ABSTRACT

In skeletal muscles, the ability to generate power is reduced during fatigue. In isolated muscles, maximal power can be calculated from the force–velocity relationship. This relationship is well described by the Hill equation, which contains three parameters: (1) maximal isometric force, (2) maximum contraction velocity and (3) curvature. Here, we investigated the hypothesis that a fatigue-induced loss of power is associated with changes in curvature of the force–velocity curve in slow-twitch muscles but not in fast-twitch muscles during the development of fatigue. Isolated rat soleus (slow-twitch) and extensor digitorum longus (EDL; fast-twitch) muscles were incubated in Krebs–Ringer solution at 30°C and stimulated electrically at 60 Hz (soleus) and 150 Hz (EDL) to perform a series of concentric contractions to fatigue. Force–velocity data were fitted to the Hill equation, and curvature was determined as the ratio of the curve parameters a/F0 (inversely related to curvature). At the end of the fatiguing protocol, maximal power decreased by 58±5% in the soleus and 69±4% in the EDL compared with initial values in non-fatigued muscles. At the end of the fatiguing sequence, curvature increased as judged from the decrease in a/F0 by 81±20% in the soleus and by 31±12% in the EDL. However, during the initial phases of fatiguing stimulation, we observed a small decrease in curvature in the EDL, but not in the soleus, which may be a result of post-activation potentiation. In conclusion, fatigue-induced loss of power is strongly associated with an increased curvature of the force–velocity relationship, particularly in slow-twitch muscles.

INTRODUCTION

Human exercise performance is determined by the ability of skeletal muscles to generate power, which is reduced during fatigue. Maximal power (Pmax) depends on the non-linear relationship between contractile force and shortening velocity during shortening contractions. To assess Pmax experimentally, data points of force and velocity are obtained and these have been shown to be well described mathematically by a hyperbolic equation first introduced by A. V. Hill (1938). This equation contains three parameters: (1) the maximal isometric force (Fmax), (2) the maximum velocity of unloaded shortening (Vmax) and (3) the curvature of the force–velocity (FV) relationship.

During fatigue, all three of the abovementioned parameters may be affected. Thus, it is well established that both Vmax and Fmax decrease during fatigue, contributing to the loss of maximal power (Jones et al., 2006). It has been suggested that an increased FV curvature during fatigue may exacerbate the loss of power (Jones, 2010), while a decrease in curvature will attenuate the loss of power (Devrome and MacIntosh, 2018). However, presently, there is no consensus about the association between fatigue and the curvature in the FV relationship.

Two studies found that the curvature increased considerably during fatigue (Jones et al., 2006; Kristensen et al., 2017). Specifically, in human adductor pollicis muscles, the increased curvature was found to account for 40% of the decrease in Pmax during fatigue. The remaining loss of Pmax was accounted for by a loss of Fmax (40%) and Vmax (20%) (Jones et al., 2006). Likewise, a fatigue-induced increase in curvature was found to contribute 45% to the loss of Pmax in rat soleus muscles while Fmax contributed 28% and Vmax contributed 27% (Kristensen et al., 2017).

In contrast, three studies reported that the curvature decreased during fatigue, and thereby attenuated the loss of power (Barclay, 1996; Curtin and Edman, 1994; Devrome and MacIntosh, 2018). One possible explanation for this discrepancy could be that the studies which observed an increase in curvature (Jones et al., 2006; Kristensen et al., 2017) were performed on muscles containing mainly slow-twitch fibers, whereas the other studies were performed on fast-twitch muscles/fibers (Barclay, 1996; Curtin and Edman, 1994; Devrome and MacIntosh, 2018). This indicates that fatigue-induced changes in FV curvature may vary according to fiber type, although this has not been experimentally addressed.

Further, the cellular mechanisms responsible for variation in FV curvature are not fully known with regard to both general factors that determine curvature as well as factors that change the FV curvature during fatigue. However, the FV curvature is thought to vary with the relative number of active cross-bridges at a given relative velocity. If, during fatigue, the rate of attachment is decreased relatively more than Vmax, a decreased relative amount of cross-bridges would be attached at a given velocity, which theoretically would increase the curvature (Gilliver et al., 2011; Kristensen et al., 2017).

In addition, as fatigue may develop in distinct phases (Cairns et al., 2008; Westerblad and Lannergren, 1994) and as the loss over time of both Fmax and Vmax is non-linear (Jones et al., 2006; Westerblad and Lannergren, 1994), it is likely that the changes in FV curvature also occur in separate phases. Therefore, as fatigue progresses, the relative change in the parameters of the FV curve may change. This has not been extensively studied previously in either fast- or slow-twitch muscles.

To address the abovementioned issues, we conducted a study with the main purpose of examining the hypothesis that loss of power induced by fatiguing contractions is associated with changes in curvature of the FV curve in slow-twitch muscles but not in fast-twitch muscles during the development of fatigue. Furthermore, as we partially confirmed this hypothesis, we also examined whether a change in the rate of attachment assessed through the constant of tension redevelopment (Ktr) could account for the fiber type-dependent changes observed in curvature during fatigue. Studies were carried out using two different rat muscles, the soleus and extensor digitorum longus (EDL), containing mainly slow- and fast twitch-fibers, respectively.

MATERIALS AND METHODS

Muscle preparations and buffers

All experiments were performed on isolated rat muscles in vitro. All handling and use of animals complied with Danish animal welfare legislation. Experiments were carried out using soleus and EDL muscles from 4-week-old male or female Wistar rats, Rattus norvegicus (Berkenhout 1769), weighing approximately 90–100 g (Janvier Labs, Le Genest-Saint-Isle, France). Soleus muscles from these rats consist primarily of slow-twitch fibers, whereas EDL muscles consists primarily of fast-twitch fibers (Soukup et al., 2009). In total, 38 muscles from 19 animals were used in the experiments. Of these, one muscle was discarded because it detached from the transducer during the stimulation protocol, and another muscle was discarded because it only produced 60% of the force in the contralateral muscle, probably as a result of damage incurred during dissection.

The rats were fed ad libitum and were kept at a constant temperature (21°C) and day length (12 h). The animals were killed by a cervical dislocation followed by decapitation. Muscles were isolated with the proximal end attached to the bone (tibia) and the distal end with a portion of the tendon left intact. At the proximal end, the bone was fixed to a holding clamp. At the distal end, a short polyester thread was tied close to the tendon–muscle intersection and connected the preparation to a metal rod attached to the lever arm. This minimized the part of the distal tendon that could be stretched during contractions although the proximal part was still intact.

The standard incubation medium was Krebs–Ringer bicarbonate solution containing (mmol l−1): 122 NaCl, 25 NaHCO3, 2.8 KCl, 1.2 KH2PO4, 1.2 MgSO4, 1.3 CaCl2 and 5.0 d-glucose; 100 ml fresh solution was used to fill the incubation chamber at the start of each experiment and this solution was maintained at 30°C and equilibrated with a mixture of 95% O2 and 5% CO2 throughout the experiment. For all buffers, pH was between 7.30 and 7.40 at room temperature, corresponding to an average pH of 7.44 at 30°C.

Concentric contractions

Concentric contractions were elicited as previously described (Pedersen et al., 2013). In short, muscles were mounted on a length- and force-controlled lever system (model 305, Aurora Scientific, Aurora, ON, Canada) at optimal muscle length for isometric twitch force production (L0) in the Krebs–Ringer solution and equilibrated for at least 30 min before starting the experiments. DMC v. 4.1.6 software (Aurora Scientific) was used to control electrical stimulation and force/length control of the levers during the contractions. This allowed for simultaneous sampling of muscle force and length at 1000 Hz. Muscle contractions were evoked via field stimulation using supramaximal constant voltage applied through two platinum plate electrodes. Unless otherwise noted, pulses of 0.2 ms duration were used in brief trains of 0.75 s (soleus) and 0.2 s (EDL) at a tetanic frequency of 60 Hz (soleus) and 150 Hz (EDL).

Measured velocity and force data points, which were used to fit to the Hill equation, were found by controlling force and measuring velocity using the afterload technique (Bullimore et al., 2010). The position of the lever arm was maintained at L0 during stimulation until the force produced by the muscle reached a preset load, after which the muscle was allowed to shorten isotonically. The shortening velocity was obtained by taking the 40 ms moving average of length changes over the entire contraction and identifying the maximal shortening velocity achieved during this period. After each contraction, the relaxed muscle was re-extended to L0.

A criticism against the method that we have used in this study (see Fig. 1C) is that full tetanic Ca2+ concentration may not have been reached at the time when shortening begins. This may result in an underestimation of the shortening velocity, particularly at the lowest loads where the muscle starts to shorten early after onset of stimulation. However, as previously shown (Kristensen et al., 2017), applying isometric pre-contraction followed by release to an isotonic load does not yield higher values for V at low loads, because V cannot be measured reliably very early after the release because of artefacts related to tendon and measurement apparatus. Therefore, the applied method was the one yielding the most reliable data for V at different loads.

Fig. 1.

Hill curves fitted to force–velocity(FV) data and the sequence of loads. (A,B) Experimental data points of force and velocity during the first FV cycle in the fatigue protocol for the soleus (A) and extensor digitorum longus (EDL; B). Corresponding data points for force and velocity were fitted to the Hill equation (r2=0.997). The chronological sequence of loads used during the FV cycle is indicated (1–7). (C) Data for a single contraction from a soleus muscle with a load of 25 g. Velocity was measured as the highest rolling average over 40 ms during muscle shortening. The part of the trace where force and velocity were measured is in gray.

Fig. 1.

Hill curves fitted to force–velocity(FV) data and the sequence of loads. (A,B) Experimental data points of force and velocity during the first FV cycle in the fatigue protocol for the soleus (A) and extensor digitorum longus (EDL; B). Corresponding data points for force and velocity were fitted to the Hill equation (r2=0.997). The chronological sequence of loads used during the FV cycle is indicated (1–7). (C) Data for a single contraction from a soleus muscle with a load of 25 g. Velocity was measured as the highest rolling average over 40 ms during muscle shortening. The part of the trace where force and velocity were measured is in gray.

To establish a non-fatigued control FV curve, six concentric contractions were performed plus one isometric contraction. The concentric contractions used different levels of loads of the lever arm, ranging between 2.5% and 90% of the isometric force of the non-fatigued muscle and 250 s pauses were inserted between contractions. Data points from these seven contractions were used to establish one non-fatigued FV curve (see ‘Curve fitting, calculations and statistics’, below). To establish fatigued FV curves, the seven contractions were repeated 9 times while allowing only 4 s (soleus) or 5 s (EDL) pauses between contractions, yielding a total of 61 contractions. This procedure allowed us to use contractions to induce fatigue and to construct sequential FV curves with increasing degrees of fatigue. After the fatiguing protocol, muscles were rested for 1 h, after which a recovery FV curve was determined using the same procedure as for the non-fatigued control FV curve.

To investigate the effect of post-activation potentiation on the FV curve, an additional experiment was designed. In this experiment the non-fatigued FV curve was measured twice as described above. However, one of the times, muscles were stimulated with 5 Hz for 20 s (soleus) or 10 s (EDL) to induce post-activation potentiation, 1.3 s prior to every contraction. To eliminate possible incubation-duration and carry-over effects, the order of the pre-stimulated FV curve and the control FV curve was randomized.

Cross-bridge cycle rate

To assess the rate of cross-bridge attachment, the constant of tension redevelopment (Ktr) was measured by shortening and re-extending the muscle as described previously (Brenner, 1988; Kristensen et al., 2017). In brief, muscles were electrically stimulated in trains of 1 s (soleus) and 0.4 s (EDL). The muscle was first kept at L0 for 0.5 s (soleus) and 0.2 s (EDL) of the stimulation to allow tetanic force to fully develop. Then, the holding force of the lever arm was reduced to 0 for 10 ms, which caused the muscle to shorten. Thereafter, the muscle was quickly re-stretched (<2 ms) to the original length.

The sequence of loads during FV curve determination

While establishing control FV curves, the seven contractions used were all recorded under non-fatigued conditions because of the 250 s pauses between each contraction. Therefore, the time sequence of loads had no material effect on the shape and parameters of the FV curve. However, during the fatigue protocol, FV curves were determined while the muscles were progressively fatiguing. As seven contractions were used to determine each FV curve, the muscles would be more fatigued during the 7th contraction than during the 1st contraction of a FV cycle (the seven contractions used to make one FV curve). Our goal was to establish FV curves which represented a good estimate of the FV curve of a muscle fatigued to an average fatigue level during each FV cycle. Therefore, in pilot experiments (not shown), we determined which sequence of loads would best fulfill this purpose, as explained below.

The time sequence of loads used in non-fatigued conditions and early part of the fatigue sequence in the experiments for the soleus was: 5 g, 40 g, isometric, 25 g, 1.5 g, 50 g and 10 g; and for the EDL: 5 g, 55 g, isometric, 40 g, 1.5 g, 80 g and 20 g (see Fig. 1). As the muscles fatigued and the force-generating capacity diminished, we reduced the absolute loads to keep the force of the concentric contractions between 2.5% and 90% of the isometric force at all times, but the sequence between the different relative loads remained the same. In some experiments, two extra contractions were added after each FV cycle in order to measure the Ktr and twitch force.

As illustrated in Fig. 1, this time sequence was chosen so that the middle load (usually the load at which the muscles produced the most power) was placed in the middle of the time sequence (and therefore at a time when the muscles were closest to the average fatigue level of the specific FV cycle). This was flanked by the two most extreme loads (the isometric point and the point with the highest velocity, V1.5). Of the four remaining loads, two were placed earlier and later in the time sequence. This time sequence was determined to yield the FV curve shape most representative of the average level of fatigue in the specific FV cycle.

Curve fitting, calculations and statistics

The recorded force and length data were analyzed using custom-written software (SVX, Department of Sport Science, Aarhus University, Denmark). Corresponding data points for velocity and force obtained from the concentric contractions were fitted to the Hill equation:
formula
(1)
where V is velocity, a and b are constants and F0 is the estimated maximal isometric force. All Hill fits had an r2 value above 0.98. For each muscle and for each condition, the parameters a, b and F0 were obtained. Fitting of FV curves to the Hill equation was performed using force as the response variable, as this gave rise to the least variability in the estimates of parameters of the Hill equation. Curves were also fitted to a power equation, a variant of the Hill equation:
formula
(2)
From the two equations, maximal power (Pmax) and the curvature were calculated. The curvature was determined as the unitless parameter a/F0, with decreased a/F0 reflecting increased curvature. Maximum velocity of unloaded shortening (Vmax) was determined by extrapolation of the power–velocity curves rather than the FV curves because this was found to yield the most reliable estimates.
The contribution to the loss of power of changes in each of the three parameters was calculated as explained in Gilliver et al. (2009). First, the fraction (M) of F0 at which Pmax was generated was calculated as:
formula
(3)
where G is F0/a (Woledge et al., 1985). The component of Pmax that can be ascribed to the curvature of the FV relationship, independently of F0 and Vmax, is given by M2, which gives:
formula
(4)

Based on this equation, the percentage change in each of the three parameters during fatigue can be calculated to give the contributions to the loss of power for each individual parameter expressed as a percentage of total power loss.

For Ktr measurements, all force data points from the re-stretch experiments were fitted to the following single exponential equation using a non-linear least-squares regression (MATLAB v.8.6.0.267246, MathWorks, Natick, MA, USA):
formula
(5)
where A0 is the final steady-state force, as explained elsewhere (Kristensen et al., 2017).

All data are expressed as means±95% confidence interval (CI). To examine the relative difference in changes in Fmax, Vmax and a/F0 between the two muscle types during the development of fatigue, a two-tailed, unpaired t-test was used. Statistical differences between the two groups were tested at three different points: when Pmax was reduced by 5%, 20% and 55%. In the experiments designed to investigate the effect of post-activation potentiation on the FV curvature, the statistical significance of the difference between the pre-stimulated and non-pre-stimulated muscles was ascertained using a two-tailed, paired t-test. All tests were performed using SigmaPlot 13.0 (Systat Software, San Jose, CA, USA). Statistical significance was accepted at P<0.05.

RESULTS

In both soleus and EDL muscles, FV curves were substantially changed by the fatiguing protocol, as exemplified in Fig. 2A,B. Decreases in Fmax and Vmax, and increases in FV curvature (decreased a/F0) were observed in both muscle types and Pmax was reduced considerably (see Fig. 2C–F).

Fig. 2.

FV curves and power curves duringfatiguing stimulation. (A,B) FV curves from individual muscles (A, soleus; B, EDL). The top red curve represents the non-fatigued state, the bottom red curve represents the most fatigued state, while the eight other curves represent intermediate fatigue states. (C,D) Data from the same muscle (C, soleus; D, EDL) converted to relative values of Fmax and Vmax, to better visualize the changes in curvature. (E,F) Corresponding power curves for the same two muscles (E, soleus; F, EDL).

Fig. 2.

FV curves and power curves duringfatiguing stimulation. (A,B) FV curves from individual muscles (A, soleus; B, EDL). The top red curve represents the non-fatigued state, the bottom red curve represents the most fatigued state, while the eight other curves represent intermediate fatigue states. (C,D) Data from the same muscle (C, soleus; D, EDL) converted to relative values of Fmax and Vmax, to better visualize the changes in curvature. (E,F) Corresponding power curves for the same two muscles (E, soleus; F, EDL).

In both muscle types, Pmax decreased continuously throughout the entire fatiguing protocol as shown in Fig. 3A. On average, Pmax had decreased to 42±5% in the soleus and 31±4% in the EDL of the non-fatigued values at the end of the fatigue protocol. After 1 h of rest, Pmax had returned to 85±5% (soleus) and 70±6% (EDL) of the non-fatigued values.

Fig. 3.

Relative changes in Pmax and FV curve parameters during fatigue and after 1 h of rest. (A) Maximal power (Pmax) decreased continuously during the fatiguing stimulations for both muscle types. (B) The same pattern was observed for maximal isometric force (Fmax), although there was a greater decrease in fast-twitch EDL muscles. (C) Initially, maximum velocity of unloaded shortening (Vmax) increased in both muscle types, and only started to decrease later in the protocol. (D) The ratio of the curve parameters (a/F0) decreased continuously during the protocol and to a large extent in the soleus muscles, whereas in the EDL muscles, an initial increase was observed that was followed by a gradual decline in a/F0. N=5 for both soleus and EDL. All data are expressed as means±95% confidence interval (CI).

Fig. 3.

Relative changes in Pmax and FV curve parameters during fatigue and after 1 h of rest. (A) Maximal power (Pmax) decreased continuously during the fatiguing stimulations for both muscle types. (B) The same pattern was observed for maximal isometric force (Fmax), although there was a greater decrease in fast-twitch EDL muscles. (C) Initially, maximum velocity of unloaded shortening (Vmax) increased in both muscle types, and only started to decrease later in the protocol. (D) The ratio of the curve parameters (a/F0) decreased continuously during the protocol and to a large extent in the soleus muscles, whereas in the EDL muscles, an initial increase was observed that was followed by a gradual decline in a/F0. N=5 for both soleus and EDL. All data are expressed as means±95% confidence interval (CI).

Similarly, Fmax decreased continuously throughout the entire fatiguing protocol, although in the soleus muscles, Fmax decreased only to 70±9%, while in the EDL muscles, Fmax decreased to 42±5% (see Fig. 3B). After the rest period, Fmax returned to 90±9% (soleus) and 77±4% (EDL) of the non-fatigued values.

In contrast, Vmax did not decrease uniformly throughout the entire fatiguing protocol. Initially, Vmax increased in both muscle types (see Fig. 3C), and only started to decrease during the second (soleus) or third (EDL) FV cycle. At the end of the fatigue protocol, Vmax was decreased to 80±3% in the soleus and 85±3% in the EDL, and after 1 h of rest, Vmax returned to 93±2% (soleus) and 86±3 (EDL) of the non-fatigued values.

In the soleus muscles, a considerable decrease in a/F0 was observed, which progressed continuously throughout the entire fatiguing protocol, indicating an increased curvature of the FV curve. The a/F0 value decreased in a pattern close to what was observed for Pmax. In EDL, in contrast, there was an initial increase in a/F0 of 9±4% in the first two FV cycles, and thereafter a/F0 decreased moderately during the later stages of the fatigue protocol. Thus, at the end of the fatigue protocol, a/F0 had decreased to 19±20% (soleus) and 69±12% (EDL) of the non-fatigued values (see Fig. 3D). In contrast to Pmax, Fmax and Vmax, a complete recovery in a/F0 was observed following 1 h of rest in both muscle types. Thus, in the soleus muscles, a/F0 recovered to 100±7% of the non-fatigued value, and in the EDL muscles, a/F0 recovered beyond the level observed in the non-fatigued muscles to 119±12%.

In order to make sure the performance of the muscles did not deteriorate over time in our ex vivo set-up, we also did a baseline and recovery FV curve in a set of muscles that were not fatigued (1 soleus, 1 EDL). Here, Pmax changed less than 2% following 1 h of rest in non-fatigued muscles (data not shown).

Loss of Pmax during fatigue as determined from each of the parameters of the FV curve

As shown in Fig. 4, the relative contributions to the loss of Pmax from the individual changes in Fmax, Vmax and a/F0 varied somewhat during the fatigue protocol, particularly in the initial stages of the fatigue stimulation protocol. However, after the fourth FV cycle, the relative contributions of each parameter were more or less constant for both muscle types. At the end of the fatiguing protocol, the contribution to the total loss of Pmax was 25±10% from Fmax, 17±3% from Vmax and 58±14% from a/F0 in the soleus muscle. In the EDL muscle, the contribution to the loss of Pmax was 64±6% from Fmax, 16±3% from Vmax and 20±9% from a/F0.

Fig. 4.

The relative contribution of Vmax, Fmax and FV curvature to the loss of Pmax. (A,B) The contribution of each of the three FV curve parameters during the fatigue protocol for the soleus (A) and EDL (B), expressed as a percentage of the total loss of power. The contribution of each of the three parameters was more or less constant after the fourth FV cycle. N=5 for both soleus and EDL. All data are expressed as means±95% CI.

Fig. 4.

The relative contribution of Vmax, Fmax and FV curvature to the loss of Pmax. (A,B) The contribution of each of the three FV curve parameters during the fatigue protocol for the soleus (A) and EDL (B), expressed as a percentage of the total loss of power. The contribution of each of the three parameters was more or less constant after the fourth FV cycle. N=5 for both soleus and EDL. All data are expressed as means±95% CI.

The differences between the two muscle types in terms of the contributions to the loss of Pmax from the FV curve parameters during fatigue were examined at three different fatigue levels: when Pmax was reduced by 5%, 20% and 55%. No significant differences in the contribution from Vmax were observed between the soleus and EDL muscles at any of the three fatigue levels (5%, P=0.347; 20%, P=0.07; 55%, P=0.486). However, as clearly seen in Fig. 5, loss of Fmax accounted for a larger proportion of the loss of Pmax in the EDL muscles than in the soleus muscles, and a/F0 accounted for a smaller proportion. These differences between the two muscle types were significant at all three levels of fatigue (P≤0.001).

Fig. 5.

The contribution of Vmax, Fmax and FV curvature tothe loss of Pmax. (A,B) The total loss of Pmax (bottom line) and how much each of the three FV curve parameters (Fmax, Vmax and a/F0) contributed to the reduction during the fatigue protocol in the soleus (A) and EDL (B). N=5 for both soleus and EDL.

Fig. 5.

The contribution of Vmax, Fmax and FV curvature tothe loss of Pmax. (A,B) The total loss of Pmax (bottom line) and how much each of the three FV curve parameters (Fmax, Vmax and a/F0) contributed to the reduction during the fatigue protocol in the soleus (A) and EDL (B). N=5 for both soleus and EDL.

Post-activation potentiation

An obvious difference in the fatigue responses between the soleus and EDL muscles was the initial increase in a/F0 during fatigue that was seen only in the EDL muscles. As it has been shown that post-activation potentiation in fast-twitch muscle fibers may reduce FV curvature (Grange et al., 1995), this muscle type difference could possibly be ascribed to post-activation potentiation co-occurring with fatigue in the EDL muscles. To test this notion, we performed an experiment where the non-fatigued FV curve was measured twice. However, one of the times, post-activation potentiation was elicited by repeated twitch stimulation prior to the contractions used to determine the FV curve.

As shown in Table 1, pre-stimulation did increase a/F0 by 23±17% (P=0.005) in the EDL muscles, while a modest decrease in a/F0 by 7±1% (P≤0.001) was seen in the soleus muscles compared with control muscles. Furthermore, pre-stimulation induced a decrease in Pmax by 5±2% (P<0.001) in the soleus muscles, and a non-significant increase in the EDL muscles by 1±5% (P=0.647). Likewise, a small decrease in Fmax (P=0.049) was observed in the soleus muscles, and a non-significant decrease in the EDL muscles by 5±7% (P=0.09). No significant differences were observed in Vmax in any of the two muscle types.

Table 1.

The effect of pre-stimulation on the force–velocity (FV) curvature

The effect of pre-stimulation on the force–velocity (FV) curvature
The effect of pre-stimulation on the force–velocity (FV) curvature

Furthermore, in some experiments, we added a twitch at the end of each FV cycle, in order to assess the degree of potentiation from the size of the twitch. The size of the twitch increased after the first FV cycle to 137±5% of non-fatigued values in the EDL muscles, before it decreased throughout the rest of the protocol to 62±9%. For the soleus muscles, no initial increase was observed, and the twitch size decreased throughout the fatiguing protocol to 50±5% (see Fig. 6).

Fig. 6.

Changes in the constant of tension redevelopment (Ktr) and twitch during fatigue. (A,B) The change in Ktr and twitch size during the fatiguing protocol for soleus (A) and EDL (B). N=6 for both soleus and EDL. All data are expressed as means±95% CI.

Fig. 6.

Changes in the constant of tension redevelopment (Ktr) and twitch during fatigue. (A,B) The change in Ktr and twitch size during the fatiguing protocol for soleus (A) and EDL (B). N=6 for both soleus and EDL. All data are expressed as means±95% CI.

Cross-bridge cycle rate

FV curvature is thought to represent the ratio between the net forward rate constant (f+g1), and the reverse rate constant for the transition back to the non-force-generating state (g2) in the cross-bridge cycle (Huxley, 1957). This means that the curvature will change if the rates of attachment and/or detachment are changed disproportionately to Vmax (Brenner, 1988; Gilliver et al., 2011). To assess the rate of cross-bridge attachment, Ktr was measured at the end of each FV cycle in some experiments. Ktr increased after the first FV cycle to 105±5% in the soleus and 120±12% in the EDL, before it started to decrease. At the end of the fatiguing protocol, Ktr was decreased to 72±11% in the soleus and 96±26% in the EDL (see Fig. 6).

DISCUSSION

The present study on isolated whole rat soleus and EDL muscles shows that loss of power induced by repeated fatiguing stimulation is associated with an increase in the curvature of the FV relationship in the soleus and, in contrast to our hypothesis, also in the EDL muscles during severe fatigue. Theoretically, an increase in curvature would, all else staying the same, lead to a decrease in power. Therefore, fatigue-induced increases in curvature play a contributory role to the fatigue-induced loss of power. However, the magnitude and direction of change in curvature vary with the degree of fatigue; for example, in the soleus muscles, the FV curvature increases throughout the entire fatigue protocol but in the EDL muscles, a small decrease in curvature is observed during moderate fatigue.

Furthermore, the association between fatigue-induced loss of power and decreases in Fmax and Vmax varies with fiber-type composition and the degree of fatigue. For example, Fmax decreases throughout the entire fatigue protocol in both muscle types, but more prominently in EDL muscles, whereas Vmax increases slightly in early fatigue in both muscle types before it starts to decrease.

The effect of fatigue on the parameters of the FV curve

The finding that Fmax decreased from the onset of fatigue and throughout the entire fatiguing protocol is in agreement with several earlier studies conducted with different experimental set-ups and preparations including single Xenopus fibers (Westerblad and Lannergren, 1994), mouse muscles in vivo (Allen et al., 2011) and human muscles in vivo (Jones et al., 2006). In the study by Westerblad and Lannergren (1994), the decrease in Fmax was described to occur in three different phases, with an initial, rapid decline (phase 1), followed by a period of relatively stable force (phase 2) and a final phase with more rapid decline (phase 3). The initial force decrease in phase 1 has been proposed to be a result primarily of an increase in intracellular inorganic phosphate concentration, whereas the decrease in phase 3 has been ascribed to a reduction in Ca2+ release from the sarcoplasmic reticulum and Ca2+ sensitivity (Allen et al., 2008; Westerblad and Lannergren, 1994). From our results, such phases are not clearly distinguishable (see Fig. 3B). This may be due to the fact that force measurements in whole muscle reflect a summed response from many fibers, and even if individual fibers did develop fatigue in three distinct phases, they would do so with some temporal variation, resulting in a smoothed fatigue profile of the whole muscle. It is also possible that the fatigue procedure used here, where we measured Fmax only every 7th contraction, may not allow discrimination of such fatigue phases as force loss over time is not observed in as much detail as if we had measured Fmax at every contraction.

The small increase in Vmax observed in the beginning of the fatigue stimulation protocol agrees with findings of earlier studies (Jones et al., 2006; Westerblad and Lannergren, 1994). The underlying mechanism for this increase is not clear (Amorena et al., 1990; Jones et al., 2006). However, a simultaneous initial increase in Ktr observed in our data suggests that the increase in velocity is a result of a faster attachment rate in the cross-bridge cycle.

The subsequent fatigue-induced decrease in Vmax is thought to be due to slower ATP hydrolysis or a slower ADP release step in the cross-bridge cycle. ADP build-up has been shown to decrease unloaded maximal velocity (Westerblad et al., 1998), as has a severe reduction in pH (Knuth et al., 2006; Overgaard et al., 2010). We have recently shown that a reduction in tetanic intracellular Ca2+ concentration also reduces Vmax in soleus muscles (Kristensen et al., 2017). Potentially, all three mechanisms could affect ATP hydrolysis and/or ADP release and thereby reduce Vmax, as observed in the present study.

The fatigue-induced changes in the curvature of the FV relationship have been subject to substantially less research compared with the reduction in Fmax and Vmax (Fitts, 2008). In the soleus muscles, we found here that the curvature increased continuously from the onset of fatigue, resulting in a considerable increase over the entire fatigue protocol. This is in agreement with previous studies (Jones, 2010; Kristensen et al., 2017) performed on slow-twitch muscles, but not all (Barclay, 1996). In contrast, in EDL muscles, we observed a decrease in curvature in the early stages of the fatigue protocol, and only a modest increase was observed throughout the rest of the fatigue protocol. In EDL muscles, the curvature was not increased beyond non-fatigue values until Pmax had already decreased by 30%. In agreement with this, the curvature was reduced in fatigued mouse EDL fibers when Pmax was reduced by 15% (Barclay, 1996) and in frog tibialis anterior fibers when Pmax was reduced by 13% (Curtin and Edman, 1994). Both these studies only investigated mild fatigue, and did not test whether the curvature would have increased if the muscles had been fatigued more.

In contrast to our results, a recent study by Devrome and MacIntosh (2018) observed that the curvature was reduced during fatigue in rat fast-twitch gastrocnemius muscle, even though power was reduced by 70–75%. It is not clear what the reason for these contradictory findings is, although several differences between the study conditions could contribute. Thus, Devrome and MacIntosh (2018) used an in situ set-up whereas we used isolated muscles and it is possible that the lack of blood flow to the muscles in our set-up might contribute to the increased curvature. Furthermore, Devrome and MacIntosh (2018) produced fatigue by consecutive contractions for 3 min, leading to a fatigue level that was kept constant as judged by contraction force or contraction velocity for 5 min by further contractions while the FV curve was measured. However, as seen in the present study, Fmax, Vmax and a/F0 do not recover at the same rate, which allows for the possibility that curvature was partly recovered during an apparently constant level of fatigue (as judged from force or contraction velocity). Further research is needed to resolve the cause of these contradictory findings.

Cellular mechanism(s) behind changes in curvature

In the two-state Huxley model of cross-bridge action (Huxley, 1957), the curvature is inversely related to (f+g1)/g2 where f is the rate constant for attachment, g1 is the rate constant for detachment where the cross-bridges can develop force and g2 is the rate constant for detachment of negatively strained cross-bridges and thereby determines Vmax. The sum of the Huxley rate constants (f+g1) is equivalent to Ktr. During contractions, f is thought to be several times higher than g1, which ensures a reasonably high proportion of attached cross-bridges. This means that any changes in Ktr would be a result of changes in the rate of attachment (f) (Brenner, 1988; Gilliver et al., 2011; Kristensen et al., 2017).

We measured a significantly greater fatigue-induced decrease in Ktr than in Vmax in the soleus muscles. This would result in a decreased proportion of cross-bridges in the attached state at any given velocity, and a greater curvature of the FV curve, which is consistent with our observations (see Fig. 7). Furthermore, during early fatigue, we observed an increase in the ratio between Ktr and Vmax in EDL muscles, which would mean that the rate constant for attachment is increasing relatively more than Vmax, and an increased number of cross-bridges are in the attached state at a given velocity. This is likewise in agreement with the observed decrease in curvature during early fatigue in EDL. The reason for the relatively small recovery in Vmax and Ktr in the EDL muscles is not known, but it is possibly a result of limited oxygen availability during fatigue.

Fig. 7.

The relationship between Ktr/Vmax and a/F0. The ratio of Ktr and Vmax, plotted against a/F0 for the soleus muscles (A) and the EDL muscles (B). The FV curvature is related to the ratio between Ktr and Vmax and if this ratio decreases, then the curvature will increase. r2 for the linear regression was 0.90 for the soleus and 0.56 for the EDL. Note, these data are from a different group of muscles from those shown in Fig. 3. N=6. All data are expressed as means±95% CI.

Fig. 7.

The relationship between Ktr/Vmax and a/F0. The ratio of Ktr and Vmax, plotted against a/F0 for the soleus muscles (A) and the EDL muscles (B). The FV curvature is related to the ratio between Ktr and Vmax and if this ratio decreases, then the curvature will increase. r2 for the linear regression was 0.90 for the soleus and 0.56 for the EDL. Note, these data are from a different group of muscles from those shown in Fig. 3. N=6. All data are expressed as means±95% CI.

The small reduction in curvature seen at the beginning of fatigue, and the overall smaller increase in curvature observed in EDL muscles, is probably influenced by post-activation potentiation co-occurring with fatigue. This is supported by a study showing that post-activation potentiation is able to reduce the curvature in the non-fatigued muscles (Grange et al., 1995). In most of the experiments of the current study, the control contractions were performed in a non-fatigued and non-potentiated state. However, during repeated contractions to induce fatigue, it is likely that a phosphorylation of the myosin regulatory light chain occurs, and thereby potentiated the muscles, as shown by the increased twitch size. Thus, there could be two opposing mechanisms at play: post-activation potentiation, which reduces curvature, and fatigue, which increases curvature (see Fig. 8). Along this line of thinking, during the first FV cycles, post-activation potentiation is the dominating phenomenon and curvature is therefore reduced. However, at some point, post-activation potentiation reaches a maximum. Fatigue, in contrast, continues to develop, which increases the curvature throughout the rest of the protocol.

Fig. 8.

Theoretical representation of how post-activation potentiation affects the curvature of the FV relationship in EDL muscles. The data to establish the non-fatigued and fatigued curves are from the same EDL muscle as depicted in Fig. 2, but are expressed relative to Fmax and Vmax to better visualize the difference in curvature. The non-fatigued curve+post-activation potentiation was manipulated so that a/F0 was increased by 23% compared with the fresh curve. The fatigued curve−post-activation potentiation was manipulated so that a/F0 was decreased by 23% compared with the fatigued curve. The change of 23% was chosen as it was the average change in a/F0 between the non-fatigued EDL muscles and the post-activation potentiation initiated EDL muscles.

Fig. 8.

Theoretical representation of how post-activation potentiation affects the curvature of the FV relationship in EDL muscles. The data to establish the non-fatigued and fatigued curves are from the same EDL muscle as depicted in Fig. 2, but are expressed relative to Fmax and Vmax to better visualize the difference in curvature. The non-fatigued curve+post-activation potentiation was manipulated so that a/F0 was increased by 23% compared with the fresh curve. The fatigued curve−post-activation potentiation was manipulated so that a/F0 was decreased by 23% compared with the fatigued curve. The change of 23% was chosen as it was the average change in a/F0 between the non-fatigued EDL muscles and the post-activation potentiation initiated EDL muscles.

We found that pre-stimulation to initiate post-activation potentiation in otherwise non-fatigued muscles resulted in a substantial increase in a/F0 in EDL muscles, indicating that myosin light chain was phosphorylated, while no change in Pmax was observed. If post-activation potentiation had been induced entirely without any fatigue development, an increase in Pmax would have been expected. However, pre-stimulation in itself may induce a small degree of fatigue, which is supported by the results in the soleus muscles where Pmax, Fmax and a/F0 all decreased slightly but significantly after pre-stimulation.

We reported absolute values for shortening velocity and force rather than values normalized for fiber length or cross-sectional area. Since the dimensions of the EDL and soleus in 4 week old rats, including fiber lengths and cross-sectional area, have been reported to be approximately similar (Layman et al., 1980), it may be appropriate to directly compare the absolute values of shortening velocity between the soleus and EDL. Furthermore, the curvature does not depend on whether force and velocity are given in absolute or relative units and can, therefore, be compared between the two muscle types.

Conclusion

In conclusion, changes in Fmax, Vmax and FV curvature are all significant contributors to the loss of Pmax during severe fatigue in isolated whole rat soleus and EDL muscles. However, the contributions from each individual parameter differ between muscle types and vary with the degree of fatigue. Thus, the contribution to loss of Pmax from increased curvature is substantially higher in soleus muscles than in EDL muscles, whereas the contribution from a decreased Fmax is markedly higher in the EDL muscles. Therefore, to assess the changes in dynamic exercise performance or muscle functionality during fatigue, it is crucial to include measurements of all three parameters of the FV curve. If only maximal isometric strength and maximal contraction velocity are measured in a study of fatigue, the present data suggest that important components of fatigue will be overlooked, as increased curvature accounts for about half of the total loss of power in slow-twitch muscles.

Acknowledgements

We thank Cuno Rasmussen, Gitte Hartvigsen and Janni Mosgaard Jensen for skilled technical assistance in the laboratory, together with Sebastian Skejø for help analyzing the Ktr data.

Footnotes

Author contributions

Conceptualization: A.K., O.B.N., K.O.; Methodology: A.K., O.B.N., T.H.P., K.O.; Validation: A.K., K.O.; Formal analysis: A.K.; Investigation: A.K.; Data curation: A.K., K.O.; Writing - original draft: A.K.; Writing - review & editing: A.K., O.B.N., T.H.P., K.O.; Visualization: A.K.; Supervision: O.B.N., T.H.P., K.O.; Project administration: O.B.N., T.H.P., K.O.; Funding acquisition: O.B.N., T.H.P., K.O.

Funding

This study was funded by the Danish Council for Independent Research (4004-00538B), as well as Helga and Peter Kvornings foundation (DC274023-KMU).

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Competing interests

The authors declare no competing or financial interests.