運動冗長性の研究が中枢性疾患のリハビリテーションにもたらすもの

pa"rL-zai}te

ca35tsca8e

357-365"

_(2008fii)

tuSFreagdiM

Implications

of

Research

on

Motor

Redundancy

Neurological

Patients

"

John

P.

Scholz,

PhD,

PTi).

Masayoshi

Kubo,

Abstract

Reeent

tionaltribution,

feature

is

are

flexitorIlg21tltlg

a

tion.patternsto

be

used that

faciachieved

'

fbr

Rehabilitation

of

ScD,

pT2)

research suggests

that

two

important

features

need

to

be

identified

to

adequately characterize a

synergy.

These

features

are

defined

and

illustrated

in

this urticle.

The

first

feature

is

the relative on average. of

the

motor elements

to

the

moverrient

that

underlies

the

function

being

performed,

This

referred

to

as

the

''sharing"

pattern.

The

second

feature

captures

how

the

different

moror elements

bly

assembled across repetition$ of

the

task.

This

feature

provides

for

error compensation.

is

important

multi-tasking

behavior,

and requires motor redundancy.

A

number of studies with

healthy

individuals

varlety of

tasks

are

briefly

reviewed,

illustrating

the

use of motor redundancy

for

error

compensa-Patients

with a stroke and,

presumabty.

those

with other neurological

impairments,

exhibit altered sharing

as well as an apparent

limitation

in

decoup]ing

joint

space, which

is

necessary

for

motor redundancy effectively while

performance

remalns successful,

If

so,

then

the

developmenr

of

training

strategies

litare

the

tearning

of

joint

or muscle

decoupling

is

important.

A

few

examples of

how

this

might

be

m

the

context of reaching are

discussed.

lntroduction

A

frequently

used

term

in

the

field

of neurological

reha-bilitation

is

`synergyl

_{Historicatly,}

this

term

has

been

used

to

refer tn the atypical

_patterns

of

joint

and underlying

mus-c]eorganization

following

a stroke or truumatic

brain

injury.

Brunnstromi)

defined

four

atypical synergies

in

each of the upper and

gower

extremities,

fer

example.

These

atypical

motor synergies

define

retatively

fixed

_patterns

of

joint

cou-pling

that

make normal

function

difficult

at

best.

For

exam-ple,

it

is

wetl

known

that

stroke survivors with moderate

to

severe

impairments

have

great

difficulty

extending

the

elbow of their

impaired

arrn

in

combinatinn with etevation of

the

shoulderL).

Such

atypical synergTes

limTt

the

fiexibili-ty

with which

the

motor elements can

be

combined

for

func-*ll

2]

ffetVCltrta)orfihCLFasErk,to,

0) iP i

tf

iJ

_ift

-

_t.

_H

_).

_I:

_S

_t:

Cb

t

S

0)

t･vv.7)ltIV.ng\esi

±

-\Fl･

(*M)

Cerrespondence/

_John

P.

Scholz,

PhD,

PT.

Department

of

Physicat

Therapy

University

of

Deiaware

307

McKinly

Laboratory,

NevL'ark,

I)E

T9716,

US.

.nL

piizavademaaki',Nv:deta･?eF

Masayoshi

Kub",

ScD.

PT/

Depurtmcnt

ef

Physjcal

Therapy.

}S'iigata

L'niversiLy

of

Health

and

Welfare,

Niigata

City,

Japan

Key

words :

Synergy,

redundancy, ceordination, stroke

tlon.

In

contrast

the

word synergy

is

more commonly used

in

the

motor contro]

literature

in

the

context or norrnaT

func-tion,as

indicated

by

the

phrase

`functional synergies'3) i).

This

phrase

refers

to

the

spatio-temporal organization of

the

mus-cles and

joints

involved

in

a

particular

motor act,

Synergies

have

been

identified

as

patterns

of coupting among spinal

neuronal ensembles that

_give

rise to

different

limb

lrajec-tories

in

the

frog5)6),

to

muscle

Enkages

undertying

postur-al responses

in

the cat7)S) and

human9),

to

the coordinated action of multipte

fingers

that

generate

a

particutar

totai

force

outputie)ii), to

the

coupling among muttiple

joints

dur-ing

the

execution of reaehing

tasksi2)M)

and the sit-to-stand

behaviori4),

to

name a

few.

Synergy

is

generally

referred

te

as

the

way the central nervous system

(CNS)

achieves

coor-dination

among

the

motor elements.

Such

linkages

appar-entty simptify

the

brain's

control of movements

beeause

the

details

of

the

spatio-temporul coupling among the muscles

and

joints

are

presumed

to

be

regulated

by

neural centers

downstream

from

cortical and,

perhaps,

subcortical

struc-tures,

In

some theoretical circ[es

they

are

presumed

teoccur

by

processes

of self-organization among

the

activity ef ull

358

ew.iffiza\

lead

to

atypical couplings

(synergies)

ef the motor elements

rhat

lirnit

norma]

function

suggests

that

certical and

sub-certical structures are

intimatety

involved

in

synergy

mation.

The

neural

basis

nf synergy

formation

is

not the

focus

of

this

article,

however.

If

movement synergies underlie the normal abiJity

tD

per-form

functional

motor

tasks,

and atyplcal synergies

dominate

the

behavior

of many

patients

with neurological

impairments,

then

a

better

understanding of synergy

tormation

by

reha-bilitation

specialists

is

crucial

if

we are

to

better

help

neu-rological

patients

impreve

their

motor

function,

This

includes

an understanding of

the

key

features

of a

functional

syner-gy

as well as an understancling of

how

to

influence

syner-gy

formation.

Atthough

eur understanding of synergies

has

increased

substantially

in

recent

years,

our understanding of

synergy

formation

is

still

limited

alld

quite

general.

In

this

article,

I

will attempt to

provide

some

insights

that

may

be

helpful

to

the

clinician

trying

to

assist

patients

to

learn

func-tionally appropriate synergies

for

a

given

motor

task.

This

discussion

depends

on an understanding and appreciation

for

moter redundancy, which will

be

described

below.

Features

of a

Synergy

Sharing.

As

previously

noted, altho-gh most recent

inves-tigations

of synergies

have

occurred

in

relation

to

the

per-formance

of

tasks

(for

exceptions, see

Gielen

and van

Zuylen.

Igs6iG);

van

Zuylen

et al.,

1988i7)),

the

definition

of a

syner-gy

has

typieally

been

related to

function

only

indirectly.

Indeed,

the most common characzertzation ef a synergy

is

limited

to a

description

of

how

the

various motor eLements combine

in

the

overalt motor output, not specifically re]ated to the

_goat

ef the task,

This

feature

of a synergy

has

been

referred

to

as

the

`sharing

pattern'

by

Latash

and

leaguesiS).

The

feature

is

most ctearly

illustrated

by

consid-ering a simple example,

Take,

for

exampte,

the

act of

providing

cardiopulmonary resuscitation

to

an

infant.

The

index

and middle

fingers

are used

to

apply a

force

to

the

chest

that

is

sufficient

to

achieve aclequate airflow while not

too

large

as

to

cause

injury.

Thus,

the

rate of and

total

force

applied must

be

well-controlled.

Let

us assume,

for

illustration,

that

the

maximum

force

applied on each compression

is

1

Newton

(N}.

If

we attach

fDree

transducers

to

the

fingertip

of each

finger,

we can

measure

the

applied

force

precisely.

Over

anumber of

force

pulses,

one can ascertain

how

much of

the

total applied

force

is

contributed

by

each

finger,

In

generaL

although

the

force

contributions of each

finger

will

fluctuate

somewhat across repetitions,

they

witl

be,

on average, relatively censtantii).

In

this

examp]e, we are

likeiy

to

find

that

the

index

finger

contributes, on average, about

O,6

N

of

force,

while

the

mid-dle

finger

contributes about

O.4

N

of

force.

We

consider this

g35igrg8e

to

be

the average sharing of the workload

between

the

two

fingers.

Does

this

feature

alone

define

a synergy?

The

simplicity of

this

example makes

it

relatively easy

to

see

the

relationship

between

the

centribution of

individual

motor elements and

the

function

or

goal.

The

situation

is

less

c]ear

for

more complex

tasks

that

invotve

a

greater

number of

degrees

of

freedom

(DOFs),

We

use

DOFs

in

this context

in

amore

general

sense

than

the

number of

planes

of motion at each

jointiY).

Rather,

DOF

is

used

here

to

mean

the number of motor elements

involved

in

a task

that

have

the

potential

to

vary

independentty.

Note

that

having

the

potential

to

vary

independentty

does

not mean

that

the

ner-vous system actualty controls these variables

independently

of each other.

The

notion of a synergy,

in

fact

suggests oth-erwise.

For

exumple, with the use of

fine

wire electrodcs and

biofeedback,

persons

can

learn

to

activate single motor

units

independently.

However,

it

is

unlikely that sending

independent

motor commands

from

the

brain

te

each motor

unit

is

the

strategy used

to

control a reaching movement!

Whar

DOFs

are censidered

in

analyzing a

_given

task

a]so

depends

on one's

level

of

interest,

i,e,,

joint

coordination,

mus-cle coordination, coordination of

different

neuronat

ensem-bles,

etc,

In

the

simpte example above

the

number of motor ele-ments,

the

index

and middte

finger

iorces,

exceeded

the

number of

task-related

controt variables,

the

total

finger

force.

Thus,

the system

is

said

to

be

redundant, atthough

minimally so

in

this example.

The

unit of measure was

iden-ticat

across

levels,

hewever,

Le.

Newtons

of

force,

simplify-ing

somewhat comparisons across

leve]s,

If

we consider

instead

the

sharing

pattern

among

joints

used

to

transport

the

hand

to

a

target

in

three-dimensional

space,

the

degree

of redundancy

is

increased,

_perhaps

involv-ing

as many as

10

joint

anglesi2).

In

addition, unlike

the

force

exampte,

the

units of measure

differ

across

levels,

joint

motions

being

rneasured

in

radians,

hand

motion measured

in

meters.

Recent

attempts

to

identify

the

sharing

pattern

among

the

rnotor elements

for

more complicated

tasks

involving

a

larger

number of redundant elements

have

used matrix

factorization

techniques

such as

_principal

component analysis

(PCA).

Such

methods

identify

the

covariation among the motor elements across repetitions of task

_performance

or across variations of

particular

task

parameters,

e.g,, move-ment speed20).

Generally,

a smaller nunnber of new variables obtained

by

combing

in

different

ways

the

original motor elements

have

been

found

to

account

for

asignificant amount of

the

total

variance of

the

data,

For

example,

in

studying

postural

perturbations

and

locomotion

in

cars,

Lacquaniti

et

aL2i) showed

that

motions of the ankle,

knee

ancl

hip

jojnts

were confined

to

a

_plane

in

three-dimensional

jeint

space.

lmplications

ef

Research

on

Motor

Redundancy

three

_joints

so

that

their

motions covaried

in

a

predictable

way,

presurnably

reducing

the

number

DOFs

requiring

CNS

control

from

three

to

two.

New

combinations of motor ments

identified

by

methods similar to

PCA

have

been

siclered

by

some

investigaters

to

represent elemental motor

synergies7).

According

to

these

authors,

the

elementary

ergies can

be

combined

in

avariety of ways

to

achieve

ferent

motor outputs, e.g.

different

responses

to

postural

turbations

that occur

in

slightly

different

directions,

In

trast,

Latash

and colleagues

_prefer

to refer

to

such

goupings of muscles revealed

by

methods

like

PCA

as modes

of muscle action.

The

modes can

be

combined

in

fiexibte

ways

to

form

different

synergies.

The

difference

in

these

two

approaches may

be

subtle,

but

the

latter

approach emphasizes

the

fact

that synergies require a

direct

link

to

function

via an additional

feature,

namely error

tion

or

task

fiexibility.

That

is,

metheds used

to

ize

synergies such as

PCA

do

not relate

the

newty

died

combinatiens of variables

directly

to changes

in

relatecl variables.

Thus,

it

cannot

be

certain

that

the

binations

of motor elements

identified

as eovarying

by

such methods are related

directly

to

the

task

being

considered rather

than

other concurrent motor

processes

that

may not

be

as obvious,

Moreover,

there

may

be

different

task

meters requiring control

for

task

success and a

given

binarion

of motor elements

identified

by

methods such as

PCA

may

be

related

to

the

control of any one or allof

these

parameters,

For

example, reaching

to

a

target

with

the

hand

obviously requires control

of

the

hand's

trajectory,

but

may

also require

_precise

control of the

hand's

orientation

in

space

as well as

the

trajectory of

the

arm's center of massL'2).

To

which of

these

variables are the newly

identified

tions

of motor elements most relatecl?

The

results of such

analyses,

therefore,

have

to

be

further

related

to

the

changes

in

different

task-re]evant

_parameters

te

_gain

a

fuller

standing of

the

contribution of

these

combinations of motor

elements

to

function,

From

our

perspective,

these

_groupings

are not

themselves

synergies

but

modes ef coupling.

Rather,

we

believe

that the

CNS

combines these

different

modes to construct

functional

synergies

for

a

given

task,

Error

compensation or

task

flexibility.

Recentty,

colleagues

Gregor

SehOner

of

the

Ruhr

Univer$ity

in

Germany.

Mark

Latash

of

Penn

State

University

and

John

Scholz

of the

University

of

Delaware

have

argued

that

the most

tant

feature

of a

funetional

synergy

is

the

ability of

the

CNS

to achieve an

identical

task

performance

while combining

the

motor etements

in

different

ways,

implying

task

bilityiS)23).

This

feature

of synergies,

in

our view,

is

what

makes synergies

functional,

However,

this

feature

is

cal]y overlooked

in

operational

definitions

of asynergy.

Note

that

this

feature

requires motor redundancy,

For

example,

for

Rehabilitation

of

Neurological

Patients

359

if

we

limit

arm motion

to

the

horizontal

plane

and splint all

joinrs

of

the

body

and arm

to

prevent

all

but

shoulder and

elbow

joint

motion

in

the

horizontal

plane,

then there

is

a unique mapping

between

the two-dimensional

hand

position

and

the

values of the two

joint

angles,

No

other

combina-tion

can achieve the same

hand

position.

Thus,

without redundancy,

there

is

no

fiexibility.

Adding

the

wrist

joint,

however,

allows

the

possibiliy

for

a variety of combinations of

the

three

_jeints

to

achieve

the

same

hand

position

(i.e.,

three

joint

DOFs

minus

two

hand

_position

DOFs

equals one redundant

DOF).

The

more motor e]ements available,

then,

the more redundancy available

for

task

flexibility.

It

can

be

recognized easily

that

such

flexibility

is

important

for

most

functional

_performance.

For

exannple,

in

a non-redundant

sys-tem,

if

the output of ene motor eiement

is

in

error or an etement cannot achieve

its

normal value

due

to

an external

perturbation

(e,g.

a

joint's

motion

is

blocked>,

the

task

is

unsuccessful.

Prevent

one

jeint

of a two

joint

arm

from

achieving

its

required

_position

and the other

joint

cannot

compensate

to

achieve

the

prescribed

two-dimensional

hand

position

(Fig.

1).

Numerous

exmples of error compensation or

task

flexibil-ity

have

been

provided over the past

deeade

for

tasks

rang-ing

from

force

production with a set of

fingersiO)24},

to

reach-ing

tasksi2) i3),to

_posturat

control tasks]4)25

'27).

Note

that

task

flexibility

or error compensation will

be

reflected

by

greater

variability of

the

rnotor elements

{e,g.

joint

motion or

firing

patterns

ef muscies) aeross repetitions, while variabillty

in

the

values of task variables relatecl

to

task

success, e.g.

the

hand's

movement

path,

should

be

limited.

The

difficulty

is

in

relating,

for

example,

the

space of

joint

rnotions

to

exter-nal coordinate space

in

which

the

hand's

path

is

measured

because

these

spaces are

typically

of

different

dimensions

as we[1 as

being

measured

in

units

that

are not

commen-surate, as mentioned previously,

Sch6nerzz)

developed

a method

to

address

this

problem

by

making use of

forrnal

models

that

can relate

task

and elernental spaces.

His

approach, called

the

Uncontrolled

Manifold

or

UCM

approach, was

later

implemented

by

Schelz

and

SchonerLP)

in

a study of

joint

kinematics

and

by

Latash

and colleagues

in

studying

finger

force

control and muscle synergies underlying

pestural

contro125)

(Fig.

2).

For

exam-ple,

in

one experiment sllbjects were asked

to

produce

a

sinusoidal

_pattern

of change of

the

sum of

four

finger

forces24).

with no specific

instructions

about

how

to

combine

forces

across

fingers.

The

subjeets'

perfbrmance

exhibited a

reiatively consistent average sharing ef

forces

among the

four

fingers

across sinusoidal changes

in

the

force

magni-tude

and across repetitions at a

given

total

force

level.

I{owever,

the

individual

finger

forces

also

exhibited a

degree

360

£

k

B

Fig.

1

T]]ustration

to

a

hypethetTcal

is

presumed

ro

hold

ity

that

there

is

With

the

wrist

jemt

DOFs,

shoulder

horizontal

abduction-adduction and eibew

flcxion-extension

are availabte

to

controt

the

two-dimension-al

pointer-tip

path

in

the

horizontal

plane.

Therefore,

there

is

no redundancy at

the

joint

levet

and only one unique

com-bination

of

the

two

joints

that

can acliieve a

given

pointer-tip

position

along

its

path

to

the turget.

Each

of

the

hand

positions

at the start of movement

(S>,

at

two

different

times

ulong

the

movement

(Li

and

L2)

and at

the

target

(T)

can

be

represented

in

joint

space

by

combinations of

the

three

joints.

where

the

vatue of

the

wrist

joints

is

fixed

at each

point

due

the splint.

The

combined

joint

positions

are

indi-cnted

by

the

blaek

dots

in

Fig,

2C.

The

dashed

line

con-necting

the

black

dots

represents

the

ovcrall

joint

path

that

leads

to

the

pointer-tip

path

illustratcd

in

Fig.

2A.

B.

By

freeing

the

wrist

from

the

splint

there

are now

three

joint

DOFs

that

can

be

used

to

control the

two-dimensional

point-er-tip

_path

in

the

horizontal

_plane.

For

the

_pointer-tip

posi-tions ai

times

ti and

tL,

and the rarget

(T).

we

iltustrate

rwo possib]e cembinations of

the

three

joints

that cun uchieve

the same

poTnter-tip

position

with red

filled

dots

in

Fig,

2C,

In

that

figure,

the

dorted

line

represenrs one ef a

family

of

possible

joint

paths which would give rise

the

_pointer-tip

path

illustrated

in

Fig,

2B

(dashed

line).

The

lines

perpen-dicular

to

the

dotted

line

in

Fig.

2C

represent

portions

of

UCMs

defined

at each

point

atong

the

hand

path

in

Fig.

2B.

For

exampte, at

time

ti

in

Fig.

2C

there

is

a

fainily

of

joint

combinations, those

that

ITe

along

the

line

_{perpendlcular}

to

the

dotted

tine,

that all would yield the same pointer-tip

posi-tion at ti

in

Fig.

2B,

Given

this redundancy

in

joint

space,

iC

one

joint

does

not exactly

the

same angle at,

fer

exam-ple.

time

ti

on a given reach,

the

other

joints

can

cempen-sate

by

changing

their

ang]e slightly.

As

long

as

the

joinr

cembinatien remains en the

CJCM

for

that

point

in

time,

the

sanie pointer-rip path will

be

achieved.

method of analyzing the combined variance of the

finger

forces

into

two components, nne component

that

reflects

error compensation or

the

usc of

flexible

cembinutions of

finger

forces

to

achieve

the

same

total

foree,

and onc

cem-ponent

that

leads

to errors or i,ariabMty

in

totat

force

prc}

duction,

revealed

that

the

former

cemponent was signifi-eantly

targer

than

the

latter

component.

Thus,

most of the variancc

in

finger

force

_production

was consistent with the

use of motor redundancy to achieve

_performance

fiexibility.

This

wus

particu]arly

true

when

the

magitude of

total

torce

increased

during

the

sinusiod, a

finding

that

is

not

trivial

paefiiit"

C.

...,.-･･1-h...

tttttt

1

tttt

l'ioi.liSr.t)lli

'

llffllllilliiri

i,

Vi

.ixe2o

of

the

role of

jelnt

redundancy related

horizontal

plane

reaching

task.

The

hand

a

pointer

rigidly, ussuming

for

simplic-no ]noi,ement of

joints

within

the

hand.

A.

'

_fixed

_in

place

by

a splint, only two

joinl

rg35tsig8V

because

studies of

force

production

tasks

in

non-redundant

effector sysrems reveal

that

force

output variability

es with

the

rnagnitude of

force3-]3i).

Instead.

the

component of variabi]ity

that

would

lead

to error

in

the

rotal

force

put

actua]ly

decreased

at

these

higher

forces

at

the

same

time

that the component of

force

variability censistent with

error compensation

increased,

emphasizing the advuntuge of

has,ing

redundant et'fectors to achieve task success.

Note

thut

this

variability

11kely

has

significant

importance

for

tion

as welL

That

Ts,

most

tactTle

receptors are

dynamic,

responding

te

changes in

force

or

pressure

ralher lhan

reg-istering

static

force.

Thus,

the

variability of

force

contribu-tions

of

individual

fingers

to

the

totat

force

output

for

a

given

task

provides

for

continuous

force

information

to

the

CNS.

t'Xt

the

same

time,

making sure

that

this

variabitity

rernains

Iargcly

",ithin

the

LJC),(

ensures accurate

perfor-mance.

An

additional example comes

from

posturu]

euntrol

tasks.

A

common characterizatiun of the control of upright

stand-ing

is

that

the

body

is

centrolled as either an

inverted

pen-dulum,

with control

primarily

limited

Lo

the

ankle

_joint,

or

a

deuble-inverted

pendulum

inx,olving

both

the

hip

and ankle

jo{nt.

.aLlthough

most contemporary

investigaters

would net

view a single

inverted

_pendulum

model as realistic, several

recent modeling studies of sensory estimation underlying

postural

control are, nonetheless,

based

on

this

assump-tion32

36).

Note

that

if

posturat

control

involves

stabilizing

the

positiun

of

the

center of inass

(COM)

over

the

base

of

sup-port37)38),

a control strategy

timited

to

the

ankte

joinr

can

provide

such stability only

through

precise

control of

the

ankle's angular

position,

limiting

{ts

variability.

This

is

becausc

ankle motion alone would cause

CO]v'I

positional

changes.

There

is

no redundancy

in

such a

posturat

control model

to

allow compensation

for

ankle

joint

motion and

sta-bility

of the

COM

pesition.

Of

course,

it

can readily

be

seen

that

a

postural

control scheme

limited

te

the

ankte

is

impos-sibte

because

ankle

torques

induce

interactive

moments at

adjacent

joints

which are

tikely

''felt''

a]ong

the

entire

kine-matic chain.

Thus,

even

if

_proximal

joints

are

kept

from

mox,ing

in

an ankle control scheme, muscular control at other

joinTs

is

required to

limit

or eliminate

their

motion.

Of

course,

adding the

hip

joint

to the control scheme adds a

degree

of redundancy at

least

with respect

to

controtling

the

hori-zontal

CO}v{

position.

Thus,

hip

and ankle motions can covary to

keep

the

COM

_postion

re]atively cunstant

(Of

course, ihis

discussion

ignores

the

fact

that

some amount of

COM

motion

is

typical

and even

desireable

during

_quiet

standing

for

long

periods,

However,

it

must clearly

be

limited).

[Jntil

reeently, a

postural

controt scheme

involving

both

the ank]e and

hip

joints

was

limited

to

posturat

responses to

perturbtions9).

Implications

of

Research

on

Mutor

A.

Mictdle

Finger

Force UCM/edundancyTeskErro eeea.eeo

Redundancy

for

B. uc

Redun

lndex

Finger

Ferce

Rehabilitation

of

Neurologicat

Patients

MiddleFinger

force

or

361

Fig.

2

Illusiration

of

UCM

method and

two

hypothetical

results related

to

adrninistering

CPR

to an

infant

by

ing

forces

wirh

the

index

and middle

fingers

(see

text

for

detai]s),

The

figures

show the maximunn

force

_produced

by

each

finger

on each

force

pulse.

The

_UCM

method of analysis

provides

to

address

the

error compensation or

bility

feature

of a synergy

by

partitioning

the

varinnce of

the

motor e]ements,

here

the

finger

forces.

into

two

ponents.

One

component

dees

not adversely affect the relei,ant task variable,

here

torat

finger

force,

and represents

fiexible

cornbinations of

the

motor elements consistent with astabte i,alue of

the

task

variable.

The

second component

Ts

variance of

the

motor elements which

leads

to

variability of

the

task

variable.

The

first

step

in

the

UCM

method

is

to

reference

the

measured va]ues of

the

motor elements

to

their

average value across repetitions.

Ttius,

in

the

ure

is

plotted

the

mean-free va]ues of

the

index

and middte

finger

forces,

which centers rhe

distributions

at zero

ferce.

The

next step

is

to

define

a

format

moclel

that

relates

the

motor elements

to

the

task variabte.

In

kinematic

ses,

this

might

take

the

form

of a

geometric

medel

that

relates cosine

functions

of

the

segment

lengths

and

joint

angles

to

thc

spatial

_posilion

of

the

hand.

The

formal

mudel

is

then

used

to

define

the

subspace within

the

space ef the niotor elements within which variuions of

these

elemcnts

does

not affect the task variabte.

In

this

simple

cated example,

this

is

relatively

triviaL

Because

the

detaiLs

of

the

method

huve

been

described

in

a number of recent artictes. we

liniit

ourselves

here

to

this

simpic

illustration

and

focus

on

the

geometric

interpretation

of

the

method.

.iXrmed

with a

forma]

model

that

relates

the

space of metor elements

to

the

space uf

task-level

variables,

the

UCM,

or the subspace of motor element space within which changes

in

the

motor elements

do

net affect

the

task

variable,

as well as

the

subspace orthogonal

to

the

UCM

can

be

defined.

Because

in

this example

there

are

two

DOFs

at

the

tevel

of motor etements

{Le.

two

_finger

ferces)

and one

1)OF

at the

task

tcveL

_(i.e.

totat

finger

force),

the

UCM

is

one

dimensional

<2

elementary

DOFs

-

1

task

DOF}.

Thus,

it

can

be

represented

by

a

line

in

the

space of

the

fingcr

forces

that,

for

the

control of

total

force,

is

oriented

45-degrees

to

the

index

and middle

finger

axes with rregative siepe.

Finger

force

variations

that

lie

along

this

line

yietd

an

identieal

total

force,

e.g,

O.5-F[

+

_O.5-FM,

_O.4-FT

_&

_O.6-Fxi,

O.35-Fi

&

O.65-FM,

etc,

In

contrast, vuriations a]ong

the

axis

that

is

erthogonal

to

the

_IJC}L,I,

with a

positive

s]upe,

leads

to

changes

in

the

total

force

away

from

1.e

N.

Now

consider

the

pattern

of

hypothetical

results

in

the

left

paneL

The

data

suggests that the

hypothetical

subject attempted

to

produce

the

required

total

force

through

precise

control of each

individual

finger

force.

Plorting

each

finger's

force

as a

poTnt

in

finger-force

space yie]cls a circular

distributien

ef

data

points.

Keeping

the

distriburion

relatix,ely small

(red

dots

in

figure),

i.e.

retativety good control of each

finger'

force,

teads

to reasonable control of the totat

force.

However,

this contro] strategy al]ows

for

minimat

flexibility.

No

evidence

for

error compensation

is

present:

i.e,

an

increase

in

force

in

one

finger

leads

with equal probabi]ity to an

increase

or

decrease

in

the

ferce

of the other

finger.

With

poorer

individual

finger

force

control

(circle

expanded lo

include

gray

dots),

the total

foree

will

be

]nore variable.

The

UC]vf

method would

proceed

by

representing each

data

point

in

this

space

by

a vector and

then

projecting

that

x,ector onto

the

LJCM

and

the

orthogonal axis and

ing

the

length

of projection.

This

is

illustrated

tor

two points

in

the

figure,

where the projection of one

is

longer

along

the

IJCM

while the

projeetion

of the other

is

longer

along the orth{)gonal axes.

"Fhcn

the variance of the projection

lengths

are computed and normalized

to

the

number of

dimensions

of each subspace, one can see

for

the

example

in

the

ieft

_panej

that

the

_projeclions

wiil spread eveniy ucross

both

axes,

_yiclding

relatively equai variances within eaeh

subspace.

In

contrast, the panel on the right shows a

hypothetical

example of error compensation.

Although

some

data

points

lie

off of

the

line

representing

the

UC)i[,

most of the

data

distrTbution

lies

close lo and

paralle]

to

the

UC)vl

if

not

directly

on

it,

It

is

easy

to

see that the same

_projectTon

method wilt

_yietd

higher

variance a]ong the

UCM

rhan

in

the

orthogonat subspaee,

indicating

that

an

increase

or

cleerease

in

the

force

or one

finger

will

lead

with

high

probability

to a

decrease

or

increase,

respectively,

in

the

force

of the other

finger.

Thus,

there

is

error compensation and

dence

for

a synergy uniting the two

fingers.

Because

the method

is

geometric and examines the variance of the

ative projection

tengths

within each subspace. the strength of a synergy ean

be

delermined

by

the

degree

to

which

the

variance within the

LJCM

exceeds variance

in

the

ortogonal subspace:

the

greater

the

difference,

the

stronger the

synergy.

In

this

way, a

functional

synergy

is

related

to

the

vatue of a

task-relevant

variable

through

the

_geemetric

model

that

defines

the

UCM

and orthogonal subspaces.

Although

this

simp]e example could

be

illustrated

as easily with simpLe correlations,

this

not

the

ease

for

more

plicated

systems of many

DOFs

and where

the

units of measure of the motor elements and

task-relatcd

variables are

quite

ditterent

(e.g.

joint

angles and

hand

spatial

position).

Details

of

the

method

for

such cases can

be

found

in

Scholz,

Reisman

and

Sch"ner

2C}Ol

and

Tseng,

Scholz,

SchOner

and

Hotchkiss

2003.

Maryland

recently argued

for

the

simu]taneous

_presence

of

tion

is

important

{This

discussion

is,

of course,

oversimpli-ankle and

hip

coordination "modes" underlying the control

fied

by

ignoring

the c"ntrol of posture

i]i

the medial-lateral of quiet standing/]9 d2).

Note,

however.

that even a control

dirnension}.

Is

there

evidence

for

the use of motor

redun-strategy

invoEving

both

the

hip

and ankle

is

non-redundant

dancy

in

the controt of

pesture?

362

ee\fiza7

Jeng-Feng

Yang,

Vijaya

Krishnamoorthy

and

Wei-Li

Hsu

have

_questioned

the

notion

that

posturai

contrel

is

largely

limited

to control of the ank]e and

hip

jointsZe)27)43).

For

example,

it

was shown

that

multiple

joints

along

the

kine-matic chain exhibit movement

during

prolonged

perieds

of

quiet

standing that

is

equal

to

or

greater

than ankle and

hip

_joint

motions27}.

Moreover,

the

combinecl motion

vari-ability of all

joints

was shown to

be

strucured such

that

most of that variabilty was consistent with error compen-sat{on, or the use of

flexible

joint

variations that resulted,

nonetheless,

in

a relatively stable

COM

pesition,

Only

a small

portion

of

the

joint

variance

led

to

COM

variability,

Thus,

the

postural

control system appears

to

be

organized around

the

use of redundant

DOFs

to

achieve stable

performance

through

flexible

coordination

patterns

among

the

joints

of

the

body.

A

similar conclusion

has

been

arrived at

based

on

studies of rnuscle synergies related to the

_production

of

antic-ipatory

postural

responses25).

A

potential

advantage of a controt scheme

that

utilizes motor redundancy

is

the

ability

to

perform

multiple

tasks

simultaneously without

the

tasks

adversely affecting each other.

For

example, most of us

have

had

the experience of walking

inte

a

dark

room with our

hands

fuLi,

e.g. while

hoLding

bimanually

a

loaded

tray.

We

eould

put

the

tray

down

{if

we can

tocate

a

table

!}

and

then

turn

on

the

light

switch.

But

people

witl often

fiip

the

switch with their e}bow

by

rotating

their

shoulder and adjusting more

distat

joints

while continuing

tD

hold

the

tray.

To

do

this

without spilling

the

contents of

the

tray requires the use of motor

redun-dancy.

Although

the

guards at

Buckingham

Patace

may need

to

stand rigidly

for

long

periods

of

time,

most

individuals

perform

activities

with

their

head,

trunk

andlor extremities while standing.

All

of these activities

are

_potentially

dis-turbing

to the

body's

_posture,

or

the

COM

_position,

We

recently

have

completed a study te

test

the assumption rhat

motor redundancy

is

used

by

the

CNS

to

achieve sucessful multi-task

performance

(manuscript

in

preparation).

The

study examined the effect ef

performing

an upper

extrem-ity

targeting

task

alone or combined with a

ball

balancing

task on the control of the

COM

position

during

upright

standing.

The

results

indicated

that

the

additional

joint

vari-ance contributed

by

the

arms when

performing

the

target-ing

task cornpared to

_quiet

standing occurred alrnost

com-pletely

within a subspace of

joint

space representing

flexi-bile

combinatiens of

joint

motion

that

did

not affect

the

COM

position.

This

component of

joint

variance wus

further

increased

when adding

the

ball

balancing

task

to

the

tar-geting

task.

In

contrast, although

joint

variance

that

led

to

COM

positional

variabitity

increased

slightly with

the

added

tasks,

these

changes were an order of magnitude smaller and were not significant.

ca35kas8e

These

studies and many others

have

suggested that the control scheme usecl

by

the

CNS

to

achieve

functionat

task

performance

is

one that makes use of the available motor

redundancy whenever needecl

for

error compensatien or

more

general

task

fiexibility,

as when

performing

multiple

tasks

simultaneously.

If

true,

how

is

this

abitity compromised

in

patients

with

brain

damage

due.

for

example,

to

stroke

and what

implications

does

this

have

for

rehabilitation of

functional

movement

performance?

Deficits

of

functional

synergies

in

stroke

Despite

the characterization of

the

movement

patterns

exhibited

by

stroke survivors as abnormal synergiesi), our

uiiderstanding of

how

the

two

features

of a synergy are affeeted

in

stroke and other

brain

injuries

is

still

incomplete.

Our

laboratory

has

perfermed

several recent studies

attempting

to

address this

question,

investigating

in

partic-ular the ability of stroke survivors to use redundancy

for

perfermance

fiexibility.

We

limit

the

_present

_discussion

to a

consideration of upper extremity

tasks.

Sharing.

It

seerns clear

that

the

relative contribution of

indivdual

joints

to

the

hand's

movement trajectory

in

reach-ing

tasks

differs

in

stroke survivors

from

those

of

healthy

age-matched

individuals.

This

conclusion

is

consistent with

the

descriptions

of

hemiparetic

synergies

described

by

Brunnstromi),

altheugh

those

descriptive

categorizations

were not related

directly

to

function.

Levin44)

showed

that

patlents

with

hemiparesis

following

a stroke

have

limited

ability to coupte

their

elbew and shoulder

joint

movements

in

a

fiexible

manner

clepending

on

the

part of the

work-space

in

which

they

reach and whether

they

are allowed to use the trunk to assjst

the

movement45)46),

putients

follow-ing

a stroke

have

great

dithculty,

for

example, coupling active shoulder elevation with elbow extensioni)2}.

Thus,

the

contributien of elbow

joint

motion

to

the

hand's

movement when reaching

forward

and slightly upward

is

substantiatly

less

while

the

contributien of

trunk

motion

is

greater

com-pared

to

heatthy

individuals46).

The

mechanism underlying

such

difficulties

may

be

related

to

the

inability

to

flexibly

modulate muscle stretch refiex

thresholds

_properly

to

achieve appropriate

levels

of reciprocal

innervation

and cocontraction at each

joint

and

the

limited

coupling of

these

thresholds

across

jeints

of

the

]imb

in

persons

fol)owing

a

stroke'M.

Moreover,

we

have

shown

that

moderately

impaired

persons

with

hemiparesis

exhibit a smaller

nurn-ber

of

joint

eoordination modes compared

to

mildly

impaired

persons,

who appeared

to

be

more

like

healthy

controi

sub-jectsos).

Jeint

coordination modes represent subsets of

dif-ferent

combinations among

the

10

upper extremity

joints

(including

scaputar motien) examined

during

the reaching

Irnplications

of

Researeh

on

Motor

Redundancy

smatler

in

number

than

the

number of

joint

angles,

yet

accounted

for

a similar amount of

the

total

joint

tyZU),

It

may

be

the

fiexible

coupling of

these

different

dination

modes

that

allew

for

performance

fiexibility.

Thus.

the smaHer number of such coordination modes

found

in

more

impaired

patients

likely

limits

their

performance

ibMty.

Error

compensation or

task

flexibility.

Note

that

the

ing

feature

of a syllergy

is

captured

in

the

above

t{on

in

two

ways.

First,

the

proportional

contribution ef each

joint

angle

to

each coordination mode

defined

by

PCA

cates

how

each

joint

shares

in

the

uctivity of each mode.

Second.

how

the

different

coordination modes

identified

by

PCA

are combined to

form

functional

synergies

identifies

yet another

level

of sharing25).

However,

the

above

discussion

suggests

that

coordination

flexibility

already can

be

re]ated

to

the

availability of

ferent

modes

for

synergy

formation.

This

flexibility

may

be

related to

difficulty

that patients

have

combining

basic

dination

modes to

_perform

adequate reaches to

dfiererent

parts

of the workspace,

Further

exploration of this

nomenon

is

needed,

however,

The

aspect of

task

flexibiiity

emphasized above

is

related to the ability to couple a

given

set ef

joint

angles

in

fiexible

ways across repetitions of a

task, which may

be

u reflection of error compensation.

We

oriRinally

thought

that

_joint

variance of stroke survivorg would

be

related

less

to error compenation and more to

inconsistent

hand

paths

during

reaching.

However,

although

patients

with mild

to

moderate

impairments

exhibited more overall

joint

variance

than

age-matched control subjects. more of this variance stillrefiected

flexible

jeint

tions

than

error variance, as was

the

case with contrel

jects"a)49}.

Nevertheless,

the

patients

had

higher

joint

ance that

led

te an

inconsistent

hand

path across repetitions

than

did

control subjects.

What

we

have

concluded

frem

the

data

obtained

to

date

is

that the coordination

deficits

of stroke survivors reflect

dienculty

in

decoupling

different

regions of

joint

space.

Such

decoupling

is

necessary

to

allow

for

fiexible

combinations of

joint

motion while at

the

same

time

resisting

joint

nations

that

would result

in

an

inconsistent

hand

path.

Put

another way,

if

ten

joint

angles contribute

to

a required

three-dimensional

movement of

the

hand,

then

there

is

a

dimensional

subspace of

the

IO-dimensienal

_joint

space

in

which allcombinations of

joint

angles are equivalent with

respect to the

hand's

_position

at a

_given

_percentage

of

the

reach.

Variability

within

that

subspace can

provide

for

ment

flexibility

underlying,

for

example, error compensation or multi-rask

performance.

In

a sense, control of

the

joint

combination within

this

subspace

is

unnecessary unless other

task

constraints are

broughr

to

bear.

I{owever,

_joint

combi-for

Rehabilitation

of

Neurological

Patients

363

nations

in

the

remaining subspace of

joint

space will

tead

to

incensisteneies

of

the

hand's

position

across repetitions

and must

be

resisted.

It

is

this

decoup]ing

of control

that

stroke survivors are

predicted

to

have

dirnculty

achieving.

This

ability to

_decouple

different

regiens of

joint

space requires a

high

degree

of musclef'joint coordinatien.

Impjications

for

rehabilitation

of

stroke

survivors

and other neurologically

impaired

individuals

Although

sve

have

been

_gainillg

insight

about

the

deficits

of

the

two

features

of

functionai

synergies

in

patients

fol-lowing

stroke, more work clearly

is

required

to

understand

the

mechanisms underlying movement

dysfunction

in

indi-viduals with neurolegical

impairments,

let

alone

how

to

best

address

the

preblems

therapeutically.

However,

some

pre-liminary

suggestiens are

possible

based

on

the

recent work

on synergy

formation.

For

exampLe,

if

a major souree of the

deficits

seen

in

stroke survivors

is

an

inability

to

adequately

clecouple

joint

spaee,

then

_practice

should

be

aimed at

helping

them

learn

how

to

do

this

more effectively.

But

how?

For

one

thing,

our

discussion

above

has

emphasized

the

fact

that

the

shar-ing

and,

in

particular,

the error compensation

features

are what make a synergy

functional,

This

suggests

to

us

that

practice

needs

to

be

performed

in

the

context of

functional

tasks,

not movements.

But

this

fact

alone

does

not ensure

that

subjects will

learn

the

appropriate

decoupling

of

mus-cle and

joint

coordination spaces.

Variable

_practice

would appear to

be

essential to

foster

the

use of motor redundancy

in

the

_performance

of

func-tional

tasks.

The

importance

of variable

practice

to

learning

is

net a new

insight

of coursese sc}.

However,

the

commen

emphasis on variable

practice

implies

variability of

the

over-all

task,

e.g.

the

practice

of walking on

different

surfaces or of reaching

to

different

parls

of

the

workspace.

Although

this

ernphasis

is

undoubtedly

important,

our emphasis

in

the

current context

is

on

the

need

to

practice

var{able move-ment

patterns

while emphasizing

task

success.

The

assump-tion

is

that

such

_praetice

is

needed

to

effectively

Iearn

to

decouple

the

space of motor elements so

that

variations

that

aclversely affect

task

performance

are resisted while

utiliz-ing

available motor redundancy.

This

is,

adrnittedly, an untested

hypothesis

at

present.

What

strategies can

be

used

to

accomplish

practice

of vari-able coordination

patterns?

Consider,

for

exampte,

the

train-ing

of reaching.

One

might

have

the

patient

initiate

repeti-tive

reaching with

their

irnpaired

limb

from

the

same

initial

hand

positien

to

a

target

located

in

a

given

part

of

the

work-space.

but

varying slightiy

the

initial

joint

configuration across repetitions.

This

could

be

repeated

then

for

different