Journal of Applied Biomechanics, 2006; 22:255-263. © 2006 Human Kinetics, Inc.
Optimal Pennation Angle of the Primary Ankle Plantar
and Dorsiflexors: Variations With Sex, Contraction
Intensity, and Limb
Kurt Manal, Dustyn P. Roberts, and Thomas S. Buchanan
University of Delaware Center for Biomedical Engineering Research
Ultrasonography was used to measure the pennation angle of the human tibialis anterior (TA),
lateral gastrocnemius (LG), medial gastrocnemius (MG), and soleus (Sol). The right and left
legs of 8 male and 8 female subjects were tested
at rest and during maximum voluntary contraction (MVC). Joint angles were chosen to control
muscle tendon lengths so that the muscles were
near their optimal length within the length–
tension relationship. No differences in pennation
angle were detected between the right and left
legs. Another consistent finding was that the pennation angle at MVC was significantly greater
than at rest for all muscles tested. Optimal pennation angles for the TA, MG, and Sol were significantly greater for the men than for the women.
Optimal pennation angles for the TA, LG, MG,
and Sol for the male subjects were 14.3°, 23.7°,
34.6°, and 40.1° respectively, whereas values
of 12.1°, 16.3°, 27.3°, and 26.3° were recorded
for the female subjects. The results of this study
suggest the following: (1) similar values for
pennation angle can be used for the right and
left TA, LG, MG, and Sol; (2) pennation angle
is significantly greater at MVC than at rest for
all muscles tested; and (3) sex-specific values for
optimal pennation angle should be used when
modeling the force-generating potential of the
primary muscles responsible for ankle plantar
and dorsiflexion.
The authors are with the Center for Biomedical Engineering
Research, Department of Mechanical Engineering, University
of Delaware, Newark, DE 19716.
Key Words: ultrasound, in vivo, isometric contraction, modeling, gender
The medial gastrocnemius (MG), lateral gastrocnemius (LG), and the soleus (Sol) combine to
form the triceps surae muscle group. This group
converges into the Achilles tendon and comprises
the dominant plantar flexors of the ankle, generating the largest of the lower limb sagittal plane joint
moments during walking (Eng & Winter, 1995).
How the MG, LG, and Sol contribute to this large
plantar flexion moment and knowledge about the
relative timing of these forces can enhance our
understanding of normal and pathological gait.
Direct measures of muscle force are not yet practical
and therefore indirect methods are used to estimate
muscle forces in vivo. Buchanan and colleagues
described one such method; an EMG-driven Hill
model, which has been used to estimate joint
moments and individual muscle forces (Buchanan
et al., 2004, 2005).
The maximum isometric force a muscle generates occurs when the fibers are at an optimal length
and the muscle is fully activated. The corresponding pennation angle is the optimal pennation angle,
and it is an important consideration when using
musculoskeletal models to estimate muscle force
(Zajac, 1989). Real-time Ultrasonography can be
used to image architectural features of muscle in
vivo (Fukashiro et al., 2006), and therefore it is possible to use ultrasound to measure subject-specific
estimates of optimal pennation angle.
255
256
Manal, Roberts, and Buchanan
When it is not possible to measure subject-specific pennation angles, estimates can be obtained
from the literature. One source commonly used
by those constructing musculoskeletal models is a
summary of cadaver-based measures tabulated by
Yamaguchi and colleagues (Yamaguchi et al., 1990).
For example, Bogey et al. (2005) used pennation
angles for the triceps surae originally reported by
Wickiewicz and colleagues (1983). Pennation angle
for the LG measured from three cadavers ranged
between 5° and 10°, whereas in vivo ultrasound
recordings from six male subjects during maximum voluntary contraction (MVC) averaged 31°
± 6° (Kawakami et al., 1998). Pennation angles in
both studies were measured with the limbs in the
same configuration (i.e., knee extended and ankle in
plantar flexion), and therefore this large difference
(>20°) resulted because cadaveric material does not
contract. Muscle contraction causes fiber shortening,
leading to an increase in fiber pennation angle. Since
optimal pennation angle is the pennation angle at
maximum isometric force, literature values recorded
from cadaveric specimens tend to underestimate this
value and contribute to erroneous muscle force estimates. Narici and colleagues discuss this limitation
and others when using cadaveric data to characterize
in vivo muscle function (Narici et al., 1996).
In vivo ultrasound measures have shown that
pennation angle for the triceps surae varies with joint
angle (i.e., fiber length) and contraction intensity
(Maganaris, 2003; Maganaris et al., 1998; Narici
et al., 1996). Perhaps the most dramatic example
of this was a 45° increase for the MG, increasing
from 22° at rest with the knee extended and ankle
in dorsiflexion to 67° at MVC with the knee flexed
and the ankle in plantar flexion (Kawakami et al.,
1998). This large increase was not an isolated case,
but rather the average of six male subjects. The
relationship between fiber length and contraction
intensity for the triceps surae has not been reported
for women.
Other factors that should be considered when
obtaining pennation angle values from the literature
include sex, age, and perhaps even side-to-side differences, which may be related to limb dominance.
For example, ultrasound recordings of pennation
angles for the MG, LG, and Sol measured at rest
were significantly greater for men compared with
women (Chow et al., 2000). Similar sex differences
for the MG at rest have been reported by others
(Abe et al., 1998; Kanehisa et al., 2003; Kubo et
al., 2003b). It is unclear from these studies whether
differences in optimal pennation angle exist between
men and women because these data were recorded
while the subjects were at rest. Interestingly, Kubo
and colleagues found differences only between
young men and women, but not for older men. Previous research suggests that muscle fiber pennation
angle increases through adolescence (Binzoni et al.,
2001), reaches a plateau that extends until later in
life, and then decreases with further aging (Kubo et
al., 2003a). Thus, age is a potentially confounding
factor when making fiber pennation angle comparisons or when selecting a value from the literature.
The tibialis anterior (TA) acts as an antagonist
to the MG, LG, and Sol, and therefore accurate estimates of pennation angle for the TA are of interest
when modeling the ankle joint. Pennation angles for
the TA range between 10° and 20° depending on the
ankle angle and contraction intensity (Hodges et al.,
2003; Ito et al., 1998; Maganaris & Baltzopoulos,
1999). Note that data for male and female subjects
were averaged in the Hodges study and the Ito study,
whereas Maganaris and Baltzopoulos tested only
male subjects. No study has reported gender-specific
optimal pennation angle for the TA.
There is a void in the literature reporting femalespecific estimates of optimal pennation angle for
the primary ankle plantar and dorsiflexors (TA,
MG, LG, and Sol). This information is important
when investigating sex difference in muscle function (e.g., strength, excursion, contraction velocity)
and modeling the force-generating potential of these
muscles. Thus, the primary goal of our study was
to record optimal pennation angle for these muscles
and to investigate whether significant differences
exist between men and women. Of secondary interest was to document fiber pennation angle changes
from rest to MVC, and to assess whether pennation
angles differ from side-to-side.
Methods
Eight male and eight female subjects between the
ages of 20 and 50 with no history of musculoskeletal
injury were recruited from the general University
of Delaware population. This age range was chosen
to minimize the potentially confounding effect of
age. The mean (range) weight, height, and age of
the subjects was 181 (155–220) lb, 70 (67–75) in.,
Optimal Pennation Angle
and 24 years (20–30) for the men and 146 (130–
180), 65 (63–69), and 24 (21–34) for the women,
respectively. All subjects provided written informed
consent prior to participation, and the study was
approved by the Human Subjects Review Board of
the University of Delaware.
Maximum isometric force varies with joint
angle. In this study, muscles were tested at joint
angles that corresponded to their optimal fiber
length, i.e., the length at which the muscle generates
the greatest force. This was approximated using a
lower extremity biomechanical model of the leg
(Delp et al., 1990). With the knee fully extended,
the model estimated that the TA produces the most
force near the limit of plantar flexion (about 30°) and
the triceps surae (MG, LG, and Sol) force peaks all
occur around the natural limit of dorsiflexion (20°).
Maximum isometric force for these muscles is plotted as a function of ankle angle (Figure 1).
Subjects were seated in the chair of a Biodex
System 3 dynamometer (Biodex, Shirley, NY). The
knee was fully extended and the foot placed in the
heel cup of the ankle attachment and positioned
perpendicular to the shank. This ankle angle was
defined as 0°. The axis of rotation of the dynamometer was aligned to coincide with an approximate
sagittal plane ankle axis passing through the lateral
malleolus. The thigh was strapped to the chair to
minimize translations of the leg during contractions,
257
and the chair back was angled slightly to decrease
strain on the biarticular muscles that cross the hip
and knee. The subjects wore sneakers and the shoe
was strapped tightly to the footplate to maintain a
given joint angle during contraction. Data for the
TA trial were collected at 30° of plantar flexion,
and the MG, LG, and Sol trials were done at 20° of
dorsiflexion. The analogue moment output from the
Biodex was sampled at 1 kHz.
Ultrasound images were obtained with a variable frequency 60-mm linear transducer (Aloka5000, Tokyo, Japan). For the TA, LG, and MG, the
transducer was placed over the muscle belly and
adjusted until aligned in the plane of the muscle
fibers. It has been shown that there is no significant
change in muscle architecture over the length of
these muscles (Maganaris & Baltzopoulos, 1999;
Maganaris et al., 1998). The Sol was imaged deep
to both the MG and LG. Most images were taken at
10 MHz B-mode, with an occasional adjustment to
7.5 MHz for subjects with thicker calf muscles. The
depth, B-mode gain (brightness), and orientation of
the probe was set on each scan to obtain an optimal
image. All images were stored in DICOM format
on magneto-optical disks for later analysis.
Resting values for the TA pennation angle
were taken with the ankle in 30° of plantar flexion.
Two maximum voluntary contractions (MVCs)
were then collected while simultaneously recording
Figure 1 — Estimated maximum isometric force
of the primary ankle plantar and dorsiflexors as a
function of ankle angle. MG = medial gastrocnemius, LG = lateral gastrocnemius, Sol = soleus, TA
= tibialis anterior. Note that the MG, LG, and Sol
muscles all generate maximum force at approximately 20° of dorsiflexion and the TA generates
maximum force at approximately 30° of plantar
flexion.
258
Manal, Roberts, and Buchanan
ultrasound data. A period of 5 s was allowed for each
contraction, and the ultrasound image was frozen
during the plateau region of the contraction when
the joint moment displayed on the Biodex monitor
had stabilized. A similar process was conducted for
the triceps surae. Key differences were as follows:
(1) the ankle was set at 20° of dorsiflexion and (2) a
complete sequence of resting and MVC trials were
collected for the LG, and then repeated for the MG.
The Sol was imaged deep to both the LG and MG
during all contractions. Pennation angles for the TA,
MG, and LG represent the average of two trials for
each muscle, whereas the pennation angle for the
Sol was the average of four trials (i.e., two trials
deep to the MG and two deep to the LG).
Pennation angles for all muscles were measured
off-line using the angle measurement function on
the Aloka unit. The pennation angle for the TA was
measured as the angle of insertion of the superficial fibers to the central aponeurosis of the muscle.
Pennation angles for the MG, LG, and Sol were
measured as the angle the fascicles inserted into the
deep aponeurosis between the gastrocnemius and
soleus muscles (see Figure 2).
A three-factor ANOVA with two repeated measures (contraction intensity and limb) was used to
test for differences in pennation angle with a level
of significance set at 0.05. Separate ANOVAs were
conducted for each muscle. In addition, a preliminary analysis using different data than reported
herein was conducted to assess the reliability of our
ultrasound measurements. This process is described
in the following section.
Results
Reproducibility of the ultrasound measurements was
assessed for the right LG of one healthy male subject
with the knee fully extended and the ankle in 20°
of dorsiflexion. The thickest superior/inferior and
medial/lateral portion of the calf in a relaxed state
was marked and a total of twenty images were taken
from the marked site. After each individual scan,
the image was stored and the ultrasound transducer
removed and repositioned for the next scan, with
an elapsed time of approximately 1 min between
successive scans. Images were then retrieved and
measured with the angle measurement function
of the ultrasound unit while the investigator was
blinded to the measured angle. The coefficient of
variation (COV) was used to assess the repeatability,
where COV equals the standard deviation divided
Figure 2 — Ultrasound image of the MG (α) and Sol (β). The aponeurosis deep to the MG is clearly visible separating the MG
and the Sol.
Optimal Pennation Angle
by the mean (Rutherford & Jones, 1992). In this
case, the average pennation angle was 13.3° with a
standard deviation of 1.1, yielding a COV of 8.5%
for repeat scanning.
The reproducibility of the angle measurement
was tested on one image of the previous set. Ten
measurements of pennation angle were carried out
on the same image. The average pennation angle
was 12.9° with a standard deviation of 0.5, yielding a COV of 4.2% for repeat measurements. These
variations compare favorably with values reported
in the literature (Fukunaga et al., 1997; Maganaris
et al., 1998).
Sex, contraction intensity, and limb-specific pennation angle measurements are reported in Table 1.
Two findings are evident when inspecting this table.
259
First, pennation angles for the right and left legs were
similar at a given contraction intensity within sex
for each muscle. The main effect of limb (right vs.
left) was not statistically significant for any of the
muscles tested. This finding is depicted in Figure 3.
Another consistent finding was that pennation angle
increased between rest and MVC (p < 0.001 for all
muscles), with men exhibiting a greater increase
compared with women. This relationship is illustrated in Figure 4. With regards to the comparison of
primary interest, the male subjects had significantly
larger optimal pennation angles for the TA, MG, and
Sol muscles compared with the females (Figure 5).
Optimal pennation angle for the LG was 7° larger
for the male subjects; however, the difference was
not statistically significant (p = 0.093).
Table 1 Pennation Angle Measured at Rest and Maximum Voluntary Contraction for the Right (R)
and Left (L) Legs of the Male And Female Subjects. Pennation Angle Is Reported as Degrees With
Standard Deviations in Parentheses.
Lateral Gastrocnemius
(LG)
Tibialis Anterior (TA)
Male
Rest
MVC
Female
Male
Medial Gastrocnemius
(MG)
Female
Male
Soleus (Sol)
Female
Male
Female
R
L
R
L
R
L
R
L
R
L
R
L
R
L
R
L
9.4
9.3
8.7
9.1
13.7
12.8
12.3
11.1
18.7
18.6
15.7
16.2
20.6
19.3
14.3
16.4
(2.2)
(1.4)
(1.0)
(1.0)
(4.2)
(2.4)
(3.3)
(3.4)
(2.7)
(3.3)
(2.3)
(1.6)
(7.4)
(4.6)
(4.3)
(3.8)
14.7
14.0
12.1
12.1
23.4
24.0
15.2
17.4
34.9
34.3
27.5
27.1
40.4
39.9
25.3
27.3
(2.3)
(2.2)
(1.4)
(1.5)
(8.9)
(10.6)
(3.8)
(5.5)
(6.4)
(7.3)
(5.5)
(7.4)
(7.6)
(7.8)
(8.4)
(7.5)
Figure 3 — The main effect
of limb (right vs. left) was
not statistically different for
any of the muscles tested.
The bars atop each column
represent the standard error
of the mean.
Figure 4 — Relationship between contraction intensity (rest vs. maximum voluntary contraction [MVC]) and sex. Note that the
pennation angle at MVC was greater than at rest for both men and women and that the increase was greater for the male subjects.
The bars represent the standard error of the mean at each contraction intensity.
Figure 5 — Optimal pennation angle was significantly
greater for the male subjects
(p < 0.05) for the muscles
denoted by an asterisk. The
bars atop each column represent the standard error of
the mean.
260
Optimal Pennation Angle
Discussion
The results of our study reveal several important
findings that should be considered when choosing
pennation angle values from the literature. For
example, we found that the pennation angles for
the primary plantar and dorsiflexors for the right
and left ankles were similar for a given muscle. The
motivation for this comparison stemmed from findings that subjects with hypertrophied arm muscles
had larger pennation angles than control subjects
(Kawakami et al., 1993). This led to the question
whether side-to-side differences in muscle architecture might be related to limb dominance. In a
study by Tate et al. (2006), vastus medialis muscle
volume was observed to be larger in the dominant
legs of young athletes whereas vastus lateralis was
observed to be larger in the nondominant legs.
Kearns and colleagues examined side-to-side differences in soccer players and found that muscle
thickness and fascicle length for the MG between
the dominant and nondominant limbs was greater
for soccer players than for controls (Kearns et al.,
2001). However, fiber pennation angle was not
statistically different. In another study, increases
in quadriceps strength and cross-sectional area
were reported following a 3-month training period;
however, fiber pennation angle for the vastus lateralis and intermedius did not change (Rutherford
& Jones, 1992). Taken together, and in light of our
findings, it appears that the same pennation angle
can be used for the right and left legs for the TA,
LG, MG, and Sol muscles.
Another finding that was consistent for all
muscles was that pennation angle at MVC was
significantly greater than the angle measured at rest
(p < 0.001 for all muscles). Not only were the differences significant, the magnitude of the increase
for the triceps surae muscles was noteworthy, with
increases of approximately 10°, 16°, and 21° for the
LG, MG, and Sol measured for the male subjects.
Similar trends have been reported in studies that
compared changes in pennation angle to changes in
torque or force produced by whole muscle groups
(Ito et al., 2000; Maganaris et al., 1998; Narici et al.,
1996). The female subjects in our study exhibited
the same trend, although the increase in pennation
angle was smaller than the males’, with increases
of approximately 5°, 11°, and 11° for the LG, MG,
and Sol.
261
Previous studies reported fascicle angles for
the TA to range between 10° and 20° depending on
the ankle angle and contraction intensity (Hodges
et al., 2003; Ito et al., 1998; Maganaris & Baltzopoulos, 1999a). Fiber pennation angle for the TA in
our study fell within this range, and there was only
a small increase between rest and MVC of 3° and
5° for the female and male subjects respectively. It
appears that the TA is less sensitive to changes in
joint angle and contraction intensity than the triceps
surae. Although the difference in optimal pennation angle for the TA was statistically significant,
the actual difference was only a couple of degrees.
These results suggest that one value for pennation
angle can be used for both sexes and across a full
range of contraction intensities without significantly
affecting muscle force estimates.
Isometric contraction causes muscle fibers
to shorten, which is accompanied by changes in
fascicle girth and muscle geometry (Otten, 1988).
This dynamic chain of events highlights a limitation of cadaver-based estimates of pennation angle.
Cadaveric material does not shorten, and thus pennation angle is primarily influenced by the limb
configuration in which the cadaver was fixed. Limb
configuration is also a concern when ultrasound is
used to measure pennation angle in vivo. A striking
example of this is seen in Table 1 of data reported
by Kawakami and colleagues (1998). They reported
a resting pennation angle of 32° ± 4° for the MG
with the knee flexed and the ankle in plantar flexion,
increasing to 59.5° ± 5° when the knee was extended
and the ankle in dorsiflexion. Both measurements
were taken at rest and therefore did not include the
effect of contraction intensity. When maximally
contracted, the pennation angle increased to 67°.
The physiological relevance of this value may be
debatable given that such a limb configuration is
not encountered during functional movements.
However, other measurements at joint angles typical
of walking clearly show that pennation angles for
the triceps surae are in excess of 30°. It appears that
pennation angles of 30° or more are the norm for
the triceps surae, in contrast to previous suggestions
that pennation angles of this magnitude are rarely
encountered (Lieber, 1992).
From a modeling perspective, it may be
advantageous to choose a pennation angle that was
measured with the limb in approximately the same
configuration as the joint angles that will be tested.
262
Manal, Roberts, and Buchanan
What value to choose when modeling a dynamic
task is less obvious because the joint angles are
constantly changing. Our preference is to measure
pennation angle with the limb positioned such that
the muscles of interest are near their optimal fiber
length (Figure 1). The pennation angle at this length
with the muscle fully activated is the optimal pennation angle. One advantage of measuring optimal
pennation angle is that it is an input parameter to our
Hill muscle model (Buchanan et al., 2004), and as
these models become increasingly subject-specific
it is helpful to use sex-based values for optimal
pennation angle, especially for muscles that are
highly pennate.
Muscles with large pennation angles allow
more fibers to be arranged in parallel within a given
cross-sectional area, increasing the force-generating
potential. Clearly, different force estimates would
result when using a 20° cadaver-based estimate of
pennation angle and a value of 40° measured in
vivo when modeling the force contribution of the
Sol to the Achilles tendon force. Achilles tendon
force during walking is large, in excess of 2,000
newtons (Finni et al., 1998; Komi et al., 1992), and
thus to best represent the actual force generated
by the fibers one should use anatomically realistic
values for pennation angle. To this end, one of the
main findings of our study was that male subjects
had significantly larger optimal pennation angles for
the TA, MG, and Sol compared with the female subjects (Figure 5). Even though the difference for the
TA was only 2° and would not likely affect muscle
force estimates, the difference for the gastrocnemii
was approximately 7°, and a 14° difference was
noted for the Sol. Thus, based on the magnitude of
this difference, especially for the Sol, sex-specific
values of optimal pennation angle should be used
when modeling the triceps surae.
It is hoped that the results of our study and the
data reported will serve as a reference for future
studies that wish to use architecturally appropriate
estimates of optimal pennation angle when modeling
muscle forces about the ankle.
Acknowledgments
The authors wish to thank Joseph Gardinier for his
assistance with data collection. This work supported, in part, by NIH grants R01-HD38582 and
P20-RR16458.
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