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Biomechanics of Muscle: WITH PARTICULAR APPLICATION TO STUDIES OF GAIT HERBERT ELFTMAN J Bone Joint Surg Am. 1966;48:363-377.
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O*I4,
Biomechanics WITH
PARTICULAR
BY An
human
r1ime mmmovemmment
with
Course
comitrolled
arc
ELFTMAN, Lecture,
is built
body
a quarter
APPLICATION
HERBERT
Instructional
nmuscies.
striate
TO
PH.D.*,
The
aroumid
by
billion
of Muscle
NEW
American
For
this
OF
YORK,
Academy
a cOlflplex
mmmuscle fibers
STUDIES
GAIT
N.
of Orthopaedic
of bomic levers purpose
artfully
Y.
each
Surgeons
whose
posit-iomm
immdividual
assemmmbled
amid
is provided
immf-o mmiuscles
ammo! at-
to the
skeletal levers iii strategic positions. Motion is coorditmated through the nervous system, which can devise progranis for commiplicafed activities, store timenmi for later use, arid modulate f-heir performmmamice under the immfluemmcc of feedback signals. facimed
l)reselifaf-iomm
This
than lurloscs
factors
fessiommal sidered
of the
amid those
first
bionmechammics
of mmmuscle will
enml)hasize
sonic
of these
of-hers. No f-reatmmment of Iimuscle biomecimammics adequate can ever be sinmple, but if the I)ropert-ies of single fibers
mmmore
of nervous
coordimiation
last,
for are
sommme of time difficulties
procon-
will
be
mmminimmiized.
Intrinsic Ami average
imummman
met-er
imi diammieter.
20,000
discs
quently
fiber
are
400
times
the
at rest
secfiomms mmmost readily
size
of the
Muscle
is five
Z nmembramies
sommmefimmmes called
iii describing
cami be visualized
about.
of Single
fiber
nmuscle
Trammsverse
that
used
Properties
Fibers
ceimtinmcters
divide
the
sarcomeres,
!ommg and
fiber
although
.05
that
tcrmmi
is mmmorc fre-
of fibrils rather thami fibers. Time structure i)y means of a nmodel. The Ummited States
average
human
muscle
disc
mmmilli-
immto approximmmately
ammo! has
of time olinme is
simmmilar propor-
tiomis. Timus a simmglc nmuscle fiber cami be rcprescmmted by a stack of 20,000 dimes, which would mmmake a colummmmi over sixty feet high. Each disc comif-aimms about three mmmilliomi filaments of myosimm, ommly omme of which is showmi imi Figure 1. Parallel to the nmyosimi are filaimmemmts of actimm, amicimored to time Z nmcmbrammc. Nervous excitation causes mmmyosimi amid
actin
to develop
f-he mmmutual
attraction
f-hat
is the
source
of nmuscle
temi-
siomm.
The
Length-Tension Iii many
Curve
ways
fact
that
This
l)lmenmonmenOli
time immost inmporf-ammt
if-s potemmtial
femmsiomi
was
first-
siimgle
depemids
mmmeasurcd
on
by
characteristic its
Blix
length 4,5,6,
of f-he mmmuscle fiber at
a
the
Swedish
mmmommmenmtof
is the
excitatiomm.
physiologist,
in 1891.
The contribution 22,26 is illustrated by drawn l)erpemmdicular time
leimgth-tensiomi
with
time nmyosin
area
of
interactiomm
Omi time other of-her of
the *
York, VOL.
of actin amid myosin to the lcmmgth-temisioni relationship 19,2o,2m, the graph imi Figure 1. This graph is so desigmmed that a limme frommm the end of the right-hand actin filanmemmt will intersect curve at f-lie al)propriate point-. If the sarcomcrc is stref-ched, stayimmg iii l)ositiomm, the actin filamemit will sliole further out, its the myosin will decrease, if time fiber shortemis, the two
with
hand,
amid when they overlap mmmyosin encoumitered
they after
l)epartnmemit
College
of Amiatonmy,
will hot-h timey pass of Physiciamis
amid the tension will olinmimmish. act-in filammmemmts slide toward each
be affect-ed by the reversed polarization the mmmidolle mieutral segmmmeimf. Owimig and
Surgeomms,
Columbia
University,
to New
N. Y. 10032. 48-A,
NO.
2, MARCH
1966
363
364
A.A.O.S.
this
relatioumsimip Flme
ramige.
rest
15101
iP1
at
LECTURE
factors, time t-emmsiomi o!ecreases its time fiber’ slmortemms in this f-lie t-emision is greatest is calleol, sommmewhat arbitrarily,
which
rFhme first
mimay be
comimmect-ive teImsiOli
iim (hfleremmt
f-issue,
ijicance
ummi-il it
mmiuscle
Figure
in
single
fiber
zero
niuscies
Tens the
\Viiich
give
total
time
ion
fiber
wimemm
f-he fiber
f-lint )ass
over
other
fact-or
fascia,
which
tensiomm
o!evelops
curve
frommm
are
clue
is time uresemmce
commtributes
for
to
of sarcommmeres of
passive
it mimust
be
aolded
time mmiuscle.
ip
cami l)rOdU(’e
(!ecmetmses
is a)proxinma1-ely only
differemit
differemmces
of lommg chains
Time
teimsiomi
Relations/i
nmuscle
sommiewimat
These
consists
commmmective-tissue
to
are
2-A.
of comitm’acf-iomm.
After
of the Length-
reason,
eIicim
states
tensiomi
femmsiomm becommies
imm time whole simowmi
immcluo!immg sam(olemmmmmma amid
acf-ommmyosimm
‘fime
timis
is that
mvlmeii stref-cimeol.
time if/fl
iommshi is ammo! are
sarcommmere
factors.
wimich
ii i’elat
m-lemmgf
mm time
two
S
ama! of-her
lemmgt-h
COURSE
letigtii.
those
to
IXSTItUCTr0NAL
omme joint
-1.0
nmust
as
time
fiber
simorteims,
60 ler
cent
of rest
lengtim.
For
have
fii)ers
nearly
timree
timmies
R
2
0
-0.5
U)
z
Ui
I-
LENGTH
-
ACT N ________________________________________ _\
-Ic
-‘
-‘
:;
-\
r
r
:
r
z
z
z Fmu.
1
Part of omme sar(’ommiere simowim at restlemmgth. The di.stamice betweemi the menmbranes (Z) is 2.2 micra. Whemi time mmmyosimmfilanmeimt is fixed imi position, shortenimig timid lemmgtiiemmimig occur bysymnmetrical slidimmg of time mictimm filaments with respect to the nmyosimm. The chamige iii tension associated with length (‘lmammges (‘liii be followed omm time iemigth-temisiomi diagrani iy observimig the Positiomi of the dotted limme as it mmamves to the right or left with time actimi. It desigmiates rest lemmgth.
as lotmg as time distance This
joimit-.
timrouglm
k’mmgtim allomvs
and still retaiim some relat-iolmsimul) i)etweemr sioleratiomi in evaluating
force
fiber
wimiclm they
themmm to exert whemm
short-eu
(ltmrimmg commil)lete
mmmaximmmtmnmforce
mmmovemmmemmt of time
wimemm t-imey immitiate
mimovemiment
time mimaximmmummi mmmovemmmemmtis conmpleted.
Timis
close
lemmgt-ii ammo! ahmml)lit-ude of shomtemmimmg is aIm immiporf-ammt contime ProsPective efficacy of a sui)stit-tmt-e immuscle after tenolon
trammsfer.
Iii t.mvo-joiumt nmuscles, of extemmsom’s are classic examples, conimimoolat-e
timemmmselves commiplef-ely
mmiaxinmummm mmmovemmmemmt ili
ftmllv
joimmts
decreasing kimec shown
which time imammistrings f-he fiber lemmgf-h is too
extemioleo! (droppimig
is commmpletely in Figure
uies
to time cimange
associated
the
joints.
hanmst-rimmgs
dowmm time lemmgt-h-tension flexed.
2-A.
f-lie
The
Time opposite
muscles
are
commdition,
ami(l time (ligital flexors ammo! simort for the mimuscies to ac-
immlemigtim ivimicim would accommmpamiy If a persomm stammdimmg with his hip
to flex
one
curve
kmmee, he will ummt-il it reaches
tlmemm in a state
passive TIlE
of active
immsufficiemmcy, JOURNAL
OF
BONE
feel
the
zero)
temmsiomm
before
the
immsufficiency, cami he illustrated ANI)
JOINT
SURGERY
as
HERBERT
by keeping conditions
the kmiee stretchimmg
insufficieimcy
of
inmsufficiermcy
the
extend
the
of Speed Time
imm whicim
stimulated produce
or change
being
used
those
active
of
the
the
nmuscle
has
as
iii
result
time
either
so
physiology
lemmgtim clmammges,
is rarely
require
which
temisiomis
all
fotmmic! outsio!c with
of
time
fimmgers
to
; fiexiomm of
states
Isommmef-ric simmce
f-he
beemi
illustrated
lemmgfim at
contractiomi,
active
the
have f-lie
by
whicim
it
was
slowly. Muscles mmiust frequemitly aim exferhmal load. Such activity
laboratory,
iim which
vary
far
mmiaimmtaimmed
immsimortemmimmg.
commtractiomi,
ext-emmsor
wrist is extendeol these joimits.
Produced commsidered
mmommiemmclature for
that
Isotommic
365
MUSCLE
conimoim
when the it to govern
immlemmgfh is kmmowmi as ami isommiet-ric stat-es
life
on Tension relatiommships
in modermm
stability.
OF
has changed lemigth extremimely emiough temmsioim to coummterbalance
just
without
immability
of Contraction
lemmgth-temmsion
situations
normal
the
is
immterphalammgeal joimits completely lenmgthemms f-he mmmuscle amid enables
wrist
Effect
BIOMECHANICS
fully extemmded amid then attemptimmg hip flexiomm ; ummo!er timese of the comimmective-tissue elements will bring about passive the hip joint reaches its limit of mimoveimmemit. A gooo! example
before
lommg
active
ELFTMAN:
contraction muscles
t-emmsion
of just
is as commmmomm hi are
remimains
laboratory,
time immStantammeous
time t.ermim contraction
of mmmuscle inst-eaol so
imimport-ammt
commstamit
for
while
simmce miatural
f-he
mmmovememmts
load. I
U
I
z
I
Li
I
U
I I
-LO
z
U)
0
z
U)
z
Li
Li
-Q5> U 4
L
.6
.8
.6
LENGTH CONTRACTION
ISOMETRIC
j
CONTRACTION FIG.
2-B
2-A:
Lemigth-temisiomm diagram for isometric contractiomm of a muscle fiber. The differemices this diagram amid Fig. 1 are dime to the arrangememit of sarcomeres in series immthe fiber amid of passive stretch of commnective-tissue elements, CT., which add to the active temmsiomm of
betweemm effect actonmyosimi, M. Fig. 2-B: Length-tensiomm diagranm metric values for comparison. When veloped is greater than the isometric the tensiomm is less than isometric to
the
The Figure
general 2-B.
duction
effect
The
wit-h
speed will depemmdimmg while
tO
.8
LENGTH
2-A
FIG.
Fig.
1.0
of speed
isometric
immfinmitcly
always
it is active
slow
simeed.
of contractioim
curve,
produce
the
on
for fast- comitractiomi (solid limme). The dotted limie shows isoa muscle is stimulated amid themm stretched, the temisiomm dotension; whereas when the muscle shortemis after stinmulatiomi, a degree that depends on the speed of simortemmimig.
chammge
less Iii
will increase
drawn
as
of length.
f-haim
on
tension, fashiomi,
its t-emmsionm, sometimes
l)roo!Imctiomm
is
simowim
iii
limme, represents
A nmusclc
isometric
a commmplemmmentary
teimsiomi
a dotted
fiber
temmsiomm prosimortenimig at a fimmite
time anmounfstret-ciming
sufficiemitly
of
o!ecreasc
time mmmuscle rapidly
to rupture
muscle
or
tendomm.
Work
Done Physical
VOL.
48-A,
NO.
by Muscle work 2, MARCH
and
on Muscle
is defimmeol as 1966
time l)rOdUct
of force
timmmes time distaimce
timrougim
366
A.A.O.S.
INSTRUCTIONAL
COURSE
LECTURE
L PASSIVE -.
MAXIMUM
STRETCH
WORK
ACTIVE
a
ISOTONIC Fmu. 3-A
Fa;.
STRETCH
SHORTENING Fmu.
3-B
3-C
Fig. 3-A: Time work done by a niuscie imi three experimmmemmts imm which time muscle was passively st ret(’iie(l tmmi(1 t hemi stimmimilated to a. givemm temmsiomm, with slmi)sequemmt isot-omiic simortemmimig. Time work (lomme is (‘qual tii tue shaded area imi eacim experinmemmt simice time work domme is the product of force t immies cliamige of lemmgth. Fig. 3-B: \laximimumim work of which the nmiiscle is capai)le is attaimied by passive stretch, stimulat iomm, timid t imemi decrease imi temmsiomm as the nmuscle shortemi.s. Fig. 3-C: A miiimscle fiber remmmovimmg emiergy from the bod’ as it is actively stretCiie(I amid subse(m(iemitlY slu)rtemiecl; the dotted area measures the excess of energy received during stretchimmg over amid tii)Ove time work domie iii shortemiimig immdicated by the lined area.
it- mmmoves. Althougim
mviiich reoluires
time
oloes
imot
wom’k,
t-imem’e is
vork
o!Omme
Oh
omm its
till’
o!egradat-iomm olescetiol iim(
mntmscle. Pi1551V(lY
fronm
au isonmetric of
mmmove. Likewise,
siimce
it- does
exl)emmdifure
nmetabolic am unloao!ed
mmmoveimmemmtbut at-f-acimnmemmt-s.
mmmuscle.
This
to heat,
is invaluable
imeigimt-s
by
3-A
st-retcimed
comivertimmg
diagram
lemigt-im-temisiomi ligume
trammsfer
simovs
three
commtm’action energy, nmuscle
mmoforce. When
Potemmtial
or
ba-c!
the
booly
imm each
o!oimmg
teimsiomm shorterms,
stretches
a muscle,
usually
work
is
by
its
folloveol
to slow
its nmovemmmemmt ammo! to cami be dissipated. of the vork olonme by amid on of wimich time mmmuscle was first
to heat
visualizatiomi
comit-racfiomms,
exerted
lemmgtimemms without
to time mimuscie, emmergy
fummct-iomi amid
simmce time force
a nmtmscle exerting
atm external
in allowimig
imo work
simortemms
When
of emmergy
allows
iem’fom’mmis a useful
it does
which
to nmaximmiummi lemmgt-h amid timemi stimulated
to aim active
TENDON
temmsion
OF
ORIGIN
MUSCLE FIBERS TENDON
OF
JOINT
AXIS
.-.-----
?5
-15
.05
Flu. 4-A FIG. 4-B Fig. 4-A: Time lemmgtim of a muscle fiber capai)le of producimig 180 degrees of flexiorm while shortening 40 l)0 (‘emit- of its rest lemmgth is short-e.st whemi time muscle imiserts near the joimit. Whemi the distanmce fromim time joimit axis to the poimmt of imisertiomi omm the simort i)omme segmemit is more thami 0.25 times the lommger bone segmimemmt, complete flexiomm is mmot possible. Fig. 4-B: Typical niimscle comistructiomi with short fibers attached to temidons of origin amid insertiomi. The limme of aetiomm of the muscle amid its lever arnm with respect to the joimit axis are showmi. THE
JOURNAL
OF
BONE
AND
JOINT
SURGERY
HERBERT
equal
to a suspemided
the amouhmt contractiomms
weight
showhi by is measured
:
ELFTMAN
the
that
was
BIOMECHANICS
then
lifted
as the nmuscle
obtained
mmiaxinmumim
amount
by
commtract-ion
isotoimic
imi Figure
3-B.
stimulated
to f-he
achieved,
although
wimat
lined
areas.
area.
The
Here
of
simice
f-he
line amid the base at an imiternmediafe
which
Obviously,
nmay
isotommically
hue. It is obvious temmsion f-imammat
1mm f-he shorfenmimig area
that
is thus
to
Immany
to
together
iii
a
fibers
mmmuscle
(wide
black
bamids),
immg to 60 per
each
capable
creases as the 1)Oimmt of fiber joimmt axis, umit-il f-he longest of time short
lemmgth
their
will imot be bug
a
chamice
niatter
of
f-hat-
lost-
exanml)le
froimm time body.
(rest-)
of
fibers
capacities
shows fibers.
the
fiber
product-ion
these
unit-ed
of fleximig
forces
must
to
be
the
large
gaf-here!
fummcf-iomial
re-
omie of the limmmif-ations imimposed Three mmmuscle fibers are showmi
joimit
through
lemmgth.
The
180
degrees
by
lemmgfh of fiber
siiortemm-
needed
iii-
atf-achmmmcmmt- to f-he distal bomme mmmoves fart-imer frommi time fiber simowmm stretches fronm origilm to imiserf-iomm. If time
bomme lever
nmmuscle fiber
actually
is a general
emmergy
the
body,
1’igure 4-A of muscle
of ifs greatest
cent
iii
human
adapt-s
(iuireniemmts of f-he joimifed skeletomm. by f-he lemigtim-temmsiomm characteristics
physical
cooperate
of the
which
fashiomm
it-s tensioim be
The arrows immdicate timat time to the sumim of time dotted ammo! did work eoiimal to f-he limmed
muscle
total
3-C
be
length,
of Muscles
nmust
f-he joints
commfrol
with canmiot
Figure
mmever
with
mmmaximmiunm lemmgth,
slowly
specificatiomis
f-he
f-he
cami vary
to
shorten
approached.
followed,
equal
capable
tensiomi
stretched to
these
be closely
is
the
when emmergy is to be dissipated. stretched, acceptimig energy equal
imappemm actively
Simmce
that
allowed
Structure
emiough
a nmuscle
it requires
mmmuscle is passively
curve.
they
dotted
work
f-emmsiomm, amid
isonmetric
nmay
mmmuscle was
of
isonmef-ric
followihmg
of
short-cued
exf-remmme.
The
as
367
MUSCLE
horizoimtal arrows. Simmce f-he work done by each of these by the product of force and shortemming, time work domme will
be equal to f-he area betweemi the force-excursion that for isotonic commtract-iomms more work is done either
OF
is mimore fhamm omme-fourth
emmough
to produce
a full
mimost- hunmmaim muscles
are
that
of time bug
180 degrees arranged
omie, time
of flexiomm. It is not
alniost
parallel
to time
bommes.
The nummmher of mmmuscle fibers required in each nmuscle to give it sufficient stremigtim is so large that- packimig problenis arise. Simice f-lie mmmuscle fibers or fiber bundles must be arranged parallel for f-heir immdividual forces to sunmmaf-e, a (Oilveniemit
packing
fibers
are
shapes
syst-enum
attached,
consistent
force
Figure
the
Whemi
.
arraimgemmmemmf
pennate
in
with
developed
fiber
is a temmoiomm of origimi
as
4-B.
space
curved
gives
of Capacity
of Muscle
Imi est-immiat-imig the remmmenmbereo!
of the
fiber
which
it
roughly
f-imat- time
for
fummctiommal dist-ammce
capacity
olepenmds
are
nonmemiclature
to
f-he
total
to which be
time
wrapped
greatly
cut of
cross
sectiomi. now
of all the
force,
nmaxinmunm or
fifty
isometric l)011mm015
muscles NO.
2,
MARCH
in
time 1966
ler
iii
force
square
imummmami
body
and
into
frohmm
time
dissection,
iii
bipennate
time
ammo! itmulti-
Work
of f-he nmuscle f-lie
sect-ion
in Figure
nmuscle
Simice
nmyosin
of all
of
4-B,
camm shorten
nmuscle.
imumimber of
cross
fimose
of immuscle
the
Production
which
the
on
ficiemmt
48-A,
def-racf-immg
surfaces
lemmgt-h, mmot f-he lemmgfh of f-he emit-ire
camm olevelop proport-iommal
sectiomm,
Force
through
to as f-lie physiological
VOL.
f-hemi
muscles.
Estimation
for
the
to
of insertion
nmay
without
temmdon
rise
a temidomi
temmdomms
available
these
disclosed
and
These
it nmmust- be is a fracfiomi
time mmmaxinmunm force
filammmemmt-s present-,
time fibers,
usually
is
if.
referreol
Mammy est-inmafes have beemm made of time coefbeing in the mmeighborhooo! of 3.3 kilograms
use
per
inch.
square
cemmtinieter
Simmce the
is a)proximmmately
total
of
physiological
physiological six square
cmoss feet,
cross
section
if all were
to
368
A.A.O.S.
contract
simimultaiieously
twemmty-two such
as
mmmaximmmumim
Fick
proximmmatiomm three
tabulated
could
times
be
by his
of the
to
work
fiber
olo .66 kilogram
control
No
that
forces
time
could
Consideratiomi (Fig. 3-B) the
a force
of
realized,
authori-
do
by
some
multiplying
of the areas under suggest-s f-hat. a better
ammioumit
overestimimated
of
of
f-he
excellent
is
simortenimmg
the ap-
by
one-
mmmaximmmummm temmsiomi by
fables
for
body
kmmee, the
joint
is always
time reference
axis
shifts
as the poimmt
is ijrovided
Each
of work
under
optimum
Body
work
capacity
in the
about
the
be, there in more
movement
its
mass,
since
centinmcter
of
circummistances.
body
joints
because
which
they
connect
can them.
is always aim axis about which complicated joints, such as
progresses
muscle
by
cubic
Segments
effective
segments
for
do
section.
are
a joint may each imistant;
at
can
cross
on
produce
the
occurring
muscle
tinmes
of Muscles
comnplicated
mmmovemiient
army
centimeter
muscles
rotation
mmmatter how
was
muscle
otherwise
length
Action nih
Fick
exert
relationship
each
mmmultiplyimmg
Since
estimates,
esfimmiate
coulol
that
would
by six.
is l)roportiommal
milUscie
work
LECTURE
they
lemmgth-temmsiomm
the
obtaimmed
mimodermm
l)e (livioled
A rough
this
leimgth
optimmmumn
time mmmaximmmummi t-cmision.
simould
COURSE
by nmaximmmunm shortening. diagrahmm for mimaxinmummi work
force
lengt-im-temmsion half
at
tons. f-lie imimporf-ammcc of the
Before
ties
INSTRUCTIONAL
but
its
instantaneous
the the
position
actiomi.
Simice
f-lie human body moves by a series of rotations of segments, the most of f-he effect of muscle is the moment of force (torque) which the immuscle caim exert-. Time nmomehmt of force immvolves the tension immthe muscle, labeled
useful
nmeasure
F in
4-B,
Figimm’e
multiplied
by its lever
arm,
labeled
1. The
lever
arm
is best
defined
as f-he length of a perpendicular between the limie of action of the muscle and the axis of f-lie joimmt. Iii similar fashiomm, f-he weight TV has a lever arm d. If the force of gravity acf-immg on time weight and the force of contraction of the muscle are the only forces act-immg on f-his body segmcmmt, no motion will occur if F X 1 + W X d = 0. Whemm accelerat-iomms occur, they cami be included iii these referred to either as effective forces or inertia forces. ,Joint
Gompi’ession
and
calculations
amid
are
Stability
Muscles amid joiimts funictiomm immclose cooperatiomm. The joints assist the lYT mmmeammsof arficular surfaces mvhicim guide the nmovemmmemmts that the muscles ing
to
prooluce.
l)roviole fh deltoiol forth
Time
sf-ability. shoulder when
the
immtime scapula
I’igure
of the
1mm f-his
mmmuscles are
commiplef-ed
the
deltoid
the
pull
axis
in
the
Figure
5-A
of the
deltoid
mmmuscle pull
joimit,
commjunct-ion
in
of the
deltoid
mmeuf-ralize
commmpressive by
the
force
addif-iomm
other
forces exerted
cuff
labeled but arc
wit-h
commtribute
added by
of gravitational
to f-he
that
THE
of the calls
reaction
the
constitute
to
equal
hummmerus
passes
well
conic
to
I. Their
a
rotate
and
(miot
the
opposite
shown
f-he
effective JOURNAL
outside
in the
f-he
the
rescue.
mmmonmemits of
additive of
commibimmed arid
action acromiomm
to joimit commmpression. The vector which portrays
muscles
S arid
the
of f-he muscle
omi the
compression
rotator
each
Wimemm these
shoulder
joimit to
the
on
muscles are try-
the
of
shows
amid joimit
f-he teimdemmcy
5-B,
Figure
coml)ressionm
mmmeasures pull
to
sifuatiomi
showmi
commmpressiomi. resulf-amit
Time
mmmeasures f-he comitributiomi of the deltoid 5-B shows a more perilous situatiomi.
,
conf-ribimtiomm
time joimit
in
to the
sufficient
as amm exammmple.
joimmt ; together
reactiomi
This
reactiomm
lai)rummm.
serve
provide
is elevated.
mmmommmetmt of which
scapula. diagrammm)
imi refurmi,
will
humerus imm the
a reacfiomm
couple,
mmmuscles,
joint
the
then
nmuscles.
Two force
cuff about
s amid i, to joint
forces, o!eltoio!,
the glenoid
we Time
obtain picture
R, the cami
forces. OF
BONE
AND
JOINT
SURGERY
be
HERBERT
ELFTMAN:
BIOMECHANICS
OF
5-A
FIG.
369
MUSCLE
5-B
FIG.
Fig. 5-A: Commtributiomm of the deltoid muscle to stability of time elevated by time reaction to time pull of the muscle passimig well withimm the glemmoid
simoulder labrmmm
joint.
joimmt is shown to compress the
.
Fig. 5-B: Imi this position of the shoulder, outside time glemmoid laI)rnmm. Time addition balamice but their joimit rea(’tiomms (s amid nmore favorably placed for joimmt stability. timid effective forces are also iniportant.
the reactiomi to the pull of time deltoid, D,is located well of two cuff nmimscles, S amid J,wmthi them.r mimommmemmtsin i) additive provmdes a resultammt jommit reaction, H, much 1mm additiomi to time mimuscimlar forces showmm here, gravity
IN
CHANGE 6-A
FIG.
LENGTH-
CM.
6-B
FIG.
Fig. 6-A : 1ime st ret (ii-simort cmi cycle. I )iagranm of t ime posterior delt oid miiuscle aidi mmg gravity to svimmg the arm at more thami its miatural frequency. As the arni swimigs forward the imiusele is stretched as it decelerates the arnm with imicreasimig force umitil it exerts nmaximunm temisiomm at mmmtiximiiummmlemmgth with the mimotion mmmomemmtarily stopped. The nmmmscle then shortemms, acceleratimmg time arnm with docreasimig force umitil it agaimi passes the vertical position. Fig. 6-B: The stretch-simortemm cycle of the (‘alf muscles dmmrimig rumimmimig. (Adapted frommm Time Actiomm of Muscles in the Body by herbert Elftman. Biological Symposiimm, Voltimime 3, pg 201, 1941.)
Time Stretch-Shorten
Cycle
?ilammy mmmovenmemit-s of time body immovemmieimt-s
therefore
are
first
stretcimeol
simimilar to those
illustrated
by
the
oscillation
gravity.
Figure
swings
forvarol
witim decreasing
before
6-A
accelerating
wimemm time armii swimmgs forwaro! as it. slows
down
backwa-m’d.
Time
at
wimich rIii
VOL.
48-A,
fume
general NO.
the
forward
nmaxinmummm the
velocity
sigmiificaimce
2, MARdI
1966
are
such
that
Time
ommaim oro!immary
of an arm forced shows time arnm first velocity
until
backward.
l)ast
Time
the
swing force
time mmiuscles
themm simorten.
of gravity
ai(lihig
posit-ion
amid
timese
these
muscles
are
amid mmmay, indeed,
a higher
frequeimcy
imm a
vertical
posit-iomi
by
be
mmmuscles
fm’oimmwhich
it
mmmoimmeimtam’ilyat il-s u)permmmost deltoid
posit-iomi
mmiuscle
wimicim control of
to
posterior
amid fimially
imi time
pemmdulum
it stops
vertical
act-iomis
mmiuscle
becomimes
; time immuscle is timen
shortemms is exerteol
as it accelerates at- ifs
active
stretched time swing
mimaxinmumim
lemigth,
is zero.
of this
stretcim-simortemi
cycle
is further
enmpimasized
by
370
A.A.O.S.
1igure
6-B,
siomi
which
iim hot-li
crease
is based
lemmgt-h,
with
as
f-he
this
tion
frommm time work
mmom’mimalsequence
Two-Joint
with
gemmerosity
will
of niore
be used
during
the
for
stretched
by this
muscles
tend
events
takimmg
is what
is suppheo!
the
cunmulative
actually
to
pass
place
fiber-lemigth in all
over
being
IN
tensiomm imi one muscle sequemmce.
stretched
amid
in omme nmuscle
are
shortemmed
Figure
7,
they at
which
are
ammother.
records
hip
7
of two,
shortemi
If separate receivimig elimimmate
more
slowly,
kmmee flexors amid hip energy, amid the hip this duplicatiomi of
amid follow
the mmormal
.
dissipatiimg
imistead
emmergy.
arid
follow
muscles
of two
The
the are
hanistrimmg
mmormal that
; short-emmimig
are
expenditure left
amid
to the
control.
less efficient Basic
tainied,
suggest
that
mmmuscle
cami do
stretch-shorten
temisiomm is produced
is slower
timan
all
this
sequence
imi the
as
ahmd mimaimionc-joimmt
mmmus-
by temmdomm action; It is therefore mmot
f-he nmuscles of the hunmami body are orgammized imito lomig nmuscles amid able to perform the gemmcral actiomm imitcmmded with efficiency
of emmergy
represents
is usually
nmammy joimmts
movcnmemmt
The
two-joint additiomm
would
a fashion
they by
This
they replace; emmcrgy is tramisferrcd fronm omme joimit to ammother the stretcim-shortemi cycle, with its advamitages, is achieved. timat
over
rummninig If ommiy omie-joimit mmmuscles were available, a hip shortemmimig arid doing positive work, while a kmmee flexor
trememmdous emmergy-saving showmi in the figure. The advamitages of two-joint
spamimmimig
pass
LENGTH-CM.
instead
with
surprising
which
muscles
joimmts.
nmimscles. Actual records of rummmiimmg . the knee muscle would be stretched, work. The hamstring muscles (right)
amid kmiec nioniemits during extemisor would have been
walkimig
confirmmma-
The term simice the
immtwo-joimmt the
while
is illustrated
FIG.
both
ole-
suggest-ion
received
mimuscles
joimmt-s immsuch
at omie joimit
happemis
Emmergy-snivimig by two-joimmt extensors were employed (left), muscle WoUld shortemm, doing
effort, maintain stretcim-shortemi
with
movememit
CHANGE
des arid
has
by
The
mmo mmew principles.
allow
the
time body
beemi mmoted that
to
two-joimmt
taimmed
is followeol
shortemmimig.
time muscle
in temm-
increase
emmergy,
the usefulness of this arrammgenment. mnore than two joint-s are immvolved,
immdicates
already
mmot sufficient
was
rfhe
.
absorbs
subsequemmt
sommme energy
which
evemi when
joimmf-s aohis
It has
rfhat
published
amid
of Hill.
timaim omie joiimf-
that-
previously
is stretched
saves
LECTURE
Muscles
rfie
muscle
COURSE
on a figure
mimuscle
lcmmgfim amid f-cnsiomi
that-
nmore
INSTRUCTIONAL
siimmplest forward
the
type
The
finer
short
nmuscles.
Factors
in Gait
adjustnmemmts
of gait, from which all other surface. Once the average
omi a level
pattern a repetifiomm
of gait of
the
repeats first
itself except
JOURNAL
the
details
of
types can be approached, is forward speed has beemm oh-
every two steps; for the exchange THE
of
OF
evemi of left BONE
the for AND
sccommd right. JOINT
step
SURGERY
HERBERT
:
ELFTMAN
BIOMECHANICS
FIG.
OF
371
MUSCLE
8
Saliemit features of an average step modeled after Fischer’s secommd experinment 16#{149} The body is divided immto three cardinal parts: the head, arms, and trunk (HAT) and two lower extremities, for each of which the center of gravity may be followed with simfficiemit accuracy by a parallelogranm constructiomm at the kmmee. Phase 1 shows beginning of double support with relative swimmg of lower extremities completed and body center of gravity almost at lowest elevation and maximum forward speed. Phase 2 shows maximum speed of swing of extremities with respect to each other amid the body center of gravity approaching highest elevation amid mimiimum forward velocity. The last t\V() piiases repeat the first two but with left foot imi contact.
The
nmovements
movement,
such
during
as
the
gait
be
can
rhythmic
comisidered
swing
under
of arms
and
two
legs
imeadimmgs:
relative
to
intermial
each
of-her
without changimmg f-he position of the center f-he body as a whole; amid external movement,
of gravity or the angular mommiemitumim of the translation of the center of gravity
of the
this
are
body
amid rotation
of the
body
illustrated
in Figure
8. The
lower
nmemmt at phase body
cemiter
which
1 (left) of gravity
is relatively
Control
small
of Internal Control
are
respect their swing
to each kinetic
imm
it at phase is showmm
a nmajor
portiomm
anmoumit
of energy emmergy
emmergy
expemmditure 48-A,
NO.
external
camimmot
result
the
curves
2, MARCH
of work
must swimmg
imm the camm 1966
done
by
of the muscles. flow of kinetic
emmergy
that
16
move-
nmovemmmemmt of the
of the
be accomimplisimed
body
as a whole,
alomie
lower
be decreased
is
muscles
of
by
part
forces,
ammo!
increase
arid
decrease
in kimmef.ic cimergy
amid
the
succeeding
dewith as the
decrease
In both cases nmctabolic energy is useol. energy of internal movehmment represents
expenditure
be supplied
by extermmal
with frictiomi amid plastic of the lower extremities
other, as shownm in Figure 8, immvolves alternate energy, as showmi iii Figure 9. The immcrease
of
nmovemenfs imiternmal
by Muscles
movcnmemmts
lower-extrenmity
kinetic
VOL.
3. The
relative
; f-he rotatiomi
accomplished almost emmt-ircly by muscles, cmmt-erimig to a lesser degree. The swimmging
is the
of these
their
is imot showim.
Move,-nents
accelerates
for
space
Some
start
amid complete
is accommmplished by stretchimig Commfrol of the ebb and
step
center.
extremities
through
here,
of immternmal
so they formation
about
the
nmuscle
represented
of
wit-imout
Figure
body
durimmg
gait
amid themm removed by the nmaxinmum 9.
altcrimmg
The
ommly way
average
velocity
Time
during value imi whichm
mmet
each of time this
amid lemmgth
372
A.A.O.S.
INSTRUCTIONAL
COURSE
LECTURE
C-)
0
m Li-
0
Li +2 z U)
+1
Li
.-J 0
w RO
LS
LO FIG.
RS
9
changes for time step simowmi immFig. 8. The upper grapim shows how the kimietic emiergy amid emmergy of the body as a whole conmpemm.sate durimig the step. The curve labeled KER is the mirror image of the KE curve; if the PE curve coimmeided with the KE!? curve, time nmuscles would mmot need to supply amiy emmergy for movememmt of the body as a whole. The lower part of the figure shows the kinetic emiergy of the relative niovenmemitof the lower extremities with respect to each other. This emmergy nmust be supplied by nmuscie. Energy
potemitial
of ste1)
to flatten
iS
the
out
kinetic
emmergy curve
by
providimmg
fall. Time limit of emmergy-savimmg by this device is shown by lower part of Figure 9. This situation cami only be obtaimmed celeratiomm
to
Internal swimmgimmg,
ami average during
tiomms
process.
of the
of External
external mimovenments to those of time imiterimal
The
are
Movement
trunk
and
mmot restricted
timey
to
comitribute
the
of ammy extremity
head,
a commimon
and
lower-extremity
immajor
may
part
also
occurrence
Movements of time body mimovememmts,
by Gravity during except
and
be
of
imi nmammy types
Muscles
the body as a whole are exaggerated in abmiormal mmornial gait as well, if for mmoother reasomi thamm the
gaits but are importammt great care which nmust be
exercised to mmminimize them. Guarded rotatiomm of the hips, for immstammce, lessemis lever armmi by wimicim the ground reactiomi affects total vertical spimm. Time translation of the cemmf-er of gravity of the body during gait is shown Figure are
8. Althougim time
gravity energy variatiomis
the
balanced
level walkimmg go through cycles for forward tramislatiomi. Time rota-
of
ill the
rise
gait. Control
similar
walkimig
mmormmmal i)erforniamlce
energy involved in this by a coummfer-miiovemmienit of disordered
rapid
velocity.
mmmovcmmmemmtsduring but
a mnore
time dotted himme in the by immstanitammeous ac-
vertical
its lateral umidulatiomms
umidergoes. of time body ill potential
The
forward
as a whole
mmmovemmmcmmtsare ammo! chammges velocity
amid time vertical
immmportant, imm forward is
time
of mmmuch greater
which
velocity
largest
ummdulat-iomms
commtributor
are
the
ccmmter time
images
JOURNAL
OF’ BONE
AND
JOINT
of
kimmetic
of the
emmergy. THE
in
significance to
faithful
the
SURGERY
HERBERT
Time vertical in
movememmts
8 amid are
Figure
potential
tigators
also
fumictiomi
to
of muscle
Immstead
of
each
that
step
OF
of gravity
I)otemitia!
curve
impressive
is the
foe
373
MUSCLE
of the
energy
are
gravity
is to battle muscle
cemiter
as the
during
envisage
BIOMECHANICS
of the
shown
energy 2,28
ELFTMAN:
body
are
in Figure
and
led
of efficiemmt
amid that
body
were
to
gravity,
KER
curve
PE
imives-
time mimajor
gravity.
combating
follow
time actual
imm
changes
imiammy early
gait
however,
it
camm be
seemm froni
that time kimmet-ic energy of the body waxes arid wammes so as to cooperate in keeping the total energy of the body relatively constammt. If f-he rise following
depicted
9. The
curve,
(the the
mirror
muscles
image would
of
KE
the
Figure
instead
curve)
mmeed to commtribut-e
9
with gravity amid fall of the miothiimg
of to
the
H H
C
FIG.
FIG.
10-A
FIG.
10-B
10-C
Fig.
10-A: Basic fundamentals of muscle control of the trajectory of the body as a whole by det-ermining the ground reaction. The square represents the mass of the body as a whole with an arrow for its instant velocity. The ground reaction(R) is the result of the reaction to gravity (G) amid the effective, or inertia, force (A) reflecting the acceleratiomi of the body. The body is vaultimmg through space on a rigid rod, the reaction is perpendicular to the trajectory, and the chammges in kinetic emmergy are due to gravity. Fig. 10-B: The ommly change is to show a lower extremity requiring muscle momemmt.s, H,K, amid A, to keep it rigid. For simplicity we shall regard this extremity as weight-less. The muscle momemits, H,K, and A are proportmonal to their lever arms, h,k, and a. The muscles use metabolic energy for tension maintenance but do no physical work. Fig. 10-C: Action of the muscles changing the trajectory of the body. The ratio of muscle moment.s, dictated by the nervous system, determines the position of the groummd reactiomm amid the magnitude of the muscle moments determines the acceleration.
exterimal
energy
center
of
of gravity
management
imi
which
of the
body
way
movememmts weight
the
limbs
effective
weightless
ground
the
acceleratiomm
tial
emmergy
management
A
to simplify ,
cooperate
is illustrated in a box
OIi a pole.
force,
resulting
muscles “
concentrated
as if vaultimmg
Skillful
body.
the eniergy that for the normal walker
is easier
The body
the
which reaction,
of the
immf-erchmammge.
the
of the
muscle must than for the
minimizes
with
gravity
in Figures
10-A,
surrounding
details.
the
trajectory
of the
contribute. anmputee. in controlhimmg
10-B, center
In Figure
10-A,
the
amid 10-C, body
external
which
of gravity
the
body
rflmis skillful
amid
depict comisider
moves
forward
The external forces are the reaction to gravity, G, amid f-he is the product of the mass amid acceleration of the body. The R, is perpendicular to the instant velocity of f-he body, body No
is derived muscle
cmmt-irely activity
from
gravity,
is immvolved.
amid
kimiet-ic
amid
potemm-
374
A.A.O.S.
Iii
Figure
10-B
the
INSTRUCTIONAL
pole
has
COURSE
beemi
replaced
by
simowmm. rrlme ground reactiomi has miot changed through time figure (dotted himme). It is necessary tiomm to ankle
1)revemmt
further
Plammtar-flexor a. 1mmthe same
arnm, tively,
can
tiomm of the nietabolic
doing
be
flexioim muscle,
way
the
calculated.
of action
emmergy
to
lever
of the
various
arms
nmaimmf-aimm tension
to the kmiee
of the t
but
segmemits,
joimmt-s. The
of the
reaction,
body
ammgulateo!
as
amid its line of action is projected for mmiuscles to be in isometric contrac-
be equal
must
monmeimts
The
hue
mmophysical
of the
A,
LECTURE
amid
are
hip
muscles
amid s, arc riot
mmiomemmt of force
reactiomm,
R,
amid
chammging
of the
time
K arid
muscles
showmm.
timmies
lever
H, respec-
the
lmoimmt-s of imit-ersec-
The
muscles
length
and
are
usiimg
therefore
are
work.
3
#{247} VELO FIG. Emmergy
comisunmption
fronm the experiments bolic energy, above
iii walking
at various
CI IV 11
combimmatiomis
of Atzler amid Herbst The that used in standing, required
contour
of step
lines
lemigth
of the
amid velocity,
nipper
graph
replot-ted
show weight
the meta-
to move omme kilogram of body omme meter The mimminmum emiergy expemiditure for each velocity is shown by a limme which passes amid mmear E amid F, which refer to the steps ammalyzed by me 8 amid by Fischer 16.17, The lower graph shows the emiergy consumptiomm above that for stammding plotted in two ways. The solid limme simows the COSt imm calories of trammsportimmg omme kilogram of body weight omme horizontal meter; it ha.s a defiumite minimum where the efficiemicy of the locomotor apparatus is greatest. The hrokemm limme shows emmergy comm.sumptiomi immcalories per kilogram minute; whemm the ba.sal expemmditure for stammdimig ( 17.2 calories per kilogram mimmute) is added to this it reflects the stress to which the body is subjected. horizommtally. through 0.50
In Figure has
10-C,
stinmulateol
about action
H, K,
time imiuscles
enough
motor
assertimmg
positive
provide
commtrol.
The
mmmonments of force
mmervous
systenm
(H,
amid A)
K,
hip, kmmee, amid ankle. Simmce a weightless hinmb is assuimmed, time ground rewill be the same for each joimmt. When the mmcrvous systemim produceol momemmts ammo!A , it deternmimmed the direction of the groummd react-ion by their proportions the
amid time mmmagmmit-imdcof the ommly upwaro!
arni
arc
ummits to
with
acceleratiomm
respect
to the
acceleratiomi by their mmmagmmitudes. rFhe result but also amigular acceleration simmce the reaction body
center
will
be
has
a lever
riot
of gravity. THE
JOURNAL
OF
BONE
AND
JOINT
SURGERY
HERBERT
ELFTMAN:
Energy A detailed
the
amialysis
physical
of the
work
systenm
Such
also
therapeutic
are
procedures
ummusually
An
1 1.
vel1
Herbst. The Their subject
of gait
the
metabolic
for
tensiorm
consumption
the
information
metabolism
under
experiment
of this
at each
riot
It is important
mmmoveniemit
mmmore
tracteol
frommi that The
solid
to mmote that, the
accurately,
durimmg
hue
mmiemmf-s
choose
upward
the
of these
in order
optimmmummmline. 1mmthe lower part
evaluatiomm
This this
of the
calories curve sort
have
The
by
curve
requirement
to f-he
distance,
and
Ralston
taneously, motor
there unit
are
fibers for
of motor
units
of fibers
in each
miumber
was
ummit imm the
susceptible
number the
right
represents
able to walk effect ommcmmcrgy
the of
in a muscle unit,
of increnmemmts
belief
but
the
to
Imi the
to determine
(solid
himme). of
gaits.
limme) shows
would
to
Measuremmmenmts
emiergy
time olata imi the This nmethod of
peak
the
to each
load
be
that
immdicaf-cd
restimig
by
sfandimig
value
is mmthe
emiergy
on time gra)h.
of Muscles that
mammy muscle
fibers
mm a given
nerve. The mmumber of muscle fibers few fibers in each unit of the extraocular gastrocmicmius
13
motor
that
muscles
by
the
with commtrol.
nmay be a better number
Although
ummit always
graduated
simmce the which
useful
1 1 (broken
added
(‘lose
ways.
horizontally
by multiplyimig by the velocity.
mimmute,
very
two
of abmmornmal
instance,
in each
closely
iii
shape.
efficiency
is so arranged
per
number
mmmuscle activity.
of the
beemi sub-
corresponding
meter
evaluatiomm
for
Control
all of the
the ated
are for
was
were
16
it is most
one
kilogram
fronm each motor varies from the
the semiting
data
cost
has
to
velocity
of Figure
heart, per
subject,
is justification more
f-he
part
calories
fibers
that
left
(F)
a characteristic
for
lower
of muscle
1600
rcasomm to believe
from
commsunmptiomi
omme kilogram
Nervous
muscles
emmergy
standing
of Fischer
imi goimmg a given
upomm the
muscle receive branches each of these nmotor units
amid that
omie mvhemm it is not
if 17.2
inrmervatiomm
the
only velocity in nmef-abohisni mmmeasureThe assunmptiomm that an individual will is not always true, although it is interestimig
against
for f.imis particular
The
Atzler
values shown horizontally
the
subject
graph
nminufc amid is obtained per kilogrammm meter)
placed
f-he graph,
the
is plotted
the
iii
kilogram (calories
Time load
8
mimmimum
is f-he mimost useful on
to represent
1 1 , time energy
above
done
heemm used
secommd
portamit. values
of Figure
a definite
commsummipfiomi per curve below this plottimmg
(E)
nmine
up in transporting
has
by
by
provided The weight
of step at which this subject lemmgth of step has a profoummd
conibimmationi
graph
work
used
performed
is
27
conditions
combinations
of the
across
exl)erinmemit.
subjects,
imi the
different
custommm of reporting
efficient
historic
two
optimmmumim hue the
usual
imm amm imiadequate
thie nmost
that
of
available
walking.
sweepimmg
; the
results
nmaintemmance.
controlled was
out two
replotted in the upper part of Figure combinations of length of step and
nietabohismmi
the commmbinmatiomms of speed amid length mmiost- efficiently at each velocity. The comisummmption
and usually
type
take
of these
advamitages
frommm which the contour lines of this figure were commstructed. the emmergy immcalories used for movimmg omme kilogram of body omie immet-er.
they
only
productiomm
the
comimputimmg
energy
cost of
but
involves
7,8,10
physical
understanding
of over-all
desigmied
the
data that they collected are walked at twenty different
; his oxygen
velocity
an
mechanisms,
restricted to a measurernermt meamms of oxygen consumption. and
requirements
needed
for
and
in Walking
and
energy
is desirable
375
OF MUSCLE
in shortening,
stretched,
of the
aim analysis
energy
by muscles
as they
but
fumictiomis,
Consumption
of the
done
BIOMECHANICS
index
there
fewer
of effective systemmi
simul-
fibers f-he
iii
other
camm recruit
each hand,
control
of ummits commmes closer
miervous
is rio
commtract
On
in
thamm
to repregradu-
376
A.A.O.S.
Time feedback fummctiomms 25
two
maimmtenammce
orgamis
of information Omme is regulation contraction ; this muscle spindles,
of
amid the
feremmt fibers.
The
cermmimig how
well
infornmationm
mmmay or
sensory
other the
may
problems
in
COURSE
is feeding
to the
is succeeding not
LECTURE
concerning muscle of intrinsic factors regulation is mediated which have gamma
function nmuscle
termmmimmatiomis from \-lanmy
INSTRUCTIONAL
reach
mmervous
immproducing
go to a variety of locomotion
progranm
nmore information time complicated
be obtained actioims
concerning the extent and the time it takes
effect nmodulafion. The ordinary are too short for the production OIl which
part be applicol.
can
of the
contractions of a tetanus
succeeding
cycles
Future iii the
The immformation classic
methods. sequence
ciated
with
other
criteria
The use of devices
motor
pattermis
bodies
is a challenge
an even
to
for the
informatiomm
broader
new
sources
froni
current
goes beyond by a variety
spectrum
activity
will
of tension
data
production
Harmonious
will
concerning the if it can be asso-
useful
variations in muscle power presents the
of energy.
that available of experimental
of instrumentation
has contributed become more
monitoring
of the electric using external
The
resemblance It is essential
of Study
future.
of action
contractions. the commtrol
Methods
that
bears slight laboratories.
of muscles during mmormal movements and it would be interesting to know
afferenmt
Electromyography of muscle groups but
centers. ummsolved.
24,
contained in the present paper by adding later data gathered
immthe
comm-
movememit. This by a variety of
to which the higher centers for feedback inmforniation to
23,29
It is to be expected
be employed
information
of higher remain
elegamit perfornmance of which human beings are capable to the primimitive reflex movements studied in physiology that
system
the desired and is served
comisciousness
which messages the neural control
contraction presumably has within the muscle, such as largely by the Golgi tendon efferent fibers as well as af-
in non-isometric
as sources possibility function
of signals of linking
for old
of reconstructed
to biomechanics.
References E., amid 1927.
1. ATZLER, 291-328, 2.
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SAUNDERS, EBERHART, Normal and Pathological Gait. J. Bone and Joint Surg., STEINDLER, ARTHUR: Kinesiology of the Human Body ditions. Springfield, Charles C Thomas, 1955.
Muscle.
Speed
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Immt.
H. D.: The Major Determimmammts imm 35-A : 543-558, 1953. under Normal amid Pathological Con-
Correction A mmumber S. Reich
omm The
Reconstruction
The whether
of typographical Selection (High
first
recent-
On page
line or
205,
errors of Patients
Osteotomy
of text
203
is still legend
for
should
.
.
Fig.
VOL.
48-A,
page
NO.
209,
7, second
Reference
2, MARCH
1966
Hip
Imistructiomial
Fractures
Graft
or Both)
read
“The
Course
for in the
Lecture
Prosthetic
or
Jammimary
treatment
1966
Other issue
of fractures
of the
for
23.
.“
3-C,
On page 207, 25th line of text, for Haa.s On
in the
with
or Bone
on page
unimnited, immthe
occurred
line,
next
to the
read
Ha.ss.
for
945-955
la.st read
line, 745-755.
28 read
by Dr. Types of The femoral
Rudolph of
Hip
Joimrnal. neck,
