The Journal of Experimental Biology 202, 529–541 (1999) 529 Printed in Great Britain © The Company of Biologists Limited 1999 JEB1633

MUSCLE STRAIN HISTORIES IN SWIMMING MILKFISH IN STEADY AND SPRINTING GAITS

STEPHEN L. KATZ*, ROBERT E. SHADWICK AND H. SCOTT RAPOPORT Center for Marine Biotechnology and Biomedicine and Marine Biology Research Division, Scripps Institution of Oceanography, La Jolla, CA 92093-0204, USA *Present address and address for correspondence: Zoology Department, Duke University, PO Box 90325, Durham, NC 27708-0325, USA (e-mail: [email protected])

Accepted 10 December 1998; published on WWW 3 February 1999

Summary Adult milkfish (Chanos chanos) swam in a water-tunnel over that speed range, while tail-beat frequency increased flume over a wide range of speeds. Fish were instrumented by 140 %. While using a sprinting gait, muscle strains with sonomicrometers to measure shortening of red and became bimodal, with strains within bursts being white myotomal muscle. Muscle strain was also calculated approximately double those between bursts. Muscle strain from simultaneous overhead views of the swimming fish. calculated from local body bending for a range of locations This allowed us to test the hypothesis that the muscle on the body indicated that muscle strain increases rostrally shortens in phase with local body bending. The fish swam to caudally, but only by less than 4 %. These results suggest at slow speeds [U<2.6 fork lengths s−1 (=FL s−1)] where only that swimming muscle, which forms a large fraction of the peripheral red muscle was powering body movements, and body volume in a fish, undergoes a history of strain that is also at higher speeds (2.6>U>4.6 FL s−1) where they similar to that expected for a homogeneous, continuous adopted a sprinting gait in which the white muscle is beam. This has been an implicit assumption for many believed to power the body movements. For all studies of muscle function in many fish, but has not been combinations of speeds and body locations where we had tested explicitly until now. This result is achieved in spite simultaneous measurements of muscle strain and body of the presence of complex and inhomogeneous geometry bending (0.5 and 0.7FL), both techniques were equivalent in the folding of myotomes, collagenous myosepta and predictors of muscle strain histories. Cross-correlation tendon, and the anatomical distinction between red and coefficients for comparisons between these techniques white muscle fibers. exceeded 0.95 in all cases and had temporal separations of less than 7 ms on average. Muscle strain measured using Key words: fish, swimming, Chanos chanos, milkfish, sonomicrometry within the speed range 0.9–2.6 FL s−1 sonomicrometry, locomotion, musculo-skeletal mechanics, showed that muscle strain did not increase substantially biomimetics.

Introduction The myotomal swimming muscle of fish is arranged as a assumptions that each myotome is mechanically linked to its series of interconnected blocks that lie along each side of the neighbors and that the force trajectories that they generate must body. Anatomically, this represents a departure from the pass from one myotome to the next along the body. In this familiar vertebrate locomotor design, and understanding the model, the wave of undulation represents the accumulation of mechanical consequences of the myotomal system is an muscle strain history along the body. As a consequence, each important goal of current research in fish biomechanics. The muscle acts locally – i.e. lateral bending produced by muscle present study investigates the magnitude and phase contraction occurs at approximately the same location on the relationships between the strain of myotomal muscle and local body as the muscle itself. If true, then one can calculate muscle body curvature in a representative teleost, the milkfish (Chanos strain amplitude and phase from body kinematics, specifically, chanos). from midline curvature. Over a hundred years ago Sir George Cayley proposed that Importantly, fish myotomes are not cubic blocks but are the swimming movements of trout resulted from the sequential highly folded and nested together in the longitudinal body axis activation of the blocks of muscle segments on each side of the (Nursall, 1956; Jayne and Lauder, 1995b). Consequently, one body, thus generating a wave of undulation that traveled myotome may span several intervertebral joints. Furthermore, posteriorly (Bone et al., 1995). This synthesis was based on the adjacent myotomes are separated by collagenous myoseptal 530 S. L. KATZ, R. E. SHADWICK AND H. S. RAPOPORT sheets that serve as insertion sites for the muscle fibers within captured with nets and transported to the Kewalo Basin each myotome and attach to the vertebral midline and the skin laboratory facility of the National Marine Fisheries Service in (Wainwright, 1980; Westneat et al., 1993). An additional Honolulu, Hawaii, USA. Of all individual fish examined in this feature is the anatomical distinction between functionally study (eight), only four produced data that met the selection different muscle fiber types. In most fishes, red fibers (used for criteria for all components of this study. Therefore, the sample low-intensity sustained swimming) are located in a lateral size for all statistical comparisons or descriptions represents wedge of parallel-fibered muscle close to the skin. White fibers the contribution of four fish. Fish were maintained in circular (used for high-intensity burst swimming) comprise the bulk of ponds 7 m in diameter and 1.2 m deep with a constant flow- the nested cones of muscle in the myotomes (Bone, 1966; through of sea water. Fish were fed frozen squid and mackerel Rome et al., 1984; Jayne and Lauder, 1993). This complex daily and also consumed green algae in the tanks. All fish used geometry makes it difficult to identify discrete force in this study were maintained in good health and feeding for trajectories across myotomes a priori, and therefore difficult long periods (more than 3 months) before being used in to accept or reject Cayley’s model. experiments. The temperature was maintained at ambient Although several studies of fish muscle dynamics have used ocean temperatures (approximately 20–24 °C) and ambient body curvature to calculate muscle strain amplitude and phase light cycles. Fish chosen for this study ranged from 1440 to (Videler and Hess, 1984; van Leeuwen et al., 1990; Rome et al., 2160 g in mass and from 45.6 to 51.3 cm in fork length (FL). 1993; Johnson et al., 1994), i.e. accepting Cayley’s assumption Post mortem examination indicated that the lateral red muscle that muscle contractions cause local bending, very few have extended from 0.25FL to the caudal peduncle at 0.95FL. attempted to verify the validity of this approach by comparison However, the wedge of lateral red muscle tapers at its rostral with direct strain measurements. One such method involves and caudal terminations. Rostral to a location of 0.3FL, the sonomicrometry, a technique that gives very accurate cross-sectional area of red muscle is 0.6 cm2, or less than 2 % measurements of the distance between two small piezoelectric, of total muscle area, and less than 10 % of the average red ultrasound probes that can be implanted in live tissue. If the muscle cross-sectional area from 0.3FL to 0.85FL. Caudal to probes are aligned with the shortening axis of muscle fibers, they a location of 0.85FL, the red muscle tapers to less than 0.4 cm2. give a direct and real-time measurement of the muscle strain. In Surgical procedures followed guidelines for animal care laid a sonomicrometry study of steady swimming in scup Stenotomus out by the animal subjects committee of the University of crysops, Coughlin et al. (1996) concluded that local body California, San Diego, CA, USA. Fish were anesthetized via bending, using simple beam theory, accurately predicted strains immersion in an oxygenated solution of MS-222 in superficial red muscle. In contrast, sonomicrometry of fast- [Finquel:methane tricaine sulfonate (Argent Chemical starts in trout Oncorhynchus mykiss led Covell et al. (1991) to Laboratories), 1:1000 (w/v) in sea water] buffered with sodium conclude that shortening of deep white muscle produced bending bicarbonate or Tris base (pH≈7.8). During surgery, the animal at more caudal locations and thus that local curvature was not a was supported on a chamois cradle and ventilated with a more good predictor of muscle strain. These two results are not dilute solution of oxygenated, buffered MS-222 (1:17500). necessarily incompatible and may, in fact, represent differences Swimming protocols were performed in a swim-channel in the organization of force transduction pathways in the treadmill described previously (Korsmeyer et al., 1997). The different fiber types. However, at this point, we cannot resolve tunnel has a volume of 3000 l. It is instrumented to monitor whether it is valid to calculate white muscle strain from midline and maintain temperature and O2 content. The maximum kinematics or whether the complex myotomal geometry working section dimensions are 113 cm (length) × 22.5 cm constrains the muscle from deforming as a homogeneous beam. (width) × 32.5 cm (height) (cross-sectional area 731 cm2). The In this study, we have used video image analysis and water tunnel has a mirror above the working section tilted at sonomicrometry to determine the time course and amplitude of 45 ° so that a camera located to the side of the tunnel can obtain strain in red and white muscle of milkfish during steady dorsal views of the swimming fish. A correction for solid swimming gaits powered by red muscle, as well as in high- blocking was employed in the manner of Bell and Terhune speed burst swimming involving white muscle. By comparing (1970) to correct the swimming speeds of the fish. A reference the strains measured ultrasonically with those calculated from grid on the floor of the working section of the swim tunnel local curvature, we can test the following hypothesis: that body provided a scale for spatial measurements. Spatial bending during swimming occurs as it would in a continuous measurements required a small correction for parallax that beam, with the consequence that muscle strain can be results from the fish being closer to the camera than to the floor calculated from midline kinematics, and that this is true of the tunnel. This was accomplished by normalizing all whether the movements are powered by red or white muscle. measurements by the ratio of the actual distance from the rostral tip of the fish to the location of a reflective dorsal marker (measured post mortem) to the apparent distance (measured in Materials and methods the video image with respect to the reference marks on the floor Fish collection and husbandry of the tunnel). Swimming data were not used if the fish did not Adult specimens of milkfish (Chanos chanos Forskål) were maintain a constant speed (i.e. remain over the working section obtained from Hawaiian farm stocks. Individuals were at a given flow rate) for at least 30 s. Muscle strain in swimming milkfish 531

Kinematic data were collected using video and required the outside of the fish using any device other than the thin lead placement of a reflective marker as a positional reference on wires. Also, the insertion point at the skin was located dorsally the dorsal surface of the fish. A small (<3 mm diameter) disk at least 3 cm from the position of the crystals within the muscle of reflective material (ScotchLite, 3M) was single-sutured in all cases, with the lead wires threaded subcutaneously from superficially along the dorsal midline just rostral to the first the crystals to the skin surface. This is a distinct approach from dorsal fin, which corresponds to the approximate location of that adopted by Coughlin et al. (1996), who anchored their the minimum amplitude of lateral motion of the fish during crystals close to the skin. If significant shear between the skin swimming. and the immediately subcutaneous muscle were to occur, we Since water-tunnel speed was easily varied, we could felt that anchoring the crystals immediately under the insertion observe muscle strains at arbitrary swimming speeds to see point would force the probes to track the strain in the skin whether the fish altered the amplitude of muscle strain to swim rather than in the subcutaneous muscle. faster. Since sonomicrometry data are sampled relatively Sonomicrometry is subject to two important artifacts related continuously in time, we used sonomicrometry to examine the to the alignment of the crystals. First, it is important to maintain relationship between strain amplitude and swimming speed. the alignment of the planar acoustic emission and receiving Since the video images were sampled discretely in time, but fields of the crystals. During implantation of the arbitrarily in space, we used the video-image analysis to sonomicrometry probes, the envelope of the arriving acoustic calculate muscle strains as a function of body location. signal is monitored on an oscilloscope. A sharp or abrupt envelope of the 5 MHz signal was indicative of good crystal Sonomicrometry alignment. The position of the crystals could be manipulated The sonomicrometry probes consist of small piezoelectric during surgery to obtain good alignment before the wires were crystals. Each dimension to be measured required two crystals, sutured in place, anchoring the crystals. Second, preliminary, one an acoustic (5 MHz) emitter and one a receiver, which trial-and-error experimentation indicated that it was possible to were 2 mm long and 2 mm diameter tubular sections obtain good alignment of the acoustic emission and receiving (Sonometrics Corporation, London, Ontario, Canada). fields of the crystals, but poor alignment of the axis between Individual crystals were attached to 30 gauge, Teflon-coated the crystals with the shortening axis of the muscle fibers. This lead wires. Each crystal had an epoxy coating which created produced results that were good measurements of the distance an acoustic lens. The circular cross section of the crystal tubes between the crystals, but poor indices of muscle shortening in and epoxy coating together created a predominantly planar the presence of confounding lateral bulging of the contracting acoustic emission field that facilitated alignment of the crystal muscle. In all cases, the exact location of the sonomicrometry pairs. These probes were threaded down a tunnel in the muscle crystals was determined during a post mortem examination. If produced by the previous insertion of a 14 gauge needle. Each crystal orientation was not clearly aligned with the muscle probe was anchored by suturing the lead wires at the skin shortening axis, the data from that fish were discarded. All surface. wires were collected in a slim bundle at the skin surface and Three pairs of probes were implanted to obtain simultaneous passed out of the swim tunnel. The sonomicrometry probes muscle strain measurements from three locations within the resided in the muscle for the duration of the experiment. muscle on the left side of each fish. Two probe pairs were The crystals were controlled using a Triton System-6 introduced into the superficial red muscle in two longitudinal sonomicrometry unit (Triton Technology Inc. San Diego, CA, locations identified pre-operatively as 0.5FL and 0.7FL. At the USA). The sonomicrometry unit generates the timing signal anterior of these two longitudinal locations, one pair of that excites the emitter crystal and changes the state of a sonomicrometry probes was also placed in the myotomal white bistable circuit. Detection of the arrival of the acoustic signal muscle at a depth approximately half-way between the skin and at the receiver crystal is monitored and resets the state of the backbone. Exact locations of the crystal pairs were measured bistable circuit. The time between changes in the bistable during a post mortem examination. For all fish (N=4), the mean circuit is integrated and then converted into a d.c. output that longitudinal position of the anterior crystal pair was is sampled as an analog signal by the computer-based data- 0.54±0.02FL (mean ± S.D.), and the mean longitudinal position acquisition system and multiplied by the speed of sound of the posterior pair was 0.72±0.01FL. The mean depth of the through muscle to calculate the distance between the crystals. crystal pairs placed in the deep location was 1.71±0.19 cm The sonomicrometer has an output filter with a 5 ms delay. This below the skin, which corresponded to the mid-thickness of the was removed from the muscle strain time bases. All three fillet. The mean resting distance between the crystals was sonomicrometer channels, as well as the light-emitting diode 1.4±0.2 cm, or less than 3 % of the mean fork length. (LED) time synchronizing signal (see below), were sampled at If our hypothesis were to prove false, a consequence would 500 Hz. Failure of the sonomicrometer to detect correctly the be that the muscle might shorten out of phase with the adjacent arrival of the acoustic signal resulted in a ‘drop-out’, or short- skin and skeleton. Therefore, it was necessary to prevent the duration, large-magnitude spike in the d.c. output of the anchoring of the sonomicrometry probes from limiting the sonomicrometer. These drop-outs were removed from the data potential motion of the probes themselves as much as possible. by linear interpolation between the data immediately preceding This was achieved by not anchoring the crystals from the and following the drop-out. If the drop-out duration was 532 S. L. KATZ, R. E. SHADWICK AND H. S. RAPOPORT greater than three consecutive 500 Hz samples, the data set was hand margins of the fish when viewed from above. We then discarded. After being sampled and calibrated, the averaged the coefficients of these polynomials to determine a sonomicrometry data were low-pass-filtered with a finite polynomial function for the position of the midline of the fish. impulse response filter using a Blackman window with a −3dB Fig. 1 shows a representative image from a video sequence, as cutoff of 60 Hz and roll-off of 70 dB per decade. well as the sequence of points used to define the body midline. Each of the margins was described by 30–45 points. As shown Video image analysis in Fig. 1, the most rostral digitized location was actually caudal Swimming kinematics were measured from overhead views to the tip of the snout. To maximize the spatial resolution of of swimming fish, collected on video using a single camera and the digitizing process, the image captured on video was the tilted 45 ° mirror. The video images were synchronized to enlarged to the point where the end of the rostrum was no the sonomicrometry data using a flashing LED in the video longer in the field of view. It was decided that, since there is field of view. The excitation voltage of the LED was sampled little or no bending of the bony skull, the absence of points in as an additional channel in the data-acquisition system. This this region was reasonable to improve spatial resolution. The technique has been employed successfully in the study of coordinates of the digitized points were normalized in the x swimming in mackerel and tuna (Shadwick et al., 1998). Fish direction (i.e. the direction of travel) to the position of the were filmed at 60 Hz with a CCD VHS camera, and the images reflective marker located on the dorsal midline. Since were stored on video tape. Images were downloaded to polynomial fits are less reliable near the extremes of the data, computer via a RasterOps video-interface board (RasterOps points were digitized over a longer portion of the body than Corporation, Santa Clara, CA, USA), and coordinates were that containing red muscle (approximately 0.2–0.95FL, see measured using NIH Image software (National Institutes of Fig. 1) to provide the best possible estimate of body bending Health, Bethesda, MD, USA). A minimum of four tail beats over the region of the body that is of interest (0.3–0.8FL). was digitized for each swimming sequence. Since the camera Calculations of curvature and strain, however, were only made collects images at 60 Hz, but tail-beat frequency increases with over the region of the body that did contain red muscle. The swimming speed, there were different numbers of fields per tail fourth-order polynomial curve was fitted to the coordinates of beat at the different speeds. The lowest temporal resolution of the digitized points using a least-squares algorithm that 15 points per tail beat period occurred at the highest speed of employed Gaussian elimination to optimize the coefficients of 4.6 FL s−1, when the fish employed a tail-beat frequency of the polynomial (Walpole and Myers, 1989). The fits of the 3.9 Hz. Repeated digitization and measurement of a known test polynomial exceeded an r2 of 0.98 in all cases. Therefore, each object indicated that the spatial resolution of the system was fitted curve defined a function of position in space, z(x), that less than 1.0 mm, or ±0.2 % FL. The location of the midline of described the lateral undulation of the body at one moment in the fish in each image was determined by fitting a fourth-order time. As pointed out elsewhere, there is a geometric difference polynomial function to the points defining the left- and right- between this lateral deflection of the body and the curvature of

Fig. 1. (A) A single video image of a milkfish swimming at 3.9 FL s−1, where FL is fork length. The digitized points used for calculating the functions that describe the left and right margins of the fish are displayed. The points are magnified by five diameters to identify them in this view, the actual points were smaller. The location of the dorsal reflective marker used as a positional reference is indicated with a cross. The image is viewed through a 45 ° mirror; thus, the left side of the fish is up and the right side is 21 down. The shaded bar indicates the longitudinal B extent of the calculated strain in red muscle. 17 Note that the digitized points span a greater longitudinal range than the region over which 13 strain was calculated. The arrows indicate the longitudinal locations of the sonomicrometer 9 crystals placed in this particular fish (0.52L and Lateral position (cm) 0.71L). (B) Example of the fourth-order 5 -10 10 40 polynomial curves fitted to the points defining 0 20 30 the left- and right-hand margins of the fish Longitudinal position (cm) shown in A as well as the averaged polynomial that describes the body midline position. The ordinate has been positioned such that the reflective dorsal marker in A has a coordinate of zero on the abscissa. Muscle strain in swimming milkfish 533 the body (Jayne and Lauder, 1995a; Katz and Shadwick, 1998). history of muscle strain using cross-correlation. This approach Curvature of the line at each point on the line, κ(x), was amounts to calculating the correlation coefficient between two calculated in the same manner as by van Leeuwen et al. (1990) time series and then sliding one of these series relative to the using the following equation: other in time and determining the correlation between the time z′′(x) series as a function of the time shift or lag applied. Coefficients κ(x) = –––––––––– , can vary between −1 and 1, with values close to unity [1+z′(x)2]2/3 indicating that the two time series are good indicators of each where the first and second derivatives of z(x) with respect to x other. Cross-correlation coefficients that are close to unity, but are indicated by z′(x) and z″(x), respectively (Shanks and with large lags indicate that, while the two time series are good Gambill, 1969). Calculations of strain (ε) were made from predictors of each other, they do not co-occur in time. In this these images assuming that the body of the fish was a study, a large lag would indicate that the muscles are not continuous beam. If the body of the fish were truly a shortening (as indicated by sonomicrometry) in phase with continuum, local ε in a peripherally located swimming muscle local body bending and our hypothesis that the body is bending a distance q away from the body midline on the left side would like a beam would not be supported. Analysis of variance be −qκ (van Leeuwen et al., 1990; Katz and Shadwick, 1998). (ANOVA), confidence intervals and cross-correlation Measurements of q(x) were made by subtracting the left-hand coefficients were calculated using Statgraphics Plus for margin of the body at each position x from the estimated Windows (version 2.1, Manugistics, Inc. Rockville, MD, midline at position x when z′(x) was zero. The muscle strain at USA). a position x, ε(x), was simply the product −q(x)×κ(x). Calculations of derivatives and curvature were made using MathCad software (MathSoft Inc., Cambridge, MA, USA). Results In the same manner as outlined in Katz and Shadwick General results (1998), the phase relationships between the functions for z and In this study, we observed milkfish swimming over a wide κ were determined by performing a Fourier transform of the range of speeds. The lowest speed observed was 0.9 FL s−1, and data at each position on the body. Data that progressed through the highest swimming speed was 4.6 FL s−1. All fish time were created by taking each function for z(x) and κ(x) for demonstrated two gaits. Fish demonstrated a steady swimming one video field and appending them onto the previous video gait at speeds below 2.6 FL s−1. Steady swimming was fields to create a function describing the body deflection, z(x,t), characterized by relatively regular and symmetrical and the body curvature, κ(x,t). This function could then be oscillations in tail-beat amplitude and muscle strain. An sampled in the appropriate direction to produce the function example of the muscle strains calculated using z(t) or κ(t) and then Fourier-transformed to generate the sonomicrometry during a 6 s segment from a 30 s bout of magnitude and phase for the swimming frequency at each steady swimming is displayed in Fig. 2A. These data are position of the body. Differences in phase between z and κ representative of the modest beat-to-beat variability observed were calculated by subtracting the phase of one variable from in muscle strain amplitude as well as the regularity of the tail- the phase of the others at each point on the body. To facilitate beat frequency exhibited in this gait. Muscle strain excursions comparison with other data sets, we have presented the phase in this gait had a characteristic frequency at each swimming as fractions of a cycle, with the lateral excursions of the tail tip speed. At speeds above 2.6 FL s−1, fish switched to a different defining a relative phase of zero. The use of fractions of a cycle gait characterized as sprinting. Fig. 2B gives an example of the means that half a cycle is equal to 0.5 on the ordinate and is muscle strain history displayed during a 6 s segment sampled equivalent to 180 °, or π/2. Since the body undulation waves from a 30 s bout of sprint swimming from the same location progress rostrally to caudally in time, they precede the phase and the same fish as in Fig. 2A. This gait consisted of a small of the tail and are negative in sign. Additionally, the wave of number, typically one or two, of large-amplitude tail beats κ arrives at a point on the body earlier than does the wave of separated by three or four smaller-amplitude tail beats that z, and so the relative phase for κ is more negative than for z. were similar to, but not as regular in frequency as, the tail beats The frame of reference is defined such that lateral deflection displayed during steady swimming. Indeed, those muscle (i.e. z) to the right side of the fish is negative and to the left shortening events immediately following a large-amplitude side of the fish is positive. To express a characteristic strain for burst were generally smaller and slower than those a particular swimming speed or location on the body, strains immediately preceding a burst. These characteristics of the are rectified and the peaks measured and averaged for each data variability in muscle strain during the sprinting gait were set. These are referred to as maximal or peak strains. reflected in the tail-beat amplitude measured from video recordings (see below). Statistics and analysis of time series Since the fish were able to maintain position in the working Estimates of strain based on sonomicrometry and those section of the swim tunnel for at least 30 s using either of these based on image analysis can deviate in two ways; either in gaits, the distinction between steady swimming and sprinting magnitude or in phase. We have described the agreement, or is used here to indicate that at lower speeds the gait had a lack of agreement, between these two estimates of the time characteristic frequency, but that at higher speeds it clearly did 534 S. L. KATZ, R. E. SHADWICK AND H. S. RAPOPORT

A Steady swimming Fig. 2. (A) A 6 s example of muscle strain 8 recorded using sonomicrometry from a 6 milkfish swimming steadily at 1.62 FL s−1, 4 where FL is fork length, with a tail-beat 2 frequency of 1.88 Hz. These data are for red 0 muscle strain occurring at 0.51FL. (B) A 6 s -2 example of muscle strain from a milkfish -4 sprint-swimming at 3.03 FL s−1. These data Muscle strain (%) -6 -8 are from the same fish and for the same 0 1 2 3546 anatomical location as in A. Note that the B Sprint swimming muscle strain scale is different in A and B. In 18 contrast to A, the data in B show the 12 variability in frequency. Large-amplitude muscle strains associated with large-amplitude 6 tail beats in the burst portion of the gait are 0 indicated by the shaded regions. These muscle -6 excursions are distinctive in having a shorter

Muscle strain (%) -12 period and greater amplitude than either the -18 inter-burst muscle excursions in B or the 0 1 2 3546 steady swimming excursion shown in A. Time (s) not. Anticipating that the large-amplitude tail beats seen during muscle at the 0.53FL location was 0.95 with zero lag, while sprint swimming are different in character both from the the coefficient for the deep white muscle at the same location steady-swimming gait and from the inter-burst tail beats, we was 0.98 with zero lag, and the coefficient for the red muscle have separated the muscle strain data during bursts from those at the 0.71FL location was 0.97 with a zero lag. For these data, during non-burst tail beats for the purposes of statistical the mean strain is 7.5 % for superficial red muscle and 4.25 % analysis. for the white muscle at 0.53FL; the mean strain is 10 % for the Fig. 3 is a plot of tail-beat frequency (fTB) as a function of red muscle at 0.71FL. swimming speed (U) for all fish that met the selection criterion Fig. 5 presents the calculated muscle strain for five tail beats (N=4). Below a speed of 2.6 FL s−1 (i.e. over the range of from the same fish shown in Fig. 4, in this case swimming at steady swimming speeds) the data fit a linear relationship between frequency and speed very well (fTB=0.98U+0.12; 2 5 r =0.94, Fs=308.36, d.f.=1,19, P<0.01). In the sprinting gait, in contrast, the time between tail beats was highly variable. So although we can calculate fTB, this aperiodic character makes 4 a single frequency an inadequate and uninformative description of the data. This is manifest in the dramatic increase in variability seen in fTB calculated for the data above 3 2.6 FL s−1 in Fig. 3, and is why we did not extend the regression to these data. The fact that the regression line has a slope less than unity, but an intercept greater than zero, 2 Sprint swimming indicates that at some point the regression line will intersect a

line of unity; from Fig. 3 this intersection will occur just above frequency (Hz) Tail-beat the highest value of U observed in steady swimming. 1 Steady swimming Comparison of sonomicrometry and video-image analysis 0 Fig. 4 is a plot showing calculated muscle strain for four tail 0 1 2 3 4 5 − beats from a milkfish swimming at 2.3 FL s 1. As in other Swimming speed (FL s-1) examples of the steady swimming gait, the strain histories show a regular frequency, in this case 2.6 Hz. Strains for the Fig. 3. Plot of tail-beat frequency (fTB) versus swimming speed (U) for the milkfish in this study (N=4). Speeds above 2.6 FL s−1 are superficial red muscle (Fig. 4A,C) and deep myotomal white indicated by the shaded region to distinguish the steady swimming muscle (Fig. 4B) derived from sonomicrometry (lines) are gait (U<2.6 FL s−1) from the sprinting gait (U>2.6 FL s−1) (where FL compared with estimates of strain from video image analysis is fork length). The regression line is described by the equation: 2 (filled circles). The two methods of calculating muscle strain fTB=0.98U+0.12 (r =0.94, Fs=308.36, d.f.=1,19, P<0.01). Because clearly agree well. The maximum cross-correlation fTB is uninformative in the sprinting gait, the regression is calculated coefficients for the two estimates of strain in superficial red and presented for the steady swimming data only. Muscle strain in swimming milkfish 535

10 0.53FL 0.53FL A 15 A 5 10

0 5 0 -5 -5 -10 0.53FL B 5 0.53FL 5 B 0 0 -5 -5

Muscle strain (%) 0.71FL C 0.71FL C Muscle strain (%) 15 10 10

5 5

0 0 -5 -5 -10

-10 -15 -20 -15 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Time (s) Time (s) Fig. 5. Comparison of muscle strain calculated from videography Fig. 4. Comparison of muscle strain calculated from videography (filled symbols) and from sonomicrometry (continuous lines) at two (filled symbols) and from sonomicrometry (continuous lines) at two locations on the body (0.53FL and 0.71FL, where FL is fork length) locations on the body (0.53FL and 0.71FL, where FL is fork length) and at two depths in the myotomes at 0.53FL for a milkfish and at two depths in the myotomes at 0.53FL for a milkfish swimming at 2.8 FL s−1. These data are for the same fish as in Fig. 4, swimming at 2.3 FL s−1. At this speed, the fish is using a steady gait. but in this case it is using a sprinting gait. (A) Muscle strain (A) Muscle strain calculated at 0.53FL for superficial red swimming calculated at 0.53FL for superficial red swimming muscle located in muscle located in close apposition to the skin. (B) Muscle strain close apposition to the skin. (B) Muscle strain calculated at 0.53FL calculated at 0.53FL for white muscle located within the conic for white muscle located within the conic myotome. At this myotome. At this swimming speed, the white muscle is not expected swimming speed, the white muscle is expected to be recruited. to be recruited. (C) Muscle strain calculated at 0.71FL for superficial (C) Muscle strain calculated at 0.71FL for superficial red swimming red swimming muscle located in close apposition to the skin. muscle located in close apposition to the skin.

2.8 FL s−1. At this speed, the fish adopted the sprinting gait and strain of 13 % during large-amplitude bursts and of 6 % the muscle strain histories show a large beat-to-beat variability between bursts, while the deep white muscle had a strain of in amplitude and irregular frequency. The maximum cross- 6 % during the bursts and of 3 % between the bursts. At 0.71FL, correlation coefficient for the strains calculated from this the red muscle had a strain of 15 % during the bursts and of recording for the red muscle at 0.53FL was 0.96, with the video 7 % for the intervening tail beats. data lagging behind the sonomicrometry data by one Comparing the video and sonomicrometry data for all fish observation (i.e. 16.7 ms). The maximum cross-correlation (N=4), positions (N=2), speeds (N=5) and gaits, the mean coefficient for the strains calculated for the deep white muscle cross-correlation coefficient was 0.96±0.03 (mean ± S.E.M.), at 0.53FL was 0.95, with the video data preceding the with the video data preceding the sonomicrometry data by sonomicrometer data by one observation. The cross-correlation 6.25±22.8 ms. The mean cross-correlation coefficient was not coefficient for the red muscle at 0.71FL was 0.97, with the different from 1.0 (ts=1.33, d.f.=24, P>0.1), and the estimate video data preceding the sonomicrometer data by two of the mean temporal separation between video and observations (i.e. 33.4 ms). At 0.53FL, the red muscle had a sonomicrometry data was not different from zero (ts=0.28, 536 S. L. KATZ, R. E. SHADWICK AND H. S. RAPOPORT d.f.=24, P>0.5). This validates the assumption that sprint swimming were not significantly different and therefore sonomicrometry and video image analysis give equivalent formed a homogeneous group (mean peak strain 5.8±0.95 %). estimates of muscle strain. The mean muscle strain for the posterior location on the body Comparison of deep white and superficial red muscle strain for large-amplitude burst tail beats during sprinting was measured using sonomicrometry at the same longitudinal 11.9±0.83 % and was significantly larger than the mean value location (0.53FL) showed that deep muscle strain lagged for non-bursting tail beats. superficial muscle strain by 3.06±17.8 ms (N=20). This lag was There was no significant relationship between speed and red not statistically different from zero (ts=0.17, d.f.=19, P>0.5), muscle strain during steady swimming for either the anterior indicating that the superficial red and deep white muscle strains body location (0.53FL) or the posterior location (0.72FL). For were occurring simultaneously. This validates the use of video the anterior location, there was a tendency for the red muscle to estimate muscle strain, which makes the assumption that the strains to increase; however, the correlation was not significant entire lateral half of the fish bends as if it were a continuous (Fs=2.48, d.f=1,19, P=0.13), and the slope of the linear fit to 2 beam. the data did not differ from zero (slope=0.61, ts=1.57, r =0.12, P>0.1). For the posterior location on the body, there was a Muscle strain and swimming speed similar positive trend, although this was also not significant Fig. 6 presents the estimated mean peak red muscle strain at (Fs=0.12, d.f=1,19, P=0.73), and the slope of the linear fit to approximately 0.53FL and 0.72FL for five speed classes. the data was also positive, but not significantly so (slope=0.21, 2 Analysis of variance indicated that there were significant ts=0.34, r =0.007, P>0.5). It seems that speed increases are differences between the mean peak red muscle strain at achieved primarily by changes in tail-beat frequency and not different speeds at both the anterior location on the body through changes in muscle strain or work per cycle during (Fs=6.14, d.f.=5,23, P<0.01) and the posterior location steady swimming. This pattern has also been observed in the (Fs=6.18, d.f.=5,23, P<0.01). A posteriori testing indicated that red muscle of trout (Oncorhynchus mykiss) during steady the peak strain amplitude of red muscle at the anterior position swimming (Hammond et al., 1998). However, during sprint consisted of two homogeneous populations; the steady- swimming, when white muscle is presumably recruited (Rome swimming classes and the interburst sprint-swimming class and Sosnicki, 1991; van Leeuwen et al., 1990), the strain had a mean value of 5.2±0.65 %, and the large-amplitude amplitudes increase significantly relative to steady-swimming strains in the burst events in sprinting averaged 9.8±1.3 % levels. (P<0.05 in each case, Fisher’s least significant difference procedure). Muscle strains at the posterior location at all the Strains along the length of the body steady swimming speeds and inter-burst muscle strains during Fig. 7 presents peak strains in superficial red muscle calculated using video image analysis as a function of position 14 along the fish body. The data span the region of the body that Sprint swimming contains red muscle (0.3–0.85FL). The data show that the 12 amplitude of muscle strain is larger in the posterior region of the fish than in the anterior region. Analysis of variance 10 indicated that there were significant differences between the Steady swimming mean muscle strain for all positions at all speeds. A posteriori 8 testing indicated that muscle strains at 0.8FL were significantly 6 larger than at 0.3FL. Since the body of red muscle is continuous down the length of the fish, it does not seem 4 prudent to explore statistically all the potential differences that Peak muscle strain (%) may exist between locations along the body of the fish. Suffice 2 to say that our estimate of muscle strain increases from anterior to posterior such that posterior strains are significantly larger. 0 0 1234 It is also apparent that the relationship between strain and Swimming speed (FL s-1) body position is similar for all swimming speeds investigated here and for both gaits. The fish do not use their muscle in a Fig. 6. Red muscle strain measured using sonomicrometry as a different manner as they swim faster. Rather, they increase the function of swimming speed. Data are means ± S.E.M.(N=4 fish, frequency of contraction to produce faster swimming. Indeed, 13–30 tail beats per fish). Data are grouped into four speed classes even when they are producing the very large-amplitude that used the steady swimming gait and one class that employed the muscle contractions during the bursts in sprinting, the sprinting gait. Measured muscle strains in the sprinting gait are presented as strains within large-amplitude bursts (filled symbols) relationship between relative strain at the front and back of and strains between bursts (open symbols). Data are presented for the fish is conserved. At the slowest speed, strain amplitudes two anatomical locations: 0.54FL (circles) and 0.72FL (squares), increase by 3.3 % from 4.2 to 7.5 % (∆ε=3.3 %) from 0.3 to where FL is fork length. The shaded region indicates speeds 0.8FL (Fig. 7A), while at the highest speed and largest muscle (>2.6 FL s−1) defined as sprinting. strain amplitudes the increase at these locations was from 7.2 Muscle strain in swimming milkfish 537

10 0.2 1.71 FL s-1 1.71 FL s-1 A A 8 0 -0.2 6 -0.4 4 -0.6 2 -0.8 0 -1 2.54 FL s-1 B 8 2.54 FL s-1 B 0 6 -0.2

4 Phase (fraction of cycle) -0.4 2 -0.6 Peak muscle strain (%) 0 -0.8 -1 3.25 FL s C -1 10 -1.2 8 0.2 0.4 0.6 0.8 1 Position on fish (l/FL) 6 Fig. 8. (A) Relative phase of body undulation or lateral deflection, 4 z(x) (filled symbols), and body curvature, κ(x) (open symbols), calculated using videography as a function of position on the body 2 for fish swimming at a modest speed (1.71 FL s−1, where FL is fork 0 length) using the steady swimming gait. Data are means ±95 % 0.2 0.4 0.6 0.8 1 confidence intervals for the same fish as in Fig. 7. The phase of Position on fish (l/FL) lateral deflection of the tail tip is defined as zero. Since the wave of lateral deflection of particular segments of the body proceeds from Fig. 7. (A) Red muscle strain calculated using videography as a head to tail, the relative phase of lateral excursions of those segments function of position on the body for fish swimming at a modest speed occurs earlier in time, and therefore the relative phase is negative. − (1.71 FL s 1, where FL is fork length) using the steady swimming Likewise, the wave of body midline curvature occurs earlier in time gait. Data are means ±95 % confidence intervals for three fish. (B) As than the lateral deflection at each point on the body, so the relative in A, but for the highest speed at which the fish use the steady phase of curvature is more negative than lateral deflection at the − swimming gait (2.54 FL s 1). (C) As in A, but for the sprinting gait same body location. See text for further details. (B) As in A, but for − (3.25 FL s 1). Filled symbols are peak strains during sprinting tail the highest speed at which the fish would use the steady swimming beats, open symbols are for inter-burst tail beats. gait (2.54 FL s−1). to 10.8 % (∆ε=3.4 %) (Fig. 7C). The fact that the magnitude In particular, Fig. 8 shows that the wave in z travels down of this change in strain (∆ε) is speed-independent and the the body in a straight line, indicating that the wave of lateral observation that other species of fish may have dramatically deflection travels at a constant rate. The slope of the regression different values of ∆ε (see below) suggest that there is some line relating the phase of lateral deflection (τ) to position in geometric feature of these fish that imparts a particular space in fractional body length (l/FL) at 1.71 FL s−1 is: 2 location-dependence to strain amplitude, independent of τ=0.95(l/FL)−0.94 (r =0.99, Fs>7000, d.f.=1,34, P<0.0001). speed. The slope of the regression line relating the phase of τ to l/FL −1 2 at 2.54 FL s is: τ=0.91(l/FL)−0.91 (r =0.99, Fs>20000., Phase of muscle strains along the length of the body d.f.=1,34, P<0.0001). Thus, statistics verify what is apparent To develop a complete understanding of how the muscles on inspection – that these are straight lines. While the slopes are used in milkfish, we need to know the timing of the strain of these lines are similar, they are statistically different as well as its magnitude. Fig. 8 presents the phase of lateral (ANCOVA, Fs=7.88, d.f.=1,2, P<0.01). However, the lack of deflection, z(x), and curvature of the midline, κ(x), as a function a clear mechanical role for these phases makes it hard to draw of location on the body. These phase data correspond to the any functional conclusions from these small differences. Since strain data in Fig. 7A,B for the same swimming speeds. the abscissa is defined in units of body length and the ordinate Because tail beats during sprinting do not have a specific in units of tail-beat period, the inverse of the slopes of these periodicity, we have not attempted to calculate a relative phase lines defines the relative progression speed (V) of the wave of for this unsteady gait. lateral deflection in body lengths per tail-beat period (Videler 538 S. L. KATZ, R. E. SHADWICK AND H. S. RAPOPORT and Hess, 1984). For a swimming speed of 1.71 FL s−1, this rate irrespective of the fact that a single myotome cone may overlap is 1.05, while for a speed of 2.54 FL s−1 the rate is 1.10. These several anatomical segments. One might have expected that values are larger than the averages reported by Videler and synchronously activated muscle would shorten synchronously Hess (1984) for the mackerel Scomber scombrus (1.02) and for and that a phase difference would then be manifest between the saithe Pollachius virens (0.98), but are within the same shallow and deep sonomicrometer measurements of strain range. Both Videler and Hess (1984) and Katz and Shadwick since these overlapping, nested cones of muscle arise from (1998) observed that the waves of z and κ were approximately different anatomical segments. in phase at a body location of 0.25FL in mackerel. Fig. 8 The finding that the body acts like a continuous beam, as suggests that z and κ in milkfish approach being in phase at a manifest in red muscle strain histories, is in agreement with a more posterior location of 0.4FL. number of previous studies. For instance, Shadwick et al. That the wave of z proceeds down the body at a constant (1998) examined the function of the swimming muscle in a rate has been observed by other authors for numerous fish Pacific mackerel Scomber japonicus using X-ray videography. species (e.g. Videler and Hess, 1984; Katz and Shadwick, Radio-opaque, gold beads were surgically implanted into the 1998; Müller et al., 1997). The relative phase of curvature of muscle of the fish, which was then allowed to swim in a small the midline, however, travels from head to tail at a changing flume placed in the beam of a video-radiography apparatus. rate manifest in the non-linear line connecting the open Local changes in muscle length, indicated by the distance symbols in Fig. 8. It has been shown that this pattern is an between the gold beads, were well correlated in time with inevitable consequence of the changing geometry of the estimates of muscle strain deduced from local body curvature amplitude envelope of body undulations adopted by these fish and thickness. The data were presented for one specimen (Katz and Shadwick, 1998), and has also been observed swimming at one speed, and thus no general conclusions could recently in the red muscle of trout during steady swimming be drawn. However, under these circumstances, their findings (Hammond et al., 1998). At a swimming speed of 1.71 FL s−1 indicated that, at least in some fish, local curvature is a very the relative phases of z and κ are not statistically different reliable indicator of local red muscle strain (Shadwick et al., between 0.36 and 0.44FL (Fig. 8A), but at 0.85FL κ precedes 1998). z by 0.15 of a cycle, or 56 °. At a swimming speed of Agreement between sonomicrometry and image analysis 2.54 FL s−1, the relative phases of z and κ are never statistically was also reported for scup Stenotomus chrysops red muscle by the same, but approach each other closest at 0.4FL (Fig. 8B); Coughlin et al. (1996) using sonomicrometry and high-speed at 0.85FL, κ precedes z by 0.13 of a cycle or 48 °. This phase videography. They showed that, for peripherally located red difference was not statistically different at these two speeds in muscle, strain calculated from sonomicrometry is very well the caudal portion of the animal (l/FL>0.5FL). The increase in correlated with local body bending. These authors also phase between z and κ to approximately 50 ° in the caudal reported that, on average, the degree of temporal correlation portion of the animal has been observed previously in mackerel between the techniques was between 0.001 and 0.01 of a tail- (Katz and Shadwick, 1998). beat cycle, although the specific technique that produced these values was not presented. So, although there is good agreement between the conclusions of Coughlin et al. (1996) and our own, Discussion a direct, quantitative comparison between the data is difficult. Comparison of sonomicrometry and video strain estimates Also, those authors did not report measurements from deep In all the conditions in which we examined in these fish, we myotomal muscle during steady or sprint swimming. They did found that sonomicrometry measurements of strain were well find that red muscle strain amplitude may triple or even correlated in magnitude and time with strains calculated from quadruple between 0.3 and 0.5FL at a given speed. The measurements of body curvature. The primary consequence of increase in strain amplitude in milkfish in the present study was this conclusion is that, in spite of being heterogeneous in much smaller over the same range of body locations. This structure, the body of the fish is bending as a continuous beam. difference may be of significance to the current debate Beam-like behavior is displayed in relatively slow, steady concerning how red muscle powers swimming. swimming where only the peripherally located red muscle powers the body undulations and the deeper, inactive white Does all the swimming muscle perform a similar muscle is passively strained. This behavior is also displayed in mechanical job? faster, sprinting gaits where the entire side of the fish is The present study concerns muscle strain histories, and so contracting to produce propulsive movements. So, in spite of far we have not commented on force production by these the complex folding and nesting of the myotomes and the muscles. Given the highly folded geometry of fish myotomes, anatomical separation of the red and white muscle fibers, the force trajectories are ambiguous (Johnsrude and Webb, 1985). fish acts as a continuous beam. This conclusion is perhaps Even if one could implant an appropriate force transducer into particularly surprising in the light of the finding of Jayne and the lateral red muscle during steady swimming, the fraction of Lauder (1995b) that the majority of the volume of the the total force generated by more rostral myotomes that the myotome, in particular that portion consisting of nested cones transducer sensed would still be unknown. One would also (their E1, E2, H1 and H2), is activated synchronously, need to know the fraction of force generated by a given muscle Muscle strain in swimming milkfish 539 that is conducted directly to the spine via myosepta and that more carefully the history of muscle shortening, it was shown fraction conducted caudally via the skin in order to generate a that all the red muscle is probably activated in a manner to complete force budget for each segment of red swimming produce primarily positive work and negligible negative work muscle (Katz and Jordan, 1997). Such information is not in fish such as mackerel (Katz and Shadwick, 1998). Similarly, available and, therefore, we can only roughly estimate what the van Leeuwen (1992) predicted that the white muscle of carp potential for power output might be for any fish. will produce net positive work all along the body during sprint In the absence of a complete force budget, our current swimming. understanding of how muscle powers the swimming of fish However, several reports have suggested that anterior must rely on inferences drawn from mapping the results of in swimming muscle has such a small strain that the amount of vitro experiments onto the pattern of electromyographic work available to power swimming is minimal and that the activity and the strain histories of muscles in vivo. The recently significant majority of swimming power arises in the most popularized, oscillatory work-loop technique has facilitated caudal myotomes (Rome et al., 1993; Coughlin et al., 1996). this approach to estimating muscular performance in Although we have observed that muscle strain increases in swimming fish. In the oscillatory work-loop technique, isolated posterior muscle, the observed increase is modest compared muscle fibers are subjected to sinusoidal length changes and with that reported by Rome and Sosnicki (1991), Rome et al., phasic stimulation, mimicking the cyclic in vivo loading (1993), Jayne and Lauder (1995a) and Coughlin et al. (1996). conditions (Josephson, 1985; Rome et al., 1990, 1993). Thus, In particular, Rome et al. (1993) suggest that, in the scup the work-loop technique is highly appropriate for determining Stenotomus chrysops, muscle strain amplitude triples between realistic values of power output and efficiency of fish muscle 0.29FL and 0.54FL for fish swimming at close to 3 FL s−1. In (Johnson and Johnston, 1991; Johnson et al., 1994; Moon et contrast, our results show a much smaller increase, from 4.5 % al., 1991; Rome and Swank, 1992; Altringham et al., 1993; to 7 % strain, for similar locations on the body and a similar Rome et al., 1993). Traditional estimates of power output using swimming speed. Recent measurements using sonomicrometry in vitro force–velocity curves derived from isotonic shortening of red muscle strain in trout during steady swimming suggest experiments are inappropriate for modeling fish swimming that on average strain is less in trout than in milkfish, but the muscle because these measurements only consider force ∆ε (2.7 %) from 0.35FL to 0.65FL in trout (Hammond et al., produced during shortening and will overestimate the in vivo 1998) is similar. In contrast, the magnitude of ε(x) that we power output (Swoap et al., 1993). report for milkfish at slow swimming speeds is almost the same Attempts to map in vitro experiments on isolated muscle as that in mackerel (Shadwick et al., 1998). The latter study, samples onto the whole animals have used body curvature to in fact, predicted that net positive work would occur all along calculate local muscle strain histories and electromyography to the length of the red muscle. In any case, neither the milkfish calculate local patterns of muscle activation. Using curvature nor the mackerel shows an increase in muscle strain amplitude as an index of muscle strain, studies on carp and saithe white to the extent reported for the scup. muscle (Hess and Videler, 1984; Van Leeuwen et al., 1990; We can suggest two potential reasons for this difference: Altringham et al., 1993) suggest that in these fish the anterior either there has been a technical error in the calculation of muscles are activated with the appropriate phase to produce muscle strain or there are real differences in how these maximal positive work. In contrast, more posterior muscles are different species of fish use their muscles. It is unlikely that a actively stretched (i.e. do negative work) during an increasing technical error is responsible since so many separate proportion of the cycle, thus acting as transmission elements technologies seem to agree within each study. For example, for the power from more rostral contractions. The caudal-most good agreement is achieved in each paired comparisons of the muscles are predicted to do predominantly negative work, thus three techniques we have discussed above (sonomicrometry, functioning essentially as tendons rather than as actuators video radiography and external image analysis). Thus, we (Videler, 1993). A contrasting view is that of Rome et al. conclude that there are real differences in the way that different (1993), who proposed that, for superficial red muscle in scup, species use their red muscle to power swimming. Since we the posterior fibers generate the majority of the power for have observed similarly large magnitudes of muscle shortening swimming, by virtue of their larger strain and relatively earlier in the anterior myotomes of both mackerel (Shadwick et al., activation compared with the anterior fibers. Johnson et al. 1998) and milkfish, we must conclude that these fish are (1994) have corroborated this view for posterior muscles in capable of generating a good deal of positive work from these Micropterus salmoides. muscles during swimming. Indeed, the use of a fish such as the If muscle strain is correlated with body curvature, then a scup, which has a small strain amplitude in anterior myotomes, detailed appreciation of the geometry of the body undulations and which in turn has led in part to the current lack of synthesis in swimming fish is required to estimate strain (Katz and in our understanding of the use of red muscle to power Shadwick, 1998). In the past, imprecise calculations of body swimming in fish, may have been no more than serendipity. curvature have contributed to the conclusion that posterior red We suggest that in future an appreciation of potential muscle is activated too early in the shortening history of the differences between species in the use of swimming muscles muscle to produce significant amounts of positive work should be incorporated into conclusions regarding how various (Williams et al., 1989; Wardle et al., 1995). By specifying fish power swimming. 540 S. L. KATZ, R. E. SHADWICK AND H. S. RAPOPORT

Steady swimming, sprinting and fast-start sprint swimming locations on the body. Thus, it is hard to interpret this index of Clearly, the presence of collagenous myosepta and the body bending quantitatively but, in brief, the wave of undulation anatomical distribution of red and white muscle fibers violates produces larger deviations from linearity caudally than rostrally. the assumption that the body is a homogeneous continuum. It Therefore, a decrease in linearity of the midline should is perhaps surprising then that we observe a mean lag that does correspond to an increase in total bending and, in particular, to not differ from zero between deep (white) and shallow (red) greater bending caudally. As Covell et al. (1991) point out, the muscle. Even though the transition to the sprinting gait in these technique is relatively insensitive to position on the body, so the fish is accompanied by an increase in muscle strain, there is no fact that we reach a different conclusion may be simply a result temporal separation between deep and shallow muscle. of exploiting a technique that has a finer spatial resolution. Previously, it was hypothesized that shortening red muscle that However, it is also possible that, although both gaits use white was in close apposition to the skin might be constrained to muscle, fast-start performance is functionally different from track the skin strain history, but that the surrounding, inactive, sprint swimming. The most obvious potential difference is the white muscle would be less likely to do so (Katz and Shadwick, presence of large inertial loads in fast-starts that should not be 1998). In the steady swimming gait, we did not observe this present in a sprinting gait. Ahlborn et al. (1997) have described pattern; the active red muscle at the skin as well as the inactive large impulses on the initial tail excursions of modeled fast-starts white muscle located half-way between spine and skin tracked that are reduced on subsequent tail excursion that occur within each other with high fidelity (Fig. 4). Shadwick et al. (1998) developed flow. If white muscle contracts in a fast-start against also found that muscle located at various depths within the a large inertial load, it may be possible mechanically to load myotomes shortened in phase with local body curvature at the elastic elements or for anterior myotomes to perform negative slow speeds for which they had data. Importantly, in the work on caudal myotomes. Indeed, Johnston et al. (1995) have sprinting gait, the shallow red muscle as well as the now active, suggested that, in fast-starts of the short-horned sculpin deep white muscle still tracked each other in time. Given that Myoxocephalus scorpius, the caudal myotomes are active while we did not use simultaneous electromyography, we must rely being lengthened. In this case, some shearing will occur within on the work of others, which indicates that in bursting gaits the the myotomes and muscle segment shortening may not be white muscle is recruited (Bone, 1966; Jayne and Lauder, temporally correlated with local body bending. In our 1993; Rome et al., 1984). Certainly, this inference is supported observations of sprint swimming, in contrast, the loading is by the dramatic increase in muscle strain we observe in the occurring within developed flow and one might expect that, large-amplitude tail beats that the fish produces in the sprinting while inertial forces may be large, they are occurring over time gait. If these were powered by red muscle in the absence of and the impulse will be modest. In fact, van Leeuwen (1992) has white muscle, the red fibers would need to have a total suggested that in sprint swimming of carp negligible negative shortening of almost 30 % of their maximal length. This seems work is done by the bulk of white muscle at any point on the unlikely. In addition, van Leeuwen (1992) has predicted that, body. Thus, there is reason to believe that fast-starts and sprint at the high fTB seen in sprinting gaits, the red muscle is swimming are not equivalent in their use of white muscle, and incapable of producing significant positive work to power we might not expect our results to match those of Covell et al. swimming. However, Johnson et al. (1994) have shown in (1991). work-loop studies of red muscle from the bass Micropterus salmoides that a fTB of 4 Hz does not prohibit net positive work This work was performed at the Kewalo Basin Research production. In any event, if the white muscle is being recruited Laboratory of National Marine Fisheries Service. For their during these large-amplitude tail beats, the fact that the hospitality and technical assistance, the authors thank Richard superficial red muscle and the white muscle are still tracking Brill, Kathy Cousins and Tim Lowe at Kewalo. The authors each other indicates that in this gait the whole side of the fish would like to thank James Covell and Richard Pavalec for is contracting together to produce a bend in the body that is helping with all aspects of the sonomicrometry technology. very like a homogeneous continuum. While the general result The authors would also like to thank Archibald Tuttle, Emilio that the entire thickness of the fillet is bending as a continuum Lazardo, Racquel Darrian, Torre Knower, Earl Keese and two has been assumed in many previous studies (van Leeuwen et anonymous referees for help at various points in the al., 1990; van Leeuwen, 1992; Rome and Sosnicki, 1991; preparation of this material. This research was funded by Rome et al., 1993; Jayne and Lauder, 1995b), the present study National Science Foundation grant (IBN95-14203). is the first to validate this assumption with direct measurements. Covell et al. (1991) concluded that infast-starts of trout the References white muscle is shortening in phase with more caudal body Ahlborn, B., Chapman, S., Stafford, R., Blake, R. W. and Harper, segments. This suggested that the white muscle was acting over D. G. (1997). Experimental simulation of the thrust phase of fast- some distance rather than locally. They arrived at this conclusion start swimming of fish. J. Exp. Biol. 200, 2301–2312. by correlating muscle segment shortening measured via Altringham, J. D., Wardle, C. S. and Smith, C. I. (1993). Myotomal sonomicrometry with deviations from linearity of the whole- muscle function at different points on the body of a swimming fish. body midline. They did not measure curvature at specific J. Exp. Biol. 182, 191–206. Muscle strain in swimming milkfish 541

Bell, W. H. and Terhune, L. D. B. (1970). Water tunnel design for Muscle energetics and power output of isolated fish fast muscle fisheries research. Fish. Res. Bd Can. Tech. Rep. 195, 69pp. performing oscillatory work. J. Exp. Biol. 158, 261–273. Bone, Q. (1966). On the function of the two types of myotomal Müller, U. K., van den Heuvel, B. L. E., Stamhuis, E. J. and muscle fiber in elasmobranch fish. J. Mar. Biol. Ass. U.K. 46, Videler, J. J. (1997). Fish foot prints: morphology and energetics 321–349. of the wake behind a continuously swimming mullet (Chelon Bone, Q., Marshall, N. B. and Blaxter, J. H. S. (1995). Biology of labrosus Risso). J. Exp. Biol. 200, 2893–2906. Fishes, second edition. Glasgow, Scotland: Blackie Academic and Nursall, J. R. (1956). The lateral musculature and the swimming of Professional. 332pp. fish. Proc. Zool. Soc. Lond. B 126, 127–143. Coughlin, D. J., Valdes, L. and Rome, L. C. (1996). Muscle Rome, L. C., Funke, R. P. and Alexander, R. McN. (1990). The length changes during swimming in scup: sonomicrometry influence of temperature on muscle velocity and sustained verifies the anatomical high-speed cine technique. J. Exp. Biol. performance in swimming carp. J. Exp. Biol. 154, 163–178. 199, 459–463. Rome, L. C., Loughna, P. T. and Goldspink, G. (1984). Muscle Covell, J. W., Smith, M., Harper, D. G. and Blake, R. W. (1991). fiber recruitment as a function of swim speed and muscle Skeletal muscle deformation in the lateral muscle of the intact temperature in carp. Am. J. Physiol. 247, R272–R279. rainbow trout Oncorhynchus mykiss during fast-start maneuvers. J. Rome, L. C. and Sosnicki, A. A. (1991). Myofilament overlap in Exp. Biol. 156, 453–466. swimming carp. II. Sarcomere length changes during swimming. Hammond, L., Altringham, J. D. and Wardle, C. S. (1998). Am. J. Physiol. 260, C289–C296. Myotomal slow muscle function of rainbow trout Oncorhynchus Rome, L. C. and Swank, D. (1992). The influence of temperature on mykiss during steady swimming. J. Exp. Biol. 201, 1659–1671. power output of scup red muscle during cyclical length changes. J. Hess, F. and Videler, J. J. (1984). Fast continuous swimming of Exp. Biol. 171, 261–281. saithe (Pollachius virens): a dynamical analysis of bending Rome, L. C., Swank, D. and Corda, D. (1993). How fish power moments and muscle power. J. Exp. Biol. 109, 229–251. swimming. Science 261, 340–342. Jayne, B. C. and Lauder, G. V. (1993). Red and white muscle Shadwick, R. E., Steffensen, J. F., Katz, S. L. and Knower, T. activity and kinematics of the escape response of the bluegill (1998). Muscle dynamics in fish during steady swimming. Am. sunfish during swimming. J. Comp. Physiol. A 175, 123–131. Zool. 38, 755–770. Jayne, B. C. and Lauder, G. V. (1995a). Speed effects on midline Shanks, M. E. and Gambill, R. (1969). Calculus of the Elementary kinematics during steady undulatory swimming of largemouth bass, Functions. New York: Holt, Rienhart & Winston. 545pp. Micropterus salmoides. J. Exp. Biol. 198, 585–602. Swoap, S. J., Johnson, T. P., Josephson, R. K. and Bennett, A. F. Jayne, B. C. and Lauder, G. V. (1995b). Are muscle fibers within (1993). Temperature, muscle power output and limitations on burst fish myotomes activated synchronously? Patterns of recruitment locomotor performance of the lizard Dripsosaurus dorsalis. J. Exp. within deep myomeric musculature during swimming in Biol. 174, 185–197. largemouth bass. J. Exp. Biol. 198, 805–815. van Leeuwen, J. L. (1992). Muscle function in locomotion. In Johnson, T. P. and Johnston, I. A. (1991). Power output of fish Mechanics of Animal Locomotion (ed. R. McN. Alexander). Adv. muscle fibres performing oscillatory work: effect of seasonal Comp. Env. Physiol. 11, 191–250. Heidelberg: Springer-Verlag. temperature change. J. Exp. Biol. 157, 409–423. van Leeuwen, J. L., Lankheet, M. J. M., Asker, H. A. and Osse, Johnson, T. P., Syme, D. A., Jayne, B. C., Lauder, G. V. and J. W. M. (1990). Function of red axial muscles of carp (Cyprinus Bennett, A. F. (1994). Modeling red muscle power output during carpio): recruitment and normalized power output during steady and unsteady swimming in largemouth bass. Am. J. Physiol. swimming in different modes. J. Zool., Lond. 220, 123–145. 267, R481–R488. Videler, J. J. (1993). Fish Swimming. London: Chapman & Hall. Johnsrude, C. L. and Webb, P. W. (1985). Mechanical properties Videler, J. J. and Hess, F. (1984). Fast continuous swimming of two of the myotomal musculo-skeletal system of rainbow trout, Salmo pelagic predators, saithe (Pollachius virens) and mackerel gairdineri. J. Exp. Biol. 119, 71–83. (Scomber scombrus): a kinematic analysis. J. Exp. Biol. 109, Johnston, I. A., van Leeuwen, J. L., Davies, M. L. F. and Beddow, 209–228. T. (1995). How fish power predation fast-starts. J. Exp. Biol. 198, Wainwright, S. A. (1980). To bend a fish. In Fish Biomechanics (ed. 1851–1861. P. Webb and D. Weihs), pp. 68–91. New York: Preager. Josephson, R. K. (1985). Mechanical power output from a striated Walpole, R. E. and Myers, R. H. (1989). Probability and Statistics muscle during cyclic contraction. J. Exp. Biol. 114, 493–512. for Engineers and Scientists, fourth edition. New York: Macmillan Katz, S. L. and Jordan, C. E. (1997). A case for building integrated Publishing Co. models of aquatic locomotion that couple internal and external Wardle, C. S., Videler, J. J. and Altringham, J. D. (1995). Tuning forces. Proceedings of the 10th International Symposium on into fish swimming waves: body form, swimming mode and muscle Unmanned, Unteathered Submersibles. AUSI. function. J. Exp. Biol. 198, 1629–1636. Katz, S. L. and Shadwick, R. E. (1998). Curvature of swimming fish Westneat, M. W., Hoese, W., Pell, C. A. and Wainwright, S. A. midlines as an index of muscle strain suggests swimming muscle (1993). The horizontal septum: mechanisms of force transfer in produces net positive work. J. Theor. Biol. 193, 243–256. locomotion of scombrid fishes (Scombridae: Perciformes). J. Korsmeyer, K. E., Chin Lai, N., Shadwick, R. E. and Graham, J. Morph. 217, 183–204. B. (1997). Heart rate and stroke volume contributions to cardiac Williams, T. L., Grillner, S., Smoljaninov, V. V., Wallen, P., output in swimming yellowfin tuna: response to exercise and Kashin, S. and Rossignol, S. (1989). Locomotion in lamprey and temperature. J. Exp. Biol. 200, 1975–1986. trout: the relative timing of activation and movement. J. Exp. Biol. Moon, T. W. J. D., Altringham, J. D. and Johnston, I. A. (1991). 143, 559–566.