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Amer. Zool., 36:582-598
Functional Morphology of Aquatic Flight in Fishes: Kinematics, Electromyography,
and Mechanical Modeling of Labriform Locomotion
Mark W. Westneat
Department of Zoology, Field Museum of Natural History, Chicago, IL 60605
SYNOPSIS
Labriform locomotion is the primary swimming mode for many fishes that use the pectoral fins to generate thrust
across a broad range of speeds. A review of the literature on hydrodynamics, kinematics, and morphology of pectoral
fin mechanisms in fishes reveals that we lack several kinds of morphological and kinematic data that are critical for
understanding thrust generation in this mode, particularly at higher velocities. Several needs include detailed three-
dimensional kinematic data on species that are pectoral fin swimmers across a broad range of speeds, data on the
motor patterns of pectoral fin muscles, and the development of a mechanical model of pectoral fin functional
morphology. New data are presented here on pectoral fin locomotion in Gomphosus varius, a labrid fish that uses the
pectoral fins at speeds of 1-6 total body lengths per second. Three-dimensional kinematic data for the pectoral fins of
G. varius show that a typical "drag-based" mechanism is not used in this species. Instead, the thrust mechanics of
this fish are dominated by lift forces and acceleration reaction forces. The fin is twisted like a propeller during the fin
stroke, so that angles of attack are variable along the fin length. Electromyographic data on six fin muscles indicate
the sequence of muscle activity that produces antagonistic fin abduction and adduction and controls the leading edge
of the fin. EMG activity in abductors and adductors is synchronous with the start of abduction and adduction,
respectively, so that muscle mechanics actuate the fin with positive work. A mechanical model of the pectoral fin is
proposed in which fin morphometrics and computer simulations allow predictions of fin kinematics in three
dimensions. The transmission of force and motion to the leading edge of the fin depends on the mechanical advantage
of fin ray levers. An integrative program of research is suggested that will synthesize data on morphology,
physiology, kinematics, and hydrodynamics to understand the mechanics of pectoral fin swimming.
INTRODUCTION
Most fishes use their pectoral fins in some way
for propulsion, turning, braking, or balance. For
many species, thrust from the pectoral fins is the
primary mode of swimming. Fishes that use
pectoral fin swimming as their primary locomotor
mode include many of the labroid fishes, (wrasses,
damselfishes, and surfperches), surgeonfishes and
butterflyfishes, skates and rays, holocephalans,
and others. These primary pectoral fin propulsors
are from divergent phylogenetic positions and
comprise 15-20% of living fishes. Despite the
species diversity of pectoral fin swimmers,
flapping locomotion in fishes has received little
recent attention in comparison to undulatory
locomotion in fishes or to flapping flight in birds,
bats, and insects.
Paired fin propulsion in fishes was of ancient
interest, however. Aristotle (4th century BC)
suggested that all fishes with pectoral fins used
them for propulsion and that the caudal fin was
for steering. Borelli (1680), Pettigrew (1874), and
Breder (1926) described pectoral motions and
included pectoral propulsors in their
classifications of swimming modes in fishes.
Recent literature on pectoral fins includes several
studies on the kinematics (Webb, 1973; Blake,
1979; Geerlink, 1983; Archer and Johnston,
1989; Gibb et al., 1994; Drucker and Jensen,
1996), morphology (Blake, 1981a; Geerlink,
1989), and hydrodynamics (Blake, 1981b, 1983a,
1983b) of pectoral fin locomotion. These studies
identified the major levels of design in pectoral
fin systems that relate to the mechanics and
evolution of this mode of propulsion.
However, few fish species that use pectoral
propulsion have been studied, and no research has
provided a detailed, quantitative analysis of
behavior or mechanics in fishes that are primary
pectoral propulsors across a broad range of
speeds. Integrative studies are needed to link
morphology, kinematics, physiology and
hydrodynamics to the thrust produced by this
widespread locomotor mechanism.
The objectives of this paper are to review
previous literature on pectoral fin propulsion in
fishes and to summarize new data on the
functional morphology of locomotion in the
labrid Gomphosus varius (the bird wrasse). This
fish is a high performance labriform swimmer at
speeds up to 8 total lengths per second (TL•s-1).
Three sets of data on the locomotion of G. varius
are presented: kinematics, electromyography, and
biomechanical modeling. These data address the
following questions: (1) what are the 3-
dimensional motions of the pectoral fin during
the locomotor stroke? (2) what are the patterns of
muscle activity that drive the pectoral fin? and (3)
what is the musculoskeletal mechanism of pectoral
propulsion? The discussion then focuses o n
integrating studies of morphology, kinematics,
M. W. Westneat Aquatic flight in fishes
2
muscle physiology, and hydrodynamics of
pectoral fins.
Review: pectoral morphology, hydrodynamics,
and fin kinematics.
The morphological basis of pectoral propulsion
has been described in the cichlid Sarotherodon
niloticus (Geerlink, 1979), and two labrid fishes in
the genus Coris (Geerlink, 1989). Description of
pectoral girdle morphology, the structure of fin
rays, muscle origin and insertion, and tendon
morphology led Geerlink (1979) to propose
mechanisms for fin ray motion at the joints
between the rays and the pectoral girdle. The
muscle origins and insertions and the attachments
of tendons to the bases of fin rays suggested two
major axes of rotation for pectoral fin rays:
motion in an anteroposterior plane and in the
dorsoventral plane (Geerlink, 1989). The leading
edge fin ray articulates with the scapula in a
saddle-shaped joint, which also allows biaxial
motion of the fin ray (Geerlink, 1979). Further
mechanical modeling of this system is proposed
here in which morphometric data on pectoral
design and lever mechanics are used to generate a
predictive model that accounts for skeletal and
muscular architecture.
Hydrodynamic models for pectoral fin thrust in
fishes have been proposed for the two extreme
ends of the spectrum of flapping propulsion:
drag-based and lift-based thrust. Drag-based
swimming has been modeled as pectoral fin
“rowing," in which the fin is brought forward
parallel to the direction of movement, and thrust
backward broadside during the power stroke to
generate drag-based thrust (Blake 1979). In lift-
based pectoral fin propulsion, the pectoral fins
flap dorsoventrally with a low angle of attack to
the direction of forward progression (Blake
1983a, 1983b). This dichotomy of drag vs. lift
has driven hydrodynamic modeling of pectoral
locomotion, although Vogel (1994) illustrated a
trade-off between the two modes. Drag-based
rowing is an efficient method at low velocity,
when flow over the fin is minimal, whereas a lift-
based mode is superior at higher speeds, when
chordwise flows over the fin are high. Vogel
(1994) pointed out that neither mode is likely to
be used exclusively across a range of speeds.
In addition to lift and drag, acceleration
reaction forces due to the oscillatory motion of
the fin sweeping water fore and aft are important
components of pectoral locomotion. Daniel
(1984) summarized the phenomenon nicely:
"while drag is the resistance to motion through a
fluid, the acceleration reaction is resistance to
changes in velocity of that motion." The
acceleration reaction has been a major focus of
previous models of aquatic flapping propulsion
(Blake, 1983a; Daniel, 1988) in which the size
and shape of an oscillating appendage, rate of
change in velocity of the propulsor, and forward
speed combine to determine the importance of
this force in a particular situation. A common
measure for the unsteadiness of a flow situation is
the reduced frequency parameter,
σ: σ= f l U-1,
where f= frequency, l = fin chord length, and U =
forward speed (Lighthill, 1975). This variable
shows that flows around the fin are most unsteady
when fin beat frequency is high and forward
speed is low. As σ increases, the flow experienced
by a chord of fin is low because there is less time
for flow circulation to build. This reduces lift,
although acceleration reaction may compensate
for the loss of lift (Daniel, 1984). The reduced
frequency parameter is known only for a few
pectoral swimmers among fishes (Gibb et al.,
1994; Arreola and Westneat, 1996). Estimation of
the effects of acceleration reaction will be critical
to analyses of pectoral swimmers operating at
high speeds because of a trade-off in the ability of
a fin to generate lift and acceleration reaction
forces.
The hydrodynamic studies described above
have stimulated much of the current interest in
pectoral flapping by aquatic swimmers, yet few
kinematic data exist for the testing of such
models. Blake's (1979, 1980) model of drag-
based swimming was formulated using data o n
pectoral kinematics during slow swimming (0.5
TL•s-1) of an angel fish, Pterophyllum eimecki,
but the assumptions and predictions of the model
have not received further testing (see Lauder and
Jayne, 1996). Lift-based models of flapping flight
in birds (Rayner, 1988), bats (Norberg, 1990) and
insects (Ellington, 1984; Dickinson, 1994) have
received significant testing with kinematic data
and flow visualization studies. However,
hydrodynamic theories of pectoral locomotion in
fishes (Blake, 1983a; Daniel, 1988) are just
beginning to inspire studies of pectoral kinematics
that will prove useful in testing and refinement o f
those models.
Kinematic data (Webb, 1973; Geerlink, 1983;
Gibb et al., 1994; Drucker, 1996; Lauder and
Jayne, 1996) have shown that a simple "lift vs.
drag" dichotomy is usually not present. Rather,
the two strategies are combined in different ways,
depending upon speed, to generate the net
propulsive force. Webb (1973) studied the
surfperch, Cymatogaster aggregata swimming
across a range of swimming speeds from 0-5
TL•s-1. C. aggregata increased frequency and
amplitude of fin motion with increased velocity.
Two kinematic patterns were present in C.
aggregata, each of which produced both lift and
drag. Lift forces apparently canceled out over the
stroke cycle, so that only drag and acceleration
M. W. Westneat Aquatic flight in fishes
3
reaction were important for forward thrust (Webb,
1973). Pectoral fin kinematics were highly
variable in the labrid Coris formosa swimming in
still water at velocities up to 0.8 TL•s-1 (Geerlink,
1983). Complex pectoral motions in C. formosa
included both anteroposterior and dorsoventral
motion, as well as fin bending along the axis of
the rays and chordwise curling or cambering o f
the fins. Geerlink (1983) suggested that a model
of the pectoral fin as a blade or planar structure
was likely to be of limited use in calculating the
true propulsive forces for most pectoral motions.
Three-dimensional kinematics of marked
pectoral fins have been obtained for bluegill
sunfish, Lepomis macrochirus (Gibb et al., 1994)
and for bass, Micropterus salmoides (Lauder and
Jayne, 1996). This methodological breakthrough
allowed the measurement of variables such as
stroke plane and angle of attack that have figured
critically in previous studies of flight mechanics
of birds and insects. Consideration of the angle of
attack of particular parts of the fin suggested that
lift-based locomotion may also be present in
bluegill.
Kinematic data across the entire natural range
of swimming speeds have been collected for few
species that are primary pectoral swimmers
(Drucker, 1996). The apparent diversity of
pectoral kinematics emerging from recent work
indicate the need for detailed 3-D kinematics in
primary pectoral swimmers. Pectoral locomotion
in the family Labridae, for whom labriform
locomotion is aptly named, is the focus of the
current work on morphology, kinematics, and
electromyography of this mode of swimming.
Functional morphology of labriform
locomotion in Gomphosus varius
The goal of the remainder of this paper is to
present data on several complementary
approaches to pectoral locomotion, including
descriptive morphology, detailed kinematics of
the fin movements in three dimensions,
electromyographic analysis of pectoral muscle
activity, and mechanical modeling of pectoral fin
mechanisms.
Morphology of the pectoral fin.
The descriptive anatomy of the pectoral girdle,
pectoral musculature, and fins in fishes has been
founded by a strong comparative literature
(Shann, 1920; Starks, 1930). To study the
mechanical design of pectoral fins in labrid fishes,
I followed Geerlink's (1989) general approach to
the description of pectoral girdle morphology.
This anatomy is used below to present a
biomechanical model that uses morphometric data
on skeletal elements, muscles, and tendons in
combination with lever mechanics to generate
predictions of pectoral fin ray motion.
The pectoral girdle (Fig. 1A) is the anchor
upon which the pectoral muscles originate. The
anteroventral surfaces of the cleithrum, both
laterally and medially, as well as scapula and
coracoid, are the sites of attachment for abductor
and adductor musculature (Fig.1B, 1C). The first
pectoral fin ray is a short, thick ray that articulates
with the scapula in a synovial joint. The first and
second pectoral rays are tightly connected by
connective tissues to form a single rotational
element that forms the leading edge of the
pectoral fin (Fig. 1A). Pectoral rays 2-16 in G.
varius have their bases imbedded in a fibrous pad
that separates them from the underlying radials.
Pectoral fin shape is determined largely by
relative fin ray length: the anterodorsal rays of G.
varius are the longest and the rays taper in length
from dorsal to ventral to form a wing-shaped fin.
Six major pectoral muscles actuate the fin
during locomotion. Three muscles form the
abductor complex that abducts the fin in the
downstroke. The abductor superficialis and
abductor profundus (Fig. 1B) are broad, flattened
muscles that originate on the anterolateral face of
the cleithrum and insert via the abductor tendons
onto pectoral rays 2-16. The arrector ventralis
(Fig. 1C) also attaches along the anterolateral
edge of the cleithrum, lying medial to the
abductor superficialis. The arrector ventralis
inserts onto the anterior base of the first pectoral
ray by a stout tendon. The adductor complex (not
illustrated) is composed of three major muscles
and two smaller muscles. The adductors
superficialis and profundus originate on the
anteromedial surface of the cleithrum and insert
via adductor tendons onto pectoral rays 2-16.
These muscles are antagonists to the abductors
superficialis and profundus. The arrector dorsalis
originates anteroventrally on the medial face o f
the cleithrum and inserts onto the anterior base of
the first pectoral ray by a stout tendon, as an
antagonist to the arrector ventralis. Other adductor
muscles include the adductor radialis, originating
on the caudal margins of the scapula and
coracoid, inserting on pectoral rays 14-16, and the
coracobrachialis, attaching to the rear portion of
the coracoid and ventral margin of the fourth
radial.
Three-dimensional kinematics of Gomphosus
To understand the hydrodynamic mechanisms
that produce thrust from pectoral fins, detailed
knowledge of pectoral fin motion is necessary. To
achieve this, I present data on three-dimensional
kinematics of the fins of G. varius (Figs. 2 - 5).
To summarize the methods, the fins of fishes were
labeled with tiny strips of thin, light aluminum
that have a bright, reflective red or white surface
M. W. Westneat Aquatic flight in fishes
4
(CokeTM cans). Markers were attached to the fins
of anesthetized (methane sulfonate) fishes by
bending the aluminum into a ring around fin
rays. No glue was necessary, and the behavior of
the fins appeared the same as the unmarked fin.
Fin markers were placed on the fin tip, two points
on the leading edge, and two points on the trailing
edge (Fig. 2B). The leading and trailing edge
markers established two hydrodynamic wing
chords that were largely parallel to the flow across
the fin during locomotion (Fig. 4A). The fish
swam in a flow tank of volume 360 liters and
working area dimensions of 30 x 30 x 120 cm
(108 l). Tank speeds were 15 to 70 cm/s at
Reynolds numbers (for the fin chord) of about
4000-9000. Video images were recorded at 60Hz
in two views: lateral view and a dorsal view
reflected by placing a mirror at 45° in the tank.
Videos were digitized with a custom digitizing
program developed by J. Walker. X, Y, and Z
coordinates were measured for each of the fin
markers (Fig. 4A), and the center of mass of the
fish.
To compute three dimensional kinematic
variables, the anteroposterior axis of the fish was
the x-axis, dorsoventral axis was the y-axis, and
left-right was the z-axis. Kinematic variables
computed include frequency (number of fin beat
cycles per second), 3-dimensional stroke angle (a
measure of amplitude), duration of activity of
each component of the stroke (abduction and
adduction), velocity of the center of body mass in
X (anteroposterior) and Y (dorso-ventral)
directions, path of the fin tip in 3 dimensions,
stride length, stroke plane angle, angle of attack of
the two marked fin chords relative to the direction
of body motion, reduced frequency parameter,
and advance ratio (forward speed / fin tip speed).
In contrast to other studies of labriform
propulsion, bird wrasses did not swim steadily in a
flow tank below about 1 TL•s-1. At low flow tank
speeds they turned, maneuvered and accelerated
with the pectoral fins. Steady labriform
locomotion occurred from about 1.2 - 6.0 TL•s-
1. At top speeds, most individuals swam to
exhaustion using only the pectoral fins, although
some individuals augmented labriform swimming
with kick-and-glide axial propulsion. Frequency
increased linearly with swimming speed across the
range of 1.2 to 6 TL•s-1 (Fig. 3A). Stroke angle,
the 3-dimensional angular rotation of the leading
edge, also increased with swimming speed,
ranging from around 80° to nearly 140° (Fig.
3B). As velocity increased, the durations of
abduction (Fig. 3C) and adduction (Fig. 3D)
decreased. There was no refractory period or
"pause" phase after adduction in the bird wrasse.
Rather, protraction of the fin began immediately
following adduction. The percentage of the stride
of each part of the fin stroke was relatively the
same across swimming speeds, with abduction
comprising about 60% of the stroke duration at
all speeds (Fig. 3E). This pattern in G. varius is
different from that found in Lepomis (Gibb et al.,
1994) and Cymatogaster (Webb, 1973) in which
the percent stride time for abduction decreased
and that for refractory period increased. This
result suggests that bird wrasses gain thrust from
their abduction phase across a range of speeds.
The pectoral fin tip traced a figure-8 path that
was nearly perpendicular to the body axis and
direction of motion (Fig. 4B). At the end of
adduction the fin was pressed against the lateral
body surface. The fin then rotated rostrally to
peel the leading edge away from the body in
preparation for abduction (video in Fig. 2B). At
maximal abduction, the leading edge of the fin
flipped rapidly dorsally to produce the first stage
of adduction (video in Fig. 2E). A lateral view o f
the path of the fin tip relative to the fish's body
(Fig. 4B) shows that the stroke plane angle of the
leading edge during abduction was close to 90°
(vertical), and the average stroke plane angle set
by anterior- and posterior-most fin excursions was
70° to the horizontal. A lateral view of the fin tip
relative to the water velocity (Fig. 4C) reveals the
stride length of a fin beat, the total distance
traveled during one beat cycle. Stride length
increased nearly linearly with swimming speed in
the bird wrasse, with a slope close to 1.0. During
adduction, fin motion rarely translated posteriorly
faster than the water flow (Fig. 4C), this occurring
only at the lowest swimming speeds. This means
that a classic drag-based mechanism cannot be
operating in the bird-wrasse. All propulsive forces
during the upstroke must thus be derived from
other hydrodynamic sources (lift and acceleration
reaction).
The velocity of the center of mass in the
direction of swimming (Fig. 4D) was roughly
constant during abduction, decreased by several
cm/s during the fin flip transition from abduction
to adduction, and then increased sharply during
adduction. This suggests that during abduction,
drag on the extended fins was largely offset b y
thrust from lift or acceleration reaction, and that
most propulsive force for accelerating forward
was generated during adduction. The velocity of
the center of mass of the body in the Y-direction
(dorsoventral axis) reveals that the body of the
bird wrasse bounced up and down in response to
oscillating lift vectors (Fig. 4E). The body rose
during abduction and fell during adduction, a
behavior similar to other lift-based aquatic
locomotion such as that of penguins (Clark and
Bemis, 1979).
Three dimensional kinematic data allowed
calculation of three variables important to
M. W. Westneat Aquatic flight in fishes
5
hydrodynamic thrust mechanics: angle of attack,
advance ratio, and reduced frequency parameter.
To precisely calculate the angle of attack of a
flapping appendage is extremely difficult,
requiring 3-dimensional coordinates from
multiple positions on the fin and calculation of
the resultant water velocity (the vector sum of the
freestream, flapping, and induced velocities). The
induced velocity is the velocity vector of the
increased momentum of accelerating water. It is
difficult to measure directly and is usually
estimated using a hydrodynamic model (Blake,
1979). Other problems include the potential for
flexible fin membranes to develop camber
(anteroposterior arching of the fin). Finally, the
direction of the resultant water velocity is a
function of both time and position along the fin.
A chord is thus not always a property of fin shape,
but a dynamic feature of potentially changing fin
geometry and resultant water velocity. These
problems will be even more severe for planar fin
blade elements that cover all or part of the fin
surface.
Despite these problems, angles of attack were
calculated for a proximal and distal chord (Fig.
5). Chords were used rather than treating the fin
as a planar blade due to the lift-based nature of
Gomphosus locomotion and because accurate
angles of attack (relative to water velocity) cannot
be calculated for a planar fin surface due to the
fact that the fin twists along its length (see below).
The angle of attack is the angle between the chord
and a frontal plane. The angle of attack was
highly variable depending upon its position along
the fin length (proximal or distal) and upon
swimming speed (Fig. 4A, Fig. 5). The proximal
chord (Fig. 5A, 5C) and distal chord (Fig. 5B, 5D)
had a similar angle of attack with respect to
direction of motion only at peak adduction (e.g.,
position 1 in Fig. 5A and 5C) and peak abduction
(e.g. position 8 in Fig. 5C and 5D). However, the
angles of attack were strikingly different during
the downstroke and upstroke (e.g. compare the
angle during frame 10 in Fig. 5C and 5D).
During peak velocity of the fin, the fin was twisted
along its length like a propeller. During abduction
the angle of attack of the proximal chord with
respect to the direction of forward motion was
greater than that of the distal chord. During
adduction, the reverse was true. To calculate the
hydrodynamic thrust generated by the twisted fin
acting as a propeller blade, the net flow circulation
around the fin during both abduction and
adduction must be calculated or measured. This
will require an integrated approach that will
incorporate both flow circulation for lift and the
changes flow vectors due to acceleration reaction.
A measure of the ability of the fin to generate
circulation around the wing for lift-based thrust is
provided by the advance ratio, the ratio of forward
speed to fin tip speed. The advance ratio for bird
wrasses ranged from 0.5 at low velocities up to
about 1.7 at high swimming speeds, indicating
that forward speeds are high enough relative to fin
speed for lift generation. These values are in the
range of other flapping fliers that generate flow
circulations around the wing for lift generation,
including insects and aquatic birds (Vogel, 1994).
The importance of the acceleration reaction in
locomotor mechanics is summarized by the
reduced frequency parameter, calculated as fin
beat frequency multiplied by fin chord length
divided by swimming speed. Gomphosus varius
swam with a reduced frequency of about 1.5 at
low speeds, decreasing to 0.6 at high velocities.
Unsteady effects due to acceleration of fluid
during oscillation of an appendage are considered
important above 0.5. These results suggest that
both lift and acceleration reaction forces play
important roles in the flapping locomotion of G.
varius, the two perhaps contributing differentially
to the overall thrust budget as forward velocity
increases.
Motor patterns of the abductor and adductor
muscles during labriform locomotion.
The mechanism of force generation by pectoral
fins depends upon multiple levels of design,
including musculoskeletal design, kinematics, and
the motor patterns of the muscles driving the fins.
Kinematics have shown that variable fin behaviors
occur within the same species and individual, such
as the two pectoral movement patterns identified
in Cymatogaster aggregata (Webb, 1973).
Geerlink (1989) found a high level of variability
in the kinematics of 2 labrids and a cichlid fish,
and suggested that "cybernetic factors" and not
morphological variation explained kinematic
variation. Clearly, a complete understanding of
the mechanics of pectoral fin locomotion in fishes
requires data on the motor patterns of the muscles
that drive the behavior of the flapping fins.
Despite an increased emphasis on neuromotor
patterns in aquatic locomotion (Rome et al., 1993;
Wardle et al., 1995), no study has documented the
activity of pectoral muscles during swimming.
To address this issue, I present
electromyographic (EMG) data on the activity o f
the six major pectoral muscles in Gomphosus
varius. EMG data were recorded from 3
individuals over a range of swimming speeds from
1.0 - 4.8 TL•s-1. Fishes were anesthetized with
methane sulfonate (FinQuel, Aldrich). Bipolar,
fine wire electrodes were constructed from 0.05
mm diameter, insulated, stainless steel wire.
Insulation was stripped from a 1.0 mm section of
each wire to form an electrode tip with two bare
wire sections 1.5- 2.0 mm apart. Electrodes were
threaded through a 25 gauge needle for
M. W. Westneat Aquatic flight in fishes
6
implantation into muscles. Care was taken to
standardize electrode construction to minimize
signal variation due to electrodes.
Electrodes were implanted into the three major
abductors and three major adductors of the left
pectoral fin by sliding the syringe needle beneath
scales, through skin, and into the target muscle.
Lateral muscles implanted were the arrector
ventralis, abductor superficialis, and abductor
profundus (Fig. 1). Medial muscles implanted
were the arrector dorsalis, adductor superficialis,
and adductor profundus (Fig. 1). Electrode wires
were run dorsally to a suture at the base of the
first dorsal spine, where they were glued together
to form a single cable that extended 40-50 cm
from the fish. EMG signals were amplified by a
factor of 5,000 - 10,000 by AM Systems Model
1700 amplifiers, filtered by a 100 Hz high pass
filter, and recorded on a TEAC 8 channel DAT
tape recorder. EMGs were later digitized by an
analog-to-digital converter driven by LabVIEW 2
software (National Instruments Corp., Austin
Texas). The sample rate was 5000 points per
second per channel. The digital record was then
analyzed using a custom six channel analysis
algorithm using LabVIEW 2. Each channel was
visually inspected to determine the baseline noise
level, and a cut-off amplitude was chosen, below
which all values were set to zero. This allowed
repeatable identification of the onset and offset
point of each muscle burst within a particular
EMG record. EMGs were synchronized with
kinematic data by pulsing a 5 volt square wave t o
the EMG tape deck and to a flashing light-
emitting diode on the video view. Electrode
placement was confirmed by dissection of the
specimen after the experiment.
The muscular motor patterns of labriform
swimming behavior were estimated by 16 EMG
variables: muscle activity duration (6 muscles),
muscle amplitude (6 muscles), and onset time of
muscles relative to the arrector ventralis (5
muscles). Amplitude was computed as the area
under the curve of a rectified (all values made
positive) EMG signal: EMG area equaled the sum
of the signal heights multiplied by burst duration
and divided by sample number. In addition, the
points of maximal abduction and adduction from
the kinematic records were identified on each
EMG trace.
The results show that the basic motor pattern o f
pectoral propulsion is that of alternate activity of
the antagonistic abductor and adductor groups
(Fig. 6). Starting at the maximal adduction with
fins against the body, the abduction phase begins
with activity of the arrector ventralis muscle
before the other abductors (Fig. 6, top). The
arrector ventralis likely rotates the fin forward to
initiate the peel of the leading edge away from the
body. The abductor superficialis and profundus
are then active with the arrector ventralis to
produce the downstroke of the fin. Immediately
following maximum abduction, adduction begins
with the fin flip, initiated by activity of the
arrector dorsalis muscle. Then the adductor
superficialis and profundus are active in
synchrony with fin adduction.
Frequency and amplitude of EMG activity
increased with increasing swimming speeds. The
durations of abductors were significantly greater
than adductors, with the abductor profundus
showing the longest duration. However, EMG
durations did not change significantly as a
function of forward velocity (compare Figs. 6A
and 6B). Rather, the inter-EMG lag time between
cycles decreased with increased speed. The onset
time of the abductor profundus and superficialis
relative to arrector ventralis did not change
significantly as a function of speed, but the onset
time of the adductors relative to arrector ventralis
decreased at higher velocities.
The motor patterns of fin flapping muscles give
us substantial insight into the neuromotor basis of
labriform swimming. The integration of EMG
data with kinematics reveals that EMG activity of
abductors is synchronous with the onset and
action of abduction, and that adductor EMG is
synchronous with adduction. These results are in
contrast to EMG data collected for undulatory
axial locomotion (reviewed in Wardle et al., 1995),
the activity of pectoral muscles in bird flight (Dial
et al., 1991), and the activity of the flight muscles
of insects (Tu and Dickinson, 1994). These
previous studies have shown that EMG activity in
axial fish muscle and flight muscle begins
substantially before the behavior that the muscle is
responsible for producing. In fishes, axial muscles
are active in a traveling wave down the body that
precedes axial bending of the vertebrae to which
the muscle attaches. Similarly, the massive
pectoralis muscle driving the downstroke during
bird flight begins activity well before wing
reversal and the initiation of the downstroke. The
muscle mechanics in these systems must involve
one or both of two phenomena: delay in muscle
force after EMG activity is observed or a
significant amount of negative work performed
by the muscle. This is apparently not the case in
the flapping aquatic flight of Gomphosus varius.
Arrector ventralis activity is synchronous with
initiation of abduction, arrector dorsalis activity is
synchronous with the fin flip beginning
adduction, and the large antagonistic abductor
and adductor muscles are active during the major
rotational motions of the fin in downstroke and
upstroke. These EMG results suggest that
Gomphosus has fine motor control of both fin
shape, fin twist, and the position of individual fin
rays during both downstroke and upstroke.
M. W. Westneat Aquatic flight in fishes
7
Biomechanical modeling of the pectoral fin.
The behavior of fin flapping during labriform
locomotion is determined by mechanical design
and motor inputs to muscles. One way to integrate
data on structure, kinematics, and
electromyography and to test hypotheses
regarding mechanical design is by modeling of
the pectoral fin complex. A 3-dimensional
mechanical model of the leading edge of the
pectoral fin of Gomphosus was derived by using
lever theory to analyze the actions of the fin ray
when subjected to force generated by fin muscles.
The model exists in two forms: physical model
and computer model. First, a scaled physical
model was constructed of wood, wire, and small
custom-made pulleys at the Duke University
BioDesign Studio. Building the physical model
yielded an improved understanding of fin ray
mechanics. For example, the model demonstrated
visually that the precise lever ratio of fin ray
length below and above the tendon insertion
greatly influenced the motion resulting from
muscle inputs.
The computer model accepts morphometric
data on the geometry of the pectoral girdle, the
lengths of muscles, and the lever metrics of the fin
rays in three views: lateral (Fig. 7A), frontal (Fig.
7B), and medial. Once the geometry of the fin is
established, the model simulates various patterns
and degrees of muscle contraction. Due to the
importance of the action of the leading edge in
determining fin ray motion, the computer model
first predicts the action of the arrector ventralis on
pectoral rays 1 and 2 and calculates the positions
of other rays as they follow the leading edge.
Thus, the role of the computer model is to
generate predictions about behavior based on the
geometric arrangement of the muscles and bones
and the motor pattern of muscles.
The action of the arrector ventralis muscle (Fig.
8) is critical to the start of fin abduction during
which the fin is rotated forward (protraction) and
rotated laterally (abduction). When the fin is in
the adducted position (Figs. 8A, 8C) the leading
edge fin ray is the y-axis in both left lateral (Fig.
8A) and left frontal view (Fig. 8C). In lateral view,
action of the arrector ventralis pulling from point
13 to point 2, and rotating around point 1 (the
origin) protracts the fin (Fig. 8B). In frontal view,
the arrector ventralis pulls from point 18 to point
2, rotating the fin around point 1 to abduct the fin
(Fig. 8D). The vector sum of these two rotations
in the XY and YZ plane is a precise prediction of
the stroke angle generated by contraction of the
arrector ventralis.
Results from modeling three muscles of the fins
in three Gomphosus varius specimens revealed the
differential control of the motion of the leading
edge of the fin. The action of the leading edge in
abduction was simulated by arrector ventralis and
abductor profundus contraction. A range of
muscle contractions from 1% to 15% of adducted
(resting) length of each muscle was simulated. For
the arrector ventralis, muscle actions resulted in an
anteroventral angular rotation of 21 to nearly
160° (Fig. 9A). This stroke angle was contributed
to by similar angular rotations in the XY and YZ
planes (Fig. 9A). In contrast, simulation of a
similar range of abductor profundus contraction
resulted in leading edge rotation of 8 to almost
120° (Fig. 9B). The angular rotation due to
motion in the XY plane was greater than that in
the YZ plane. For adduction, the action of the
arrector dorsalis was simulated in a similar
manner, showing a range of angular rotations of 8
to 120°, similar to that of the abductor profundus
(Fig. 9C).
These predicted stroke angles are remarkably
similar to the stroke angle seen in living,
swimming fishes (Fig. 3B). The transmission o f
rotational motion to the leading edge partly
depends upon the velocity advantage, the output
lever length divided by input lever length. This
variable is the inverse of the mechanical
advantage. In figure 8A for example, the velocity
advantage of the leading edge is equivalent to the
distance from point 2 to the fin tip (not shown)
divided by distance 2-1. The arrector ventralis has
a relatively large input lever, giving it a velocity
advantage of 16.1. The velocity ratio of the
abductor profundus mechanism had a greater
velocity ratio of 20.1, and the arrector dorsalis
velocity advantage was lower, at 12.2. These lever
advantages illustrate the trade-off between the
transmission of motion and force. The arrector
dorsalis, with its relatively low velocity ratio and
higher mechanical advantage, is capable o f
transmitting a greater amount of force from
muscle contraction during the power stroke.
Because both the arrector ventralis and abductor
profundus insert on the leading edge with
different lever ratios, the fin is capable of forceful
as well as rapid motion during locomotion.
To test this model rigorously, morphometric
data are being collected for the same individuals
for which the kinematics and electromyographic
patterns are known. In addition, the computer
model is being modified to calculate the positions
of all fin rays relative to fin base due to the
activity of both abductors and adductors. This will
allow computation of important locomotor
features such as the path of the fin tips, chordwise
angle of attack, and the angular velocity of fin
motion. Kinematics will provide a test of the
accuracy of model predictions.
DISCUSSION
Emerging from a review of the literature are
several important ideas that form a basis for
understanding pectoral fin locomotor mechanics
M. W. Westneat Aquatic flight in fishes
8
and several areas in need of study to enhance our
understanding of propulsion by fin flapping.
Hydrodynamic models have largely inspired the
field of finbased locomotion. It is appropriate to
apply these models to a range of taxa, and test
them with detailed kinematic data in situations that
fit the assumptions of the models. Kinematic data
are clearly a major area of future work for the
biology of fin propulsion: few species have been
measured at high speeds characteristic of many
pectoral fin propulsors (up to 6 or 8 TL•s-1). As
Gibb et al. (1994) noted, fewer still have detailed
kinematic data in three dimensions that will allow
interpretation of thrust mechanics.
Three-dimensional kinematic data for the bird
wrasse indicate that the pectoral fin generates
propulsive thrust primarily from lift and
acceleration reaction. In contrast to fishes using
the fins at low speeds, little or no drag-based
rowing is performed. The advance ratio and
reduced frequency of the bird wrasse suggest a
trade-off in the importance of these two sources
of propulsion across the natural range of
swimming speeds. The reduced frequency
indicates that wrasses are dealing with unsteady
flows. Labriform locomotion may provide a
useful biological system to explore the interaction
of lift forces and acceleration reaction forces.
The problems of measuring angle of attack
will yield to additional detailed 3-dimensional
data of pectoral locomotion. There is active
debate on the relative benefits of computing
chordwise angles of attack versus attack angles of
planar fin surfaces. For lift-based locomotion,
such as that of Gomphosus, angles of attack o f
chord lengths will provide the best estimates o f
this important parameter. The pectoral fin is
twisted like a propeller during swimming, and
angular fin velocities change rapidly along the fin
length. Thus, angles of attack of chord lengths of
the fin are variable along the fin length, and
variable at different stages of the beat cycle.
Angles of attack of large, planar fin areas will thus
be in error. In addition, fin twist and the rapid
velocity changes during oscillation render quasi-
steady computations of propulsive forces
problematic. Studies of pectoral propulsion
should strive to develop a hydrodynamic model
that can combine the relative contributions of
drag, lift, and acceleration reaction by using
kinematic data and knowledge of patterns of flow
circulation around the pectoral fin (Daniel, 1984).
Other major features of pectoral locomotion
that are associated with increasing swimming
speed are pectoral beat frequency, stride length,
and electromyographic patterns. The relative
proportion of time taken by each component o f
the stroke cycle is fairly constant across velocities.
Further analysis of the hydromechanical thrust
forces during each stroke will enable the
calculation of the duty factor (proportion of each
stroke cycle that produces forward thrust) of each
stroke behavior (see Drucker, 1996). Future
research should strive to integrate stroke
kinematics, thrust estimates, and stride length so
that duty factors of the pectoral stroke can be
compared across taxa.
Information regarding the neuromotor patterns
of labriform locomotion is also critical to a full
understanding of labriform locomotion. Recent
EMG studies have provided information on the
motor patterns of the myomeres in fishes during
undulatory locomotion (Wardle et al., 1995, Jayne
and Lauder, 1995). These data have played a
central role in the calculation of work and power
done by muscle during swimming (Rome et al.,
1993). If the thrust budget of labriform swimmers
can be deduced, including the relative
contributions of the downstroke and upstroke,
then calculations of the work, power, and
efficiency of each muscle group can proceed.
Such analyses will prove valuable in comparative
studies of the evolution of locomotor mechanics
in the diverse phylogenetic groups of fishes that
use pectoral propulsion.
Finally, I suggest that mechanical models of fin
morphology provide a means for testing concepts
of the pectoral fin function across diverse forms.
The mechanical design of the pectoral girdle,
musculature, and fin ray levers can be integrated
by a mechanical model based on morphometrics
that reflect functionally important fin dimensions.
Such models are a useful tool for predicting the
mechanical results of changes in morphology and
motor patterns in musculoskeletal systems. Future
modeling studies will combine esti-mates of
muscle contraction force and velocity with lever
ratios that determine the relative transmission of
force and motion to the fin rays. Comparisons of
kinematics, muscle actions, skeletal mechanisms,
and fin shapes in the context of mechanical
models will be crucial for mechanical and
evolutionary analyses of pectoral propulsion.
ACKNOWLEDGMENTS
Thanks to John Long and George Lauder for
the organization of our symposium, at which I was
inspired by the high levels of interest and
advancement in the study of locomotion.
Particular thanks go to Jeff Walker for his
valuable insight and hard work on our kinematics
research, and to Margaret Pizer for her work on
the mechanical models. Thanks also to M. Hale, J.
Walker, and the anonymous reviewers for
comments on the manuscript. This research was
funded by National Science Foundation grant
IBN-9407253.
M. W. Westneat Aquatic flight in fishes
9
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Figure 1. Morphology of the pectoral fin of Gomphosus varius. (A) Lateral view of the osteology of
the pectoral girdle, radials, and fin rays. Note the connection of the short P1 ray to the long P2 ray to
form the leading edge of the fin blade. (B) Lateral view of the abductor superficialis muscle and
abductor profundus muscle, illustrating their origin on the anterolateral surface of the cleithrum, and
insertion via tendon across the fibrocartilage pad onto the fin ray bases. (C) Lateral view of the
abductor musculature with the abductor superficialis removed to reveal the arrector ventralis. Note the
insertion of the arrector ventralis onto the P1 ray.
M. W. Westneat Aquatic flight in fishes
11
Figure 2. Video images of pectoral locomotion by Gomphosus varius in lateral view and dorsal
(mirror) view, with a labeled left pectoral fin. (A) Fin is adducted. (B) Start of abduction, in which the
dorsal view shows lateral motion of the fin tip and lateral view shows protraction of the fin. Fin
markers in lateral view (see white arrows) appear light against the dark body. (C) Mid-abduction stage
at which the fin is cambered in lateral view and approaches maximal anterior rotation in dorsal view.
Fin markers in dorsal view (see dark arrows) appear dark against the white grid. (D) Near maximal
abduction, the twisting of the fin is apparent and the overall angle of attack of the fin is low. (E) The
fin flip during which the leading edge of the fin is brought rapidly upward and backward to begin
adduction. (F) Fin is nearly fully adducted.
M. W. Westneat Aquatic flight in fishes
12
frequency (Hz)
0.0
4.0
8.0
02 46
frequency
A
duration (s)duration (s)
% stride time
velocity (TL•s-1)
0.0
0.2
0.4
024 6
abduction
C
0
50
100
0 246
E
abduction
adduction
0.1
0.2
024 6
adduction
D
0.0
60
100
140
0246
angular rotation (°)
B
stroke angle
Figure 3. Kinematic profiles of pectoral fin motion in Gomphosus varius across a speed range of 1-6
total lengths per second (TL•s -1 ). The frequency (A) of fin beats increases with swimming speed.
The stroke angle (B) increases with increased swimming speed, whereas the durations of the
abduction phase (C), and adduction phase (D) decrease with increasing swimming speed. However,
the percentage of stride time (E) expressed as a percentage of the total beat duration is constant
across this velocity range.
M. W. Westneat Aquatic flight in fishes
13
proximal chord
distal chord
fin tip path
fin markers
fin base
adducted position
abducted position
direction of swimming
fin tip
A
x-axis (cm)
time (s)
x-axis (cm)
B
C
D
E
-4
-2
0
2
velocity (cm/s)
time (s) 0
0.175
0.35
54
58
62
0
-4
0
4
time (s)
0
2
4
12 8 4 0
0
2
4
864 20
y-axis (cm)
velocity = 1.4 TL•s-1 velocity = 3.2 TL•s-1
adduction
abduction
0
2
4
024
y-axis (cm)
x-axis (cm)direction of swimming
20
23
26
0
0.175
velocity (cm/s)
0
2
4
02 4
y-axis (cm)
x-axis (cm)
fin tip
relative to fish
fin tip relative
to water flow
fin tip relative
to water flow
fin tip
relative to fish
center of mass
forward motion
center of mass
forward motion
center of mass
vertical motion
center of mass
vertical motion
00.1250.25
0.1250.25 time (s)
0.35
Figure 4. Representative kinematic profiles of pectoral fin motion in Gomphosus varius at two
different speeds; 1.4 and 3.2 TL•s -1 . The left fin of the fish is depicted during swimming from left to
right in all plots. (A) Diagram of the pectoral fin at maximal abduction and maximal adduction to
illustrate the positions of the fin markers at the fin tip and the ends of a proximal and distal chord
along the fin. (B) Plot of the path of the fin tip from lateral view in relation to the body of the fish.
Note the "figure-8" pattern and the steep stroke plane angle. (C) Plot of the path of the fin tip from
lateral view in relation to the velocity of the water. The stride length is
shown as the distance traveled along the x-axis. (D) Velocity of forward motion of the fish's center of
mass during a single pectoral fin stroke. (E) Velocity of dorsoventral motion of the fish's center of
mass during a single pectoral fin stroke. Abduction (open circles) is associated with the body rising
due to lift on the fin.
M. W. Westneat Aquatic flight in fishes
14
velocity=1.4 TL•s-1
-2
-1.5
-1
-0.5
-0.5 0 0.5 1
-2
-1.5
-1
-0.5
-1 -0.5 0 0.5 1
1
3
5
7
9
11
12
14
15
16
17 1
3
5
7
8
9
10
11
12
proximal chord
velocity=4.1 TL•s-1
Y-axis (cm)
Y-axis (cm)
X-axis (cm) X-axis (cm)
AC
-2
-1.5
-1
-0.5
0
-0.5 0 0.5 1 1.5
1
3
5
7
9
11
12
14
15
16
17 18
-3
-2.5
-2
-1.5
-1
-0.5
0
-1 -0.5 0 0.5 1 1.5
1
3
4
5
6
7
8
9
10
11
12
distal chord
Y-axis (cm)
Y-axis (cm)
X-axis (cm)
X-axis (cm)
BD
Figure 5. Angle of attack, relative to a frontal plane, of a proximal and distal fin chord during
swimming at two different speeds (1.4 and 4.1 TL•s-1). Open circles are the positions of fin markers
during abduction, closed circles are adduction, and numbers refer to video fields during one
complete pectoral fin beat. The proximal chord (A and C) has a positive angle of attack at the lower
speed, but in late abduction (open circles) and early adduction has a negative angle of attack at the
higher speed. The distal chord has a negative angle of attack at both speeds during much of the
stroke. Positions of the distal and proximal chords at a particular image number illustrates that the fin
twists along its length during both abduction and adduction.
M. W. Westneat Aquatic flight in fishes
15
-2.0
0
2.0
mV
A. 1.7 TL•s-1
-2.0
0
2.0
mV
abductor profundus
-2.0
0
2.0
mV
arrector dorsalis
-2.0
0
2.0
mV
adductor superficialis
-2.0
0
2.0
mV
time (s)
0 0.1 0.2 0.3 0.4
adductor
p
rofundus
-2.0
0
2.0
mV
-2.0
0
2.0
mV
-2.0
0
2.0
mV
abductor profundus
-2.5
0
2.5
mV
-2.0
0
2.0
mV
-2.0
0
2.0
mV
time (s)
0 0.1 0.2 0.3 0.4
-2.5
0
2.5
mV
B. 3.8 TL•s-1
arrector ventralis
abductor superficialis
arrector dorsalis
adductor superficialis
adductor profundus
arrector ventralis
abductor superficialis
maximum adduction
maximum abduction
maximum adduction
maximum abduction
Figure 6. Electromyograms for six pectoral muscles at 1.7 TL•s -1 and 3.8 TL•s -1 . Kinematic
landmarks of maximum adduction and maximum abduction are indicated on the EMG traces.
Arrector ventralis begins the motor pattern of the abductor muscles, and the abductor profundus
shows long duration activity during the downstroke. To actuate the fin flip and the beginning of
adduction, the arrector dorsalis initiates the activity of the adductor complex that is active during the
upstroke.
M. W. Westneat Aquatic flight in fishes
16
Figure 7. Morphometric data from lateral and frontal views used as input to a 3-dimensional
mechanical model of fin motion. (A) Left lateral view showing morphometrics of 1st fin ray (1-4),
fin rays (5-9), and pectoral girdle shape (10-15). (B) Frontal view showing morphometrics of 1st fin
ray (1-3), fin tip (5), and pectoral girdle shape (12-19). Points with same number in both views are
identical, allowing triangulation in X, Y, and Z planes.
M. W. Westneat Aquatic flight in fishes
17
left lateral
X
Y
3
2
1
4
15
14
13
12
11
10
9
B
protraction
arrector
ventralis
abductor
profundus
X
Y
protraction
anterior posterior
retraction
3
2
1
4
15
14
13
12
11
10
9
arrector
ventralis
abductor
profundus
A
Y
Z
adduction abduction
medial lateral
1
2
3
15
16
17
12
18
19
C
arrector
ventralis
adductor
profundus
Y
Z
abduction
1
2
3
15
16
17
12
18
19
D
arrector
ventralis
adductor
profundus
left frontal
Figure 8. Mechanical diagram of pectoral anatomy illustrating the design of the model used to
compute fin ray kinematics from morphometric data. (A) The geometry of pectoral girdle, rays, and
musculature determine the resting state of the mechanical model in lateral view. (B) Lateral view of
simulated action of fin ray protraction by contraction of the arrector ventralis. (C) The geometry of
pectoral girdle, rays, and musculature determine the resting state of the mechanical model in frontal
view. (B) Frontal view of simulated action of fin ray abduction by contraction of the arrector
ventralis.
M. W. Westneat Aquatic flight in fishes
18
0
40
80
120
0 4 8 12 16
angular rotation (°)
B. abductor profundus
angular rotation (°)
0
40
80
120
160
0 4 8 12 16
A. arrector ventralis
XY plane
YZ plane
3D stroke angle
C. arrector dorsalis
XY plane
YZ plane
angular rotation (°)
0
40
80
120
0 4 8 12 16
muscle contraction (%)
C. arrector dorsalis
XY plane
YZ plane
3D stroke angle
XY plane
YZ plane
3D stroke angle
Figure 9. Predictions of the biomechanical model for fin motions as a result of simulated muscle
contractions of the (A) arrector ventralis, (B) abductor profundus, and (C) arrector dorsalis. The
motion in the XY (lateral) plane, YZ (frontal) plane, and the resultant 3-dimensional fin stroke angles
are shown. Predicted stroke angles are similar to those shown by 3-dimensional kinematics (Fig. 3B).
