1/f, Fractal, Chaos, and Small worldin the brain

Jaeseung Jeong, Ph.DDepartment of Bio and Brain Engineering,

KAIST

The Length of Coastline of Britain

Fractal – Self-similarity

Fractal

As a non-fractal object is magnified, no new features are revealed.

As a fractal object is magnified, ever finer features are revealed. A fractal object has features over a broad range of sizes.

Self-similarity

The magnified piece of an object is an exact copy of the whole object.

Complex dynamics of heart rate variability

Breakdown of a fractal physiological control mechanism can lead ultimately either to a highly periodic output dominated by a single scale or to uncorrelated randomness.

Zipf’s Law

George Zipf's 1949 observation that the frequency of words used in the English language followed a powerlaw distribution is a profound thing. It not only defined Zipf's Law, which gives a simple rule to explain why some words (e.g. the, of, and) are far more commonly used than others.

The origin of Fractal Music

1. Introduction : Self-Organization

- A process of attraction and repulsion in which the internal organization of a system, normally an open system, increases in complexity without being guided or managed by an outside source (From Wikipedia)

- Typically displays Emergent Properties

Self-Organized Criticality: The origin of 1/f in the Brain

Sandpile criticality

• Like a child's sand castle, seeds rain down onto a mound that grows until it can't grow any more. A complex balancing act keeps the mound stable until it reaches the "point of criticality"-the point at which the system "fails," creating avalanches that change the mound's shape.

• Each avalanche relieves pressure on the pile, allowing it to begin growing again. Similar patterns of alternating growth and failure show up in many complex systems.

Criticality or critical points

• Criticality indicates the behavior of extended systems at a phase transition where scale invariance prevails.

• The many constituent microscopic parts bringing about macroscopic phenomena that cannot be understood by considering a single part alone.

1. Introduction : Self-Organization

“bird flocks, … ant colonies, highway traffic, market economies, immune systems – in all of these systems patterns are determined not by some centralized authority but by local interactions among decentralized components”

Resnic, 1995

Getting on top of self-organized criticality

Take a sand pile built up by dropping grains onto it at a steady rate. The angle of the slope will be controlled by the frictional strength of the material. This was well known to Coulomb in the eighteenth century.

Brain and complex network (graph) theory

Undirected graph Directed graph Weighted graph

Boccaletti et al., 2006Liu, 2008

Node (vertex) : Brain region or voxel, channel of EEG/MEG

Link (edge) : Functional or anatomical connection between nodes

Network analysis can reveal structural and functional organization of the brain (Liu, 2008)

Small-world and scale-free organization of voxel-based resting state functional connectivity in the human brain

van den Heuvel et al., Neuroimage, 2008

normal, resting-state, voxel-based(N=10,000),zero-lag temporal correlation, bandpass-filtered(0.01-0.1Hz),unweighted, small-world and scale-free : optimal network organizationbalance between maximum communication efficiency andminimum wiring

AD, damage modeling, weighted graph, efficiency

Constructing Brain Networks

Bullmore and Sporns, 2009

Brain is a small-world network

high clustering coefficient (C) – high resilience to damage in local structures low average path length (L) – high level of global communication efficiency Brain functional network has small-world structure, while this property may be disrupted in damaged brain such as AD (vulnerability to damages, decreased communication efficiency between distant brain regions … )

Watts and Strogatz, 1998

high C high C low Chigh L low L low L

Previous study 2

A resilient, low-frequency, small-world human brain functional network with highly connectedassociation cortical hubs Achard et al., The Journal of Neuroscience, 2006

MODWT (Maximal Overlap Discrete Wavelet Transform) at 6 frequency scales

healthy young subjects, resting-state,parcellation(90 region-based), unweighted,small-world, NOT scale-freeresilient to targeted attack than SF network

AD, voxel-based, weighted, efficiency, region attack

Spontaneous eyeblinking activity

• Time duration “in the blink of an eye”

0.2-0.3 sec

• Frequency of the eye-blinking

15-20 times/min

14,000 times/day

5,250,000 times/year

360,000,000 times/lifespan

• Time duration of eyes-closed for blinking

75 mins./day

Functional roles of spontaneous eye-blinking

• “On the act of blinking” Eric Ponder and WP Kennedy, The Quarterly journal of experimental physiology (1927)

Protect eyeballs from injury or maintaining a healthy ocular surface by inducing the formation of the preocular tear film.

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Sauna experiments & Parkinsonian patients

Eyeblinking is controlled by the brain

• Women are eye-blinking more frequently than men.

• The blink-rate is highly dependent on attention and cognitive states.

• Blink activity is substantially influenced by experimental manipulation of dopaminergic circuits in the basal ganglia.

• Significantly, altered blink-rates are also observed in several neuropsychiatric disorders that are known to affect dopaminergic neurotransmission.

• Interesting experiment on eye-blinking during reading in the library.

Eyeblinking is an epiphenomenon of information processing of the brain?!

Anxiety increases eyeblinking

Why do we study eyeblinking?

• For better understanding of eye-blinking

• Dopaminergic circuits in the basal ganglia can be monitored by eye-blink activity.

• Eye-blinking activity can be used to control computer/machine.

Eyeblink is a signal of decision-making

• Despite the emphasis of previous studies on defining the changes in EBR under various cognitive or behavioral states, the timing or temporal patterning of eyeblinks during specific cognitive processes has been examined only rarely.

• [Clue] During the reading of written text, a large proportion of eyeblinks occur at or near the end of a line of text, before gaze returns to the beginning of the next line.

• Also, eyeblinks occur when subjects shift their gaze, a so-called “gaze-evoked blink.”

• Our hypothesis is that eyeblinks may signal the end of one cognitive process, the beginning of another, or the shift of one of these processes to the other.

How is the eyeblinking changed

during cognitive tasks?

Eyeblinks in the Stroop task

Participants name the color of the ink (red, yellow, blue, green) in which words are written or read the words. The words themselves either denote colors or objects unrelated to colors, and are variously grouped into three stimulus conditions:

(1) congruent, in which the word denotes a color that matches the ink in which the word is written.

(2) incongruent, in which the word denotes a color other than the ink in which the word is written.

(3) neutral, in which the word denotes an object unrelated to color.

Stroop TaskWord reading vs Color naming

GREEN YELLOW

BLUE BLUE

YELLOW GREEN

SPOT RED

Stroop facilitation and interference

• Stroop “facilitation”

The naming of ink colors for congruent stimuli is faster, and therefore produces shorter Reaction Times (RTs), than the naming of colors for neutral stimuli.

• Stroop “interference”

The naming of ink colors for conflict stimuli is slowed, and therefore produces longer RTs, than the naming of colors for neutral or congruent stimuli,

This interference is attributed by many to the greater automaticity of word reading than color naming, requiring greater cognitive control and a greater allocation of attentional resources, and therefore slowing responses to avoid error on the task.

300

400

500

600

Congruent Incongruent Control

tim

e (

ms

)

BLUEBLUE

interference

facilitation

SPOT

• Dalrymple-Alford & Budayr (1966): First to encourage presentation & timing of stimuli individually. This method now dominates

The possible role of eyeblinks

• We found the statistically highly significant temporal proximity of blinks to the vocal response stage of information processing, rather than during stimulus presentation or during gaze fixation between stimuli.

• This suggests that the cognitive process that the blinks accompany is either the termination of stimulus processing, the beginning or end of the motor response, or the change in set from one of these to the other.

Tourette’s syndrome

• Tourette Syndrome (TS) is a complex neurobehavioral disorder characterized by a changing pattern of motor and vocal tics which begins in childhood. To be considered TS, the symptoms should last more than a year.

TS disease progress

Neural substrates of TS

Frontal-subcortical cuircuit- Basal ganglia : collection of large

subcortical nuclear mass- neostriatum, striatum : Caudate

nucleus + putamen :- Corpus striatum : caudate,

putamen, globus pallidus - Lentiform nucleus : putamen and

glubus pallidus- Ventral striatum : ventromedial

part of th putamen and caudate nucleus, nucleus accumbens, …

Complex tic dynamics

• To investigate whether tic dynamics is deterministic or stochastic.• To quantify the severity and progress of the disease. • Early detection of TS and transient tics using inter-tic interval

(ITI) dynamics.

The temporal dynamics of tics in Tourette Syndrome

BS Peterson et al. The temporal dynamics of tics in Gilles de la Tourette Syndrome, Biological Psychiatry (1998)

Tic patterns of Tourette’s syndrome

Fractal

As a non-fractal object is magnified, no new features are revealed.

As a fractal object is magnified, ever finer features are revealed. A fractal object has features over a broad range of sizes.

Physics(Dynamics) Neuroscience

• Theory driven:

– first principles

• Reductionism:

– simplify the world

• Qualitative understanding:

– mathematics

• Empirical and descriptive:

– phenomena

• Systems level:

– details of the system

• Quantitative understanding:

– measurements

• Paradigm Shift

– Complex: real systems

– Synthesis: whole-istic

– Systems neuroscience using mathematical models

– Universality among the diversity: Brain