Functional Morphology of Aquatic Flight in Fishes: Kinematics, Electromyography, and Mechanical Modeling of Labriform Locomotion 1

Transcription

1 AMER. ZOOL., 36: (1996) Functional Morphology of Aquatic Flight in Fishes: Kinematics, Electromyography, and Mechanical Modeling of Labriform Locomotion 1 MARK W. WESTNEAT Department of Zoology, Field Museum of Natural History, Roosevelt Road at Lake Shore Drive, Chicago, Illinois 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 (wrasses, damselfishes, and surfperches), Most fishes use their pectoral fins in surgeonfishes and butterflyfishes, skates some way for propulsion, turning, braking, and ra y s ' holocephalans, and others. These or balance. For many species, thrust from primary pectoral fin propulsors are from dithe pectoral fins is the primary mode of vergent phylogenetic positions and cornswimming. Fishes that use pectoral fin P rise 15-20% of living fishes. Despite the swimming as their primary locomotor mode species diversity of pectoral fin swimmers, include many of the labroid fishes, flapping locomotion in fishes has received little recent attention in comparison to undulatory locomotion in fishes or to flapping From the Symposium Aquatic Locomotion: New flight in birds, bats, and insects. Approaches to Invertebrate and Vertebrate Biome- p aj r e d fin, sion in fishes was of an _ r r cnantcs presented at the Annual Meeting ot the Society for Integrative and Comparative Biology, De- cient interest, however. AnStOtle (4th cencember 1995, at Washington, D.C. tury BC) suggested that all fishes with pec- 582

2 AQUATIC FLIGHT IN FISHES 583 toral 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; fake, 1979; Geerlink, 1983, 1989; Gibb et al., 1994; Drucker and Jensen, 1996), morphology (Blake, 1981a), and hydrodynamics (Blake, 1981&, 1983a, V) 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 (TLsec" 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 on integrating studies of morphology, kinematics, muscle physiology, and hydrodynamics of pectoral fins. Review: pectoral morphology, hydrodynamic models, 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, b). 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 liftbased 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 resis-

3 584 MARK W. WESTNEAT tance 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, a: a = flu~', where f = frequency, 1 = 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 cr 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 on pectoral kinematics during slow swimming (0.5 TL-sec ') 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, 1983«; Daniel, 1988) are just beginning to inspire studies of pectoral kinematics that will prove useful in testing and refinement of 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-sec" 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 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-sec- 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 of 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

4 585 AQUATIC FLIGHT IN FISHES 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 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. IB, 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 radials coracoid X flnra ys postcleithrum abductor profundus FIG. 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 PI 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 PI ray. LOCOMOTION IN GOMPHOSUS VARIUS

5 586 MARK W. WESTNEAT Three-dimensional kinematics of Gomphosus varius 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 (Coke 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 FIG. 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. 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 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. IB) are broad, flattened muscles that originate on the anterolateral face of the cleithrum and insert via the abductor tendons onto pectoral rays 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 These muscles are antagonists to the abductors superficialis and profundus. The arrector dorsalis originates anteroventrally on the medial face of 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.

6 I-BH AQUATIC FLIGHT IN FISHES 587 N 3 T duration ^ CO o.o- 100 I 50- tfi 1 '*' frequency B 0 c stroke angle abduction ) D adduction 2 ill i 2 J"% I! abduction 1 4 i 4 m I i i mm gj ii ffl np adduction velocity (TL's' 1 ) FIG. 3. Kinematic profiles of pectoral fin motion in Gomphosus varius across a speed range of 1 6 total lengths per second (TLsec"'). 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. t e volume 360 liters and working area dimensions of 30 X 30 X 120 cm (108 liter). Tank speeds were 15 to 70 cm/sec at Reynolds numbers (for the fin chord) of about 4,000-9,000. Video images were recorded at 60 Hz 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 (dorsoventral) 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-sec" 1. At low flow tank speeds they turned, maneuvered and accelerated with the pectoral fins. Steady labriform locomotion occurred from about TL-sec" 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 TLsec" 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

7 588 MARK W. WESTNEAT adducted position fin tip path. fin tip -distal chord fin base proximal chord B D abducted position velocity = 1.4TL-S' 1 fin markers direction of swimming O abduction adduction velocity = 3.2 TL # s~* m x-axis (cm) direction of swimming x-axis (cm) JT fin fin tip relative ~^&-^t, ** to water flow TJ& SS, 4 x-axis (cm) 1 j^ time (s) time (s) FIG. 4. Representative kinematic profiles of pectoral fin motion in Gomphosus varius at two different speeds; 1.4 and 3.2 TLsec '. 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.

8 AQUATIC FLIGHT IN FISHES f) <; A velocity =1.4 TL-s" 1, 17 1 Q 16»T\\\ -0.5 velocity=4.1 TL*J o ximal o Y-axis i in ( Z ==s=pfrfo " <J^ X-axis (cm) X-axis (cm) X-axis (cm) FIG. 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 TLsec 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. 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 of the path of the fin tip relative

9 590 MARK W. WESTNEAT 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 dragbased 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 by 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 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, C) and distal chord (Fig. 5B, D) had a similar angle of attack with respect to direction of motion only at peak adduction {e.g., position 1 in Fig. 5A and C) and peak abduction {e.g., position 8 in Fig. 5C and D). 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 D). 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

10 AQUATIC FLIGHT IN FISHES 591 for lift and the changes in flow vectors due to acceleration reaction. A measure of the ability of the fin to generate circulation around the wing for liftbased 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 of the six major pectoral muscles in Gomphosus varius. EMG data were recorded from 3 individuals over a range of swimming speeds from TL-sec~'. 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 mm apart. Electrodes were threaded through a 25 gauge needle for 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. 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 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 Lab- VIEW 2 software (National Instruments Corp., Austin Texas). The sample rate was 5,000 points per second per channel. The digital record was then analyzed using a custom six channel analysis algorithm using Lab VIEW 2. Each channel was visually inspected to determine the baseline noise level, and a cut-off amplitude was chosen, be-

11 592 MARK W. WESTNEAT 2.0- A 's" 1 mv 0 mv m - H 0.2 time (s) FIG. 6. Electromyograms for six pectoral muscles at 1.7 TLsec ' and 3.8 TL-sec '. 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. low 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 to 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 of 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

12 AQUATIC FLIGHT IN FISHES 593 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 Fig. 6A and B). 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 thefinflip 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. 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 predic-

13 594 MARK W. WESTNEAT FIG. 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. tions 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 (Fig. 8A, C) 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 18 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

14 AQUATIC FLIGHT IN FISHES 593 A 3l B 3 protraction tf /ft <Jretraction Protraction adduction 15 adductor profundus abductor profundus arrector left lateral abductor profundus 11 arrector ventralis FIG. 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. 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 18 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 of 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 advan-

15 596 MARK W. WESTNEAT "a A. arrector ventralis A 3D stroke angle XY plane O YZ plane ^ I I i j.11-- i i * I B. abductor profundus 3D stroke angle 80- XY plane 1 O YZ plane p C. arrector dorsalis 3D stroke angle XY plane O YZ plane i S muscle contraction (%) FIG. 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). tage 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 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 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 of transmitting a greater amount of force from muscle contraction during the power stroke. Because both the arrector ventralis and abductor profundus 16 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 and several areas in need of study to enhance our understanding of propulsion by fin flapping. Hydrodynamic models have largely inspired the field of fin-based 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-sec-'). As Gibb et ai, (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 in-

16 AQUATIC FLIGHT IN FISHES 597 teraction 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 of chord lengths will provide the best estimates of 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 detailed 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 of 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 estimates 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 REFERENCES Aristotle, fourth century B.C. Movement of animals. English translation by E. S. Forster, 1937, Heinemann, London.

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