Heritability

of

a

skeletal

biomarker

of

biological

aging

Changes

in

the

skeletal

system

which

include

age-related

bone

and

joint

remodeling

can

potentially

be

used

as

a

biomarker

of

biological

aging

The

aim

of

the

present

study

was

to

investigate

the

extent

and

mode

of

inheritance

of

skeletal

biomarker

of

biological

aging

osseographic

score

-LRB-

OSS

-RRB-

in

a

large

sample

of

ethnically

homogeneous

pedigrees

The

investigated

cohort

comprised

Chuvashian

families

and

included

men

aged

years

-LRB-

mean

-RRB-

and

women

aged

years

-LRB-

mean

-RRB-

The

TOSS

transformed

OSS

standardized

in

age

groups

for

each

sex

was

analyzed

as

a

BA

index

We

evaluated

familial

correlations

and

performed

segregation

analysis

Results

of

our

study

suggest

the

familial

aggregations

of

TOSS

variation

in

the

Chuvashian

pedigrees

In

a

segregation

analysis

we

found

a

significant

major

gene

-LRB-

MG

-RRB-

effect

in

the

individual

's

TOSS

with

a

dominant

most

parsimonious

model

-LRB-

-RRB-

Genetic

factors

-LRB-

MG

genotypes

-RRB-

explained

of

the

residual

OSS

variance

after

age

adjustment

and

after

including

sex-genotype

interaction

they

explained

of

the

residual

variance

Results

of

our

study

also

indicated

that

the

inherited

difference

in

the

skeletal

aging

pattern

in

men

lies

mostly

in

the

rate

of

aging

but

in

women

in

the

age

of

the

onset

of

the

period

of

visible

skeletal

changes

Introduction

Biological

age

-LRB-

BA

-RRB-

estimates

the

functional

status

of

an

individual

in

reference

to

his

or

her

chronological

peers

on

the

basis

of

how

well

he

or

she

functions

in

comparison

with

others

of

the

same

chronological

age

-LRB-

Borkan

and

Norris

-RRB-

Changes

in

the

skeletal

system

which

include

age-related

bone

and

joint

remodeling

can

potentially

be

used

as

a

biomarker

of

BA

Skeletal

aging

measures

are

strongly

correlated

with

the

status

of

the

vital

health

systems

-LRB-

Gabriel

et

al.

Kiel

et

al.

Kadam

et

al.

Kalichman

et

al.

-RRB-

and

ultimately

with

survival

rates

-LRB-

Johansson

et

al.

Haara

et

al.

-RRB-

The

rate

of

degenerative

changes

in

the

skeleton

may

reflect

an

individual

's

biological

resistance

immunity

functional

or

health

status

in

reference

to

his

or

her

chronological

age

Therefore

age-related

skeletal

changes

can

possibly

be

used

as

an

index

of

BA

Roentgenography

is

one

of

the

common

methods

used

to

assess

health

status

and

age-related

changes

in

bones

and

joints

-LRB-

Plato

Plato

et

al.

-RRB-

Previously

Kobyliansky

et

al.

-LRB-

-RRB-

reported

an

osseographic

scoring

-LRB-

OSS

-RRB-

system

that

uses

hand

radiographs

to

assess

skeletal

aging

OSS

is

a

synthetic

measure

for

assessing

skeletal

aging

based

on

radiographic

features

of

the

hand

combining

both

osteoporotic

and

osteoarthritic

changes

of

hand

bones

and

joints

This

system

was

originally

suggested

by

Pavlovsky

-LRB-

-RRB-

and

has

been

used

in

BA

evaluations

in

population

studies

-LRB-

Kobyliansky

et

al.

Livshits

et

al.

Pavlovsky

and

Kobyliansky

-RRB-

Importantly

OSS

has

been

shown

to

highly

correlate

with

chronological

age

in

adults

of

different

ethnic

groups

-LRB-

Karasik

et

al.

Kalichman

et

al.

-RRB-

Accumulating

research

shows

that

single

gene

changes

in

yeast

worms

and

rodents

can

significantly

alter

life

span

-LRB-

Kenyon

et

al.

Kaeberlein

et

al.

Cheng

et

al.

McBurney

et

al.

-RRB-

The

observation

that

the

first-degree

relatives

of

human

centenarians

are

both

disease

resistant

and

have

longer

than

average

life

spans

implies

a

genetic

component

to

human

longevity

-LRB-

Perls

et

al.

Atzmon

et

al.

-RRB-

Current

estimates

based

on

twin

studies

indicate

that

the

human

life

span

is

heritable

-LRB-

McGue

et

al.

Herskind

et

al.

Gudmundsson

et

al.

Perls

et

al.

-RRB-

Genetic

factors

may

also

significantly

contribute

to

interindividual

differences

in

BA

-LRB-

Karasik

et

al.

-RRB-

In

variance

component

genetic

analysis

performed

in

Karasik

's

study

-LRB-

-RRB-

genetic

factors

explained

of

the

total

variance

of

the

BA

index

based

on

OSS

measurements

The

aim

of

our

study

was

to

investigate

the

extent

and

mode

of

inheritance

of

a

skeletal

biomarker

of

biological

aging

-LRB-

OSS

-RRB-

in

a

large

sample

of

ethnically

homogeneous

pedigrees

Materials

and

methods

Sample

The

population

sampled

consisted

of

native

Chuvashians

residing

in

numerous

small

villages

in

the

Chuvashia

and

Bashkartostan

Autonomies

of

the

Russian

Federation

The

data

were

gathered

in

three

field

studies

during

August/September

of

-LRB-

individuals

-RRB-

May/June

of

-LRB-

individuals

-RRB-

and

September

-LRB-

individuals

-RRB-

by

investigators

from

the

Department

of

Anatomy

and

Anthropology

Sackler

Faculty

of

Medicine

Tel

Aviv

University

-LRB-

Israel

-RRB-

and

the

Institute

of

Anthropology

Moscow

University

-LRB-

Russia

-RRB-

The

expeditions

were

part

of

a

Chuvashia

Skeletal

Aging

Study

-LRB-

ChuSAS

-RRB-

project

whose

main

aim

was

to

investigate

the

different

aspects

of

skeletal

aging

within

the

Chuvashia

population

All

information

collected

and

measurements

taken

during

all

expeditions

were

done

by

the

same

team

of

investigators

The

investigated

cohort

comprised

families

and

included

men

aged

years

-LRB-

mean

-RRB-

and

women

aged

years

-LRB-

mean

-RRB-

The

Chuvashian

population

is

characterized

by

a

stable

family

structure

with

traditional

relationships

For

generations

the

Chuvashians

have

resided

under

the

same

environmental

conditions

and

have

not

been

exposed

to

an

outside

genetic

flow

-LRB-

El

chinova

et

al.

-RRB-

In

the

present

study

we

collected

data

from

residents

of

a

number

of

small

villages

-LRB-

with

a

predominant

Chuvashian

population

-RRB-

located

in

the

Volga

region

A

rural

population

is

more

homogeneous

than

urban

in

terms

of

ethnicity

occupation

and

physical

activity

The

study

participants

shared

similar

living

economic

and

professional

conditions

with

most

individuals

employed

in

agriculture

or

in

other

occupations

involving

physical

labor

Data

from

to

of

the

families

-LRB-

including

all

family

members

who

were

living

in

the

area

at

the

time

of

the

expedition

-RRB-

were

obtained

Since

almost

every

individual

was

related

to

one

of

the

families

we

were

able

to

collect

data

on

up

to

of

the

population

in

each

village

Data

obtained

from

self-completed

questionnaires

and

confirmed

during

the

interview

included

sex

age

age

at

menarche

age

at

menopause

and

occupation

Menopause

was

defined

as

months

without

menstruation

Age

at

last

menstruation

was

considered

as

menopausal

age

In

order

to

minimize

the

possible

recall

bias

the

investigators

excluded

from

the

analyses

all

women

who

had

doubts

about

their

age

at

menarche

The

anthropometrical

measurements

-LRB-

weight

stature

etc.

-RRB-

were

also

collected

using

standard

methodology

In

the

studied

sample

there

were

no

individuals

with

known

rheumatoid

or

psoriatic

arthritis

or

users

of

steroid

medication

Subjects

with

post-traumatic

hand

osteoarthritis

were

excluded

from

the

study

All

procedures

involved

were

consensual

The

subjects

signed

an

informed

consent

form

and

the

entire

project

was

approved

by

the

Helsinki

Ethics

Committee

of

Tel-Aviv

University

Additional

information

about

the

studied

population

can

be

found

in

our

previous

publications

sex

and

age-related

variations

of

the

somatotype

-LRB-

Kalichman

and

Kobyliansky

-RRB-

reproductive

indices

such

as

age

at

menarche

and

at

menopause

-LRB-

Kalichman

et

al.

a

-RRB-

and

sex

and

age-related

variations

of

OSS

-LRB-

Kalichman

et

al.

-RRB-

Hand

radiographs

Single

plain

radiograms

of

both

hands

were

taken

from

each

study

participant

in

the

postero-anterior

position

with

the

X-ray

source

located

cm

above

using

a

standard

radiographic

technique

as

described

in

detail

by

Livshits

et

al.

-LRB-

-RRB-

Hands

were

placed

on

the

same

film-containing

plate

to

avoid

any

film

or

development

variation

It

was

exposed

for

s

at

mA

without

intensifying

screens

at

kV

OSS

evaluation

An

individual

's

OSS

was

determined

by

the

occurrence

of

the

following

-LRB-

a

-RRB-

bone

proliferations

-LRB-

spurs

-RRB-

including

apiostoses

-LRB-

tufting

of

distal

phalangeal

tuberosity

-RRB-

osteophytes

enthesophytes

of

the

juxta-articular

area

and

at

midshaft

-LRB-

b

-RRB-

manifestations

of

bone

porosity

such

as

resorption

of

trabeculae

development

of

lacuna

-LRB-

juxta-articular

osteopenia

-RRB-

and

erosion

of

cortex

-LRB-

c

-RRB-

loci

of

osteosclerosis

defined

as

enostosis

and

sclerotic

nuclei

and

subchondral

sclerosis

and

-LRB-

d

-RRB-

non-traumatic

joint

deformities

defined

as

narrowing

of

joint

cavities

and

periarticular

bone

corrosion

-LRB-

Kobyliansky

et

al.

Pavlovsky

and

Kobyliansky

Karasik

et

al.

Kalichman

et

al.

-RRB-

Phalanges

of

the

to

fingers

of

the

left

hand

were

examined

The

first

finger

-LRB-

thumb

-RRB-

does

not

directly

project

in

a

standard

X-ray

and

was

therefore

not

utilized

The

presence

of

a

given

feature

but

not

its

level

of

development

was

documented

for

each

OSS

estimate

The

overall

number

of

those

skeletal

aging

features

was

used

as

an

OSS

Each

radiograph

was

read

by

an

experienced

skeletal

researcher

according

to

the

accepted

protocol

of

OSS

evaluation

Ten

X-rays

were

read

and

then

re-read

by

the

investigator

to

estimate

the

intra-observer

reliability

of

the

readings

All

discrepancies

were

reviewed

for

systematic

errors

This

exercise

continued

until

the

reliability

was

high

-LRB-

k

-RRB-

Afterwards

the

investigator

read

the

remaining

X-rays

still

blinded

to

patient

identifiers

Before

reading

each

batch

of

X-rays

one

re-read

X-rays

which

had

been

previously

read

to

calibrate

one

's

readings

to

a

standard

The

intra-observer

reliability

-LRB-

kappa

statistics

-RRB-

was

-LRB-

P

-RRB-

The

intraclass

correlation

for

the

OSS

was

-LRB-

P

-RRB-

OSS

reflects

amount

of

skeletal

changes

occurring

stochastically

during

the

life-span

and

therefore

it

is

characterized

by

strong

increase

of

trait

variance

with

age

-LRB-

Kalichman

et

al.

and

Fig.

-RRB-

It

is

reasonable

to

assume

that

not

the

deviation

of

OSS

from

the

age-group

mean

but

only

relative

rate

of

OSS

accumulation

with

age

can

be

inherited

Consequently

we

constructed

a

trait

using

the

standardization

in

age-sex

groups

to

equalize

the

means

and

variances

in

the

whole

age

range

for

both

sexes

The

resulting

trait

TOSS

-LRB-

transformed

OSS

-RRB-

was

further

analyzed

The

biological

meaning

of

this

trait

is

the

relative

position

of

individual

-LRB-

higher

or

lower

than

average

values

of

OSS

-RRB-

in

his/her

age-sex

group

expressed

in

the

units

of

SD

specific

for

each

group

This

accurately

fit

the

definition

of

BA

as

the

functional

status

of

an

individual

in

reference

to

his

or

her

chronological

peers

-LRB-

Borkan

and

Norris

-RRB-

Fig.

OSS

values

and

standard

deviations

-LRB-

SD

-RRB-

in

age

groups

of

years

for

men

and

women

Statistical

and

genetic

analysis

Prior

to

any

other

evaluations

the

descriptive

statistics

reflecting

the

basic

characteristics

of

the

studied

sample

were

computed

in

the

whole

sample

and

within

age

groups

of

years

At

the

first

stage

we

computed

familial

-LRB-

spouses

parent-offspring

and

sib-sib

-RRB-

correlations

between

the

corresponding

TOSS

levels

to

examine

the

potential

genetic

effect

on

the

skeletal

biomarker

of

BA

The

segregation

analysis

as

implemented

in

the

statistical

package

MAN

-LRB-

Malkin

and

Ginsburg

-RRB-

was

utilized

in

this

study

to

test

a

mode

of

inheritance

of

the

skeletal

biomarker

of

BA

TOSS

Only

individuals

older

than

were

included

in

the

analysis

since

the

high

prevalence

of

zero

OSS

values

in

younger

individuals

make

the

standardization

approach

unacceptable

More

precisely

in

two

age

groups

younger

than

years

the

distribution

of

TOSS

significantly

deviated

from

normal

-LRB-

for

frequencies

gave

P

-RRB-

whereas

in

all

older

age

groups

did

not

-LRB-

P

-RRB-

Only

pedigrees

having

at

least

one

measured

pair

of

relatives

were

included

in

the

analysis

The

mixed

model

of

inheritance

-LRB-

Morton

and

MacLean

Elston

Lalouel

Beaty

Ginsburg

and

Livshits

-RRB-

estimates

the

effects

of

a

potential

major

gene

and

possible

multifactorial

effects

and

is

described

in

detail

in

numerous

publications

including

the

aforementioned

The

parameters

that

had

been

estimated

in

the

general

model

are

defined

as

follows

p

the

population

frequency

of

allele

-LRB-

assuming

diallelic

gene

locus

-RRB-

μgs

the

average

genotypic

value

of

individuals

having

genotype

g

and

sex

s

-LRB-

g

and

corresponds

to

genotypes

and

respectively

-RRB-

the

trait

variance

in

individuals

having

the

same

major

gene

genotype

g

it

estimates

the

trait

variation

resulting

from

the

effect

of

all

possible

environmental

factors

and

potential

minor

genes

τg

the

transmission

probability

parameter

which

estimates

the

probability

that

a

parent

of

genotype

g

transmits

allele

to

the

next

generation

ρ

β

and

ε

are

partial

correlations

between

the

trait

's

residuals

adjusted

for

a

major

gene

effect

in

spouses

parents/offspring

and

the

siblings

respectively

A

transmission

probability

test

described

by

Ginsburg

and

Livshits

-LRB-

-RRB-

was

used

to

estimate

the

significance

of

the

major

gene

-LRB-

MG

-RRB-

effect

A

best-fitting

and

most

parsimonious

Mendelian

model

was

established

after

dropping

all

non-significant

parameters

Using

the

procedure

implemented

in

the

package

MAN

-LRB-

Malkin

and

Ginsburg

-RRB-

and

parameters

estimated

for

the

most

parsimonious

model

we

determined

the

most

likely

MG

genotype

combination

for

each

pedigree

We

divided

our

sample

into

groups

according

to

sex

and

the

determined

individual

genotype

of

putative

BA-related

MG

for

genotypes

having

distinguishable

genotypic

values

To

analyze

the

age

dependence

of

OSS

as

a

primary

-LRB-

directly

measured

-RRB-

BA-related

index

in

groups

of

potentially

different

inherited

BA

we

used

the

stochastic

model

described

in

detail

by

Kobyliansky

et

al.

-LRB-

-RRB-

We

estimated

for

each

group

the

following

aging

population

parameters

the

earliest

age

at

which

the

first

signs

of

OSS

can

be

found

q

the

individual

probability

of

revealing

the

first

signs

of

OSS

changes

per

chronological

time

unit

assuming

an

individual

's

age

and

B

the

coefficient

characterizing

the

rate

of

OSS

changes

per

time

unit

-LRB-

per

year

-RRB-

after

the

process

of

aging

has

started

Next

we

built

the

age-dependent

expectation

of

the

mean

OSS

level

for

each

group

according

to

sex

and

predicted

MG

genotype

Using

the

likelihood

ratio

test

we

compared

the

extent

of

stochastic

model

approximation

both

accounting

for

the

MG

genotype

group

and

without

it

Eventually

we

used

ANOVA

as

implemented

in

STATISTICA

-LRB-

StatSoft

-RRB-

to

test

the

differences

between

parameters

of

female

organism

development

such

as

age

at

menarche

and

age

at

menopause

in

MG

genotype

groups

Results

Figure

shows

the

OSS

mean

values

and

SD

in

age

groups

of

years

Up

to

age

men

have

higher

OSS

scores

than

women

After

age

OSS

in

women

was

higher

compared

with

men

and

the

sex

difference

in

the

OSS

scores

increases

up

to

the

end

of

the

age

range

The

OSS

variance

in

age

groups

increases

rapidly

up

to

age

Familial

correlations

of

TOSS

-LRB-

Table

-RRB-

showed

no

significant

correlation

for

spouses

but

parent-offspring

and

sibling

correlations

were

significant

This

indicates

the

existence

of

a

clear

familial

aggregation

of

TOSS

variation

in

the

Chuvashian

pedigrees

which

can

not

be

explained

by

pure

common

environmental

effects

We

investigated

the

nature

of

TOSS

inheritance

later

using

segregation

analysis

Because

of

the

method

by

which

TOSS

was

constructed

-LRB-

standardization

within

each

sex-age

group

-RRB-

in

the

segregation

model

the

sex

effects

were

not

significant

The

other

results

are

presented

in

Table

and

support

the

MG

hypothesis

regarding

trait

inheritance

The

most

parsimonious

Mendelian

model

was

dominant

The

recessive

allele

with

a

population

frequency

of

corresponded

to

relatively

slow

aging

For

the

most

parsimonious

Mendelian

model

total

proportion

of

TOSS

variance

explained

by

the

model

was

Using

this

model

we

predicted

the

most

likely

MG

genotype

combination

for

each

pedigree

included

in

the

analysis

Because

of

the

dominant

nature

of

the

most

parsimonious

model

we

divided

all

individuals

into

two

groups

with

potentially

different

genotypic

values

-LRB-

-RRB-

homozygous

on

allele

and

-LRB-

-RRB-

all

the

rest

Using

a

stochastic

model

of

aging

-LRB-

Kobyliansky

et

al.

-RRB-

we

constructed

the

model

of

age

dependence

of

directly

measured

OSS

for

a

whole

sample

and

for

each

predicted

genotype

group

separately

with

and

without

considering

the

effects

of

sex

Table

presents

the

parameters

of

four

resulting

models

and

a

comparison

between

them

According

to

the

likelihood

ratio

test

-LRB-

LRT

-RRB-

Model

which

included

only

the

effect

of

age

has

a

significantly

worse

extent

of

approximation

than

both

Model

which

included

the

effect

of

genotype-age

and

Model

which

included

the

effect

of

sex-age

The

extent

of

approximation

was

significantly

higher

for

the

effect

of

genotype-age

which

explained

of

the

residual

OSS

variance

after

only

adjustment

for

age

and

lower

for

the

effect

of

sex-age

-LRB-

-RRB-

Model

which

includes

all

age-sex-genotype

effects

showed

a

significantly

higher

extent

of

approximation

in

comparison

with

other

models

and

explained

of

the

residual

OSS

variance

after

adjustment

for

age

After

adjustment

for

age

and

sex

the

residual

parent-offspring

correlation

of

OSS

was

significant

but

became

non-significant

after

adjustment

for

the

sex-age-genotype

Table

correlations

of

TOSSRelativesRN

of

pairsPSpouses0.083330.15Parent-offspring0.127550

Sib

Table

analysis

for

TOSS

-LRB-

OSS

standardized

in

age

groups

of

years

for

each

sex

-RRB-

ParameterMain

modelsRestricted

modelsGeneralMendelianEqual

τ-sArbitrary

τ-sMendelian

most

parsimoniousEqual

μ1

ρ0

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

β0

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

ε0

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

Log

LH

χ2

NS

-LRB-

-RRB-

-LRB-

-RRB-

NS

-LRB-

-RRB-

NS

-LRB-

-RRB-

-LRB-

-RRB-

NS

P

P

Number

in

parentheses

in

the

χ2

row

specifies

a

comparative

columnConstraints

denotation

-LSB-

-RSB-

parameter

is

fixed

to

shown

value

parameter

is

constrained

to

be

equal

to

the

parameter

above

in

the

tableTable

of

stochastic

aging

models

estimated

for

OSS

data

without

grouping

-LRB-

-RRB-

and

grouped

according

to

predicted

genotype

-LRB-

-RRB-

sex

-LRB-

-RRB-

or

both

sex

and

predicted

genotype

-LRB-

-RRB-

or

Model

-LRB-

d.f.

-RRB-

Model

-LRB-

d.f.

-RRB-

Log

LH

Log

LH

χ2

-LRB-

-RRB-

Model

-LRB-

d.f.

-RRB-

Model

-LRB-

d.f.

-RRB-

Log

LH

Log

LH

χ2

-LRB-

-RRB-

χ2

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

genotype

corresponding

to

lower

values

of

TOSS

in

segregation

analysis

the

minimal

age

at

which

initial

bone

changes

occurred

in

a

group

q

the

group

probability

that

an

individual

will

first

develop

involutive

bone

change

after

age

B

the

group

rate

of

aging

-LRB-

bone

change

-RRB-

per

time

unit

TM

the

expected

mean

age

in

a

group

in

which

the

first

bone

change

occurred

number

in

parentheses

indicates

the

comparative

model

for

LRT

all

LRT

values

are

significant

with

P

Figure

shows

a

scatterplot

of

OSS-age

for

the

predicted

genotypes

in

both

sexes

and

the

corresponding

curves

of

age-dependent

OSS

expectation

given

by

the

stochastic

model

For

women

in

the

group

of

genotype

-LRB-

with

slow

skeletal

aging

-RRB-

the

age

at

menarche

was

significantly

higher

-LRB-

P

-RRB-

than

in

the

group

of

genotypes

or

the

group

mean

difference

was

year

The

difference

in

the

age

at

menopause

was

in

the

same

direction

but

not

significant

for

the

whole

sample

Note

that

our

sample

includes

women

strongly

influenced

by

difficult

life

conditions

during

World

War

II

In

these

women

the

variance

in

the

age

at

menopause

is

increased

in

comparison

with

the

normal

population

For

women

whose

year

of

birth

-LRB-

the

normal

part

of

the

population

-RRB-

the

age

at

menopause

was

higher

in

group

than

in

other

group

-LRB-

P

-RRB-

the

group

mean

difference

was

year

Fig.

values

for

predicted

genotype

groups

black

gray

or

To

compare

our

findings

with

results

of

other

authors

we

quantitatively

analyzed

the

similarity

of

differently

constructed

BA

indices

The

correlation

between

the

BA

index

proposed

by

Karasik

et

al.

-LRB-

-RRB-

and

TOSS

was

in

the

Chuvashian

population

The

correlations

between

the

BA

index

used

by

Livshits

et

al.

-LRB-

-RRB-

versus

the

BA

of

Karasik

et

al.

-LRB-

-RRB-

and

TOSS

were

estimated

as

and

correspondingly

Though

the

resemblance

of

the

indices

may

be

influenced

by

population

type

the

aforementioned

BA

indices

are

sufficiently

similar

Discussion

In

the

present

study

we

evaluated

the

extent

and

mode

of

inheritance

of

a

skeletal

biomarker

of

BA

We

constructed

this

biomarker

-LRB-

TOSS

-RRB-

to

be

maximally

fitted

according

to

the

BA

definition

it

reflects

the

intensity

of

an

individual

's

skeletal

changes

in

relation

to

its

coevals

of

the

same

sex

and

the

range

of

the

index

does

not

depend

on

the

age

cohort

We

previously

evaluated

the

association

between

OSS

as

an

index

of

BA

with

morbidity

in

a

general

Chuvasha

population

-LRB-

Kalichman

et

al.

-RRB-

Statistically

significant

association

was

found

in

the

present

study

between

age-adjusted

OSS

and

rheumatic

morbidity

Morbidities

such

as

ischemic

heart

disease

pulmonary

diseases

traumatic

brain

injuries

and

gynecological

diseases

also

showed

differences

between

mean

values

of

OSS

in

affected

vs.

non-affected

individuals

However

after

correction

for

multiple

testing

the

statistical

significance

was

insufficient

The

association

between

OSS

and

diabetes

mellitus

was

close

to

significant

-LRB-

P

-RRB-

and

we

surmise

that

with

a

larger

sample

of

diabetic

individuals

a

clear-cut

association

will

be

confirmed

It

is

well-established

that

genetic

factors

play

an

important

role

in

an

individual

's

BA

-LRB-

Karasik

et

al.

-RRB-

Our

finding

suggests

the

familial

aggregations

of

TOSS

variation

within

the

Chuvashian

pedigrees

The

evaluation

of

heritability

of

the

skeletal

biomarker

of

BA

in

segregation

analysis

suggested

the

existence

of

a

MG

effect

with

a

most

parsimonious

dominant

model

A

number

of

BA

indices

based

on

age-related

skeletal

changes

were

previously

proposed

and

analyzed

in

different

populations

Livshits

et

al.

-LRB-

-RRB-

analyzed

the

OSS

measurement

in

the

Turkmenian

population

They

used

the

age-adjusted

OSS

values

as

a

BA

index

This

index

showed

a

significant

familial

parent-offspring

correlation

of

which

is

approximately

the

same

as

for

TOSS

in

our

study

-LRB-

-RRB-

Nevertheless

in

their

segregation

analysis

of

the

age-adjusted

OSS

the

Mendelian

model

was

rejected

A

possible

reason

is

that

a

simple

age

adjustment

does

not

equalize

the

residual

variance

of

OSS

which

significantly

increases

with

age

As

a

result

parents

and

offspring

received

a

BA

index

with

different

amplitude

and

this

difference

probably

prevented

establishing

MG

inheritance

in

segregation

analysis

Other

phenotypes

of

BA

as

well

are

characterized

by

substantial

heritability

Thus

functional

age

-LRB-

other

term

for

BA

-RRB-

has

been

assessed

by

a

general

linear

regression

model

of

many

biomarkers

in

Minnesota

twins

-LRB-

years

old

-RRB-

A

subset

of

these

biomarkers

-LRB-

mostly

physiological

variables

-RRB-

identified

by

a

factor

analysis

had

heritability

of

-LRB-

Finkel

et

al.

-RRB-

Duggirala

et

al.

-LRB-

-RRB-

have

reported

that

BA

measured

according

to

Uttley

and

Crawford

-LRB-

-RRB-

had

a

substantial

genetic

component

-LRB-

heritability

ranging

from

in

one

Mennonite

geographical

subsample

to

in

the

other

-RRB-

Karasik

et

al.

-LRB-

-RRB-

studied

a

sample

that

included

members

of

pedigrees

from

the

Framingham

Heart

Study

the

log-transformation

was

used

to

reduce

the

growth

of

OSS

variance

with

age

A

special

BA

index

was

constructed

by

adjusting

the

individual

's

age

for

log-transformed

OSS

with

cubic

polynomial

The

log-transformation

automatically

excludes

from

the

analysis

all

individuals

with

zero

OSS

-LRB-

note

that

for

ages

the

zero

OSS

value

is

meaningful

and

denotes

a

low

BA

-RRB-

For

the

resulting

trait

the

genetic

variance

component

analysis

showed

that

sex

height

the

body

mass

index

and

in

women

menopausal

status

and

estrogen

use

jointly

explained

approximately

of

the

total

variance

of

BA

index

Genetic

factors

explained

an

additional

The

genome

search

for

this

BA

index

revealed

a

number

of

potential

chromosomal

regions

in

the

two-point

analysis

but

for

multipoint

only

the

region

on

chromosome

remained

significant

The

variance

component

analysis

used

by

Karasik

et

al.

-LRB-

-RRB-

a

priori

assumes

a

polygene

mode

of

inheritance

Our

segregation

analysis

results

confirm

the

findings

about

a

significant

genetic

effect

and

furthermore

suggest

the

existence

of

a

MG

effect

in

an

individual

's

TOSS

with

a

dominant

most

parsimonious

model

The

MG

hypotheses

may

be

to

some

extent

supported

by

the

fact

that

in

the

multipoint

variance

component

linkage

analysis

by

Karasik

et

al.

-LRB-

-RRB-

only

one

chromosomal

region

showed

a

significant

LOD

score

-LRB-

likelihood

ratio

greater

than

-RRB-

We

found

that

genetic

factors

-LRB-

MG

genotypes

-RRB-

explained

of

the

residual

OSS

variance

after

adjustment

for

age

and

after

including

the

sex-genotype

interaction

they

explained

of

the

residual

variance

For

TOSS

the

MG

effect

was

Additionally

we

compared

the

age

dependence

of

OSS

by

directly

measuring

the

individual

's

skeletal

health

index

in

predicted

MG

genotype

groups

Kobyliansky

et

al.

-LRB-

-RRB-

proposed

a

two-stage

stochastic

statistical

model

of

the

population

aging

pattern

for

OSS

The

implied

stages

are

as

follows

-LRB-

-RRB-

the

period

of

life

between

birth

and

the

apparent

onset

of

skeletal

changes

-LRB-

t

ti

-RRB-

defined

as

the

latent

period

and

-LRB-

-RRB-

the

period

of

visible

changes

beginning

after

ti

-LRB-

which

is

not

the

same

in

different

individuals

-RRB-

when

involutive

changes

occur

continuously

throughout

the

remaining

life

Applying

this

model

separately

in

predicted

genotype

groups

we

compared

their

aging

features

by

means

of

model

parameters

-LRB-

q

B

-RRB-

The

earliest

age

of

the

first

visible

changes

was

almost

the

same

in

all

sex-genotype

groups

about

years

The

probability

per

year

of

transition

from

the

latent

to

the

visible

changes

period

q

was

for

genotype

about

of

probability

for

other

individuals

This

was

especially

expressed

for

women

and

it

results

in

greater

values

of

the

average

transition

age

TM

-LRB-

years

in

and

for

the

others

-RRB-

The

rate

of

aging

B

was

also

significantly

different

in

the

predicted

genotype

groups

but

this

difference

was

expressed

more

for

men

Thus

we

can

conclude

that

the

inherited

difference

in

the

aging

pattern

lies

in

men

mostly

in

the

rate

of

aging

but

in

women

it

is

in

the

age

of

onset

of

the

period

of

visible

changes

An

additional

finding

was

that

in

the

group

-LRB-

slow

aging

-RRB-

for

women

the

age

at

menarche

was

significantly

greater

-LRB-

P

-RRB-

than

in

the

group

-LCB-

OR

-RCB-

For

women

born

after

-LRB-

those

whose

maturation

period

was

not

influenced

by

WW

II

or

the

subsequent

rehabilitation

period

-RRB-

the

age

at

menopause

was

also

greater

in

the

group

-LRB-

P

-RRB-

Thus

there

is

a

positive

relation

between

the

rate

of

sexual

development

and

the

rate

of

aging

characterized

by

degenerative

skeletal

changes

The

rate

of

sexual

development

is

positively

associated

with

intensity

of

normal

metabolism

which

also

may

lead

to

accelerated

aging

Early

onset

of

menarche

is

also

known

to

be

linked

to

other

aging

conditions

such

as

elevated

blood

pressure

and

glucose

intolerance

compared

with

later

maturing

girls

independent

of

body

composition

-LRB-

Remsberg

et

al.

-RRB-

The

main

molecular

characteristic

of

aging

is

the

progressive

accumulation

of

damages

in

macromolecules

that

result

on

macro

level

in

heterogeneity

of

tissues

and

degenerative

changes

Rattan

-LRB-

-RRB-

pointed

out

three

major

sources

of

this

damage

-LRB-

-RRB-

reactive

oxygen

species

-LRB-

ROS

-RRB-

and

free

radicals

formed

due

to

external

inducers

of

damage

-LRB-

for

example

ultra-violet

rays

-RRB-

and

as

a

consequence

of

cellular

metabolism

-LRB-

-RRB-

nutritional

glucose

and

its

metabolites

and

their

biochemical

interactions

with

ROS

and

-LRB-

-RRB-

spontaneous

errors

in

biochemical

processes

such

as

DNA

duplication

transcription

post-transcriptional

processing

translation

and

post-translational

Bessenyei

et

al.

-LRB-

-RRB-

reviewed

data

concerning

SNPs

associated

with

life

span

positioned

in

a

variety

of

genes

regulating

metabolic

processes

apoptosis

stress

response

-LRB-

see

also

Singh

et

al.

-RRB-

and

immune

response

Several

polymorphisms

in

ER-alpha

-LRB-

estrogen

receptor

that

are

known

to

play

significant

role

in

skeletal

development

-RRB-

were

reported

to

be

associated

with

life

span

-LRB-

Bessenyei

et

al.

-RRB-

and

with

both

osteoarthritis

-LRB-

Jin

et

al.

-RRB-

and

osteoporosis

-LRB-

Albagha

et

al.

-RRB-

related

phenotypes

The

VDR

-LRB-

vitamin

D

receptor

-RRB-

gene

is

also

known

to

be

associated

with

both

types

of

degenerative

changes

in

certain

skeletal

sites

-LRB-

Uitterlinden

et

al.

Yue

et

al.

-RRB-

A

great

number

of

genes

with

significant

association

signals

were

cited

in

recent

reviews

of

Loughlin

-LRB-

-RRB-

-LRB-

osteoarthritis

-RRB-

and

Liu

et

al.

-LRB-

-RRB-

-LRB-

osteoporosis

-RRB-

de

Boer

et

al.

-LRB-

-RRB-

described

studies

of

mice

with

a

mutation

in

XPD

a

gene

encoding

a

DNA

helicase

that

functions

in

both

repair

and

transcription

Mice

with

mutation

were

found

to

exhibit

many

symptoms

of

premature

aging

including

osteoporosis

and

kyphosis

osteosclerosis

early

greying

cachexia

infertility

and

reduced

life-span

So

OSS

the

index

comprising

various

accumulated

degenerative

skeletal

changes

despite

to

different

molecular

mechanisms

which

are

involved

in

bone

loss

cartilage

loss

and

other

OSS

components

may

be

under

genetic

control

of

some

polymorphic

genes

taking

part

in

DNA

repair

pathways

transcription

and

translation

control

and/or

some

polymorphic

genes

controlling

intensity

of

normal

metabolism

that

influence

the

rate

of

molecular

damage

-LRB-

Kirkwood

and

Austad

-RRB-

This

supports

the

assumption

that

OSS

as

a

skeletal

biomarker

of

BA

can

be

used

to

evaluate

the

organism

's

general

aging

status

B O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B I O O O O O O O O O O O O O O O B I O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

osseographic score
skeletal aging
chuvashia
biological aging
heritability


Biomechanics

of

Traumatic

Brain

Injury

Influences

of

the

Morphologic

Heterogeneities

of

the

Cerebral

Cortex

Traumatic

brain

injury

-LRB-

TBI

-RRB-

can

be

caused

by

accidents

and

often

leads

to

permanent

health

issues

or

even

death

Brain

injury

criteria

are

used

for

assessing

the

probability

of

TBI

if

a

certain

mechanical

load

is

applied

The

currently

used

injury

criteria

in

the

automotive

industry

are

based

on

global

head

kinematics

New

methods

based

on

finite

element

modeling

use

brain

injury

criteria

at

lower

scale

levels

e.g.

tissue-based

injury

criteria

However

most

current

computational

head

models

lack

the

anatomical

details

of

the

cerebrum

To

investigate

the

influence

of

the

morphologic

heterogeneities

of

the

cerebral

cortex

a

numerical

model

of

a

representative

part

of

the

cerebral

cortex

with

a

detailed

geometry

has

been

developed

Several

different

geometries

containing

gyri

and

sulci

have

been

developed

for

this

model

Also

a

homogeneous

geometry

has

been

made

to

analyze

the

relative

importance

of

the

heterogeneities

The

loading

conditions

are

based

on

a

computational

head

model

simulation

The

results

of

this

model

indicate

that

the

heterogeneities

have

an

influence

on

the

equivalent

stress

The

maximum

equivalent

stress

in

the

heterogeneous

models

is

increased

by

a

factor

of

about

with

respect

to

the

homogeneous

model

whereas

the

mean

equivalent

stress

is

increased

by

at

most

This

implies

that

tissue-based

injury

criteria

may

not

be

accurately

applied

to

most

computational

head

models

used

nowadays

which

do

not

account

for

sulci

and

gyri

Introduction

The

brain

is

often

one

of

the

most

seriously

injured

parts

of

the

human

body

in

case

of

a

road

traffic

crash

situation

The

incidence

rate

and

mortality

rate

in

Europe

are

estimated

to

be

and

per

of

the

population

per

year

respectively

Traumatic

brain

injury

-LRB-

TBI

-RRB-

is

therefore

considered

as

a

widespread

problem

Understanding

the

mechanisms

inducing

TBI

is

necessary

for

reducing

the

number

of

occurrences

e.g.

by

developing

more

appropriate

protective

systems

and

diagnostic

tools

Brain

injury

criteria

are

used

for

the

assessment

of

the

probability

of

TBI

for

certain

mechanical

loading

conditions

The

most

commonly

used

injury

criterion

in

the

automotive

industry

is

the

Head

Injury

Criterion

-LRB-

HIC

-RRB-

It

is

developed

to

predict

TBI

resulting

from

a

translational

acceleration

of

the

head

One

of

the

drawbacks

of

the

HIC

is

that

it

is

based

on

global

kinematic

data

to

predict

TBI

whereas

actual

brain

damage

is

caused

at

the

cellular

level

as

a

consequence

of

tissue

strains

and

stresses

Furthermore

it

is

based

on

experimental

data

in

which

only

anterior

posterior

contact

loading

has

been

applied

to

human

cadavers

not

accounting

for

angular

accelerations

of

the

head

For

a

better

approximation

of

the

relation

between

TBI

and

a

mechanical

load

more

advanced

methods

have

been

developed

For

instance

three-dimensional

finite

element

-LRB-

FE

-RRB-

head

models

have

been

developed

to

predict

brain

injury

With

these

numerical

head

models

different

injury

mechanisms

and

loading

conditions

can

be

distinguished

However

in

these

models

the

heterogeneous

anatomy

of

the

cerebrum

is

usually

represented

by

a

relatively

homogeneous

geometry

A

comparison

between

the

homogeneous

geometry

of

a

typical

finite

element

head

model

and

the

complex

structure

of

a

real

brain

is

given

in

Fig.

The

main

function

of

the

heterogeneous

morphology

is

to

increase

the

cortical

surface

in

order

to

obtain

a

more

complex

level

of

the

brain

functions

The

most

recent

numerical

head

models

include

ventricles

and

the

invaginations

of

the

dura

mater

but

include

the

convolutions

of

the

cerebral

cortex

Consequently

the

stresses

and

strains

that

are

predicted

from

these

models

likely

do

not

represent

actual

tissue

stresses

and

strains

at

least

in

the

cortex

Therefore

although

tissue-based

injury

criteria

may

be

used

their

accuracy

is

expected

to

be

limited

This

might

prohibit

the

direct

use

of

tissue-based

injury

criteria

Such

criteria

predict

injury

at

the

tissue

level

and

are

based

on

in

vitro

and

in

vivo

experiments

For

a

direct

application

of

tissue-based

injury

criteria

in

a

computational

head

model

a

more

detailed

description

of

the

biomechanical

behavior

of

the

cerebrum

may

be

required

which

can

be

achieved

by

including

its

morphologic

heterogeneities

in

these

models

A

few

two-dimensional

FE

models

of

the

brain

containing

the

convolutions

of

the

cerebral

cortex

have

been

described

in

literature

Miller

et

al.

compared

different

modeling

techniques

for

the

relative

motion

between

the

brain

and

the

cranium

Nishimoto

and

developed

a

model

to

investigate

the

relation

between

brain

injury

and

the

HIC

However

these

models

have

not

been

developed

with

the

purpose

of

investigating

the

local

biomechanics

at

the

level

of

these

convolutions

No

conclusions

have

been

drawn

from

these

studies

on

the

biomechanical

influence

of

the

heterogeneities

of

the

cerebral

cortex

due

to

the

limited

spatial

resolution

of

the

mesh.Figure

-LRB-

a

-RRB-

Numerical

head

model

developed

by

Claessens

-LRB-

b

-RRB-

Lateral

view

of

the

human

brain

Adapted

from

Welker

et

al.

Physical

experiments

have

been

conducted

in

several

studies

to

investigate

the

biomechanical

consequences

of

the

heterogeneities

of

the

cerebrum

In

a

study

by

Bradshaw

et

al.

a

gel-filled

chamber

that

represented

the

brain

and

skull

in

a

coronal

plane

including

the

falx

cerebri

and

the

sulci

of

the

cerebral

cortex

was

subjected

to

a

rotation

with

a

peak

acceleration

of

approximately

rad

s

An

increase

of

the

maximum

principle

strain

in

the

cerebral

cortex

due

to

the

sulci

was

found

The

aim

of

this

study

is

to

investigate

the

biomechanical

influences

of

the

morphologic

heterogeneities

in

the

cerebral

cortex

To

achieve

this

several

two-dimensional

FE

models

with

detailed

geometries

of

a

part

of

the

cerebral

cortex

have

been

developed

Also

an

FE

model

with

a

homogeneous

morphology

of

the

cortex

has

been

made

The

loading

conditions

are

based

on

simulations

with

a

computational

head

model

as

used

by

Brands

et

al.

The

results

of

the

simulations

of

the

heterogeneous

models

will

be

compared

to

those

of

the

homogeneous

model

Methods

In

this

study

plane

strain

models

of

small

sections

of

the

cerebrum

are

made

using

the

FE

code

Abaqus

-LRB-

HKS

Providence

USA

-RRB-

An

explicit

time

integration

is

used

anticipating

a

dynamic

load

with

a

high

magnitude

and

a

short

duration

The

time

increments

are

limited

by

the

stability

condition

which

is

determined

in

the

global

estimator

function

in

Abaqus

Geometries

To

investigate

the

influence

of

the

heterogeneities

of

the

cerebral

cortex

a

homogeneous

model

and

three

heterogeneous

models

have

been

developed

The

heterogeneous

models

which

are

shown

in

Figs.

and

have

detailed

geometries

of

a

small

part

of

the

cerebrum

including

also

a

part

of

the

cerebrospinal

fluid

-LRB-

CSF

-RRB-

The

cranium

is

modeled

by

a

boundary

constraint

as

will

be

detailed

further

on

Since

the

dura

mater

and

the

arachnoid

are

connected

to

the

inside

of

the

cranium

in

the

region

that

is

modeled

it

is

assumed

that

they

can

be

ignored

for

this

situation

The

pia

mater

which

is

a

thin

and

delicate

membrane

covering

the

brain

is

also

not

included

since

it

is

expected

to

have

no

mechanical

influence

for

the

used

loading

conditions

The

same

assumption

is

used

for

the

arachnoid

trabeculae

which

extend

from

the

arachnoid

to

the

pia

mater

and

are

less

existent

inside

the

sulci

Figure

-LRB-

a

-RRB-

Heterogeneous

geometry

and

-LRB-

b

-RRB-

its

spatial

discretization

-LRB-

c

-RRB-

Heterogeneous

geometry

-LRB-

d

-RRB-

Heterogeneous

geometry

-LRB-

e

-RRB-

Homogeneous

geometry

The

first

geometry

has

one

narrow

sulcus

on

the

right

hand

side

and

a

small

part

of

a

sulcus

on

the

left

hand

side

The

second

geometry

contains

two

deeper

and

wider

sulci

than

the

other

two

geometries

The

third

geometry

consists

of

one

vertical

sulcus

and

one

partly

horizontal

sulcus

where

horizontal

and

vertical

refer

to

the

x

and

y-direction

respectively

These

geometries

which

represent

typical

stylized

shapes

of

the

cerebral

cortex

are

based

on

the

topological

studies

by

Mai

et

al.

The

left

and

right

boundaries

of

the

models

are

chosen

to

be

periodic

i.e.

the

internal

geometries

near

the

opposite

boundaries

match

The

periodicity

of

the

boundary

conditions

will

be

explained

further

on

The

models

do

not

distinguish

between

gray

-LRB-

cerebral

cortex

-RRB-

and

white

matter

In

Fig.

the

homogeneous

model

is

shown

Similar

to

the

heterogeneous

models

it

also

consists

of

CSF

and

brain

tissue

but

it

does

not

contain

any

gyri

and

sulci

The

outer

dimensions

of

each

model

are

mm

by

mm

The

meshes

consist

of

bi-linear

quadrilateral

reduced

integration

elements

with

hourglass

control

The

heterogeneous

models

also

contain

a

small

number

of

triangular

elements

The

total

number

of

elements

of

the

heterogeneous

models

ranges

from

to

elements

The

homogeneous

geometry

consists

of

elements

Material

Properties

For

the

material

properties

of

the

CSF

a

nearly

incompressible

low

shear

modulus

elastic

solid

has

been

assumed

since

the

shear

stress

in

the

brain

tissue

due

to

the

applied

loading

conditions

is

estimated

to

be

about

a

factor

higher

than

that

in

the

CSF

The

material

properties

are

listed

in

Table

The

shear

modulus

of

CSF

is

estimated

from

the

loading

conditions

that

are

described

further

on

by

using

in

which

G

is

the

elastic

shear

modulus

η

is

the

viscosity

γ

is

the

estimated

shear

strain

and

is

the

estimated

shear

rate

Because

two

different

loading

conditions

have

been

used

also

two

different

estimates

for

the

CSF

shear

modulus

have

been

used

However

with

these

shear

moduli

being

much

lower

than

that

of

the

brain

tissue

the

exact

values

of

these

estimates

do

not

affect

the

outcome

of

this

study

The

bulk

modulus

is

obtained

from

literature

Table

material

parameters

Bulk

modulus

-LRB-

GPa

-RRB-

Shear

modulus

-LRB-

Pa

-RRB-

Time

constant

-LRB-

s

-RRB-

a

b

Brain

98840.00013835.50.012231.20.3567.14.623.6112.12.7954.3

aShear

modulus

in

case

of

loading

condition

AbShear

modulus

in

case

of

loading

condition

B

The

material

properties

of

the

brain

tissue

are

described

by

a

non-linear

viscoelastic

constitutive

model

that

has

been

developed

by

Hrapko

et

al.

This

model

was

found

to

accurately

describe

the

response

of

brain

tissue

for

large

deformations

in

both

shear

and

compression

This

model

is

extended

here

to

account

for

compressibility

The

constitutive

model

consists

of

an

elastic

part

denoted

by

the

subscript

e

and

a

-LRB-

deviatoric

-RRB-

viscoelastic

part

denoted

by

the

subscript

ve

with

N

viscoelastic

modes

The

total

Cauchy

stress

tensor

is

written

asin

which

the

superscripts

h

and

d'

denote

the

hydrostatic

and

the

deviatoric

part

respectively

For

simplicity

the

subscript

i

indicating

the

number

of

the

viscoelastic

mode

will

be

omitted

from

this

point

on

The

hydrostatic

part

of

Eq

-LRB-

-RRB-

is

defined

aswhere

K

is

the

bulk

modulus

and

is

the

volume

change

ratio

The

deviatoric

elastic

mode

describes

a

non-linear

response

to

the

deformation

gradient

tensor

F

which

is

given

bywhere

G

is

the

elastic

shear

modulus

is

the

isochoric

part

of

the

Finger

tensor

B

and

and

are

the

first

and

second

invariant

of

the

isochoric

Finger

tensor

respectively

A

C

and

b

are

fitting

parameters

describing

the

non-linearity

of

the

elastic

response

The

third

term

on

the

right

hand

side

of

Eq

-LRB-

-RRB-

consists

of

the

summation

of

the

viscoelastic

modes

The

deformation

gradient

tensor

F

is

partitioned

into

an

elastic

deformation

gradient

tensor

and

a

viscous

deformation

gradient

tensor

by

assuming

multiplicative

The

decomposition

involves

a

fictitious

intermediate

state

which

could

exist

after

application

of

merely

the

viscous

deformation

gradient

tensor

This

is

the

stress-free

state

which

after

application

of

the

elastic

deformation

tensor

transforms

into

the

final

state

The

third

term

on

the

right

hand

side

of

Eq

-LRB-

-RRB-

describes

the

viscoelastic

contribution

to

the

stress

as

follows

with

G

the

shear

modulus

the

isochoric

part

of

the

elastic

Finger

tensor

and

a

a

fitting

parameter

The

viscous

deformation

is

assumed

to

be

volume-invariant

i.e.

and

The

viscous

rate

of

deformation

tensor

is

calculated

from

the

flow

rule

aswhere

the

dynamic

viscosity

η

is

a

function

of

the

scalar

equivalent

stress

measure

for

which

the

Ellis

model

is

adopted

with

subscripts

and

denoting

the

initial

and

infinite

values

respectively

The

initial

value

for

the

viscosity

is

defined

as

η0

Gλ

whereas

the

infinite

viscosity

is

defined

as

η

Here

λ

refers

to

the

time

constant

Although

differences

between

the

material

properties

of

the

gray

and

white

matter

may

exist

these

differences

are

not

well

characterized

Therefore

no

distinction

between

gray

and

white

matter

has

been

made

in

this

study

except

for

the

investigation

of

the

influence

of

varying

the

material

properties

of

gray

matter

with

respect

to

those

of

white

matter

-LRB-

see

the

Discussion

and

Conclusions

-RRB-

For

simulating

a

head

impact

situation

representative

of

road

traffic

accidents

an

extra

viscoelastic

mode

with

a

smaller

time

constant

has

been

added

to

the

behavior

as

characterized

by

Hrapko

et

al.

The

extra

is

based

on

the

experimental

data

from

Hrapko

and

co-workers

in

combination

with

the

data

by

Shen

et

al.

The

linear

material

properties

are

listed

in

Table

The

values

of

the

non-linear

viscoelastic

parameters

are

shown

in

Table

Table

material

parameters

for

brain

tissueElasticViscousA

τ0

PaC

n

a

b

Boundary

Conditions

The

boundary

conditions

have

been

chosen

such

that

they

represent

the

biomechanical

influences

of

the

surroundings

on

the

cerebral

cortex

model

Figure

shows

the

labeling

of

the

corner

nodes

and

the

boundaries

The

symbols

x

and

y

denote

the

components

of

position

vector

with

respect

to

a

Cartesian

vector

basis

whereas

u

and

v

are

the

components

of

the

displacement

vector

with

respect

to

this

basis.Figure

of

corner

nodes

and

boundaries

The

Young

's

modulus

of

the

cranium

is

much

higher

than

that

of

brain

tissue

Still

in

a

contact

loading

situation

of

the

head

the

deformation

of

the

skull

is

important

because

it

initiates

strain

waves

in

the

brain

tissue

In

this

study

however

only

inertial

loading

of

the

head

is

considered

and

therefore

the

cranium

is

assumed

to

be

rigid

The

cranium

is

incorporated

in

the

boundary

condition

at

Γ3

Because

of

the

low

shear

modulus

of

the

CSF

the

influence

of

the

rigid

constraint

associated

with

the

cranium

at

boundary

Γ3

in

the

x-direction

can

be

neglected

Provided

no

rotation

of

the

model

occurs

the

constraint

equation

for

all

nodes

on

boundary

Γ3

iswith

vs

the

vertical

displacement

of

the

skull

The

boundaries

Γ2

and

Γ4

are

subjected

to

periodic

boundary

These

constraints

imply

that

throughout

the

deformation

process

the

shapes

of

the

opposite

boundaries

Γ2

and

Γ4

remain

identical

to

each

other

while

the

tractions

on

opposite

boundaries

are

opposite

to

satisfy

stress

continuity

which

can

be

written

aswith

the

Cauchy

stress

tensor

and

the

unit

outward

normal

vector

of

boundary

Γi

The

lower

boundary

Γ1

of

the

brain

tissue

in

the

model

lies

adjacent

to

brain

tissue

in

neighboring

regions

Therefore

boundary

Γ1

has

to

be

constrained

accordingly

The

applied

constraint

on

Γ1

is

obtained

by

tying

all

nodal

displacements

on

Γ1

to

a

linear

interpolation

between

the

displacements

of

corner

nodes

and

For

any

node

on

boundary

Γ1

this

results

inwith

the

subscript

denoting

the

initial

configuration

The

displacements

of

corner

nodes

and

are

prescribed

and

calculated

from

the

applied

loading

conditions

The

loading

conditions

of

the

cerebral

cortex

model

-LRB-

micro-level

in

Fig.

-RRB-

are

based

on

the

loading

conditions

that

have

been

used

by

Brands

et

al.

for

a

three-dimensional

numerical

head

model

-LRB-

macro-level

in

Fig.

-RRB-

In

that

model

an

eccentric

rotation

has

been

applied

to

the

skull

to

simulate

an

angular

head

acceleration

around

the

neck-shoulder

joint

in

the

sagittal

plane

in

the

anterior

posterior

direction

The

eccentricity

has

been

chosen

to

represent

a

typical

neck

length

The

axis

of

rotation

has

been

positioned

at

mm

below

the

anatomical

origin

i.e.

the

ear

hole

projected

to

the

sagittal

plane

The

rotation

of

the

head

model

consists

of

two

successive

sine

functions

that

describe

the

angular

acceleration

Figure

loading

conditions

of

the

cerebral

cortex

model

-LRB-

micro-level

-RRB-

are

derived

from

the

region

of

interest

in

a

parasagittal

cross-section

-LRB-

mm

offset

from

the

midsagittal

plane

-RRB-

of

the

head

model

-LRB-

macro-level

-RRB-

Shown

at

the

macro-level

is

the

equivalent

stress

field

of

the

head

model

at

ms

In

Eqs

-LRB-

-RRB-

and

-LRB-

-RRB-

the

angular

acceleration

is

given

in

rad

s

The

loading

conditions

are

applied

to

the

cerebral

cortex

model

by

means

of

body

forces

In

all

integration

points

of

the

elements

in

the

model

a

non-uniform

body

force

is

imposed

that

reversely

simulates

the

inertial

forces

in

which

represents

the

distributed

load

per

unit

of

volume

ρ

is

mass

density

t

is

time

and

refers

to

the

acceleration

in

the

x-direction

that

is

represented

by

these

body

forces

Note

that

for

the

head

model

the

loading

conditions

contain

an

angular

component

whereas

the

cerebral

cortex

model

uses

translational

loading

conditions

Because

only

a

small

part

of

the

head

is

modeled

and

because

of

the

small

rotation

of

the

head

model

with

a

maximum

of

the

loading

of

the

cerebral

cortex

model

is

assumed

to

be

translational

in

x-direction

only

The

loading

conditions

of

the

cerebral

cortex

model

i.e.

the

representative

accelerations

are

calculated

from

the

head

model

-LRB-

from

the

region

indicated

in

Fig.

-RRB-

in

two

different

approaches

In

the

first

approach

the

input

accelerations

of

the

head

model

are

used

to

define

the

loading

condition

of

the

cerebral

cortex

model

This

approach

will

be

referred

to

as

loading

condition

A.The

translational

acceleration

can

be

calculated

usingwith

the

angular

acceleration

which

is

defined

by

Eqs

-LRB-

-RRB-

and

-LRB-

-RRB-

and

r

the

radius

from

the

axis

of

rotation

-LRB-

neck-shoulder

-RRB-

in

the

head

model

to

a

point

in

the

region

of

interest

The

radius

r

is

a

function

of

the

y-position

in

the

cerebral

cortex

model

It

varies

between

r

-LRB-

-RRB-

m

at

boundary

Γ1

to

r

-LRB-

-RRB-

m

at

Γ3

The

accelerations

at

Γ1

and

Γ3

are

depicted

in

Fig.

All

other

accelerations

are

interpolated

linearly

between

these

two

boundaries

thereby

creating

a

gradient

across

the

height

of

the

model

The

acceleration

gradient

is

important

for

the

resulting

shear

stresses

Figure

shows

the

acceleration

profile

of

the

cerebral

cortex

model

The

accelerations

are

used

to

calculate

the

body

forces

as

a

function

of

both

time

and

y-position

The

disadvantage

of

this

loading

condition

is

that

a

spatially

constant

acceleration

gradient

is

assumed

and

therefore

it

does

not

account

for

the

influence

of

the

geometry

of

the

cranium

To

account

for

the

geometry

of

the

head

another

loading

condition

has

been

developed

that

is

described

next.The

second

approach

loading

condition

B

uses

output

accelerations

from

a

global

head

model

simulation

as

the

input

of

the

cerebral

cortex

model

For

this

a

modified

version

of

the

head

model

as

used

by

Brands

et

al.

has

been

employed

in

the

simulation

code

Madymo

in

which

the

constitutive

model

for

brain

tissue

by

Hrapko

et

al.

has

been

implemented

The

accelerations

obtained

from

the

region

inside

the

box

in

Fig.

from

the

head

model

are

imposed

on

the

cerebral

cortex

model

Hence

the

influence

of

the

geometry

of

the

head

is

modeled

indirectly

by

means

of

an

acceleration

profile

that

is

obtained

from

the

head

model.The

displacements

of

the

brain

tissue

in

the

head

model

in

the

field

of

interest

are

almost

entirely

in

the

x-direction

justifying

the

assumption

of

inertial

loading

-LRB-

of

the

cerebral

cortex

model

-RRB-

in

the

x-direction

only

In

Fig.

the

acceleration

profiles

as

a

function

of

the

y-position

are

shown

at

and

ms.

Similar

to

loading

condition

A

the

accelerations

are

used

to

calculate

the

body

forces

as

a

function

of

both

time

and

y-position

Figure

condition

A.

-LRB-

a

-RRB-

Acceleration

at

the

upper

and

lower

boundary

of

the

cerebral

cortex

model

-LRB-

b

-RRB-

Acceleration

profiles

at

different

timesFigure

condition

B

displacement

-LRB-

top

-RRB-

and

acceleration

-LRB-

bottom

-RRB-

profiles

derived

from

the

output

of

the

head

model

In

order

to

quantify

the

influence

of

the

morphologic

heterogeneities

the

equivalent

stress

is

used

in

which

is

the

deviatoric

part

of

the

Cauchy

stress

tensor

The

equivalent

stress

is

chosen

because

the

simulations

are

based

on

an

angular

acceleration

of

the

head

in

which

deviatoric

stresses

are

considered

to

be

the

most

important

The

maximum

principal

strain

is

considered

important

as

well

with

respect

to

diffuse

axonal

brain

injury

Therefore

also

the

maximum

principal

logarithmic

strain

is

used

to

quantify

the

influence

of

the

morphologic

heterogeneities

Results

Figure

depicts

the

development

in

time

of

the

equivalent

stress

fields

for

the

homogeneous

model

-LRB-

top

row

-RRB-

and

the

heterogeneous

models

from

the

simulation

with

loading

condition

A.

Stress

concentrations

are

present

in

the

heterogeneous

models

at

the

surface

of

the

brain

tissue

between

two

gyri

at

and

ms.

Near

boundary

Γ1

all

heterogeneous

models

have

lower

equivalent

stresses

compared

to

the

homogeneous

model

at

ms.Figure

equivalent

stress

fields

as

a

result

of

loading

condition

A

In

order

to

obtain

a

good

comparison

of

the

results

for

all

geometries

during

the

complete

simulation

time

the

maximum

and

mean

equivalent

stress

from

the

simulations

with

loading

condition

A

are

shown

in

Fig.

as

a

function

of

time

It

shows

the

stresses

in

the

brain

tissue

only

It

can

be

noticed

that

the

heterogeneous

models

have

a

higher

maximum

equivalent

stress

than

the

homogeneous

model

Among

the

heterogeneous

configurations

geometry

causes

a

noticeably

lower

maximum

equivalent

stress

of

Pa

compared

to

geometries

and

with

a

maximum

equivalent

stress

of

approximately

Pa.

The

large

maximum

equivalent

stress

in

heterogeneous

geometry

lasts

longer

than

the

stresses

of

the

other

geometries

The

maximum

equivalent

stress

of

the

homogeneous

model

reaches

a

value

of

Pa.

The

mean

equivalent

stresses

are

nearly

the

same

for

all

geometries.Figure

and

mean

equivalent

stress

for

the

heterogeneous

and

homogeneous

models

as

a

result

of

loading

condition

A

To

investigate

the

influence

of

the

heterogeneities

the

equivalent

stress

of

the

cerebral

cortex

in

the

heterogeneous

models

is

taken

relative

to

that

of

the

homogeneous

model

For

the

maximum

equivalent

stress

this

will

be

done

by

taking

the

maximum

values

whereas

for

the

mean

equivalent

stress

this

will

be

done

by

taking

the

time

averaged

values

The

maximum

equivalent

stress

of

the

heterogeneous

models

and

is

and

times

higher

than

the

homogeneous

model

respectively

The

mean

equivalent

stress

of

the

heterogeneous

models

and

with

respect

to

the

homogeneous

model

is

and

respectively

The

equivalent

stress

fields

obtained

with

loading

condition

B

are

displayed

in

Fig.

During

the

beginning

of

the

simulation

the

equivalent

stress

fields

in

the

brain

tissue

are

comparable

for

all

models

When

the

field

of

higher

equivalent

stress

moves

downwards

the

heterogeneities

result

in

local

peak

stress

concentrations

which

can

be

seen

at

ms

for

geometries

and

Later

on

at

ms

the

heterogeneous

geometries

and

have

less

influence

on

the

equivalent

stress

fields

The

differences

of

geometry

with

respect

to

geometries

and

are

a

consequence

of

the

deeper

sulci

in

geometry

Figure

equivalent

stress

fields

as

a

result

of

loading

condition

B

The

maximum

and

mean

equivalent

stress

of

the

cerebral

cortex

as

a

function

of

time

obtained

with

loading

condition

B

is

shown

in

Fig.

The

maximum

equivalent

stress

is

higher

for

the

heterogeneous

models

than

for

the

homogeneous

models

but

not

for

the

complete

duration

of

the

simulation

After

about

ms

the

maximum

equivalent

stress

of

the

heterogeneous

models

drops

to

approximately

the

same

magnitude

as

the

one

obtained

for

the

homogeneous

model

For

the

heterogeneous

models

the

maximum

equivalent

stress

reaches

values

of

approximately

and

Pa

for

geometries

and

respectively

The

homogeneous

model

has

a

maximum

equivalent

stress

reaching

Pa.

Also

the

moment

in

time

at

which

the

maximum

occurs

differs

from

one

geometry

to

the

other

The

mean

equivalent

stress

values

of

all

the

geometries

are

similar.Figure

and

mean

equivalent

stress

for

the

heterogeneous

and

homogeneous

models

as

a

result

of

loading

condition

B

To

quantify

the

influence

of

the

heterogeneities

the

equivalent

stress

of

the

brain

tissue

of

the

heterogeneous

models

is

taken

relative

to

the

homogeneous

model

in

the

same

manner

as

described

previously

for

loading

condition

A

The

maximum

equivalent

stress

of

the

heterogeneous

models

and

has

increased

by

and

with

respect

the

homogeneous

model

respectively

The

mean

equivalent

stress

of

the

heterogeneous

models

and

is

and

again

relative

to

the

homogeneous

model

respectively

The

distribution

of

maximum

principal

strains

for

loading

condition

B

at

ms

is

shown

in

Fig.

One

can

notice

that

a

concentration

of

maximum

principal

strains

at

ms

occurs

in

the

same

location

as

the

equivalent

stress

concentration

at

ms

-LRB-

Fig.

-RRB-

both

in

case

of

loading

condition

B

The

same

method

for

the

quantification

of

the

influence

of

the

heterogeneities

is

used

but

with

the

maximum

principal

strain

instead

of

the

equivalent

stress

For

the

simulations

with

loading

condition

A

the

peak

maximum

principal

strain

in

the

brain

tissue

of

the

heterogeneous

models

and

has

increased

with

respect

to

the

homogeneous

model

by

and

respectively

If

loading

condition

B

is

used

the

increases

are

and

respectively.Figure

maximum

principal

logarithmic

strain

field

as

a

result

of

loading

condition

B

at

ms

Discussion

and

Conclusions

In

this

study

the

influences

of

the

heterogeneities

in

the

cerebral

cortex

were

investigated

This

was

done

with

FE

models

of

several

different

geometries

from

small

detailed

parts

of

the

cortex

In

a

preliminary

study

the

boundary

constraints

were

tested

The

loading

conditions

were

derived

from

a

numerical

head

model

In

order

to

determine

which

constraints

on

the

boundaries

would

represent

the

surroundings

best

a

preliminary

study

was

conducted

in

which

several

different

constraints

were

applied

to

boundaries

Γ1

and

Γ3

The

different

conditions

on

boundary

Γ3

i.e.

rigid

constraint

or

slip-condition

in

the

x-direction

did

not

contribute

to

differences

in

the

results

of

the

brain

tissue

This

was

probably

caused

by

the

low

shear

modulus

of

the

CSF

For

boundary

Γ1

several

different

boundary

conditions

were

tested

and

compared

to

the

results

of

models

with

the

same

width

but

with

twice

the

height

of

the

models

in

this

study

By

comparing

the

normal

and

the

high

models

the

boundary

condition

at

boundary

Γ1

that

represented

adjacent

brain

tissue

could

be

determined

The

periodic

boundary

condition

that

was

applied

to

boundaries

Γ2

and

Γ4

was

used

because

of

the

assumed

periodicity

in

the

cerebral

cortex

Since

the

loading

conditions

were

dynamic

they

could

not

be

applied

to

the

model

by

directly

imposing

a

deformation

which

would

induce

boundary

effects

For

this

reason

an

indirect

deformation

was

imposed

by

means

of

body

forces

This

approach

worked

well

for

the

first

ms

of

the

simulation

which

had

a

total

duration

of

ms.

After

ms

the

deformations

of

the

brain

tissue

differed

from

the

deformations

derived

from

the

head

model

that

were

indirectly

applied

to

the

model

-LRB-

Figs.

and

-RRB-

Therefore

only

the

first

ms

of

the

simulation

are

considered

to

be

realistic

Loading

condition

A

was

derived

from

the

acceleration

pulse

that

has

been

applied

to

a

head

model

The

equivalent

stress

fields

of

the

homogeneous

models

caused

by

loading

condition

A

-LRB-

Fig.

-RRB-

showed

no

similarities

to

the

equivalent

stress

field

of

the

head

model

-LRB-

Fig.

-RRB-

Provided

that

the

equivalent

stress

field

of

the

head

model

is

realistic

loading

condition

A

can

be

considered

unrealistic

Loading

condition

B

was

obtained

from

the

resulting

accelerations

in

the

region

of

interest

of

the

head

model

The

equivalent

stress

fields

of

the

homogeneous

models

from

simulations

with

loading

condition

B

-LRB-

Fig.

-RRB-

were

approximately

similar

to

the

stress

fields

in

the

corresponding

region

of

the

head

model

-LRB-

Fig.

-RRB-

during

the

first

ms.

Nevertheless

differences

in

the

equivalent

stress

fields

existed

at

the

surface

of

the

cortex

This

is

due

to

the

CSF

layer

in

the

cerebral

cortex

model

being

described

elastically

with

a

low

shear

modulus

as

opposed

to

the

head

model

which

contains

a

relatively

stiff

CSF/dura

layer

In

spite

of

all

these

obvious

differences

by

comparing

these

two

loading

conditions

it

was

shown

that

the

different

loading

conditions

have

hardly

any

effect

on

the

relative

mean

and

maximum

equivalent

stress

and

the

relative

peak

maximum

principal

logarithmic

strain

Hence

the

mechanical

influences

of

the

heterogeneities

of

the

cerebral

cortex

seem

to

be

independent

of

the

loading

conditions

The

constitutive

model

for

brain

tissue

was

based

on

experiments

on

porcine

white

matter

This

was

used

as

a

substitute

for

human

brain

tissue

as

it

was

readily

available

and

it

allowed

to

conduct

experiments

with

a

shorter

post-mortem

time

Experiments

conducted

by

Prange

et

al.

on

fresh

human

brain

tissue

indicated

that

its

mechanical

properties

are

approximately

stiffer

than

those

of

fresh

porcine

brain

tissue

Although

the

constitutive

model

for

brain

tissue

in

the

cerebral

cortex

model

was

not

based

on

human

brain

tissue

the

geometries

of

the

models

were

based

on

the

human

cerebrum

This

assumption

is

expected

to

have

more

effect

on

the

absolute

equivalent

stress

than

on

the

relative

equivalent

stress

which

is

dominated

by

the

heterogeneities

of

the

model

Furthermore

no

distinction

between

the

mechanical

properties

of

white

and

gray

matter

was

made

so

that

the

material

properties

of

the

cerebral

cortex

which

consists

of

gray

matter

were

based

on

experiments

on

white

matter

as

well

In

their

results

Prange

et

al.

found

differences

between

the

material

properties

of

the

corpus

callosum

i.e.

the

white

matter

that

connects

the

two

cerebral

hemispheres

and

the

cerebral

cortex

but

not

between

the

corona

radiata

i.e.

the

white

matter

that

lies

inferior

to

the

cerebral

cortex

and

the

cerebral

cortex

Nevertheless

in

several

other

studies

of

head

and

brain

models

different

material

properties

were

used

for

gray

and

white

matter

based

on

the

assumption

that

white

matter

was

more

fibrous

than

gray

matter

Therefore

simulations

of

the

cerebral

cortex

model

with

shear

moduli

for

gray

matter

ranging

from

to

with

respect

to

the

shear

moduli

white

matter

were

conducted

as

well

The

results

of

these

simulations

indicated

that

the

material

properties

had

an

effect

on

the

magnitude

of

the

equivalent

stress

but

not

on

the

regions

in

which

the

peak

equivalent

stress

was

observed

The

equivalent

stress

of

the

heterogeneous

model

relative

to

the

homogeneous

model

was

hardly

affected

by

the

different

material

properties

In

this

model

the

meninges

and

the

blood

vessels

were

considered

to

have

no

mechanical

influence

on

the

cerebral

cortex

for

the

used

loading

conditions

Although

Jin

et

al.

suggested

that

the

pia-arachnoid

complex

can

have

a

mechanical

influence

on

the

brain

tissue

during

an

impact

it

is

still

not

clear

if

it

would

affect

the

influence

due

to

the

gyrification

of

the

cerebral

cortex

In

a

study

performed

by

Ho

and

Kleiven

it

was

found

that

the

vasculature

of

the

brain

can

be

neglected

as

far

as

the

mechanical

influences

are

concerned

in

a

head

model

not

containing

the

gyrification

of

the

cortex

In

order

to

validate

this

model

a

comparison

with

physical

experiments

is

required

However

data

of

physical

experiments

at

a

typical

length

scale

of

this

level

is

rather

limited

Parallel

to

this

study

the

results

of

physical

experiments

in

which

brain

slices

have

been

accelerated

showed

increased

equivalent

strains

near

the

sulci

Furthermore

some

studies

showed

that

angular

accelerations

of

the

head

induce

high

stress

concentrations

in

and

near

the

cerebral

cortex

Another

method

of

validation

can

be

performed

by

comparing

the

results

of

the

model

to

clinically

observed

injury

It

has

been

shown

that

small

cortical

infarcts

exist

in

diffuse

brain

injury

at

the

bottom

of

the

sulci

This

is

in

accordance

with

the

locations

of

the

high

stress

and

strain

regions

in

the

cerebral

cortex

model

The

two

loading

conditions

and

the

different

geometries

resulted

in

different

equivalent

stress

fields

The

simulations

with

loading

condition

A

resulted

in

a

lower

mean

and

maximum

equivalent

stress

compared

to

the

simulations

with

loading

condition

B.

However

relative

to

the

homogeneous

model

it

was

observed

that

the

equivalent

stress

was

almost

independent

of

the

different

loading

conditions

used

in

this

study

The

differences

between

the

several

heterogeneous

geometries

had

more

influence

on

the

relative

mean

and

maximum

equivalent

stress

The

morphologic

heterogeneities

of

the

cerebral

cortex

led

to

an

increase

of

the

maximum

equivalent

stress

by

a

factor

of

about

depending

mostly

on

the

geometry

whereas

the

relative

mean

equivalent

stress

values

of

all

the

geometries

were

and

for

loading

condition

A

and

B

respectively

Furthermore

the

peak

maximum

principal

logarithmic

strain

was

increased

by

a

factor

of

about

due

to

the

morphologic

heterogeneities

of

the

cerebral

cortex

This

is

a

strong

indication

that

predictions

of

brain

injury

obtained

from

head

models

with

a

homogeneous

cerebrum

should

be

interpreted

with

care

To

obtain

a

more

accurate

assessment

of

injury

the

influence

of

the

morphologic

heterogeneities

in

the

cerebral

cortex

should

be

accounted

for

O O B I I O O O O O O O O B I B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O B I O O B I O O O O O O B I O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O

traumatic brain injury
brain tissue
cerebrum
cerebral cortex