Error

correction

in

bimanual

coordination

benefits

from

bilateral

muscle

activity

evidence

from

kinesthetic

tracking

Although

previous

studies

indicated

that

the

stability

properties

of

interlimb

coordination

largely

result

from

the

integrated

timing

of

efferent

signals

to

both

limbs

they

also

depend

on

afference-based

interactions

In

the

present

study

we

examined

contributions

of

afference-based

error

corrections

to

rhythmic

bimanual

coordination

using

a

kinesthetic

tracking

task

Furthermore

since

we

found

in

previous

research

that

subjects

activated

their

muscles

in

the

tracked

-LRB-

motor-driven

-RRB-

arm

we

examined

the

functional

significance

of

this

activation

to

gain

more

insight

into

the

processes

underlying

this

phenomenon

To

these

aims

twelve

subjects

coordinated

active

movements

of

the

right

hand

with

motor-driven

oscillatory

movements

of

the

left

hand

in

two

coordinative

patterns

in-phase

-LRB-

relative

phase

-RRB-

and

antiphase

-LRB-

relative

phase

-RRB-

They

were

either

instructed

to

activate

the

muscles

in

the

motor-driven

arm

as

if

moving

along

with

the

motor

-LRB-

active

condition

-RRB-

or

to

keep

these

muscles

as

relaxed

as

possible

-LRB-

relaxed

condition

-RRB-

We

found

that

error

corrections

were

more

effective

in

in-phase

than

in

antiphase

coordination

resulting

in

more

adequate

adjustments

of

cycle

durations

to

compensate

for

timing

errors

detected

at

the

start

of

each

cycle

In

addition

error

corrections

were

generally

more

pronounced

in

the

active

than

in

the

relaxed

condition

This

activity-related

difference

was

attributed

to

the

associated

bilateral

neural

control

signals

-LRB-

as

estimated

using

electromyography

-RRB-

which

provided

an

additional

reference

-LRB-

in

terms

of

expected

sensory

consequences

-RRB-

for

afference-based

error

corrections

An

intimate

relation

was

revealed

between

the

-LRB-

integrated

-RRB-

motor

commands

to

both

limbs

and

the

processing

of

afferent

feedback

Introduction

Recently

the

relative

importance

of

perceptual

processes

for

motor

control

in

general

and

bimanual

coordination

in

particular

has

been

intensely

debated

-LSB-

e.g.

see

target

article

of

Mechsner

-LRB-

-RRB-

and

associated

commentaries

-RSB-

Despite

differences

in

the

conceptual

interpretation

of

empirical

findings

there

is

ample

evidence

that

perceptual

factors

affect

bimanual

coordination

For

example

beneficial

effects

of

augmented

visual

feedback

on

rhythmic

bimanual

coordination

have

been

observed

-LRB-

Swinnen

et

al.

Byblow

et

al.

Mechsner

et

al.

-RRB-

in

combination

with

changes

in

concurrent

neural

activity

-LRB-

Debaere

et

al.

Carson

et

al.

-RRB-

In

addition

it

has

been

shown

that

perturbations

of

proprioception

using

tendon

vibration

result

in

disruption

of

the

temporal

coordination

between

the

limbs

-LRB-

Verschueren

et

al.

Steyvers

et

al.

-RRB-

On

the

other

hand

however

recent

studies

have

indicated

that

important

characteristics

of

rhythmic

bimanual

coordination

are

not

primarily

attributable

to

somatosensory

feedback

-LRB-

Ridderikhoff

et

al.

Spencer

et

al.

-RRB-

suggesting

a

key

role

for

afference-independent

-LRB-

i.e.

open-loop

-RRB-

control

processes

Collectively

these

findings

motivated

the

present

study

on

kinesthetic

tracking

which

-LRB-

-RRB-

examined

the

closed-loop

control

processes

underlying

rhythmic

bimanual

coordination

and

-LRB-

-RRB-

addressed

the

potential

interplay

between

open-loop

and

closed-loop

control

in

the

production

of

rhythmic

bimanual

movements

In

the

present

study

we

focus

on

rhythmic

bimanual

movements

performed

at

the

same

frequency

Such

movements

are

characterized

by

the

presence

of

only

two

stable

coordination

patterns

that

can

be

performed

without

training

-LRB-

Zanone

and

Kelso

-RRB-

and

that

are

defined

in

terms

of

the

relative

phase

between

the

hands

-LRB-

Φ

-RRB-

In

most

cases

one

pattern

-LRB-

in-phase

coordination

Φ

simultaneous

activation

of

homologous

muscles

-RRB-

is

more

stable

than

the

other

pattern

-LRB-

antiphase

coordination

Φ

alternated

activation

of

homologous

muscles

-RRB-

-LRB-

Kelso

Swinnen

-RRB-

These

characteristics

imply

that

the

functional

consequences

of

various

control

processes

can

be

appreciated

directly

in

terms

of

their

contribution

to

the

stability

difference

of

in-phase

and

antiphase

coordination

In

general

these

control

processes

can

be

classified

according

to

three

sources

of

interlimb

interactions

One

of

these

sources

is

afference-independent

and

refers

to

open-loop

processes

involved

in

the

integrated

timing

of

the

feedforward

signals

to

both

limbs

The

other

two

sources

are

associated

with

closed-loop

processes

a

reflex-like

interaction

resulting

in

phase

entrainment

by

contralateral

afference

and

intentional

corrections

of

the

timing

based

on

the

perceived

error

in

the

relative

phase

This

conceptual

framework

is

motivated

and

described

in

detail

elsewhere

-LRB-

Ridderikhoff

et

al.

-RRB-

In

previous

studies

we

found

that

the

stability

difference

between

in-phase

and

antiphase

coordination

depended

mainly

on

the

integrated

timing

of

the

feedforward

control

signals

-LRB-

Ridderikhoff

et

al.

-RRB-

and

that

phase

entrainment

by

contralateral

afference

did

not

affect

this

difference

-LRB-

Ridderikhoff

et

al.

-RRB-

As

regards

the

second

afference-based

source

of

interlimb

interactions

timing

corrections

based

on

the

perceived

relative

phase

a

more

complex

picture

emerged

which

motivated

the

present

study

as

discussed

in

the

following

paragraphs

Kinesthetic

tracking

tasks

have

been

used

to

assess

the

role

of

afference-based

interactions

between

the

limbs

in

rhythmic

bimanual

coordination

by

examining

the

coordination

of

unilateral

active

rhythmic

movements

with

motor-driven

oscillations

of

the

contralateral

limb

-LRB-

Viviani

et

al.

Stinear

and

Byblow

Ridderikhoff

et

al.

-RRB-

In

agreement

with

the

stability

characteristics

of

rhythmic

bimanual

coordination

two

previous

studies

on

kinesthetic

tracking

have

demonstrated

differences

between

in-phase

and

antiphase

coordination

One

study

revealed

a

more

variable

relative

phase

and

larger

response

times

on

a

secondary

task

for

antiphase

coordination

than

for

in-phase

coordination

-LRB-

Stinear

and

Byblow

-RRB-

The

other

study

showed

that

the

mean

relative

phase

was

more

susceptible

to

an

external

stimulus

-LRB-

i.e.

less

stable

-RRB-

during

antiphase

coordination

than

during

in-phase

coordination

-LRB-

Ridderikhoff

et

al.

-RRB-

Thus

the

study

of

kinesthetic

tracking

indicated

that

afference-based

interlimb

interactions

may

contribute

to

the

stability

difference

between

in-phase

and

antiphase

coordination

In

terms

of

the

aforementioned

-LRB-

afference-based

-RRB-

sources

of

interlimb

interaction

these

pattern-related

stability

differences

should

be

attributed

to

corrections

based

on

the

perceived

error

in

the

relative

phase

because

phase

entrainment

by

contralateral

afference

has

been

found

to

stabilize

in-phase

and

antiphase

coordination

in

equal

measure

-LRB-

Ridderikhoff

et

al.

Ridderikhoff

et

al.

-RRB-

In

our

previous

work

we

found

that

muscle

activation

patterns

during

kinesthetic

tracking

exhibited

a

striking

similarity

to

the

patterns

observed

in

normal

bimanual

coordination

even

though

muscular

activity

was

neither

required

nor

of

any

consequence

for

the

movement

pattern

of

the

motor-driven

hand

-LRB-

Ridderikhoff

et

al.

-RRB-

In

contrast

if

motor-driven

movements

were

used

to

induce

phase

entrainment

by

contralateral

afference

-LRB-

i.e.

when

one

limb

was

moved

passively

but

no

coordination

between

the

limbs

was

required

-RRB-

such

activation

patterns

were

not

observed

-LRB-

Ridderikhoff

et

al.

-RRB-

Thus

the

spontaneously

adopted

tendency

of

subjects

to

activate

their

muscles

as

if

they

were

moving

along

with

the

motor-driven

movement

appeared

directly

related

to

the

requirement

of

achieving

a

particular

coordination

pattern

between

the

limbs

In

principle

such

spontaneous

muscle

activation

in

the

driven

limb

may

serve

several

purposes

It

may

be

for

instance

that

it

reflects

coactivation

of

gamma-motoneurons

to

enhance

the

sensitivity

of

muscle

spindles

-LRB-

Gandevia

et

al.

-RRB-

However

this

possibility

is

less

likely

because

several

studies

reported

an

increase

of

detection

thresholds

-LRB-

Wise

et

al.

-RRB-

and

attenuation

of

muscle

sense

-LRB-

Collins

et

al.

-RRB-

during

voluntary

contractions

-LRB-

see

Proske

for

a

review

-RRB-

Alternatively

it

may

be

that

the

activation

of

muscles

in

the

motor-driven

arm

reflects

the

use

of

an

internal

control

signal

specifying

the

bimanual

movement

pattern

Considering

that

our

previous

work

has

indicated

a

crucial

contribution

of

afference-independent

interlimb

interactions

to

the

stability

of

the

normal

bimanual

coordination

-LRB-

Ridderikhoff

et

al.

-RRB-

this

internal

control

signal

may

well

be

generated

reliably

in

an

open-loop

fashion

Hence

in

the

context

of

kinesthetic

tracking

this

open-loop

control

signal

may

provide

a

suitable

reference

against

which

the

error

in

the

relative

phasing

-LRB-

based

on

afferent

signals

-RRB-

could

be

determined

Such

involvement

of

motor

commands

in

limb

kinesthesis

was

recently

demonstrated

empirically

-LRB-

Gandevia

et

al.

-RRB-

and

has

been

advocated

as

a

fundamental

principle

of

motor

control

involving

predictions

of

the

movement

's

sensory

consequences

via

efference

copy

-LRB-

e.g.

Wolpert

and

Ghahramani

Scott

-RRB-

Note

that

this

second

account

of

the

EMG

activity

in

the

driven

limb

which

in

fact

served

as

a

working

hypothesis

for

the

present

study

implies

an

intimate

relation

between

two

of

the

aforementioned

sources

of

interlimb

interaction

viz.

error

correction

based

on

the

perceived

relative

phase

and

the

integrated

timing

of

the

feedforward

signals

-LRB-

providing

the

reference

pattern

-RRB-

The

aim

of

the

present

study

was

to

examine

the

afference-based

error

corrections

in

detail

using

a

kinesthetic

tracking

task

with

a

specific

focus

on

the

role

of

the

muscle

activity

in

the

motor-driven

arm

to

elucidate

the

interplay

of

closed-loop

and

open-loop

control

processes

in

rhythmic

bimanual

coordination

We

compared

the

performance

during

in-phase

and

antiphase

coordination

to

further

our

understanding

of

the

potential

contribution

of

closed-loop

control

processes

to

the

differential

stability

of

these

patterns

In

addition

we

examined

the

stability-related

effects

of

bilateral

muscle

activation

during

kinesthetic

tracking

on

the

resulting

coordinative

stability

To

address

the

latter

issue

we

compared

two

conditions

in

which

subjects

were

either

instructed

to

keep

the

motor-driven

limb

relaxed

or

to

activate

their

muscles

as

if

moving

along

with

the

imposed

motor-driven

movement

For

the

latter

condition

the

phase

relations

at

the

level

of

neural

control

signals

-LRB-

based

on

electromyographic

data

-RRB-

and

at

the

behavioral

level

-LRB-

kinematics

-RRB-

were

compared

The

neural

control

signals

represent

the

reference

signal

that

may

be

used

for

the

prediction

of

sensory

consequences

of

the

ongoing

movement

whereas

the

kinematic

phase

relation

reflects

the

actual

quality

of

the

performance

In

both

conditions

we

performed

an

extensive

analysis

of

the

correlations

between

various

kinematic

variables

to

uncover

the

underlying

structure

of

the

timing

corrections

based

on

the

-LRB-

perceived

-RRB-

errors

in

the

relative

phase

Materials

and

methods

Subjects

Twelve

healthy

subjects

-LRB-

male

female

aged

years

-RRB-

volunteered

to

participate

All

subjects

were

right-handed

according

to

their

scores

on

a

common

handedness

questionnaire

-LRB-

Oldfield

-RRB-

They

had

no

previous

experience

with

the

task

and

reported

no

-LRB-

history

of

-RRB-

neurological

disorders

The

local

ethics

committee

approved

the

experiment

and

all

subjects

gave

their

written

informed

consent

before

the

experiment

was

conducted

Apparatus

Subjects

sat

in

a

height-adjustable

chair

with

their

elbows

slightly

flexed

and

their

feet

supported

Each

forearm

was

placed

in

the

apparatus

in

a

neutral

position

-LRB-

thumbs

up

and

palms

facing

inward

-RRB-

and

its

position

was

restrained

-LRB-

by

the

support

surface

on

the

medial

and

ventral

side

by

two

vertical

foam-coated

supports

on

the

dorsal

side

and

by

one

horizontal

foam-coated

support

on

the

lateral

side

-RRB-

to

prevent

movements

about

the

elbow

Both

hands

were

fixated

against

the

flat

manipulanda

using

two

Velcro

straps

with

all

fingers

extended

The

apparatus

only

permitted

flexion

extension

movements

of

the

wrist

in

the

horizontal

plane

The

right

manipulandum

was

mounted

on

a

potentiometer

-LRB-

Sakae

type

linearity

-RRB-

to

register

wrist

joint

angles

during

active

movement

while

the

left

was

connected

to

a

servo-controlled

motor

that

moved

the

hand

passively

The

potentiometer

's

output

voltage

was

digitized

by

a

ADC

-LRB-

Labmaster

DMA

-RRB-

and

stored

on

a

microcomputer

at

a

sampling

frequency

of

Hz

The

active

movements

were

recorded

with

a

precision

of

about

The

passive

movements

were

generated

using

a

DC

brush

motor

-LRB-

PARVEX

type

-RRB-

that

was

controlled

by

a

PC-mounted

servo

controller

-LRB-

type

-RRB-

The

maximum

torque

of

the

motor

was

such

that

subjects

were

unable

to

alter

the

trajectory

of

the

applied

movements

and

the

maximum

error

in

the

trajectory

of

the

passive

movements

was

Subjects

wore

earmuffs

with

built-in

stereo

earphones

-LRB-

Bilsom

Flex

II

-RRB-

which

provided

a

moderate

level

of

white

background

noise

to

eliminate

any

auditory

feedback

from

the

motion

of

the

motor

A

white

opaque

screen

was

used

to

eliminate

visual

feedback

of

the

hand

movements

Surface

electromyograms

-LRB-

EMG

-RRB-

were

obtained

from

M.

flexor

carpi

radialis

-LRB-

FCR

-RRB-

and

M.

extensor

carpi

radialis

-LRB-

ECR

-RRB-

of

both

arms

A

bipolar

arrangement

of

disposable

electrodes

-LRB-

Medicotest

Ag/AgCl-electrodes

square

mm

pick-up

area

-RRB-

was

attached

with

a

center-to-center

distance

of

cm

after

cleansing

and

abrasion

of

the

skin

The

electrodes

were

positioned

in

the

center

of

the

muscle

belly

on

the

line

from

origin

to

insertion

as

determined

by

palpation

EMG

signals

were

sampled

at

Hz

-LRB-

TMS

International

type

ASD

bits

ADC

-RRB-

after

band-pass

filtering

-LRB-

Hz

-RRB-

and

stored

on

a

microcomputer

Procedure

Subjects

were

instructed

to

perform

smooth

oscillatory

movements

about

the

right

wrist

in

such

a

way

that

-LRB-

-RRB-

peak

flexion

and

peak

extension

of

both

wrists

were

attained

simultaneously

-LRB-

in-phase

pattern

-RRB-

or

-LRB-

-RRB-

peak

flexion

of

one

hand

coincided

with

peak

extension

of

the

other

hand

-LRB-

antiphase

pattern

-RRB-

To

achieve

this

the

timing

of

the

active

right

wrist

movements

had

to

be

coordinated

with

the

motor-driven

movements

of

the

left

wrist

Only

subjects

that

were

able

to

perform

both

movement

patterns

in

at

least

one

of

two

selection

trials

at

the

start

of

the

experiment

were

included

-LRB-

one

candidate

subject

failed

to

meet

this

criterion

-RRB-

After

the

selection

trials

the

EMG

electrodes

were

applied

and

subsequently

all

subjects

performed

maximum

voluntary

contractions

-LRB-

MVCs

-RRB-

by

generating

an

isometric

flexion

or

extension

torque

with

each

arm

for

approximately

s.

For

the

purpose

of

normalization

of

the

EMG

the

maximum

root

mean

square

-LRB-

RMS

-RRB-

value

of

two

separate

MVC

measurements

was

used

in

the

analysis

Additional

instruction

was

given

to

subjects

with

respect

to

the

muscle

activity

in

the

left

-LRB-

driven

-RRB-

arm

Subjects

were

required

either

to

keep

the

muscles

of

the

left

-LRB-

driven

-RRB-

arm

as

relaxed

as

possible

-LRB-

relaxed

condition

-RRB-

or

to

activate

the

muscles

of

the

left

arm

as

if

they

were

moving

along

with

the

motor-driven

manipulandum

-LRB-

active

condition

-RRB-

The

resulting

-LRB-

Pattern

-RRB-

-LRB-

Activity

-RRB-

conditions

were

performed

in

separate

blocks

of

trials

the

order

of

which

was

counterbalanced

across

subjects

Each

block

of

trials

started

with

at

least

four

practice

trials

to

familiarize

the

subjects

with

the

task

-LRB-

if

necessary

maximally

four

additional

practice

trials

were

allowed

-RRB-

Once

the

subject

was

able

to

perform

the

task

properly

based

on

visual

assessment

by

the

experimenters

six

experimental

trials

were

performed

that

were

used

for

the

analysis

For

the

motor-driven

movements

of

the

left

wrist

sinusoidal

trajectories

with

an

average

movement

frequency

of

Hz

and

mean

amplitude

of

-LRB-

i.e.

a

range

of

motion

of

about

the

neutral

position

of

the

wrist

-RRB-

were

used

To

create

a

challenging

tracking

task

the

period

length

and

the

amplitudes

were

varied

within

a

trial

Because

pilot

experiments

had

shown

that

too

much

variability

induced

high

levels

of

-LRB-

mainly

tonic

-RRB-

muscle

activity

in

the

relaxed

condition

a

moderate

level

of

variability

was

selected

i.e.

intermediate

between

natural

variability

and

perfectly

sinusoidal

trajectories

as

used

in

previous

studies

-LRB-

Ridderikhoff

et

al.

Stinear

and

Byblow

respectively

-RRB-

Subjects

started

with

a

low

level

of

variability

in

the

selection

trials

-LRB-

SDfrequency

Hz

SDamplitude

-RRB-

which

was

increased

in

a

step-wise

fashion

during

the

practice

trials

to

the

level

of

variability

used

in

the

experimental

trials

-LRB-

SDfrequency

Hz

SDamplitude

-RRB-

To

assure

a

smooth

start

and

finish

of

the

trial

the

amplitude

of

the

motor-driven

movements

was

gradually

increased

-LRB-

from

-RRB-

and

decreased

-LRB-

to

-RRB-

during

the

first

and

last

s

of

a

trial

respectively

The

duration

of

a

trial

was

s.

To

avoid

transient

effects

and

to

exclude

the

cycles

in

which

the

amplitude

of

the

passive

movement

was

adjusted

the

first

and

the

last

s

of

the

trial

were

discarded

leaving

s

per

trial

for

analysis

Data

reduction

-LRB-

kinematics

-RRB-

Figure

illustrates

and

defines

the

features

of

the

time

evolution

of

the

joint

angles

on

which

the

analyses

of

the

kinematics

were

based

Because

systematic

differences

in

coordination

were

present

depending

on

whether

peak

flexion

or

peak

extension

was

chosen

as

reference

the

relative

phase

between

the

hands

-LRB-

Φ

-RRB-

was

calculated

for

each

cycle

as

for

flexion

and

as

for

extension

where

ty

i

and

tx

i

indicate

the

time

of

the

ith

peak

flexion

or

peak

extension

of

the

right

and

left

hand

respectively

-LRB-

for

a

similar

method

see

e.g.

Carson

et

al.

-RRB-

A

positive

relative

phase

meant

that

the

right

hand

was

lagging

the

left

hand

Circular

statistics

-LRB-

Mardia

-RRB-

was

used

to

calculate

the

mean

and

the

circular

standard

deviation

of

the

relative

phase

-LRB-

SDΦ

-RRB-

The

absolute

error

of

the

relative

phase

-LRB-

AEΦ

-RRB-

was

defined

as

the

absolute

difference

between

the

mean

relative

phase

and

the

required

relative

phase

-LRB-

for

in-phase

for

antiphase

-RRB-

Fig.

kinematic

features

of

one

full

cycle

of

both

hands

illustrated

for

the

in-phase

coordination

pattern

Moments

of

peak

flexion

and

extension

at

the

start

of

the

ith

cycle

in

each

hand

are

designated

by

tj

ik

where

k

indicates

flexion

-LRB-

F

-RRB-

or

extension

-LRB-

E

-RRB-

and

j

refers

to

the

right

hand

-LRB-

y

-RRB-

or

left

hand

-LRB-

x

-RRB-

The

durations

of

the

ith

full

cycle

between

two

moments

of

peak

excursion

are

designated

by

Δtj

ik

The

duration

of

the

ith

half

cycle

is

designated

by

δtj

il

where

l

indicates

the

orientation

of

the

hand

at

the

end

of

the

half

cycle

flexion

-LRB-

F

-RRB-

or

extention

-LRB-

E

-RRB-

The

-LRB-

signed

-RRB-

error

at

the

start

of

the

ith

cycle

is

designated

by

εik

The

definition

of

the

-LRB-

signed

-RRB-

errors

depends

on

the

coordination

pattern

and

is

defined

in

terms

of

the

relative

timing

of

corresponding

peak

excursions

in

both

hands

-LRB-

flexion

flexion

and

extension

extension

for

in-phase

flexion

extension

and

extension

flexion

for

antiphase

-RRB-

In

a

previous

study

-LRB-

Ridderikhoff

et

al.

-RRB-

we

showed

that

kinesthetic

tracking

performance

can

also

be

meaningfully

evaluated

in

terms

of

correlations

-LRB-

RFC

FC

full

cycle

-RRB-

between

the

signed

timing

error

at

peak

flexion

or

peak

extension

-LRB-

εi

-RRB-

and

the

duration

of

the

following

full

cycle

of

the

right

-LRB-

actively

moving

-RRB-

hand

-LRB-

Δty

i

-RRB-

The

rationale

behind

this

measure

is

that

if

an

error

in

the

relative

phasing

is

detected

at

the

start

of

the

ith

cycle

this

error

may

be

compensated

for

by

adapting

the

duration

of

the

next

cycle

resulting

in

negative

values

of

RFC

Motivated

by

the

aforementioned

differences

between

flexion

and

extension

that

were

observed

for

the

relative

phase

-LRB-

see

also

Results

-RRB-

we

also

calculated

the

correlation

between

this

error

in

the

relative

timing

and

the

duration

of

the

following

half

cycle

of

the

right

hand

-LRB-

RHC

HC

half

cycle

-RRB-

RFC

and

RHC

are

intimately

related

in

that

the

error

correction

made

during

a

full

cycle

is

the

sum

of

the

error

corrections

made

during

its

two

half

cycles

provided

that

the

latter

two

corrections

are

independent

of

each

other

However

in

general

this

proviso

is

not

met

because

part

of

the

correction

in

the

second

half

cycle

may

in

fact

compensate

for

errors

that

arose

in

the

first

half

cycle

which

is

reflected

by

two

additional

temporal

correlations

First

deviations

in

the

duration

of

the

first

half

cycle

of

the

left

-LRB-

driven

-RRB-

hand

-LRB-

as

a

consequence

of

the

variability

of

the

imposed

reference

trajectory

-RRB-

may

result

in

errors

at

the

start

of

the

second

half

cycle

that

lead

to

adaptation

of

the

duration

of

the

consecutive

half-cycle

of

the

right

hand

This

dependency

is

reflected

in

positive

between-hands

correlations

-LRB-

Rxy

-RRB-

between

the

durations

of

a

half-cycle

of

the

left

-LRB-

driven

-RRB-

hand

and

the

following

half-cycle

of

the

right

hand

Second

if

in

each

half-cycle

the

errors

are

overcompensated

a

sequence

of

alternating

longer

and

shorter

half-cycles

is

obtained

Such

a

dependency

is

reflected

by

negative

within-hand

correlations

-LRB-

Ryy

-RRB-

between

the

successive

half-cycles

of

the

right

hand

Thus

positive

values

of

Rxy

and

negative

values

of

Ryy

reflect

dependencies

between

the

error

corrections

in

successive

half

cycles

that

reduce

their

contributions

-LRB-

RHC

-RRB-

to

the

full

cycle

error

corrections

RFC

These

four

temporal

correlations

-LRB-

RFC

RHC

Rxy

and

Ryy

-RRB-

provide

information

about

the

temporal

structure

of

the

performance

in

terms

of

the

timing

of

peak

flexion

and

peak

extension

of

the

wrist

As

such

these

measures

are

more

closely

related

to

the

underlying

control

processes

than

the

global

performance

measures

based

on

the

relative

phase

Exact

definitions

of

-LRB-

the

relations

between

-RRB-

these

measures

can

be

found

in

the

Appendix

in

terms

of

the

underlying

covariances

Because

systematic

differences

were

found

between

the

actual

timing

of

peak

flexion

and

that

of

peak

extension

the

effects

of

these

two

orientations

on

the

error

correction

measures

-LRB-

RFC

and

RHC

-RRB-

as

obtained

for

timing

errors

at

peak

flexion

or

peak

extension

of

the

right

-LRB-

actively

moving

-RRB-

hand

in

relation

to

the

duration

of

the

following

-LRB-

full

or

half

-RRB-

cycle

of

this

hand

were

examined

as

well

In

addition

the

effects

of

orientation

on

Ryy

and

Rxy

were

evaluated

by

comparing

the

correlations

between

the

durations

of

the

two

successive

half-cycles

following

either

peak

flexion

or

peak

extension

of

the

right

-LRB-

actively

moving

-RRB-

hand

In

this

way

the

implications

of

Ryy

and

Rxy

for

the

effects

of

orientation

that

were

observed

for

RFC

could

be

discerned

-LRB-

see

Appendix

and

Fig.

-RRB-

Data

reduction

-LRB-

EMG

-RRB-

EMG

records

were

bandpass

filtered

-LRB-

Hz

-RRB-

using

a

second-order

bidirectional

-LRB-

zero-lag

-RRB-

Butterworth

filter

-LRB-

Merletti

et

al.

-RRB-

To

visualize

the

average

muscle

activity

within

a

cycle

eight

bins

were

defined

in

relation

to

the

continuous

phase

of

the

movement

Θ

arctan

-LSB-

-LRB-

dθ/dt

-RRB-

-LRB-

2πfθ

-RRB-

-RSB-

where

θ

and

-LRB-

dθ/dt

-RRB-

are

joint

angle

and

joint

angular

velocity

respectively

and

f

is

the

movement

frequency

Thus

each

bin

represented

an

equal

part

of

the

phase

of

the

hand

oscillation

The

first

bin

was

centered

around

Θ

-LRB-

i.e.

peak

extension

-RRB-

and

the

fifth

bin

was

centered

around

Θ

-LRB-

i.e.

peak

flexion

-RRB-

For

each

bin

the

RMS

of

the

EMG

was

calculated

and

normalized

to

that

obtained

for

the

MVC

In

addition

to

the

comparison

of

conditions

in

terms

of

the

average

-LRB-

normalized

-RRB-

amplitudes

the

similarity

of

the

rEMGs

of

homologous

muscles

was

assessed

using

the

weighted

coherence

Specifically

the

weighted

coherence

reflects

the

degree

of

similarity

-LRB-

or

phase

locking

-RRB-

of

the

activity

bursts

in

the

homologous

muscles

in

terms

of

a

weighted

average

of

the

coherence

in

the

vicinity

of

the

movement

frequency

-LRB-

i.e.

in

the

frequency

band

in

which

these

bursts

occur

-RRB-

yielding

values

between

-LRB-

no

phase

locking

-RRB-

and

-LRB-

perfect

phase

locking

-RRB-

Thus

the

weighted

coherence

is

an

estimate

of

the

strength

of

the

interlimb

coupling

at

the

level

of

the

neural

control

signals

-LRB-

Ridderikhoff

et

al.

-RRB-

In

the

present

study

it

was

used

to

evaluate

differences

in

this

regard

between

the

relaxed

and

active

conditions

and

between

flexor

and

extensor

muscles

The

weighted

coherence

-LRB-

Porges

et

al.

-RRB-

of

the

full-wave

rectified

EMG

-LRB-

rEMG

-RRB-

of

homologous

muscles

-LRB-

CW

-RRB-

was

calculated

aswhere

Δf

defines

a

bandwidth

around

the

movement

frequency

f

-LRB-

Δf

Hz

-RRB-

Py

is

the

power

spectrum

of

the

rEMG

of

the

right

arm

and

Cxy

is

the

coherence

of

the

rEMGs

of

the

homologous

muscles

in

the

left

and

right

arm

The

power

spectra

and

the

coherence

were

estimated

with

Welch

's

modified

periodogram

method

-LRB-

Oppenheim

and

Schafer

-RRB-

using

a

Hanning

window

of

three

cycles

In

addition

the

phase

relations

between

rEMGs

and

joint

angles

θ

were

studied

to

compare

the

temporal

relations

observed

at

the

level

of

the

neural

control

signals

to

those

observed

at

the

behavioral

level

This

is

of

particular

importance

for

the

analysis

of

the

contribution

of

the

bilateral

motor

commands

to

the

performance

in

the

active

condition

The

phase

shift

between

rEMG

and

θ

was

obtained

from

the

cross-spectrum

of

rEMG

and

θ

estimated

at

the

movement

frequency

-LRB-

using

the

same

parameters

as

for

the

weighted

coherence

-RRB-

Because

flexion

corresponded

to

negative

values

of

θ

the

phase

shift

between

the

EMG

of

FCR

and

θ

was

adjusted

by

-LRB-

cf.

Ridderikhoff

et

al.

-RRB-

Likewise

the

relative

phases

between

the

rEMGs

of

homologous

muscles

were

determined

from

the

cross-spectrum

of

rEMGs

of

muscles

in

the

left

and

right

arm

The

constant

error

of

these

relative

phases

was

defined

as

the

signed

difference

between

the

mean

relative

phase

and

the

required

relative

phase

-LRB-

for

in-phase

for

antiphase

-RRB-

with

negative

values

indicating

a

relative

phase

lead

of

the

activity

in

the

right

arm

The

calculation

of

these

measures

required

that

the

signals

in

question

were

phase

and

frequency

locked

which

implied

that

both

measures

could

only

be

obtained

for

the

active

condition

because

only

in

this

condition

the

rEMG

of

the

muscles

in

the

left

-LRB-

motor-driven

-RRB-

arm

satisfied

this

requirement

For

both

measures

-LRB-

i.e.

the

phase

shifts

between

rEMG

and

θ

and

the

relative

phases

between

rEMGs

of

homologous

muscles

-RRB-

the

values

obtained

for

FCR

and

ECR

were

analyzed

separately

to

examine

differences

in

the

relative

timing

of

flexors

and

extensors

in

relation

to

effects

of

coordinative

pattern

-LRB-

for

both

measures

-RRB-

and

limb

-LRB-

for

the

phase

shifts

between

rEMG

and

θ

-RRB-

In

addition

the

values

obtained

for

FCR

and

ECR

were

averaged

to

obtain

a

global

measure

for

the

phasing

of

the

neural

control

signals

to

the

limbs

-LRB-

Viviani

et

al.

-RRB-

To

visualize

the

main

temporal

relations

in

the

movement

system

the

relative

phase

between

the

neural

control

signals

the

phase

shifts

between

the

neural

control

signals

and

the

movements

of

the

left

and

right

hand

and

the

average

relative

phase

between

the

hands

were

examined

in

conjunction

In

the

active

condition

FCR

of

the

left

-LRB-

driven

-RRB-

arm

of

two

subjects

showed

substantial

reactive

activity

comparable

in

magnitude

to

that

observed

in

the

relaxed

condition

-LRB-

see

Fig.

peak

at

bin

open

symbols

-RRB-

in

addition

to

the

normal

timing

of

muscle

activation

that

was

required

in

this

condition

-LRB-

see

Fig.

peak

at

bin

filled

symbols

-RRB-

This

reactive

activity

was

to

some

extent

present

in

most

subjects

-LRB-

as

indicated

by

the

peaks

in

Fig.

which

was

created

without

using

the

data

of

these

two

excluded

subjects

-RRB-

but

typically

much

less

pronounced

For

the

two

excluded

subjects

the

large

amplitude

of

the

reactive

activity

resulted

in

a

shift

of

the

dominant

frequency

of

the

power

spectrum

of

left

FCR

in

this

condition

to

twice

the

movement

frequency

-LRB-

i.e.

two

bursts

per

cycle

-RRB-

The

EMG

data

of

these

subjects

were

excluded

from

the

analyses

because

their

inclusion

resulted

in

a

number

of

additional

significant

effects

that

could

all

be

attributed

to

this

reactive

activity

but

were

not

representative

for

the

EMG

data

of

the

group

as

a

whole

It

should

be

noted

however

that

all

phenomena

mentioned

in

the

Results

section

were

also

observed

for

the

excluded

subjects

Statistical

analysis

Statistical

analyses

of

the

kinematics

were

performed

using

a

-LRB-

Pattern

in-phase

vs.

antiphase

coordination

-RRB-

-LRB-

Activity

active

vs.

relaxed

-RRB-

-LRB-

Orientation

flexion

vs.

extension

-RRB-

repeated

measures

analysis

of

variance

-LRB-

ANOVA

-RRB-

Also

EMG-related

measures

were

analyzed

with

repeated

measures

ANOVAs

involving

various

question-specific

designs

which

are

described

in

the

corresponding

subsections

of

the

Results

To

facilitate

the

interpretation

of

the

results

obtained

with

ANOVA

paired-sample

t-tests

were

used

for

post

hoc

analysis

of

the

significant

results

-LRB-

P

-RRB-

and

effect

sizes

-LRB-

f

-RRB-

were

calculated

in

terms

of

the

partial

η2

-LRB-

Cohen

-RRB-

The

correlations

were

transformed

to

normally

distributed

variables

using

the

Fisher

transform

The

same

transformation

was

applied

to

the

weighted

coherence

-LRB-

Rosenberg

et

al.

-RRB-

Whereas

the

inferential

analyses

were

based

on

the

transformed

values

the

corresponding

untransformed

values

-LRB-

bounded

on

the

interval

-LSB-

-RSB-

for

the

correlations

and

on

the

interval

-LSB-

-RSB-

for

the

coherence

-RRB-

are

presented

for

reasons

of

clarity

Results

Adequate

performance

of

a

trial

was

determined

using

the

following

inclusion

criteria

-LRB-

-RRB-

the

number

of

cycles

performed

by

the

right

hand

and

the

-LRB-

driven

-RRB-

left

hand

should

be

the

same

-LRB-

i.e.

no

phase

wrapping

-RRB-

-LRB-

-RRB-

AEΦ

should

be

smaller

than

and

-LRB-

-RRB-

the

within-trial

fluctuations

of

the

relative

phase

should

be

within

a

range

of

In

total

trials

-LRB-

-RRB-

were

excluded

from

the

analysis

trials

in

the

active

condition

-LRB-

trials

for

in-phase

coordination

and

trials

for

antiphase

coordination

-RRB-

trials

in

the

relaxed

condition

-LRB-

trials

for

in-phase

coordination

and

trials

for

antiphase

coordination

-RRB-

In

each

condition

all

subjects

were

capable

of

performing

the

task

in

at

least

three

trials

in

an

adequate

fashion

Relative

phase

Statistical

analysis

of

AEΦ

-LRB-

see

Fig.

-RRB-

revealed

a

significant

effect

of

Activity

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

indicating

that

AEΦ

was

larger

for

the

active

condition

-LRB-

mean

between-subjects

SD

-RRB-

than

for

the

relaxed

condition

-LRB-

-RRB-

In

addition

a

significant

Pattern

Orientation

interaction

was

found

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

Post

hoc

analysis

demonstrated

two

significant

differences

underlying

this

interaction

viz.

between

in-phase

and

antiphase

coordination

at

peak

extension

-LRB-

vs.

respectively

-RRB-

and

between

flexion

and

extension

during

antiphase

coordination

-LRB-

vs.

respectively

-RRB-

The

same

statistical

results

were

obtained

for

the

constant

errors

in

relative

phasing

-LRB-

not

shown

-RRB-

because

the

errors

were

almost

always

in

the

same

direction

-LRB-

i.e.

negative

-RRB-

indicating

that

the

right

-LRB-

actively

moving

-RRB-

hand

was

leading

in

time

Fig.

Mean

absolute

error

of

the

relative

phase

-LRB-

AEΦ

-RRB-

b

Standard

deviation

of

the

relative

phase

-LRB-

SDΦ

-RRB-

Results

obtained

for

the

relative

timing

of

peak

flexion

-LRB-

black

bars

-RRB-

and

peak

extension

-LRB-

gray

bars

-RRB-

are

shown

for

in-phase

-LRB-

IP

-RRB-

and

antiphase

-LRB-

AP

-RRB-

both

for

the

conditions

in

which

the

muscles

of

the

left

hand

were

active

-LRB-

AC

-RRB-

or

relaxed

-LRB-

RE

-RRB-

Error

bars

indicate

the

standard

error

of

the

mean

To

examine

the

stability

of

the

coordinative

patterns

statistical

analysis

of

SDΦ

-LRB-

see

Fig.

-RRB-

was

conducted

which

revealed

significant

effects

of

Activity

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

and

Pattern

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

These

effects

resulted

from

respectively

a

larger

SDΦ

in

the

relaxed

condition

than

in

the

active

condition

-LRB-

vs.

-RRB-

and

a

larger

SDΦ

for

antiphase

coordination

than

for

in-phase

coordination

-LRB-

vs.

-RRB-

Movement

amplitude

To

examine

whether

the

different

activity

levels

of

the

muscles

in

the

left

-LRB-

driven

-RRB-

arm

had

an

effect

on

the

amplitude

of

the

movements

about

the

right

wrist

the

range

of

motion

-LRB-

i.e.

the

difference

in

peak

extension

and

peak

flexion

-RRB-

was

determined

for

each

cycle

averaged

per

condition

and

subjected

to

a

-LRB-

Pattern

-RRB-

-LRB-

Activity

-RRB-

repeated

measures

ANOVA

The

analysis

solely

revealed

a

significant

effect

of

Activity

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

resulting

from

a

larger

movement

amplitude

in

the

active

condition

than

in

the

relaxed

condition

-LRB-

range

of

motion

vs.

respectively

-RRB-

Temporal

correlations

between

kinematic

variables

The

average

correlations

between

the

signed

error

and

the

duration

of

the

following

full

cycle

-LRB-

RFC

-RRB-

or

half

cycle

-LRB-

RHC

-RRB-

are

shown

in

Fig.

b

respectively

Statistical

analysis

of

RFC

revealed

significant

effects

for

Activity

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

Pattern

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

and

Orientation

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

RFC

was

more

pronounced

-LRB-

larger

absolute

values

-RRB-

for

the

active

condition

than

for

the

relaxed

condition

-LRB-

vs.

-RRB-

for

the

in-phase

pattern

than

for

the

antiphase

pattern

-LRB-

vs.

-RRB-

and

for

errors

at

peak

flexion

than

for

errors

at

peak

extension

-LRB-

vs.

-RRB-

Fig.

correlations

between

the

signed

timing

error

and

the

duration

of

the

following

full

cycle

-LRB-

RFC

a

-RRB-

or

half

cycle

-LRB-

RHC

b

-RRB-

of

the

right

-LRB-

actively

moving

-RRB-

hand

Results

are

shown

for

in-phase

-LRB-

IP

-RRB-

and

antiphase

-LRB-

AP

-RRB-

both

for

the

conditions

in

which

the

muscles

of

the

left

hand

were

active

-LRB-

AC

-RRB-

or

relaxed

-LRB-

RE

-RRB-

RFC

was

calculated

for

full

cycles

following

the

error

at

two

different

orientations

of

the

right

-LRB-

actively

moving

-RRB-

hand

peak

flexion

-LRB-

black

bars

-RRB-

and

peak

extension

-LRB-

gray

bars

-RRB-

RHC

was

calculated

for

the

flexion

half

cycles

following

the

error

at

peak

extension

-LRB-

black

bars

-RRB-

and

the

extension

half

cycles

following

the

error

at

peak

flexion

-LRB-

gray

bars

-RRB-

Error

bars

indicate

the

standard

error

of

the

mean

Statistical

analysis

of

RHC

revealed

significant

effects

for

Activity

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

and

Pattern

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

indicating

larger

absolute

values

for

the

active

condition

than

for

the

relaxed

condition

-LRB-

vs.

-RRB-

and

for

the

in-phase

pattern

than

for

the

antiphase

pattern

-LRB-

vs.

-RRB-

In

addition

for

RHC

significant

Activity

Pattern

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

and

Pattern

Orientation

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

interactions

were

found

Post

hoc

analysis

revealed

that

the

first

interaction

effect

resulted

from

a

larger

absolute

value

of

RHC

for

in-phase

coordination

in

the

active

condition

than

for

the

three

other

combinations

of

Activity

and

Pattern

-LRB-

see

Fig.

-RRB-

The

second

interaction

effect

was

due

to

a

larger

absolute

value

of

RHC

for

the

extension

half-cycle

in

the

in-phase

pattern

than

for

the

three

other

combinations

of

Pattern

and

Orientation

-LRB-

see

Fig.

-RRB-

The

main

effects

of

Activity

and

Pattern

were

qualitatively

the

same

for

RHC

and

RFC

but

the

effect

of

Orientation

was

markedly

different

An

explanation

of

this

difference

was

found

in

a

formal

analysis

of

the

relation

between

the

underlying

RHC

and

RFC

which

demonstrated

that

-LRB-

unlike

differences

related

to

Activity

or

Pattern

-RRB-

differences

between

flexion

and

extension

in

RHC

are

completely

unrelated

to

those

in

RFC

-LRB-

see

Appendix

-RRB-

Two

additional

factors

are

involved

in

the

relation

between

RHC

and

RFC

-LRB-

see

Materials

and

methods

and

Appendix

-RRB-

which

were

captured

by

the

within-hand

and

between-hands

correlations

of

the

durations

of

successive

half

cycles

-LRB-

Ryy

and

Rxy

respectively

-RRB-

The

effect

of

Orientation

in

RFC

can

be

attributed

completely

to

-LRB-

the

covariances

underlying

-RRB-

Ryy

and

Rxy

-LRB-

see

Appendix

-RRB-

However

also

for

the

other

factors

-LRB-

Activity

and

Pattern

-RRB-

the

relation

between

RHC

and

RFC

may

be

affected

by

Ryy

and

Rxy

given

the

potential

dependencies

between

error

corrections

in

successive

half-cycles

Thus

the

temporal

correlations

were

examined

further

in

terms

of

the

within-hand

correlation

Ryy

and

the

between-hands

correlation

Rxy

Analysis

of

the

between-hands

correlation

Rxy

-LRB-

Fig.

-RRB-

revealed

no

significant

effects

In

contrast

significant

effects

of

Activity

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

and

Orientation

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

were

found

for

the

within-hand

correlation

Ryy

The

effect

of

Activity

revealed

that

the

values

of

Ryy

for

the

active

condition

were

more

negative

than

for

the

relaxed

condition

-LRB-

vs.

-RRB-

The

effect

of

Orientation

indicated

that

the

correlations

between

the

extension

half

cycle

and

the

following

flexion

half

cycle

were

more

negative

-LRB-

gray

bars

in

Fig.

-RRB-

than

those

between

the

flexion

half

cycle

and

the

following

extension

half

cycle

-LRB-

black

bars

in

Fig.

-RRB-

The

consequences

of

Ryy

and

Rxy

for

RFC

are

illustrated

in

Fig.

d

respectively

which

show

the

contributions

of

the

covariances

underlying

Ryy

and

Rxy

to

RFC

according

to

the

relations

derived

in

the

Appendix

The

temporal

relations

expressed

by

Ryy

and

Rxy

both

result

in

a

reduction

of

RFC

-LRB-

i.e.

they

reduce

the

effects

of

the

half

cycle

error

corrections

see

Materials

and

methods

-RRB-

the

effect

of

the

former

being

larger

than

that

of

the

latter

-LRB-

compare

Fig.

d

-RRB-

Both

correlations

resulted

in

a

larger

reduction

of

RFC

for

errors

at

peak

extension

than

for

errors

at

peak

flexion

which

explains

the

aforementioned

effect

of

Orientation

obtained

for

RFC

In

addition

the

effect

of

Activity

for

Ryy

revealed

that

the

error

corrections

in

successive

half-cycles

were

more

correlated

for

the

active

condition

than

for

the

relaxed

condition

This

implied

that

in

particular

in

the

active

condition

a

part

of

the

adjustments

of

the

half-cycle

durations

-LRB-

captured

by

RHC

-RRB-

compensated

for

overcorrection

in

the

preceding

half-cycle

Fig.

correlations

of

the

durations

of

successive

half-cycles

obtained

during

in-phase

-LRB-

IP

-RRB-

and

antiphase

-LRB-

AP

-RRB-

coordination

while

the

muscles

of

the

left

-LRB-

driven

-RRB-

hand

were

active

-LRB-

AC

-RRB-

or

relaxed

-LRB-

RE

-RRB-

a

within-hand

correlations

-LRB-

Ryy

-RRB-

b

between-hands

correlations

-LRB-

Rxy

-RRB-

c

and

d

indicate

the

relative

contributions

of

the

covariances

underlying

the

within-hand

and

between-hands

factors

-LRB-

Cyy

and

Cxy

respectively

-RRB-

by

expressing

them

as

a

fraction

of

the

covariance

underlying

RFC

-LRB-

i.e.

CFC

-RRB-

negative

values

indicate

a

reduction

of

the

absolute

value

of

RFC

-LRB-

see

Appendix

-RRB-

To

facilitate

comparison

the

values

of

Ryy

and

Rxy

are

presented

in

the

same

order

as

the

corresponding

values

of

RFC

in

Fig.

Error

bars

indicate

the

standard

error

of

the

mean

The

legends

of

a

and

b

also

apply

to

c

and

d

respectively

Legends

FHC

flexion

half

cycle

EHC

extension

half

cycle

the

arrows

specify

the

temporal

order

of

the

half

cycles

Whereas

the

second

half

cycle

is

always

performed

by

the

right

hand

the

first

half

cycle

is

performed

either

by

the

right

hand

-LRB-

Ryy

and

Cyy

a

and

c

-RRB-

or

by

the

left

hand

-LRB-

Rxy

and

Cxy

b

and

d

-RRB-

EMG

The

average

amplitudes

of

the

EMGs

-LRB-

normalized

to

MVC

amplitude

-RRB-

during

the

movement

cycle

are

presented

in

Fig.

which

exposes

five

noteworthy

characteristics

of

the

EMG

data

First

in

the

right

arm

the

EMG

amplitudes

were

smaller

in

the

relaxed

condition

than

in

the

active

condition

-LRB-

compare

open

and

filled

symbols

respectively

in

Fig.

b

-RRB-

corresponding

to

the

observed

differences

in

range

of

motion

between

these

conditions

Second

in

line

with

the

task

requirements

the

EMG

amplitudes

of

the

muscles

in

the

left

arm

were

in

general

much

smaller

in

the

relaxed

condition

than

in

the

active

condition

-LRB-

compare

open

and

filled

symbols

respectively

in

Fig.

d

-RRB-

Third

for

left

FCR

in

the

relaxed

condition

a

distinctive

-LRB-

reactive

-RRB-

peak

in

the

EMG

amplitude

was

observed

at

bin

i.e.

the

moment

at

which

the

lengthening

of

the

muscle

started

-LRB-

open

symbols

in

Fig.

-RRB-

Fourth

for

left

ECR

in

the

relaxed

condition

the

EMG

amplitude

showed

a

slight

modulation

during

the

movement

cycle

that

mimicked

that

of

normal

activation

patterns

-LRB-

compare

open

symbols

in

Fig.

with

the

curves

in

Fig.

-RRB-

Fifth

both

left

FCR

and

ECR

in

the

active

condition

-LRB-

filled

symbols

in

Fig.

d

respectively

-RRB-

were

shifted

leftward

with

respect

to

the

-LRB-

motor-driven

-RRB-

movement

compared

to

the

timing

of

right

FCR

and

ECR

when

compared

to

the

-LRB-

self-generated

-RRB-

movement

-LRB-

Fig.

b

respectively

-RRB-

Note

that

this

phase

advance

of

the

EMG

in

the

left

arm

relative

to

the

corresponding

hand

motion

was

possible

because

-LRB-

in

contrast

to

the

right

hand

-RRB-

the

movements

of

the

-LRB-

motor-driven

-RRB-

left

hand

were

completely

independent

of

its

muscle

activity

Fig.

EMG

amplitudes

-LRB-

RMS

values

-RRB-

of

FCR

-LRB-

a

right

c

left

-RRB-

and

ECR

-LRB-

b

right

d

left

-RRB-

averaged

over

subjects

at

eight

phases

of

the

movement

cycle

Each

graph

shows

the

muscle

activity

for

the

conditions

in

which

the

muscles

of

the

left

-LRB-

driven

-RRB-

arm

were

either

active

-LRB-

filled

symbols

-RRB-

or

relaxed

-LRB-

open

symbols

-RRB-

for

in-phase

-LRB-

triangles

solid

lines

-RRB-

and

antiphase

coordination

-LRB-

circles

dashed

lines

-RRB-

separately

Weighted

coherence

The

weighted

coherence

of

the

rEMG

of

homologous

muscles

is

shown

in

Fig.

Statistical

analysis

using

a

-LRB-

Pattern

-RRB-

-LRB-

Activity

-RRB-

-LRB-

Muscle

-RRB-

repeated

measures

ANOVA

revealed

significant

effects

of

Activity

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

and

Muscle

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

as

well

as

a

significant

Activity

Pattern

interaction

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

The

effect

of

Activity

revealed

that

the

weighted

coherence

was

larger

in

the

active

condition

than

in

the

relaxed

condition

-LRB-

vs.

-RRB-

The

effect

of

Muscle

showed

that

the

weighted

coherence

was

larger

for

ECR

than

for

FCR

-LRB-

vs.

-RRB-

indicating

a

greater

similarity

of

the

EMG

activity

for

extensor

than

for

flexor

muscles

Post

hoc

analysis

of

the

Activity

Pattern

interaction

revealed

no

significant

differences

between

in-phase

and

antiphase

coordination

for

either

the

active

condition

or

the

relaxed

condition

-LRB-

or

vice

versa

-RRB-

although

the

weighted

coherence

was

larger

for

in-phase

than

for

antiphase

in

the

active

condition

-LRB-

vs.

-RRB-

but

smaller

for

in-phase

than

for

antiphase

in

the

relaxed

condition

-LRB-

vs.

-RRB-

Fig.

weighted

coherence

-LRB-

CW

-RRB-

of

the

rectified

EMGs

of

homologous

muscles

FCR

-LRB-

black

-RRB-

and

ECR

-LRB-

gray

-RRB-

during

in-phase

-LRB-

IP

-RRB-

and

antiphase

-LRB-

AP

-RRB-

coordination

both

for

the

conditions

in

which

the

muscles

of

the

left

-LRB-

motor-driven

-RRB-

hand

were

active

-LRB-

AC

-RRB-

or

relaxed

-LRB-

RE

-RRB-

Error

bars

indicate

the

standard

error

of

the

mean

Temporal

relations

in

the

active

condition

In

the

active

condition

the

relative

phase

was

determined

at

two

levels

at

the

behavioral

level

-LRB-

kinematics

-RRB-

and

at

the

level

of

the

neural

control

signals

-LRB-

based

on

rEMG

-RRB-

This

distinction

is

important

because

for

the

right

hand

the

phase

shift

between

EMG

activity

and

kinematics

was

constrained

by

the

effector

dynamics

of

the

wrist

-LRB-

Ridderikhoff

et

al.

-RRB-

whereas

these

constraints

did

not

affect

the

phase

shift

for

the

left

-LRB-

motor-driven

-RRB-

hand

Hence

the

two

levels

were

not

tightly

coupled

in

this

kinesthetic

tracking

task

To

examine

the

relations

between

these

levels

four

different

phase

relations

were

studied

in

conjunction

the

phase

shifts

between

neural

control

signals

and

behavior

for

-LRB-

-RRB-

the

right

hand

and

-LRB-

-RRB-

the

left

hand

and

the

relative

phase

between

the

limbs

at

-LRB-

-RRB-

the

behavioral

level

and

-LRB-

-RRB-

the

level

of

neural

control

signals

The

results

regarding

the

relative

phase

at

the

behavioral

level

were

presented

in

the

preceding

In

the

next

two

subsections

the

other

phase

relations

-LRB-

i.e.

the

phase

shifts

between

rEMG

and

kinematics

and

the

relative

phase

between

rEMGs

of

homologous

muscles

-RRB-

are

presented

The

results

are

combined

in

the

final

subsection

to

provide

an

overall

picture

of

the

temporal

relations

in

the

active

condition

across

these

different

levels

Phase

shifts

between

EMG

and

kinematics

In

the

active

condition

differences

between

the

left

and

right

hand

were

observed

with

respect

to

the

timing

of

the

muscle

activity

relative

to

the

ongoing

movement

-LRB-

see

Fig.

-RRB-

To

analyze

these

differences

the

phase

shifts

between

rEMG

and

kinematics

-LRB-

see

Table

negative

values

indicate

that

the

EMG

is

leading

the

kinematics

-RRB-

were

examined

using

a

-LRB-

Hand

-RRB-

-LRB-

Pattern

-RRB-

-LRB-

Muscle

-RRB-

repeated

measures

ANOVA

This

revealed

a

significant

effect

of

Hand

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

indicating

larger

phase

shifts

for

the

left

hand

than

for

the

right

hand

-LRB-

vs.

-RRB-

In

addition

significant

Hand

Muscle

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

Hand

Pattern

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

and

Hand

Pattern

Muscle

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

interactions

were

found

Post

hoc

analysis

demonstrated

that

the

Hand

Muscle

interaction

occurred

because

the

phase

shifts

for

ECR

and

FCR

differed

significantly

for

the

right

hand

-LRB-

vs.

-RRB-

but

not

for

the

left

-LRB-

motor-driven

-RRB-

hand

The

Hand

Pattern

interaction

post

hoc

analysis

revealed

that

the

phase

shifts

during

in-phase

and

antiphase

coordination

differed

significantly

for

the

left

-LRB-

motor-driven

-RRB-

hand

-LRB-

vs.

-RRB-

but

not

for

the

right

hand

Post

hoc

analysis

of

the

three-way

interaction

revealed

that

the

phase

shift

for

the

left

FCR

during

antiphase

coordination

deviated

from

the

overall

pattern

it

was

significantly

different

from

the

phase

shift

during

in-phase

coordination

-LRB-

in

the

absence

of

significant

differences

between

in-phase

and

antiphase

for

any

of

the

other

muscles

-RRB-

and

it

was

not

significantly

different

from

the

phase

shift

for

right

FCR

during

antiphase

coordination

-LRB-

whereas

all

other

left-right

comparisons

yielded

significant

differences

for

both

coordinative

patterns

-RRB-

Table

shifts

between

rectified

EMG

and

joint

angles

in

the

active

condition

-LRB-

mean

between-subjects

SD

-RRB-

as

determined

from

the

cross-spectrum

of

these

variables

at

the

movement

frequencyHandMuscleIn-phaseAntiphaseLeftFCR

ECR

RightFCR

ECR

Relative

phasing

of

EMG

The

relative

phase

between

the

rEMG

of

homologous

muscles

in

the

active

condition

was

calculated

for

FCR

and

ECR

The

constant

errors

with

respect

to

the

reference

values

for

in-phase

-LRB-

-RRB-

and

antiphase

-LRB-

-RRB-

coordination

-LRB-

see

Table

-RRB-

were

subjected

to

a

-LRB-

Pattern

-RRB-

-LRB-

Muscle

-RRB-

repeated

measures

ANOVA

The

analysis

revealed

significant

effects

of

Pattern

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

Muscle

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

and

a

significant

Pattern

Muscle

interaction

-LRB-

F

-LRB-

-RRB-

P

f

-RRB-

The

effect

of

Pattern

resulted

in

a

significantly

larger

constant

error

for

in-phase

than

for

antiphase

coordination

-LRB-

vs.

positive

values

indicate

a

relative

phase

lead

of

the

activity

in

the

left

arm

-RRB-

The

effect

of

Muscle

indicated

that

the

average

constant

errors

for

FCR

and

ECR

were

significantly

different

-LRB-

vs.

-RRB-

Post

hoc

analyses

of

the

Pattern

Muscle

interaction

revealed

a

significant

difference

between

the

constant

errors

for

in-phase

and

antiphase

coordination

for

FCR

but

not

for

ECR

-LRB-

see

values

in

Table

-RRB-

Table

constant

errors

in

the

relative

phase

for

kinematics

and

EMG

in

the

active

condition

-LRB-

mean

between-subjects

SD

-RRB-

LevelIn-phaseAntiphaseKinematics

EMG

°F

or

the

EMG

the

obtained

values

are

presented

for

homologous

FCR

and

ECR

separately

The

mean

of

the

constant

errors

for

FCR

and

ECR

was

adopted

as

the

constant

error

of

the

neural

control

signal

Negative

-LRB-

positive

-RRB-

values

indicate

that

the

right

limb

is

leading

-LRB-

lagging

-RRB-

the

left

limb

Relative

phasing

of

neural

control

signals

and

behavior

To

gain

insight

into

the

neurobehavioral

basis

of

error

correction

we

examined

the

phase

relations

between

the

neural

control

signals

and

the

overt

behavior

in

the

active

condition

For

this

purpose

the

phasing

of

the

neural

control

signals

was

estimated

for

each

limb

separately

by

taking

the

average

of

the

values

obtained

for

FCR

and

ECR

-LRB-

see

Tables

-RRB-

The

resulting

phase

relations

are

displayed

schematically

for

in-phase

and

antiphase

coordination

in

Fig.

which

illustrates

the

muscle-independent

phase

relations

addressed

in

the

previous

two

paragraphs

showing

only

the

effects

of

Hand

and

Pattern

First

the

phase

shift

between

the

neural

control

signal

and

the

wrist

movements

was

larger

for

the

-LRB-

motor-driven

-RRB-

left

hand

-LRB-

dashed

arrows

-RRB-

than

for

the

right

hand

-LRB-

solid

arrows

-RRB-

significant

effect

of

Hand

Second

the

constant

error

in

relative

phase

between

the

EMGs

of

homologous

muscles

was

larger

for

in-phase

than

antiphase

coordination

-LRB-

compare

the

corresponding

diagrams

-RRB-

significant

effect

of

Pattern

Third

it

can

be

appreciated

from

the

figure

that

the

phase

shift

between

EMG

and

kinematics

-LRB-

larger

shifts

in

the

left

hand

i.e.

longer

dashed

arrows

for

in-phase

than

for

antiphase

coordination

-RRB-

depended

on

the

combination

of

hand

and

pattern

significant

Hand

Pattern

interaction

Finally

the

diagrams

indicate

that

on

average

the

error

in

the

relative

phase

was

smaller

for

the

neural

control

signal

than

for

the

kinematics

-LRB-

respective

values

are

presented

in

Table

-RRB-

Fig.

illustrating

temporal

relations

in

the

active

condition

for

in-phase

-LRB-

left

panel

-RRB-

and

antiphase

-LRB-

right

panel

-RRB-

coordination

Circles

represent

signal

sources

θ

is

the

joint

angle

and

ξ

is

the

neural

control

signal

-LRB-

derived

from

the

EMG

averaged

over

FCR

and

ECR

-RRB-

The

length

of

the

arrows

indicates

the

phase

shifts

between

the

neural

control

signal

and

the

kinematics

-LRB-

arrows

point

in

the

direction

of

time

-RRB-

The

error

of

the

relative

phase

Φ

is

equal

to

the

inclination

angle

of

the

line

connecting

the

circles

at

either

the

kinematic

-LRB-

θ

-RRB-

or

the

control

level

-LRB-

ξ

-RRB-

The

target

values

of

Φ

are

indicated

by

the

gray

horizontal

lines

and

the

dotted

lines

represent

the

relative

error

in

Φ

in

the

relaxed

condition

-LRB-

available

for

kinematics

only

-RRB-

Discussion

The

goal

of

the

present

study

was

to

gain

more

insight

into

the

error

correction

processes

as

allegedly

implicated

in

bimanual

coordination

-LRB-

Ridderikhoff

et

al.

-RRB-

To

this

end

we

examined

the

temporal

adjustments

of

the

actively

moving

-LRB-

right

-RRB-

limb

in

a

kinesthetic

tracking

task

based

on

the

perceived

-LRB-

error

in

the

-RRB-

relative

phase

between

the

limbs

In

particular

subjects

tracked

their

motor-driven

left

hand

with

the

actively

moving

right

hand

to

achieve

in-phase

or

antiphase

coordination

in

conditions

where

the

left

hand

musculature

was

activated

-LRB-

as

if

moving

along

with

the

reference

movement

-RRB-

or

kept

as

relaxed

as

possible

In

addition

the

relation

between

bimanual

-LRB-

between-limbs

-RRB-

and

unimanual

-LRB-

within-limb

-RRB-

factors

was

examined

Unimanual

and

bimanual

factors

were

dissociated

by

comparison

of

several

-LRB-

related

-RRB-

temporal

correlations

and

by

examining

the

phase

shifts

between

neural

control

signals

and

kinematics

both

within

and

between

limbs

In

line

with

our

research

questions

the

analysis

focused

on

two

aspects

of

the

measurements

which

are

discussed

in

detail

in

the

next

two

subsections

-LRB-

-RRB-

differences

in

error

correction

between

in-phase

and

antiphase

coordination

and

-LRB-

-RRB-

effects

of

muscle

activity

in

the

driven

-LRB-

left

-RRB-

limb

on

these

error

corrections

and

on

the

overall

performance

of

the

task

In

the

last

two

subsections

we

will

then

address

the

observed

differences

between

the

left

and

right

hand

and

between

flexors

and

extensors

in

terms

of

the

phase

shifts

between

EMG

and

kinematics

and

the

relative

timing

of

flexion

and

extension

Before

embarking

on

these

discussions

it

should

be

noted

that

the

stability

of

the

bimanual

patterns

was

affected

by

the

muscle

activity

in

the

motor-driven

limb

as

SDΦ

was

larger

in

the

relaxed

condition

than

in

the

active

condition

Furthermore

the

variability

of

the

relative

phase

-LRB-

SDΦ

-RRB-

was

smaller

for

in-phase

than

for

antiphase

coordination

This

basic

observation

confirmed

the

result

of

an

earlier

study

on

kinesthetic

tracking

-LRB-

Stinear

and

Byblow

-RRB-

and

indicated

that

also

in

normal

bimanual

coordination

the

stability

difference

of

in-phase

and

antiphase

coordination

may

be

partly

dependent

on

afference-based

error

corrections

Error

corrections

We

performed

an

in-depth

analysis

of

the

corrections

in

the

timing

of

the

movements

of

the

right

-LRB-

actively

moving

-RRB-

limb

based

on

the

perceived

errors

in

the

relative

phase

Since

our

analyses

of

the

kinematics

concerned

the

timing

of

discrete

events

-LRB-

i.e.

peak

extension

and

peak

flexion

-RRB-

the

shortest

possible

time

scale

to

study

error

corrections

was

related

to

compensatory

adjustments

of

the

duration

of

the

half-cycle

following

the

detected

error

The

related

measure

-LRB-

RHC

-RRB-

indicated

that

the

error

corrections

were

more

pronounced

for

in-phase

than

for

antiphase

coordination

and

that

they

were

characterized

by

larger

absolute

values

for

the

active

condition

than

for

the

relaxed

condition

in

line

with

the

observed

effects

for

SDΦ

Additional

analysis

of

the

compensatory

adjustments

of

the

duration

of

the

full

cycle

following

the

detected

error

-LRB-

RFC

-RRB-

showed

that

both

error

correction

effects

persisted

on

a

longer

time

scale

Therefore

we

conclude

that

corrections

in

the

movement

timing

of

the

right

hand

based

on

the

perceived

errors

in

the

relative

phase

underlie

the

observed

stability

effects

-LRB-

SDΦ

-RRB-

of

the

examined

coordination

patterns

-LRB-

in-phase

vs.

antiphase

-RRB-

and

muscle

activity

It

is

important

to

consider

error

corrections

at

different

time

scales

because

the

dependency

of

the

corrections

performed

in

successive

half-cycles

may

vary

over

conditions

-LRB-

see

Materials

and

methods

-RRB-

The

results

revealed

that

in

the

present

study

these

dependencies

between

successive

half-cycles

were

reflected

mainly

by

the

within-hand

correlation

Ryy

indicating

an

important

role

for

the

unimanual

coordinative

processes

underlying

the

rhythmic

movements

of

the

right

hand

This

role

is

of

particular

importance

for

the

interpretation

of

the

significant

Pattern

Activity

interaction

observed

for

RHC

suggesting

more

pronounced

error

corrections

during

in-phase

coordination

in

the

active

condition

Because

the

results

obtained

for

Ryy

demonstrated

larger

dependencies

between

successive

half-cycles

in

the

active

condition

than

in

the

relaxed

condition

the

effects

related

to

muscle

activity

were

reduced

at

a

longer

time

scale

-LRB-

RFC

-RRB-

As

a

consequence

the

Pattern

Activity

interaction

was

not

significant

for

RFC

and

thus

appeared

to

be

of

little

functional

relevance

in

terms

of

the

coordinative

stability

This

illustrates

how

unimanual

coordination

-LRB-

the

flexion

extension

coupling

in

terms

of

Ryy

-RRB-

may

impinge

on

the

effects

of

interlimb

interactions

-LRB-

the

error

corrections

in

terms

of

RHC

-RRB-

in

bimanual

coordination

Two

additional

discrepancies

between

RHC

and

RFC

were

found

in

relation

to

effects

of

the

orientation

of

the

hand

-LRB-

flexion

or

extension

-RRB-

This

was

not

surprising

because

RHC

and

RFC

are

unrelated

by

definition

with

respect

to

these

effects

As

shown

both

analytically

-LRB-

for

the

underlying

covariances

see

Appendix

-RRB-

and

empirically

all

differences

between

flexion

and

extension

in

RFC

are

attributable

to

the

correlations

between

the

durations

of

successive

half-cycles

within

the

right

hand

-LRB-

Ryy

-RRB-

and

between

hands

-LRB-

Rxy

-RRB-

Specifically

the

effect

of

orientation

of

the

hand

obtained

for

RFC

was

not

related

to

error

corrections

based

on

the

perceived

relative

phase

but

rather

reflected

an

asymmetry

in

the

coupling

of

the

unimanual

flexion

and

extension

half-cycles

as

captured

by

Ryy

In

contrast

differences

in

the

strength

of

the

error

corrections

during

the

flexion

and

extension

half-cycles

are

indicated

by

effects

of

orientation

observed

for

RHC

Analysis

of

RHC

revealed

a

significant

Pattern

Orientation

interaction

which

indicated

more

pronounced

error

corrections

in

the

half-cycle

following

peak

flexion

of

the

left

-LRB-

motor-driven

-RRB-

hand

in

particular

in

the

extension

half-cycle

during

in-phase

coordination

-LRB-

Fig

-RRB-

In

line

with

this

result

we

observed

the

smallest

errors

in

the

mean

relative

phase

at

the

end

of

the

half-cycles

with

the

most

prominent

error

corrections

-LRB-

i.e.

at

peak

extension

during

in-phase

and

at

peak

flexion

during

antiphase

coordination

see

Fig

-RRB-

A

tentative

explanation

of

these

findings

is

that

-LRB-

relative

-RRB-

timing

errors

were

detected

most

accurately

at

peak

flexion

of

the

driven

hand

and

that

as

a

consequence

the

corrections

in

the

following

half-cycle

were

most

effective

leading

to

the

highest

accuracy

in

the

relative

phase

at

the

end

of

these

half-cycles

With

respect

to

the

two

adopted

measures

of

error

correction

-LRB-

RHC

and

RFC

-RRB-

these

analyses

demonstrated

that

both

measures

should

be

evaluated

in

conjunction

to

assess

the

net

effect

of

error

corrections

in

relation

to

the

effects

of

movement

pattern

and

muscle

activity

whereas

RHC

offers

additional

insight

into

the

differences

between

flexion

and

extension

in

this

respect

The

analyses

of

the

temporal

correlations

revealed

several

important

global

characteristics

of

the

afference-based

error

corrections

underlying

rhythmic

bimanual

coordination

Although

the

analyses

demonstrated

that

error

corrections

occur

during

the

next

half-cycle

it

is

important

to

emphasize

that

the

precise

time

course

of

the

error

corrections

remains

unknown

That

is

these

methods

do

not

reveal

how

long

it

takes

until

the

ongoing

movements

are

adapted

to

compensate

for

perceived

errors

except

for

showing

that

such

changes

occur

within

the

next

half-cycle

Although

in

principle

it

is

possible

that

timing

errors

are

detected

throughout

the

cycle

and

not

only

at

peak

flexion

and

peak

extension

there

is

ample

evidence

indicating

that

coordinated

rhythmic

movements

are

characterized

by

the

presence

of

so-called

anchor

points

-LRB-

Beek

-RRB-

that

is

discrete

points

in

the

cycle

that

have

particular

significance

for

the

control

of

timing

Furthermore

several

studies

have

demonstrated

that

anchoring

occurs

when

peak

flexion

and/or

peak

extension

are

coinciding

with

an

external

stimulus

-LRB-

Byblow

et

al.

Fink

et

al.

-RRB-

These

findings

provide

a

rationale

for

the

use

of

the

moments

of

peak

flexion

and

peak

extension

in

the

analysis

of

the

temporal

structure

of

the

bimanual

coordination

pattern

and

the

instructions

to

subjects

in

terms

of

the

timing

of

peak

flexion

and

peak

extension

-LRB-

see

Materials

and

methods

-RRB-

may

have

helped

to

establish

such

anchor

points

in

the

present

study

However

further

research

regarding

the

existence

of

anchor

points

in

the

processing

of

kinesthetic

feedback

and

the

time

course

of

the

adjustments

is

required

for

which

the

analyses

in

the

present

study

may

serve

as

departure

point

For

our

current

purposes

RHC

and

RFC

provided

important

insights

into

the

average

amount

of

corrective

activity

that

occurs

at

two

relevant

time

scales

in

terms

of

the

same

kinematic

measures

that

were

used

to

assess

the

performance

in

terms

of

the

relative

phase

between

the

hands

The

effects

of

muscle

activity

in

the

driven

limb

The

second

objective

of

this

study

was

to

examine

the

neurobehavioral

basis

of

error

correction

To

this

aim

we

manipulated

the

muscle

activity

in

the

motor-driven

limb

by

instructing

subjects

either

to

activate

their

muscles

in

accordance

with

the

ongoing

motion

or

to

keep

them

as

relaxed

as

possible

The

average

EMG

amplitudes

-LRB-

Fig.

-RRB-

clearly

showed

that

this

manipulation

of

muscle

activity

was

successful

in

the

sense

that

subjects

managed

by

and

large

to

avoid

activating

the

muscles

in

the

motor-driven

left

hand

in

the

relaxed

condition

This

was

further

underscored

by

the

fact

that

the

values

of

the

weighted

coherence

of

rEMGs

of

homologous

muscles

in

the

relaxed

condition

did

not

exceed

those

obtained

in

previous

studies

involving

passive

-LRB-

i.e.

motor-driven

-RRB-

hand

movement

-LRB-

Ridderikhoff

et

al.

Ridderikhoff

et

al.

-RRB-

In

those

studies

subjects

had

been

explicitly

instructed

to

ignore

the

motor-driven

movement

-LRB-

i.e.

no

coordination

between

the

hands

was

required

-RRB-

in

order

to

study

phase

entrainment

by

contralateral

afference

implying

that

the

resulting

values

of

the

weighted

coherence

can

be

regarded

as

a

baseline

for

the

effect

of

motor-driven

movement

per

se

In

contrast

in

the

active

condition

the

changes

in

the

EMG

amplitude

of

the

motor-driven

hand

resembled

those

observed

for

actively

performed

rhythmic

wrist

movements

-LRB-

as

obtained

for

the

right

hand

-RRB-

and

significantly

larger

coherence

of

the

homologous

muscle

activity

was

observed

For

a

proper

evaluation

of

the

adopted

methodology

it

is

relevant

to

note

that

the

experiment

actually

involved

a

dual

task

paradigm

because

in

all

conditions

subjects

were

instructed

to

perform

the

required

bimanual

pattern

and

at

the

same

time

control

the

muscle

activity

in

the

driven

arm

The

additional

cognitive

load

that

is

associated

with

performance

of

a

secondary

task

may

have

augmented

the

intrinsic

stability

differences

between

in-phase

and

antiphase

coordination

-LRB-

Temprado

et

al.

-RRB-

However

the

results

did

not

indicate

a

differential

effect

of

the

two

secondary

tasks

-LRB-

active

vs.

relaxed

condition

-RRB-

on

the

stability

difference

between

in-phase

and

antiphase

-LRB-

i.e.

no

Activity

Pattern

interactions

were

observed

for

SDΦ

-RRB-

From

this

we

conclude

that

the

additional

cognitive

load

imposed

by

the

secondary

task

was

the

same

for

the

active

and

relaxed

condition

and

that

the

dual

task

paradigm

did

not

confound

the

comparison

between

these

conditions

In

other

words

we

are

confident

that

the

observed

differences

between

these

conditions

can

be

ascribed

to

the

differences

in

muscle

activity

associated

with

these

conditions

rather

than

differences

in

cognitive

load

On

the

other

hand

the

dual

task

character

of

the

present

manipulations

may

explain

why

the

present

results

regarding

the

SDΦ

of

in-phase

and

antiphase

coordination

agreed

with

those

reported

in

the

study

of

Stinear

and

Byblow

-LRB-

-RRB-

in

which

an

additional

amplitude

matching

of

the

movements

was

required

but

not

with

our

previous

-LRB-

single

task

-RRB-

experiment

on

kinesthetic

tracking

-LRB-

Ridderikhoff

et

al.

-RRB-

Muscle

activity

clearly

had

a

beneficial

effect

on

coordinative

stability

as

the

variability

of

the

relative

phase

was

significantly

smaller

in

the

active

condition

than

in

the

relaxed

condition

-LRB-

Fig.

-RRB-

In

addition

the

adopted

measures

related

to

the

error

correction

processes

underlying

kinesthetic

tracking

showing

larger

compensatory

adjustments

of

the

timing

of

the

right

hand

in

the

active

condition

-LRB-

RHC

and

RFC

Fig.

-RRB-

indicated

that

kinesthetic

afference

was

processed

more

effectively

in

this

condition

Consequently

it

seems

unlikely

that

the

muscle

activity

during

kinesthetic

tracking

that

we

observed

in

our

previous

study

-LRB-

Ridderikhoff

et

al.

-RRB-

was

merely

a

byproduct

due

to

neural

However

in

addition

to

these

benefits

of

muscle

activity

we

also

found

that

the

absolute

-LRB-

and

constant

-RRB-

errors

in

the

mean

relative

phase

were

larger

in

the

active

condition

than

in

the

relaxed

condition

-LRB-

Fig.

-RRB-

indicating

that

the

coordinative

pattern

was

performed

less

accurately

in

the

former

condition

Thus

muscle

activation

during

kinesthetic

tracking

resulted

in

more

pronounced

and

proficient

error

corrections

in

bimanual

timing

but

these

corrections

appeared

to

be

performed

with

respect

to

less

accurate

reference

values

In

explaining

this

reduced

accuracy

in

the

active

condition

it

proved

essential

to

dissociate

the

temporal

relations

between

the

limbs

observed

at

the

level

of

neural

control

signals

and

those

observed

at

the

behavioral

level

because

these

levels

may

involve

separate

reference

signals

In

the

relaxed

condition

only

the

relative

phasing

at

the

behavioral

level

-LRB-

kinematics

-RRB-

is

available

as

reference

for

the

error

corrections

In

contrast

the

presence

of

a

bilateral

neural

control

signal

in

the

active

condition

implies

that

the

relative

phase

between

the

neural

control

signals

-LRB-

or

motor

outflow

-RRB-

may

also

be

used

as

reference

-LRB-

e.g.

by

means

of

anticipation

of

the

sensory

consequences

of

the

ongoing

movement

based

on

efference

copies

-RRB-

Comparison

of

the

constant

errors

at

the

two

levels

-LRB-

Table

-RRB-

suggested

an

attraction

toward

the

proper

timing

of

the

neural

control

signals

resulting

in

larger

errors

in

the

relative

phase

at

the

behavioral

level

-LRB-

Fig.

-RRB-

This

observation

also

revealed

a

discrepancy

between

the

relative

phases

at

the

two

levels

which

resulted

from

an

inadequate

timing

of

the

neural

control

signals

of

the

motor-driven

hand

as

explained

in

the

next

subsection

This

interpretation

of

the

results

underscores

that

bimanual

coordination

benefited

from

muscle

activity

during

kinesthetic

tracking

because

the

bilateral

motor

commands

were

used

-LRB-

e.g.

via

efference

copy

-RRB-

as

a

reference

signal

for

movement-elicited

afference

The

presence

of

this

reference

signal

which

presumably

allowed

for

prediction

of

the

sensory

consequences

of

the

bimanual

movement

resulted

in

more

prominent

error

corrections

leading

to

a

smaller

variability

of

the

relative

phase

in

the

active

condition

Thus

the

evidence

suggested

that

an

intimate

sensorimotor

integration

which

has

been

proposed

in

the

context

of

discrete

goal-directed

movements

-LRB-

e.g.

Wolpert

and

Ghahramani

Scott

-RRB-

also

underlies

the

coordination

of

rhythmic

bimanual

movements

In

the

context

of

the

present

study

this

interpretation

can

account

for

the

observed

effects

of

muscle

activation

on

the

stability

as

well

as

the

accuracy

of

the

relative

phase

Timing

of

the

EMG

activity

in

the

motor-driven

arm

Unlike

the

phase

shifts

between

EMG

and

kinematics

of

the

left

-LRB-

motor-driven

-RRB-

arm

observed

in

the

present

study

the

muscle

activity

observed

during

kinesthetic

tracking

in

our

previous

study

-LRB-

Ridderikhoff

et

al.

-RRB-

was

adequately

timed

with

respect

to

the

ongoing

motor-driven

movement

A

possible

explanation

for

this

unexpected

discrepancy

between

these

two

studies

may

be

related

to

the

instructions

given

to

the

subjects

In

the

active

condition

of

the

present

study

subjects

were

explicitly

instructed

to

activate

their

muscles

whereas

subjects

did

this

spontaneously

-LRB-

i.e.

without

instruction

-RRB-

in

our

previous

study

Given

the

instruction

to

activate

the

muscles

as

if

moving

along

with

the

passive

movement

subjects

seemed

to

have

aimed

at

generating

contact

forces

that

gave

the

impression

that

they

were

pushing

or

pulling

the

manipulandum

in

the

correct

direction

Comparison

of

the

EMG

amplitudes

in

the

left

-LRB-

motor-driven

-RRB-

arm

and

the

right

-LRB-

actively

moving

-RRB-

arm

-LRB-

Fig.

-RRB-

indicated

that

this

was

accomplished

by

an

earlier

activation

of

the

muscles

in

the

left

arm

-LRB-

relative

to

the

ongoing

movement

-RRB-

and

an

increase

of

the

EMG

amplitude

-LRB-

i.e.

an

increase

of

the

muscle

torque

-RRB-

These

changes

substantially

increased

the

forces

acting

between

the

hand

and

the

manipulandum

in

the

direction

of

the

ongoing

movement

Note

also

that

the

EMG

activity

was

minimal

at

the

moments

of

peak

excursion

i.e.

when

the

movement

changed

direction

-LRB-

see

Fig.

-RRB-

In

other

words

the

results

suggested

that

subjects

in

effect

sought

after

the

expected

sensory

consequences

of

moving

something

This

may

be

regarded

as

a

misinterpretation

of

the

instruction

because

truly

moving

along

requires

the

elimination

of

contact

forces

altogether

Flexor

extensor

differences

during

active

rhythmic

wrist

movement

In

addition

to

the

effects

of

afference-based

interlimb

interactions

-LRB-

as

reflected

in

the

error

corrections

-RRB-

the

flexion

and

extension

phases

were

also

affected

by

the

unimanual

control

processes

underlying

the

rhythmic

movement

of

the

-LRB-

right

-RRB-

wrist

itself

In

this

regard

an

asymmetry

was

found

in

the

correlations

between

successive

flexion

and

extension

half-cycles

-LRB-

Ryy

-RRB-

indicating

that

the

durations

of

the

flexion

half-cycles

were

adapted

more

to

changes

in

the

duration

of

the

extension

half-cycle

than

vice

versa

-LRB-

Fig.

-RRB-

Studies

on

unilateral

rhythmic

movements

have

also

reported

an

asymmetric

relation

between

flexion

and

extension

half-cycles

in

rhythmic

finger

movements

-LRB-

Balasubramaniam

et

al.

-RRB-

and

a

more

adequate

temporal

control

of

wrist

flexion

than

wrist

extension

-LRB-

Carson

Carson

and

Riek

-RRB-

An

adaptive

relation

between

the

relative

timing

of

FCR

and

ECR

on

the

one

hand

and

the

resulting

wrist

movements

on

the

other

hand

was

also

indicated

by

the

analysis

of

the

phase

shifts

between

EMG

and

kinematics

Different

phase

shifts

were

obtained

for

FCR

and

ECR

in

the

right

hand

but

not

in

the

left

hand

in

which

timing

of

EMG

and

kinematics

were

unrelated

Such

differences

in

the

relative

timing

of

FCR

and

ECR

activity

during

rhythmic

wrist

movements

have

been

reported

before

-LRB-

Ridderikhoff

et

al.

-RRB-

and

may

reflect

adaptations

to

the

different

physiological

properties

of

these

muscles

that

would

affect

the

movement

trajectories

unless

compensated

for

Furthermore

the

EMG

analysis

revealed

that

the

coherence

between

left

and

right

ECR

was

larger

than

the

coherence

between

left

and

right

FCR

may

be

related

to

the

finding

that

neural

cross-talk

effects

were

larger

for

extensor

than

for

flexor

muscles

-LRB-

Ridderikhoff

et

al.

-RRB-

These

combined

results

point

to

a

more

independent

control

of

the

timing

of

FCR

in

the

context

of

rhythmic

wrist

movement

Conclusion

The

present

study

revealed

two

characteristics

of

the

error

corrections

based

on

the

kinesthetically

perceived

relative

phase

that

are

relevant

to

the

understanding

of

rhythmic

bimanual

coordination

and

supplement

the

findings

of

our

previous

study

on

the

sources

of

interlimb

interaction

involved

in

this

type

of

task

-LRB-

Ridderikhoff

et

al.

-RRB-

First

the

corrections

were

more

effective

during

in-phase

than

during

antiphase

coordination

resulting

in

a

smaller

variability

of

the

relative

phase

in

the

former

condition

This

effect

may

be

attributable

to

differences

in

the

kinesthetic

perception

of

variability

in

in-phase

and

antiphase

coordination

-LRB-

Wilson

et

al.

-RRB-

and

indicated

that

afference-based

error

corrections

contribute

to

the

well-known

stability

difference

of

these

bimanual

patterns

-LRB-

Kelso

Swinnen

-RRB-

Thus

although

somatosensory

feedback

is

not

essential

for

the

stability

differences

between

in-phase

and

antiphase

-LRB-

Spencer

et

al.

-RRB-

the

present

study

showed

that

afference-based

error

corrections

augment

the

stability

difference

resulting

from

open-loop

processes

underlying

the

integrated

timing

of

the

efferent

signals

to

both

limbs

-LRB-

Ridderikhoff

et

al.

-RRB-

Second

the

corrections

-LRB-

and

as

a

consequence

pattern

stability

-RRB-

were

enhanced

if

the

muscles

in

the

motor-driven

arm

were

activated

as

if

the

limb

was

moving

along

with

the

motor

On

the

other

hand

the

accuracy

of

the

relative

phasing

between

the

limbs

was

decreased

in

this

situation

indicating

that

the

corrections

were

based

on

a

different

reference

signal

than

in

the

relaxed

condition

The

most

likely

explanation

for

these

findings

was

that

the

bilateral

neural

control

signal

provided

a

reference

for

the

evaluation

of

the

kinesthetic

afference

in

the

sense

that

on

the

basis

of

this

signal

the

sensory

consequences

-LRB-

of

the

bimanual

movement

pattern

-RRB-

could

be

anticipated

A

closed-loop

control

process

that

exploits

this

kind

of

prediction

is

apparently

more

effective

in

terms

of

the

stabilization

of

the

relative

phase

This

result

suggests

an

intimate

relation

between

the

integrated

timing

of

the

feedforward

signals

-LRB-

underlying

the

bilateral

activation

pattern

if

both

hands

are

moving

actively

-RRB-

and

the

use

of

kinesthetic

feedback

in

rhythmic

bimanual

coordination

bimanual coordination
rhythmic movement
kinesthesis
proprioception
electromyography