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DORSIFLEXOR AND PLANTARFLEXOR TORQUE-ANGLE AND TORQUE-VELOCITY
RELATIONSHIPS OF CLASSICAL BALLET DANCERS AND VOLLEYBALL PLAYERS
V. B. Frasson
1
, D. E. Rassier
2
, W. Herzog
3
, M. A. Vaz
4
1
Faculty of Physical Therapy, Pontific Catholic University of Rio Grande do Sul, Porto Alegre, RS, Brazil
2
Faculty of Education, Department of Kinesiology and Physical Education, McGill University, Montreal, QUE, Canada
3
Faculty of Kinesiology, University of Calgary, Calgary, AB, Canada
4
School of Physical Education, Federal University of Rio Grande do Sul, Porto Alegre, RS, Brazil
Resumo:
O objetivo desse estudo foi comparar as relações torque-ângulo e torque-velocidade e a ativação dos
músculos flexores plantares e dorsiflexores entre bailarinas clássicas (n=14) e atletas de voleibol
(n=22). O pico de torque dos flexores plantares e dorsiflexores foi avaliado durante contrações
voluntárias máximas isométricas nos ângulos de -10°, 0°, 10°, 20°, 30°, 40° e 50°, e durante contrações
concêntricas nas velocidades angulares de 0°/s, 60°/s, 120°/s, 180°/s, 240°/s, 300°/s, 360°/s e 420°/s.
Sinais eletromiográficos (EMG) de superfície foram obtidos dos músculos gastrocnêmio medial, sóleo e
tibial anterior. A amplitude de movimento de dorsiflexão foi semelhante entre os grupos, enquanto
bailarinas apresentaram maior amplitude de flexão plantar do que atletas de voleibol. Enquanto nos
músculos flexores plantares a relação torque-ângulo das bailarinas deslocou-se para a esquerda
quando comparada à das atletas de voleibol, nos flexores dorsais ela se deslocou para a direita nos
menores comprimentos musculares. Os torques normalizados em todas as velocidades de flexão
plantar e dorsiflexão foram mais elevados nas bailarinas do que nas atletas de voleibol. Os sinais EMG
do gastrocnêmio medial e do sóleo permaneceram aproximadamente constantes entre os diferentes
ângulos articulares nas bailarinas, mas diminuíram com a redução no comprimento muscular no caso
das atletas de voleibol. Os sinais EMG do tibial anterior aumentaram com a redução dos ângulos do
tornozelo em ambos os grupos. Os sinais EMG dos dorsiflexores nas diferentes velocidades angulares
foram semelhantes nos grupos, enquanto os sinais EMG do sóleo e do gastrocnêmio foram mais
elevados nas bailarinas comparados aos das atletas de voleibol. As adaptações dos flexores plantares
podem ser explicadas por alterações musculares intrínsecas e alterações na ativação voluntária
máxima, enquanto para os músculos dorsiflexores somente mudanças nas propriedades intrínsecas
parecem explicar os resultados observados. Os torques relativos mais elevados das bailarinas
comparados aos das atletas de voleibol são provavelmente resultantes da ativação aumentada dos
flexores plantares e de um maior comprimento de fibra dos dorsiflexores.
Palavras-chave: propriedades mecânicas musculares, eletromiografia, ballet clássico, voleibol.
Abstract:
The purpose of this study was to compare the torque-angle and torque-velocity relationships, and
the electromyographic (EMG) activity of the plantar- and dorsiflexor muscle groups of classical ballet
dancers (n=14) and volleyball players (n=22). Peak torques of the ankle plantar- and dorsiflexor
muscles were evaluated for maximal voluntary isometric contractions performed at seven different ankle
angles (-10°, 0°, 10°, 20°, 30°, 40°, 50°) and for maximal effort, concentric, voluntary contractions
performed at angular velocities of 0°/s, 60°/s, 120°/s, 180°/s, 240°/s, 300°/s, 360°/s and 420°/s. Bipolar
surface EMG signals were obtained from gastrocnemius medialis, soleus and tibialis anterior muscles,
and ankle range of motion was measured with a goniometer. The range of motion for dorsiflexion was
the same for both groups, while ballet dancers had a greater range for plantarflexion than volleyball
players. For the plantarflexor muscles, the torque-angle relationship was shifted to the left for the ballet
dancers compared to the volleyball players, while for the dorsiflexor muscles it was shifted to the right
for short dorsiflexor lengths. The normalized torques at all speeds of plantar- and dorsiflexion were
greater for the ballet dancers than the volleyball players. The gastrocnemius medialis and soleus EMGs
remained nearly constant across all angles for the ballet dancers, but decreased with decreasing
muscle length in the volleyball players. The tibialis anterior EMGs increased with decreasing ankle
angles in both groups. The normalized dorsiflexor EMGs were the same for both groups across all
speeds, while the EMGs for soleus and gastrocnemius were significantly greater for the ballet dancers
than the volleyball players. These results support the idea that systematic physical activity changes the
in vivo torque-angle and torque-velocity relationships in accordance with functional demands. The
greater relative torques for the ballet dancers than volleyball players are likely caused by the increased
activation of the plantarflexors and an increased fiber length for the dorsiflexors.
Keywords: muscle mechanical properties, electromyography, classical ballet, volleyball.
Adaptation of Skeletal Muscle Mechanical Properties
Brazilian Journal of Biomechanics, Year 8, n.14, May 2007
32
INTRODUCTION
It is widely known that skeletal muscles adapt to
their mechanical environment. Increased muscle use
is shown to cause muscle hypertrophy, whereas
reduced muscle use leads to muscle loss or atrophy.
However, the chronic changes in the mechanical
properties of muscles as a result of chronic training
are not completely understood.
It has been suggested that torque-angle
relationships may differ substantially in subjects who
use muscle groups differently according to specific
chronic training [e.g. Kitai and Sale 1989; Herzog et al.
1991]. Assuming that the moment arm geometry does
not change with chronic training, and there is no
systematic difference across groups of athletes,
differences in the torque-angle relationships must be
associated with changes in the intrinsic force-length
relationships of the synergistic muscles, and/or
changes in maximal voluntary activation as a function
of joint angle.
The torque-velocity relationship is also affected
by training [Moffroid and Whipple, 1970; Lesmes et al.,
1978]. For example, sprinters and athletes in high
power events show higher torques at increasing
speeds of contraction compared to long distance
runners or endurance athletes [Johansson et al., 1987;
Taylor et al., 1991].
The purpose of this study was to compare the
plantarflexor and dorsiflexor torque-angle and torque-
velocity relationships for two special populations:
classical ballet dancers and volleyball players.
Classical ballet dancers use the plantarflexors mostly
in a shortened and the dorsiflexors in a lengthened
position when maintaining whole body weight on the tip
of their toes, while volleyball players use the same
muscles mostly in a dorsiflexed position. In addition,
ballet dancers show increased ankle plantarflexor
flexibility compared to normal subjects [Hamilton et al.
1992; Wiesler et al. 1996], while the active range of
ankle motion of volleyball players is similar to that of
the normal population [Richards et al., 2002]. These
different functional demands change the mechanical
environment of muscle groups, and may change the
mechanical properties of these muscles within each
training or athlete group.
METHODS
Thirty-six female subjects (ballet dancers = 14;
volleyball players = 22) gave written informed consent
to participate in this study. The Ethics Committee of
the University approved all experimental procedures.
Classical ballet dancers had at least eight years of
training (with a minimum of two daily hours of practice,
five times a week), and volleyball players had an
average of five years of experience (with a minimum of
four daily hours of practice, three times a week).
Range of Motion
The active range of plantar- and dorsiflexor
motion was evaluated with a goniometer. The 0°
reference angle was defined with the foot
perpendicular to the shank axis. Plantarflexion was
defined positive.
Torque
Peak torque of the plantar- and dorsiflexor
muscles was evaluated for maximal voluntary
isometric contractions obtained at seven different
ankle angles (-10°, 0°, 10°, 20°, 30°, 40°, 50°) and for
maximal voluntary isokinetic contractions at eight
nominal angular velocities (0°/s, 60°/s, 120°/s, 180°/s,
240°/s, 300°/s, 360°/s, 420°/s) using a Cybex Norm
(Lumex & Co., Ronkonkoma, New York, USA)
isokinetic dynamometer. All subjects performed a
series of submaximal contractions at different ankle
angles and angular velocities for warming up and
familiarization with the dynamometer prior to the tests.
Subjects were placed in a prone position on the
dynamometer chair. The right foot was fixed onto a
footplate by Velcro straps. The ankle joint axis, defined
by a line connecting the lateral and medial malleolus,
was aligned with the machine’s axis of rotation.
Subjects performed a maximal voluntary isometric
contraction with the ankle joint positioned at seven
different angles: -10°, 0°, 10°, 20°, 30°, 40°, and 50°.
Three maximal voluntary contractions were performed
at each of the eight test velocities. Subjects were
instructed to reach their maximal force in
approximately one second, and to hold the maximal
effort for at least one more second before relaxing. If
subjects felt that the contraction was not maximal, or if
the contraction was not maintained for at least one
second, the test was repeated. The order of the joint
angles and of the angular velocities was randomly
assigned for each subject, and two-minute intervals
were observed between contractions to avoid fatigue.
At the end of the entire protocol, the first trial was
repeated to assess the possible effects of fatigue.
Electromyographic Signals
Bipolar surface electromyographic (EMG)
signals (AMT-8, Bortec Biomedical, Canada) were
obtained from the gastrocnemius medialis, soleus and
tibialis anterior muscles. The skin underneath the
recording electrodes was prepared using standard
procedures [e.g. Basmajian and De Luca, 1985].
Electrodes were placed on the distal third of the
muscles, along the approximate direction of the
muscle fibers. A ground electrode was placed on the
skin over the tibia. EMG signals were recorded at a
frequency of 2000 Hz using Windaq data collection
(16-bit resolution, +10 Volts) and playback software
(Dataq Instruments, Akron, OH, USA), and stored on a
Pentium (200MHz) personal computer.
V. B. Frasson, D. E. Rassier, W . Herzog, M. A. Vaz
Revista Brasileira de Biomecânica, Ano 8, n.14, Maio 2007
33
Data Analysis
EMG data were extracted for segments of one
second from the plateau (middle) region of the
isometric torque signals for each of the seven joint
angles. From the three maximal isokinetic voluntary
contractions, the contraction with the highest torque
was selected for data analysis. EMG data were
extracted for the entire concentric contractions. EMG
signals were band-pass filtered using cut-off
frequencies of 3Hz and 800 Hz, and root mean square
(RMS) values were calculated.
Means and standard errors of the torques and
of the RMS values at each joint angle and speed were
calculated for the ballet dancers and volleyball players.
After determining the joint angle at which peak
torque was achieved for each group, torque and RMS
values were normalized for each subject relative to the
torque and RMS values obtained at that angle. For the
dorsiflexor torque-angle relationship, which showed an
ascending and descending part, the ankle angle of
maximal torque was determined by fitting Gaussian
curves to the torque values above 75% of maximum
and differentiating the torque-angle curve with respect
to the angle and identifying the unique angle of zero
slope [Jones et al. 1997; Talbot and Morgan 1988;
Whitehead et al. 2003].
Torques and RMS values were also normalized
with respect to the maximal isometric contraction for
the concentric contractions.
In order to compare the torque and RMS values
of the plantar- and dorsiflexors between the two
groups across all ankle angles and all angular
velocities, a two-way (group, angle/velocity) analysis of
variance for repeated measures (angle/velocity) was
performed. W hen a significant interaction was
observed, post-hoc analyses were performed with
Newman-Keul's test. One-way analysis of variance for
repeated measures was used to determine statistical
differences between the first and last trials to test for
fatigue effects. One-way analysis of variance was
used to determine differences in the joint range of
motion between the two groups. A 0.05 level of
significance was adopted for all tests.
RESULTS
Ballet dancers showed a greater plantarflexor
range of motion than the volleyball players (p<0.001,
Figure 1). The dorsiflexor range was similar for both
groups. The total range of motion for the ballet
dancers was greater than that for the volleyball players
(p<0.001).
-20
0
20
40
60
80
100
PF DF
Ankle Angle (degrees)
Ballet
Volleyball
*
Figure 1. Plantarflexor and dorsiflexor ankle joint range of motion of
classical ballet dancers and volleyball players (PF =
plantarflexion; DF = dorsiflexion; ٭=p<0.05). Mean values
and standard errors correspond to both right and left
ankle joint range of motion for each group.
Torque and Angle Relationship
The plantarflexor torque-angle relationship was
different between the two groups (p<0.001; Figure 2A).
Maximal torque increased continuously with
decreasing plantarflexion (or increasing muscle length)
for the volleyball players, while ballet dancers reached
a plateau between 0° to -10°. Ballet dancers had
consistently higher relative torque values compared to
the volleyball players for all ankle angles studied,
except of course, at an ankle angle of -10° which was
defined as 1.0 for both groups.
The torque-angle curve for the dorsiflexor
muscles had a similar shape for the two groups of
athletes. However, volleyball players were able to
produce relatively higher torques at short dorsiflexor
muscle lengths (i.e. ankle angles between -10° and
10°) compared to ballet dancers (p<0.05; Figure 2B).
There was no shift of peak torque occurrence in the
dorsiflexor torque-angle relationships between the two
groups.
Torque-Velocity Relationship
The normalized torque for plantarflexors and
dorsiflexors as a function of ankle angular velocity is
shown in Figure 3. Plantarflexor torque was the same
for the two groups at all angular velocities (Figure 3A).
Dorsiflexor torque was greater in ballet dancers than in
volleyball players at angular velocities of 120°/s and
greater (Figure 3B).
Adaptation of Skeletal Muscle Mechanical Properties
Brazilian Journal of Biomechanics, Year 8, n.14, May 2007
34
0
0,2
0,4
0,6
0,8
1
1,2
-1001020304050
Ankle Angle (degrees)
Torque (Nm/Nmmax)
Ballet
Volleyball
A
0
0,2
0,4
0,6
0,8
1
1,2
-10 0 10 20 30 40 50
Ankle Angle (degrees)
Torque (Nm/Nmmax)
Ballet
Volleyball
B
Figure 2. Plantarflexor (A) and dorsiflexor (B) torque-angle
relationship of classical ballet dancers and volleyball
players. Torque values were normalized relative to the
peak torque value of each group (mean ± S.E.).
Muscle Activation
EMG activity of the gastrocnemius medialis
decreased with decreasing plantarflexor angles in the
ballet dancers, and it increased in the volleyball
players (Figure 4A). The normalized RMS values of
soleus remained about constant across ankle angles
for ballet dancers, and increased with decreasing
plantarflexor ankle angles (decreasing muscle length)
for the volleyball players (Figure 4B).
There was an increase in the normalized RMS
values of the tibialis anterior muscle with decreasing
muscle length for both groups (Figure 5).
Root mean square values of the gastrocnemius
and soleus EMGs for the ballet dancers were greater
than for the volleyball players (Figures 6A and 6B,
respectively), while the values for tibialis anterior were
the same (Figure 7).
The initial and final torque and EMG values (of
plantar- and dorsiflexors) were similar for all subjects
of both groups, indicating that fatigue did not affect the
results.
0
0,2
0,4
0,6
0,8
1
1,2
0 60 120 180 240 300 360 420
Velocity (degrees/s)
Torque (Nm/Nm
max
)
Ballet
Volleyball
A
0
0,2
0,4
0,6
0,8
1
1,2
0 60 120 180 240 300 360 420
Velocity (degrees/s)
Torque (Nm/Nm
max
)
Ballet
Volleyball
B
Figure 3. Plantarflexor (A) and dorsiflexor (B) torque-velocity
relationships of classical ballet dancers and volleyball
players. Torque values (mean ± S.E.) were normalized
relative to the peak torque value of each group.
DISCUSSION
Torque-Angle Relationship
A primary purpose of this study was to compare
the torque-angle relationship of two distinct groups of
athletes (classical ballet dancers and volleyball
players) with different demands for the ankle joint
muscles. Female ballet dancers often work with the
ankle in a hyper-extended position, while volleyball
players use the ankle joint for jumping within a
“normal” range of motion. The results obtained in this
study support the hypothesis that chronic training
changes the torque-angle relationship.
V. B. Frasson, D. E. Rassier, W . Herzog, M. A. Vaz
Revista Brasileira de Biomecânica, Ano 8, n.14, Maio 2007
35
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
-1001020304050
Ankle Angle (degrees)
EMG RMS (mV/mVmax)
Ballet
Volleyball
A
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
-1001020304050
Ankle Angle (degrees)
EMG RMS (mV/mVmax)
Ballet
Volleyball
B
Figure 4. RMS values (mean ± S.E.) of the EMG signal of
gastrocnemius medialis (A) and soleus (B) muscles at
the seven different ankle joint angles. RMS values were
normalized relative to the RMS value obtained at the
contraction of highest torque for each subject
.
Plantarflexion
The ballet dancers had a greater plantarflexor
range of motion than the volleyball players. The
dancers were also stronger at short plantarflexor
lengths, and had greater levels of activation at short
plantarflexor lengths. The ballet dancers reached the
plateau of the torque-angle relationship at the longest
muscle lengths tested. These results might be
explained in different ways, but it is tempting to
speculate that ballet dancers may have a smaller
number of sarcomeres arranged in series in their
plantarflexor fibers. If this was indeed the case, each
individual sarcomere would be longer for a given
muscle length.
The results obtained in this study are
conceptually the same as those obtained by Herzog et
al. [1991] for the force-length relationship of the rectus
femoris in high performance runners and cyclists.
Because of the flexed hip angle in cycling, cyclists use
the rectus femoris at a chronically shortened length
compared to the runners. In accordance with this
specific chronic use, cyclists’ rectus femoris was
strong at short and weak at long muscle lengths while
the reverse result was found for runners.
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
-10 0 10 20 30 40 50
Ankle Angle (degrees)
EMG RMS (mV/mVmax)
Ballet
Volleyball
Figure 5. RMS values (mean ± S.E.) of the EMG signal of tibialis
anterior muscle at the seven different ankle joint angles.
RMS values were normalized relative to the RMS value
obtained at the contraction of highest torque for each
subject.
Dorsiflexion
The dorsiflexor range of motion and muscle
activation values were similar between ballet dancers
and volleyball players. However, compared to the
ballet dancers, the volleyball players were relatively
stronger at short dorsiflexor lengths (i.e. from -10° to
10°).
This increased torque production for the
volleyball players cannot be explained by an increase
in muscle activation, as the tibialis anterior EMG was
similar between the two groups, suggesting that the
increased torque in the volleyball players at short
dorsiflexor lengths is associated with changes in
muscle properties. One possible explanation is that
although there is no shift in the ankle angle at which
peak torque occurs, there is a significant shift of the
torque-angle relationship at short muscle lengths (i.e.,
a shift of the ballet dancers’ torque-angle relationship
to the right).
Torque-Velocity Relationship
The relative torques of ballet dancers were
greater than the torques of volleyball players at speeds
of dorsiflexion of 120°/s and above, while EMGs in
dorsiflexion were similar for the two groups of athletes.
The torque-velocity relationships for plantarflexion
were similar, although there was an increase in the
relative EMG of the plantarflexors of the ballet dancers
at all speeds.
Plantarflexion: The similarity in the normalized
plantarflexion torque values between the two groups
was expected. This result is intuitively appealing as the
range of motion in dorsiflexion, which determines the
amount of stretch of the plantarflexor group, is similar
Adaptation of Skeletal Muscle Mechanical Properties
Brazilian Journal of Biomechanics, Year 8, n.14, May 2007
36
between the two groups, and therefore differences in
fiber length should not be expected.
0
0,5
1
1,5
2
2,5
3
0 60 120 180 240 300 360 420
Velocity (degrees/s)
EMG RMS (mV/mV
isom
)
Ballet
Volleyball
A
0
0,5
1
1,5
2
2,5
3
0 60 120 180 240 300 360 420
Velocity (degrees/s)
EMG RMS (mV/mV
isom
)
Ballet
Volleyball
B
Figure 6. RMS values (mean ± SE) of the gastrocnemius medialis
(A) and soleus (B) muscles at different angular velocities.
RMS values were normalized relative to the RMS value
obtained at the contraction of highest torque for each
subject.
0
0,5
1
1,5
2
0 60 120 180 240 300 360 420
Velocity (degrees/s)
EMG RMS (mV/mV
isom
)
Ballet
Volleyball
Figure 7. RMS values (mean ± SE) of the tibialis anterior muscle at
different angular velocities. RMS values were normalized
relative to the RMS value obtained at the contraction of
highest torque for each subject.
Why are ballet dancers able to activate their
plantarflexors more effectively during shortening
contractions than volleyball players? This study cannot
provide a conclusive answer to this question, but ballet
dancing, in contrast to volleyball playing, requires
sustained and precisely controlled contractions of the
plantarflexor group, and thus, activation might be
much better trained in these athletes than the
volleyball players.
Dorsiflexion: The increase in relative torques
for the ballet dancers at all speeds of dorsiflexion
cannot be explained by changes in muscle activation,
as EMGs were the same between the two groups of
athletes. Therefore, it appears that the differences in
dorsiflexion torques are associated with intrinsic
differences in the dorsiflexor muscles. Greater torques
at the same angular speed of movement could be
associated with a greater proportion of fast twitch
fibers or an increase in fiber lengths in the ballet
dancers compared to the volleyball players The ballet
dancers have a greater range of plantarflexion (by
24°), and since excursion is known to be a potent
stimulator for sarcomere addition [Koh & Herzog,
1998], fiber length may be longer in the ballet dancers,
which could explain the observed results.
CONCLUSION
The results of this study suggest that human
muscles adapt to functional demands associated with
chronic training in athletes. Therefore, chronic training
may not only increase the size, strength, and oxidative
capacity of muscles as demonstrated in previous
studies [Jones & Carter, 2000; Ahtiainen et al., 2003;
Izquierdo et al., 2005], but might also affect the force-
velocity and force-length relationships, which are
typically assumed to be invariant.
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ACKNOWLEDGEMENTS
The authors would like to thank CAPES-Brazil,
CNPq-Brazil and UFRGS-Brazil for financial support.
The authors declare that the experiments conducted in
the present study comply with the current laws of
Brazil. This study was also partially supported by the
Canada Research Chairs’ Programme (WH).
Corresponding Author:
Marco Aurélio Vaz
School of Physical Education
Federal University of Rio Grande do Sul
Rua Felizardo, 750
Porto Alegre, RS, Brazil, 90690-200
Tel.: 55-51-3308-5860
Fax.: 55-51-3308-5858
E-mail: marcovaz@esef.ufrgs.br
