Perception

of

limb

orientation

in

the

vertical

plane

depends

on

center

of

mass

rather

than

inertial

eigenvectors

We

performed

two

experiments

to

test

the

hypothesis

that

the

perception

of

limb

orientation

depends

on

inertial

eigenvectors

-LRB-

ei

-RRB-

against

the

alternative

hypothesis

that

it

depends

on

the

center

of

mass

vector

-LRB-

CM

-RRB-

Whereas

ei

constrains

the

dynamic

torques

involved

in

angular

rotation

CM

constrains

the

static

torque

necessary

to

keep

the

limb

aloft

in

the

gravitational

field

Hence

possible

effects

of

ei

and

CM

on

kinesthetic

judgments

must

be

related

to

the

dynamic

and

static

torques

respectively

involved

in

moving

and

positioning

a

limb

In

the

first

experiment

blindfolded

participants

matched

with

upper

arms

supported

the

orientation

of

their

forearms

while

the

forearms

ei

and

CM

were

manipulated

relative

to

the

elbow

The

manipulation

of

the

vector

CM

alone

induced

a

matching

bias

as

did

the

combined

manipulation

of

ei

and

CM

whereas

the

manipulation

of

ei

alone

did

not

In

the

second

experiment

participants

positioned

their

unseen

and

unsupported

right

arm

at

an

indicated

spatial

configuration

while

ei

and

CM

of

the

right

forearm

were

manipulated

as

in

Experiment

As

in

the

first

experiment

forearm

positioning

was

affected

by

the

independent

manipulation

of

CM

and

the

combined

manipulation

of

ei

and

CM

but

not

by

the

independent

variation

of

ei

Moreover

of

the

manipulations

affected

upper

arm

positioning

These

results

refute

the

claim

that

the

perception

of

limb

orientation

-LRB-

in

the

vertical

plane

-RRB-

is

based

on

ei

and

demonstrate

for

the

first

time

the

implication

of

a

limb

segment

's

CM

in

the

perception

of

its

orientation

Introduction

How

do

we

perceive

where

our

limbs

are

in

space

without

having

to

look

at

them

continuously

Although

this

question

is

fundamental

to

the

understanding

of

both

perception

and

motor

control

it

is

far

from

resolved

Investigations

of

the

neurophysiological

basis

of

kinesthesis

have

produced

many

relevant

findings

but

they

have

also

highlighted

the

need

for

psychophysical

concepts

that

pertain

to

the

role

of

mechanical

in

particular

kinetic

information

in

kinesthetic

experiences

as

is

illustrated

by

a

brief

overview

of

the

pertinent

literature

Given

that

the

relative

position

of

limb

segments

is

specific

to

a

particular

set

of

joint

angles

the

neurophysiological

basis

of

kinesthesis

has

been

sought

primarily

in

neural

signals

providing

geometric

information

related

to

joint

angles

In

principle

such

signals

may

come

from

mechanoreceptors

in

joint

skin

and

muscle

The

role

of

joint

receptors

proved

to

be

modest

at

best

as

they

were

found

to

be

mostly

silent

in

the

mid-range

of

motion

and

to

fire

only

at

the

extremes

of

a

joint

's

movement

range

-LRB-

e.g.

Burgess

and

Clark

Clark

and

Burgess

Grigg

and

Greenspan

-RRB-

Similarly

no

prominent

role

of

cutaneous

receptors

in

signaling

joint

angles

was

established

-LRB-

Gandevia

-RRB-

leaving

muscle

receptors

as

the

primary

candidates

for

signaling

limb

geometry

Although

skeletal

muscles

contain

both

Golgi

tendon

organs

and

muscle

spindles

only

the

latter

are

currently

thought

to

reliably

signal

muscle

length

and

hence

inform

about

limb

geometry

-LRB-

Kandel

et

al.

-RRB-

Goodwin

and

colleagues

firmly

established

this

view

by

showing

that

tendon

vibrations

targeted

at

primary

and

secondary

spindle

endings

induced

marked

illusory

joint

displacements

-LRB-

e.g.

Goodwin

et

al.

b

-RRB-

More

recently

Ribot-Ciscar

et

al.

-LRB-

-RRB-

showed

that

the

exclusive

reliance

on

primary

muscle

spindle

afferents

may

in

theory

lead

to

the

accurate

perception

of

joint

angle

It

is

thus

beyond

doubt

that

geometrical

information

pertaining

to

joint

angles

primarily

signaled

by

muscle

spindles

plays

an

important

role

in

kinesthesis

Yet

it

has

become

apparent

that

our

sense

of

limb

position

and

movement

is

not

based

exclusively

on

geometric

information

Signals

of

a

kinetic

nature

-LRB-

i.e.

relating

to

force

or

effort

-RRB-

which

presumably

can

not

be

conveyed

by

muscle

spindles

probably

provide

positional

information

as

well

Rymer

and

D'Almeida

-LRB-

-RRB-

demonstrated

such

kinetic

influences

by

showing

that

errors

in

perceived

finger

orientation

occur

upon

the

generation

of

isometric

contractions

They

attributed

this

effect

to

a

central

mechanism

receiving

muscle

force

information

from

Golgi

tendon

organs

Results

of

Worringham

and

Stelmach

-LRB-

-RRB-

suggested

that

limb

kinesthesis

depends

on

gravitational

torque

-LRB-

Ng

-RRB-

which

would

also

imply

that

it

has

a

kinetic

component

The

significance

of

information

related

to

muscular

force

or

effort

was

amplified

further

by

recent

findings

indicating

a

kinesthetic

effect

of

muscular

effort

-LRB-

Proske

et

al.

Walsh

et

al.

Winter

et

al.

-RRB-

motor

outflow

signals

-LRB-

Gandevia

et

al.

-RRB-

and

muscle

activity

-LRB-

Prud

homme

and

Kalaska

-RRB-

Given

the

accumulating

evidence

that

signals

related

to

muscular

force

or

effort

are

involved

in

kinesthesis

one

may

wonder

how

information

relevant

to

kinesthetis

is

extracted

from

such

kinetic

signals

This

issue

is

far

from

trivial

because

unlike

muscle

spindle

activity

tendon

organ

activity

or

motor

outflow

corrolaries

bear

no

direct

relation

to

muscle

length

or

joint

angle

This

fact

may

have

contributed

to

the

now

widespread

view

put

forward

by

McCloskey

-LRB-

-RRB-

that

motor

outflow

corollaries

are

only

used

to

filter

out

spindle

discharges

related

to

changes

in

muscle

activity

so

as

to

obtain

accurate

muscle

length

information

-LRB-

see

Gandevia

-RRB-

Yet

it

is

possible

that

both

afferent

and

efferent

kinetic

signals

contribute

to

kinesthesis

independent

of

muscle

spindle

activity

Information

about

muscular

force

directly

reflects

the

dynamic

and

static

torques

involved

in

actively

moving

or

positioning

a

limb

Through

Newton

's

laws

of

motion

those

torques

are

linked

to

the

limb

's

mass

distribution

in

space

Therefore

a

promising

psychophysical

approach

may

be

to

postulate

that

an

independent

kinetic

foundation

of

kinesthesis

resides

directly

in

specific

characteristics

of

the

limb

's

mass

distribution

Taking

such

an

approach

Pagano

and

colleagues

-LRB-

e.g.

Pagano

and

Turvey

Pagano

et

al.

Garrett

et

al.

-RRB-

hypothesized

that

the

perception

of

a

limb

's

spatial

orientation

depends

on

its

inertial

eigenvectors

-LRB-

ei

-RRB-

which

represent

a

characteristic

of

a

limb

's

mass

distribution

related

to

the

direction

in

which

it

resists

rotation

-LRB-

see

the

appendix

for

a

more

detailed

explanation

of

the

physical

meaning

of

inertial

eigenvectors

-RRB-

Relative

to

a

given

point

in

space

any

rigid

object

has

three

orthogonal

eigenvectors

and

For

a

forearm

rotating

around

the

elbow

and

describe

a

plane

through

the

elbow

orthogonal

to

the

forearm

's

longitudinal

axis

The

axis

of

minimal

resistance

against

rotation

roughly

coincides

with

the

forearm

's

longitudinal

axis

The

possible

kinesthetic

role

of

ei

in

general

and

in

particular

resides

in

the

fact

that

they

reflect

the

forearm

's

spatial

orientation

In

studying

limb

kinesthesis

it

is

essential

to

recognize

that

information

about

ei

is

only

available

when

a

perceiver

actively

rotates

his

or

her

forearm

After

all

ei

is

related

to

the

resistance

against

rotation

and

thus

exclusively

affects

the

dynamic

torques

involved

in

rotation

When

a

forearm

is

held

stationary

the

required

muscular

torque

only

has

a

static

component

and

is

therefore

independent

of

ei

The

so-called

inertial

eigenvector

hypothesis

was

introduced

by

Pagano

and

Turvey

-LRB-

-RRB-

and

corroborated

in

numerous

subsequent

studies

-LRB-

Pagano

et

al.

Garrett

et

al.

Pagano

and

Turvey

Turvey

Pagano

Riley

and

Turvey

Riley

and

Pagano

Bernardin

et

al.

Riley

et

al.

-RRB-

All

pertinent

experiments

adopted

a

similar

method

in

which

a

single

load

was

attached

to

the

limb

at

a

distance

from

its

longitudinal

axis

thereby

breaking

its

coincidence

with

With

the

exception

of

a

recent

study

by

Craig

and

Bourdin

-LRB-

but

see

Riley

and

Pagano

Riley

et

al.

-RRB-

it

was

found

that

the

perception

of

limb

orientation

was

biased

towards

which

was

taken

as

evidence

for

the

hypothesis

in

question

The

studies

by

Pagano

et

al.

-LRB-

-RRB-

and

Garrett

et

al.

-LRB-

-RRB-

are

of

particular

interest

for

the

present

study

because

they

specifically

addressed

the

perception

of

limb

orientation

in

a

vertical

-LRB-

i.e.

gravitational

-RRB-

plane

and

found

that

it

was

affected

by

the

aforementioned

manipulation

of

However

close

scrutiny

of

this

manipulation

reveals

that

an

alternative

explanation

is

possible

The

placement

of

a

single

load

off

the

forearm

's

longitudinal

axis

not

only

introduces

a

rotation

of

the

vector

relative

to

the

elbow

but

also

displaces

the

forearm

's

center

of

mass

Similar

to

we

view

the

center

of

mass

as

a

vector

originating

at

the

elbow

-LRB-

CM

-RRB-

and

its

displacement

as

a

rotation

of

this

vector

Importantly

CM

and

constitute

principally

different

characteristics

of

the

forearm

's

mass

distribution

Whereas

ei

exclusively

affects

the

dynamic

torques

involved

in

limb

rotation

the

vector

CM

exclusively

affects

the

static

gravitational

torque

-LRB-

Ng

-RRB-

A

dependence

of

kinesthesis

on

CM

would

thus

imply

a

fundamentally

different

kinetic

basis

than

a

dependence

on

ei

Yet

the

possibility

that

CM

rather

than

governed

the

results

of

Pagano

et

al.

-LRB-

-RRB-

and

Garrett

et

al.

-LRB-

-RRB-

has

never

been

tested

experimentally

In

order

to

disentangle

the

effects

of

both

variables

and

thus

to

test

the

inertial

eigenvector

hypothesis

against

the

center

of

mass

hypothesis

ei

and

CM

must

be

varied

independently

We

accomplished

such

a

manipulation

and

experimental

test

in

the

experiments

reported

below

Experiment

In

the

first

experiment

we

tested

the

inertial

eigenvector

hypothesis

against

the

center

of

mass

hypothesis

using

a

forearm-matching

task

similar

to

that

employed

by

Pagano

et

al.

-LRB-

-RRB-

and

Garrett

et

al.

-LRB-

-RRB-

The

inertial

eigenvector

hypothesis

predicts

that

variation

in

is

sufficient

to

induce

a

matching

bias

Hence

according

to

this

hypothesis

a

matching

bias

should

occur

in

all

conditions

in

which

is

manipulated

According

to

the

center

of

mass

hypothesis

a

pointing

bias

should

occur

upon

rotation

of

the

vector

CM

irrespective

of

the

orientation

of

In

the

present

experiment

the

mass

distribution

of

the

forearms

was

manipulated

such

that

and

CM

either

varied

independently

or

covaried

-LRB-

as

was

the

case

in

the

experiments

of

Pagano

and

colleagues

-RRB-

thus

allowing

for

a

critical

test

of

the

two

hypotheses

of

interest

Method

Twenty

healthy

participants

-LRB-

female

and

male

all

right-handed

mean

age

years

SD

years

-RRB-

participated

voluntarily

in

the

experiment

They

were

not

familiar

with

the

type

of

experiment

or

the

rationale

behind

it

The

experiment

which

was

conducted

in

accordance

with

the

Declaration

of

Helsinki

was

approved

formally

by

the

ethical

committee

of

our

faculty

and

carried

out

with

the

adequate

understanding

and

written

informed

consent

of

all

participants

Participants

were

blindfolded

and

sat

on

a

stool

with

their

upper

arms

resting

on

a

wooden

surface

They

were

to

match

the

orientation

of

their

unseen

forearms

to

which

carbon

fiber

frames

with

two

brass

loads

were

fixed

in

order

to

achieve

the

desired

orientations

of

and

CM

-LRB-

see

Fig.

-RRB-

Fig.

experimental

setup

of

Experiment

Participants

were

blindfolded

and

sat

on

a

stool

with

their

upper

arms

resting

on

a

wooden

surface

oriented

at

a

angle

with

the

horizontal

Participants

armpits

touched

the

upper

edge

of

the

wooden

surface

and

their

upper

arms

were

positioned

in

parallel

and

flush

with

the

wooden

surface

The

carbon

fiber

frames

used

to

attach

loads

to

the

forearms

-LRB-

see

text

for

a

detailed

description

-RRB-

were

to

remain

in

parallel

vertical

planes

while

forearm

orientation

was

matched

by

flexion

and

extension

of

the

elbows

Two

straws

with

a

length

of

cm

extended

from

the

upper

end

of

the

proximal

crosspieces

preventing

the

loads

from

touching

the

upper

arms

and

marking

the

maximal

allowed

elbow

flexion

The

straws

are

visible

inside

the

dotted

circle

Each

carbon

fiber

frame

consisted

of

a

stem

cm

in

length

and

cm

in

diameter

and

two

parallel

crosspieces

both

cm

in

length

and

cm

in

diameter

that

were

pierced

through

the

stem

at

a

angle

These

crosspieces

were

placed

cm

apart

with

the

most

distal

crosspiece

at

cm

from

the

distal

end

of

the

stem

The

total

mass

of

each

frame

was

g

The

frames

were

fixed

to

the

ventral

side

of

the

forearm

along

its

longitudinal

axis

and

their

distal

tips

protruded

from

the

closed

hand

between

the

ring

finger

and

the

middle

finger

The

crosspieces

were

positioned

at

a

distance

of

and

cm

respectively

from

the

medial

epicondyl

of

the

humerus

A

thin

straw

with

a

length

of

cm

protruded

from

the

upper

part

of

the

proximal

crosspiece

-LRB-

see

Fig.

-RRB-

preventing

the

upper

arm

from

contacting

the

loads

Moreover

by

touching

the

upper

arm

it

signaled

the

smallest

elbow

angle

allowed

in

the

experiment

-LRB-

approximately

-RRB-

Forearm

matching

occurred

in

eight

experimental

conditions

and

a

control

condition

In

the

experimental

conditions

two

cylindrical

brass

loads

were

attached

to

the

frames

to

achieve

the

desired

orientations

of

and

CM

The

experimental

manipulations

are

illustrated

in

Fig.

and

the

exact

masses

and

positions

of

the

loads

in

the

eight

experimental

conditions

are

reported

in

Table

The

magnitude

and

direction

of

rotation

induced

by

the

loads

was

calculated

by

adding

the

loads

inertia

tensors

relative

to

the

elbow

to

that

of

the

unloaded

forearm

-LRB-

using

the

parallel

axis

theorem

-RRB-

and

subsequently

calculating

the

new

orientation

of

and

by

diagonalizing

the

resulting

tensor

In

conditions

and

was

thus

manipulated

toward

flexion

in

one

arm

-LRB-

the

right

arm

in

condition

the

left

arm

in

condition

-RRB-

and

toward

extension

in

the

other

without

manipulating

CM

resulting

in

a

difference

between

the

eigenvectors

of

the

forearms

In

conditions

and

CM

was

manipulated

toward

flexion

in

one

arm

-LRB-

the

right

arm

in

condition

the

left

arm

in

condition

-RRB-

and

toward

extension

in

the

other

without

manipulating

resulting

in

a

CM

difference

between

the

forearms

In

conditions

and

both

and

CM

were

manipulated

such

that

there

was

a

and

CM

difference

between

both

forearms

In

conditions

and

one

arm

remained

unloaded

-LRB-

the

left

arm

in

condition

the

right

arm

in

condition

-RRB-

and

loads

were

attached

to

the

other

arm

in

a

symmetrical

way

i.e.

without

inducing

a

rotation

of

either

or

CM

A

ninth

condition

in

which

both

forearms

remained

unloaded

served

as

control

condition

The

maximal

value

of

Ng

about

the

elbow

was

equal

in

both

arms

in

all

conditions

except

for

conditions

and

which

were

included

to

explicitly

test

for

the

effect

of

Ng

suggested

by

Worringham

and

Stelmach

-LRB-

-RRB-

In

conditions

through

the

placement

of

the

loads

merely

induced

an

asymmetrical

mass

distribution

relative

to

the

forearm

's

longitudinal

axis

Fig.

experimental

manipulations

of

the

vectors

and

CM

CM

is

the

vector

from

the

elbow

joint

to

the

average

position

of

the

-LRB-

loaded

-RRB-

forearm

's

mass

-LRB-

i.e.

the

effective

point

of

origin

of

gravitational

force

-RRB-

The

eigenvector

is

the

axis

through

the

elbow

joint

about

which

the

-LRB-

loaded

-RRB-

forearm

's

rotational

inertia

is

minimal

Panel

a

shows

the

loads

as

they

were

attached

to

one

of

the

forearms

in

conditions

and

-LRB-

in

which

the

other

forearm

remained

unloaded

-RRB-

The

loads

are

equal

in

mass

are

placed

at

equal

but

opposite

distances

from

the

forearm

's

longitudinal

axis

and

have

equal

distances

to

elbow

They

thus

do

not

induce

a

rotation

of

either

CM

or

relative

to

an

unloaded

arm

In

panel

b

-LRB-

conditions

and

-RRB-

the

asymmetrical

load

placement

causes

both

vectors

and

CM

to

be

rotated

towards

the

loads

In

panel

c

-LRB-

conditions

and

-RRB-

the

loads

have

equal

mass

and

are

placed

at

equal

but

opposite

distances

from

the

forearm

's

longitudinal

axis

so

that

no

rotation

of

CM

is

induced

Yet

the

loads

have

different

distances

to

the

elbow

so

that

they

do

induce

a

rotation

of

Panel

c

thus

represents

the

independent

variation

of

Finally

in

panel

d

-LRB-

conditions

and

-RRB-

the

two

loads

are

placed

equidistant

from

the

forearm

's

longitudinal

axis

and

have

different

distances

to

the

elbow

as

in

panel

c

but

now

their

masses

differ

with

the

heaviest

load

being

closest

to

the

elbow

This

leads

to

CM

being

rotated

towards

the

greatest

load

while

still

coincides

with

the

longitudinal

axis

Panel

d

thus

represents

the

independent

variation

of

CMTable

and

positions

of

the

loads

and

corresponding

rotations

of

and

CM

in

the

experimental

conditions

of

experiment

forearmLeft

forearmLoad

-LRB-

g

-RRB-

x

ya

-LRB-

cm

-RRB-

Mass

-LRB-

g

-RRB-

x

y

-LRB-

cm

-RRB-

Mass

-LRB-

g

-RRB-

x

y

-LRB-

cm

-RRB-

Mass

-LRB-

g

-RRB-

x

y

-LRB-

cm

-RRB-

ΔCMc

ax

refers

to

the

distance

of

the

load

's

center

of

mass

from

the

elbow

along

the

arm

's

longitudinal

axis

y

refers

to

the

orthogonal

distance

of

the

load

's

center

of

mass

from

the

arm

's

longitudinal

axis

where

a

positive

-LRB-

negative

-RRB-

distance

indicates

a

position

on

the

radial

-LRB-

ulnar

-RRB-

side

of

the

indicates

the

angle

between

the

smallest

eigenvector

-LRB-

-RRB-

of

the

left

and

the

right

forearm

A

positive

angle

indicates

that

of

the

right

forearm

was

manipulated

towards

elbow

flexion

and

of

the

left

forearm

towards

elbow

extensioncΔCM

indicates

the

angle

between

the

center

of

mass

vector

-LRB-

CM

-RRB-

of

the

left

and

the

right

forearm

A

positive

angle

indicates

that

CM

of

the

right

forearm

was

oriented

towards

elbow

flexion

and

CM

of

the

left

forearm

towards

elbow

extension

Participants

performed

the

nine

conditions

in

nine

corresponding

trial

blocks

Before

each

trial

block

they

assumed

a

position

in

which

one

arm

was

flexed

at

an

elbow

angle

of

which

was

achieved

by

letting

the

tip

of

the

straw

just

touch

the

upper

arm

and

the

other

arm

was

fully

extended

Note

that

in

this

starting

position

a

perceptual

reference

was

ensured

both

in

the

flexed

arm

-LRB-

by

the

straw

-RRB-

and

in

the

fully

extended

arm

-LRB-

by

the

end

of

the

elbow

's

movement

range

-RRB-

preventing

any

drift

effects

over

trials

From

this

position

one

of

the

forearms

-LRB-

the

target

arm

-RRB-

was

moved

towards

the

other

forearm

until

the

experimenter

called

out

stop

The

experimenter

ensured

that

this

stop

signal

was

given

at

a

different

arm

orientation

in

each

trial

The

other

arm

-LRB-

the

matching

arm

-RRB-

was

then

moved

towards

the

target

arm

until

the

participant

perceived

the

orientation

of

the

two

forearms

to

be

identical

At

this

moment

the

participant

stopped

the

movement

and

called

out

ja

-LRB-

yes

-RRB-

After

registering

the

orientation

of

both

forearms

-LRB-

see

below

-RRB-

the

experimenter

instructed

the

participant

to

assume

the

starting

position

for

the

next

trial

The

arm

that

was

flexed

at

the

start

of

the

previous

trial

was

now

extended

and

vice

versa

The

target

arm

was

alternately

the

left

and

the

right

arm

Participants

were

instructed

to

keep

both

arms

and

the

crosspieces

they

enclosed

with

their

hands

in

a

vertical

-LRB-

i.e.

sagittal

-RRB-

plane

at

all

times

Each

trial

block

was

started

with

either

the

left

or

the

right

arm

extended

and

with

either

the

extended

or

the

flexed

arm

as

the

target

arm

The

four

resulting

starting

configurations

were

counterbalanced

across

participants

with

each

individual

participant

starting

all

trial

blocks

from

the

same

assigned

configuration

Each

trial

block

consisted

of

two

series

of

eight

matching

trials

In

one

series

the

extended

arm

was

the

target

arm

and

in

the

other

the

flexed

arm

was

the

target

arm

All

participants

performed

matching

trials

in

total

-LRB-

trial

blocks

trials

per

block

-RRB-

The

duration

of

an

experimental

session

was

approximately

min

Forearm

orientation

was

measured

using

a

active

movement

registration

system

-LRB-

Optotrak

Northern

Digital

Inc.

Waterloo

Canada

-RRB-

which

was

calibrated

using

a

coordinate

frame

with

one

axis

aligned

with

the

gravitational

vertical

and

one

parallel

to

the

horizontal

axis

described

by

participants

elbow

and

shoulder

joints

During

the

experiment

the

position

of

four

infrared

markers

was

registered

two

markers

on

the

distal

tip

of

each

frame

stem

and

two

markers

on

the

horizontal

axes

described

by

the

two

elbow

joints

and

the

two

shoulder

joints

respectively

The

latter

two

markers

were

placed

on

an

adjustable

carbon

fiber

frame

to

the

left

of

the

participants

after

they

assumed

the

correct

starting

position

In

this

starting

position

both

armpits

contacted

the

upper

edge

of

the

wooden

board

which

ensured

that

the

elbow

joints

as

well

as

the

shoulder

joints

described

a

horizontal

axis

The

experimenter

registered

the

position

of

the

four

markers

each

time

a

participant

indicated

that

the

orientation

of

the

forearms

was

matched

For

each

participant

and

for

each

trial

the

angle

of

the

two

elbow

joints

projected

onto

a

sagittal

plane

was

calculated

from

the

position

data

of

the

four

Optotrak

markers

The

elbow

angles

of

both

arms

were

subsequently

averaged

to

obtain

the

angle

around

which

matching

occurred

in

each

trial

To

obtain

the

direction

and

magnitude

of

matching

errors

the

elbow

angle

of

the

right

arm

was

subtracted

from

that

of

the

left

arm

A

positive

matching

error

thus

indicated

that

elbow

angle

was

smallest

in

the

right

arm

that

is

that

the

right

arm

had

a

flexion

bias

relative

to

the

left

arm

Finally

matching

errors

in

the

control

condition

were

subtracted

from

those

in

each

experimental

condition

to

obtain

matching

biases

due

to

the

eight

experimental

manipulations

We

first

examined

the

range

of

elbow

angles

around

which

matching

occurred

in

each

condition

the

pattern

of

matching

errors

within

conditions

and

the

matching

errors

in

the

control

condition

Subsequently

we

analyzed

the

matching

errors

according

to

a

repeated

measures

analysis

of

variance

-LRB-

ANOVA

-RRB-

with

condition

-LRB-

levels

-RRB-

and

repetition

-LRB-

levels

-RRB-

as

within-subject

factors

Finally

we

tested

the

matching

biases

due

to

the

eight

experimental

manipulations

using

one-sample

two-tailed

t

tests

Results

and

discussion

The

average

and

the

range

of

the

elbow

angles

around

which

matching

occurred

in

each

of

the

nine

conditions

was

-LRB-

SD

over

conditions

-RRB-

and

-LRB-

SD

over

conditions

-RRB-

respectively

The

low

standard

deviations

indicate

that

both

the

average

and

the

range

of

matching

angles

only

differed

marginally

between

conditions

Before

turning

to

the

effects

of

our

experimental

manipulations

on

the

matching

errors

we

first

examined

matching

errors

within

conditions

Participants

showed

a

significant

overshoot

of

the

target

arm

's

orientation

with

the

matching

arm

-LRB-

t

-LRB-

-RRB-

P

η2

-RRB-

which

is

in

keeping

with

Worringham

and

Stelmach

-LRB-

-RRB-

but

not

with

Pagano

et

al.

-LRB-

-RRB-

who

did

not

find

such

an

effect

Matching

errors

of

a

representative

participant

in

the

control

condition

are

shown

in

Fig.

The

alternating

pattern

of

errors

in

this

figure

is

a

manifestation

of

the

aforementioned

overshoot

effect

After

all

the

left

and

the

right

arm

alternatingly

assumed

a

flexed

starting

position

so

that

an

overshoot

of

the

target

arm

would

alternatingly

lead

to

a

positive

and

a

negative

matching

bias

In

this

way

matching

biases

due

to

overshoot

canceled

out

after

averaging

over

trials

Accordingly

in

the

control

condition

matching

errors

did

not

deviate

significantly

from

zero

-LRB-

P

-RRB-

after

averaging

over

trials

-LRB-

mean

SD

across

participants

-RRB-

However

partly

due

to

a

tendency

to

overshoot

the

target

arm

error

variability

across

trials

was

considerable

-LRB-

SD

see

Fig.

-RRB-

This

trial-to-trial

variability

is

comparable

to

that

reported

by

Soechting

-LRB-

-RRB-

Fig.

errors

of

a

representative

participant

in

the

control

condition

of

Experiment

in

which

no

loads

were

attached

to

the

forearms

The

alternating

pattern

of

errors

over

trials

reflects

a

tendency

to

overshoot

the

target

arm

with

the

matching

arm

The

ANOVA

performed

on

the

matching

errors

in

all

conditions

revealed

that

they

were

affected

significantly

by

condition

-LRB-

F

-LRB-

-RRB-

P

-RRB-

but

neither

by

repetition

-LRB-

P

-RRB-

nor

by

the

condition

repetition

interaction

-LRB-

P

-RRB-

Figure

shows

the

average

matching

biases

-LRB-

with

confidence

intervals

-RRB-

due

to

the

eight

experimental

manipulations

No

significant

effect

of

was

found

-LRB-

P

and

P

in

conditions

and

respectively

-RRB-

In

contrast

the

difference

in

CM

orientation

resulted

in

significant

matching

biases

of

in

condition

-LRB-

t

-LRB-

-RRB-

P

η2

-RRB-

and

of

in

condition

-LRB-

t

-LRB-

-RRB-

P

η2

-RRB-

The

combined

manipulations

of

and

CM

had

similar

effects

A

difference

of

and

CM

orientation

between

the

arms

resulted

in

significant

matching

biases

of

in

condition

-LRB-

t

-LRB-

-RRB-

P

η2

-RRB-

and

of

in

condition

-LRB-

t

-LRB-

-RRB-

P

η2

-RRB-

A

negative

-LRB-

positive

-RRB-

matching

bias

implied

that

the

flexion

of

the

right

arm

relative

to

the

left

arm

was

smaller

-LRB-

greater

-RRB-

than

in

the

control

condition

The

direction

of

the

significant

effects

of

conditions

through

was

consistent

with

the

hypothesis

that

perceived

orientation

would

be

biased

towards

CM

Finally

loading

one

of

the

arms

symmetrically

-LRB-

i.e.

without

rotating

either

or

CM

-RRB-

while

leaving

the

other

arm

unloaded

did

not

induce

significant

matching

biases

relative

to

the

control

condition

-LRB-

t

-LRB-

-RRB-

P

η2

for

condition

t

-LRB-

-RRB-

P

η2

for

condition

-RRB-

although

there

was

a

trend

towards

an

extension

bias

in

the

loaded

arm

-LRB-

see

Fig.

-RRB-

Such

an

extension

bias

would

be

consistent

with

the

direction

of

the

effect

of

Ng

-LRB-

or

muscular

effort

-RRB-

reported

in

the

literature

-LRB-

Worringham

and

Stelmach

Proske

et

al.

Walsh

et

al.

Winter

et

al.

-RRB-

More

importantly

the

significant

effect

of

CM

in

conditions

and

together

with

the

absence

of

a

significant

effect

of

in

conditions

and

indicates

that

the

results

of

Pagano

et

al.

-LRB-

-RRB-

and

Garrett

et

al.

-LRB-

-RRB-

should

be

interpreted

in

retrospect

as

a

sensitivity

to

CM

rather

than

ei

Fig.

matching

biases

relative

to

the

control

condition

in

the

different

manipulation

conditions

of

Experiment

A

positive

bias

implies

that

the

flexion

of

the

right

arm

relative

to

the

left

arm

was

greater

in

that

manipulation

condition

than

in

the

control

condition

Error

bars

show

the

confidence

interval

of

the

matching

biases

Only

was

rotated

in

conditions

and

only

CM

was

rotated

in

conditions

and

and

and

CM

were

rotated

together

in

conditions

and

In

conditions

and

rotations

were

toward

flexion

in

the

right

arm

and

toward

extension

in

the

left

arm

-LRB-

and

vice

versa

in

conditions

and

-RRB-

In

conditions

and

and

CM

were

not

rotated

only

Ng

differed

between

the

two

forearms

in

condition

-LRB-

-RRB-

it

was

greater

in

the

right

-LRB-

left

-RRB-

arm

Given

that

people

can

perceive

the

orientation

of

their

limbs

in

space

and

not

only

relative

to

each

other

one

may

wonder

whether

the

present

results

favoring

the

center

of

mass

hypothesis

generalize

to

the

perception

of

the

orientation

of

an

unsupported

arm

in

extrinsic

space

In

this

situation

loading

the

forearm

not

only

affects

the

torques

around

the

elbow

joint

as

was

the

case

in

the

present

experiment

but

also

the

torques

around

the

shoulder

joint

In

principle

this

could

restrict

or

alter

the

implication

of

CM

in

the

perception

of

limb

orientation

These

possibilities

were

investigated

in

Experiment

Experiment

In

the

second

experiment

we

manipulated

and/or

CM

of

the

forearm

in

the

same

manner

as

in

Experiment

but

this

time

to

test

their

effects

on

the

perception

of

the

orientation

of

an

unsupported

arm

in

a

vertical

plane

Based

on

the

results

of

Experiment

we

hypothesized

that

perceived

forearm

orientation

would

be

affected

by

CM

and

not

by

We

further

hypothesized

that

the

manipulations

would

not

affect

the

perceived

orientation

of

the

upper

arm

even

though

we

recognized

that

loading

the

forearm

does

affect

the

torque

at

the

shoulder

when

the

upper

arm

is

not

supported

The

latter

hypothesis

was

motivated

from

the

insight

that

the

shoulder

torque

can

only

be

informative

about

the

orientation

of

the

upper

arm

when

the

elbow

torque

is

taken

into

account

as

well

We

reasoned

that

manipulation

of

the

forearm

's

CM

would

induce

torques

at

the

elbow

indicating

an

altered

forearm

orientation

Given

that

the

corresponding

change

in

the

torque

pattern

at

the

shoulder

is

consistent

with

this

change

in

forearm

orientation

we

further

reasoned

that

it

too

would

indicate

an

altered

forearm

orientation

rather

than

an

altered

upper

arm

orientation

Method

Twenty

healthy

participants

-LRB-

female

and

male

all

right-handed

mean

age

years

SD

years

-RRB-

participated

voluntarily

in

the

experiment

They

were

not

familiar

with

the

type

of

experiment

or

the

rationale

behind

it

The

experiment

which

was

conducted

in

accordance

with

the

Declaration

of

Helsinki

was

approved

formally

by

the

ethical

committee

of

our

faculty

and

carried

out

with

the

adequate

understanding

and

written

informed

consent

of

all

participants

The

experimental

setup

is

shown

in

Fig.

Participants

were

seated

on

a

stool

besides

a

vertical

wooden

board

Their

right

arm

and

shoulder

were

placed

through

a

circular

hole

in

the

board

between

two

overlapping

pieces

of

lycra

cloth

that

prevented

them

from

looking

through

the

hole

to

the

other

side

of

the

board

Participants

were

wearing

a

T-shirt

of

which

the

right

sleeve

was

rolled

up

to

just

above

the

acromion

to

allow

the

placement

of

a

marker

on

the

shoulder

-LRB-

see

below

-RRB-

The

stool

was

adjusted

such

that

the

projection

of

the

forearm

on

the

vertical

plane

could

coincide

with

line

segments

through

and

that

of

the

upper

arm

with

line

segment

The

experimental

task

consisted

of

matching

the

orientation

of

the

unseen

forearm

with

line

segment

or

while

maintaining

the

upper

arm

parallel

to

line

segment

Line

segments

and

were

oriented

at

angles

of

and

respectively

relative

to

horizontal

Line

segment

was

oriented

at

an

angle

of

relative

to

horizontal

which

corresponded

to

the

orientation

of

the

upper

arm

support

in

Experiment

Brass

weights

were

attached

to

the

forearm

by

means

of

a

carbon

fiber

frame

as

in

Experiment

to

achieve

the

desired

orientations

of

the

vectors

and

CM

-LRB-

see

Fig.

-RRB-

The

straw

used

in

Experiment

to

prevent

arm

orientations

smaller

than

about

was

not

used

in

the

present

experiment

because

the

risk

that

loads

would

contact

the

upper

arm

was

much

smaller

than

in

Experiment

Fig.

experimental

setup

of

Experiment

Participants

sat

on

a

stool

besides

a

vertical

wooden

board

Their

right

arm

and

shoulder

were

placed

through

a

circular

hole

in

the

board

between

two

overlapping

pieces

of

lycra

cloth

Participants

were

wearing

a

T-shirt

of

which

the

right

sleeve

was

rolled

up

to

uncover

the

shoulder

The

stool

was

adjusted

such

that

the

projection

of

the

right

forearm

on

the

vertical

plane

could

coincide

with

line

segments

and

-LRB-

and

relative

to

horizontal

respectively

-RRB-

and

the

projection

of

the

upper

arm

with

line

segment

-LRB-

relative

to

horizontal

-RRB-

The

experimental

task

consisted

of

matching

the

orientation

of

the

unseen

forearm

alternately

with

line

segments

and

while

maintaining

the

unsupported

upper

arm

parallel

to

line

segment

The

carbon

fiber

frame

used

to

attach

loads

to

the

forearm

-LRB-

see

text

for

a

detailed

description

-RRB-

was

to

remain

parallel

to

the

board

at

all

times

Arm

positioning

was

required

in

seven

experimental

conditions

and

a

control

condition

Load

placements

in

the

experimental

conditions

were

equal

to

those

in

experiment

The

exact

masses

and

positions

of

the

loads

can

thus

be

found

in

the

five

leftmost

columns

of

Table

-LRB-

i.e.

those

referring

to

the

right

arm

-RRB-

In

conditions

and

was

independently

manipulated

by

towards

extension

and

towards

flexion

respectively

resulting

in

a

difference

in

orientation

between

the

two

conditions

A

difference

in

CM

orientation

was

achieved

between

conditions

and

and

a

difference

in

the

orientation

of

both

and

CM

was

achieved

between

conditions

and

In

condition

loads

were

attached

to

the

forearm

in

a

symmetrical

way

i.e.

without

inducing

a

rotation

of

either

or

CM

An

eighth

condition

in

which

the

forearm

remained

unloaded

served

as

control

condition

The

eight

conditions

were

performed

in

eight

corresponding

trial

blocks

Before

each

trial

block

participants

assumed

a

position

in

which

the

upper

arm

was

oriented

parallel

to

line

segment

and

the

arm

was

either

fully

flexed

or

fully

extended

-LRB-

counterbalanced

across

participants

-RRB-

The

experimenter

then

called

out

one

of

the

numbers

through

to

indicate

the

target

line

segment

for

the

forearm

upon

which

the

participant

rotated

his

or

her

forearm

around

the

elbow

towards

the

target

line

segment

Participants

were

instructed

to

stop

moving

the

arm

and

push

a

button

with

the

left

hand

when

they

perceived

their

forearm

to

be

parallel

to

the

target

line

segment

and

their

upper

arm

to

be

parallel

to

line

segment

If

the

arm

was

initially

fully

flexed

-LRB-

extended

-RRB-

participants

subsequently

fully

extended

-LRB-

flexed

-RRB-

their

arm

The

experimenter

then

called

out

a

new

target

line

segment

and

the

forearm

was

again

rotated

about

the

elbow

-LRB-

albeit

in

opposite

direction

-RRB-

to

match

the

orientation

of

the

indicated

line

segment

Participants

thus

alternated

between

full

elbow

flexion

and

full

elbow

extension

and

assumed

the

instructed

arm

configuration

as

a

pause

in

each

elbow

flexion

and

extension

movement

They

were

instructed

to

keep

the

crosspieces

they

enclosed

with

their

right

hand

parallel

to

the

wooden

board

at

all

times

In

each

trial

block

participants

matched

the

orientation

of

their

forearm

with

each

of

the

three

target

line

segments

four

times

resulting

in

a

total

of

trials

per

block

Throughout

each

trial

block

the

upper

arm

was

to

remain

parallel

to

line

segment

All

participants

thus

performed

a

total

of

matching

trials

-LRB-

trial

blocks

trials

per

block

-RRB-

The

duration

of

an

experimental

session

was

approximately

min

The

configuration

of

the

arm

was

measured

using

Optotrak

The

position

of

six

infrared

markers

was

continuously

registered

at

Hz

during

each

trial

block

a

marker

on

the

tip

of

the

carbon

fiber

frame

-LRB-

marker

-RRB-

a

marker

on

either

side

on

the

distal

crosspiece

-LRB-

markers

and

-RRB-

a

marker

on

the

lateral

epicondyl

of

the

humerus

-LRB-

marker

-RRB-

a

marker

just

below

the

acromion

on

the

deltoid

muscle

-LRB-

marker

-RRB-

and

finally

a

marker

-LRB-

marker

-RRB-

connected

to

the

button

in

participants

left

hand

The

latter

marker

only

emitted

infrared

light

when

the

button

was

pushed

For

each

participant

and

for

each

trial

the

orientation

of

the

upper

arm

and

forearm

was

calculated

from

the

position

data

of

markers

and

The

target

orientations

of

forearm

-LRB-

or

relative

to

horizontal

-RRB-

and

upper

arm

-LRB-

relative

to

horizontal

-RRB-

were

subtracted

from

the

actual

orientations

that

forearm

and

upper

arm

had

at

each

moment

the

button

was

pushed

Errors

in

forearm

and

upper

arm

orientation

were

analyzed

according

to

a

repeated

measures

analysis

of

variance

-LRB-

ANOVA

-RRB-

For

forearm

orientation

errors

we

analyzed

condition

-LRB-

levels

-RRB-

target

-LRB-

levels

corresponding

to

line

segments

and

see

Fig.

-RRB-

and

repetition

-LRB-

levels

-RRB-

as

within-subject

factors

For

errors

in

upper

arm

orientation

we

analyzed

only

the

factors

condition

and

repetition

The

difference

in

positioning

errors

between

conditions

and

-LRB-

manipulation

-RRB-

and

-LRB-

CM

manipulation

-RRB-

and

-LRB-

combined

and

CM

manipulation

-RRB-

and

and

-LRB-

Ng

manipulation

without

and

CM

rotation

-RRB-

collapsed

over

targets

were

subsequently

compared

using

paired-samples

two-tailed

t

tests

Note

that

in

the

present

experiment

four

t

tests

rather

than

eight

-LRB-

as

in

Experiment

-RRB-

sufficed

because

only

one

arm

was

manipulated

rather

than

two

Results

and

discussion

The

average

error

in

aligning

the

forearm

with

line

segments

and

was

in

upward

direction

The

ANOVA

performed

on

these

errors

revealed

that

they

were

affected

significantly

by

condition

-LRB-

F

-LRB-

-RRB-

P

-RRB-

and

target

-LRB-

F

-LRB-

-RRB-

P

-RRB-

but

not

by

repetition

-LRB-

P

-RRB-

The

target

effect

indicated

that

a

lower

line

segment

was

associated

with

smaller

upward

forearm

positioning

errors

than

a

higher

line

segment

of

the

two-way

interactions

was

significant

-LRB-

all

P

's

-RRB-

whereas

the

three-way

interaction

just

reached

significance

-LRB-

F

-LRB-

-RRB-

P

-RRB-

As

the

latter

effect

had

a

marginal

effect

size

and

had

no

readily

apparent

origin

we

abstained

from

seeking

an

account

for

it

The

results

of

the

paired

t

tests

performed

on

forearm

positioning

errors

are

shown

in

Fig.

No

significant

effect

of

adding

mass

in

a

symmetrical

configuration

was

found

-LRB-

P

-RRB-

The

effect

of

was

also

non-significant

-LRB-

P

-RRB-

In

contrast

CM

rotation

significantly

affected

forearm

orientation

-LRB-

t

-LRB-

-RRB-

P

η2

-RRB-

as

did

rotation

of

and

CM

together

-LRB-

t

-LRB-

-RRB-

P

η2

-RRB-

A

difference

of

CM

orientation

alone

was

accompanied

by

a

difference

in

forearm

orientation

A

difference

of

both

and

CM

orientation

corresponded

to

a

difference

in

forearm

orientation

As

expected

a

more

downward

-LRB-

upward

-RRB-

orientation

of

the

forearm

's

CM

always

accompanied

a

more

upward

-LRB-

downward

-RRB-

forearm

orientation

Fig.

in

forearm

orientation

between

conditions

and

-LRB-

manipulation

-RRB-

and

-LRB-

CM

manipulation

-RRB-

and

-LRB-

combined

and

CM

manipulation

-RRB-

and

and

-LRB-

Ng

manipulation

-RRB-

in

Experiment

In

conditions

and

-LRB-

and

-RRB-

and/or

CM

were

manipulated

downward

-LRB-

upward

-RRB-

In

condition

in

which

loads

were

attached

to

the

frame

symmetrically

Ng

was

larger

than

in

condition

in

which

no

loads

were

attached

to

the

frame

For

and/or

CM

manipulation

-LRB-

three

leftmost

bars

-RRB-

a

positive

difference

indicates

that

downward

manipulation

was

associated

with

a

more

upward

forearm

orientation

For

Ng

manipulation

-LRB-

rightmost

bar

-RRB-

a

negative

difference

indicates

that

a

greater

Ng

was

associated

with

a

more

downward

forearm

orientation

Error

bars

show

the

confidence

interval

of

the

orientation

differences

The

average

error

in

aligning

the

upper

arm

with

line

segment

was

in

downward

direction

The

ANOVA

performed

on

these

errors

revealed

that

they

were

only

significantly

affected

by

repetition

-LRB-

F

-LRB-

-RRB-

P

-RRB-

The

main

effect

of

condition

and

the

condition

repetition

interaction

just

failed

to

reach

significance

-LRB-

P

and

P

respectively

-RRB-

The

paired

t

tests

revealed

that

neither

CM

rotation

nor

rotation

significantly

affected

upper

arm

orientation

errors

-LRB-

both

P

's

-RRB-

The

effect

of

symmetrical

mass

addition

was

also

non-significant

-LRB-

P

-RRB-

Finally

no

effect

of

the

combined

and

CM

manipulation

was

revealed

albeit

that

this

effect

approached

significance

-LRB-

P

-RRB-

In

sum

forearm

orientation

was

affected

in

a

very

similar

way

as

in

the

matching

task

of

Experiment

whereas

the

unsupported

upper

arm

was

not

affected

or

only

marginally

at

best

by

the

manipulation

of

and/or

CM

The

results

thus

corroborate

both

hypotheses

forwarded

in

the

introduction

to

the

present

experiment

General

discussion

With

the

overarching

aim

to

uncover

the

kinetic

foundation

of

kinesthesis

we

tested

the

inertial

eigenvector

hypothesis

against

the

alternative

hypothesis

that

the

perception

of

limb

orientation

in

the

vertical

plane

depends

on

CM

To

this

end

two

experiments

were

conducted

one

in

which

the

orientations

of

the

forearms

had

to

be

matched

-LRB-

Experiment

-RRB-

and

one

in

which

the

orientation

of

a

single

arm

had

to

be

matched

to

an

external

reference

configuration

-LRB-

Experiment

-RRB-

The

results

of

both

experiments

supported

the

center

of

mass

hypothesis

and

were

inconsistent

with

the

inertial

eigenvector

hypothesis

Experiment

revealed

that

the

results

of

Pagano

et

al.

-LRB-

-RRB-

and

Garrett

et

al.

-LRB-

-RRB-

should

be

interpreted

in

retrospect

as

a

sensitivity

to

CM

rather

than

ei

Experiment

generalized

the

results

of

Experiment

for

forearm

matching

with

the

upper

arm

supported

to

orienting

a

single

unsupported

limb

with

respect

to

extrinsic

space

In

particular

the

results

of

Experiment

indicated

that

forearm

manipulation

in

a

vertical

plane

shifted

perceived

forearm

orientation

in

that

plane

without

causing

a

significant

shift

in

the

perceived

orientation

of

the

upper

arm

The

combined

results

of

Experiments

and

raise

the

crucial

question

how

CM

might

mediate

limb

kinesthesis

We

address

this

question

at

two

levels

first

extensively

in

terms

of

the

torques

involved

and

then

briefly

and

more

tentatively

in

terms

of

possible

neurophysiological

mechanisms

In

both

experiments

placing

mass

symmetrically

-LRB-

see

Fig.

-RRB-

had

no

significant

effect

on

the

perception

of

forearm

orientation

but

did

show

a

trend

towards

an

extension

bias

in

the

heavier

arm

It

may

be

that

adding

mass

symmetrically

only

had

a

small

effect

which

could

explain

the

inconsistency

of

previous

findings

in

this

regard

In

particular

whereas

the

results

of

Worringham

and

Stelmach

-LRB-

-RRB-

indicate

an

effect

of

symmetrical

mass

placement

Soechting

-LRB-

-RRB-

as

well

as

Darling

and

Hondzinski

-LRB-

-RRB-

failed

to

find

such

an

effect

More

important

for

the

present

discussion

is

the

suggestion

in

the

latter

studies

that

Ng

does

not

play

a

significant

role

in

limb

kinesthesis

This

suggestion

stands

in

stark

contrast

with

the

marked

effects

of

CM

found

in

the

present

experiments

which

necessarily

imply

that

Ng

plays

a

role

in

limb

kinesthesis

albeit

in

a

different

manner

than

considered

previously

After

all

as

we

already

noted

in

the

introduction

Ng

is

the

only

detectable

variable

affected

by

CM

rotation

So

how

does

CM

affect

Ng

and

how

is

this

different

from

the

Ng

manipulation

in

previous

studies

and

our

conditions

with

symmetrical

mass

addition

In

an

unloaded

arm

Ng

is

a

sinusoid

function

of

arm

inclination

that

reaches

its

maximum

at

a

horizontal

arm

orientation

and

becomes

zero

when

the

arm

is

vertical

-LRB-

see

solid

gray

curve

in

Fig.

-RRB-

Adding

loads

symmetrically

-LRB-

as

shown

in

Fig.

-RRB-

may

be

viewed

as

a

scaling

of

this

relationship

That

is

it

increases

Ng

at

each

inclination

angle

by

a

constant

factor

so

that

the

maximum

-LRB-

minimum

-RRB-

of

Ng

still

occurs

at

a

horizontal

-LRB-

vertical

-RRB-

arm

orientation

-LRB-

see

the

dotted

black

curve

in

Fig.

-RRB-

Yet

a

rotation

of

CM

by

asymmetric

mass

addition

-LRB-

as

shown

in

Fig.

d

-RRB-

not

only

scales

but

also

horizontally

shifts

this

relationship

so

that

the

maximum

of

Ng

no

longer

occurs

at

a

horizontal

arm

orientation

-LRB-

see

the

solid

black

curve

in

Fig.

-RRB-

Hence

this

horizontal

shift

reflects

the

rotation

of

the

vector

CM

One

may

therefore

conclude

that

Ng

plays

an

indirect

role

in

the

perception

of

limb

orientation

namely

as

a

mediator

of

CM

orientation

rather

than

Ng

magnitude

itself

being

informative

about

limb

orientation

Fig.

depiction

of

the

relationship

between

Ng

and

arm

inclination

angle

-LRB-

i.e.

the

angle

of

the

arm

's

longitudinal

axis

with

the

horizontal

-RRB-

in

an

unloaded

arm

-LRB-

gray

solid

curve

-RRB-

a

symmetrically

loaded

arm

-LRB-

black

dotted

curve

-RRB-

and

an

asymetrically

loaded

arm

in

which

CM

is

rotated

-LRB-

black

solid

curve

-RRB-

Whereas

symmetrical

mass

addition

only

changes

the

scaling

of

the

relationship

CM

rotation

also

induces

a

horizontal

shift

We

propose

that

the

latter

shift

governs

the

sensitivity

to

CM

demonstrated

in

the

present

study

In

a

vertical

plane

the

perception

of

limb

orientation

relative

to

extrinsic

coordinates

-LRB-

e.g.

the

gravitational

vertical

-RRB-

has

often

been

found

to

be

more

accurate

than

perception

with

respect

to

intrinsic

coordinates

-LRB-

e.g.

joint

angle

or

the

trunk

and

head-longitudinal

axes

Soechting

Worringham

and

Stelmach

Worringham

et

al.

Darling

Darling

and

Hondzinski

-RRB-

It

follows

from

the

present

results

that

the

use

of

extrinsic

coordinates

in

limb

kinesthesis

may

substantially

benefit

from

CM-related

information

conveyed

by

a

horizontal

shift

of

Ng

as

a

function

of

arm

inclination

which

could

explain

this

higher

accuracy

in

extrinsic

coordinates

The

issue

of

extrinsic

versus

intrinsic

coordinate

systems

is

also

a

relevant

dimension

when

comparing

the

center

of

mass

hypothesis

with

the

inertial

eigenvector

hypothesis

Unlike

CM

ei

can

not

aid

the

perception

of

limb

orientation

in

extrinsic

earth-fixed

coordinates

After

all

as

we

noted

in

the

introduction

the

possible

perceptual

role

of

ei

resides

exclusively

in

its

effect

on

the

dynamic

torques

involved

in

limb

rotation

which

are

independent

of

a

limb

's

orientation

in

extrinsic

space

Hence

the

perception

of

limb

orientation

through

the

detection

of

inertial

eigenvectors

necessarily

implies

an

intrinsic

coordinate

system

similar

to

that

involved

in

the

detection

of

muscle

length

or

joint

angle

This

important

point

was

overlooked

by

Garrett

et

al.

-LRB-

-RRB-

who

found

that

their

manipulation

of

ei

-LRB-

and

implicitly

CM

-RRB-

affected

the

perception

of

forearm

orientation

relative

to

the

gravitational

vertical

and

interpreted

this

as

an

effect

of

ei

It

follows

from

the

preceding

argument

that

this

interpretation

was

invalid

because

ei

being

gravity

independent

can

not

convey

such

information

Hence

irrespective

of

the

present

empirical

evidence

Garrett

et

al.

-LRB-

-RRB-

could

have

attributed

their

findings

to

gravity-dependent

information

Because

the

experimental

tasks

in

the

present

study

allow

for

the

use

of

extrinsic

as

well

as

intrinsic

axes

the

apparent

dominance

of

CM

over

ei

can

not

be

explained

in

terms

of

their

respective

coordinate

systems

So

what

did

underlie

the

difference

in

perceptual

effect

between

ei

and

CM

in

the

present

experiments

The

answer

may

reside

in

their

respective

signal-to-noise

ratios

or

saliences

-LRB-

cf.

van

de

Langenberg

et

al.

-RRB-

Recall

that

information

about

ei

is

only

reflected

in

the

dynamic

torques

involved

in

active

limb

movement

In

the

present

experiments

as

well

as

in

Pagano

et

al.

-LRB-

-RRB-

and

Garrett

et

al.

-LRB-

-RRB-

the

arms

were

moved

at

a

relatively

low

angular

velocity

implying

that

the

contribution

of

dynamic

torques

to

the

muscular

tension

was

small

relative

to

the

static

torque

Ng

It

follows

that

the

salience

of

ei

must

have

been

low

relative

to

that

of

CM

which

exclusively

affects

Ng

In

general

one

can

say

that

during

slow

movements

or

stationary

postures

the

salience

of

CM

will

be

superior

to

that

of

ei

During

fast

movements

the

salience

of

ei

will

increase

at

the

cost

of

the

salience

of

CM

which

leaves

open

the

possibility

that

the

perception

of

arm

orientation

in

fast

movements

at

least

in

intrinsic

coordinates

is

affected

by

ei

as

well

The

results

of

Experiment

generalized

the

role

of

CM

from

matching

the

orientation

of

contralateral

forearms

to

orienting

a

single

arm

in

extrinsic

space

They

further

showed

that

the

perception

of

upper

arm

orientation

was

unaffected

by

the

manipulation

of

the

forearm

's

CM

even

though

the

manipulation

affected

Ng

at

both

the

elbow

and

the

shoulder

due

to

the

absence

of

an

upper

arm

support

The

latter

finding

may

be

explained

in

two

ways

Participants

may

have

exploited

Ng

at

the

shoulder

to

obtain

information

about

the

configuration

of

the

whole

arm

in

space

as

we

anticipated

in

the

introduction

to

Experiment

or

they

may

have

discounted

it

only

taking

Ng

into

account

at

the

elbow

The

latter

alternative

would

suggest

that

the

role

of

CM

in

the

perception

of

limb

orientation

pertains

only

to

the

most

distal

rigid

segment

whereas

the

former

alternative

would

suggest

that

its

role

is

more

general

supporting

the

perception

of

the

orientation

of

both

proximal

and

distal

limb

segments

This

issue

may

be

resolved

in

experiments

in

which

the

center

of

mass

vectors

of

both

distal

and

proximal

limb

segments

-LRB-

e.g.

both

the

forearm

and

the

upper

arm

-RRB-

are

manipulated

in

tasks

similar

to

that

used

in

Experiment

In

seeking

an

encompassing

account

of

the

perception

of

limb

orientation

it

is

important

to

note

that

we

only

tested

the

effect

of

CM

and

manipulations

in

the

vertical

plane

Manipulation

of

CM

in

the

horizontal

plane

would

only

affect

the

direction

of

Ng

not

its

magnitude

and

hence

can

not

be

mediated

by

the

aforementioned

horizontal

shift

in

the

relationship

between

arm

orientation

and

Ng

magnitude

-LRB-

see

Fig.

-RRB-

In

a

recent

study

-LRB-

van

de

Langenberg

et

al.

-RRB-

we

tested

the

effect

of

horizontal

CM

and

manipulations

in

a

pointing

task

similar

to

that

adopted

in

Experiments

and

of

Pagano

and

Turvey

-LRB-

-RRB-

We

found

essentially

the

same

pattern

of

results

as

in

the

present

study

Perceived

arm

orientation

was

affected

by

the

horizontal

manipulation

of

CM

but

not

by

that

of

It

thus

appears

that

humans

are

sensitive

to

changes

in

both

torque

magnitude

and

direction

and

hence

to

CM

rotations

in

Another

important

point

of

discussion

is

that

the

observed

perceptual

biases

were

consistently

smaller

than

the

magnitude

of

CM

rotation

as

was

the

case

in

previous

studies

on

the

effect

of

vertical

-LRB-

CM

and

-RRB-

rotations

-LRB-

Pagano

et

al.

Garrett

et

al.

-RRB-

However

the

relative

sizes

of

our

effects

-LRB-

i.e.

of

the

actual

CM

rotation

-RRB-

were

smaller

than

those

observed

in

those

previous

studies

-LRB-

i.e.

of

the

actual

CM

rotation

-RRB-

We

suspect

that

this

difference

is

related

to

differences

in

the

magnitude

of

CM

manipulation

which

was

in

our

Experiment

and

only

about

in

Pagano

et

al.

-LRB-

-RRB-

and

Garrett

et

al.

-LRB-

-RRB-

In

a

study

on

the

effect

of

horizontal

-LRB-

and

CM

-RRB-

rotations

Bernardin

et

al.

-LRB-

-RRB-

adopted

three

manipulation

magnitudes

in

a

single

experiment

and

indeed

found

a

strong

negative

relationship

between

effect

size

and

manipulation

magnitude

-LRB-

upon

an

increase

of

CM

manipulation

from

about

to

about

effect

size

decreased

from

to

-RRB-

In

addition

to

manipulation

magnitude

other

factors

such

as

manipulation

direction

-LRB-

i.e.

horizontal

or

vertical

-RRB-

and

exploration

style

may

also

influence

the

magnitude

of

CM

's

effect

on

the

perception

of

limb

orientation

These

factors

should

be

explored

further

in

future

research

Regardless

of

their

precise

contributions

however

one

can

already

conclude

that

the

perceptual

biases

introduced

by

manipulating

CM

and

are

in

general

incomplete

It

follows

from

this

general

observation

that

additional

information

unrelated

to

either

CM

or

must

have

been

employed

The

use

of

information

unrelated

to

CM

is

also

apparent

in

conditions

in

which

the

arm

's

CM

can

not

be

detected

such

as

when

the

limb

is

moved

passively

to

a

certain

position

-LRB-

see

e.g.

Lee

et

al.

Ulkar

et

al.

-RRB-

or

when

gravity

is

absent

-LRB-

see

e.g.

Lackner

and

DiZio

-RRB-

Notwithstanding

the

preceding

qualifications

the

present

findings

clearly

underscore

that

there

is

a

kinetic

component

to

limb

kinesthesis

which

has

important

implications

for

its

possible

neural

basis

More

specifically

the

apparent

dependence

of

limb

kinesthesis

on

CM

points

to

an

important

role

of

neural

signals

related

to

muscular

torque

or

effort

As

noted

in

the

introduction

several

other

psychophysical

studies

provided

support

for

this

view

-LRB-

Rymer

and

D'Almeida

Prud

homme

and

Kalaska

Proske

et

al.

Walsh

et

al.

Winter

et

al.

Gandevia

et

al.

-RRB-

Although

these

studies

clearly

challenge

the

view

that

limb

kinesthesis

relies

on

muscle

spindle

activity

alone

-LRB-

see

Ribot-Ciscar

et

al.

-RRB-

they

do

not

discard

the

possibility

that

signals

related

to

muscular

torque

or

effort

only

serve

to

accurately

interpret

spindle

discharges

in

terms

of

muscle

length

changes

as

proposed

by

McCloskey

-LRB-

see

also

Gandevia

-RRB-

The

effect

of

CM

on

limb

kinesthesis

indicates

that

in

addition

to

such

an

indirect

role

kinetic

signals

may

convey

information

about

the

distribution

of

a

limb

's

mass

in

space

and

hence

directly

affect

kinesthesis

independent

of

geometric

information

about

muscle

length

or

joint

angle

Golgi

tendon

organs

seem

particularly

suited

for

fulfilling

this

function

given

that

their

activity

is

closely

associated

with

muscle

force

-LRB-

Kandel

et

al.

-RRB-

This

implies

that

the

possible

implication

of

Golgi

tendon

organs

in

limb

kinesthesis

may

need

to

be

reconsidered

and

that

a

mechanism

akin

to

that

suggested

by

Rymer

and

d'Almeida

-LRB-

-RRB-

may

indeed

be

possible

kinesthesis
information
center of mass
inertial eigenvectors
gravitational torque