Pergamon
Copyright
J. Biomeckpnics, %I. 29, No. 4, Pp. 513-523, 1996
0 1996 Eisevier Science Ltd. All rights rcsemd
Printed in Great Britain
OOZl-9290/96
$15.00 + M
MECHANICAL
OUTPUT
FROM INDIVIDUAL
MUSCLES
DURING
EXPLOSIVE
LEG EXTENSIONS:
THE ROLE OF ~IARTICULAR
MUSCLES
Ron Jacobs,*Maarten F. Bobbert and Gerrit Jan van Ingen Schenau
Department
of FunctionalAnatomy,Facultyof HumanMovementSciences,
Vrije Universiteit,
vande Boechorststraat
9, 1081BT Amsterdam,
The Netherlands
Abstract-The main result of this study is that biarticular leg muscles contribute significantly to the work done at
joints, due to transfer of power during explosive leg extensions. In particular, a net power transfer was shown from
hip to knee joint during jumping and sprinting.
Seven elite athletes performed explosive one legged jump and sprint push-offs. Kinematics, ground reaction
forces and el~tromyography (EMG) of leg muscles were recorded. The mechanical output of six individu~ muscle
groups was estimated by using Hill-based muscle models. The EMG and kinematics served as input to these
models.
For jumping as well as for sprinting, the model estimated similar results for the relative work contribution done
about a joint due to transfer of power by the biarticular muscles. Rectus femoris showed a power transfer from hip
to knee joint, while in contrast hamstrings showed a power transfer from knee to hip joint. Regardless of these
opposite directions of power transfer, a net transfer occurred from the hip to the knee joint.
The relative work contribution of hamstrings done in hip extension was 7% in jumping and 11% in sprinting.
For rectus femoris, the relative work contribution done in knee extension was 21% in jumping and 31% in
sprinting. Power transferring actions by gastrocnemius from knee to ankle contributed 25% in jumping and 28%
in sprinting to the work done in pIantar flexion.
These results support the hypothesis that the action of biarticular muscles contributes to a net transfer of power
from proximal to distal joints during explosive leg extensions. This action of the biarticular muscles causes an
efficient conversion of body segment rotations into the desired translation of the body centre of gravity.
in jumping, usingonly kinematicsasinput to Hill-based
musclemodels to estimate soleusand gastrocnemius
The existenceof biarticular muscleshasfascinatedmany forces,the relative contribution to the total amount of
researchers(seeIngen Schenauet al., 1990).In previous work doneat the anklejoint dueto the transferaction of
studieson jumping and sprinting, the hypothesiswas gastr~nemiuswas quantified (Bobbert et al., 1986).As
forwarded that bia~icu1~ musclesplay an impo~ant a result,they computedthat 25% of the total amount of
role in transferringpower from proximal to distaljoints work doneabout the ankle isdue to a transferaction by
(Bobbert and Ingen Schenau,1988; Jacobsand Ingen gastrocnemiusfrom kneeto anklejoint.
Schenau,1992a).Specifically,a proximal to distal power
The questionthen arosewhether a net flow of power
transfer is believed to causean efficient conversionof from hip to kneejoint could also be demonstrated.In
successiverotational motions of body segmentsinto jumping, electromyographic(EMG) activity of rectus
translation of the body centre of gravity (BCG). The fermoriswasrecordedduring simultaneouship and knee
mechanismby which this is accomplishedis thought to extension;however,no estimatesof rectusfemorisforces
be the timely activation of rectusfermorisand gastrocne- wereavailable.Moreover, hamstringswerealsofound to
mius before the end of push-off. Activation of rectus beactive. To estimatethe flow of powerfrom hip to knee
femoriswas proposedto decreasethe angular acceler- joint, individual forcesof hip and kneemuscleshaveto be
ation of the trunk, which, combinedwith the onset of estimated.However,the indeterminacyproblemimpedes
kneeextension,ensuedin power being transferredfrom a straightforwardcalculation.An approachfor obtaining
hip to kneejoint. Similarly, activation of gastrocnemius theseestimatescanbe the useof kinematicsand EMG as
prior to the end of the push-offtransferredpower gener- input to musclemodels.In the presentstudy, this is done
ated by the kneeextensorsfrom knee to ankle joint.
for one-leggedjumping and sprinting. Analogous ap
The transfer action of gastrocnemiusfrom knee to proacheswereappliedto estimatethe mechanicaloutput
ankle joint was demonstrated for jumping (Bobbert et al., of the planar flexorsduring walkitlg, stepping(Hof et al.,
1986).Basedon simulationexperiments of plantar flexors
1983,1987)and running (Hof, 1990;Jacobset af., 1993)
and of the jaw musclesduring mastication(Ruijven and
Received in jkkxl $xm: 2 SeFfem~
1994.
Weijs, 1990).
*Current address and address of correspondence: Dr Ron
It is important to test the role of biarticular musclesin
Jacobs, Dept of Mechanical Engineering, Lab of Biomechanical
Engineering,
Universityof Twente,P.O. Box 217,7500AE jumping aswell asin sprinting, sinceboth tasksstart at
similarjoint anglesand are basedon a proximal to distal
Enschede, The Netherlands.
INTRODUCTION
513
514
R. Jacobs et al.
sequence of muscle activation but the translation of BCG
is different (Bobbert and Ingen Schenau, 1988; Jacobs
and Ingen Schenau, 1992a). In the sprint, a more reciprocal activation between hamstrings and rectus femoris
muscles was found compared to the activation patterns
in the jump (see Jacobs and Ingen Schenau, 1992a).
In the present study, we quantified the contribution of
the biarticular hamstrings, rectus femoris and gastrocnemius to the work done about joints due to the phenomenon of power transfer between adiacent joints in onelegged jumping and sprinting.
b)
METHODS
Subjects and experimental
Seven elite male athletes(age 23 f 2 yr, body mass
77.8+ 4.3kg, upper leg length 46.8+ 1.5cm, lower leg
length 43.0f 1.6cm) participated in this study. After
warming-up,subjectsperformedstandardisometriccontractions (SICs) to obtain referenceEMG levels. Since
the subjectswereprimarily runnersand not familiar with
performing one-leggedjumping, they were allowed to
practice jumping before the experiment session.Subsequently, each athlete performed three one-legged
maximalexecuted vertical jumps as well as three maximal executedsprint push-offs.During the execution of
both tasks,the movementpattern, ground reaction forces,and EMG of eight leg muscleswere recorded.The
analysisof the sprint push-offsfocusedon the second
stancephase after leaving the starting blocks, during
which the body is mainly acceleratedin the horizontal
direction. The analysisof the jump push-offsfocusedon
the phasefrom the initial squat position to foot-off.
Methods used for the analysisof both tasks will be
describedbriefly sincethey have been set out in detail
previously (Bobbert and Ingen Schenau,1988;Jacobs
and Ingen Schenau,1992a).
Kinematics
ix
procedure
and kinetics
Landmark coordinates(Fig. 1) were extracted from
tine film with the aid of a motion analyzer (Dynamic
Frame, NAC), and low-pass-filtered(zero phaselag by
bidirectional application of a fifth approximation, second-orderButterworth filter) with a net cut-off frequency
of 16Hz. Thesecoordinateswere usedto calculatethe
orientation of four body segments
in a sagittalplane,and
joint angleswere calculatedasthe anglesbetweenadjacent body segments(Fig. 1). The ground reaction force
vector wasrecordedby meansof a force platform (Kistler, type 9281B).Instantaneousnet momentsabout hip,
knee and ankle joints were obtained by meansof linked-segmentmodelling. Hip and knee extension momentsand plantar flexion momentsweredefinedaspositive. Net joint powerwascalculatedby multiplication of
net joint momentand joint angular velocity.
Electromyography
Surfaceelectrodeswere applied to the skin over gluteusmaximus,semitendinosus
and bicepsfermoris(caput
Fig. 1. (a) Positionsof landmarksappliedto the skinof the
subjectand to the forceplatform.(b) Definitionof anglesin
joints. N, H, K and A indicateneck,hip, kneeand ankle,
respectively.
OH,6kand0* indicateangles
in hip,kneeandankle
joints,respectively.
longum), vastus medialisand lateralis, rectus femoris,
soleusand gastrocnemiusmedialis.The subjectswore
a skin suit to reducemovementartefactsdue to swinging
of cables.Landmarksremainedvisible through openings
in the suit. The EMG signalsweretransmittedtelemetrically (BIOMES 80),filtered to further reducemovement
artefacts(bandpass25-200Hz), and sampledat 500Hz.
Subsequently,thesesignalswere rectified and low-passfiltered (zero phaselag by bidirectional application of
a fifth approximation, second-orderButterworth filter)
with a net cut-off frequency of 75 Hz.
Muscle model
Six musclegroupsweremodelled:three monoarticular
muscles,gluteusmaximus(GU), vasti (VA, asan average
of vasti medialisand lateralis)and soleus(SO),and three
biarticular muscles,hamstrings(HA, as an average of
semitendinosus
and bicepsfemoris CL), rectus femoris
(RF) and gastrocnemius(GA) (Fig. 2). Forces of these
individual musclegroups were estimatedby meansof
Hill-basedmusclemodels.The experimentallymeasured
kinematics and EMGs served as input to the model
(Fig. 3).
The musclemodel comprisesthree parts: (1) EMG
which servesas estimatorof musclestimulation.(2) Activation dynamicscorrespondingto the transformation
of musclestimulation to active state of the contractile
apparatus,and (3)muscledynamicscorrespondingto the
transformationof active stateto muscleforce. A description of theseparts follows together with the computational procedurefor calculatingindividual muscleforce.
Muscle stimulation. To obtain estimatesof muscle
stimulation,surfaceEMG recordswereused.Although it
would have beenmore ideal to use individual excitation
of all motor units, it was not possibleat this time to
record unitary activity from singlemotor units during
explosivemovements.The only accessiblemeasurewas
Role of biarticular muscles
RF
HA
VA
Fig.2. An illustrationof thepositionof the legmuscles.
GU is
gluteus maximus,
HA ishamstrings
(semitendinosus and biceps
femoris CL), VA is vasti (vastus medialis and lateralis), RF is
rectus femoris,
SOissoleus
andGA isgastrocnemius.
the surface EMG reflecting the spatial and temporal
activity of many motor units (Hermenset al., 1986; Ruijven and Weijs, 1990).In surfaceEMG, firing rate and
recruitment control are indistinguishable(Zajac, 1989).
Thus, increasesin EMG coincidewith either active motor units discharging faster and/or additional motor
units beingrecruited. Given the fact that both firing rate
and motor unit recruitment increasewith excitatory
drive to the muscle,EMG can meaningfully be interpreted as the net neural control signal to the muscle
(Zajac, 1989).Therefore, it was acceptableto use the
rectified surfaceEMG as a reliableestimator of muscle
stimulation. Maximal EMG wasestimatedby multiplying the EMG measuredduring SIC by the ratio of maximum joint moment to joint moment during SIC. In
doing so, it was assumedthat during SIC the muscles
involved in delivering the moment were producing the
samerelative force (Table 1). Subsequently,all EMG
valueswere expressedin percentagesof this maximum
(Fig. 3).
Activation dynamics. Active state, defined by Ebashi
andEndo (1968)asthe relative amount of calciumbound
to troponine, is related to the level of stimulation of the
muscle(estimated from EMG). This processcan be
modelledby a first-order processaccording to Hatze
(1981).The concentration of free calcium (algebraically
relatedto active state)and length of contractile element
of the musclef&f served as state variables. Instantaneoustime derivatives of calcium concentration were
calculatedfrom instantaneousvaluesof calciumconcentration, L,-r, and musclestimulation.The transfo~ation
of stimulation to active state wasscaledto the relative
amount of slow twitch fibresaccordingto Hatze (1981).
Estimationsof thesepercentageswere depicted on the
basisof data reported by Yamaguchiet al. (1990).
~~scZedy~m~cs. The useof Hill-basedmusclemodels
yieldsan adequatedescriptionof muscledynamicsin the
515
context of modellingof multi-joint behaviour(e.g.Winters, 1990).Soestet al. (1992)describeda general-purposeHill-type musclemodelcomprisedof a serieselastic
element(SEE), a contractile element(CE), and an elastic
element(PEE) parallel to the CE (Fig. 4). The force of
SEE and PEE dependsin a non-linearway on length of
theseelements(Ls,, and &us, respectively).The force of
GE dependson active state,length of CE (Lcz and velocity of CE (Vc,).
Where possible,parametervalues were derived from
morphologicaldata reported in the literature [seeSoest
et al. (1995)for a definition of the parameters].A number of parameterswere given identical values for all
muscles:stretch of SEE at maximum isometric force
(FMAx) was set to 4% of SEE slack length (ESEEMAX;
Morgan et al., 1978);LCEat which active force waszero
was set to 0.44 and 1.56 times &efoPTl. Hill’s force
velocity parametersa/F,,, andb/LcE(opTj werescaledto
the percent of slow twitch fibers according to Winters
(1990).Valuesof the musclespecificparametersare listed
in Table 1 (seealso Soest et af., 1995).CE optimum
lengthswerederived from estimatedsarcomerenumbers
(Huijing, pers. commun.). Relative values of maximal
isometricforce of agonistswere basedon musclecrosssectional areas, whereasabsolute values of the total
maximal isometricforce werechosenin sucha way that
realisticmaximalisometricmomentswereobtained.SEE
slack lengthswere chosenin sucha way that the joint
angle at which the isometricjoint moment is maximal
correspondswith experimentallyobtainedisometricmoment-anglerelations.The musclemomentarm data used
in this study werederived from experimentallyreported
data by Grieve et al. (1978) and Visseret al. (1991),aswell
as from Huijing et al. (in preparation). Moment arm
values as well as LCE(oP1)
and LsLACKfor each subject
were scaledto the ratio of upper leg length (for GU,
HA, VA and RF) or lower leg length (for SO and
GA) obtained experimentally to the upper and lower
segmentlengthsat which thesevalueswere determined
(seeTable 1).
Computational procedure. Sincemusclemasswasneglected,the instantaneousmuscleforce (FszE)was calculated from LsEEf&z = Loi - Lcr). From Fc,, Vc,
was computedaccordingto the force-velocity relationship.To completethe computationalcircle (Fig. 5), new
,!,cr and Ca valueswereobtainedby integrating Vcuand
rate of changeof calcium concentrationwith respectto
time.
Treatment of data
The jump push-off phasewas defined as the phase
starting at the instant that the body’s centre of mass
started moving in the vertical direction and ending at
toe-off. The sprint push-off phase was defined from
touchdown to toe-off. Simulationswereperformedstarting 75 msbeforethe push-offphaseand endingat toe-off
(t = 0). Previous researchshowed that subjects performedboth explosivetasksin a rather stereotypedmanner as expressedby the small variability (Bobbert and
516
R.Jacobset al.
Jump push-off
Sprint push-off
EMG
EMG
GU
HA
VA
1
GA
-300
-200
-100
0
Angles (deg)
Angles (deg)
-200
time (ms)
-100
time (ms)
0
Fig.3. TypicalEMG andjoint angledatathat havebeenused as inputto themuscle
models
recorded from
the samesubjectin jumpingand sprinting.The EMG of six musclegroupsis shown: GU is gluteus
maximus, HA is hamstrings (semitendinosus and biceps femoris CL), VA is vasti (vastus medialis and
lateralis), RF is rectus femoris, SO is soleus and GA is gastrocnemius. Maximal EMG was estimated by
multiplying the EMG measured during SIC by the ratio of maximum joint moment to joint moment during
SIC.Subsequently,
all EMG values wereexpressed
in percentages
of thismaximum.
Thejoint angles
of hip
(solid), knee (long dashes) and ankle (small dashes) are shown. The jump push-off phase was defined as the
phase starting at the instant that the body’s centre of mass started moving in the vertical direction (about
- 310 ms) and ending at toe-off (0 ms). The sprint push-off phase was defined from touchdown (about
- 160 ms) to toe-off (0 ms). The start of the push-offs is indicated by a thin vertical line. Simulations were
performed starting 75 ms before the push-off phase and ending at toe-off.
<
LCE
F
L~EE 4
‘PEE
Fig. 4. Structure of the model to simulate the individual muscle
forces. The model consists of a series elastic element (SEE),
a contractile element (CE) and an elastic element (PEE) parallel
to CE.
Ingen Schenau,1988;Jacobsand Ingen Schenau,1992a).
Therefore, in this study only mean time histories of
curvesand valuesare given. Individual time historiesof
all variableswerenormalizedto 100%of the meanstance
time(Winter, 1983).From thesenormalizedcurves,mean
curves for each subject and the total group were obtained.
Individual musclemomentswereobtainedby multiplication of the calculatedmuscle-tendonforce (FYTC)and
the momentarm. The power producedby the muscular
part of the musclemodels(Pa) wasobtainedby multiplication of V, and FcE and the power of the tendinous
part in seriesof the musclemodels(PSEE)
wascalculated
Role of biarticular muscles
517
Table 1. Values of the muscle specific parameters. D is the average moment arm;
&E(OPT) means optimum CE length; LsLacK is SEE slack length; Fuax is maximum
isometric force given for one leg; ST is the percentage of slow twitch fibres. Length
values (D, LCE(oPT)and LLAcx) were scaled by the percentage of subject specific
segment lengths and the segment lengths at which these values were determined;
upper leg length of 0.44 m and a lower length of 0.40 m
DHIP
Cm)
GU
HA
VA
RF
0.062
0.077
0.035
DKNEE
(m)
(ml
0.017
&E(OPT)
L SLACK
F MAX
04
(ml
(NJ
0.200
0.150
0.370
0.160
0.360
0.246
0.382
2650
6000
5400
930
4235
2370
0.104
0.026
0.042
0.042
SO
GA
D ANKLE
0.046
0.046
Fig. 5. Flow diagram for simulation used for studying the individual muscle behaviour. Joint angles and EMG served as
inputs to the muscle model. The derivative of LCE(iCE) Ca (Ca)
are calculated by the model. Integrating (INT) these values with
respect to time, new L, and Ca are obtained. The calculated
muscle force (FMTc) is a function of LcE and active state (Q).
by multiplication of Vsu, and FMrc. In order to determine the power transferred(PTRANS),
e.g.from hip to the
kneejoint by RF, the Ft,,rCproducedby RF wasmultiplied first by the momentarm of RF at the hip, resulting
in the moment of RF about the hip, and secondby the
hip angularvelocity, resultingP,sANsfor RF. PTrUNs
was
calculatedfrom knee to hip joint for HA, from hip to
kneejoint for RF and from knee to anklejoint for GA.
To decidewhetherthe modelgavean accuraterepresentation of the real system,the model outcome was
evaluated. To evaluate the model, for jumping and
sprinting,similarity wascheckedbetweenexperimentally
acquired net joint moments(by meansof inverse dynamics)and the sumof the estimatedmoments(by means
of musclemodel). The net hip momentswerecompared
with the sum of GU, HA and RF moments,net knee
momentswere comparedwith the sum of VA, RF, HA
and GA moments,and net ankle momentswere comparedwith the sumof SO and GA moments.In addition,
net joint powerswere relatedto the total summationof
individual musclepower curves(includingPCE and PSEE)
correspondingto the particular joint. Work valueswere
calculated by integration of the power curves with respectto time.
0.093
0.081
0.045
0.049
52
58
47
40
81
50
Sincethe model parameterswerebasedon an ‘initial
guess’from the literature, the questionarisesasto what
extent model predictions will be affected by changing
theseparameters.To determinethe influenceof relative
changesof the parameterschoiceson modelpredictions,
for a rangeof parametersa sensitivity analysiswasperformedfor the plantar flexors, accordingto the method
proposedby Winters and Stark (1988).It wasfound that
an increasein Fvax and momentarm valuespositively
influencedthe amplitudeof the plantar flexion moment,
ascould be expected.Changesin the time constantof the
activation dynamicsand EsEEMaX
affected the rise and
declineof the plantar flexion momentcurve.
RESULTS
AND
DISCUSSION
In the present study, the contribution of biarticular
musclesto the work done about joints due to power
transfer was estimatedin jumping and sprinting. To
estimatethe individual contribution of muscles,Hillbasedmusclemodelswereusedin which measuredEMG
and kinematicsservedasinput.
This sectionwill focusfirst on the comparisonof the
musclemodel output and the resultsfrom inverse dynamics.Subsequently,the power output of the individual
muscleswill be presented.The main hypothesisaddressing the net transferof powerfrom hip to kneejoint will be
discussed.Finally, the importance of the biarticular
musclesin the executionof multi-joint movementswill be
discussed.
Evaluation of muscle model output with resultsfiom
inverse dynamics
Figure 6 showsthe comparisonbetweenthe individual
estimatedmusclemomentscrossinga particular joint
and the correspondingnet joint momentsobtainedfrom
inversedynamics(seethe Methods section).As can be
expected,therewasno perfectmatch.However,basedon
this comparison the conclusion was drawn that the
musclemodel can be usedfor the intended quantification.
There are a number of different sourcesthat can account for the discrepancies.First, the comparisonwas
518
R. Jacobs et al.
M-hip (Nm)
400.
Jump
push-off
-100.
::L----l
M-knee
-200 -
(Nm)
M-ankle
(Nm)
-300,
’
M-knee
(Nm)
M-ankle
(Nm)
*
4wI
300.
200.
100.
i,t
-300
-250
-200
-150
time (ms)
-100
-50
0
-150
.
-140
-120
-100 -80
-60
time (ms)
.1
-40
-20
0
Fig. 6. Mean time histories (n = 7) of the net hip, knee and ankle joint moments obtained by inverse
dynamics (solid line) and the sum of the estimated individual muscle moments corresponding to that
particular joint (dotted line) for jumping and sprinting. The following comparisons are made: for the hip
between the net moment and the sum of moments of HA, RF and GU, for the knee between the net knee
moment and the sum of moments of HA, GA, RF and VA, for the ankle between the net ankle moment and
the sum of moments of GA and SO.
made between a net joint moment and a summed moment of only a few muscles (2 to 4). Some of the deviations could have been minimized by modelling other
muscles which were also activated, e.g. tibialis anterior,
the deep polyarticular plantar flexors and iliopsoas (see
Jacobsand Ingen Schenau,1992%Nilssonet al., 1992).
Second,basedon the sensitivity analysisof the model,
FmX, moment arm and EmsMaxinfluencethe shapeof
the individual musclemomentcurves.For instance,FM,
was basedon the literature and assumedto be constant despitethe interindividual differencesin maximal
isometric force Finally, surface EMG could only be
used as an estimator of stimulation (seethe Methods
section).
The contribution of a muscleto externalwork depends
on the amount of power a musclecan generate.Figure
7 showsthe net joint powersbasedon the inversedynamic calculations,together with the sumof individual
musclepowersestimatedby the musclemodelfrom the
correspondingjoint (seethe Methods section).Baaedon
this comparison,the musclemodelwasagainconsidered
appropriatefor the powertransferquantification, despite
Role of biarticuiar muscles
519
P-hip (VV)
P-hip (vq
l”Or/
*7--===l
P-knee (W)
P-knee (W)
25M)w
::iI
P-ankle (W)
P-ankle (W)
1500
2500
1000
1500
500
500
0
-500
-500
-so0
-250
-200
-150
-100
-50
0
time (ms)
-1500
-160
-140
-120
-100
-80
-60
-40
-20
time (ms)
Fig. 7. Mean time histories (n = 7) of the net hip, knee and ankle joint powers
obtainedby inverse
dynamics
(solid line) and the sum of the estimated individual muscle powers corresponding to that particular joint
(dotted line) for jumping and sprinting. With respect to the comparison of both power curves see the
information in Fig. 6.
discrepanciesbeingamplified by the angular velocity of
eachjoint.
lower power values for the plantar flexors when compared to this previousstudy.
Note that in compa~ngthe presentresultsof jumping
Poweroutput of in~ivi~uulmuscles
and sprinting, the total duration of the push-off was
Figure 8 showsthe power curves of contractile and longer for jumping than for sprinting: 310 and 160ms,
serieselasticelementsof monoarticular and biarticular respectively.In addition, somedifferent patterns of the
musclesaswell asthe curvesof the transferredpower by estimatedpower curvesexist, which will be describedin
biarticular muscles.The estimatedpower curvesof the generaltermsonly. First, in sprinting,HA aswell asVA
plantar flexors in one-leggedjumping are quite similarto musclesliberated a considerableamount of positive
previous estimationsof these power curves (Bobbert
power in the first part of the push-off. In jumping, HA
et al., 1986).The fact that the subjectsin the presentstudy alsoliberatedmost of the positive power in the first part
were not consideredefite jumpers, as in the study by of the push-off, while relatively lesspositive power was
Bobbert et al. (1986),was demonstratedby somewhat producedby VA in this phase.Second,in jumping all the
R. Jacobs et al.
800
600
400
200
0
-200
-400
time (ms)
-1
the (ms)
Fig. 8. Mean time histories (n = 7) of the power output of the muscle fibers (solid line) and series elastic
element (dashed line) for the six muscle groups as well as the transferred power for the biarticular HA, RF
and GA muscles (dotted line) for jumping and sprinting.
Role of biarticular muscles
positive power, whereas,in sprinting,
the plantar flexors producednegativepower starting at
touchdownand endingat - 90 ms.During the explosive
part of the push-off phase(the last 90 ms), the total
amount of positive musclepower liberated by GU was
still high in jumping, while in sprintingthe total amount
of positive power liberated by GU decreasedto zero
during the explosivephase.
To makea realisticcomparisonbetweenjumping and
sprinting the work values were calculated for the last
90 ms(respectivelyTables2 and 3).In this period of time,
angular velocities of the hip, knee and ankle joint increasedconsiderablyin sprinting aswell as in jumping
(seeBobbert and Ingen Schenau,1988;Jacobsand Ingen
Schenau,1992a),and during this period all musclescontributed to positivework in the sprint. The differencein
work output of all the six musclesas estimatedby the
modelwas 122J in jumping and 103J in sprinting.
muscles produce
The role of biarticular
521
Table 3. Model calculations of work done about the hip, knee
and ankle joint of contributions of muscle fibres (W,,) and series
elastic tendon (W,,,) and of the contribution of transportation
) by HA, RFandGA for thelast90msof thepush-offin
( wTR,NS
one-legged jumping
Joint
Muscle
Hip
GU
HA
RF
VA
RF
HA
GA
SO
Knee
Ankle
WC,
14
1
7
3
37
6
-1
0
Total
Total
W TRANS
15
3
- 19
13
- 19
19
-3
43
18
-3
- 14
- 14
3
10
11
14
22
28
72
31
0
103
12
GA
WSEE
muscles in power transfer
As stated in the Introduction, the phenomenonof
power transferby biarticular musclesrequiresthat these
musclesdistribute power from onejoint to another. The
total amount of power liberated by all musclesis not
affected, but the distribution is directed where power
could be applied more effectively. It is known for GA,
from a previous study, that this muscleplays a unique
role in power transfer from knee to ankle joint in oneleggedjumping (Bobbert et al., 1986).In the present
study, a similarconclusioncould alsobe drawnfor GA in
sprinting.
One of the questionsto be answeredin the present
study waswhether a net power transferaction occurred
from hip to kneejoint. The absolutework contribution
due to power transfer is shown in Tables 2 and 3 for,
respectively,jumping and sprinting.In Fig. 9, the relative
work contribution due to the transfer action of HA, RF
and GA is shownaswell asthe direction of transfer.This
relative work contribution of biarticular muscleswas
calculated by taking the ratio of work due to power
Jump push-off
c/
Sprint push-off
11 %
31 %
28 %
Table 2. Model calculations of work done about the hip, knee
and ankle joint of contributions of muscle fibres ( Wca) and series
elastic tendon ( Ws,,) and of the contribution of transportation
( wTRANS ) by HA, RF and GA for the last 90 ms of the push-off in
one-legged jumping
Joint
Muscle
Hip
GU
HA
RF
VA
RF
HA
GA
SO
GA
Knee
Ankle
Total
BM 29:4-I
WSEE
WC,
22
3
1
1
44
5
4
2
17
Total
wTRANS
2
23
6
- 15
- 15
15
-2
49
21
-2
- 13
- 13
8
7
8
13
24
29
96
26
0
122
Fig. 9. The relative work contribution of the biarticular muscles
(HA, RF and GA) to the work done about a joint due to its
unique action in transfering power is illustrated as well as the
direction of the transfer action. These values were calculated
over the last 90 ms. The work values for jumping and sprinting
during the last 90 ms are, respectively: for the hip 29 and 28 J, for
the knee 70 and 61 J and for the ankle 53 and 50 J (see Tables
2 and 3). During both tasks, there is a net transfer of power from
the hip to the knee and finally to the ankle joint.
transfer to the total amount of work produced by the
muscles
around that particular joint (seeTables2 and 3).
In both tasks,jumping and sprinting, similar results
werefound for power transfer.For RF a transferaction
occurred from the hip to the knee joint. However, HA
522
R. Jacobs et at
contributed to a transferaction from the kneeto the hip
joint. The amount of work due to transferfrom kneeto
hipjoint by HA wasconsiderablylower than from hip to
kneejoint by RF (Tables2 and 3). For the last 90 msin
jumping and sprinting,it wascalculatedthat the absolute
work for hip extensiondue to transferof HA was,respectively, 2 and 3 J, while the absolutework for kneeextensiondue to transferof RF was,respectively,15and 19J.
Collectively, a net power transfer action occurred from
hip to kneejoint.
Also, the biarticular musclescontributed significantIy
to the work doneat joints. This is shownby the relative
work contribution dueto powertransferasillustratedfor
jumping and sprinting in Fig. 9. For HA, the relative
work contribution to the total amount of work in hip
extension was, respectively, 7 and 11%. For RF, the
relative contribution to the total amount of work in knee
extensionattained valuesof, respectively,21 and 31%.
Power transfer actions by gastrocnemiuscontributed,
respectively,25 and 28% to the total amount of work in
plantar flexion. For gastrocnemiusin jumping similar
relative valueswereobtainedasin the previousstudy on
jumping (Bobbert et al., 1986).
Theseresultssupport the hypothesisthat actions of
biarticular musclescontribute to power transfer actions
from proximal to distaljoints during explosiveleg extensions.The work done by large monoarticular muscles
spanningthe proximal joints is efficiently transferredto
distal joints by the action of biarticular muscles.This
power transferallowshigh power output at distaljoints
despitethe smallerdistal muscles.
The present resultsare complementary to those of
a previousstudy in which we examinedthe role of HA
and RF in a static experiment (Jacobs and Ingen
Schenau,1992b).Subjectswere instructed to generate
constantforceswith their foot in different directionson
the ground.A very high correlation of 0.97wasfound betweenthe differenceof net hip and kneemomentand the
differencein EMG activity of HA and RF. Hence,it was
concludedthat HA and RF distribute the net knee and
hip momentsin order to meetthe specificdemandsof a
statictask.For the dynamicsituationin the presentstudy,
it is further concludedthat the biarticular musclescontribute to a distribution of net power during dynamic tasks.
In their optimal control modelfor jumping, Pandy and
Zajac (1991)replacedthe biarticular GA with a monoartitular plantar flexor. Surprisingly, this adjustmentresulted in a minor differencein performance,with the
conclusionthat the action of GA is not different from
that of any other monoarticularplantar flexor. However,
Leeuwenand Spoor (1992)arguedthat the momentarm
of GA in the kneejoint was unrealisticallysmallin the
Pandy and Zajac model.Usinga more realisticmoment
arm of GA in the kneejoint, Soestet al. (1992)showed
that the biarticularity of GA did affect jumping performance.However, neither Pandy and Zajac (1990)nor
Soestet al. (1992a)includedan anatomicalconstraint(see
e.g.Bobbert and Ingen Schenau,1988)in their optimization routines. Becauseof this, their modelsallow peak
kneeextensionvelocitiesat full extension[seeFig. 6 of
Pandy et al. (1990)and Fig. 4 of Soest et al. (199211
which in a real situation will damagejoint structures.
Since no anatomical constraint has been included in
optimal control models,the questionof to what extent
the biarticularity of musclesinfluencesperformanceis
still an open one.
~cknaw~edgemen~s-We gratefully acknowledge discussions we
have had with Dr Arthur J. van Soestand thank him for
allowing us to use his software of the muscle model. We are also
indebted to Ron Hogeweg (MSc.) and Maurice Aarts (M.&z.) for
their support in the programming and data processing. This
study was supported by the Foundation for Biophysics which is
funded by the Netherlands Organization for Scientific Research
(NWO).
REFERENCES
Bobbert, M. F., Huijing, P. A. and Ingen Schenau, G. J. van
(1986) An estimation of power output and work done by the
human triceps surface mu~l~tendon complexin jumping.J.
3ia~chunics 18, 899406.
Bobber&M. F. andInnenSchenau,
G. J. van119881
Coorciination of vertical jumping. J. Biomechanics 21; 2411-262.
Ebashi. S. M. and Endo. M. 09681 Calcium ion and muscle
con&action. Prog. Biodhys. Mol. &al. 18, 12.5183.
Grieve,D. W., Pheasant,
S.andCavanagh,
P. R. (1978)Predic-
tion of gastrocnemius length from knee and ankle posture. In
Biomechanics VI-A (Edited by Asmussen, E. and Jorgensen,
K.), pp. 405-412. University Park Press, Baltimore.
Hatze, H. (1981) Myocybernetic control models of skeletal
muscle.Universityof SouthAfrica,Muckleneuk, Pretoria.
Hermens, H. J., Boon. K. L. and Zilvold. G. (19861. The clinical
useof surfa&EM& Medica Physiea 9, 1i9-l&.
Hof, A. L. (1990) Effects of muscle elasticity in walking and
Basedon the resultsof the presentstudy, additional
mnning. In multiple Muscle Systems:3iamechun~cs and Moveevidencewasobtainedfor the hypothesisthat biarticular
ment Orga~izatjon (Edited by Winters, J and Woo, S. L.-Y.),
leg musclesplay an effectiverole in power transfer from
pp. 591-607. Springer, Berlin.
proximal joints to distal joints. The question can be Hof, A. L., Geelen, B. A. and Van den Berg, J. W. (1983) Calf
muscle moment, work and efficiency in level walking; role of
askedwhether power transfer by biarticular musclesenseries elasticity. J. Biomechanics 16, 523-537.
hancesthe performanceof a task. To study the influence Hof, A. L., Pronk, C. N. A. and Best, J. A. (1987) Comparison
of biarticular muscleson the performanceof a task, an
between EMG to force processing and kinetic analysis for the
intervention must take place to the human musculo- calf muscle moment in walking and stepping. J. Biomechanics
20, 167-178.
skeletalsystem.Unfortunately, this cannot be done exSchenau, G. J. van, Bobbert, M. F. and Soest, A. J. van
perimentally in humans.What can be done is to make Ingen
(1990) The unique action of bi-articular muscles in leg extena model of the human musculoskeletalsystemand to
sions. In Multiple Muscle Systems: Biomechanics and Moveoptimize it to a certain objective function (seee.g.Pandy
ment Organization (Edited by Winters, J. and Woo, S. L.-Y.),
pp. 591607. Springer, Berlin.
and Zajac, 1991;Soestet al., 1992).
Role of biarticular muscles
Jacobs, R., Bobbert, M. F. and Ingen Schenau, G. J. van (1993)
Function of mono- and biarticular muscles in running. Med.
Sci. Sports Exert. 25, 1163-l 173.
Jacobs, R. and Ingen Schenau, G. J. van (1992a) Intermuscular
coordination in a sprint push-off. J. Biomechanics
25,
953-965.
Jacobs, R. and Ingen Schenau, G. J. van (1992b) Control of an
external force in leg extensions in humans. J. Physiol. 457,
611626.
Leeuwen, J. L. van and Spoor, C. W. (1992) On the role of
bi-articular muscles in human jumping. J. Biomechanics 25,
207-208.
Morgan, D. L., Proske, U. and Warren, D. (1978) Measurements
of muscle stiffness and the mechanism of elastic storage of
energy in hopping kangaroos. J. Physiol. 282, 253-261.
Nilsson, J. E., Andersson, E. and Thorstensson, A. (1992) Activation patterns of individual muscles in the hip flexor synergy
during walking and running. J. Biomechanics 25, 787.
Pandy, M. G. and Zajac, F. E. (1991) Optimal muscular coordination strategies for jumping. J. Biomechanics 24, l-10.
Pandy, M. G., Zajac, F. E., Sim, E. and Levine, W. S. (1990) An
optimal control model for maximum-height human jumping.
J. Biomechonics 23, 1185-l 198.
Ruijven, L. J. van and Weijs, W. A. (1990) A new model for
calculating muscle forces from electromyograms. Eur. J. Appl.
Physiol. 61, 479485.
Soest, A. J. van, Huijing, P. A. and Solomonov, M. (1995) The
523
effect of tendon on muscle force in dynamic and isometric
contractions; a simulation study. J. Biomechanics 28,801-807.
Soest, A. J. van, Schwab, A. L., Bobbert, M. F., and Ingen
Schenau, G. J. van (1992) The influence of the bi-articularity of
the gastrocnemius muscle on vertical jumping performance:
a simulation study. J. Biomechanics 26, l-8.
Visser. J. J.. Hooekamer. J. E.. Bobbert. M. F. and Huiiina, P. A.
(1991) Length-and moment arm of human leg r&&es as
a function of knee and hip angles. Eur. J. Appl. Physiol. 61,
453460.
Winter, D. A. (1983) Moments of force and mechanical power in
jogging. J. Biomechanics 16, 91-97.
Winters, J. M. (1990) Hill-based muscle models: a systemsengineering perspective. In Multiple Muscle Systems: Biomechanics
and Movement
Organization
(Edited by Winters, J. and Woo,
S. L.-Y.), pp. 69-93. Springer, Berlin.
Winters, J. M. and Stark, L. (1988) Estimated mechanical properties of synergistic muscles involved in movements of a variety of human joints. J. Biomechanics 21, 1027-1041.
Yamaguchi, G. T., Sawa, A. G. U., Moran, D. W., Fessler, M. J.
and Winters, J. M. (1990) A survey of human musculotendon
actuator parameters. In Multiple
Muscle
Systems:
Biomechanics and Movement
Organization
(Edited by Winters, J.
and Woo, S. L.-Y.), pp. 717-774. Springer, Berlin.
Zajac, F. E. (1989) Muscle and tendon: properties, models,
scaling, and application to biomechanics and motor control.
CRC Crit. Rev. 17, 359411.