The influence of strain and activation on the locomotor function of rat ankle extensor muscles

The intrinsic properties of a muscle can be split into three main categories: (1) the stress–strain relationship; (2) the stress–strain rate relationship; and (3) activation–deactivation kinetics. Measurement of these properties typically occurs in vitro during isotonic loading of fully activated isolated muscle, small fibre bundles or single fibres. Such information has revealed much about muscle function, and has provided an initial insight into the diversity and similarity that exists between muscles proposed to fulfil specific roles during a range of motor tasks. The loading conditions under which these properties are defined are, however, very simple and do not generally represent patterns of loading, activation and length changes that occur in vivo. Improving understanding of the mechanical behaviour of muscles in vivo, therefore, depends on the measurement of the activity and length changes of specific muscles during normal locomotion.

Recent advances in technology have enabled a more complete picture of in vivo muscle function to be developed. Sonomicrometry techniques, have enabled in vivo muscle fascicle length trajectories to be recorded in a number of species and skeletal muscles under a variety of locomotor conditions (e.g. Biewener et al., 1998; Biewener et al., 2004; Carroll, 2004; Daley and Biewener, 2003; Donley et al., 2005; Gillis and Biewener, 2001; Gillis and Biewener, 2002; Higham et al., 2008; Hoffer et al., 1989; Sanford and Wainwright, 2002; Wakeling and Johnston, 1999). An important finding of these reports is that the mechanical behaviour of a muscle is not fixed, and can alter in response to changes in locomotor condition. For example, turkey ankle extensor muscles undergo much greater strains during incline locomotion than during locomotion on the flat (Gabaldon et al., 2004; Roberts et al., 1997). In addition, muscles are also able to adapt their mechanical work output, in response to changes in locomotor conditions, by changing the timing of myoelectric activity in relation to force production (Daley and Biewener, 2003; Gabaldon et al., 2004).

There is a wide range of information available on the contractile and physiological properties of rat muscles (Armstrong and Phelps, 1984; Close, 1964; Close and Luff, 1974; Delp and Duan, 1996; Schiaffino and Reggiani, 1996), and this model is commonly used in a wide range of physiological studies. Despite this, in vivo muscle fascicle behaviour of rat muscle during locomotion has only been documented in two reports, both focusing on proximal hind limb muscles: biceps femoris and vastus lateralis (Gillis and Biewener, 2001; Gillis and Biewener, 2002). The soleus, plantaris and medial gastrocnemius muscles in the rat have distinctly different fibre type populations (Armstrong and Phelps, 1984; Delp and Duan, 1996) and therefore provide a useful example with which to investigate how different fibre type populations adapt their mechanical work and power output through changes in mechanical behaviour (fascicle strain and strain rates) and/or activation timing in relation to force production. We present the first report of in vivo muscle fascicle strain and strain rates for rat ankle extensor muscles during treadmill locomotion at a range of velocity/incline combinations. These data represent a valuable opportunity to investigate how systematic changes in locomotor velocity and incline influence in vivo muscle fascicle behaviour in a group of anatomically synergistic muscles, with distinctly different mechanical properties and fibre type populations. As rat muscle has been used extensively in studies of muscle physiology and mechanics, it is of value to quantify the in vivo conditions under which these tissues function. We therefore also investigate the influence of muscle fascicle mechanical properties, myoelectric intensity, activation timing and duration and muscle fascicle strain and strain rate on the potential for force and power production during locomotion using a simple muscle model. Detailed reports of myoelectric data and some measurements of fascicle strains and strain rates have been reported elsewhere (Hodson-Tole and Wakeling, 2007; Hodson-Tole and Wakeling, 2008a; Hodson-Tole and Wakeling, 2008b).

Myoelectric and sonomicrometric data were collected from the soleus, plantaris and medial gastrocnemius muscles of the right hind limb of 19 female Sprague Dawley rats [approximate age 5–6 months; mass 250.07±18.57 g (mean±s.d.)]. The rats were housed in pairs in cages, maintained on standard rat feed and kept in a temperature-controlled room (20°C) with a 12 h:12 h light:dark cycle. All rats had undergone a five week training programme during which time they were acclimatised to run on a custom-built, motorised treadmill at nine speed (20–50 cm s⁻¹) and incline (0–25 deg.) combinations. All procedures were conducted in accordance with current UK Home Office regulations.

Surgical and data collection procedures have previously been described elsewhere (Hodson-Tole and Wakeling, 2007). Rats received a subcutaneous injection of atropine (0.01 mg kg⁻¹) and were anaesthetised using halothane gas (4% induction; 1.75–2% maintenance). The right hind limb and an area on the back over and just caudal to the scapulae were shaved, scrubbed (4% chlorhexidine gluconate solution, E-Z Scrub, Becton, Dickinson and Co., Franklin Lakes, NJ, USA) and painted with a povidone iodine solution. Two incisions were made, one caudal to the scapulae and the second along the lateral aspect of the right hind limb approximately parallel to the tibia. To keep the wires from the implanted transducers secure during the post-operative recovery period and during data collection they were fed through a subcutaneous tunnel, which was created between the two incisions, so that excess wires were externalised in the region of the scapulae and the transducers were situated in the region of the muscles of interest. No signs of discomfort relating to this procedure were observed post-operatively in any of the subjects.

Offset twist-hook bipolar silver-wire electrodes (0.1 mm diameter, California Fine Wire Inc., Grover Beach, CA, USA), with tips bared of 0.5 mm of insulation, were surgically implanted into two of the muscles of interest using fine tip forceps. Approximately 2 mm separated the electrode tips in each muscle. They were placed, at a depth of approximately 3 mm, in the mid-belly region of the soleus and plantaris muscles and in the medio-caudal region of the medial gastrocnemius as this area has been identified as containing predominantly fast, myosin heavy chain type IIB fibres (Armstrong and Phelps, 1984; Delp and Duan, 1996). In addition, two sonomicrometry crystals (1.0 mm+38 gauge stainless steel lead wires, Sonometrics, London, ON, Canada) were implanted into the third muscle of interest, following the orientation of the muscle fascicles as closely as possible (see Table 1 for details of data collected from each subject). Fascicle length changes can be tracked with greater than 95% accuracy if alignment of crystals is less than 18 deg. from the alignment of the fascicle. We are confident that our crystal alignment fell within this boundary; however, it should be noted that any changes in pennation angle during contraction due to fibre rotation are not accounted for here and are likely to cause some overestimation of fascicle strain.

To ensure that each animal had full range of movement of the limb, slack wire from both types of transducer was fed under the skin in the area surrounding the hip. Excess wire in the region of the scapulae was placed into a small cotton pouch that was secured under a small jacket, fashioned for each subject from elasticised bandage (Vetwrap™, 3M United Kingdom PLC, Bracknell, UK). The jacket protected the surgical incision, secured the wires and enabled the animals to be housed in pairs post-operatively. The two incisions were sutured shut with 5-0 vicryl suture and animals received post-operative analgesia (buprenorphine, 0.01 mg kg⁻¹, subcutaneously) during the 48 h recovery period.

All data were collected 48 h post surgery in an electrically shielded room. Each rat ran a three block, randomised exercise protocol incorporating nine speed/incline conditions (0 deg. at 20, 30, 40 and 50 cm s⁻¹; 10 deg. at 20, 30 and 40 cm s⁻¹; 20 deg. and 25 deg. at 20 cm s⁻¹). During each trial the position of the right hind limb was recorded using two cameras (100 Hz, A602f, Basler, Ahrensberg, Germany) connected to the data collection computer via IEEE 1394 ports. Myoelectric signals were amplified and band-pass filtered (30–1000 Hz, CP511 A.C. amplifier, Astro-Med. Inc., West Warwick, RI, USA) and collected (3200 Hz) through a 16-bit data acquisition card (PCI-6221, National Instruments Corps., Austin, TX, USA). Sonomicrometry signals were collected (715 Hz) using sonometrics systems hardware, relayed to the data collection computer via an analog–digital converter. All systems were synchronously triggered via a 16-bit data acquisition card and data collected for periods of 30 s. On completion of the trial animals were euthanased with an intraperitoneal overdose of pentobarbitone, and dissection carried out to confirm the location of the fine-wire electrodes and sonomicrometric crystals in each of the muscles.

For each subject and condition mean measurements of strain, shortening strain (negative strain values), lengthening strain (positive strain values), peak-to-peak strain, shortening strain rate and lengthening strain rate were made for the complete stride from the Fourier series. Data from the soleus during the fastest conditions (0 deg. 40 cm s⁻¹ and 0 deg. 50 cm s⁻¹ and 10 deg. 40 cm s⁻¹) were only successfully collected from one subject, so plots of these data only show mean values and do not include values for s.e.m.

Myoelectric data were analysed using wavelet transformation as previously described (Hodson-Tole and Wakeling, 2007). Briefly, a filter bank of 20 non-linearly scaled wavelets, 0≤k≤19, was used to resolve the myoelectric signals into time–frequency space (von Tscharner, 2000). Due to the quantity of low frequency (<100 Hz) noise identified in the signal the first four wavelet domains (0≤k≤3) were excluded from further analysis, and the remaining frequency band that was analysed (4≤k≤19) covered the frequencies from 69.92 Hz to 1325.00 Hz. The intensity, i, of the signal at each wavelet domain was then calculated at each time point from the magnitude and the first-time derivative of the square of the convoluted signal. Mean intensities were calculated for strides collected during each locomotor condition.

To calculate the duration of myoelectric activity, and hence the myoelectric duty cycle, a threshold intensity was defined whereby values greater than the threshold were considered to represent myoelectric activity and values below the threshold were considered to represent times when the muscle was inactive. The thresholds were defined as twice the lowest mean level of intensity, calculated in all conditions from the period of minimum myoelectric activity (approximately 60–80% stride duration). Thresholds were calculated per individual and used to define periods of myoelectric activity within each subject before mean values were calculated for each locomotor condition. Myoelectric duty cycle was defined as the proportion of the stride duration that myoelectric activity above the defined threshold was recorded.

Two phase delay times were calculated: (1) activation phase – the time between the beginning of myoelectric activity and the time of maximum muscle fascicle strain. A positive value represented myoelectric activity beginning after maximum strain had occurred whereas a negative value represented myoelectric activity beginning before maximum strain had occurred. (2) Deactivation phase – the time between the end of myoelectric activity and the minimum muscle fascicle strain value. A negative value represented myoelectric activity ceasing before the minimum muscle fascicle strain occurred whereas a positive value represented the minimum strain value occurring before myoelectric activity had stopped.

As myoelectric and sonomicrometric measurements for each muscle were not recorded simultaneously within each individual (Table 1) it was not possible to calculate these values per subject. The calculations were therefore based on the mean muscle fascicle strain measurements and mean myoelectric on/off time values calculated for each muscle under each condition. Standard error values were therefore not calculated for these data.

Initial analysis of sonomicrometric data showed that the peak-to-peak strain in medial gastrocnemius was approximately 0.3, while in the soleus and plantaris muscles it was approximately 0.1. In order to reflect these in the model, two 1 Hz sinusoidal strain cycles were modelled with peak-to-peak strains of 0.1 and 0.3. Two 10-block activation patterns were defined, where u(t) was related to the mean myoelectric intensities recorded in the soleus and medial gastrocnemius muscles at 10 evenly spaced time windows, with the appropriate fast and slow τ_act (Fig. 1C,D). The effect of activation phase (0–100%) and duty cycle (0–100%) on total force and mechanical power production was then determined, with mechanical power output being a normalised value calculated as product of F and per cycle.

Initially, general linear model, full factorial analyses of variance (ANOVAs) were used to determine if significant differences in muscle fascicle strain, muscle fascicle strain rate or myoelectric intensity differed between muscles (SPSS® version 14.0, SPSS, Chicago, IL, USA). In these analyses muscle and condition were defined as fixed factors and subject defined as a random factor. Within each muscle significant differences in strain, strain rate and myoelectric measurements between conditions were also calculated using general linear model ANOVA. In these analyses condition was defined as a fixed factor and subject defined as a random factor. After all tests, when a factor was identified as significant (P≤0.05) post hoc Bonferroni tests were applied to identify the location of the significant differences. Results are reported as means±s.e.m.

In each condition each muscle went through a series of stretch-shortening strain cycles, which differed between muscles (Figs 2, 3, 4, 5) and were highlighted by differences in the peak-to-peak strains recorded (Fig. 6A). Both the soleus and plantaris had very low peak-to-peak strains (Δε<0.1) in all conditions, while larger values were recorded in the medial gastrocnemius (Δε>0.2). This was reflected in the statistical analysis where peak-to-peak values in the medial gastrocnemius muscle were significantly larger than in either the soleus or plantaris muscles (P<0.01, both cases). Within each muscle there were no significant differences in the peak-to-peak strain, minimum strain, maximum strain or the timing of these variables between conditions.

Mean shortening and mean lengthening muscle fascicle strain rates differed significantly between muscles (P<0.001, all cases). Significantly greater shortening and lengthening strain rates were recorded in the medial gastrocnemius muscle compared with the soleus and plantaris (P<0.001, all cases) (Fig. 6B,C). In the plantaris muscle there were significant differences in both the mean shortening (P=0.023) and the mean lengthening (P=0.002) strain rates. At 0 deg. 40 cm s⁻¹ and 0 deg. 50 cm s⁻¹ and 10 deg. 40 cm s⁻¹ mean lengthening strain rates were significantly greater than all the other conditions (P≤0.032, all cases). A similar trend was seen in mean shortening strain rates from the plantaris, where significantly faster mean shortening velocities were recorded at faster locomotor velocities (0 deg. 40 cm s⁻¹ and 0 deg. 50 cm s⁻¹ and 10 deg. 40 cm s⁻¹) compared with the slower locomotor velocities (P≤0.032). In the soleus muscle, there were no significant differences in mean shortening (P=0.590) or mean lengthening (P=0.163) strain rate values. A similar result was found in the medial gastrocnemius muscle where again no significant differences existed in mean shortening strain rates (P=0.343) or mean lengthening strain rates (P=0.092).

There were no significant differences in myoelectric duty cycle between muscles (P=0.092), although there was a trend for longer duty cycles to occur in the soleus muscle compared with the plantaris or medial gastrocnemius (Fig. 7). In the plantaris muscle, myoelectric duty cycle varied significantly between conditions (P=0.002). Differences were significant between 0 deg. 20 cm s⁻¹ and both 0 deg. 40 cm s⁻¹ and 0 deg. 50 cm s⁻¹, as well as between 0 deg. 30 cm s⁻¹ and 0 deg. 40 cm s⁻¹ (P≤0.039, all cases). Significant differences between conditions were also identified in the soleus muscle (P=0.030), where both 0 deg. 20 cm s⁻¹ and 0 deg. 30 cm s⁻¹ differed significantly to 0 deg. 50 cm s⁻¹ and 10 deg. 40 cm s⁻¹ (P≤0.006 all cases). In addition, a significant difference existed between 0 deg. 40 cm s⁻¹ and 0 deg. 50 cm s⁻¹ (P=0.028). A significant difference in myoelectric duty cycle was also found in the medial gastrocnemius muscle (P=0.021), with the difference existing between 0 deg. 30 cm s⁻¹ and 0 deg. 50 cm s⁻¹. In all muscles there was a trend for longer duty cycles to occur at faster velocities, with no differences seen between conditions with similar velocities but different inclines.

Two myoelectric phases were calculated for each muscle and condition. Initially, the activation phase relation, occurring between the beginning of myoelectric activity and the time of maximum muscle fascicle strain, was calculated (Fig. 8A). Values in the plantaris muscle were positive, indicating that myoelectric activity began after maximum strain had occurred, in all conditions when velocity >20 cm s⁻¹. When locomotor velocity was 20 cm s⁻¹ (0 deg., 10 deg., 20 deg., 25 deg.), values were negative, indicating that myoelectric activity began before maximum strain had occurred. In the soleus muscle, myoelectric activity began after maximum strain had occurred in all conditions except 10 deg. 40 cm s⁻¹, where activity began before the time of maximum strain (Fig. 8A). In the medial gastrocnemius muscle, myoelectric activity began before maximum strain had occurred in all conditions except 0 deg. 40 cm s⁻¹ where maximum strain occurred before myoelectric activity had begun (Fig. 8A).

The second phase duration to be calculated was the deactivation phase, which was the time between the end of myoelectric activity and the minimum strain value (Fig. 8B). In the plantaris muscle values were positive, indicating that myoelectric activity had ended after minimum muscle fascicle strain occurred, in all conditions except those with a velocity of 20 cm s⁻¹. In the soleus muscle, myoelectric activity ended before the minimum muscle fascicle strain had occurred during the slowest conditions, except 25 deg. 20 cm s⁻¹. The time between the end of activity and minimum strain became less as locomotor velocity increased until, at locomotor velocity >40 cm s⁻¹, myoelectric activity ended after the minimum strain value had occurred. A similar trend was seen in the medial gastrocnemius muscle where, at locomotor velocities <40 cm s⁻¹, myoelectric activity ended before minimum muscle fascicle strain occurred. At locomotor velocities of 40 cm s⁻¹ and faster minimum muscle fascicle strain occurred during the period of myoelectric activity.

The effects of activation phase (time between onset of myoelectric activity and maximum strain value) and duty cycle (duration of myoelectric activity as a proportion of stride duration) and activation pattern on total force and mechanical power production were calculated using a simple muscle model. In all simulations the highest total forces were predicted at the higher duty cycles (>50%). At higher strain amplitudes, maximum total force was only predicted when the activation phase was >25% or duty cycle was >75%. Duty cycle and activation phase had less influence on the total force produced when strain amplitude was low (0.1 peak-to-peak) and activation followed the 10-block pattern related to myoelectric activity in the soleus (Fig. 9).

Distinctive differences in total mechanical power output were apparent between simulations (Fig. 10). In all scenarios greater positive and negative values were recorded under high strain conditions (0.3 peak-to-peak). In general, when duty cycle <75% negative power occurred when activation phase was between –25% and +25%, and positive power occurred when activation phase was greater than 25%. At higher duty cycles (>75%), positive power occurred when activation phase was >0%. Differences in contour plots were subtle between the fast and slow models (Fig. 10), indicating that activation pattern and strain were more influential on mechanical power production than the individual fibre properties.

The three muscles investigated have been documented as having distinctly different morphology and fibre type populations (Armstrong and Phelps, 1984; Delp and Duan, 1996) and intrinsic properties (Caiozzo et al., 1992; De Ruiter et al., 1995; Norenberg and Fitts, 2004; Swoap et al., 1997). Data presented here may therefore be considered to represent in vivo behaviour of three distinct fibre type populations, with soleus representing a population of slower fibre types, medial gastrocnemius representing a population of predominantly faster fibre types and plantaris representing a mixed population of fibre types. The measurements of in vivo muscle fascicle strains and strain rates presented provide some insight into the behaviour and function of these muscles and hence these fibre type populations, during normal locomotion, which have not been previously reported.

The plantaris and medial gastrocnemius muscles both span the knee and ankle joints whereas the soleus muscle only crosses the ankle joint. It is therefore surprising to find that the in vivo behaviour of the plantaris was more similar to the soleus than to the behaviour of the medial gastrocnemius. Peak-to-peak strains in both the soleus and plantaris were low (<0.1) (Fig. 6A), indicating that both of these muscles worked close to isometrically in all conditions. This agrees with previous work in other animal species (Biewener and Baudinette, 1995; Fukunaga et al., 2001; Griffiths, 1991; Hoffer et al., 1989; Lichtwark and Wilson, 2006; Roberts et al., 1997) and provides further support to the proposed existence of a division of labour between proximal (mechanical work production) and distal (isometric force production) limb muscles (Biewener, 1998; Biewener and Roberts, 2000). The similarity between the strains recorded in the soleus and plantaris may be explained by their similar fascicle lengths [18.75±2.42 mm and 22.09±5.47 mm, respectively (Hodson-Tole and Wakeling, 2008a)] especially when compared with the much shorter fascicle lengths reported for medial gastrocnemius [12.23±5.50 mm (Hodson-Tole and Wakeling, 2008a)]. In addition, the plantaris has a slightly shorter moment arm about the knee joint than the medial gastrocnemius [1.90 mm versus 2.25 mm (E.F.H.-T., unpublished data)].

The low strains recorded in the soleus and plantaris muscles suggest that they do not act to generate or absorb a large amount of mechanical work or power but instead function to generate high levels of force and/or facilitate elastic energy storage in their associated tendons with small fluctuations in strain. It should also be noted that when a muscle operates at minimal strain rates its force development is very sensitive to changes in strain and thus it is possible that fluctuations in strain rate produce large changes in the force developed by the soleus and plantaris muscles. Generating high forces at low strains can be considered beneficial for two reasons. Firstly, operating at higher shortening velocities and greater power outputs would be energetically more costly (Fenn, 1924). Secondly, the force–velocity relationship of a muscle predicts that it produces greater force during slower contractions (Fig. 1B) (Hill, 1938). A given force can therefore be generated with fewer active fibres at slower muscle fascicle shortening velocities, resulting in a lower metabolic energy cost and an improved economy of locomotion (Gabaldon et al., 2004; Roberts et al., 1997). Although force was not recorded in the current study, the results of the model simulations appear to support this claim, as the activation phase and duty cycles recorded in both the plantaris and soleus correspond to regions where high total force output occurred in the model's results (Fig. 9).

The in vivo behaviour of the medial gastrocnemius was noticeably different to the soleus and plantaris muscles. The peak-to-peak strains were much greater and muscle fascicle shortening and lengthening strain rates were much higher than in the other two muscles (Fig. 6B,C). This may be the result of differences in fascicle lengths between the three muscles [12.23±5.5 mm versus soleus: 18.75±2.42 and plantaris: 22.09±5.47 mm (Hodson-Tole and Wakeling, 2008a)] or may indicate this muscle operated to generate mechanical power using greater fascicle length changes at faster strain rates. The latter suggestion, however, is contradicted by the results of the model simulations, which suggest that the activation phase and duty cycle values recorded in the medial gastrocnemius would result in negative mechanical power output (Fig. 10).

The fascicle strain and strain rates presented should be considered in light of two factors. Firstly, the medial gastrocnemius has been shown to be composed of two physiologically distinct compartments (De Ruiter et al., 1995). Recordings in the present study were only made in the proximal compartment and therefore no information on the mechanical behaviour or activation patterns within the distal compartments were collected. As the distal compartment has been shown to have fibres with significantly faster maximum shortening strain rates and greater maximum isometric stress values (De Ruiter et al., 1995), it is likely to have a significant influence on the overall force and power producing capability of the muscle. A full picture of the behaviour of the whole medial gastrocnemius muscle and its potential for power generating behaviour is therefore not possible here. Further insight and understanding of muscle mechanics could however be attained by investigating the interaction and co-ordination between physiologically different compartments within a muscle during different locomotor tasks. Secondly, the results presented here will have been influenced by the definition of L_o. The stress–strain relationship was not defined in the work presented, so L_o was defined as the mean of the maximum and minimum lengths recorded in each stride following previously reported methods (Gabaldon et al., 2004). This appeared to be the best approach for the calculation of L_o in the present study. Future work would however benefit from an approach whereby in vivo measures of L_o could be defined.

The strain trajectories within each of the muscles were very similar between locomotor conditions (Figs 3, 4, 5), indicating that, under the conditions tested here, changes in mechanical force and/or power output are a function of changes in motor control, reflected by variation in activation–deactivation times, myoelectric intensity or motor unit recruitment pattern(s), and not a function of changes in the muscles' strain characteristics. This is in agreement with previous findings in guinea fowl (Daley and Biewener, 2003), and also with data presented here where the soleus and medial gastrocnemius muscles change the deactivation phase in response to changes in velocity (Fig. 8B). The relationship between myoelectric activity and fascicle length trajectories suggest that, under some locomotor conditions, the plantaris and medial gastrocnemius muscles may utilise stretch-activated force enhancement (Edman et al., 1978; Herzog and Leonard, 2000; Lee and Herzog, 2002) to maximise power output, by activating the muscle while fascicle strain was still increasing (Fig. 8A). In addition, at the slowest locomotor velocity (20 cm s⁻¹) the plantaris may show a strategy of minimising mechanical power absorption by ending myoelectric activity before the minimum strain was reached (Fig. 8B). A strategy of minimising power absorption at the onset of muscle activity may be evident in soleus data, as in nearly all conditions myoelectric activity began after maximum strain had occurred (Fig. 8A). Such a strategy would probably limit the amount of force produced during the activation period, due to the muscle's slow activation time. It would, however, go some way to offsetting the negative power output following the end of myoelectric activity when the muscle is unlikely to have enough time to fully relax before lengthening occurs. The results of the model support the suggestion that the soleus acts to reduce the amount of negative power and, at lower duty cycles, positive power values are predicted (Fig. 10). In addition, total force output is optimised with the phase and duty cycles recorded, particularly during the simulation using the activation based on soleus activity (Fig. 9).

The simple muscle model presented was used to identify general patterns in the relationship between activation phase and duty cycle on force and power output in examples of slow and fast fibres, subjected to two different strain cycles. In this abstracted form this work is not aimed at identifying intricate details of such relationships. While we are aware that some aspects of these data, such as uncertainty of measuring precise fascicle strains due to changes in pennation angle and the influence of changing pennation angle on force output, will introduce an unavoidable degree of error to the results, we feel they will have limited impact on the general conclusions drawn from the model. Indeed, re-running the model with larger maximum eccentric force values and increased resting length values resulted in only small changes in maximum force and maximum/minimum mechanical power output values recorded (Table 3) and did not influence the overall trends seen.

The results of the model indicate that the activation pattern influences the range of duty cycle and activation phase values over which maximum power output and total force can be generated. As the pattern of activation based on the soleus data resulted in a greater area under the curve (Fig. 1C,D), this activation pattern produced the highest total force and mechanical power output and a larger area in which maximum values could be attained. This indicates that for longer activation durations the precision of the timing and proportion of the stretch–shorten cycle the muscle is active may not be critical for maximum force or power production. By contrast, the model also indicated that subtle changes in activation phase and duty cycle could profoundly affect power production/absorption, as demonstrated by the position of the plantaris data in the contour plot (Fig. 10). The mechanical properties of the fibre were predicted to have the greatest influence on mechanical power output, where interestingly the fast fibre model predicted greater power absorption during the highest strain cycle (Fig. 10). In addition, the highest strains produced the greatest positive and negative power output values but not the greatest total force values (Fig. 9). The predictions of the model did not complement conclusions that may be drawn from observations of myoelectric timing and fascicle strain trajectories in each of the muscles. This was most evident in the results of the medial gastrocnemius where greater fascicle length changes at faster rates would suggest greater power output but the model indicated that power absorption occurred. It should be noted that the model was based on typical parameter values, consistent with past studies. It is possible, however, that variations in the chosen value of L_o or maximum eccentric force would affect the mechanical predictions. We tested this possibility by re-running the model twice more; firstly with L_o set to 15% longer, and secondly with maximum eccentric force set to 180% of σ_o. It was found that these alterations resulted in very limited changes in the resulting values (Table 3) or the contour plots, and that the general conclusions presented here were unchanged. We are therefore confident that our results represent fundamental differences in the functions of the physiologically distinct fibre type populations represented here by the different ankle extensor muscles of the rat.

The results indicate that there are significant differences in the mechanical behaviour and relative activation of the three ankle extensor muscles studied. Patterns of length change were not significantly influenced by changes in locomotor velocity or incline, while myoelectric duty cycle and activation and deactivation phases did change. This indicated that, under the conditions tested here, the relative timing of muscle activation was more influential on changes in mechanical force and/or power output than changes in the muscles' strain characteristics. This suggests that the skeletal anatomy of the limb constrains the in vivo muscle fascicle behaviour of all three muscles. The neuromuscular system however has many more degrees of freedom, and can vary the timing and level of muscle activation and the combination of motor units recruited across the three muscles, and may therefore drive modulations in force and power output required to meet any given locomotor demands. In agreement with this, the model indicated that subtle changes in activation phase and duty cycle could significantly influence levels of mechanical power output. Further work should focus on the interaction between synergistic muscles, the interaction between elastic and contractile muscle elements and consider the interaction between physiologically distinct compartments within a muscle.

 
• a

  normalised activation

 
• A

  cross-sectional area

 
• c, s

  magnitude constants

 
• F

  force

 
• h

  harmonic number

 
• i

  intensity

 
• j

  angle within the gait cycle

 
• L

  length

 
• L_o

  resting length

 
• m

  curvature of stress–strain relation

 
• o

  phase constant

 
• P

  mechanical power

 
• r

  roundness

 
• s

  width

 
• t

  time

 
• u

  neural excitation

 
• w

  skewness

 
• β

  ratio of activation to deactivation rate

 
• ε

  muscle fascicle strain

 
• 

  muscle fascicle strain rate

 
• 

  maximum strain rate

 
• σ

  isometric stress

 
• σo

  maximal isometric stress

 
• τact

  activation rate constant

E.H.T. is currently funded by a Sir Henry Wellcome Post-doctoral fellowship. Many thanks go to Michael Boyd and John Thurlborne for their help with surgical procedures and care of the animals, Karin Jespers and Pattama Ritruechai for their help during data collection.