Cerebral

Cortex

October

doi

Advance

Access

publication

January

Small-World

Anatomical

Networks

in

the

Human

Brain

Revealed

by

Cortical

Thickness

from

MRI

Yong

He

Zhang

J.

Chen

and

Alan

C.

Evans

McConnell

Brain

Imaging

Centre

Montreal

Neurological

Institute

McGill

University

Montreal

QC

Canada

An

important

issue

in

neuroscience

is

the

characterization

for

the

underlying

architectures

of

complex

brain

networks

However

little

is

known

about

the

network

of

anatomical

connections

in

the

human

brain

Here

we

investigated

large-scale

anatomical

connection

patterns

of

the

human

cerebral

cortex

using

cortical

thickness

measurements

from

magnetic

resonance

images

Two

areas

were

considered

anatomically

connected

if

they

showed

statistically

significant

correlations

in

cortical

thickness

and

we

constructed

the

network

of

such

connections

using

brains

from

the

International

Consortium

for

Brain

Mapping

database

Significant

short

and

long-range

connections

were

found

in

both

intra

and

interhemispheric

regions

many

of

which

were

consistent

with

known

neuroanatomical

pathways

measured

by

human

diffusion

imaging

More

importantly

we

showed

that

the

human

brain

anatomical

network

had

robust

small-world

properties

with

cohesive

neighborhoods

and

short

mean

distances

between

regions

that

were

insensitive

to

the

selection

of

correlation

thresholds

Additionally

we

also

found

that

this

network

and

the

probability

of

finding

a

connection

between

regions

for

a

given

anatomical

distance

had

both

exponentially

truncated

power-law

distributions

Our

results

demonstrated

the

basic

organizational

principles

for

the

anatomical

network

in

the

human

brain

compatible

with

previous

functional

networks

studies

which

provides

important

implications

of

how

functional

brain

states

originate

from

their

structural

underpinnings

To

our

knowledge

this

study

provides

the

first

report

of

small-world

properties

and

degree

distribution

of

anatomical

networks

in

the

human

brain

using

cortical

thickness

measurements

Keywords

anatomy

connectivity

cortical

thickness

magnetic

resonance

imaging

morphometry

scale

free

small

world

Introduction

The

human

brain

is

a

large

interacting

complex

network

with

nontrivial

topological

properties

-LRB-

Sporns

et

al.

Stam

Eguiluz

et

al.

Salvador

Suckling

Coleman

et

al.

Achard

et

al.

Stam

et

al.

-RRB-

The

characterization

for

the

underlying

architectures

of

such

a

network

is

an

important

issue

in

neuroscience

It

can

reveal

general

principles

of

structural

and

functional

organization

in

the

human

brain

and

increase

our

understanding

of

how

the

human

brain

is

capable

of

generating

and

integrating

information

from

multiple

sources

in

real

time

-LRB-

Sporns

et

al.

-RRB-

Thus

far

most

studies

of

complex

brain

networks

in

human

have

focused

upon

exploring

connectivity

patterns

under

functional

brain

states

For

example

recent

electroencephalogram

-LRB-

EEG

-RRB-

-LRB-

Micheloyannis

et

al.

Stam

et

al.

-RRB-

magnetoencephalographic

-LRB-

MEG

-RRB-

recordings

-LRB-

Stam

-RRB-

and

functional

magnetic

resonance

imaging

-LRB-

fMRI

-RRB-

-LRB-

Eguiluz

et

al.

Salvador

Suckling

Coleman

et

al.

Achard

et

al.

The

Author

Published

by

Oxford

University

Press

All

rights

reserved

For

permissions

please

e-mail

journals.permissions@oxfordjournals.org

-RRB-

studies

have

consistently

demonstrated

that

human

brain

functional

networks

during

behavior

or

even

at

resting

state

have

the

small-world

property

a

prominent

feature

shared

by

various

social

economic

and

biological

networks

-LRB-

for

a

review

see

Strogatz

-RRB-

A

small-world

architecture

indicates

that

the

minimum

path

length

between

any

pair

of

nodes

is

approximately

equivalent

to

a

comparable

random

network

but

the

nodes

of

the

network

have

greater

local

interconnectivity

or

cliquishness

than

a

random

network

-LRB-

Watts

and

Strogatz

-RRB-

In

addition

to

the

small-world

features

Eguiluz

et

al.

-LRB-

-RRB-

demonstrated

that

human

brain

functional

networks

derived

from

experimentally

activated

fMRI

data

at

a

mesoscale

-LRB-

voxel

level

-RRB-

have

a

scale-free

power-law

connection

degree

distribution

implying

that

there

are

a

small

number

of

regions

-LRB-

hubs

-RRB-

with

an

unusually

large

number

of

connections

On

the

other

hand

another

study

from

Achard

et

al.

-LRB-

-RRB-

showed

that

functional

networks

of

the

human

brain

derived

from

restingstate

fMRI

data

at

a

macroscale

-LRB-

regional

level

-RRB-

follow

an

exponentially

truncated

power-law

distribution

implying

relatively

reduced

probabilities

of

huge

hubs

The

discrepancies

between

the

connectivity

degree

distributions

could

be

due

to

the

different

spatial

scale

analysis

and/or

experimental

conditions

of

the

subjects

applied

in

the

studies

Although

there

have

been

a

number

of

studies

investigating

functional

connectivity

networks

-LRB-

Stam

Eguiluz

et

al.

Salvador

Suckling

Coleman

et

al.

Achard

et

al.

Stam

et

al.

-RRB-

little

is

known

about

the

network

of

anatomical

connections

in

the

human

brain

Definition

of

anatomical

connectional

models

of

the

human

brain

is

usually

based

on

inferring

knowledge

from

primate

species

such

as

the

macaque

monkey

in

which

the

connection

pattern

is

well

known

-LRB-

Crick

and

Jones

Stephan

et

al.

Penny

et

al.

-RRB-

The

procedure

is

problematic

however

partly

because

of

our

poor

understanding

of

the

evolutionary

discrepancies

Direct

evidence

for

the

underlying

architecture

of

human

brain

anatomical

networks

is

still

lacking

-LRB-

Tootell

et

al.

-RRB-

Characterization

of

such

a

network

would

be

particularly

vital

to

reveal

intrinsically

structural

organizational

principles

in

the

human

brain

and

enhance

our

understanding

of

how

functional

brain

states

are

associated

with

their

structural

substrates

Recently

Sporns

et

al.

-LRB-

-RRB-

have

referred

to

the

comprehensive

detailed

structural

description

of

the

network

of

elements

and

connections

forming

the

human

brain

as

human

connectome

There

is

little

evidence

for

such

an

interesting

but

also

very

challenging

scheme

to

date

because

of

the

difficulties

of

defining

the

basic

structural

elements

of

the

human

brain

in

terms

of

network

nodes

and

connections

-LRB-

Sporns

et

al.

-RRB-

In

this

study

we

propose

an

avenue

of

research

to

characterize

large-scale

anatomical

connectivity

patterns

of

the

human

brain

using

morphological

measurements

from

in

vivo

MRI

Cortical

thickness

was

chosen

as

a

morphometric

feature

because

it

reflects

the

size

density

and

arrangement

of

cells

-LRB-

neurons

neuroglia

and

nerve

fibers

-RRB-

-LRB-

Parent

and

Carpenter

Narr

et

al.

-RRB-

Particularly

recent

studies

have

suggested

that

interregional

statistical

associations

in

cortical

thickness

provide

important

connectivity

information

in

the

human

brain

-LRB-

Worsley

et

al.

Lerch

et

al.

-RRB-

-LRB-

we

will

return

to

this

issue

in

the

Discussion

section

-RRB-

To

study

largescale

anatomical

connectivity

patterns

in

the

human

brain

we

first

segmented

the

entire

cerebral

cortex

into

areas

and

automatically

measured

regional

cortical

thickness

using

computational

neuroanatomy

Two

areas

were

considered

anatomically

connected

if

they

had

significant

correlations

of

cortical

thickness

across

a

population

of

normal

brains

drawn

from

the

International

Consortium

for

Brain

Mapping

-LRB-

ICBM

-RRB-

MRI

database

-LRB-

Mazziotta

et

al.

-RRB-

Finally

we

thresholded

the

interregional

correlation

matrix

to

construct

an

undirected

graph

and

estimated

its

statistical

and

anatomical

properties

especially

small-world

properties

and

connectivity

degree

distribution

using

graph

theoretical

analysis

This

allows

us

for

the

first

time

to

assess

the

dependencies

of

interregional

anatomical

connectivity

on

the

anatomical

relationship

between

regions

and

to

demonstrate

the

small-world

attributes

and

degree

distribution

of

human

cortical

networks

using

cortical

thickness

measurements

from

in

vivo

MRI

Materials

and

Methods

Subjects

The

subjects

scanned

were

unselected

normal

volunteers

of

the

ICBM

database

Each

subject

gave

written

informed

consent

and

this

study

was

approved

by

the

Research

Ethics

Committee

of

the

Montreal

Neurological

Institute

and

Hospital

The

scans

of

subjects

were

excluded

from

the

analysis

due

to

the

left-handedness

-LRB-

subjects

-RRB-

unknown

handedness

-LRB-

subjects

-RRB-

and

failure

of

imaging

processing

-LRB-

subjects

-RRB-

Of

the

remaining

right-handed

subjects

were

male

and

female

Ages

ranged

from

to

years

-LRB-

mean

age

standard

deviation

-RRB-

The

characteristics

of

the

subjects

have

been

described

previously

-LRB-

Watkins

et

al.

-RRB-

MRI

Acquisition

MRI

scans

were

performed

on

a

Phillips

Gyroscan

superconducting

magnet

system

and

proton

density

images

were

acquired

for

each

subject

with

the

following

sequences

-LRB-

fast

field

echo

scan

with

slices

isotropic

resolution

time

repetition

-LSB-

TR

-RSB-

ms

time

echo

-LSB-

TE

-RSB-

ms

flip

angle

-RRB-

-LRB-

multislice

fast

spin

echo

scan

with

slices

with

a

mm

overlap

TR

ms

TE

ms

-RRB-

and

proton

density

-LRB-

as

for

scan

but

with

TE

ms

-RRB-

images

of

the

whole

head

Only

image

of

each

subject

was

applied

in

this

study

Measurements

of

Cortical

Thickness

The

native

MR

images

were

first

registered

into

stereotaxic

space

-LRB-

Talairach

and

Tournoux

-RRB-

using

a

linear

transformation

-LRB-

Collins

et

al.

-RRB-

Simultaneously

images

were

corrected

for

nonuniformity

artifacts

using

the

algorithms

-LRB-

Sled

et

al.

-RRB-

The

registered

and

corrected

images

were

further

segmented

into

gray

matter

white

matter

cerebrospinal

fluid

and

background

using

an

advanced

neural

net

classifier

-LRB-

Zijdenbos

et

al.

-RRB-

The

inner

and

outer

gray

matter

surfaces

were

then

automatically

extracted

from

each

MR

volume

using

the

Constrained

Laplacian-based

Automated

Segmentation

with

Proximities

-LRB-

CLASP

-RRB-

algorithm

-LRB-

MacDonald

et

al.

Kim

et

al.

-RRB-

and

cortical

thickness

was

measured

in

native

space

using

the

linked

distance

between

surfaces

at

vertices

throughout

the

cortex

The

measurement

in

native

space

provided

an

unadjusted

estimate

of

absolute

cortical

thickness

-LRB-

Shaw

et

al.

-RRB-

A

representative

cortical

thickness

map

was

shown

in

Figure

The

CLASP

cortical

thickness

algorithm

has

been

validated

using

both

manual

measurements

-LRB-

Kabani

et

al.

-RRB-

and

simulation

approaches

-LRB-

Lerch

and

Evans

Lee

et

al.

-RRB-

and

recently

applied

to

Alzheimer

's

disease

-LRB-

Lerch

et

al.

-RRB-

and

cortical

development

studies

-LRB-

Shaw

et

al.

-RRB-

Individual

cortical

thickness

maps

were

parcellated

using

the

Automated

Nonlinear

Image

Matching

and

Anatomical

Labeling

package

-LRB-

Collins

et

al.

Robbins

et

al.

-RRB-

By

registering

each

subject

's

MR

images

to

a

presegmented

volumetric

template

using

nonlinear

deformations

-LRB-

Collins

et

al.

-RRB-

the

labels

of

brain

regions

were

transformed

to

the

cortical

surface

by

assigning

the

value

of

the

voxel

label

to

each

vertex

on

the

surface

An

average

cortical

parcellation

was

generated

by

finding

the

anatomical

label

with

the

highest

occurrence

at

each

vertex

-LRB-

Fig.

-RRB-

and

separate

cortical

regions

were

identified

for

each

hemisphere

-LRB-

Supplementary

Table

-RRB-

Cortical

thickness

for

each

region

was

measured

as

the

mean

thickness

of

all

vertices

defined

as

belonging

to

that

region

Construction

of

Anatomical

Connection

Matrix

A

key

issue

in

characterizing

human

brain

networks

is

the

construction

of

the

anatomical

connection

matrix

-LRB-

Sporns

et

al.

-RRB-

To

address

this

issue

in

this

study

we

first

defined

anatomical

connection

as

statistical

associations

in

cortical

thickness

between

brain

regions

-LRB-

Fig.

-RRB-

Such

a

morphometry-based

connection

concept

has

been

introduced

by

the

recent

studies

-LRB-

Worsley

et

al.

Lerch

et

al.

-RRB-

The

statistical

similarity

in

cortical

thickness

between

regions

was

measured

by

computing

the

Pearson

correlation

coefficient

across

subjects

and

interregional

correlation

matrix

-LRB-

N

N

where

N

is

the

number

of

brain

regions

here

N

-RRB-

of

such

connections

was

acquired

using

the

brains

included

in

this

study

-LRB-

Fig.

-RRB-

Prior

to

the

correlation

analysis

a

linear

regression

was

performed

at

every

region

to

remove

the

effects

of

age

gender

age

gender

interaction

and

mean

overall

cortical

thickness

the

residuals

of

this

regression

were

then

substituted

for

the

raw

cortical

thickness

values

Because

the

correlation

analysis

was

performed

for

all

3 53/2

pairs

of

regions

it

was

necessary

to

perform

a

multiple

comparisons

correction

to

test

the

significance

of

these

correlations

We

applied

the

false

discovery

rate

-LRB-

FDR

-RRB-

procedure

-LRB-

Genovese

et

al.

-RRB-

to

correct

the

multiple

comparisons

at

a

q

value

of

Using

this

threshold

we

constructed

a

symmetric

connection

matrix

-LRB-

Fig.

-RRB-

whose

element

was

if

the

cortical

thickness

correlation

between

regions

was

statistically

significant

and

otherwise

This

binarized

connection

matrix

captures

the

underlying

anatomical

connection

patterns

of

the

human

brain

common

to

the

population

sample

under

study

The

anatomical

and

statistical

properties

of

this

network

are

further

characterized

below

It

is

also

possible

to

characterize

the

network

with

continuous

weighting

between

nodes

-LRB-

Barrat

et

al.

Jiang

et

al.

-RRB-

but

this

leads

to

complications

of

statistical

features

descriptions

in

subsequent

graph

theoretical

analysis

This

initial

study

therefore

confined

itself

to

a

simpler

on

off

connectivity

analysis

Anatomical

Connections

and

Anatomical

Distance

The

binarized

anatomical

connection

matrix

can

be

visualized

in

anatomical

space

-LRB-

Fig.

-RRB-

by

locating

cortical

regions

according

to

their

y

and

z

centroid

stereotaxic

coordinates

In

this

study

we

also

examined

the

relationship

between

the

anatomical

connections

and

their

corresponding

anatomical

distance

-LRB-

Fig.

-RRB-

The

anatomical

distance

between

regions

was

defined

as

Euclidean

distance

Dij

-LRB-

in

mm

-RRB-

between

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffi

regional

centroids

Dij

xi

xj

yi

yj

zi

zj

where

-LRB-

xi

yi

zi

-RRB-

and

-LRB-

xj

yj

zj

-RRB-

are

the

stereotaxic

coordinates

of

the

centroids

for

regions

i

and

j

The

connections

with

D

mm

were

considered

longrange

connections

shown

in

Figure

The

Euclidean

distance

used

in

the

present

study

provides

an

approximate

reflection

on

the

true

physical

distance

-LRB-

axonal

length

-RRB-

of

connections

between

regions

and

has

been

applied

in

previous

functional

brain

networks

studies

-LRB-

Salvador

Suckling

Coleman

et

al.

Salvador

Suckling

Schwarzbauer

et

al.

Achard

et

al.

-RRB-

Graph

Theoretical

Analysis

To

perform

a

graph

theoretical

analysis

the

anatomical

connection

matrix

obtained

above

was

described

as

an

undirected

graph

G

with

N

Small-World

Anatomical

Networks

d

He

et

al.

nodes

and

K

edges

where

nodes

represent

brain

regions

and

edges

represent

undirected

connections

between

regions

In

this

study

we

estimated

important

metrics

of

the

graph

G

namely

the

mean

degree

k

the

clustering

coefficient

Cp

and

the

characteristic

path

length

Lp

The

mean

degree

k

of

the

graph

G

is

the

average

of

the

degree

over

all

nodes

where

the

degree

ki

of

a

node

i

corresponds

to

the

number

of

connections

to

that

node

The

clustering

coefficient

Cp

of

the

graph

G

is

the

average

of

the

clustering

coefficient

over

all

nodes

where

the

clustering

coefficient

Ci

of

a

node

i

is

defined

as

the

number

of

existing

connections

between

the

node

's

neighbors

divided

by

all

their

possible

connections

-LRB-

Watts

and

Strogatz

-RRB-

Cp

is

a

measure

of

the

extent

of

local

cluster

or

cliquishness

of

the

network

Clearly

Cp

and

Cp

if

and

only

if

the

network

is

fully

connected

that

is

each

node

is

connected

to

all

other

nodes

The

characteristic

path

length

Lp

of

the

graph

G

is

the

smallest

number

of

connections

required

to

connect

one

node

to

another

averaged

overall

all

pairs

of

nodes

Lp

is

a

measure

of

the

extent

of

average

connectivity

or

overall

routing

efficiency

of

the

network

In

this

study

we

also

defined

the

mean

shortest

path

length

Li

of

a

node

i

as

the

average

of

the

shortest

path

lengths

between

this

node

and

all

other

nodes

in

this

network

The

nodes

with

the

smallest

Li

or

largest

ki

were

considered

the

hubs

of

the

network

-LRB-

Achard

et

al.

-RRB-

real

real

To

examine

the

small-world

properties

the

values

of

Cp

and

Lp

of

the

anatomical

network

were

compared

with

those

of

random

networks

We

generated

these

random

graphs

using

the

random

rewiring

procedure

described

by

Maslov

and

Sneppen

-LRB-

-RRB-

and

Milo

et

al.

-LRB-

-RRB-

which

preserves

the

same

number

of

nodes

mean

degree

k

and

degree

distribution

as

the

real

network

Typically

a

small-world

network

should

fulfill

the

following

conditions

real

rand

real

rand

c

Cp

Cp

and

k

Lp

Lp

-LRB-

Watts

and

Strogatz

-RRB-

These

conditions

can

also

be

summarized

into

a

simple

quantitative

measurement

small

worldness

r

c/k

-LRB-

Humphries

et

al.

Achard

et

al.

real

rand

-RRB-

implying

that

the

magnitude

ratio

between

Cp

and

Cp

is

real

rand

greater

than

the

magnitude

ratio

between

Lp

and

Lp

In

this

study

we

real

real

primarily

report

the

results

of

Cp

and

Lp

of

the

anatomical

network

of

the

human

brain

based

on

the

FDR

thresholded

correlation

matrix

-LRB-

Genovese

et

al.

-RRB-

It

is

reasonable

that

the

small-world

attributes

can

change

with

the

correlation

thresholds

When

the

threshold

is

increased

some

weaker

connections

will

be

dropped

out

and

the

resulting

graphs

will

become

sparser

leading

to

a

decrease

of

the

mean

degree

-LRB-

Fig.

-RRB-

When

the

correlation

threshold

reaches

an

value

of

Rmax

the

mean

degree

of

the

resulting

network

will

be

less

than

the

log

of

the

number

of

nodes

-LSB-

i.e.

k

log

N

-RSB-

and

small-world

properties

are

not

estimable

-LRB-

Watts

and

Strogatz

Achard

et

al.

-RRB-

To

explore

the

influence

of

thresholding

on

the

small-world

attributes

in

this

study

we

applied

the

maximum

range

of

correlation

thresholds

-LRB-

R

Rmax

with

an

incremental

interval

of

-RRB-

to

the

correlation

matrix

and

repeated

the

small-world

analysis

for

every

R

value

In

addition

to

the

small-word

attributes

we

also

examined

the

connectivity

degree

distribution

of

the

brain

network

-LRB-

Fig.

-RRB-

It

has

been

demonstrated

that

the

small-world

networks

can

be

classified

into

different

categories

-LRB-

e.g.

scale-free

and

exponentially

truncated

powerlaw

distribution

-RRB-

according

to

their

connectivity

distributions

and

each

of

which

exhibits

specific

network

behaviors

such

as

the

resilience

to

random

errors

or

hubs

attacks

-LRB-

Albert

et

al.

Amaral

et

al.

Achard

et

al.

-RRB-

Finally

the

hub

regions

in

this

network

were

identified

by

using

a

regionally

shortest

path

length

Li

averaged

over

both

hemispheres

To

visualize

the

hubs

we

also

mapped

the

human

brain

network

with

the

Pajek

software

package

-LRB-

pub/networks/pajek

-RRB-

-LRB-

Batagelj

and

Mrvar

-RRB-

using

a

Kamada

Kawai

layout

algorithm

-LRB-

Kamada

and

Kawai

-RRB-

-LRB-

Fig.

-RRB-

To

assess

the

importance

of

the

hubs

for

the

brain

network

we

individually

eliminated

the

hub

and

nonhub

regions

from

the

network

and

compared

the

changes

in

the

global

properties

-LRB-

largest

component

size

clustering

coefficients

and

characteristic

path

lengths

-RRB-

of

the

resulting

networks

using

a

t

test

significant

anatomical

connectivity

-LRB-

cortical

thickness

correlations

-RRB-

which

resulted

in

a

binarized

anatomical

connection

matrix

with

a

sparsity

of

-LRB-

-RRB-

Furthermore

we

observed

a

single

component

with

connected

nodes

and

disconnected

nodes

in

the

sparse

matrix

-LRB-

Fig.

-RRB-

In

this

study

the

properties

of

a

network

were

calculated

on

its

largest

component

Interregional

Anatomical

Connections

About

half

of

the

connections

-LRB-

-RRB-

were

intrahemispheric

involving

brain

regions

in

the

same

lobe

and

anatomically

adjacent

regions

across

different

lobes

Several

symmetrically

interhemispheric

connections

-LRB-

-RRB-

among

certain

bilaterally

homologous

regions

in

the

cerebral

hemispheres

were

also

found

to

be

very

significant

In

addition

we

also

observed

significant

asymmetrically

interhemispheric

connections

between

the

nonhomologous

regions

in

different

hemispheres

-LRB-

-RRB-

Table

included

the

most

significant

interregional

cortical

thickness

connections

-LRB-

corrected

P

-RRB-

and

their

approximately

associated

white

matter

fibers

measured

by

diffusion

imaging

in

human

Anatomical

Connections

and

Anatomical

Distance

Figure

demonstrated

the

dependencies

of

anatomical

connectivity

on

anatomical

distances

Most

of

the

significant

connections

appeared

to

have

shorter

anatomical

distances

-LRB-

D

mm

-RRB-

but

we

also

observed

some

long-range

-LRB-

D

mm

-RRB-

connections

in

this

brain

network

The

probability

of

finding

a

significant

connection

between

any

regions

for

a

given

anatomical

distance

can

be

modeled

as

an

exponentially

truncated

power

law

P

D

D

a

e

D

Dc

with

an

estimated

exponent

a

and

a

cutoff

distance

Dc

mm

-LRB-

Fig.

-RRB-

This

model

indicates

a

scaling

regimen

followed

by

an

exponential

decay

in

the

probability

of

connections

with

an

anatomical

distance

greater

than

a

cutoff

value

of

mm

To

further

explore

the

pairs

of

regions

that

pertain

to

either

the

short

or

the

long-range

connections

we

visualized

the

connection

map

in

the

anatomical

space

-LRB-

Fig.

-RRB-

In

Figure

we

observed

that

short-range

-LRB-

D

mm

-RRB-

connections

-LRB-

-RRB-

existed

predominantly

in

the

posterior

cortex

Figure

indicated

that

long-range

-LRB-

D

mm

-RRB-

connections

-LRB-

-RRB-

are

mainly

between

regions

of

the

frontal

cortex

-LRB-

superior

frontal

gyrus

-LSB-

SFG

-RSB-

middle

frontal

gyrus

-LSB-

MFG

-RSB-

inferior

frontal

gyrus

-LSB-

IFG

-RSB-

medial

front-orbital

gyrus

-LSB-

MOFG

-RSB-

and

precentral

gyrus

-LSB-

PrCG

-RSB-

-RRB-

and

regions

of

the

temporal

-LRB-

superior

temporal

gyrus

-LSB-

STG

-RSB-

middle

temporal

gyrus

-LSB-

MTG

-RSB-

inferior

temporal

gyrus

-LSB-

ITG

-RSB-

and

lateral

occipitotemporal

gyrus

-LSB-

LOTG

-RSB-

-RRB-

parietal

-LRB-

superior

parietal

lobe

-LSB-

SPL

-RSB-

precuneus

-LSB-

PCU

-RSB-

supramarginal

gyrus

-LSB-

SMG

-RSB-

and

angular

gyrus

-LSB-

AG

-RSB-

-RRB-

and

occipital

association

cortices

-LRB-

superior

occipital

gyrus

-LSB-

SOG

-RSB-

-RRB-

Small-World

Properties

In

the

present

study

we

calculated

the

clustering

coefficient

and

characteristic

path

length

for

both

of

the

cortical

thickness

real

real

connectivity

network

-LRB-

Cp

Lp

-RRB-

and

the

corresponding

random

networks

with

the

same

number

of

nodes

mean

degree

and

degree

distribution

-LRB-

Cprandom

Lprandom

-RRB-

In

other

words

the

clustering

coefficient

of

the

brain

network

is

approximately

twice

that

of

a

comparable

random

network

-LRB-

c

-RRB-

whereas

the

path

length

is

approximately

equivalent

to

the

random

network

-LRB-

k

-RRB-

Cerebral

Cortex

October

V

N

Results

Under

the

statistical

threshold

of

p

value

of

-LRB-

corrected

by

FDR

-RRB-

we

observed

that

the

pairs

of

regions

exhibited

Figure

A

flowchart

for

the

construction

of

the

human

brain

anatomical

network

using

cortical

thickness

measurements

from

MRI

-LRB-

A

-RRB-

Cortical

thickness

was

estimated

using

computational

neuroanatomy

The

native

images

were

nonuniformity

corrected

and

registered

into

stereotaxic

space

The

resulting

images

were

then

classified

-LRB-

-RRB-

to

extract

the

inner

-LRB-

-RRB-

and

outer

-LRB-

-RRB-

gray

matter

surfaces

Cortical

thickness

was

measured

at

each

vertex

-LRB-

-RRB-

-LRB-

B

-RRB-

The

cerebral

cortex

was

segmented

into

cortical

areas

displayed

on

the

average

cortex

each

color

representing

a

different

region

-LRB-

C

-RRB-

Anatomical

connection

was

defined

as

statistically

association

in

cortical

thickness

between

areas

As

an

example

of

anatomical

connections

using

cortical

thickness

correlations

used

in

this

study

we

demonstrated

that

the

thickness

of

right

middle

prefrontal

gyrus

had

significant

association

with

that

of

left

middle

prefrontal

gyrus

The

left

plot

showed

the

associations

-LRB-

r

P

-RRB-

using

raw

cortical

thickness

values

but

the

right

plot

showed

Small-World

Anatomical

Networks

d

He

et

al.

Figure

The

dependencies

of

anatomical

connectivity

on

anatomical

distance

-LRB-

A

-RRB-

Plot

of

anatomical

connections

-LRB-

cortical

thickness

correlations

-RRB-

versus

anatomical

distance

between

regions

Red

circles

indicate

the

anatomical

connections

between

bilaterally

homologous

regions

The

dotted

lines

indicate

the

values

of

correlations

under

the

FDR

threshold

-LRB-

P

-RRB-

-LRB-

B

-RRB-

Distribution

of

anatomical

distance

Frequency

indicates

the

number

of

significant

connections

for

a

given

anatomical

distance

The

figure

shows

many

strong

local-range

connections

and

a

few

long-range

connections

-LRB-

C

-RRB-

Probability

of

finding

a

significant

connection

for

a

given

distance

in

the

log

log

plot

fitted

by

an

exponentially

truncated

power

law

-LRB-

black

solid

line

-RRB-

The

observed

data

points

-LRB-

plus

sign

-RRB-

were

obtained

by

a

FDR

threshold

Distance

shown

in

figures

indicates

Euclidean

distance

between

regional

centroids

in

stereotaxic

space

thus

resulting

in

a

small-world

scalar

parameter

of

r

-LRB-

Table

-RRB-

In

Figure

we

showed

the

small-world

properties

of

the

anatomical

network

as

a

function

of

correlation

threshold

For

a

lower

threshold

value

the

corresponding

brain

network

is

almost

fully

connected

and

the

small-world

properties

are

real

real

indiscernible

-LRB-

both

Cp

and

Lp

are

close

to

-RRB-

from

the

matched

random

networks

As

the

correlation

threshold

values

increased

the

clustering

coefficient

also

increased

rapidly

-LRB-

Fig.

-RRB-

whereas

the

path

length

only

changed

slightly

-LRB-

Fig.

-RRB-

leading

to

the

increases

of

the

small

worldness

-LRB-

Fig.

-RRB-

Overall

small-world

properties

were

salient

at

higher

threshold

-LRB-

Fig.

F

-RRB-

The

small-world

models

shown

here

therefore

indicated

that

anatomical

networks

of

the

human

brain

have

greater

local

interconnectivity

or

cliquishness

and

short

mean

distance

between

regions

Connectivity

Degree

Distribution

and

Hub

Regions

In

addition

to

the

investigation

of

the

small-world

properties

we

also

examined

the

degree

distribution

of

the

anatomical

network

in

the

human

brain

Clearly

the

brain

network

does

not

follow

a

power-law

form

because

the

fitted

curve

is

not

a

straight

line

on

the

log

log

plot

-LRB-

Fig.

-RRB-

Rather

this

distribution

can

be

well

fitted

by

an

exponentially

truncated

power-law

form

P

k

ka

e

k

kc

with

an

estimated

exponent

a

and

a

cutoff

degree

kc

This

model

indicates

a

scaling

regimen

followed

by

an

exponential

decay

in

the

probability

of

finding

nodes

with

a

connection

degree

greater

than

a

cutoff

value

of

In

addition

we

also

demonstrated

that

the

exponentially

truncated

power-law

distribution

was

apparent

under

several

different

correlation

thresholds

with

only

a

slight

change

in

the

values

of

estimated

parameters

-LRB-

Fig.

-RRB-

This

distribution

model

indicated

that

the

brain

networks

included

some

hub

nodes

with

many

connections

but

prevented

the

appearance

of

huge

hubs

with

very

many

connections

Twelve

hub

nodes

of

this

network

were

identified

by

using

a

regionally

shortest

path

length

averaged

over

both

hemispheres

These

hubs

included

regions

of

the

heteromodal

or

unimodal

association

cortex

regions

of

the

primary

motor

and

sensorymotor

cortex

and

one

region

of

the

paralimbic

cortex

-LRB-

Fig.

Table

-RRB-

which

had

a

large

overlap

with

the

hub

nodes

identified

in

a

very

recent

functional

brain

network

study

associations

-LRB-

r

P

-RRB-

using

the

residuals

of

cortical

thickness

obtained

by

removing

the

effects

of

gender

age

gender

age

interaction

and

mean

overall

cortical

thickness

It

was

noted

that

the

use

of

the

residuals

removed

some

of

correlations

between

regions

Each

data

point

represents

a

single

subject

in

the

study

-LRB-

D

-RRB-

Correlation

matrix

of

the

cortical

thickness

in

the

human

brain

was

acquired

using

the

brains

from

the

ICBM

database

-LRB-

E

-RRB-

Anatomical

connection

matrix

was

constructed

by

thresholding

the

correlation

matrix

in

-LRB-

D

-RRB-

using

a

FDR

procedure

The

labeled

matrix

was

presented

below

Note

that

the

matrix

shown

here

only

included

interregional

pathways

with

strong

correlations

due

to

the

conservative

FDR

threshold

-LRB-

Genovese

et

al.

-RRB-

used

to

in

this

study

The

sparse

matrix

was

composed

of

connected

nodes

and

disconnected

nodes

including

several

unimodal

-LRB-

bilateral

cuneus

bilateral

middle

occipital

gyrus

and

left

inferior

occipital

gyrus

-RRB-

paralimbic

and

limbic

regions

-LRB-

bilateral

uncus

bilateral

insula

and

right

cingulate

region

-RRB-

R

right

L

left

For

the

abbreviations

of

the

regions

see

Supplementary

Table

-LRB-

F

-RRB-

The

thresholded

connection

matrix

was

visualized

in

anatomical

space

For

details

see

Materials

and

Methods

Cerebral

Cortex

October

V

N

Figure

Short

and

long-range

anatomical

connections

in

the

anatomical

space

-LRB-

A

-RRB-

One

hundred

and

four

undirected

edges

-LRB-

of

the

possible

connections

among

regions

-RRB-

representing

the

significant

connections

were

shown

in

a

sagittal

view

of

the

brain

Edges

were

classified

into

-LRB-

B

-RRB-

short-range

connections

-LRB-

D

mm

red

-RRB-

and

-LRB-

C

-RRB-

longrange

connections

-LRB-

D

-LSB-

mm

blue

-RRB-

The

locations

of

the

nodes

indicated

the

y

and

z

coordinates

of

the

regional

centroids

in

Talairach

space

Figure

Small-world

properties

of

the

anatomical

networks

as

a

function

of

correlation

threshold

-LRB-

A

-RRB-

The

mean

degree

of

human

brain

anatomical

networks

decreases

as

the

correlation

threshold

increases

Small-world

properties

are

not

estimable

when

the

mean

degree

of

anatomical

network

obtained

under

the

correlation

threshold

Rmax

is

less

than

log

-LRB-

N

-RRB-

-LRB-

Watts

and

Strogatz

Achard

et

al.

-RRB-

-LRB-

B

-RRB-

The

largest

component

size

decreases

as

the

correlation

threshold

increases

-LRB-

C

-RRB-

The

connectedness

tends

to

decrease

as

the

correlation

threshold

where

the

connectedness

is

assessed

by

the

reachability

matrix

recording

if

at

least

one

path

exists

between

all

pairs

of

nodes

-LRB-

Sporns

et

al.

-RRB-

-LRB-

D

-RRB-

The

clustering

coefficient

increases

as

the

correlation

threshold

increases

-LRB-

E

-RRB-

The

path

length

has

relatively

small

changes

as

the

correlation

threshold

increases

-LRB-

F

-RRB-

The

small

worldness

tends

to

increase

as

the

correlation

threshold

increases

The

black

arrows

indicate

the

values

of

small-world

properties

of

the

human

brain

anatomical

network

constructed

by

a

FDR

threshold

-LRB-

Achard

et

al.

-RRB-

To

elucidate

the

importance

of

these

hub

regions

for

the

brain

network

we

removed

the

hub

and

nonhub

regions

separately

and

compared

the

global

properties

of

the

resulting

networks

-LRB-

Fig.

-RRB-

Compared

with

the

nonhubs

the

elimination

of

the

hub

regions

only

resulted

in

slight

changes

in

the

largest

component

size

-LRB-

t

P

-RRB-

but

significant

decreases

in

the

clustering

coefficient

-LRB-

t

P

-RRB-

and

increases

in

the

characteristic

path

length

-LRB-

t

P

-RRB-

In

addition

we

also

found

that

when

individual

hub

node

was

removed

from

the

brain

network

the

characteristic

path

lengths

of

the

resulting

networks

were

real

larger

than

those

-LRB-

Lp

-RRB-

of

the

experimental

network

-LRB-

Table

-RRB-

Small-World

Anatomical

Networks

d

Discussion

This

is

the

first

study

to

our

knowledge

to

demonstrate

the

large-scale

anatomical

connectivity

patterns

in

the

entire

human

cerebral

cortex

using

cortical

thickness

measurements

We

found

significant

short

and

long-range

anatomical

connections

-LRB-

cortical

thickness

correlations

-RRB-

in

both

intrahemispheric

and

interhemispheric

regions

More

importantly

we

showed

that

the

human

brain

anatomical

network

had

small-world

properties

with

cohesive

neighborhoods

and

short

path

length

between

regions

In

addition

we

also

demonstrated

that

both

the

anatomical

network

and

the

probability

of

finding

a

connection

between

regions

for

a

given

anatomical

distance

followed

an

exponentially

truncated

power-law

model

Taken

together

He

et

al.

we

concluded

that

our

results

provided

an

important

structural

description

for

the

network

of

anatomical

connections

in

the

human

brain

Figure

The

degree

distributions

of

human

brain

anatomical

networks

for

different

correlation

threshold

values

The

black

solid

lines

indicate

exponentially

truncated

power-law

fits

in

the

log

log

plot

of

the

cumulative

probability

degree

versus

the

degree

for

the

correlation

threshold

values

Here

a

cumulative

distribution

was

used

to

reduce

the

effects

of

noise

on

this

smaller

data

set

-LRB-

Strogatz

-RRB-

Upright

triangles

correlation

threshold

R

-LRB-

corresponding

to

P

value

of

corrected

by

FDR

-RRB-

mean

degree

estimated

exponent

a

and

cutoff

degree

kc

Plus

sign

correlation

threshold

R

mean

degree

estimated

exponent

a

and

cutoff

degree

kc

Squares

correlation

threshold

R

mean

degree

estimated

exponent

a

and

cutoff

degree

kc

Interpreting

Cortical

Thickness

Correlations

Human

neuroanatomy

is

less

well

developed

than

nonhuman

neuroanatomy

because

the

common

invasive

tracer

methods

can

not

be

applied

to

the

human

brain

-LRB-

Crick

and

Jones

-RRB-

Thus

the

patterns

of

anatomical

connections

in

the

human

brain

remain

unclear

Recent

noninvasive

diffusion

MRI

techniques

have

provided

a

promising

experimental

route

toward

revealing

the

connectivity

patterns

in

vivo

in

human

but

there

continues

to

be

some

limitations

in

data

acquisition

and

processing

approaches

such

as

the

issues

of

crossing

or

intersecting

fibers

-LRB-

Dougherty

et

al.

Tuch

et

al.

-RRB-

Here

we

proposed

a

new

avenue

of

research

to

explore

the

patterns

of

anatomical

connectivity

in

the

human

brain

A

prominent

difference

between

the

current

analysis

and

previous

studies

on

the

human

anatomical

substrates

is

that

in

the

current

study

areas

are

considered

anatomically

connected

if

they

show

statistically

significant

associations

in

cortical

thickness

Although

the

exact

biological

nature

of

the

cortical

thickness

correlations

is

still

unknown

it

has

been

argued

that

the

covariation

of

the

morphological

features

-LRB-

tissue

volume

or

concentration

-RRB-

in

related

cortical

regions

may

be

resulted

from

the

mutually

trophic

influences

-LRB-

Ferrer

et

al.

-RRB-

the

contribution

of

heredity

-LRB-

Suddath

et

al.

Steinmetz

et

al.

Thompson

et

al.

-RRB-

or

common

experience-related

plasticity

-LRB-

Maguire

et

al.

Draganski

et

al.

Mechelli

et

al.

-RRB-

Recently

studies

have

also

indicated

that

these

intercorrelated

regions

may

be

a

part

of

functional

neuroanatomically

interconnected

systems

-LRB-

Andrews

et

al.

Wright

et

al.

Mechelli

et

al.

Mitelman

et

al.

-RRB-

For

instance

Andrews

et

al.

-LRB-

-RRB-

observed

that

Figure

The

topology

of

human

brain

anatomical

network

representing

significant

cortical

thickness

correlations

Regions

are

represented

as

nodes

and

connections

are

represented

as

edges

that

link

the

nodes

Hubs

regions

are

colored

in

red

and

nonhub

regions

are

colored

in

green

Black

lines

represent

long-range

connections

-LRB-

D

-LSB-

mm

-RRB-

and

gray

lines

represent

short-range

connections

The

geometric

distance

between

regions

on

the

drawing

space

approximates

the

shortest

path

length

between

them

The

network

was

visualized

with

the

Pajek

program

-LRB-

Batagelj

and

Mrvar

-RRB-

For

the

abbreviations

of

the

regions

see

Supplementary

Table

Cerebral

Cortex

October

V

N

Table

The

most

significant

interregional

cortical

thickness

correlations

-LRB-

corrected

P

-RRB-

and

their

approximate

associated

fiber

tracts

No

Region

A

Region

B

Class

Correlations

R

PoCG.R

MTG.R

SFG.R

MdFG.R

SPL.L

PrCG.R

MFG.R

LOFG.R

PHG.R

IFG.R

SFG.L

STG.R

PrCG.R

SFG.R

SFG.L

PoCG.L

MTG.L

MdFG.R

MdFG.L

PoCG.L

PrCG.L

MFG.L

LOFG.L

PHG.L

IFG.L

PrCG.L

MTG.R

SPL.R

SFG.L

MFG.L

SIH

SIH

IH

SIH

IH

SIH

SIH

SIH

SIH

SIH

IH

IH

IH

SIH

IH

Corrected

P

The

midbody

in

the

CCa

b

The

splenium

in

the

CCb

SLFc

e

The

genu

and

anterior

part

SLFc

e

The

midbody

in

the

CCa

b

The

genu

and

anterior

part

The

rostrum

in

the

CCd

The

splenium

in

the

CCb

The

genu

and

anterior

part

SLFc

e

U-fibersc

SLFc

e

The

genu

and

anterior

part

U-fibersc

D

-LRB-

mm

-RRB-

Approximate

associated

fiber

tracts

of

the

body

in

the

CCa

b

of

the

body

in

the

CCa

b

d

of

the

body

in

the

CCa

b

of

the

body

in

the

CCa

b

d

Note

List

of

the

pairs

of

connected

regions

-LRB-

descending

order

of

statistical

significance

-RRB-

with

the

most

significant

cortical

thickness

correlations

-LRB-

corrected

by

FDR

-RRB-

These

connections

were

classified

into

intrahemispheric

-LRB-

IH

-RRB-

and

symmetrically

interhemispheric

-LRB-

SIH

-RRB-

connections

R

and

P

denote

the

cortical

thickness

correlation

coefficients

between

regions

and

their

corresponding

significant

levels

D

denotes

the

Euclidean

distance

defined

as

the

distance

between

each

pair

of

regional

centroids

in

stereotaxic

space

A

pair

of

regions

with

D

-LSB-

mm

was

considered

long-range

connections

in

bold

and

short-range

connections

otherwise

Approximate

associated

fiber

tracts

for

each

cortical

thickness

correlation

observed

in

this

study

were

listed

the

rightmost

column

Note

that

the

cortical

thickness

correlations

among

regions

were

calculated

after

removing

the

effects

of

age

gender

age

gender

interaction

and

mean

overall

cortical

thickness

See

supplementary

Table

for

the

abbreviations

of

the

regions

a

Hofer

and

Frahm

b

Zarei

et

al.

c

Wakana

et

al.

d

Huang

et

al.

e

Makris

et

al.

Table

Small-world

properties

of

brain

networks

shown

in

the

present

study

and

previous

studies

Brain

networks

Human

anatomical

network

-LRB-

the

present

study

-RRB-

Human

functional

network

-LRB-

Achard

et

al.

-RRB-

Human

functional

network

-LRB-

Salvador

Suckling

Coleman

et

al.

-RRB-

Macaque

anatomical

network

-LRB-

Sporns

and

Zwi

-RRB-

Cat

anatomical

network

-LRB-

Sporns

and

Zwi

-RRB-

N

Cp

Lp

c

k

r

Note

N

Cp

and

Lp

denote

the

number

of

nodes

clustering

coefficient

and

mean

shortest

path

length

of

the

real

brain

networks

respectively

c

denotes

the

ratio

of

the

clustering

coefficient

between

the

brain

networks

and

the

constructed

random

networks

k

denotes

the

ratio

of

the

mean

shortest

path

length

between

the

brain

networks

and

the

constructed

random

networks

In

the

present

study

these

random

graphs

were

generated

using

a

random

rewiring

procedure

-LRB-

Maslov

and

Sneppen

-RRB-

r

is

a

ratio

of

c

and

k

measuring

the

small

worldness

of

a

network

For

the

details

see

Methods

and

Materials

Note

that

the

small-world

attributes

shown

in

the

present

investigation

are

much

closer

to

those

of

the

human

brain

functional

networks

compared

with

those

of

the

anatomical

brain

networks

of

macaque

and

cat

several

components

of

the

human

visual

system

-LRB-

i.e.

the

optic

tract

lateral

geniculate

nucleus

and

primary

visual

cortex

-RRB-

covary

in

volume

across

individuals

Significant

regional

gray

matter

volumetric

or

concentration

correlations

were

also

found

in

the

frontal-temporal

-LRB-

Woodruff

et

al.

Bullmore

et

al.

Mitelman

et

al.

-RRB-

and

frontal-parietal

systems

-LRB-

Wright

et

al.

Mechelli

et

al.

-RRB-

One

vital

support

for

the

present

study

is

that

Lerch

et

al.

-LRB-

-RRB-

demonstrated

a

striking

similarity

between

the

cortical

thickness

correlation

maps

of

Brodmann

Area

and

diffusion

tensor

maps

of

the

arcuate

fasciculus

-LRB-

a

language-related

neural

pathway

connecting

Broca

's

and

Wernicke

's

areas

-RRB-

suggesting

that

they

were

measuring

aspects

of

the

same

underlying

processes

All

these

processes

are

the

likely

driving

forces

behind

the

patterns

of

anatomical

connections

of

the

human

brain

herein

Cortical

Thickness

Correlations

and

Neuroanatomical

Pathway

In

this

study

we

detected

pairs

of

regions

showing

significant

correlations

in

cortical

thickness

A

question

of

Small-World

Anatomical

Networks

d

interest

is

whether

the

regions

found

to

be

associated

in

the

present

investigation

are

also

related

to

the

neuroanatomical

pathway

of

the

human

brain

To

address

this

issue

we

matched

the

most

significant

-LRB-

corrected

P

-RRB-

connections

to

the

approximate

associated

anatomical

connections

obtained

from

previous

human

diffusion

imaging

studies

-LRB-

Table

-RRB-

Several

significant

correlations

were

present

in

homologous

regions

in

a

bilateral

and

symmetrical

fashion

this

finding

can

be

explained

by

the

associations

between

these

regions

through

the

corpus

callosum

-LRB-

CC

-RRB-

a

crucial

white

matter

structure

providing

interhemispheric

communications

between

both

hemispheres

of

the

brain

Indeed

it

has

been

suggested

that

the

parcellation

of

the

CC

in

vivo

into

several

major

subdivisions

such

as

the

genu

the

body

and

the

splenium

is

based

on

the

transit

of

interhemispheric

pathways

connecting

homologous

brain

areas

-LRB-

Huang

et

al.

Hofer

and

Frahm

Zarei

et

al.

-RRB-

Thus

tracts

connecting

to

prefrontal

cortex

occupy

the

genu

and

anterior

part

of

the

body

of

the

CC

Moreover

connections

of

the

central

brain

regions

such

as

the

primary

motor

and

sensorymotor

cortex

are

located

within

the

midbody

He

et

al.

Table

Regions

of

the

human

brain

anatomical

network

and

their

statistical

properties

Regions

PrCG

SFG

SPL

MTG

PoCG

MFG

IFG

PHG

SOG

LOTG

MOTG

MdFG

STG

OP

ANG

PCU

CING

CUN

MOFG

SMG

ITG

LING

LOFG

IOG.R

Class

Primary

Association

Association

Association

Primary

Association

Association

Paralimbic

Association

Association

Association

Association

Association

Primary

Association

Association

Paralimbic

Association

Paralimbic

Association

Association

Association

Paralimbic

Association

Li

ki

Ci

p

p

Note

The

hub

regions

-LRB-

in

bold

-RRB-

in

the

anatomical

network

of

the

human

brain

were

identified

using

a

regionally

shortest

path

length

Li

and

they

were

listed

in

an

ascending

order

of

Li

These

regions

were

classified

as

Primary

Associations

and

Paralimibic

as

described

by

Achard

et

al.

-LRB-

-RRB-

ki

and

Ci

denote

the

degree

and

clustering

coefficient

of

each

region

and

denote

the

largest

p

p

component

size

clustering

coefficient

and

characteristic

path

length

of

the

resulting

network

when

region

i

was

individually

eliminated

from

the

brain

network

Note

that

when

the

hub

nodes

were

real

removed

from

the

brain

network

the

path

length

of

the

resulting

network

is

larger

than

the

path

length

Lp

-LRB-

-RRB-

of

the

experimental

network

For

the

abbreviations

of

the

regions

see

p

Supplementary

Table

of

the

CC

the

interhemispheric

connections

of

the

parietal

cortex

are

located

within

the

posterior

part

of

the

body

and

splenium

Finally

connections

of

the

temporal

and

occipital

cortex

transit

most

exclusively

through

the

splenium

of

the

CC

These

results

from

diffusion

imaging

studies

provide

an

important

support

for

our

findings

of

symmetrically

interhemispheric

correlations

in

cortical

thickness

In

addition

to

the

interhemispheric

connections

we

also

observed

significant

intrahemispheric

connections

between

SFG

MdFG

SFG

PrCG

SPL

PrCG

and

SPL

PoCG

-LRB-

Table

-RRB-

that

are

all

associated

with

the

superior

longitudinal

fascicle

-LRB-

SLF

-RRB-

linking

the

caudodorsal

prefrontal

cortex

with

the

premotor

-LRB-

PrCG

-RRB-

supplementary

motor

-LRB-

MdFG

-RRB-

and

superior

parietal

regions

-LRB-

SPL

-RRB-

-LRB-

Wakana

et

al.

Makris

et

al.

-RRB-

All

those

areas

and

the

network

they

form

via

the

SLF

are

involved

in

the

control

of

reaching

and

more

generally

movement

in

space

-LRB-

Mountcastle

et

al.

Lacquaniti

et

al.

-RRB-

The

connections

between

adjacent

areas

STG

MTG

and

SFG

MFG

-LRB-

Table

-RRB-

are

examples

of

short

association

fibers

-LRB-

e.g.

U-fibers

-RRB-

that

provide

the

means

of

interaction

for

those

adjacent

areas

participating

in

common

computations

language

processing

-LRB-

STG

MTG

-RRB-

and

higherorder

cognitive

control

-LRB-

SFG

MFG

-RRB-

-LRB-

Wakana

et

al.

Petrides

-RRB-

Additionally

in

this

study

we

also

observed

significant

cortical

thickness

correlations

among

the

IFG

STG

and

SMG

regions

-LRB-

Fig.

-RRB-

which

were

consistent

with

previous

cortical

thickness

correlation

study

-LRB-

Lerch

et

al.

-RRB-

and

fiber

tracking

-LRB-

arcuate

fasciculus

-RRB-

study

-LRB-

Parker

et

al.

-RRB-

Taken

together

these

significant

cortical

thickness

correlations

observed

in

the

present

study

are

related

to

the

major

fibers

tracts

-LRB-

CC

and

SLF

-RRB-

or

short

association

fibers

-LRB-

U-fibers

-RRB-

One

could

therefore

speculate

that

the

morphometry-based

corticocortical

correlates

provide

approximate

reflection

on

the

true

anatomical

connections

among

neuronal

elements

A

detailed

investigation

on

the

cortical

thickness

correlations

and

their

Figure

The

comparison

of

the

impacts

of

hub

and

nonhub

regions

on

network

properties

-LRB-

A

-RRB-

The

elimination

of

the

hubs

did

not

significantly

affect

the

largest

component

size

but

-LRB-

B

-RRB-

significantly

decreased

the

clustering

coefficient

and

-LRB-

C

-RRB-

increased

the

path

length

of

the

resulting

network

in

comparison

with

the

elimination

of

the

nonhub

nodes

For

the

details

of

the

hubs

in

the

brain

network

and

their

statistical

properties

see

Table

corresponding

anatomical

connections

in

the

human

brain

will

be

an

important

topic

for

future

studies

In

this

study

we

also

observed

differences

in

connectivity

patterns

in

the

left

and

right

hemispheric

regions

such

as

the

medial

and

lateral

orbital

frontal

gyrus

AG

and

lingual

gyrus

-LRB-

Fig.

-RRB-

Previous

studies

have

reported

structural

and

functional

asymmetries

in

several

regions

of

human

cortex

including

frontal

temporal

and

occipital

regions

-LRB-

for

a

review

see

Toga

and

Thompson

-RRB-

Furthermore

Mechelli

et

al.

-LRB-

-RRB-

have

also

demonstrated

interregional

asymmetric

patterns

of

associations

in

gray

matter

concentration

providing

further

support

for

our

finding

of

connection

patterns

differences

in

hemispheric

regions

In

future

it

would

be

interesting

to

examine

the

asymmetric

cortical

thickness

associations

in

details

using

Cerebral

Cortex

October

V

N

the

seed

regions

of

interest

methods

described

by

Mechelli

et

al.

-LRB-

-RRB-

Anatomical

Connections

and

Anatomical

Distance

Using

cortical

thickness

measurements

in

the

present

study

we

found

many

short-range

connections

as

well

as

some

longrange

connections

-LRB-

Figs.

and

-RRB-

Several

recent

functional

connectivity

studies

using

fMRI

have

also

demonstrated

the

local

and

long-range

connections

in

the

human

brain

-LRB-

Salvador

Suckling

Coleman

et

al.

Salvador

Suckling

Schwarzbauer

et

al.

Achard

et

al.

-RRB-

that

are

consistent

with

our

results

As

noted

in

previous

section

short-range/local

connections

may

be

associated

with

the

short

fibers

-LRB-

arcuate

or

U-fibers

-RRB-

that

constitute

the

local

circuitry

but

long-range

connections

may

be

associated

with

the

commissural

fibers

-LRB-

right-left

hemispheric

connections

-RRB-

and

intrahemispheric

association

fibers

-LRB-

e.g.

SLF

-RRB-

-LRB-

Wakana

et

al.

-RRB-

In

this

study

we

also

demonstrated

the

dependencies

of

anatomical

connectivity

on

anatomical

distance

characterized

as

a

power-law

form

with

an

exponential

cutoff

implying

that

the

probability

of

finding

a

connection

is

distributed

by

a

scale

regimen

followed

by

an

exponential

decay

in

probability

of

connections

with

an

anatomical

distance

greater

than

a

cutoff

value

-LRB-

mm

-RRB-

Such

spatial

constraints

on

connections

are

biologically

realistic

and

have

been

acknowledged

in

many

biological

systems

It

has

been

suggested

that

the

likelihood

of

long-range

connections

among

macaque

cortical

regions

decreases

with

distance

partly

because

the

concentration

of

diffusible

signaling

and

growth

factors

decays

with

distance

-LRB-

Sporns

et

al.

-RRB-

Recently

the

computational

models

of

cortical

development

based

on

this

physical

principle

have

been

proposed

to

understand

the

relationship

of

cortical

morphology

and

the

connectivity

of

normal

brains

-LRB-

Hilgetag

and

Barbas

-RRB-

These

investigations

provide

important

support

for

our

findings

of

the

dependencies

of

anatomical

connectivity

on

anatomical

distance

in

the

human

brain

It

is

also

noted

that

although

the

number

of

long-range

connections

is

limited

in

the

brain

networks

they

might

constitute

shortcuts

to

ensure

short

mean

path

lengths

of

the

whole

networks

-LRB-

Kaiser

and

Hilgetag

-RRB-

Small-World

Anatomical

Networks

of

the

Human

Brain

The

coexistence

of

many

short-range

anatomical

connections

as

well

as

some

long-range

connections

raised

the

possibility

that

the

anatomical

network

of

the

human

brain

might

have

smallworld

properties

Because

it

was

introduced

by

Watts

and

Strogatz

-LRB-

-RRB-

the

small-world

model

has

made

a

tremendous

impact

on

the

studies

of

numerous

complex

networks

from

social

economic

to

biological

networks

-LRB-

for

a

review

see

Strogatz

-RRB-

The

model

characterizes

the

architecture

of

the

networks

with

well-connected

local

neighborhoods

and

short

mean

distance

between

nodes

Recent

studies

have

suggested

that

the

human

brain

functional

networks

constructed

from

fMRI

-LRB-

Eguiluz

et

al.

Salvador

Suckling

Coleman

et

al.

Achard

et

al.

-RRB-

EEG

-LRB-

Micheloyannis

et

al.

Stam

et

al.

-RRB-

and

MEG

-LRB-

Stam

-RRB-

data

along

with

nonhuman

cortical

networks

derived

from

anatomical

tract-tracing

method

-LRB-

Hilgetag

et

al.

Stephan

et

al.

Sporns

and

Zwi

-RRB-

have

small-world

properties

Our

results

demonstrate

for

the

first

time

that

such

properties

are

also

the

characteristics

of

large-scale

anatomical

networks

of

the

human

cerebral

cortex

-LRB-

Fig.

-RRB-

The

main

features

for

the

small-world

Small-World

Anatomical

Networks

d

topology

high

clustering

coefficient

and

short

path

length

indicate

the

local

clustering

or

cliquishness

of

the

connectivity

network

and

the

small

number

of

connections

between

any

pair

of

regions

Previous

optimal

study

using

computational

simulation

-LRB-

Sporns

et

al.

-RRB-

has

demonstrated

the

emergence

of

small-world

topologies

when

networks

are

evolved

for

high

complexity

-LRB-

defined

as

the

coexpression

of

local

specialization

and

global

integration

Tononi

et

al.

Sporns

and

Tononi

-RRB-

Thus

our

finding

of

small-world

attributes

in

the

cortical

thickness

networks

reflects

a

near-optimal

organizational

pattern

for

the

evolution

of

human

brain

structures

Furthermore

we

proposed

that

the

optimal

design

of

the

human

brain

anatomical

network

might

have

important

implications

for

understanding

how

functional

brain

states

emerge

from

their

structural

underpinnings

It

has

been

suggested

that

the

structure

of

the

cerebral

cortex

is

intimately

associated

with

its

function

as

many

other

biological

systems

-LRB-

Sporns

and

Zwi

-RRB-

High

clustering

assures

the

modularized

information

processing

which

are

functionally

segregated

from

one

to

another

Short

paths

assure

effective

interactions

or

rapid

transfer

of

information

between

regions

which

are

essential

for

functional

integration

The

coexistence

of

functional

segregation

and

functional

integration

guarantees

the

effective

integration

of

multiple

segregated

sources

of

information

-LRB-

Tononi

et

al.

Sporns

and

Zwi

Sporns

et

al.

-RRB-

Our

results

of

small-world

properties

reported

here

might

thus

provide

the

underlying

structural

substrates

of

such

functional

coexistence

in

the

human

brain

To

further

address

the

associations

between

structural

and

functional

networks

of

the

human

brain

we

compared

our

results

with

the

values

of

small-world

properties

from

previous

brain

network

studies

-LRB-

Sporns

and

Zwi

Salvador

Suckling

Coleman

et

al.

Achard

et

al.

-RRB-

in

Table

Our

measurements

of

small-world

properties

in

the

human

cortical

anatomical

network

are

c

k

and

r

Salvador

Suckling

Coleman

et

al.

-LRB-

-RRB-

and

Achard

et

al.

-LRB-

-RRB-

reported

the

values

in

human

brain

functional

networks

c

k

r

and

c

k

r

respectively

whereas

Sporns

and

Zwi

-LRB-

-RRB-

reported

the

values

in

nonhuman

cortical

anatomical

networks

c

k

and

r

for

macaque

whole

cortex

and

c

k

and

r

for

cat

whole

cortex

-LRB-

Table

-RRB-

As

expected

the

values

of

small

worldness

in

this

study

are

in

closer

proximate

to

those

of

the

human

brain

functional

networks

than

macaque

and

cat

anatomical

networks

Additionally

we

real

also

found

our

absolute

values

for

Cp

and

Lp

-LRB-

Cp

and

real

Lp

-RRB-

had

a

good

match

with

Salvador

Suckling

Coleman

real

real

et

al.

's

-LRB-

-RRB-

study

-LRB-

Cp

and

Lp

-RRB-

However

it

should

be

noted

that

the

present

study

and

previous

functional

imaging

studies

used

different

subject

populations

and

image

analysis

methods

such

as

different

regional

parcellation

schemes

and

correlation

threshold

selections

These

factors

might

have

an

impact

on

the

construction

of

the

anatomical

functional

connection

matrix

that

could

eventually

influence

the

comparability

of

these

results

Thus

these

different

groups

comparisons

in

the

values

of

small-world

properties

should

be

made

cautiously

A

systematic

exploration

for

the

network

properties

of

the

human

brain

using

anatomical

and

functional

data

obtained

within

the

same

subjects

could

offer

a

more

practicable

strategy

for

mapping

the

associations

of

structural

and

functional

properties

Overall

combined

the

previous

results

and

the

current

findings

we

concluded

that

small-world

He

et

al.

properties

might

be

a

general

principle

of

structural

and

functional

organization

of

complex

brain

networks

The

Human

Brain

Anatomical

Network

is

not

Scale

Free

In

addition

to

the

small-world

properties

another

important

finding

of

this

study

is

that

the

large-scale

anatomical

network

of

the

human

brain

has

an

exponentially

truncated

power-law

degree

distribution

as

opposed

to

a

scale-free

distribution

-LRB-

Fig.

-RRB-

This

result

is

largely

compatible

with

previous

studies

in

human

brain

functional

networks

-LRB-

Achard

et

al.

-RRB-

and

nonhuman

cortical

anatomical

networks

-LRB-

Sporns

and

Zwi

-RRB-

This

truncated

power-law

distribution

indicates

that

the

human

brain

network

has

some

core

regions

but

prevents

the

appearance

of

the

huge

hubs

with

very

many

connections

Compared

with

a

scale-free

network

such

a

network

structure

shown

here

is

more

resilient

to

targeted

attacks

but

equally

resilient

to

random

errors

-LRB-

Albert

et

al.

Achard

et

al.

-RRB-

Although

the

biological

causes

underlying

this

network

topology

remain

unclear

physical

constraints

on

the

number

of

afferent

connections

a

neuron

can

support

render

the

exponentially

truncated

power-law

possible

mechanism

in

neuronal

development

-LRB-

Sporns

and

Zwi

-RRB-

Our

results

of

the

dependencies

of

interregional

anatomical

connections

on

the

anatomical

distance

-LRB-

Euclidean

distance

-RRB-

-LRB-

Fig.

-RRB-

provide

further

support

for

this

view

In

the

present

study

we

also

identified

several

hub

regions

in

the

anatomical

network

of

the

human

brain

-LRB-

Fig.

Table

-RRB-

most

of

which

are

the

heteromodal

or

unimodal

association

cortex

receiving

convergent

inputs

from

multiple

cortical

regions

Many

hubs

-LRB-

e.g.

SFG

SPL

MTG

MFG

IFG

and

SOG

-RRB-

observed

here

are

in

accordance

with

the

findings

in

the

functional

brain

network

by

Achard

et

al.

-LRB-

-RRB-

It

has

been

argued

that

hubs

in

the

brain

networks

are

regions

with

multimodal

or

integrative

function

and

their

damages

can

remarkably

affect

the

stability

and

efficiency

of

the

network

-LRB-

Sporns

and

Zwi

Achard

et

al.

-RRB-

In

the

brain

anatomical

network

while

comparing

with

the

nonhub

regions

the

elimination

of

the

hub

regions

leads

to

significant

decreases

of

the

clustering

coefficients

and

increases

of

the

path

lengths

-LRB-

Fig.

-RRB-

though

the

largest

component

size

of

the

resulting

networks

remains

significantly

unaffected

suggesting

that

the

hubs

might

be

of

particular

importance

for

not

only

the

existence

of

highly

local

clustering

but

also

the

overall

routing

efficiency

of

the

brain

network

-LRB-

the

small-world

behavior

-RRB-

We

therefore

suspected

that

the

patients

-LRB-

e.g.

schizophrenia

and

Alzheimer

's

disease

-RRB-

with

the

known

structural

and

functional

abnormality

of

the

association

cortex

might

have

altered

smallworld

properties

in

the

anatomical

networks

which

could

be

examined

in

the

future

investigations

Methodological

Issues

Some

methodological

issues

of

the

present

study

need

to

be

addressed

First

we

used

fully

automatic

and

operator-independent

procedures

to

measure

the

cortical

thickness

from

MRI

The

concern

is

that

the

cortical

thickness

measurement

results

could

be

potentially

influenced

by

the

scanning

protocols

-LRB-

Han

et

al.

-RRB-

and

image

processing

methods

implemented

-LRB-

Lerch

and

Evans

-RRB-

Second

we

applied

a

conservative

FDR

threshold

-LRB-

Genovese

et

al.

-RRB-

to

construct

the

anatomical

connection

matrix

of

the

human

brain

which

allowed

us

to

examine

only

those

pathways

with

strong

correlations

Currently

it

is

difficult

to

determine

a

definitive

threshold

in

the

construction

of

complex

brain

networks

based

upon

correlation

methods

such

as

the

human

brain

functional

network

derived

from

fMRI

-LRB-

Salvador

Suckling

Coleman

et

al.

Achard

et

al.

-RRB-

or

EEG

data

-LRB-

Micheloyannis

et

al.

Stam

et

al.

-RRB-

Future

investigations

in

the

continuous

weighted

brain

networks

could

be

helpful

to

avoid

the

thresholding

issues

Here

we

found

that

our

selected

threshold

caused

a

relatively

low

sparsity

-LRB-

-RRB-

in

comparison

with

the

sparsity

of

the

anatomical

connectivity

matrices

of

macaque

-LSB-

-LRB-

-RRB-

-RSB-

and

cat

-LSB-

-LRB-

-RRB-

-RSB-

-LRB-

Sporns

and

Zwi

-RRB-

However

it

is

difficult

to

compare

the

sparsity

of

this

matrix

with

the

anatomical

matrices

of

macaque

and

cat

because

they

were

established

using

different

methods

The

anatomical

matrices

in

macaque

and

cat

were

derived

from

tract-tracing

data

but

our

matrix

was

obtained

from

the

thresholded

cortical

thickness

correlations

Despite

this

we

still

examined

the

properties

of

our

cortical

thickness

network

with

a

sparsity

which

corresponds

to

the

sparsity

in

the

macaque

anatomical

network

-LRB-

Sporns

and

Zwi

-RRB-

and

found

c

and

k

Though

at

which

corresponds

to

the

sparsity

in

the

cat

anatomical

network

-LRB-

Sporns

and

Zwi

-RRB-

our

network

had

a

reduced

small-world

properties

c

and

k

The

discrepancies

could

be

due

to

the

fact

that

there

is

a

higher

structural

similarity

in

the

cerebral

cortex

between

the

human

and

macaque

than

the

human

and

cat

Third

a

prior

volumetric

template

was

employed

to

automatically

parcellate

the

entire

cerebral

cortex

into

different

regions

-LRB-

Collins

et

al.

-RRB-

Such

an

atlas-based

parcellation

allows

us

to

characterize

the

large-scale

connectivity

pattern

for

the

human

brain

networks

however

one

of

the

problems

is

that

there

is

interindividual

variability

in

the

anatomical

boundaries

of

regions

Currently

there

is

no

single

acceptable

strategy

for

the

cortical

parcellation

the

validity

of

the

parcellation

thus

mostly

depends

on

the

suitability

of

the

applied

atlas

Nonetheless

several

recent

studies

have

investigated

the

functional

or

anatomical

connectivity

pattern

in

the

human

brain

using

such

an

atlas-based

parcellation

strategy

-LRB-

Wright

et

al.

Salvador

Suckling

Coleman

et

al.

Achard

et

al.

-RRB-

In

future

studies

it

might

be

more

meaningful

to

parcellate

the

cerebral

cortex

based

on

a

finer

myeloarchitectonic

feature

In

addition

it

is

also

helpful

to

explore

the

impact

of

different

parcellation

schemes

on

the

network

architectures

Fourth

we

described

a

large-scale

structural

organization

for

human

brain

anatomical

networks

using

the

cortical

thickness

measurements

Currently

such

a

macroscale

description

is

more

practical

to

reveal

the

anatomical

connectivity

patterns

of

the

human

brain

than

microscale

and

mesoscale

descriptions

because

of

its

relatively

low

computational

load

and

simple

definition

in

neuronal

elements

-LRB-

regions

-RRB-

and

connections

Further

investigations

could

involve

the

characterization

of

connection

patterns

among

neuronal

elements

such

as

cortical

vertices

and

assess

the

dependencies

of

the

network

architectures

on

spatial

scales

Finally

we

used

cortical

thickness

measurements

as

a

morphological

feature

to

construct

the

anatomical

connection

matrix

of

the

human

brain

and

further

described

its

anatomical

and

statistical

properties

The

morphological

features

can

also

include

surface

area

tissue

volume

tissue

density

and

others

Our

recent

study

-LRB-

in

preparation

-RRB-

demonstrates

that

the

gray

matter

volume

networks

in

the

human

brain

also

have

the

smallworld

properties

which

are

consistent

with

the

present

study

It

will

be

interesting

to

explore

more

detailed

patterns

using

these

morphological

features

Cerebral

Cortex

October

V

N

Conclusion

To

our

knowledge

this

paper

provided

the

first

evidence

of

small-world

properties

and

degree

distribution

in

large-scale

anatomical

networks

in

the

human

brain

by

means

of

cortical

thickness

measurements

from

MRI

These

findings

are

largely

compatible

with

previous

human

brain

functional

networks

studies

thus

significantly

enhancing

our

understanding

of

how

brain

functional

states

emerge

from

their

underlying

structural

substrates

Our

results

indicate

that

the

morphometry-based

approach

we

use

here

may

be

useful

to

reveal

the

patterns

of

anatomical

connectivity

in

the

human

brain

which

opens

a

new

window

for

mechanistic

modeling

and

interpretation

of

human

brain

anatomical

networks

recently

sparked

as

the

human

connectome

-LRB-

Sporns

et

al.

-RRB-

Further

work

could

be

conducted

to

examine

whether

these

networks

properties

are

altered

during

normal

development

and

aging

as

well

as

under

specific

brain

disorders

Supplementary

Material

Supplementary

material

oxfordjournals.org

can

be

found

at

Notes

The

authors

would

like

to

thank

Dr

Pedro

Rosa

and

Jurgen

Germann

for

their

valuable

comments

regarding

the

manuscript

This

work

was

supported

by

Human

Brain

Project

grant

-LRB-

ICBM

P.I.

Dr

John

Mazziotta

-RRB-

Canadian

Institutes

of

Health

Research

grant

and

the

Killam

Foundation

Yong

He

was

supported

by

a

Jeanne

Timmins

Costello

Fellowship

of

the

Montreal

Neurological

Institute

Conflict

of

Interest

declared

Address

correspondence

to

Dr

Alan

C.

Evans

McConnell

Brain

Imaging

Centre

Montreal

Neurological

Institute

University

Street

Montreal

QC

Canada

Email

alan.evans@mcgill.ca

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