Functions of Fish Skin: Flexural Stiffness and Steady Swimming of Longnose Gar Lepisosteus Osseus

Aquatic propulsion in many fishes is driven by the progression down the body of alternating lateral flexures. These traveling waves of bending, driven by muscle, alternately stretch and compress the body’s axial structures. The structure likely to undergo the largest reconfigurations, because of its distance from the bending axis of the backbone, is the skin. The skin is in a position to influence, by means of its mechanical properties, much of the body’s undulatory motion. For this reason, we sought to understand the mechanical functions of the skin during swimming. In this study, we tested locomotor hypotheses using in vivo surgical manipulation of skin structure and in situ measurement of the flexural stiffness of the body.

In addition to its anatomical position, several other characteristics of fish skin make its study compelling. First, fish skin varies widely in structure, bearing large ganoid scales in gars (Lepistosteidae) and polypterids (Polypteridae), small scales in sharks (Elasmobranchii) and tunas (Scombridae), and no scales in swordfish (Xiphiidae) and some catfishes (Siluriformes) (Kerr, 1952; Pearson, 1981; Nelson, 1984). In spite of these differences, fish skin appears to possess an underlying structural ground plan – cross-helical fibers of collagen embedded in the dermis (e.g. Fujii, 1968; Motta, 1977; Videler, 1974; Pearson, 1981). Second, skin has a complex two-dimensional stiffness. Circumferential strain stiffens it axially, giving it the capability to transmit axial forces in lemon sharks Negaprion brevirostris (Wainwright et al. 1978) and eels Anguilla rostrata (Hebrank, 1980); however, this capability is lacking in spot Leiostomus xanthurus and skipjack tuna Katsuwonus pelamis (Hebrank and Hebrank, 1986). Third, skin is attached directly to the underlying muscles, putting it in series between muscle and propulsive elements (Pearson, 1981; Westneat et al.1993; Hale, 1996).

The role of skin during swimming has been addressed comparatively. The armored skin of longnose gar Lepisosteus osseus, with its heavy ganoid scales, is associated with reduced swimming performance during fast starts (Webb et al. 1992). When compared with the lightly scaled tiger musky, Esox lucius × Esox masquinongy, gar cover less distance during the early stages of the fast start (Webb et al. 1992). This discrepancy was thought to be caused by the presence of less myotomal muscle mass in gar (38 versus 53 % of total body mass for gar and musky, respectively), leaving gar with only 72 % of the force-generating capabilities of musky. Thus, gar appear to trade muscle mass for skin mass, which leaves them with higher inertia but greater passive predator defense during unsteady swimming. In contrast, Webb et al. (1992) detected no differences in performance during steady swimming that could be attributed to differences in muscle mass. Similar power coefficients and body curvature in both species did not support the hypothesis that armored skin would increase the cost of steady swimming and decrease the flexibility of the body. However, gar swam at much lower critical swimming speeds than did musky (1.9 versus 3.4 L s⁻¹), a difference than cannot be accounted for by the muscle mass difference alone.

Given the potential importance of skin as a locomotor organ, we asked (1) how the skin affects the flexural stiffness of the body and (2) how the skin functions during steady swimming. In terms of the stiffness of the body when the muscles are not operating, termed passive stiffness, we tested two hypotheses. First, we hypothesized that skin should add little to the passive stiffness of the body because of its cross-helical fiber arrangement, which renders a low longitudinal (axial) stiffness (Videler, 1993). Because this hypothesis is based on in vitro measurements, however, an alternative is possible – skin may stiffen the body in axial compression, tension and torsion because its bony scales and attachments to underlying myomeres do not permit it to act as a simple, cross-helical cylinder (Pearson, 1981). In the first case, we predict that any circumferential cut in the skin would not affect the body’s passive flexural stiffness (EI, in N m²); in the second case, we predict that such an effect will occur.

In terms of function during swimming, the flexural stiffness imparted to the body by the skin may play a role in determining the cycle frequency and propulsive wave speed at which the fish chooses to operate (Long and Nipper, 1996).

This wave speed hypothesis follows from work on swimming fish models, which have an undulatory wave speed determined by the flexural stiffness of their bodies (McHenry et al. 1995). We predict that any circumferential cut in the skin, provided that such cuts reduce body stiffness, should alter wave speed in proportion to the change in flexural stiffness. Since wave speed is the product of tailbeat frequency and propulsive wavelength, we would expect to see either kinematic variable decrease with decreases in body stiffness. To maintain thrust power at a given swimming speed with lower body stiffness, either tailbeat amplitude or tail depth (trailing-edge span in the dorso-ventral plane) should increase (see Webb et al. 1984; Wu, 1977).

We tested these predictions in longnose gar because their armored skin, which bears robust ganoid scales (Kerr, 1952), is thought to decrease body flexibility and swimming performance (see Webb et al. 1992). In intact, freshly killed gar, we measured the flexural stiffness of the body before and after cutting the dermis and removing scale rows. This method has the advantage of subjecting skin to more realistic strains compared with in vitro bi-axial tests in which excised skin is stretched independently of underlying muscle and connective tissue. We also measured the swimming performance of live gar before and after surgical treatments in which the fibrous dermis was cut and scale rows were removed. This procedure has the advantage of comparing different skin configuration conditions within a single species.

Longnose gar Lepisosteus osseus Linnaeus were collected from Sweetwater Creek, Martin County, North Carolina, USA, using gill nets. Once set, nets were monitored continually to minimize the amount of time any individual spent entangled. Within 8 h of capture, fish were transported to the Duke University Marine Laboratory, where they were placed in outdoor holding tanks with water temperatures between 22 and 30 °C. Fish were kept for no longer than 2 weeks, during which time they were not fed. The three individuals used for the swimming experiments were 46, 50 and 76 cm total body length (L, tip of rostrum to tip of tail). The three individuals used for the bending experiments were 64, 64 and 71 cm TL.

To measure the mechanical effect of each of the surgical treatments on the passive bending stiffness of the gar’s body, the following tests were conducted. Three freshly killed individuals were mounted in and bent on a testing machine modified from Long (1992). The region of the body at the site of the first (‘dermis cut’ treatment) and second (‘caudal scale row’ treatment) surgical treatments was chosen for examination (Figs 1, 2); the site of the third (‘precaudal scale row’) surgical treatment could not be tested since this region was altered by the gripping procedure. The gar’s body was gripped anterior and posterior to the test site by epoxy-embedded sand cradled in wooden holders that were, in turn, rigidly affixed to the bending machine. The epoxy-embedded sand provided a gripping surface of even pressure distribution and contoured shape.

Each gar was bent quasi-statically at frequencies below 1 Hz. The bending moment (N m) and angular displacement (rad) of the rotating portion of the machine were sampled digitally at 10 Hz using LabVIEW software (National Instruments) and an analog-to-digital converter (National Instruments, model NB-MIO-16L) mounted in a microcomputer (Apple Corporation, model Centris 650). After measuring the unaltered gar, flexural stiffness was measured after the dermis had been cut and finally after the caudal scale row had been removed. Statistical differences between treatments were tested using an analysis of variance (ANOVA) design similar to that described below for swimming kinematics, with individual and skin treatment as the independent variables. Two planned contrasts, unaltered versus dermis cut and dermis cut versus caudal scale row removed, tested differences between means.

In addition to flexural stiffness, the neutral zone of curvature (m⁻¹) was also measured (Fig. 3). The neutral zone of curvature is a region of little or no detectable flexural stiffness (within our resolution of 0.001 N m²) that is symmetrical on either side of the straight (zero curvature) position of the body. The end of the neutral zone was defined as the point prior to that at which the bending moment signal was large enough to be discriminated from zero.

In order to test the hypothesis that the flexural stiffness imparted by the skin to the body plays a functional role during swimming, we developed the following protocol. First, we swam individual fish at body-length-specific steady swimming speeds ranging from 0.250 to 1.000 L s⁻¹ in increments of 0.125 L s⁻¹. An individual was then anesthetized using a 1:10 000 dilution of tricaine (MS-222, Argent Chemical Laboratories); following full sedation (as defined by Summerfelt and Smith, 1990), surgery commenced. In the first surgical treatment, the dermis was cut bilaterally between the caudal scale row eight rows anterior to the dorsal fin and its posterior neighbor (Figs 1, 2; ‘dermis cut’ treatment). This position was chosen because we expected greater axial curvature, and hence skin strain, in the caudal region relative to the precaudal region (Jayne and Lauder, 1995b); also, if skin transmits force to propulsive elements, this scale row should occupy a critical position, being attached posterio-ventrally to the anal fin, which contributes substantially to the production of mechanical power during swimming in gar (Webb et al. 1992). During surgery, care was taken to avoid damaging underlying muscle tissue. The individual was allowed to recover and was video-taped swimming once it had regained full equilibrium and motor control.

For the second surgical treatment, full sedation was again induced and the caudal scale row posterior to the cut dermis was removed bilaterally (Fig. 1; ‘caudal scale row’ treatment). Care was taken to avoid cutting blood vessels. The individual was allowed to recover fully and was then video-taped swimming. During the final surgical treatment, we removed a second scale row, the nineteenth anterior to the dorsal fin (Fig. 1; ‘precaudal scale row’ treatment). The precaudal scale row treatment combined the effects of the first two surgical treatments, since both the dermal incision and scale row removal were completed simultaneously. None of these surgical treatments took more than 20 min and they always involved two investigators, one to perform the surgery and another to monitor the condition of the fish. All three fish recovered from these treatments; after the last series of swimming events, the fish were killed with an overdose of tricaine. To control for the effects of anesthesia, we swam three different individuals that were sedated and handled as if we were performing the aforementioned surgical procedures. Prior to and following the sham surgery, we measured the swimming kinematics of these individuals; no significant differences were detected.

To test the hypothesis that the treatments described above altered the swimming kinematics of the gar, we performed a mixed-model three-way ANOVA, with individual, swimming speed (‘speed’) and experimental treatment of the skin (‘skin’) as the independent variables. All three of these variables were categorical, with individual being the random effect and speed and skin being fixed effects. The interaction of speed and skin was also tested. Individual was analogous to a randomized block effect and, when treated as a main effect, compensated for the within-individuals, repeated-measures design by removing from the error term the variance component caused by individuals (Sokal and Rohlf, 1981). The effects on response variables, which are described in the next section, were tested separately as univariate models; differences between the means of treatment categories were tested with planned a priori contrasts. Prior to statistical testing, the distribution of each response variable was checked for normality by examining residuals, a probability plot, skewness and kurtosis. One variable, total relative power, was transformed to achieve a normal distribution by calculating its natural logarithm. Of the 84 possible data points in this design (three individuals, seven speeds, four skin treatments), four cells were missing for reasons given in the next section. The 46 cm gar was missing one cell – precaudal scales at 0.250 L s⁻¹. The 50 cm gar was missing one cell – unaltered skin at 0.250 L s⁻¹. The 74 cm gar was missing two cells – caudal scales at 0.875 L s⁻¹ and precaudal scales at 0.375 L s⁻¹. All statistical tests were conducted using SAS (SAS Institute, 1985).

We swam gar over a range of swimming speeds in a large flow tank (enlarged and modified from that described by Vogel, 1981) at the Duke University Marine Laboratory. The working section of the flow tank was 1 m×1 m in cross section and 3 m long. The gap-to-span ratio of the tail was always greater than 2, which ensured that individuals did not benefit energetically from wall effects (Webb, 1993). Maximum speeds in this study (1.0 L s⁻¹) were limited by the top speed of the flow tank (80 cm s⁻¹). This maximum speed is roughly half the critical swimming speed (1.9 L s⁻¹) measured in longnose gar (Webb et al. 1992).

Using a mirror mounted at 45 ° above the tank, swimming fish were video-taped (Panasonic model AG-450) at 60 images s⁻¹ at a shutter speed of 0.001 s from above and from a lateral perspective perpendicular to the longitudinal axis of the fish. To quantify swimming motions, 18 points along the dorsal midline and two points from the lateral perspective for the tail depth were digitized using a computer (Commodore model Amiga 3000) and a dynamic-tracking U-matic video deck (Sony model BVU-9200). By electronically overlaying a paused video field (time resolution of 0.017 s) and an electronic cursor, we first manually selected seven landmarks on the axial midline (nose, anterior and posterior margins of pectoral fins, anterior margin of pelvic fins, site of first and second surgeries, and tip of caudal fin). We then evenly filled in the gaps between the landmarks with the remaining 11 points. Trials were digitized only when the individual achieved relatively constant velocity over three consecutive tailbeats (stable position in flow ±0.02 L) and was positioned in the center of the tank. By failing to meet these criteria, the four (out of 84) missing cells described in the previous section were rejected.

In the region of the caudal scale row (see Fig. 1), sequential alteration of the skin increases the neutral zone of curvature and decreases the flexural stiffness of the body (Fig. 4A). For three individuals, the neutral zone of curvature ranged from a mean of 10 m⁻¹ in unaltered gar to a mean of 13 m⁻¹ with the caudal scale row removed (Table 1; Fig. 4B). The flexural stiffness of the body decreased from a mean of 0.065 N m2 in unaltered gar to a mean of 0.050 N m² in gar with the caudal scale row removed (Table 1; Fig. 4C). For both the neutral zone of curvature and flexural stiffness, the only significant differences occurred when the dermis was cut.

When the skin was altered, tailbeat amplitude, tailbeat frequency, wave speed and tail depth showed significant overall effects (Table 2). When live gar had their dermis cut posterior to the caudal scale row, tailbeat frequency decreased across the range of swimming speeds (Fig. 5A), tail depth increased (Fig. 5B) and wave speed decreased (Fig. 5C). In addition, tailbeat frequency increased linearly with increasing swimming speed (Table 2); this relationship can be described by linear regression of the mean tailbeat frequency against speed for gar with unaltered skin (N=7, r²=0.804) as y=0.975+1.655x and for gar with dermis cut (N=7, r²=0.932) as y=0.809+1.531x, where x is the swimming speed (L s⁻¹) and y is the tailbeat frequency (Hz). Tail depth did not vary significantly with changes in swimming speed (Table 2). Wave speed, the product of the tailbeat frequency and twice the posterior half-wavelength, also increased linearly with increasing swimming speed; this relationship can be described, by linear regression, for gar with unaltered skin (N=7; r²=0.854) as y=0.457+0.972x and for gar with dermis cut (N=7, r²=0.957) as y=0.229+0.871x, where x is the swimming speed (L s⁻¹) and y is the wave speed (L s⁻¹).

When live gar had the caudal scale row removed, the mean values of tailbeat amplitude, wave speed and relative total power (pooled across swimming speed) increased relative to the dermis cut values, by 25 %, 29 % and 64 %, respectively. Note that the increase in relative total power, independent of swimming speed, indicates that the percentage thrust (fraction of useful power) generated by the undulatory wave has decreased. When the precaudal scale row was removed, no significant changes were detected.

While showing no significant changes when the dermis was cut, four variables changed significantly with swimming speed (Table 2; Fig. 6). Tailbeat amplitude increased with increasing swimming speed (Fig. 6A) in a manner described by the following regression equation for gar with unaltered skin (N=7; r²=0.612), y=0.091+0.018x, and for gar with dermis cut (N=7, r²=0.321) y=0.072+0.034x, where x is the swimming speed (L s⁻¹) and y is the tailbeat amplitude (L). Relative total power increased with increasing swimming speed (Fig. 6B) in a manner described by the following regression equation for gar with unaltered skin (N=7; r²=0.812), y=−0.095+13.667x, and for gar with dermis cut (N=7, r²=0.604) y=−3.070+18.483x, where x is the swimming speed (L s⁻¹) and y is the relative total power (×10⁻⁹). While there was a significant overall effect of speed on maximal curvature of the axial midline (Table 2; Fig. 6C,D), planned contrasts detected a significant effect only between speeds of 0.250 and 0.375 L s⁻¹.

The only kinematic variables for which no significant effect of skin treatment or swimming speed could be detected were the anterior and posterior half-wavelengths (Table 2; Fig. 7). The mean value of the anterior half-wavelength was 0.335±0.0426 L (±S.E.M.; N=28 with individuals pooled). The mean value of the posterior half-wavelength was 0.276±0.0291 L (±S.E.M.; N=28 with individuals pooled).

Finally, for all the kinematic variables except anterior half-wavelength and wavespeed there were significant individual effects (Table 2). Since we were interested in generalizing our results across individuals, these effects were not explored further. Note that individual effects do not influence the significant results for skin treatment and swimming speed; this is analogous to treating individual as a randomized block effect without replication (Sokal and Rohlf, 1981).

In the mechanics of undulatory swimming, the skin of longnose gar plays an integral role: it passively stiffens the body, and the magnitude of this stiffness, in turn, influences the cycle frequency and propulsive wave speed at which the gar chooses to operate. Support for this hypothesis comes from experiments involving in vivo surgical manipulation of skin structure and in situ measurement of the flexural stiffness of the body.

The present experiments are the first to test, in live fish, the hypothesis that flexural stiffness of the body alters swimming mechanics (Blight, 1976, 1977; Long et al. 1994; McHenry et al. 1995) in a manner consistent with engineering theory of forced, harmonically oscillating beams (see Den Hartog, 1956; Long and Nipper, 1996). As predicted, when the dermis is cut between two caudal scale rows (Figs 1, 2), the passive flexural stiffness decreases (Fig. 4C) and the tailbeat frequency and propulsive wave speed decrease (Fig. 5A,C). This hypothesis has also been supported in swimming experiments on dead, electrically stimulated sunfish (Long et al. 1994) and flexible sunfish models (McHenry et al. 1995). Thus, in the case of longnose gar, it appears that the skin, and the dermis in particular, functions to stiffen the body – passively – and hence increase the tailbeat frequency at which the gar chooses to operate. Tailbeat frequency, in turn, controls the propulsive wave speed, and both variables are important in the production of thrust power by the undulatory wave (see equation 4).

If, at any single swimming speed, tailbeat frequency decreases when the dermis is cut, how are surgically altered gar able to generate enough hydrodynamic power to maintain their speed? Gar compensate for the loss of hydromechanical power (see equation 4) by increasing tail depth (Fig. 5B), which maintains the relative total power at any given swimming speed (Fig. 6B).

In addition to the importance of the dermis, the functions of the skin of gar may also depend on the scale rows. In polypterid fish, which also possess bony ganoid scales, Pearson (1981) has suggested that the dermis resists axial tension, that the scale rows resist axial compression and that the dermis and scale rows function together to resist axial torsion. It is reasonable to assume that the same principles operate in longnose gar, since their dermis and scale rows are similar in construction and arrangement to those of polypterids (Kerr, 1952). In gar, when the caudal scale row is removed, the tailbeat amplitude, wave speed and relative hydrodynamic power increase. Since removal of the scale row does not, however, alter the bending properties of the body (Fig. 4), it is difficult to interpret the functional significance of the associated kinematic changes. In addition to the resistance of axial compression (Pearson, 1981), scale rows may also function to resist medio-lateral compression applied by the underlying muscles. In mackerel and tuna, which lack ganoid scales, internal muscle pressure may resist medio-lateral compression of the body, allowing the muscles to use the skin and its associated connective tissues as a pulley for the myotomes (Westneat et al. 1993). In seahorses, the unusual axial muscles attach directly to the dermal plates which, in turn, are connected to the backbone; muscle contraction in the tail thus appears to bend the body by transmitting forces directly to the dermal structures (Hale, 1996). The myomeres of gar are attached to the scales by discrete connections (Fig. 2); a single hypaxial myotome attaches to several scale rows epaxially and a single scale row hypaxially (Gemballa, 1995). Muscle pressure may not be needed to resist compression in species with ganoid scales, since the robust and bony scales are tightly bound within a scale row and provide substantial resistance to circumferential deformation (Kerr, 1952; Pearson, 1981; Brainerd, 1994; Gemballa, 1995). Thus, on the basis of this structural organization, we propose that a gar’s scale row resists medio-lateral forces, providing myomeres with leverage and anchorage for pulling serial tendons and bending the body (Fig. 8). If this is how the scale row functions, its removal might possibly have caused the changes in swimming kinematics detected in this study. However, our experimental design does not test this model. To do so properly, muscle–skin attachments or medio-lateral stiffness would need to be altered while the relationship between muscular bending moments and body bending during swimming was directly measured.

The final experimental treatment yielded intriguing results. When the precaudal scale row was removed, the swimming kinematics did not change. Even though the effect of this treatment on flexural stiffness was not measured, it is reasonable to predict that the associated simultaneous loss of dermal connection and muscle attachment should lower bending stiffness in a manner similar to that described for the caudal skin treatments (Fig. 4). However, the precaudal region of gar does not bend as much as the caudal region beyond the neutral zone of curvature (compare Fig. 4B with Fig. 6C). Thus, the precaudal region of the body never bends enough to be influenced by the lower flexural stiffness caused by the cutting of the dermis and removal of the scale row; hence, the function of the skin may vary regionally.

As far as we know, these are the first measurements of the flexural stiffness of fish skin in situ. From the measurement of a substantial neutral zone (Fig. 4B), it appears that the skin of unaltered longnose gar permits bending at small curvatures and resists bending at high curvatures. Maximal curvature of the axial midline (Fig. 6D, caudal scale row), is approximately 15 m⁻¹ at most swimming speeds; this is approximately 5 m⁻¹ beyond the neutral zone of curvature of 10 m⁻¹ (Fig. 4B). Thus, the flexural stiffness of the skin beyond the neutral zone (Fig. 4C) functions to decelerate the lateral motion of the body. In this way, the skin passively performs a function, deceleration, that might otherwise be muscularly controlled; it does so without incurring additional mechanical work over much of the tail stroke because of the neutral zone.

How is skin organized to create both a neutral zone and bending resistance? The dermis connecting adjacent scale rows appears to play a key role (Fig. 2), since its absence significantly increases the neutral zone and decreases flexural stiffness (Fig. 4B,C). At low curvatures, it appears that the dermis is slack on both the concave and convex sides of the body. The low resistance of the neutral zone ends when the dermis is placed in tension, and resistance to bending is developed. In this model, which is similar to that developed by Pearson (1981) for polypterid fishes, the function of the bony ganoid scales is to resist compressive forces (Fig. 8). As our bending data show, however, the scale rows are necessary but not sufficient for significantly greater flexural stiffness (Fig. 4C). Our model of axial skin strain in gar is different from, but complementary to, that for circumferential strain developed by Brainerd (1994) for polypterids. In polypterids, the tissues within scale rows store elastic energy, with the connective tissues deforming and recoiling as cross-sectional shape changes during lung ventilation (Brainerd, 1994). In gar, the tissues between scales rows determine the important mechanical properties. It is likely that both models apply only to fishes with armored or heavily scaled skin.

The gar’s axial musculo-skeletal system is unusual in its lateral flexibility. When the dermis is cut and the caudal scale row is removed, the remaining muscle and backbone still show a neutral zone (Fig. 4). This is a surprising result, given that the backbones of other fishes show no such neutral zone (Hebrank, 1982; Hebrank et al. 1990; Long, 1992; J. H. Long, 1995). Gars are the only fish with opisthocoelous joints, with the centrum convex anteriorly and concave posteriorly (Goodrich, 1930). In a manner yet to be determined, this unusual intervertebral joint design may play a role in creating the neutral zone. Neutral zones are also present in the intervertebral joints of mammals, which possess an intervertebral joint with flat articular surfaces on the centra; Gal (1993) describes a range of neutral zones from 2 to 18 ° in rabbits and seals, respectively, with intermediate values for monkey, wallaby, tiger and jaguar.

An excellent predictor of swimming speed in gar is the speed of the propulsive wave (Fig. 5C). If, as we propose above, wave speed is determined by the passive and active stiffness of the body, then we would predict that the range of steady swimming speeds is modulated by muscles generating negative work and, in consequence, stiffening the body. The alternative hypothesis is that flexural stiffness remains constant and that the muscles increase mechanical power output solely through increased positive work. Tests of these hypotheses await our ability to measure in vivo muscle force.

The first vertebrates, which appeared some 450 million years ago, are characterized by the presence of external, dermal bone (J. A. Long, 1995). An extensive exoskeleton is clearly seen in the oldest complete fossil fish, Sacabambaspis, with articulated plates, oriented in obliquely inclined scale rows, covering the body (J. A. Long, 1995). While the first robust exoskeletons are often interpreted as adaptations against predation (e.g. J. A. Long, 1995; Carroll, 1988), the presence of ganoid scales in living gar and polypterids has other mechanical consequences, including enhanced station-holding (Webb et al. 1992) and passive lung inflation (Brainerd et al. 1989; Brainerd, 1994). Furthermore, the results of this study demonstrate that armored skin can play a central role in the control of body stiffness and undulatory wave motion during steady swimming. Hence, any ‘how-possibly’ explanation (sensuBrandon, 1990) of early vertebrate adaptations should consider that armored skin may represent an alternative rather than a maladaptive solution to the evolutionary challenges of aquatic locomotion.

The authors wish to thank Julia Parrish, Steve Vogel and Carlton Heine for the design and fabrication of the flow tank, Charles Pell for the design of the bending grips, Bill Kirby-Smith for logistical support at the Duke Marine Laboratory, and Bart Shepherd, Robert Suter, Steve Wainwright and two anonymous reviewers for constructive comments on the manuscript. J.H.L. and M.J.M. were supported by a grant to J.H.L. from the Office of Naval Research (N00014-93-1-0594). M.E.H. was supported by a Howard Hughes Predoctoral Fellowship. M.W.W. was supported by a grant from the National Science Foundation (IBN-9407253). Members of the Biomechanics Advanced Research Kitchen at Vassar College were instrumental throughout this project.