distribution of the cyclic relative

phase, calculated modulus 2 from the phase difference, is then determined by:

, , ,, 2

yielding a measure of phase synchrony between channels and , such that peaks in ,

correspond to coupled interactions between the two oscillators. To quantify the strength of this

interaction, the magnitude of the first Fourier mode of the distribution was computed by:

cos , sin ,

with the phase synchronization index, PSI, yielding values between 0 and 1 (where the latter

denotes maximal synchrony). In addition to computing the individual PSI for each wavelet

coefficient, PSI values were also averaged over the range of coefficients within each of three

specific frequency bands, theta (4-10 Hz), beta (12-30 Hz) and gamma (30-80 Hz).42


Experimental data were subjected to one-way analysis of variance (ANOVA) using a

Bonferroni post-hoc test. Significance was determined from comparison to interictal values

(serving as the control) in the context of perfusion with low-Mg2+/high-K+ ACSF, and p-values

are reported where significant for p < 0.05. Each sample size (e.g. n = 1) equates to a single

epileptiform event recorded from a set of dual patch-clamped cells, unless otherwise specified.

All data are reported in consistent format as mean ± S.E.M.

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6.3 Results

6.3.1 Passive Cellular Membrane Properties

Dual patch-clamp recordings of intracellular membrane potential fluctuations were

collected from three different groups of paired cells in the CA3 region of the intact mouse

hippocampus. These comprised fast-spiking interneuron pairs, fast-spiking interneuron-

pyramidal neuron pairs and pyramidal neuron pairs, with the patched cells in each pair spaced no

more than 100 μm apart.137 Passive membrane properties, namely cellular input resistance and

resting membrane potential, were measured for both cell types. Specifically, input resistance was

determined from the slope of current-voltage (i.e. I-V) curves generated at the beginning and end

of each experimental recording. Fast-spiking CA3 interneurons were found to have an input

resistance of 340.5 ± 38.2 MΩ and a resting membrane potential of -62.1 ± 1.7 mV, whereas

CA3 pyramidal neurons were characterized by a lower input resistance of 167.3 ± 26.9 MΩ and

a comparatively hyperpolarized resting membrane potential of -67.3 ± 1.3 mV (values reported

as average ± S.E.M.). Similar values have been reported in the literature,19, 140, 153, 154 confirming

cellular stability in these electrophysiological experiments using the intact mouse hippocampal

preparation.

6.3.2 Epileptiform Activity in Dual Intracellular Recordings

Perfusion with epileptogenic low-Mg2+/high-K+ ACSF reliably and consistently induced

intracellular seizure-like events in all dual-patched cells. Briefly, 16 spontaneous epileptiform

events were recorded from 7 fast-spiking interneuron pairs, with another 10 such events collected

from 6 fast-spiking interneuron-pyramidal neuron pairs and 14 similar events recorded from 7

pyramidal neuron pairs (i.e. n = 16, 10 and 14, respectively). Representative pairs of intracellular

epileptiform recordings are shown (Fig. 11, A-C), with the ictal interval defined from the onset of

dense spiking activity, independent of preictal events and often associated with a paroxysmal

depolarizing shift in membrane potential, lasting for 60 seconds of continuous epileptiform

activity. Despite subtle variations leading up to the seizure event, qualitative visualization of ictal

dynamics confirms apparent synchronization of intracellular dynamical activity between the two

signals and suggesting that both cells in each pair belonged to the same local network.

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6.3.3 Nonlinear Phase Correlations of NLA in Epileptiform Dynamics

Following selection and processing of interictal and ictal NLA signals (as described in

Chapter 5, Sections 5.2.4.1 and 5.2.4.2), a wavelet-based measure of coherence was applied to

qualitatively investigate intrinsic first-order dynamical correlations within each set of dual patch-

clamped cells. The results for dual NLA signals from three representative cell pairs are shown

(Fig. 12, A-C), revealing lower wavelet coherence in the interictal state, most notably in the theta

(4-10 Hz) and beta (12-30 Hz) frequency bands, despite greater correlations in the higher gamma

(30-80 Hz) range. In contrast, the ictal state was characterized by markedly increased wavelet

coherence in the theta and beta ranges, with subtle increases in the gamma range as well,

suggestive of increased first-order dynamical correlations spanning the frequency spectrum in

the pathological ictal state.

Wavelet bicoherence analysis was used to qualitatively investigate the higher-order

interactions underlying nonlinear phase coupling in these recordings (Fig. 13, A-C).

Interestingly, interictal NLA signals were characterized by variable phase coupling between

different cell pairs. Despite this intrinsic variability, same-frequency coupling was generally

increased across the frequency spectrum in the ictal state (shown along the diagonal in

bicoherence plots), with the most dramatic changes seen in the theta and beta frequency bands.

In addition, bicoherence plots of dual NLA signals also showed evidence for enhanced cross-

frequency coupling between lower and higher frequencies in the ictal state (shown by

measurements off the diagonal in bicoherence maps). In general, these trends were consistent

across all three groups of paired cells, suggesting that increased same- and cross-frequency phase

coupling may be a fundamental epiphenomenon underlying neurodynamical transitions into

epileptiform activity.

6.3.4 Phase Synchronization of NLA in Epileptiform Dynamics

A wavelet-based measure of phase synchrony termed the ‘phase synchronization index’

(PSI) was implemented to quantify the degree of phase coupling in dual NLA signals underlying

epileptiform dynamics recorded from the intact mouse hippocampus. Used as an estimate of the

interactive coupling strength between two independent oscillators, the PSI ranges between values

75

of 0 (asynchrony) and 1 (maximal synchrony), as shown for representative wavelet-type PSI

maps plotting signal frequency versus time (Fig. 14, A-C). In general, this analysis showed that

variable frequencies within the theta, beta and gamma frequency bands in background NLA were

asynchronous across dual recording sites during the interictal state, but that the overall PSI was

markedly increased in the ictal state consistent with enhanced synchronization.

Importantly, average PSI values calculated for each of the theta, beta and gamma

frequency bands were more revealing of this trend, as shown for three representative cell pairs

(Fig. 15, A-C). In particular, PSI values for each frequency band heterogeneously ranged

between 0 and 1 in the interictal state, with evident convergence towards maximal

synchronization (i.e. PSI ~ 1) in the ictal state. Moreover, this shift was consistently identified

across all three frequency bands, suggesting that relevant dynamical information capturing the

transition to seizure spans not only low frequencies, but higher ones as well (at least up to the

gamma range). These results were further quantified by arithmetically computing the PSI mean

and variance (Fig. 16, A-C), showing significantly increased mean PSI values and a

concomitantly reduced PSI variance (i.e. towards increased homogeneity) in the pathological

ictal state. Taken together, these results present statistical evidence for increased synchronization

of the theta, beta and gamma frequencies in dual NLA signals during the pathological ictal state.

6.4 Discussion Neurophysiological signals are becoming increasingly subjected to diverse computational

analyses in an attempt to delineate the rules of governing dynamics regulating both healthy and

pathological events in the brain. This neuroengineering approach has been further boosted by

ongoing technological advances leading to improved multi-site recordings in the experimental

and clinical realms. As a result, a clear trend has emerged with specific emphasis on the

multivariate study of parallel neuronal recordings and their inherent time- and frequency-

sensitive interdependencies, complementing traditional univariate analyses of single-site data.

Complex interaction dynamics arising within and between local neuronal networks are not

obvious, thus necessitating sophisticated methods from information theory and nonlinear

dynamical systems theory to study them further.

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Based on the results shown in this chapter, there is evidence for first-order (same-

frequency) and higher-order (cross-frequency) correlations between dual intracellular recordings

of NLA from the CA3 region of the intact mouse hippocampus using wavelet-based coherence

and bicoherence techniques (Figs. 12-13). Importantly, these features were measurably increased

in the ictal state compared to variable phase coupling in the interictal state, with the greatest

qualitative increases observed in the theta (4-10 Hz) and beta (12-30 Hz) frequency bands, and

with subtle increases in the gamma (30-80 Hz) range, as well. In addition to increased same-

frequency coupling, bicoherence plots also confirmed increased cross-frequency coupling

between lower and higher frequencies in the ictal state, suggestive of nested oscillations phase-

locked over fast and slow time scales.85 Similarly, increased cross-frequency phase

synchronization among alpha (~10 Hz), beta (~20 Hz) and gamma (~30-40 Hz) activity has also

been demonstrated for certain cognitive tasks using magnetoencephalographic recordings of

neuronal oscillations from the human cortex,161 consistent with the findings reported here but at a

comparably more macroscopic scale.

A measure of phase synchronization, the phase synchronization index (PSI), was

averaged across three frequency bands (i.e. theta, beta and gamma) and showed maximal

synchrony in the pathological ictal state (Figs. 14-16). This trend was confirmed across three

different cellular combinations of dual intracellular recordings, suggesting that this may be a

fundamental epiphenomenon of the transition to epileptiform dynamics in the CA3 region of the

intact hippocampus. The idea of increased synchrony as a mechanism contributing to the onset

and persistence of pathological seizure dynamics is an intuitive one, given that the hallmark of

epileptiform activity is typically regarded as the sudden disproportionate increase in neuronal

synchronization spanning different brain regions.8, 10 There is evidence in the literature

supporting this concept, with higher local phase synchrony (compared with fluctuating distant

synchronization across remote networks) reported for global human EEG recordings of

epileptiform dynamics, suggestive of progressive recruitment of adjacent neuronal networks in

the seizure state.8 Another study of epileptiform patterns in global EEG recordings from human

patients also revealed increased phase synchronization in local neighboring networks during

seizure-like activity,162 showing that the results shown here from in vitro experimentation are

comparable to in vivo observations. In fact, subthreshold electrical stimulation has been proposed

as an abortive intervention to reduce the reportedly higher phase synchrony underlying

77

epileptiform events in an attempt to control transitions to seizure activity, based on theoretical

and experimental models that have met with moderate success under certain conditions.163

Nevertheless, there is also recent evidence to suggest that increased synchrony is not

consistently the case, with several studies describing an initial desynchronization in the preictal

and early ictal states during epileptiform events recorded at the intracellular and global EEG

scales.93, 101 There are several reasons to account for this apparent discrepancy with the results

shown here, beginning with the fact that the experiments here were confined to analysis of

isolated background NLA signals following application of a spike attenuation algorithm to

remove large-amplitude, deterministic spikes in the foreground.136 Other important

methodological differences compared to other studies include the fact that recordings here were

performed in the CA3 region, arguably the driver of the intra-hippocampal circuit and

characterized by increased connectivity compared to CA1, 17, 42, 164 of the whole-intact mouse

hippocampus (as opposed to conventional slices). Finally, the definition of the ictal state used in

this thesis avoided inclusion of the elusive preictal interval,8, 93 placing the signals used here at a

comparatively later stage in the course of epileptiform evolution and focusing subsequent

analysis on an interval embedded within these dynamics (rather than preceding it).

Ultimately, these varied reports of fluctuating synchronization during seizure-like events

would suggest that the degree of phase synchrony within a given network is dependent on a wide

range of factors including the expansive distribution of the brain region(s) under study and the

exact experimental and computational methods used for analysis. Ongoing studies into specific

anatomical substrates and the emerging role of variable synchronization in epileptiform

dynamics are likely to clarify some of these issues and perhaps contribute to a better

neuroarchitectural understanding of the epileptiform focus as a pocket of local synchronous

networks embedded in a sea of desynchrony.8 Hence, this underscores the importance of

studying phase synchronization in biomedical signals, along with other neuroengineering

techniques, that will eventually lead to improved methodologies for detecting and perhaps

treating seizures in afflicted patients. Moreover, given the findings reported here, this supports

the hypothesis that multi-site recordings of neuronal NLA are invariably related and may be used

to detect synchronization in the local network by tracking nonlinear phase correlations during the

transition to seizure. Ultimately, this suggests that multi-spatial recordings of background NLA

78

are also important to future studies of neurodynamical transitions in the healthy and epileptic

brain, and should therefore be included in future research endeavors.

79

Figure 11. Representative dual intracellular recordings of epileptiform events in the CA3

region of the intact mouse hippocampus. A, dual whole-cell (i.e. intracellular) recordings of

seizure-like activity obtained from two fast-spiking CA3 interneurons in the stratum oriens layer

of the whole-intact mouse hippocampus, under perfusion with low-Mg2+/high-K+ ACSF. B,

similar recordings of epileptiform dynamics from a fast-spiking CA3 interneuron (top) and CA3

stratum pyramidale neuron (bottom). C, seizure-like event recorded from dual CA3 pyramidal

80

neurons. For each dual patch configuration, cells were no more than 100 μm apart. Current-

voltage (I-V) relationships for each cell are shown (top left of each trace). Ictal intervals were

defined from the onset of dense spiking activity, independent of preictal events and often

associated with a paroxysmal depolarizing shift in membrane potential, lasting for 60 seconds of

continuous epileptiform activity (represented by a horizontal line above each trace). Despite

subtle variations leading up to the seizure event, ictal dynamics appeared synchronous between

each pair of signals.

81

Figure 12. Wavelet coherence plots for representative dual NLA signals from intracellular

recordings of interictal (IIC) and ictal (IC) dynamics. A, wavelet coherence plots of

frequency versus time for dual interictal and ictal NLA recorded from two fast-spiking CA3

interneurons under perfusion with low-Mg2+/high-K+ ACSF. B, similar plots for dual NLA

signals recorded from a fast-spiking CA3 interneuron and CA3 pyramidal neuron. C, wavelet

coherence measured for comparable recordings from dual CA3 pyramidal neurons. The color

scale (right) indicates the degree of coherence, used as a measure of first-order dynamical

correlations. Coherence was lower in the interictal state, particularly across the theta (4-10 Hz)

and beta (12-30 Hz) frequency bands, with greater correlations in the higher gamma (30-80 Hz)

range. The ictal state was characterized by increased coherence in the theta and beta ranges with

subtle increases observed in gamma, as well. These findings qualitatively suggest that first-order

dynamical correlations are increased across the frequency spectrum in the pathological ictal

state.

82

Figure 13. Wavelet bicoherence plots for representative dual NLA signals from

intracellular recordings of interictal (IIC) and ictal (IC) dynamics. A, wavelet bicoherence

for dual interictal and ictal NLA signals from two fast-spiking CA3 interneurons under perfusion

with low-Mg2+/high-K+ ACSF. B, bicoherence plots for comparable recordings from a fast-

spiking CA3 interneuron and CA3 pyramidal neuron. C, similar plots for dual NLA signals

recorded from two CA3 pyramidal neurons. The color scale (right) denotes the bicoherence

measure capturing nonlinear, higher-order dynamical correlations for each dual set of recordings.

Overall, the interictal state was marked by variable correlations across the bicoherence spectrum

for each pair of neurons, without any consistent trends emerging from these results. In contrast,

the ictal state was consistently characterized by increased same-frequency coupling occurring

along the diagonal (i.e. 45-degree line drawn through the origin) of the bicoherence plots,

particularly in the theta (4-10 Hz) and beta (12-30 Hz) ranges, suggestive of increased first-order

83

phase coupling in the ictal state. Moreover, there was evidence for enhanced cross-frequency

coupling in the ictal state, manifesting either above or below the diagonal of the bicoherence

plots, implying that nonlinear phase coupling between lower and higher frequencies was also

increased in the pathological ictal state. These trends were consistent across all three different

groups of neuron pairs, suggesting that increased first- and higher-order nonlinear correlations

may be fundamental to neurodynamical transitions into epileptiform activity, rather than a cell-

specific phenomenon.

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Figure 14. Wavelet-based phase synchronization index (PSI) for representative dual NLA

signals from intracellular recordings of interictal (IIC) and ictal (IC) dynamics. A, phase

synchrony plot of frequency versus time for dual interictal and ictal NLA signals from two fast-

spiking CA3 interneurons under perfusion with low-Mg2+/high-K+ ACSF. B, similar plot for dual

NLA signals from a fast-spiking CA3 interneuron and CA3 pyramidal cell. C, phase

synchronization of comparable signals recorded from two CA3 pyramidal neurons. The color

scale (right) indicates the PSI, ranging from asynchrony (i.e. PSI = 0) to maximal

synchronization (i.e. PSI = 1), capturing the degree of interactive coupling between dual NLA

signals. In general, the interictal state was marked by heterogeneous phase asynchrony within the

theta (4-10 Hz), beta (12-30 Hz) and gamma (30-80 Hz) ranges, with qualitative evidence of

increased phase synchronization in ictal dynamics. These results imply that neuronal NLA

85

captures dynamical information content pertaining to epileptiform transitions, becoming

increasingly synchronized in the pathological ictal state across neurons in the same local

network.

86

Figure 15. Frequency-specific phase synchronization index (PSI) for dual NLA signals from

intracellular recordings of interictal (IIC) and ictal (IC) dynamics. A, plots of three separate

PSI values over time for the theta (4-10 Hz), beta (12-30 Hz) and gamma (30-80 Hz) frequency

ranges in interictal and ictal NLA signals from dual fast-spiking CA3 interneurons. B, similar

PSI plots for dual NLA signals recorded from a fast-spiking CA3 interneuron and CA3

pyramidal neuron. C, PSI plots of comparable signals from dual CA3 pyramidal cells. Average

PSI values for the interictal state ranged heterogeneously within each frequency band, between

nearly asynchronous (i.e. PSI = 0) and maximally synchronized values (i.e. PSI = 1), with

evidence of convergence towards maximal synchrony in the ictal state. This trend was consistent

for all three frequency bands in each of three different groups of paired neurons, implying that

NLA has dynamical features spanning both lower and higher frequencies, irrespective of cell

type, that capture increased phase coupling and synchronization in the pathological ictal state.

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Figure 16. Statistical mean and variance analyses of the phase synchronization index (PSI).

A, PSI mean and variance for the theta (4-10 Hz), beta (12-30 Hz) and gamma (30-80 Hz)

frequency bands for interictal and ictal NLA signals recorded from dual fast-spiking CA3

interneurons (n = 16). B, comparable plots of PSI mean and variance for dual NLA signals from

fast-spiking CA3 interneurons and CA3 pyramidal neurons (n = 10). C, PSI mean and variance

for similar recordings from dual CA3 pyramidal cells (n = 14). PSI mean values were

significantly increased towards maximal synchrony (i.e. PSI = 1) in the pathological ictal state

across all three groups of dual-patched neurons (left traces). Concomitantly, PSI variance was

significantly reduced in the ictal state (right traces). These trends, observed across the theta, beta

and gamma frequency bands, are statistical evidence for increased ictal synchronization of NLA

dynamics. Given that different cell pairs showed this trend, these findings suggest that NLA

synchrony may be fundamental to the emergence of epileptiform dynamics in the local network.

Values are reported as mean ± S.E.M. (shown by error bars). * p < 0.05 compared to interictal

values.

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7 Summary and Conclusions

7.1 Summary of Contributions The objective of this thesis was to investigate the neurodynamical features of noise-like

activity (NLA) recorded at the cellular and local network scales in in vitro preparations of mouse

and human hippocampal tissue, under healthy and epileptiform conditions. Briefly, Chapters 2

and 3 respectively introduced the relevant background and general methodologies implemented

throughout this thesis, setting the stage for the next three chapters investigating specific

neurodynamical properties of background NLA in the context of healthy and epileptiform

hippocampal activity.

In the healthy context, Chapter 4 introduced the concept of neuronal NLA as

background, time-varying fluctuations in electrical membrane potential that has been previously

attributed to the integrated activity of different sources including thermal (i.e. Johnson-Nyquist)

noise, shot noise, ionic channel fluctuations, chemical synaptic events and gap junction-related

activity.25-32, 128 In keeping with this notion, the results presented here show additional evidence

for the contributions of gap junctions and chemical synaptic channels to neuronal NLA, based on

the physiological and computational measures (i.e. wavelet and power spectral analyses)

implemented. Specifically, the application of pharmacological blockers to effectively isolate the

cell from its surrounding local network resulted in maximal suppression of spikelets, EPSPs and

IPSPs in the background NLA signal. Furthermore, measures of dynamical complexity (1⁄

spectral analysis and ) were applied to neuronal NLA, showing evidence for a spectrum of

complexity that varied with the degree of cellular interconnectivity with the surrounding local

network. In particular, high-complexity features emerged following cellular isolation under

pharmacological blockade of gap junctions and chemical synaptic channels, in contrast to

dominant low-complexity dynamics arising in the context of integration with the surrounding

network (under control and washout treatments with ACSF). This shifting range of complexity

supports the notion that brain dynamics are neither solely stochastic-like nor purely

deterministic-like, but must be viewed through the eyes of complexity theory as a hybrid system

characterized by high- and low-complexity properties. Moreover, these results show evidence

that increased complexity emerges at the expense of reduced network synchrony, consistent with

similar ideas previously reported in the literature.42 In addition, the fact that these trends were

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consistent across different cell types also implies they may be fundamental properties of NLA

dynamics at the cellular level of the nervous system. Importantly, the conclusion drawn from

Chapter 4 is that background NLA captures dynamical information about network status that

could be used to tackle the question of classifying and identifying brain states during healthy and

possibly epileptiform transitions.

Next, Chapter 5 investigated NLA complexity and the related concept of fractality as

applied to the characterization of epileptiform brain states in intra- and extracellular recordings

of seizure-like events collected from different cell types in in vitro mouse and human

hippocampal preparations. In particular, NLA signals were prepared from interictal and ictal

recordings of sufficient length to appropriately capture intrinsic dynamical information therein.

These signals were subjected to various measures of dynamical complexity, namely , ,

1⁄ and AE, ultimately showing evidence for emergent low-complexity in the pathological

ictal state, as compared to dominant high-complexity dynamics in the preceding interictal state.

Similar trends were captured at the cellular and local network scales, supporting the notion that

comparatively macroscopic recordings at the local field and possibly at the global EEG levels

capture parallel dynamical transitions to those occurring at the cellular scale.30, 35, 36 Fractal

methods were then applied to quantify the degree of self-similarity in irregular, long-range,

fluctuating correlations across multiple temporal scales in background, neuronal NLA.70, 74

Specifically, interictal NLA signals showed evidence for strong multifractal relations suggestive

of high-complexity in the interictal state, compared to reduced multifractality bordering on low-

complexity, monofractal type dynamics for ictal NLA signals. These results are comparable to

similar findings of pathological conditions in different body systems marked by deviations from

healthy, turbulent dynamics towards reduced fractality.67, 74, 80-84 Also, these trends were

consistent across the CA3 and SC regions of the mouse hippocampus, implying that

neurodynamical information was retained through the trisynaptic circuit leading from CA3 to

CA1 (via the Schaffer collaterals) and eventually to the SC region. Even more significant,

however, is the fact that these findings were consistent across different cell types from the mouse

and human hippocampus, suggestive of the fundamental and ubiquitous nature of dynamical

complexity and multifractality measured in background NLA at the cellular scale of the nervous

system. Hence, the conclusion drawn from Chapter 5 is that NLA captures a spectrum of

complexity and multifractality, ranging from high- to low-complexity dynamics, which is

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measurable at the cellular and local network scales. Moreover, these signal features may be used

to discriminate between different brain states in epileptiform activity in vitro, at least for the

interictal and ictal states described here, based on knowledge of background NLA dynamics.

To further characterize another dynamical aspect of neuronal NLA, Chapter 6 focused on

multi-spatial synchronization of dual intracellular recordings of NLA isolated from epileptiform

events arising in the intact mouse hippocampus, in vitro. Phase synchronization, in particular,

has emerged as one possible technique amongst others for studying transient, frequency-specific

phase-locking between weakly-coupled, nonlinear oscillators, independent of their amplitude

correlations, with moderate degrees of success reported in the literature for different body

systems.86, 94, 95, 97-101 Parallel to recent studies using wavelet-based coherence, bicoherence and

phase synchronization measures to explore nonlinear coupling in in vivo field recordings of

seizure-like activity in the rat hippocampus,102, 103 a similar approach was undertaken here to

investigate the possibility for phase synchronization of dual interictal and ictal NLA signals.

Coherence and bicoherence analyses respectively found increased first- and higher-order

correlations in the ictal state, as compared to interictal NLA dynamics, suggestive of increased

phase coupling emerging during the transition to seizure. These findings manifested as enhanced

same- and cross-frequency (i.e. nested) coupling in the pathological ictal state, with the greatest

increases seen in the lower part of the frequency spectrum, namely in the theta (4-10 Hz) and

beta (12-30 Hz) bands, but also at higher frequencies as well (gamma range, 30-80 Hz).42

Similarly, an index measure of phase synchrony (PSI) showed qualitative and statistical evidence

of convergence towards near-maximal synchrony in the ictal state, as compared to heterogeneous

and divergent PSI values in the interictal state for dual NLA signals. Again, these trends were

consistent across the theta, beta and gamma frequency bands, underscoring the importance of

considering lower but also higher frequencies in future neurodynamical studies of brain activity.

Based on these findings, however, Chapter 6 ultimately concludes that the dynamical complexity

of multi-spatial, neuronal NLA signals is invariably related, becoming increasingly correlated

and synchronized during transitions to the pathological ictal state, at least within the same local

network.

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7.2 Conclusions 1. Gap junctions and chemical synaptic channels are physiological contributors, at least in

part, to background, neuronal NLA.

2. There is evidence for a spectrum of dynamical complexity in neuronal NLA, ranging

from high- to low-complexity, which varies with the degree of cellular interconnectivity

to the surrounding local network.

3. The dynamical complexity and fractality inherent to background, neuronal NLA may be

used to classify and identify different epileptiform states in transitions to seizure-like

activity, at least for interictal and ictal signals recorded in vitro from mouse and human

hippocampal tissue. In this context, the pathological ictal state was characterized by

emergent low-complexity dynamics and reduced multifractal complexity (bordering on

monofractal-type dynamics), compared to high-complexity in the interictal state.

4. Similar changes in dynamical NLA complexity manifest at the cellular and local network

scales during dynamical transitions to seizure activity, at least in in vitro recordings of

epileptiform events from mouse and human hippocampal tissue.

5. Multi-spatial (i.e. dual) recordings of background, neuronal NLA are invariably related

and capture synchronization effects in the local network of hippocampal epileptiform

dynamics, in vitro. In this context, the pathological ictal state was characterized by

increased first-order (i.e. same-frequency) and higher-order (i.e. cross-frequency)

correlations, in addition to increased phase synchrony. Moreover, these trends were

apparent across the lower frequency range [theta (4-10 Hz) and beta (12-30 Hz)] but also

in higher frequency bands [gamma (30-80 Hz)].

7.3 Future Directions There are a number of future projects emerging out of the work shown here that will

require the combined efforts of physiologists, mathematicians and engineers to probe further into

the concept of noise in the nervous system. In fact, it is hoped that this thesis will lay the

92

groundwork and some of the foundation for ongoing research endeavors into studying the

mechanisms and various roles of background NLA dynamics at the cellular, local network and

global EEG scales, in addition to identifying possible ways to modulate this activity for the

purposes of manipulating pathological brain states to restore healthy brain function. From a

clinical perspective, it is ultimately hoped that future research in this area will better define a

neuromodulatory approach to monitoring and possibly treating epileptic patients based on

correction of pathological neurodynamical properties, in addition to helping patients suffering

from other dynamical diseases of the nervous system.

One important future step relies on better defining NLA as it manifests at the cellular,

local network and global EEG scales. Although many contributory sources have been implicated

at the cellular level, additional physiological studies are required to specifically investigate these

features via pharmacological or alternative means. This could entail, for example, specific

blockade of individual chemical synaptic channels (as opposed to near-total blockade, as was

applied here) to tease out the individual contributions of NMDA, AMPA and GABAergic

activity to the NLA signal. Also, the future development of improved gap junction blockers

could allow for improved targeting of these channels in additional electrophysiological

experiments, permitting a more detailed look into their relative contribution to background NLA.

In fact, it is imperative that additional in vitro animal models, combined with more eloquent in

vivo experiments, be conducted to further confirm these and other related findings. Furthermore,

in the specific context of epileptiform transitions, the experimental blockade of chemical

synaptic channels and gap junctions, in addition to Na+, K+ and Ca2+ ion channels, are

experimentally difficult without also blocking the seizure events themselves. To deal with this

technical limitation, one potential solution lies in developing improved computational

simulations to model epileptiform activity and background NLA,165 which may then be used to

study the ensuing effects on the latter following blockade of any of these channels in the context

of seizure-like events.

Another important consideration for future studies will be to focus on the elusive pre-ictal

state and related NLA therein. There is currently a great deal of controversy surrounding the

existence and timing of this epileptiform state, in addition to the underlying physiological

mechanisms that contribute to its evolution and subsequent culmination in ictal events.

Electrophysiological and neurodynamical studies will better define this transient state, perhaps

93

using real-time signal analysis, which may yield altered neurodynamical properties that may be

used for detection and possibly anticipation of seizure-like activity.

From a neurodynamics perspective, it is also important to consider mechanisms by which

cellular NLA contributes to NLA at the field and arguably global EEG scales. One approach, in

fact, lies in spike-attenuation and subsequent extraction of neural rhythms using novel

neuroengineering tools136 to individually extract dynamical rhythms and effectively isolate

residual non-rhythmic signal components from cellular, field and EEG recordings of

hippocampal epileptiform activity. Diverse measures of dynamical complexity, multifractality

and synchrony could then be applied to compare between the rhythmic and non-rhythmic

features within and across each scale to identify differences and similarities for different brain

states. In fact, one significant improvement lies in developing a real-time tracking algorithm for

computing dynamical multifractality for a given signal, given that no such program currently

exists. Other neuroengineering tools from diverse areas, including fuzzy logic approaches and

computational kernel analysis (via parametric and non-parametric methods), will also shed

further light on the dynamical behavior of NLA signals recorded in the nervous system.

In parallel to these studies, assuming that relevant, dynamical features in NLA are

identified to track brain state transitions, their subsequent manipulation via mathematical or

computational transformation of these signals could be employed to effectively correct the

pathological dynamics inherent to certain disease states. In fact, it will be important to study the

mechanisms by which chemical or electrical stimuli may be used to alter dynamical properties in

recorded physiological signals, to produce a “smart” stimulatory signal that may be recognized

and integrated into ongoing brain dynamics. In addition, this process will eventually require

future technological innovations in the form of implantable, miniaturized brain-computer

interfaces166, 167 that could be used to track and detect pathological brain dynamics, and perhaps

abort them through a real-time stimulatory strategy.

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