Isometric and isotonic muscle properties as determinants of work loop power output

Transcription

1 Pflugers Arch Eur J Physiol (1996) 432: Springer-Verlag 1996 ORIGINAL ARTICLE Rob S. James - Iain S. Young Valerie M. Cox David F. Goldspink John D. Altringham Isometric and isotonic muscle properties as determinants of work loop power output Received: 24 October 1995 / Received after revision and accepted: 1 May 1996 Abstract The power output of rabbit latissimus dorsi muscle was calculated under isotonic conditions and during oscillatory work. Isotonic shortening studies yielded a maximum power output of 12 W kg -' at a P/Po of.4 compared to a maximum power output of 32 W kg -1 obtained using the work loop technique. This difference can largely be explained by comparing actual work loops with those constructed using force velocity (P/V) and isometric data. At low cycle frequencies, work loop power output is quite close to that predicted from P/V and isometric data. However, at higher frequencies other dynamic muscle properties appear to exert a more marked effect. Key words Muscle Work Power Isotonic shortening Work loops Muscle mechanics Introduction During repetitive activity, such as locomotion, muscles experience cyclic changes in length. When a muscle generates force during such a length change, it produces work. The work output during shortening is commonly referred to as "positive work" and the work input, to reextend the muscle, as "negative work" [2]. The net work produced by the muscle is the positive work minus the negative work. The work loop technique [18] simulates the activity of a power-producing muscle by subjecting it to a series of cyclic length changes (strains) R.S. James I.S. Young ( ) J.D. Altringham Department of Pure and Applied Biology, The University of Leeds, Leeds LS2 9JT, UK V.M. Cox D.F. Goldspink Institute of Cardiovascular Research, Department of Clinical Medicine, The University of Leeds, Leeds LS2 9JT, UK R.S. James Gatty Marine Laboratory, Department of Biology, University of St. Andrews, St. Andrews, Fife KY16 8LB UK while stimulating it to contract. A plot of muscle force against the muscle strain produces a loop, the area of which represents the net work produced during a cycle of activity [18]. Average power is calculated by multiplying net work by cycle frequency. Josephson [2] discussed some of the differences between maximum instantaneous power output obtained from force velocity (P/V) curves and measurements of maximum power output derived from work loops. Positive work cannot be generated continuously during the normal operation of a muscle as this would imply that the muscle could continue to shorten indefinitely. Instead, a muscle must be re-extended during each cycle of operation, involving an amount of negative work. To minimise this negative work, the muscle should be relaxed during re-extension. Several other factors interact to determine the possible power-generating capacity of a muscle. High forces cannot be developed instantaneously; similarly, relaxation is not instantaneous, so to minimise the work of re-extension, a muscle must start to relax during shortening. The maximum power output of a muscle obtained from its P/V relationship is the product of an optimum muscle force and velocity. These optima occur only briefly (or not at all) during in vivo operation because shortening velocity and force vary continuously during a cycle of muscular contraction. Shortening deactivation [8, 12] and force enhancement due to stretch [1, 11] are also important in determining force and hence the work and power output of a muscle during cyclic operation. Josephson [2] concluded that, although P/V curves are a good measure of the instantaneous power output of a muscle, they do not provide a measurement of the "sustainable power output". Our aim was to test this hypothesis empirically and to determine the constraints imposed on muscle performance by its isometric and dynamic properties. Measurements of isotonic and isometric properties of rabbit latissimus dorsi preparations were made with the muscle in situ. Work loop experiments were carried out using the same preparations. The work and power output of the muscle, determined directly using the

2 768 work loop technique and calculated using isometric and isotonic muscle properties, were compared. Materials and methods Durch rabbits were anaesthetised using a premedication of.5 mg of Midazolam base kg-' body weight,.1 ml Hypnorm (3.2 pg fentanyl citrate,.1 mg fluanisone) kg - ' body weight, administered by subcutaneous injection. Anaesthesia was maintained by intramuscular injection of fentanyl/fluanisone and subcutaneous injection of Midazolam as necessary. Heart rate was monitored continuously be ECG and the animal's breathing was observed. A heated experimental table maintained body temperature at 37 ±.5 C. The skin of the back was reflected to uncover the underlying muscles. The medial, tendinous part of the latissimus dorsi (LD) muscle was dissected away from its attachments to the spine, lumbar fascia and ribs. The muscle was then dissected free of the underlying fascia so that it was able to move and contract unimpeded. The humeral tendon and the thoracodorsal nerve and blood vessels were left intact. The medial end of LD was sutured onto a rigid triangular plastic frame, which was attached to an isometric force transducer (Miniature Beam Load-cell, RDP Electronics, Wolverhampton, UK). This force transducer was mounted on a servo-motor that produced the cyclic strains used during work loop experiments. The LD was maintained at a steady 37±.5 C by irrigation with physiological saline. Supramaximal stimuli of 2 ms pulse width were delivered by two Teflon-coated, stainless steel electrodes, sutured to the inferior surface of the muscle, close to the main branches of the thoracodorsal nerve. The forelimbs were firmly secured to the experimental table to minimise external compliances. This preparation is particularly appropriate for the assessment of muscle power output under conditions simulating in vivo operation because the major blood vessels are left intact. Thus the problems of deterioration due to anoxia, which are often encountered in vitro [27], are avoided. Isometric measurements The stimulation amplitude and frequency producing maximum tetanic force were determined; these values were used throughout subsequent experiments. Resting muscle fibre length (L) was defined as the mean fibre length for maximum twitch force. The shape of the muscle made it necessary to estimate mean fibre length as the length of the fibres in the middle of the muscle. This will cause a small error in the strain the fibres of the muscle experienced during cyclic changes in length. We estimate that this error is less than.5%. As our results show, this error is unlikely to have any significant effect on measurements of work or power output. Maximum tetanic isometric stress (P ) and twitch and tetanic kinetics were determined: the time from stimulus to half-maximum twitch force (t5) and peak twitch force (t, oa), and the time from the stimulus to the point during relaxation when twitch force has fallen to 1% of peak twitch force (t r9o) were measured. In addition, the time from peak to half-maximum tetanic force during relaxation ('/2Rt) was recorded. Isotonic measurements A cantilever isotonic transducer (Harvard) was used for isotonic measurements. A low-friction pulley system was used to hang weights from one side of the cantilever with the LD attached to the other. Initial muscle fibre length was set at Lo with a mechanical stop preventing extension. The muscle was loaded stepwise ascending to, then descending from, the muscle's maximum isometric force (P). The ascending and descending data were compared to ensure that the muscle had not deteriorated during the course of the experiment. For each measurement, a given load (mass) was applied to the LD, which was tetanised by a 3-ms stimulation burst. The burst duration allowed maximum activation and steady shortening velocity to be attained in every case. Muscle length was monitored using a digital storage oscilloscope (Gould 164) and the shortening velocity was determined from the linear part of the shortening record. In all cases the muscle shortened by less than 12% of Lo. The preparation was allowed 5 min to recover between measurements. Maximum shortening velocity (Vmax) was determined by extrapolation of the P/V curve to give velocity at zero force. Power output was determined as the product of shortening velocity and load. A power ratio value was derived using Eq. 1 to allow comparison of muscle P/V relationships from different studies [231: Wmax/ ( Vmax'Po) (1) Wmax is the maximum power output determined from the P/V relationship, Po is the maximum muscle force at zero velocity and Vmax is the predicted maximum velocity of shortening at zero force. Work loops For work loop studies the muscle was attached to an isometric force transducer (RDP Electronics) mounted on a servo-motor. The muscle was subjected to a series of runs consisting of four sinusoidal strain cycles. During each cycle the muscle was stimulated at the tetanic fusion frequency, as determined above. Five minutes were allowed for recovery between runs. The experiment was controlled and the data collected and analysed on-line by a PC microcomputer using in-house software. Preliminary experiments showed that a strain of ±5% about Lo (1% peak-to-peak) produced maximum power output over a substantial range of cycle frequencies and the effect of varying strain at frequencies close to the frequency for maximum power output (6Hz) was small. Power output could, however, be increased at lower cycle frequencies by increasing strain. As strain had little effect on maximum power output, and to facilitate comparison of work loops, a strain of ±5% was used in all subsequent work loop experiments. The duration and phase of stimulation were varied at each cycle frequency to maximise power output (phase is expressed in degrees, where refers to LO during lengthening and a complete strain cycle is 36 ). During each work loop cycle, energy will be dissipated by the muscle due to viscoelasticity. To calculate these losses during a work loop cycle, passive loops were generated by subjecting unstimulated muscle to cyclic strains (passive work loops) of ±5% L. Control work loops, using stimulation and strain parameters yielding maximum power, were performed every fourth run to monitor any change in the muscle power output. These were used to correct for any small decreases in power output measured over the course of the experiment [4]. The experiment was concluded if muscle power declined to below 8% of its initial value. This was rarely necessary. Work decreased by about 5% from the first to the second cycle of each run, then remained almost constant over subsequent loops. Therefore, the second loop was taken to be a better representation of the steady state and was used in subsequent calculations. P/V data were obtained from work loops so that the dynamic performance of the muscle during oscillatory work and under isotonic conditions could be compared to the performance of the muscle under isotonic conditions. VNmax was calculated using a value for Vmax from isotonic measurements on the same muscle and the mean shortening velocity from the work loop was used as a value for V. P/Po was also calculated using maximum isometric stress as P, and P was measured directly from each work loop. The animals were killed at the end of the experiment by an intravenous overdose of Sagatal (pentobarbitone). The muscles were immediately removed and weighed. The volume of the muscle was determined gravimetrically, assuming a muscle density of 16 kg m-3. The cross-sectional area of the muscle was determined as

3 muscle volume divided by Lo. These measurements were used to calculate mass-specific work, power output and muscle stress. Results were obtained from both left and right LD muscles. A nonparametric statistical analysis (two-tailed P values derived from a Mann Whitney U-test) showed no significant differences between the left and right sides so data were pooled for further analysis, to minimise the number of animals required. Results The isometric properties of rabbit LD muscle, as measured in situ, are summarised in Table 1. The number of replicates (n) varies as it was not always possible to calculate each value for every experimental animal. Work loop data and isotonic P/V data for the same rabbit LD muscles are summarised in Table 2. V/V max and P/P correspond to isotonic measurements. Typical P/V and power data from isotonic experiments are shown in Fig. 1. Power output increases to a maximum then decreases with increasing load. A plot of power output against V/Vmax yields a similar shaped curve. In work loop experiments cycle frequency has a profound effect on power output. At a constant strain of ±5%, power output (net work multiplied by cycle frequency) increased with increasing frequency to a maximum, before declining at higher frequencies (Fig. 2). The net work per cycle decreases with increasing cycle frequency. During preliminary work loop experiments, a cyclic strain of ±5% L (1% peak-to-peak) produced maxi- Table 1 Data are means±sem (number of values). (Lo Resting length, tso time from onset of stimulation to 5% maximum twitch force, t 1 time from onset of stimulation to maximum twitch force, t 9 time taken, during relaxation, for twitch force to decline to 1% of its peak value, //2Rt time taken, during relaxation, for the tetanic force to decline to 5% of its peak value). L o was taken to be the length for maximum twitch force Parameter Value (n) Rabbit body mass (kg) 1.5±.1 (17) Lo (cm) 12.6±.3 (21) Muscle mass (g) 6.4±.5 (21) Maximum twitch force (N) 2.4±.2 (21) ts (ms) 13.1±.8 (2) t 1 (ms) 31.9±2.2 (2) tr9 (ms) 113.±6.(19) Maximum tetanic force: Po (N) 7.5±.4 (21) Maximum isometric stress (kn m-2) 156.±4.6 (2) '/2Rt (ms) 24.±.8 (11) 769 mum power output at a cycle frequency of about 5 Hz. Increasing strain at low cycle frequencies increased power output. The optimum strain for power output was ±12%L at2hz. However, varying strain had little effect on power at cycle frequencies at or above those yielding close to maximal power output (Fig. 2). At 5 Hz, ±5% strain yielded maximal power output with no significant difference in power output recorded for strains between ±3 and ±12% (Fig. 3). The low dependence of power upon strain at frequencies close to that for maximum power output is illustrated in Fig. 3 (data for 5%). Effect of frequency and strain upon passive work For a given strain, the amount of energy lost (negative work) increased with increasing cycle frequency, from 3% of the total work (calculated as the sum of active and passive components) at 1 Hz to a maximum of 23% at 7 Hz. At any given frequency, passive work increased with increasing strain amplitude. The number of stimuli and the phase shift required to produce maximal power output were found to decrease with increasing cycle frequency. The optimal Q to C m Power Vs V/V n.\power Vs. PlPo P-V Relative Force (P/P) Relative Velocity (V/V,,,) a Fig. 1 Results from an isotonic shortening experiment. Plots are: shortening velocity versus relative force (P/Po) power output versus P/Po and power output versus relative velocity (V/Vmax). Lines were fitted using third-order polynomial regression F Table 2 A summary of work loop data and isotonic force/velocity (P/V) data in rabbit latissimus dorsi muscle. Vmax is measured as muscle lengths per second (L s -1 ). V/Vmax and P/Po correspond to those yielding maximum power derived from isotonic measurements Parameter Work loop Isotonic Maximum shortening velocity Not applicable 5.±.3 (6) Umax (Ls') Power ratio: W,, ax/(vmax Po) Not applicable.13±. (6) Maximum power output (W-kg- ') 31.8±2.3 (9) 12.±12. (7) V/Vmax at maximum power output.4 (9).4±. (7) P/Po at maximum power output.7±.1 (9).41±. (7)

4 II Strain optimised 3, i (n>4) ^ i 3 2 _ T 3 15 f G -4 j l^ Cycle frequency (Hz) Fig. 2 The relationship between power output and cycle frequency during work loops under conditions of constant and optimised strain. Data are means, error bars indicate SEM Phase Shift (degrees) Fig. 4 The effect of varying phase from to 36, at a cycle frequency of 5 Hz. All other parameters were those which produce maximum power output at 4 8Hz 5Hz 2Hz 3 Discussion Isometric data Strain Amplitude (f% L o) The rabbit LD muscle produced a maximum isometric stress of 156 kn m-2, which falls at the lower end of the range previously reported for mammalian skeletal muscle: 155 and 159 kn m-2 for mouse and rat diaphragm muscle [4], 215 and 194 kn m-2 for rat extensor digitorum longus (EDL) and soleus muscle [27], 233 and 224 kn'm-2 for mouse EDL and soleus muscle respectively [15]. The trgo value of 114 ms is shorter than that previously reported for rabbit diaphragm muscle (175 ms, [4]). This may be expected because the LD is composed of predominantly fast-twitch fibres [13], whereas the rabbit diaphragm muscle possesses a higher percentage of slow-twitch fibres [21 ]. Fig. 3 The effect of strain on power output at different cycle frequencies, n>4 number of stimuli ranged from 33 at 1 Hz to 3 at 8 Hz and the phase shift ranged from 5 at 1 Hz to 4 at 8 Hz. A phase shift of 4 yielded maximum positive power output and a phase shift of 23 produced maximum negative power output (Fig. 4). Maximum negative work required to extend the active muscle was more than twice the maximum positive and work output. Force/velocity studies The Hill equation [14] provides a satisfactory description of intermediate P/V data but deviates from the observed P/V relationship of a muscle at high and low forces. Many studies have addressed this problem and a number of different curve-fitting equations have been used (e.g. [1, 9, 23]). Marsh and Bennett [23] proposed the use of a formula (Eq. 1) to allow the curvature of P/V relationships, derived in studies using different muscles and different curve-fitting equations, to be compared: Wmax/(Vmax Po)

5 771 This "power ratio" is relatively independent of the curvefitting equation used. In this study, we obtained a power ratio of.13, which falls within the range of values found for other fast-twitch muscles, of [1, 7, 14, 16, 241. Maximum instantaneous power was obtained at a V/V,nax value of.34 derived by fitting a third-order polynomial to P/V data using a least-squares regression analysis [1]. This value compares well with previously published results of.18 to.36 V/VmaX for carp red muscle [25] and between.29 and.33 V/Vmax for scallop adductor muscle [24]. Maximum power and efficiency of frog sartorius muscle have also been found to fall within a similar range of.23 to.35 V/V,,, ax [22, 3]. Work loops The work loops obtained in this study demonstrate that the amplitude and frequency of the strain cycle, and the duration, phase shift and frequency of stimulation all influence the average power output of LD. These variables and their effects are similar to those observed in previous studies involving a range of muscle types (e.g. [2, 3, 15, 18]). The optimal number of stimuli decreased with increasing cycle frequency. This is because fewer stimuli were required to maintain activity in the muscle during the progressively decreasing shortening period. Varying the phase of stimulation had a marked effect on work output (Fig. 4). The optimum stimulation phase at low cycle frequencies in close to 9, corresponding to peak muscle length. This phase decreases with increasing cycle frequency (4 at 6-8 Hz). A muscle requires a finite time for activation. If the muscle is stimulated during lengthening, it has time to attain higher forces before the onset of shortening, thereby increasing work output. In addition, increased force may be generated when an active muscle is stretched [1, 11]. Only a small range of stimulation phases produce net positive power output (Fig. 4). Indeed, stimulation of the muscle during lengthening results in a large negative power output, more than twice the maximum positive power output. These results agree closely with those of Johnson and Johnston [17]. Power output derived from P/V data and oscillatory work Maximum instantaneous power output, calculated as the maximum product of muscle force and isotonic shortening velocity, was 12 W kg -1. In contrast, the maximum average power output derived from work loops was only 27% of this, 32 W kg -1. Previous studies have also found work loop power output to be considerably lower than power determined from the P/V relationship; e.g. 21% for fish slow muscle [26] and 33% for frog and toad sartorius muscle [28]. The value for maximum power output derived from P/V data relates to a maximum product of force and velocity for maximally activated muscle. In contrast, the work loop technique calculates the power output of a muscle under simulated in vivo operating conditions, in which the level of activation and the shortening velocity are constantly changing [2]. Under in vivo conditions work is performed when a muscle undergoes a length change while generating force. This is said to be "positive work" during shortening and "negative work" during re-extension. Power is calculated as the product of work and cycle frequency. Since positive power can only be generated during shortening, mean power output during cyclic activity must be less than half the value for maximum power output calculated from P/V data, in this case, 6 W kg-1. This value is still twice the power output obtained from work loop studies (32 W kg -1). How can this apparent discrepancy be explained? For the power output predicted by P/V data to be sustained during repetitive activity, several conditions would need to apply: P/Po and V/Vmax must remain optimal and constant during shortening, both activation and relaxation must be instantaneous, the muscle should be fully relaxed throughout lengthening and there should be no substantial viscoelastic energy losses. These conditions are clearly not realistic. P/V data, isometric kinetics and passive muscle properties were used to construct theoretical work loops (Figs. 5 and 6). The P/V relationship, derived for each muscle, was used to calculate forces corresponding to the shortening velocity at various lengths during the work loop. A loop was then constructed assuming instantaneous force development and relaxation (Fig. Sa, dashed line) as in Josephson [19]. Figure 5b shows the time course of force development (dotted line) derived from isometric data. Isometric force was recorded against time during a tetanic contraction of the same muscle. The time course was superimposed on the force/length plot by converting each time point to a phase during the strain cycle (e.g. at a cycle frequency of I Hz,.25 s corresponds to 9 or maximum muscle length, in this case +5%). The starting phase was taken as the start of stimulation. For example, if the work loop stimulation phase was 6, the isometric force.25 s after the start of stimulation would be plotted at 6 +9 =15. It was defined that the muscle should start to relax early enough to allow the force to decline to the same resting force experienced during a work loop at minimum muscle length. The passive force recorded during a work loop was used as the base line of the theoretical work loop. It seems reasonable to assume that the muscle will produce force within the limits of its P/V relationship and isometric properties. The shaded region in Fig. Sc therefore represents a work loop constructed within these parameters. The dynamic constraints upon the maximum power output of a muscle can be illustrated by comparing the shapes of loops derived from isometric and P/V data with optimal loops obtained using the work loop technique at different cycle frequencies (Fig. 6). The force developed at the start of the shortening phase of the work loop was

6 772 Fig. 5a A work loop constructed using isotonic data, assuming instantaneous activation and relaxation (dashed line). b Isometric force development and relaxation time course (dotted line) superimposed upon the P/V loop from a. c A work loop constructed within the parameters defined by isometric and isotonic muscle properties (shaded). The experimentally derived optimal work loop at 5 Hz is shown by the bold line typically lower than that predicted from isometric and isotonic data. At low cycle frequencies of 1 and 2 Hz (Fig. 6a, b) force development and relaxation times occupy only a small proportion of the shortening phase; about 6-8% of maximum isometric force is developed for almost all of the shortening period. The resulting work loops are almost rectangular in shape and high work outputs are achieved. At higher cycle frequencies, isometric force development and relaxation times occupy larger proportions of the work loop period. In addition, the P/V relationship dictates that force is reduced as shortening velocity increases. This trend of decreasing force and proportionately longer times for force development and relaxation can be seen by looking at Fig. 6a g in turn. It is apparent that the loops obtained by the work loop technique show some differences to those derived theoretically from the combined isometric and isotonic data. Isotonic data (dashed line) predict that force should fall during the initial half of the shortening period with increasing shortening velocity. Force should then recover, during the later half of the shortening period, as shortening velocity decreases sinusoidally. However, work loop force initially remains approximately constant, then decreases more rapidly in the second half of the shortening phase. This may be due to the sustained effect of force enhancement [1] delaying, or compensating for, the influence of increasing shortening velocity. With the cessation of stimulation in the later stages of shortening, work loop force is seen to decline more steeply than predicted by isometric relaxation times. This difference becomes more apparent with increasing cycle frequency as force is maintained for longer then declines more rapidly than predicted from isometric data. This increased rate of relaxation is probably partly due to shortening-induced deactivation [8, 12] which is, to some extent, velocity dependent [3, 6]: the effect is consequently more significant at higher cycle frequencies. Shortening-induced deactivation allows stimulation to be applied for a larger proportion of the shortening period while producing minimal negative work during lengthening. Therefore, a higher force may be maintained for a greater proportion of the shortening period than predicted from isometric kinetics alone. This results in an increase in net work output [3, 5]. The optimum phase of stimulation decreases with increasing cycle frequency, so that activation of the muscle occurs during extension. This has several consequences. There is an increase in the force required to stretch the active muscle during the later part of extension and a consequent increase in the "negative" work of re-extension (particularly Fig. 6d g). However, the earlier onset of stimulation may allow the muscle to be stimulated for longer, increasing both force and work. During lengthening, the force applied to extend the muscle rises and work is performed upon the elastic and visco-elastic structures associated with the muscle. Some of this work of re-extension will be stored as elastic strain energy, which will be returned as the muscle recoils during shortening. The remainder of this energy will be lost due to visco-elasticity. Under a constant strain, visco-elastic losses are seen to increase with increasing cycle frequency [29]. These losses will further decrease the net power output of a muscle performing cyclic work. The loops constructed using combined P/V and isometric data provide quite a good approximation of loop shape (Fig. 6) and power output obtained from actual work loops (Table 3). These values for power output agree far better than estimates using isometric or P/V data alone. However, at higher cycle frequencies, work

7 773 Fig. 6a g A series of work loops constructed in the same manner as those in Fig. 5, but using data derived at different cycle frequencies. Isometric tetanic activation and relaxation time course (dotted line) and isotonic data, assuming instantaneous activation and relaxation (dashed line). A work loop constructed within the parameters defined by isometric and isotonic muscle properties is shown by the shaded area and the experimentally derived optimal work loop is shown by the solid line. The period during which the muscle is stimulated is shown in bold loop power output is higher than predicted, illustrating the influence of velocity-dependent dynamic muscle properties as discussed above. Power trajectories The variation in power output of a muscle during cyclic activity can be illustrated by plotting the data derived from work loops as power trajectories [28]. These trajectories can be compared to P/V data recorded under isotonic conditions. During isotonic shortening studies, muscle was usually maximally activated activated and produced maximum power at a particular value of V/V,nax. However, in a work loop, muscle activation is not constant and shortening velocity changes sinusoidally. At the cycle frequency for maximum net power output (5-6 Hz), variation in shortening velocity results in the LD operating at a V/Vmax that would yield less than 9% of the maximum power output predicted from the P/V curve, for about half of the shortening period (Fig. 7). At 7 Hz, force exceeds that predicted from P/V and isometric data for almost all of the shortening phase of the work loop. This agrees with the results obtained by Stevens [28]. This also agrees with this conclusion that the P/V combinations obtained during a work loop, using physiologically realistic parameters, differ from those obtained from a standard P/V curve. Table 3 Power outputs derived from the work loops constructed using isometric data, isotonic data and a combination of isometric and isotonic data as shown in Fig. 6. These values for power output are compared to the work loop power output, for the same muscle, over a frequency range of 1-7 Hz Frequency Power output Power output Power output Power output (Hz) from P/V "loops" from isometric from combined data from work loop (W-kg-1 ) "loops" (W kg -1 ) (W kg-') data (W kg-1 )

8 774 U y rn y -2 P-V 7_Hz 1 G// 5 Hz \ 1 _ mo t _1- ^ 1 ' `, Hz / 1 Hẓ... y r'' V Relative Force P/P Fig. 7 Power trajectories, with data derived from work loops, illustrating the variation in power output of a muscle during cyclic activity. These power trajectories are compared to P/V data recorded under isotonic conditions. Shortening velocity is in muscle lengths per second Isometric and isotonic measurements of force and force/velocity relationships describe particular characteristics of muscle performance. However, the maximum power output derived from isotonic measurements overestimates the "sustainable power output" of a muscle [2]. A more realistic estimate can be obtained if the isometric kinetics are also taken into account. At higher cycle frequencies the influence of other dynamic muscle properties become more apparent. Acknowledgements We would like to thank John Oughton for technical support. R.S.J. was supported by a SERC/CASE studentship, with the National Heart Research Fund. I.S.Y. and V.M.C. were funded by the British Heart Foundation and the Sir Jules Thorne Charitable Trust respectively. References 1. Altringham JD, Johnston IA (1988) The mechanical properties of polyneuronally innervated, myotomal muscle fibres isolated from a teleost fish (Myoxocephalus scorpius). Pflugers Arch 412: Altringham JD, Johnston IA (199) Modelling muscle power output in a swimming fish. J Exp Biol 148: Altringham JD, Johnston IA (199) Scaling effects on muscle function: power output of isolated fish muscle fibres performing oscillatory work. J Exp Biol 151: Altringham JD, Young IS (1991) Power output and frequency of oscillatory work in mammalian diaphragm muscle: the effects of animal size. J Exp Biol 157: Altringham JD, Wardle CS, Smith CI (1993) Myotomal muscle function at different locations in the body of a swimming fish. J Exp Biol 182: Colomo F, Lombardi V, Piazzesi G (1986) A velocity-dependent shortening depression in the development of the force-velocity relation in frog muscle fibres. J Physiol (Lond) 38: Curtin NA, Woledge RC (1991) Efficiency of energy conversion during shortening of muscle fibres from the dogfish Scyliorhinus canicula: J Exp Biol 158: Edman KAP (198) Depression of mechanical performance by active shortening during twitch and tetanus of vertebrate muscle fibres. Acta Physiol Scand 19: Edman KAP, Mulieri LA, Scubon-Mulieri B (1976) Non-hyperbolic force-velocity relationship in single muscle fibres. Acta Physiol Scand 98: Edman KAP, Elzinga G, Noble MIM (1978) Enhancement of mechanical performance by stretch during tetanic contractions of vertebrate skeletal muscle fibres. J Physiol (Lond) 281: Edman KAP, Elzinga G, Noble MIM (1982) Residual force enhancement after stretch of contracting frog single muscle fibres. J Gen Physiol 8: Ekelund MC, Edman KAP (1982) Shortening deactivation of skinned fibres of frog and mouse striated muscle. Acta Physiol Scand 116: Gillott KL, Cox VM, Wright H, Eaves LA, Williams PE, Goldspink DF (1994) The fibre type composition of the rabbit latissimus dorsi muscle. J Anat 185: Hill AV (197) First and last experiments in muscle mechanics. Cambridge University Press, London 15. James RS, Altringham JD, Goldspink DF (1995) The mechanical properties of fast and slow skeletal muscles of the mouse in relation to their locomotory function. J Exp Biol 198: Johnston IA, Altringham JD (1985) Evolutionary adaptation of muscle power output to environmental temperature: force-velocity characteristics of skinned fibres isolated from Antarctic, temperate and tropical marine fish. Pflugers Arch 45: Johnson TP, Johnston IA (1991) Power output of fish muscle fibres performing oscillatory work: effects of acute and seasonal temperature change. J Exp Biol 157: Josephson RK (1985) Mechanical power output from striated muscle during cyclic contraction. J Exp Biol 114: Josephson RK (1989) Power output from skeletal muscle during linear and sinusoidal shortening. J Exp Biol 147: Josephson RK (1993) Contraction dynamics and power output of skeletal muscle. Annu Rev Physiol 55: Kilarski W, Sjostrom M (199) Systematic distribution of muscle fibre types in the rat and rabbit diaphragm: a morphometric and ultrastructural analysis. J Anat 168: Kushmerick MJ, Davies RE (1969) The chemical energetics of muscle contraction. H. The chemistry, efficiency and power of maximally working sartorius muscle. Proc R Soc Lond [Biol] 174: Marsh RL, Bennett AF (1986) Thermal dependence of contractile properties of skeletal muscle from the lizard Sceloporus occidentalis with comments on methods for fitting and comparing force velocity curves. J Exp Biol 126: Olson JM, Marsh RL (1993) Contractile properties of the striated adductor muscle in the bay scallop Argopectans irradians at several temperatures. J Exp Biol 176: Rome LC, Sosnicki AA (199) The influence of temperature on mechanics of red muscle in carp. J Physiol (Lond) 427: Rome LC, Swank D (1992) The influence of temperature on power output of scup red muscle during cyclical length changes. J Exp Biol 171: Segal SS, Faulkner JA (1985) Temperature-dependent physiological stability of rat skeletal muscle in vitro. Am J Physiol 248: Stevens ED (1993) Relation between work and power calculated from force-velocity curves to that done during oscillatory work. J Muscle Res Cell Motil 14: Syme D (199) Passive viscoelastic work of isolated rat, Rattus norvegicus diaphragm muscle. J Physiol (Lond) 424: Woledge RC, Curtin NA, Homsher E (1985) Energetic Aspects of Muscle Contraction. Academic, London