The biomechanics of fast-starts during ontogeny in the common carp cyprinus carpio

As fish develop from larvae into adults, they undergo a series of changes in body morphology, muscle dynamics and swimming kinematics (Osse, 1990). Larvae are typically small, and their body depth is reasonably uniform because of the primordial fin. Adult fish, in contrast, are large and have an irregular depth because of changes in both body profile and the size and shape of the median fins. The changes in size and shape during ontogeny result in changes in swimming hydrodynamics and kinematics which, in turn, impose differing demands on the muscle contractile dynamics.

Swimming velocity increases with body size both for steady prolonged activity (for a review, see Videler, 1993) and for burst activity and fast-starts (e.g. Beamish, 1978; Magnuson, 1978; Hale, 1996; Williams and Brown, 1992; Temple and Johnston, 1998; James and Johnston, 1998a). During fast-start swimming, the mass-specific inertial power requirements are related to the product of velocity and acceleration (Frith and Blake, 1995; Wakeling and Johnston, 1998) and thus also increase with size. Hydrodynamic power requirements for fast-starts are limited by the power available from the muscles (Wakeling and Johnston, 1998) which, in turn, must increase for bigger fish. These increases in the mass-specific power output from the muscle may be due to differences in contractile properties or to the differences in the imposed contraction regimes resulting from the changing kinematics of swimming.

Muscle contractile properties scale with body length in fish. The Q_10cm (a Q₁₀ value for every 10 cm difference in length; Videler and Wardle, 1991) for twitch contraction frequencies was measured at 0.82–0.94 for cod Gadus morhua (Archer et al., 1990; Videler and Wardle, 1991). A Q_10cm of 0.79 has been measured for the maximum unloaded shortening velocity of fast muscle fibres in shorthorn sculpin Myoxocephalus scorpius (James and Johnston, 1998b), but no significant scaling relationship was found for this variable in dogfish Scyliorhinus canicula (Curtin and Woledge, 1988). These scaling relationships predict a maximum 11 % change in any individual contractile variable for the initial 5 cm growth of a fish. It is therefore unlikely that changes in muscle contractile properties contribute in a major way to the increase in fast-start performance during development.

In this study, the body morphologies during the ontogeny of the common carp Cyprinus carpio from a 7 mm larva to an 80 mm juvenile were measured. Fast-start escape swimming was captured on high-speed film for a series of size groups within this range, and the swimming kinematics, hydrodynamics and muscle dynamics were quantified for these fast-starts. The size-dependent limitations to the kinematics and muscle dynamics are discussed, and it is shown that the fast-start biomechanics can be explained in terms of the developmental constraints of size and shape.

Three-day-old common carp larvae Cyprinus carpio L., approximately 8 mm in total length, were supplied by Humberside Fisheries, Driffield, UK, in May 1998. The fish were reared in duplicate temperature-controlled tanks at between 20.4 and 21.1 °C with a light:dark photoperiod of 12 h:12 h. Fish were fed live Artemia for the first month and were then weened onto proprietary dry food (BOCM Pauls Ltd, UK). By the end of November 1998, the fish had reached a mean length of 60 mm.

Body morphologies were measured using the methods described by Wakeling and Johnston (1998). The following variables were measured. Direct measurements were made for total body length L and body mass m. Longitudinal and planform images were used to estimate the distributions of area, volume and mass along the fish, and variables were normalized by length L, area L² or volume L³. The body-length-specific half-width at any longitudinal position is given by ⁠, whilst area-specific variables for planform (top-view) area Ŝp and longitudinal (side-view) area Ŝl are equivalent to the mean length-specific width and depth of the fish, respectively. Length-specific distances from the snout are denoted ⁠. The length-specific radius of the first moment of volume from the snout gives a good estimate of the position of the centre of mass for a straight-stretched fish, and the masses for ten equal-length longitudinal segments were also estimated.

Freshly killed fish (N=35, 7.8<L<62.0 mm) were frozen in isopentane cooled to −159 °C in liquid nitrogen. Fish were divided into ten segments of equal length, which were set in Cryomatrix embedding medium (Shandon, PA, USA) and mounted onto a cryostat chuck. Transverse sections, 10 μm thick, were cut through the centre of each segment, mounted on glass slides and stained with Harris haematoxylin solution (Sigma-Aldrich Co. Ltd, UK). The cross-sectional area of the white muscle in each section was then determined using a microscope drawing arm and Videoplan image-analysis software (Kontron, Eching, Germany). The white muscle mass for each segment was calculated from its cross-sectional area and the segment depth, assuming a muscle density of 1.06 mg mm⁻³ (Mendez and Keys, 1960).

The body-mass-specific white muscle mass was the ratio of the total white muscle mass to m.

Fast-starts of the carp were filmed in a temperature-controlled tank measuring 500 mm×500 mm×180 mm (length ×width × depth). Fast-starts were elicited by thrusting an obliquely angled fine rod towards the snout of the fish. In all cases, the fish responded without making contact with the rod, and images from the fast-start were obtained before the water ripple from the rod passed over the fish. A frosted sheet beneath the tank was illuminated by a 250 W projector bulb. Overhead high-speed images of the fish were taken via a 45 ° mirror using both video (NAC Inc., Japan, HSV-500 C3 VCR with C3 digital high-speed video camera) and ciné (NAC E-10 camera, Ilford HP5 16 mm film) equipment at frame rates of 500 s⁻¹ and 300 s⁻¹, respectively. The light path between the fish and the cameras was 3.4 m, and zoom lenses were set so that the image diagonal corresponded to approximately eight fish lengths in both cases. Video sequences were digitized via a Win/TV image grabber card (Hauppauge, UK), whilst ciné sequences were analyzed on a NAC 160F film motion image analyzer. The standard error of digitizing a reference point on sequential frames corresponded to 0.004 and 0.002L for the video and ciné films, respectively. A 100 mm diameter circle was drawn on the underside of the tank and was used to calibrate the aspect ratio for each filming method.

The kinematic analysis of the swimming sequences followed the methods described by Wakeling and Johnston (1998) unless stated otherwise. The following description is only a summary of these methods.

The radius of curvature r was calculated for all positions along the spine. In this study, spine bending is expressed as length-specific curvature ĉ (=r/L) and takes the convention of positive values when bending is to the right and negative values when bending is to the left.

Contour plots of spine curvature against both body position and time showed that the initial body bend during the fast-start propagated as a wave of curvature travelling in a posterior direction along the spine. The length-specific velocity ^Û of the wave of curvature along the spine was given by the slope of the best-fitting straight line that connected the initial crest on such contour plots.

The force development of the white muscle fibres during the initial tail-beat of the fast-starts was determined using the methods described by Wakeling and Johnston (1999b). For each fast-start sequence, the contraction duration and change in muscle strain were determined for seven longitudinal positions between 0.3L and 0.8L, i.e. the region where the white myotomal muscle is situated. The initial muscle contraction of a fast-start is initiated by electromyographic (EMG) activity at the onset of shortening (Wakeling and Johnston, 1999c). The muscle length changes were assumed to be sinusoidal in shape, with strain amplitude and contraction durations matching those measured for the swimming fish. The predictive model for muscle force (Wakeling and Johnston, 1999b) generates force and power estimations that are statistically indistinguishable from measured force and power from live fibre preparations during realistic fast-start contraction regimes. The contractile variables used in the model correspond to those for white muscle fibres in adult carp (L=130 mm) at 20 °C, i.e. maximum isometric stress at 229.7 kN m⁻² and maximum length-specific unloaded contraction velocity at 19.65 s⁻¹ (Wakeling and Johnston, 1999b). The stimulus duration was numerically optimized for each contraction to yield the mean maximum power output, and the optimal durations ranged between 2.0 and 9.3 ms.

The total muscle power output during each fast-start was calculated as the mean power output generated at all sites along the myotome weighted by the proportion of white muscle mass located at each of those sites.

Mean values are presented with the standard error of the mean (S.E.M.). Scaling relationships were calculated from the least-squares regression lines passing through log-transformed data. The effects of body length and longitudinal position along the trunk on the force and power output from the myotomal muscle were tested with an analysis of covariance (ANCOVA) where length and position were factors in the model. Significance testing was accepted at a 95 % confidence level.

Body morphologies were determined for 104 fish ranging in length from 7 to 80 mm. The growth rate of these fish is shown in Fig. 1, and the relationship between body mass and total body length is shown in Fig. 2. The body mass m (kg) can be predicted from the total length L (m) using the following equation calculated from the linear regression through log-transformed data:

The 10 mm fish were surrounded by primordial fin-folds and showed a reasonably regular body depth along their length. Growth up to 30 mm proceeded with a gradual reduction of these fin-folds, but with development of the median and caudal fins. In this range, the body increased in both relative width and depth across the mid-region of the fish. Growth beyond 30 mm was geometric, with the fish retaining their relative body proportions, which were adult in form. These changes are shown in Fig. 3. Developmental changes in non-dimensional longitudinal area Ŝl and planform area Ŝp are shown in Fig. 4. The increases in Ŝl between 8 mm and 30 mm length are due to increases in both body depth and median fin area. Developmental changes in the length-specific distance of the centre of mass from the snout are shown in Fig. 5 and again show a gradual increase between 8 and 30 mm length, reaching a plateau in larger fish. This increase in is due to the increase in both relative width and depth across the mid-region of the fish.

The longitudinal distribution of white muscle mass is shown in Fig. 6. The 10 mm fish had the most uniform distribution of mass along their length (0.2L–0.8L), and increases in fish length occurred with increases in the proportion of white muscle in the central body region (0.3L–0.6L). The 10 mm fish had the lowest relative muscle mass of 0.197±0.027 (N=10). increased over the range 10<L<40 mm. For lengths greater than 40 mm, there was no significant effect of length on (⁠⁠, N=18).

In total, 102 fast-starts were analyzed. These were sorted by fish length into seven groups. From each group, the five starts with the greatest mean hydrodynamic power requirements were selected and represent the best third of the total analyzed sequences. The mean (± S.E.M.) lengths for these groups were: 9.9±0.22, 11.6±0.59, 21.6±0.64, 25.2±0.54, 38.7±1.03, 50.7±1.76 and 62.5±3.29 mm.

The maximum velocity V_max and acceleration A_max achieved during the first tail-beat both showed an increase with body length (Fig. 7A,B). The body-mass-specific mean power required to accelerate the centre of mass in the direction of travel also showed an increase with fish length from 1.26±0.16 W kg⁻¹ for L=10 mm to 6.97±1.13 W kg⁻¹ for L=63 mm (Fig. 8). Scaling relationships for these variables were calculated from log-transformed data for each individual start and are given in Table 1.

The length-specific maximum velocity and maximum acceleration Âmax achieved during the first tail-beat of the fast-start both showed a decrease with increasing fish length (Fig. 9A,B). The velocity of the wave of curvature Ûthat travelled in a posterior direction along the spine during the initial body bending always exceeded the maximum forward velocity of the fish and is also shown in Fig. 9A.

The duration of the initial muscle contraction increased with longitudinal position along each fish, and the time differences for the first peak in muscle strain can be determined from the velocity of the wave of curvature Û (Fig. 9A). The duration τ of the next change in peak-to-peak spine curvature and muscle strains remained constant along the length of each fish, and the mean durations of the initial contractions are shown in Fig. 10. τ increased from 16.9±0.87 ms for L=10 mm to 34.9±0.26 ms for L=63 mm. The scaling relationship for contraction duration was calculated from log-transformed data for each individual start and is presented in Table 1.

The longitudinal variation of spine curvatures is shown in Fig. 11. The mean curvatures for the 10 mm fish were lower than for all the larger sizes. In general, the length-specific spine curvature ĉ increased with longitudinal position to a value greater than 5. Spine curvatures were relatively independent of body length for L⩾12 mm. The longitudinal variation in white muscle strain is shown in Fig. 12. Again, the 10 mm fish swam using lower strains than the larger fish. For fish of length L⩾12 mm, the white muscle strain was independent of body length. The general pattern was for the greatest strains ε≈0.09 to occur in the front region of the trunk muscle ⁠. Posterior to this region, there was a gradual decrease in strain to a low value of ε≈0.03 at 0.8L.

The mean muscle stress and mass-specific power outpu ⁠, integrated over the first tail-beat, were calculated for each segment of the body trunk for each fast-start sequence (Fig. 13; Table 2). was greatest in the mid region of the fish (for L⩾12 mm) and decreased towards the caudal fibres at 0.8L. There was an increase in the power output with increasing body length. In contrast, was smallest in the mid region of the fish and increased towards the caudal fibres at 0.8L. There was an increase in the stress with increasing body length. Analysis of covariance showed that both body length and longitudinal position had a significant effect on the mean stress (P<0.001) and the mean mass-specific power output (P<0.001) (Table 3).

During ontogeny, as the body length increases in the carp, so does maximum fast-start velocity. Therefore, the Reynolds number regime in which the fish swim must also have increased. Using a kinematic viscosity of 𝒱=1.004×10⁶ m² s⁻¹ appropriate to fresh water at 20 °C and equation 1, the maximum Reynolds number reached during the fast-starts increased from 2900 for the 10 mm fish to 49 200 for the 63 mm fish. All the fast-starts were for fish starting from rest, with an initial Re=0; however, all these fish would quickly have entered the regime (Re>300; Fuiman and Batty, 1997) where inertial forces dominated the hydrodynamics.

The kinematics of body bending for all the size classes of these fish, apart from the 10 mm group, were similar (Fig. 11), suggesting that the swimming style is maintained across this developmental range. The spine curvatures for the 10 mm fish were similar to those of the larger fish for ⁠, but their curvatures increased little beyond this point towards the tail (Fig. 11). All the larger sizes, in contrast, showed increasing spine curvatures as far as the position. The kinematics of these fast-starts were similar to those for steady swimming in that waves of bending travelled along the body and the amplitude of changes in spine curvature increased in a posterior direction along the fish. The difference in kinematics between the 10 mm fish and the larger classes may reflect an increasing rigidity of the anterior part of the body (Osse, 1990).

A characteristic feature of the muscle dynamics of fast-starts is that there is a drop in mean mass-specific power output between the longitudinal positions 0.4L and 0.8L, and there is a corresponding increase in muscle stress between these locations (Fig. 13). For instance, for the 63 mm fish, the 0.8L values for mass-specific power output are 21 % and for stress are 130 % of their respective values at 0.4L.

During fast-starts, the majority of the hydrodynamic power is delivered into the water from the caudal region of the fish (Weihs, 1973; Frith and Blake, 1991), whereas the majority of the white myotomal muscle available for power generation is situated in the central region of the body. Muscle in the caudal region of the fish must act to increase the body stiffness that is needed to transmit power from the main muscle bulk to the tail. Caudal muscle fibres must therefore act as stiff elements, and this is achieved by producing higher forces at the expense of generating a high power output. Whole-body ‘work loop’ experiments have shown that increases in body stiffness do result from increases in muscle stiffness and decreases in the work done by the muscles (Long and Nipper, 1996).

Changes in muscle power and force production along the fish during fast-starts occur as a result of the decreasing strain and, therefore, strain rate experienced by the muscle (Fig. 12; Wakeling and Johnston, 1998, 1999a). Longitudinal changes in force and power production have been predicted during steady swimming as a result of phase changes between the activation and shortening of the muscle fibres (for a review, see Wardle et al., 1995). However, during fast-starts, the muscle starts to shorten immediately after activation at all longitudinal sites (Wakeling and Johnston, 1999c). The phase changes found in steady swimming between activation and shortening are not required to explain the difference in muscle function during fast-starts.

The time-dependent contractile properties of the white myotomal muscle have been shown to be slower in caudal than in rostral myotomes for cod Gadus morhua (Davies et al., 1995) and saithe Pollachius virens (Altringham et al., 1993), although no significant differences were found between these sites in the sculpin Myoxocephalus scorpius (Johnston et al., 1995; James and Johnston, 1998a). Slower contractile properties of the caudal myotomes predispose them to slow strain rates and therefore higher force production. However, the reduction in mass-specific power output resulting from the different contractile properties of the muscle between rostral and caudal sites (to 49 % in the caudal myotomes for the saithe; Altringham et al., 1993) is less than half of that which can be explained by the body kinematics and longitudinal change in muscle strain rate during fast-starts and may not even be significant (James and Johnston, 1999a). In contrast, the longitudinal change in muscle strain along the fish plays a major role in balancing muscle function between force and power production during fast-starts.

The fish were characteristically stationary with their body straight prior to the initiation of a fast-start. An initial rapid bending of the body marked the beginning of each fast-start. This body bending is the result of the interaction between torque being generated by the myotomal muscle and the resistance to bending, which is predominantly the inertia of the body and the added mass of water (Wakeling and Johnston, 1999c). The rate of bending can be expressed in terms of scaling relationships for geometric fish.

Data from the present study show that there is an increase in contraction duration with increasing body length (Fig. 10) which corresponds to a decrease in mean contraction velocity of the white muscle fibres, given that the muscle strains are similar at different sizes (Fig. 12). The scaling relationship (equation 9) is based on a number of assumptions, including geometric similarity of the fish in terms of both shape and muscle distribution, and also assuming identical muscle contractile properties and activation patterns. These assumptions are not valid across the sizes of carp in the present study, but the main conclusions of the scaling predictions hold true. Increases in body length constrain the fish to bend less rapidly because the cross-sectional muscle area, and hence force production, does not increase at the same rate as the inertial mass that resists the bending.

As fish length increases, the changing interaction between the muscle bulk and the body results in a decrease in strain rate during the initial tail-beat of the fast-start. For the case of the carp in the present study, this change occurs as an increase in the contraction duration coupled to an invariant peak muscle strain. During the brief contractions used for fast-starts, the decreasing strain rate that occurs with increasing body length causes the following changes in muscle contractile dynamics: the activation rate increases, the maximum muscle force increases, the time course for force production increases and the rate of deactivation decreases in relation to the rate of activation (Wakeling and Johnston, 1999b). The muscle power output is the product of its force and shortening velocity, and the mass-specific power showed an increase with increasing body length across the size range of carp from this study.

The increases in muscle stress and mass-specific power output with body length shown in Fig. 13 are due entirely to the changes in contraction regime because the intrinsic muscle contractile properties were assumed to be invariant during ontogeny for these fish. The change in muscle contraction regime is sufficient to account for a 42 % increase in muscle stress and a 386 % increase in mass-specific power output. However, changes in muscle composition during ontogeny may additionally predispose the muscle to an increased performance for larger fish. Indeed, the myosin ATPase for carp myotomal muscle tends to decrease in activity with ontogeny across a similar size range to that used in this study. However, this decrease was not significant (N. J. Cole and I. A. Johnston, in preparation). In other species of fish, the length-dependent changes in twitch contraction times (Archer et al., 1990; Videler and Wardle, 1991) and maximum unloaded shortening velocity (James and Johnston, 1998b) may only explain an 11 % change in contractile variables for the 50 mm range of fish lengths appropriate to the present study. The changes in muscle stress and mass-specific power output due to the different length-dependent contraction regimes therefore make a much larger contribution to the developmental changes in muscle performance than do the changes in muscle composition that occur during ontogeny.

During swimming, energy is expended for both normal and tangential components of the motion. However, it is only the tangential component of the propulsive force that causes acceleration of the fish in its direction of travel. The hydrodynamic efficiency η is the ratio of the tangential hydrodynamic force to the total hydrodynamic force. During fast-starts in pike Esox lucius, η was estimated to be between 0.16 and 0.39 and took a mean value of 0.32±0.04 (mean ± S.E.M., N=6) (Frith and Blake, 1995). The tangential inertial power requirements can be used as an estimate of the ‘useful’ tangential hydrodynamic power, and η for these pike was 0.31±0.05 using this second estimate (data in Frith and Blake, 1995).

This work was supported by a non-thematic grant (GR3/11028) from the Natural Environment Research Council of the UK.