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Introduction to Biological Neurons

1.1 Introduction

After a century of research, our knowledge of the human brain is still very much incomplete.

Hundreds of different brain areas have been mapped out in various species. Neurons in these

regions have been classified, sub-classified, and reclassified based on anatomical details,

connectivity, response properties, and the channels, neuropeptides, and other markers they

express. Hundreds of channels have been quantitatively characterized, and the regulation and

gating mechanisms are beginning to be understood. Multi-electrode recordings reveal how

hundreds of neurons in various brain areas respond to stimuli. Despite this wealth of descriptive

data, we still do not have a grasp on exactly how these thousands of neurons are supposed to

accomplish computation. To understand the minimal knowledge about how brain is doing this

enormous computation and signal processing we should have some basic knowledge of biology,

neuroscience, biochemistry, biophysics, signal& systems, networks and information theory

A vast majority of neurons respond to sensory or synaptic inputs by generating a train of

stereotypical responses called action potentials or spikes. Deciphering the encoding process

which transforms continuous, analog signals (photon fluxes, acoustic vibrations, chemical

concentrations and so on) or outputs from other neurons into discrete, fixed-amplitude spike

trains is essential to understand neural information processing and computation, since often the

nature of representation determines the nature of computation possible. Researchers, however,

remain divided on the issue of the neural code used by neurons to represent and transmit

information. Although there are many open problem in this area but to model a problem

analytically is still very much challenging.

The brain is a sophisticated and complex organ that nature has devised. In order to

understand brain function fairly, we must begin by learning how brain cells work individually

and then see how they are assembled to work together. There are mainly two types of cell in

central nervous system: Neuron and Glia. Although there are many neurons in the human brain

(about 100 billion), glia outnumber neurons by tenfold. However, neurons are more important

cells for the major functions of the brain. It is the neurons that sense changes in the environment,

communicate these changes to other neurons, and command the body’s responses to these

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sensations. Glia, or glial cells, are thought to contribute to brain function mainly by insulating,

supporting, and nourishing neighboring neurons.

1.2 Relevant Physiological Aspects

A typical neuron has four parts: (a) cell body or soma, (b) axon, (c) dendrites and (d)

neuronal membrane.

Fig1: Schematic of a neuron structure [1]

(a) Cell body or SOMA

20µm diameter, watery fluid inside called cytosol and contains organelles like nucleus,

rough ER, smooth ER, mitochondria and golgi apparatus [1]. When signal from different

dendrites propagate towards axon hillock cellbody assumed to act as a conducting and it also

performs the local energy balancing.

Fig2: Cell Body [2]

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(b) Axon

The axon, a structure found only in neurons that is highly specialized for the transfer of

information over distances in the nervous system. The axon begins with a region called the axon

hillock, which tapers to form the initial segment of the axon proper. It serves as the “telegraph

wire” that sends information over great distances. The end is called the axon terminal or terminal

button. The terminal is a site where the axon comes in contact with other neurons (or other cells)

and passes information on to them. This point of contact is called the synapse [1].

(c) Dendrite

It acts like a receiver for a neuron. The term dendrite is derived from the Greek for “tree,”

as these dendrites resemble the branches of a tree extended from the soma. The dendrites of a

single neuron are collectively called a dendritic tree. The branches are covered with thousands of

synapses. The dendritic membrane under the synapse (the postsynaptic membrane) has many

specialized protein molecules called receptors that detect the neurotransmitters in the synaptic

cleft [1].

(d) Neuronal Membrane

The neuronal membrane serves as a barrier to enclose the cytoplasm inside the neuron

and to exclude certain substances that float in the fluid that bathes the neuron. The membrane is

about 5 nm thick and is studded with proteins. The protein composition of the membrane varies

depending on whether it is in the soma, the dendrites, or the axon. Neuronal membrane gives a

neuron the remarkable ability to transfer electrical signals throughout the brain and body [1].

1.3 Action Potential

The Action potential is an electrical signal that conveys information over distances in the

nervous system. The cytosol in the neuron at rest is negatively charged with respect to the extra-

cellular fluid. The action potential is a rapid reversal of this situation such that, for an instant, the

inside of the membrane becomes positively charged with respect to the outside. The action

potential is also often called a spike, a nerve impulse, or a discharge. The action potentials

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generated by a cell are all similar in size and duration, and they do not diminish as they are

conducted down the axon. The frequency and pattern of action potentials constitute the code

used by neurons to transfer information from one location to another. Action potential has certain

identifiable parts, called the rising phase, overshoot, falling phase, undershoot, after- hyper-

polarization [1].

Fig 3: Action potential [1]

1.4 Synapse

The junction between two neurons is called a synapse. With respect to a synapse, we

refer to the sending neuron as the pre-synaptic cell and to the receiving neuron as the

postsynaptic cell. Most synapses occur on the dendrites but some occur on the somas or the

axons of other neurons. The most common type of synapse in the (vertebrate) brain is the

chemical synapse. For this type of synapse, the axon comes very close to the postsynaptic

neuron, leaving only a small gap of about 20-40 nanometers across between pre and postsynaptic

cell membranes, called the synaptic cleft. The pre-synaptic signal is transmitted across the

synaptic cleft by transformation from electrical signal into a chemical one and then back into

electrical signal on the postsynaptic side. The chemical signal is sent in the form of

neurotransmitter molecules. About 5,000 of these molecules are packaged in small spheres called

synaptic vesicles which reside in the pre-synaptic terminal [2].

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Fig 4: Synapse [1]

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Major Developments in Neuroscience and Neural

Information Theory

Review of recent literature [2, 3, 4] suggests that research on neuroscience may be classified in

three broad directions:

2.1 Experimental Neuroscience

Experimental neuroscience is an important discipline with an aim to understand the

molecular, cellular, physiological, structural and behavioral basis of normal function of the

nervous system and its diseases.

2.2 Theoretical Neuroscience

The task of understanding the principles of information processing in the brain poses,

apart from numerous experimental questions, challenging theoretical problems on all levels from

molecules to behavior. This Theoretical Neuroscience concentrates on modeling approaches on

the level of neurons and small populations of neurons, since one think that this is an appropriate

level to address fundamental questions of neuronal coding, signal transmission, or synaptic

plasticity. Neuron is a dynamic element that emits output pulses whenever the excitation exceeds

some threshold. The resulting sequence of pulses or spikes contains all the information that is

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transmitted from one neuron to the next. Signal transmission and signal processing in neuronal

systems need to be understood with the help of distributed network consists of single neurons

[3].

Integrate-and-Fire Model of the Neurons

The leaky integrate-and-fire model (LIF) [5] is one of the most elementary spiking

models and has been widely used to gain a better understanding of information processing in

neurons. In this model, the sub-threshold membrane potential of a neuron is governed by a first-

order linear differential equation

( ) - v( )( ) = C + rest

in

v tdv ti t

dt R ……………………… (1)

which corresponds to the circuit in Fig. 5 below [5]:

Fig 5: Equivalent circuit for leaky integrate-and-fire neuron [2]

In this model, the membrane time constant is = RCm . The value of m

is typically 8–

20 ms. A solution of above equation is

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0

0

1 1 (t-t ) (t- )

0

1( ) v + e ( ( ) v ) + e ( ) m m

t

rest rest int

v t v t i dC

……………(2)

By redefining the voltage reference, we can instead consider ( ) vrestv t . Replacing

( ) vrestv t by ( )v t , we have for 0t t

0

0

1 1 (t-t ) (t- )

0

1( ) e ( ) + e ( ) m m

t

int

v t v t i dC

0

0 0,

1( ) 1 ( ) + ( ) ( ) * h(t)in t

i t t v t t tC

……….(3)

Where 0

1 t

,h(t) e 1 ( ) m

tt

and “*” denotes convolution. This is true as long as ( )v t is

less than the threshold. When a neuron has just output a spike at time 0t 0 , we will assume that

the membrane potential is reset to 0( ) 0v t . Then,

1 = * hinv i

C ……………. (4)

as long as < Tv where T is the threshold function. In the above notation, we assume that ini

is causal; that is, for. Of course, the function h defined above is also causal. Suppose we let

mt . Then, 0 ,

h(t) 1 ( )t

t

. This is called the perfect / leakless integrator model. As a

generalization of the leaky integrate-and fire model, we will allow h to be any decaying causal

function and use (4) to define the membrane potential. Note that ini is a result of incoming spike

train [2, 3, 5].

Refractory Period

Output spikes from a neuron are usually well separated. Even with strong input, it is

virtually impossible to excite a second spike during or immediately after a first one. This

minimal distance between two spikes is defined as the absolute refractory period of the neuron.

The typical length of this period is about 2–4 ms. The absolute refractory period is followed by a

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state of relative refractoriness during which it is difficult, but not impossible to generate an

action potential. The relative refractory period may last around 10–20ms. Both of these

refractory phases can be modeled in the IF-model by using a decaying threshold function.

Immediately after a spike is generated, we may assume that the threshold is large (possible

infinite), and hence it is impossible for the membrane potential to built up and reach the value of

the threshold in a short amount of time. Using decaying threshold implies that as time passes, the

threshold will be at a lower value and hence it is easier to generate a spike [2].

Energy Consumption

Another important fact is that our nervous system consumes a lot of energy. Human

brains consume 20% of energy consumption for adults and 60% for infant .When we block the

neural signaling by anesthesia, the brain’s energy consumption is halved. This suggests that

about 50% of the energy is used to drive signals along axons and across synapses. In 1996, Levy

and Baxter included the amount of energy expended by neuron in their study, initiating

theoretical studies of energy-efficient coding in nervous systems [6].

2.3 Neural Information Theory or Living Information Theory [8]

Information theory, the most rigorous way to quantify neural code reliability, is an aspect

of probability theory that was developed in the 1940s as a mathematical framework for

quantifying information transmission in man-made communication systems. The theory’s rigor

comes from measuring information transfer precision by determining the exact probability

distribution of outputs given any particular signal or input. Moreover, because of its

mathematical completeness, information theory has fundamental theorems on the maximum

information transferrable in a particular communication channel. In engineering, information

theory has been highly successful in estimating the maximal capacity of communication channels

and in designing codes that take advantage of it. In neural coding, information theory can be used

to precisely quantify the reliability of stimulus–response functions, and its usefulness in this

context was recognized early. One can argue that this precise quantification is also crucial for

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determining what is being encoded and how. In this respect, researchers have recently taken

greater advantage of information-theoretic tools in three ways-

First, the maximum information that could be transmitted as a function of firing rate has been

estimated and compared to actual information transfer as a measure of coding efficiency.

Second, actual information transfer has been measured directly, without any assumptions about

which stimulus parameters are encoded, and compared to the necessarily smaller estimate

obtained by assuming a particular stimulus–response model. Such comparisons permit

quantitative evaluation of a model’s quality[10].

Third, researchers have determined the ‘limiting spike timing precision’ used in encoding, that

is, the minimum time scale over which neural responses contain information.

Information Theory in Living Systems

While applying information theory in living systems we should keep in mind that, basic

concepts and methods of classical information theory developed by Shanon and his fellow

researchers , which is very much effective for man-made communication systems may not be

always applicable to the long standing mysteries of nature. One must think critically before

applying information theoretic concept for analysis of information processing abilities of neurons

and hence our brain. One should always remember two things-

• Judicious application of Shannon’s fundamental concepts of entropy, mutual information,

channel capacity is crucial to gaining an elevated understanding of how living systems handle

sensory information what is the capacity of a single neuron channel [8, 10].

• Living systems have little if any need for the elegant block and convolutional coding theorems

and techniques of information theory because, organisms have found ways to perform their

information handling tasks in an effectively Shannon- optimum manner without having to

employ coding in the information-theoretic sense of the term [8, 10].

2.4. Comments on Outstanding Research Issues

1. Proposed models in literature do not consider complete signal flow from axon to axon

terminal and axon terminal to synaptic cleft and synaptic cleft to dendrites or cell body

and dendrite or cell body to axon hillock.

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2. All the signals that reach dendrite or cell body, do not cross threshold and generate action

potential. What happen to these signals? Will they act as jitter for next action potential???

How local energy balancing takes place???

3. Neocortex is known to exhibit memory and a functional element of neocortex is a neuron.

It is not clear from the available literature if there is any memory trace in a single neuron.

Modeling of a single neuron is still an active area of research [1, 3].

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Top-Down and Bottom-Up Approach in Neuroscience

Computational neuroscience is used to bridge the gap between the mathematical

neuroscience and experimental neuroscience. Hodgkin and Huxley combined their experiments

with a mathematical description [5], which they used for simulations on one of the early

computers . One of the central tasks of computational neuroscience is to bridge the different

levels of description by simulation and mathematical theory. The bridge can be built in two

different ways - Bottom-up models and Top-down models. Bottom-up models integrate what is

known on a lower level to explain phenomena observed on a higher level. Top-down models, on

the other hand, start with known cognitive functions of the brain (e.g., working memory), and try

to predict how neurons or group of neurons should behave in order to achieve that function.

Some examples of the top-down approach are theories of associative memory, reinforcement

learning, and sparse coding [11].

3.1. Bottom-Up Approach:

The brain contains billions of neurons that generate short electrical pulses, called action

potentials or spikes to communicate with each other. Hodgkin and Huxley’s description of

neuronal action potentials [5] is widely used framework for biophysical neuron models. In these

models, cell membrane of a neuron is described by a number of ion channels, with specific time

constants and gating dynamics that control the momentary state (open or closed) of a channel

(Fig. 6C). By a series of mathematical steps and approximations, theory has sketched a

systematic bottom-up path from such biophysical models of single neurons to macroscopic

models of neural activity [11].

In the first step, biophysical models of spike generation are reduced to integrate-and-fire

models where spikes occur whenever the membrane potential reaches the threshold (Fig. 6B).

In the next step, the population activity A(t)—defined as the total number of spikes

emitted by a population of interconnected neurons in a short time window—is predicted from the

properties of individual neurons using mean-field methods known from physics. Each neuron

receives input from many others, it is sensitive only to their average activity (“mean field”) but

not to the activity patterns of individual neurons [11].

Instead of the spike based interaction among thousands of neurons, network activity can

therefore be described macroscopically as an interaction between different populations Such

macroscopic descriptions—known as population models, neural mass models, or, in the

continuum limit, neural field models (Fig. 6A)—help researchers to gain an intuitive and more

analytical understanding of the principal activity patterns in large networks. Although the

transition from microscopic to macroscopic scales relies on purely mathematical arguments,

simulations are important to add aspects of biological realism (such as heterogeneity of neurons

and connectivity, adaptation on slower time scales, and variability of input and receptive fields)

that are difficult to treat mathematically. However, the theoretical concepts and the essence of

the phenomena are often robust with respect to these aspects [11].

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Fig6: Bottom up approach in nervous system[11]

3.2. Decision-Making: Theory Combines Top-Down and Bottom-Up

Often we have to take a decision between two alternatives (A or B), such as “Should I do

it or not?”. Psychometric measures of performance and reaction times for two alternative forced-

choice decision-making paradigms can be explained by a phenomenological drift-diffusion

model. This model consists of a diffusion equation describing a random variable that

accumulates noisy sensory data until it reaches one of two boundaries corresponding to a specific

choice (Fig. 7A). Although this model able to describe reaction time distribution, it suffers from

a crucial disadvantage, namely the difficulty in assigning a biological meaning to the model

parameters [11].

Recently, neurophysiological experiments have begun to reveal neuronal correlates of

decision making, in tasks involving visual patterns of moving random dots or vibrotactile or

auditory frequency comparison. Computational neuroscience offers a framework to bridge the

conceptual gap between the cellular and the behavioral level. Explicit simulations of microscopic

models based on local networks with large numbers of spiking neurons can reproduce and

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explain both the neurophysiological and behavioral data. These models describe the interactions

between two groups of neurons coupled through mutually inhibitory connections (Fig. 7C).

Suitable parameters are inferred by studying the dynamical regimes of the system and choosing

parameters consistent with the experimental observations of decision behavior. Thus, the pure

bottom-up model is complemented by the top-down insights of target functions that the network

needs to achieve [11].

Fig 7: Decision making in nervous system[11]

3.3. Large-scale brain networks and cognition

Much of our current knowledge of cognitive brain function has come from the modular

paradigm, in which brain areas are postulated to act as independent processors for specific

complex cognitive functions [15]. Recent research shows that this paradigm has serious

limitations and might in fact be misleading. Even the functions of primary sensory areas of the

cerebral cortex, once thought to be pinnacles of modularity, are being redefined by recent

evidence of cross-modal interactions. A new paradigm is emerging in cognitive neuroscience

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that suggests instead of working in a modular way for a cognitive function brain areas are

working conjointly as a large scale networks [12, 13, 15] .

Large-scale structural brain networks

The neuroanatomical structure of large-scale brain networks give us an idea of connected

brain areas that facilitates signaling along a particular pathway for the service of specific

cognitive functions. It is important to identify the brain areas that constitute structural network

nodes and the connecting paths that serve as structural network edges to know which

configurations of interacting areas are possible. In the past, large-scale structural brain networks

were often schematized by two-dimensional wiring diagrams, with brain areas connected by

lines or arrows representing pathways. Currently, more sophisticated network visualization and

analysis schemes are being developed and used. Principal methods to define structural nodes

and edges in the brain is described first. Some of possible functional consequences of the

structural organization of large-scale brain networks is described then [15].

Nodes

The nodes of large-scale structural brain networks are typically brain areas defined by: (i)

cytoarchitectonics; (ii) local circuit connectivity; (iii) output projection target commonality; and

(iv) input projection source commonality. A brain area can be described as a subnetwork of a

large-scale network; this subnetwork consists of neuron populations (nodes) and connecting

pathways (edges). Despite the complex internal structure of each node, it is often convenient,

particularly in network modeling research, to treat them as unitary neural masses that serve as

spatially undifferentiated (lumped) nodes in large-scale networks. The definition of nodes are

changing time to time as new methods are developed and understanding of structure– function

relations in the brain evolves .Techniques used in recent years to determine structural nodes from

neuroanatomical data include: (i) anatomical parcellation of the cerebral cortex using the

Brodmann atlas; (ii) parcellation in standardized Montreal Neurological Institute (MNI) space

using macroscopic landmarks in structural magnetic resonance imaging (sMRI) data; (iii)

subject-specific automated cortical parcellation based on gyral folding patterns; (iv) quantitative

cytoarchitectonic maps; and (v) neurochemical maps showing neurotransmitter profiles .Diverse

tradeoffs arise in the use of these techniques [15]. Classical, but still popular Brodmann

mapping scheme is used for analysis.(Details are given in appendix - 1)

Problem in node selection

A major problem being that of anatomical specificity versus extent of coverage across

the brain. This problem is particularly acute for the cerebral cortex because the borders of most

cortical regions cannot be reliably detected using macroscopic features from sMRI. The choice

of spatial scale for nodal parcellation has important consequences for the determination of

network connectivity [15].

Although newer methods offer a tighter link with the functional architecture of the brain,

but still coverage exists for only a small set of cortical regions and a wide area of human

prefrontal and temporal cortices have not yet been adequately mapped. Most anatomical

parcellation studies have focused on the cerebral cortex. Less attention has been paid to

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subcortical structures such as the basal ganglia and the thalamus, which have only been

demarcated at a coarse level using sMRI. Brainstem systems mediating motivation, autonomic

function and arousal have been poorly studied because they are very difficult to identify using in

vivo techniques. Nonetheless, it is important to identify these structures because they

significantly influence cortical signaling and thus affect cognitive function [15].

Fig 8: Structural nodes of cerebral cortex[15]

Edges

The edges connecting brain areas in large-scale structural networks are long-range axon

pathways. Network edges are directed because axon fiber pathways have direction from the

somata to the synapses, and can be bidirectional when axon pathways run in both directions

between particular brain areas. Each brain area has a unique connection set of other areas with

which it is interconnected. Network edges have variable weights based on the number and size of

axons in the pathways, and the number and strengths of functioning synapses at the axon

terminals [15].

Three main approaches are currently used to trace axon pathways, and thus determine

structural network edges.

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The first is autoradiographic tracing in experimental animals. In the macaque monkey,

this technique has provided a rudimentary map of anatomical links between major cortical areas

and more recently has successfully detailed rostro–caudal and dorsal–ventral connectivity

gradients between major prefrontal and parietal cortical areas [15].

The second approach uses diffusion-based magnetic resonance imaging methods, such as

diffusion tensor imaging (DTI) and diffusion spectrum imaging (DSI), to determine major fiber

tracts of the human brain in vivo by identifying the density of connections between brain areas

[15]. (Fig. 9).

The third approach to mapping of network edges uses anatomical features such as local

cortical thickness and volume to measure anatomical connectivity. In this approach, which has

evolved during the same recent time period as DTI technology, interregional covariation in

cortical thickness and volume across subjects is used to estimate connectivity [15].

Problem in edge selection

In autoradiographic tracing howevei it is difficult, to extrapolate from macaque

connectional neuroanatomy to that of the human brain because the degree of pathway homology

between macaque and human brains is not well understood.

Diffusionbased tractography of the entire human brain is still in its early days, but rapidly

evolving techniques are providing reliable estimates of the anatomical connectivity of several

hundred cortical nodes [12, 13]. With additional anatomical constraints on ‘seeds’ and ‘targets’

in diffusion- based tractography, it is increasingly possible to make closer links between

projection zones and cytoarchitectonic maps [15].

In the third method edges that are identified might not actually reflect axonal pathways

and precaution is required in interpreting the results. Nevertheless, networks identified using this

approach have revealed stable graph-theoretic properties [15].

Fig 9: Structural edges of cerebral cortex[15]

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Comments on Structural Nodes and Edges

Recent studies have combined both node and edge detection to identify structural

networks, either across the whole brain or within specific brain systems. At the whole-brain

level, network nodes are determined by one of the parcellation methods described above, and

then network edges are determined by DTI or DSI. If, however, structural network nodes are

inferred from DTI or DSI patterns of convergence and divergence, nodes and edges cannot be

independently identified. Within specific functional systems, such as for language or working

memory, the nodes are constrained to lie within the system and then the edges are identified by

diffusion-based tractography . The use of cytoarchitectonic boundaries to define the nodes allows

aspects of brain connectivity that are more closely linked to the underlying neuronal organization

to be uncovered in parallel [12-15].

Large-scale functional brain networks

Human brain has evolved to provide survival strategy to human in a way that one can

survive in a wide varity of ambience changes, act differently in different condition depending on

the situtiation At each moment certain set of conditions must be analyzed by human brain with

the help of perception. The set of perception along with the learned concepts produce an

immediate solution to the immediate problem and act accordingly. It is reasonable to assume that

a set of interconnected brain areas act in tandem to provide these solutions, as well as

corresponding behavior and that they interact dynamically to achieve an action. A large-scale

functional network can therefore be defined as a collection of interconnected brain areas that

interact to perform circumscribed functions. The topological form of functional networks

changes throughout an individual’s lifespan and is uniquely shaped by maturational and learning

processes within the large-scale neuroanatomical connectivity matrix for each individual [13-15].

Nodes

The characterization of functional networks in the brain requires identification of

functional nodes. However, there is no commonly agreed definition of what constitutes a

functional node in the brain. Since the advent of advanced functional electrophysiological and

neuroimaging methods, additional methodologies to define functional network nodes have

become available. A network node can be a circumscribed brain region displaying elevated

metabolism in positron emission tomography (PET) recordings, elevated blood perfusion in

functional magnetic resonance imaging (fMRI) recordings, or synchronized oscillatory activity

in local field potential (LFP) recordings. Participation of a brain area in a large-scale functional

network is commonly inferred from its activation or deactivation in relation to cognitive

function. A group of brain areas jointly and uniquely activated or deactivated during cognitive

function with respect to a baseline state can represent the nodes of a large-scale network for that

function [15].

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Problem of selection of Functional nodes

A major challenge is to determine how functional network nodes defined by different

recording modalities are related, and how they relate to structural network nodes. From the

network perspective, cognitive functions are carried out in real time by the operations of

functional networks comprised of unique sets of interacting network nodes. For a brain area to

qualify as a functional network node, it must be demonstrated that, in combination with a

particular set of other nodes, it is engaged in a particular class of cognitive functions. Although it

is not yet known how the various definitions of large-scale functional network nodes derived

from different recording modalities are related, a possible scenario is that the elevated

excitability of neurons within an area leads to elevated metabolic activity, which in turn causes

an increase in local blood oxygen availability. The elevated excitability could also cause

increased interactions between neurons within the area. Interactions between different

populations can produce oscillatory activity and can have important functional consequences if,

for example, the interactions lead to increased sensitivity of neurons within the area to the inputs

that they receive [15].

Much of the work in the field of functional neuroimaging uses the fMRI blood-oxygen-level-

dependent (BOLD) signal to identify the nodes of large-scale functional networks by relating the

joint activation of brain areas to different cognitive functions. fMRI BOLD activation has

revealed network nodes that are involved in such cognitive functions as attention [58], working

memory, language, emotion, motor control and time perception [15].

Edges

The identification of functional network edges comes from different forms of functional

interdependence (or functional connectivity) analysis, which assesses functional interactions

among network nodes. The identification of network edges, like that of network nodes, is highly

dependent on the monitoring methodology. Functional interdependence analysis can identify

network edges from time series data in the time (e.g. cross-correlation function) or frequency

(e.g., spectral coherence or phase synchrony measures) domain. In either domain, the analysis

can use a symmetric measure, in which case significant interdependences are represented as

undirected edges, or an asymmetric measure, in which case they are represented as directed

edges . Methods using directional measures include Granger causality analysis and dynamic

causal modeling . Functional interdependences must be statistically significant for them to

represent the edges of large-scale functional networks. Determination of thresholds for

significance testing of network edges is often fraught with difficulty, and the particular method

used for threshold determination can have an appreciable impact on the resulting large-scale

network. Certain graph-theoretic measures, however, do not suffer from this problem because

they take into account the full weight structure of the network. Fluctuations in neuronal

population activity at different time scales can control the time-dependent variation of

engagement and coordination of areas in large-scale functional networks . Network edges are

possibly best represented by the correlation of time series fluctuations at different time scales,

reflecting different functional network properties. The correlation of slow fluctuations at rest in

fMRI BOLD signals possibly reflects slow interactions necessary to maintain the structural and

functional integrity of networks , whereas the correlation of fast fluctuations could reflect fast

dynamic coupling required for information exchange within the network [12-15].

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Functional interdependence has been observed across a range of time scales from

milliseconds to minutes. Recent evidence suggests that slow intracranial cortical potentials are

related to the fMRI BOLD signal. It is possible that functional networks are organized according

to a hierarchy of temporal scales, with structural edges constraining slow functional edges, which

in turn constrain progressively faster network edges. Studies in both monkeys and humans

support the existence of hierarchical functional organization across time scales [15].

Intrinsic functional brain networks

Functional interdependence analysis has often been used to investigate interactions

between brain areas during task performance. Although task-based analyses have enhanced our

understanding of dynamic context-dependent interactions, they often have not contributed to a

principled understanding of functional brain networks. By focusing on task-related interactions

between specific brain areas, they have tended to ignore the anatomical connectivity and

physiological processes that underlie these interactions. Intrinsic interdependence analysis of

fMRI data acquired from subjects at rest and unbiased by task demands has been used to identify

intrinsic connectivity networks (ICNs) in the brain. ICNs identified in the resting brain include

networks that are also active during specific cognitive operations, suggesting that the human

brain is intrinsically organized into distinct functional networks. One key method for identifying

ICNs in resting-state fMRI BOLD data is independent component analysis (ICA), which has

been used to identify ICNs involved in executive control, episodic memory, autobiographical

memory, self-related processing and detection of salient events. ICA has revealed a sensorimotor

ICN anchored in bilateral somatosensory and motor cortices, a visuospatial attention network

anchored in intra-parietal sulci and frontal eye fields, a higher-order visual network anchored in

lateral occipital and inferior temporal cortices, and a lower-order visual network. This technique

has allowed intrinsic as well as task-related fMRI activation patterns to (Figure 10), (Figure 11),

be used for identification of distinct functionally coupled systems, including a central-executive

network (CEN) anchored in dorsolateral prefrontal cortex (DLPFC) and posterior parietal cortex

(PPC), and a salience network anchored in anterior insula (AI) and anterior cingulate cortex

(ACC) [15].

Fig 10: Intrinsic core network[15]

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Fig 11: Task related network[15]

A second major method of ICN identification is seedbased functional interdependence

analysis. Like ICA, this technique has been used to examine ICNs associated with specific

cognitive processes such as visual orienting attention, memory and emotion. First, a seed region

associated with a cognitive function is identified. Then, a map is constructed of brain voxels

showing significant functional connectivity with the seed region. This approach has

demonstrated that similar networks to those engaged during cognitive task performance are

identifiable at rest, including dorsal and ventral attention systems and hippocampal memory

systems. It has also revealed distinct functional circuits within adjacent brain regions: functional

connectivity maps of the human basolateral and centromedial amygdal [15].

Graph-theoretic studies of resting-state fMRI functional connectivity results have

suggested that human large-scale functional brain networks are usefully described as small-

world. Other graph-theoretic metrics such as hierarchy have been useful in characterizing

subnetwork topological properties, but a consistent view of hierarchical organization in large-

scale functional networks has yet to emerge [15].

Page 22

Problem Formulation and Methodology

In our work we have hypothised human nervous system according the following tree.

Graphical representation of human nervous system is given below-

Fig 12: Human Nervous System(HNS), Graphical representation

Page 23

Problem#1

Model human nervous system(HNS) as a large distributed network and try to predict some of the

cognitive behavior from this network mathematically.

Page 24

Appendix-1(Brodmaan Area)

Areas Broad Parts Location in Brain Functions Remarks

Area- 3,

2, 1

Primary

Somatosensory

Cortex

The lateral

postcentral gyrus

is a prominent

structure in the

parietal lobe of the

human brain and

an important

landmark. It is the

location of the

primary

somatosensory

cortex

the main sensory

receptive area for the

sense of touch

Area- 4 Primary Motor

Cortex

It is located in the

posterior portion

of the frontal lobe.

is about the same

as the precentral

gyrus.

The borders of this

area are: the

precentral sulcus

in front

(anteriorly), the

medial

longitudinal

fissure at the top

(medially), the

central sulcus in

back (posteriorly),

and the lateral

sulcus along the

bottom (laterally).

plan and execute

movements.

Page 25

Area- 5 Somatosensory

Association Cortex

is part of the

parietal cortex in

the human brain.

It is situated

immediately

posterior to the

primary

somatosensory

areas (Brodmann

areas 3, 1, and 2),

and anterior to

Brodmann area 7.

It is involved in

somatosensory

processing and

association.(The

somatosensory system is

a diverse sensory system

comprising the receptors

and processing centres to

produce the sensory

modalities such as touch,

temperature,

proprioception (body

position), and

nociception (pain). The

sensory receptors cover

the skin and epithelia,

skeletal muscles, bones

and joints, internal

organs, and the

cardiovascular system.)

Area- 6 Premotor cortex

and Supplementary

Motor Cortex

(Secondary Motor

Cortex)(Supplemen

tary motor area)

It is part of the

frontal cortex in

the human brain.

Situated just

anterior to the

primary motor

cortex (BA4), it is

composed of the

premotor cortex

and, medially, the

supplementary

motor area, or

SMA.

This large area of the

frontal cortex is believed

to play a role in the

planning of complex,

coordinated movements.

Brodmann

area 6 is also

called

agranular

frontal area 6

in humans

because it

lacks an

internal

granular

cortical layer

(layer IV).

Area- 7 Somatosensory

Association Cortex

is part of the

parietal cortex in

the human brain.

Situated posterior

this region is believed to

play a role in visuo-

motor coordination.

area 7 along with area 5

Page 26

to the primary

somatosensory

cortex (Brodmann

areas 3, 1 and 2),

and superior to the

occipital lobe

has been linked to a wide

variety of high-level

processing tasks,

including activation in

association with language

use.This function in

language has been

theorized to stem from

how these two regions

play a vital role in

generating conscious

constructs of objects in

the world.

Area- 8 Includes Frontal

eye fields

is part of the

frontal cortex in

the human brain.

Situated just

anterior to the

premotor cortex

(BA6)

believed to play an

important role in the

control of eye

movements.

Area- 9 Dorsolateral

prefrontal cortex

part of the frontal

cortex in the

human brain.

DLPFC serves as the

highest cortical area

responsible for motor

planning, organization,

and regulation.

It plays an important role

in the integration of

sensory and mnemonic

information and the

regulation of intellectual

function and action,

especially in relation to

impulse control.

It is also involved in

working memory.

However, DLPFC is not

exclusively responsible

Page 27

for the executive

functions. All complex

mental activity requires

the additional cortical

and subcortical circuits

with which the DL-PFC

is connected.

Area- 10 Anterior prefrontal

cortex (most rostral

part of superior and

middle frontal gyri)

It is the anterior-

most portion of the

prefrontal cortex

in the human

brain.

one of the least well

understood regions of the

human brain".

Present research suggests

that it is involved in

strategic processes in

memory recall and

various executive

functions.

During

human

evolution, the

functions in

this area

resulted in its

expansion

relative to the

rest of the

brain

Area- 11 Orbitofrontal area

(orbital and rectus

gyri, plus part of

the rostral part of

the superior frontal

gyrus)

It is a prefrontal

cortex region in

the frontal lobes in

the brain

It is involved in the

cognitive processing of

decision-making.

Area- 12 Orbitofrontal area

(used to be part of

BA11, refers to the

area between the

superior frontal

gyrus and the

inferior rostral

sulcus)

It occupies the

most rostral

portion of the

frontal lobe.

Not known

Area-

13, 14

Insular cortex In each

hemisphere of the

mammalian brain

the insular cortex

(often called

insula, insulary

cortex or insular

The insulae are believed

to be involved in

consciousness and play a

role in diverse functions

usually linked to emotion

or the regulation of the

body's homeostasis.

Area -14 for

non-human

primates.

Page 28

lobe) is a portion

of the cerebral

cortex folded deep

within the lateral

sulcus (the fissure

separating the

temporal lobe

from the parietal

and frontal lobes).

These functions include

perception, motor

control, self-awareness,

cognitive functioning,

and interpersonal

experience. In relation to

these it is involved in

psychopathology.

Area- 15 Anterior Temporal

Lobe

subdivisions of the

cerebral cortex in

the brain.

Area 15 was

defined by

Brodmann in

the guenon

monkey, but

he found no

equivalent

structure in

humans.

Area- 17 Primary visual

cortex (V1)

is the part of the

cerebral cortex It

is located in the

occipital lobe, in

the back of the

brain.

responsible for

processing visual

information.

Area- 18 Secondary visual

cortex (V2)

It is part of the

occipital cortex in

the human brain.

is the second

major area in the

visual cortex, and

the first region

within the visual

association area.

It receives strong

feedforward connections

from V1 (direct and via

the pulvinar) and sends

strong connections to V3,

V4, and V5. It also sends

strong feedback

connections to V1.

Area- 19 Associative visual

cortex (V3,V4,V5)

It is part of the

occipital lobe

cortex in the

Area 19 has been noted

to receive inputs from the

retina via the superior

colliculus and pulvinar,

In patients

blind from a

young age,

the area has

Page 29

human brain. and may contribute to the

phenomenon of

blindsight.

been found to

be activated

by

somatosensor

y stimuli.

Area- 20 Inferior temporal

gyrus

It is placed below

the middle

temporal gyrus,

and is connected

behind with the

inferior occipital

gyrus; it also

extends around the

infero-lateral

border on to the

inferior surface of

the temporal lobe,

where it is limited

by the inferior

sulcus.

This region believed to

play a part in high-level

visual processing and

recognition memory.

It may also be involved

in face perception, and in

the recognition of

numbers.

Area- 21 Middle temporal

gyrus

Middle temporal

gyrus is a gyrus in

the brain on the

Temporal lobe. It

is located between

the superior

temporal gyrus

and inferior

temporal gyrus

Its exact function is

unknown, but it has been

connected with processes

as different as

contemplating distance,

recognition of known

faces, and accessing

word meaning while

reading.

Area- 22 Superior temporal

gyrus, of which the

caudal part is

usually considered

to contain the

Wernicke's area

The superior

temporal gyrus is

one of three

(sometimes two)

gyri in the

temporal lobe of

the human brain,

which is located

laterally to the

On the left side of the

brain this area helps with

generation and

understanding of

individual words. On the

right side of the brain it

helps to discriminate

pitch and sound intensity,

both of which are

Page 30

head, situated

somewhat above

the external ear.

The superior

temporal gyrus is

bounded by:

the lateral

sulcus above;

the superior

temporal sulcus

(not always

present or visible)

below;

an imaginary

line drawn from

the preoccipital

notch to the lateral

sulcus posteriorly.

necessary to perceive

melody and prosody.

Researchers believe this

part of the brain is active

in processing language.

Area- 23 Ventral posterior

cingulate cortex

The posterior

cingulate cortex is

the backmost part

of the cingulate

cortex, lying

behind the anterior

cingulate cortex.

This is the upper

part of the "limbic

lobe". The

cingulate cortex is

made up of an area

around the midline

of the brain.

Surrounding areas

include the

The posterior cingulate

cortex forms a central

node in the "default

mode" network of the

brain. It has been shown

to communicate with

various brain networks

simultaneously and is

involved in various

functions.[1] Along with

the precuneus, the

posterior cingulate cortex

has been implicated as a

neural substrate for

human awareness in

numerous studies of both

Page 31

retrosplenial

cortex and the

precuneus.

the anesthesized and

vegetative (coma) state.

Imaging studies indicate

a prominent role for the

posterior cingulate cortex

in pain and episodic

memory retrieval.[2] It

has also been revealed

that increased size of

posterior ventral

cingulate cortex is related

to the working memory

performance decline.[3]

Furthermore, the

posterior cingulate may

be involved in the

capacity to understand

what other people

believe.

Area- 24 Ventral anterior

cingulate cortex.

The anterior

cingulate cortex

(ACC) is the

frontal part of the

cingulate cortex,

surrounding the

frontal part of the

corpus callosum.

It appears to play a role

in a wide variety of

autonomic functions,

such as regulating blood

pressure and heart rate,

as well as rational

cognitive functions, such

as reward anticipation,

decision-making,

empathy, impulse

control,[1] and

emotion.[2][3]

Area- 25 Subgenual area

(part of the

Ventromedial

prefrontal cortex

s an area in the

cerebral cortex of

the brain

This region is extremely

rich in serotonin

transporters and is

considered as a governor

for a vast network

involving areas like

hypothalamus and brain

stem, which influences

Page 32

changes in appetite and

sleep; the amygdala and

insula, which affect the

mood and anxiety; the

hippocampus, which

plays an important role in

memory formation; and

some parts of the frontal

cortex responsible for

self-esteem

Area- 26 Ectosplenial portion

of the retrosplenial

region of the

cerebral cortex

It is the

retrosplenial

region of the

cerebral cortex. It

is a narrow band

located in the

isthmus of

cingulate gyrus

adjacent to the

fasciolar gyrus

internally. It is

bounded externally

by the granular

retrolimbic are

Not known

Area- 27 Piriform cortex Not in human

brain

Area- 28 Ventral entorhinal

cortex

located in the

medial temporal

lobe

and functioning as a hub

in a widespread network

for memory and

navigation.

he EC-hippocampus

system plays an

important role in

autobiographical/declarat

ive/episodic memories

and in particular spatial

memories including

memory formation,

The EC is the

main

interface

between the

hippocampus

and

neocortex.

Page 33

memory consolidation,

and memory optimization

in sleep. The EC is also

responsible for the pre-

processing (familiarity)

of the input signals in the

reflex nictitating

membrane response of

classical trace

conditioning, the

association of impulses

from the eye and the ear

occurs in the entorhinal

cortex.

Area- 29 Retrosplenial

cingulate cortex

In the human it is a

narrow band

located in the

isthmus of

cingulate

gyrus.(The

cingulate cortex is

a part of the brain

situated in the

medial aspect of

the cerebral cortex.

It includes the

cortex of the

cingulate gyrus,

which lies

immediately above

the corpus

callosum, and the

continuation of

this in the

cingulate sulcus.

The cingulate

cortex is usually

considered part of

the limbic lobe.)

It receives inputs from

the thalamus and the

neocortex, and projects to

the entorhinal cortex via

the cingulum. It is an

integral part of the limbic

system, which is

involved with emotion

formation and

processing, learning, and

memory. The

combination of these

three functions makes the

cingulate gyrus highly

influential in linking

behavioral outcomes to

motivation (e.g. a certain

action induced a positive

emotional response,

which results in

learning). It also plays a

role in executive function

and respiratory control.

cingulate

cortex highly

important in

disorders

such as

depressionan

d

schizophreni

a.

Page 34

Area- 30 Part of cingulate

cortex

In the human it is a

narrow band

located in the

isthmus of

cingulate gyrus.

Area- 31 Dorsal Posterior

cingulate cortex

In the human it

occupies portions

of the posterior

cingulate gyrus

and medial aspect

of the parietal

lobe. Approximate

boundaries are the

cingulate sulcus

dorsally and the

parieto-occipital

sulcus caudally. It

partially surrounds

the subparietal

sulcus, the ventral

continuation of the

cingulate sulcus in

the parietal lobe.

Cytoarchitecturall

y it is bounded

rostrally by the

ventral anterior

cingulate area 24,

ventrally by the

ventral posterior

cingulate area 23,

dorsally by the

gigantopyramidal

area 4 and

preparietal area 5

and caudally by

the superior

parietal area 7

Page 35

Area- 32 Dorsal anterior

cingulate cortex

In the human it

forms an outer arc

around the anterior

cingulate gyrus.

The cingulate

sulcus defines

approximately its

inner boundary

and the superior

rostral sulcus (H)

its ventral

boundary; rostrally

it extends almost

to the margin of

the frontal lobe.

Cytoarchitecturall

y it is bounded

internally by the

ventral anterior

cingulate area 24,

externally by

medial margins of

the agranular

frontal area 6,

intermediate

frontal area 8,

granular frontal

area 9, frontopolar

area 10, and

prefrontal area 11

Area- 33 Part of anterior

cingulate cortex

It is a narrow band

located in the

anterior cingulate

gyrus adjacent to

the supracallosal

gyrus in the depth

of the callosal

sulcus, near the

genu of the corpus

callosum.

Page 36

Cytoarchitecturall

y it is bounded by

the ventral anterior

cingulate area 24

and the

supracallosal gyrus

Area- 34 Dorsal entorhinal

cortex (on the

Parahippocampal

gyrus)

Area 28

Area- 35 Perirhinal cortex (in

the rhinal sulcus)

Perirhinal cortex is

a cortical region in

the medial

temporal lobe

It receives highly-

processed sensory

information from all

sensory regions, and is

generally accepted to be

an important region for

memory.

Area- 36 Ectorhinal area,

now part of the

perirhinal cortex (in

the rhinal sulcus)

It is located in

temporal region of

cerebral cortex.

With its medial

boundary

corresponding

approximately to

the rhinal sulcus it

is located

primarily in the

fusiform gyrus.

Cytoarchitecturall

y it is bounded

laterally and

caudally by the

inferior temporal

area 20, medially

by the perirhinal

area 35 and

rostrally by the

temporopolar area

Page 37

38

Area- 37 Fusiform gyrus The fusiform

gyrus is part of the

temporal lobe and

occipital lobe

There is still some

dispute over the

functionalities of this

area, but there is relative

consensus on the

following:

processing of color

information

face and body

recognition (see Fusiform

face area)

word recognition (see

Visual word form area)

within-category

identification

Area- 38 Temporopolar area

(most rostral part of

the superior and

middle temporal

gyri)

It is part of the

temporal cortex in

the human brain.

BA 38 is at the

anterior end of the

temporal lobe,

known as the

temporal pole.

The functional

significance of this area

TG is not known, but it

may bind complex,

highly processed

perceptual inputs to

visceral emotional

responses

is unique to

humans

Area- 39 Angular gyrus,

considered by some

to be part of

Wernicke's area

The angular gyrus

is a region of the

brain in the

parietal lobe, that

lies near the

superior edge of

the temporal lobe,

and immediately

posterior to the

supramarginal

it is involved in a number

of processes related to

language, number

processing and spatial

cognition, memory

retrieval, attention, and

theory of mind.

Page 38

gyrus

Area- 40 Supramarginal

gyrus considered by

some to be part of

Wernicke's area

It is part of the

parietal cortex in

the human brain.

The inferior part of

BA40 is in the

area of the

supramarginal

gyrus, which lies

at the posterior end

of the lateral

fissure, in the

inferior lateral part

of the parietal

lobe.

It is probably involved

with language perception

and processing, and

lesions in it may cause

Receptive aphasia or

transcortical sensory

aphasia

Area-

41, 42

Auditory cortex The auditory

cortex is the part

of the cerebral

cortex that

processes auditory

information in

humans and other

vertebrates.

It is located

bilaterally, roughly

at the upper sides

of the temporal

lobes – in humans

on the superior

temporal plane,

within the lateral

fissure and

comprising parts

of Heschl's gyrus

and the superior

temporal gyrus,

including planum

polare and planum

A part of the auditory

system, it performs basic

and higher functions in

hearing.

Page 39

temporale

Area- 43 Primary gustatory

cortex

is defined in the

postcentral region

of cerebral cortex.

It occupies the

postcentral gyrus

and the precentral

gyrus between the

ventrolateral

extreme of the

central sulcus and

the depth of the

lateral sulcus at the

insula.

Not known

Area- 44 Pars opercularis,

part of Broca's area

n the human, this

region occupies

the triangular part

of the inferior

frontal gyrus and,

surrounding the

anterior horizontal

limb of the lateral

sulcus, a portion of

the orbital part of

the inferior frontal

gyrus. Bounded

caudally by the

anterior ascending

limb of the lateral

sulcus, it borders

on the insula in the

depth of the lateral

sulcus.

Recent neuroimaging

studies show BA44

involvement in selective

response suppression in

go/no- go tasks and is

therefore believed to play

an important role in the

suppression of response

tendencies.Neuroimaging

studies also demonstrate

that area 44 is related to

hand movements.

Area- 45 Pars triangularis

Broca's area

Brodmann area 45

(BA45), is part of

the frontal cortex

in the human

brain. Situated on

Together with BA 44, it

comprises Broca's area, a

region that is active in

semantic tasks, such as

semantic decision tasks

Page 40

the lateral surface,

inferior to BA9

and adjacent to

BA46.

(determining whether a

word represents an

abstract or a concrete

entity) and generation

tasks (generating a verb

associated with a noun).

Area- 46 Dorsolateral

prefrontal cortex

Brodmann area 46,

or BA46, is part of

the frontal cortex

in the human

brain. It is between

BA10 and BA45.

BA46 is known as

middle frontal area

46. In the human

brain it occupies

approximately the

middle third of the

middle frontal

gyrus and the most

rostral portion of

the inferior frontal

gyrus. Brodmann

area 46 roughly

corresponds with

the dorsolateral

prefrontal cortex

(DLPFC)

The DLPFC plays a role

in sustaining attention

and working memory.

Lesions to the DLPFC

impair short-term

memory and cause

difficulty inhibiting

responses. Lesions may

also eliminate much of

the ability to make

judgements about what's

relevant and what's not as

well as causing problems

in organization.

The DLPFC has recently

been found to be

involved in exhibiting

self-control.

Area- 47 pars orbitalis, part

of the inferior

frontal gyrus

Brodmann area 47,

or BA47, is part of

the frontal cortex

in the human

brain. Curving

from the lateral

surface of the

frontal lobe into

the ventral

(orbital) frontal

BA47 has been

implicated in the

processing of syntax in

oral and sign languages,

and more recently in

musical syntax.

Page 41

cortex. It is below

areas BA10 and

BA45, and beside

BA11.

This area is also

known as orbital

area 47. In the

human, on the

orbital surface it

surrounds the

caudal portion of

the orbital sulcus

(H) from which it

extends laterally

into the orbital part

of inferior frontal

gyrus

Area- 48 Retrosubicular area

(a small part of the

medial surface of

the temporal lobe)

In the human it is

located on the

medial surface of

the temporal lobe.

Not known

Area- 49 Parasubicular area

in a rodent

Area- 52 Parainsular area (at

the junction of the

temporal lobe and

the insula)

It is located in the

bank of the lateral

sulcus on the

dorsal surface of

the temporal lobe.

Its medial

boundary

corresponds

approximately to

the junction

between the

temporal lobe and

the insula.

Not known

Page 42

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