Introduction

Efficiency of exercising muscle during steady state exercise is defined as the ratio of power output to rate of energy expenditure (Gaesser and Brooks 1975). In many previous studies (Gaesser and Brooks 1975; Coyle et al. 1992; Hansen et al. 2002; Horowitz et al. 1994; Mogensen et al. 2006), external power output (P ext) has been used as an index of power output during exercise, which refers to the application of force through a distance either by a muscle or by an intact body (Stainsby et al. 1980). On the other hand, exercising muscle generates not only P ext but also internal power output (P int), defined as the power performed on the body segments (Cavagna and Kaneko 1977; Hansen et al. 2004), which implies that the expended energy above a resting level could be attributable to both P ext and P int during exercise. Therefore, total power output (P tot) including P int and P ext as the power output generated by exercising muscle should be taken into consideration when estimating “muscular efficiency” at different contraction frequencies, to avoid the underestimation of actual power output during muscle contractions given by P ext only (Ferguson et al. 2000). In previous studies based on quantification of P int, muscular efficiency has been reported to range from 21 to 30% (Ferguson et al. 2002; Hansen and Sjøgaard 2006; Luhtanen et al. 1987). This variation is thought to derive from the differences of contraction velocity and exerted force in the exercising muscle, even when the same evaluation method is used to measure muscular efficiency. In addition the same method for estimation of P int was not used in these studies. Thus, this could also explain some of the difference.

P int was estimated by measuring mechanical and metabolic energy changes in various biomechanical and physiological models (Minetti et al. 2001; Sjøgaard et al. 2002; Wells et al. 1986; Willems et al. 1995; Winter 1979). It has been reported that P int exponentially increases as a function of pedal rate during cycling and that oxygen uptake \(\left( {\dot V{\text{O}}_2 } \right)\) also exponentially increases with increasing pedal rates above a given higher pedal rate, even under the same level of P ext (Coast and Welch 1985; Foss and Hallén 2004; Seabury et al. 1977), suggesting greater O2 cost and P int at higher pedal rates. This means that muscular efficiency would be affected by greater O2 cost due to higher levels of P int with increasing pedal rates. However, there has been no study that investigated muscular efficiency during cycling based on estimation of P int in a large range of pedal rates. We hypothesized in this study that muscular efficiency could decrease at higher pedal rates during cycling exercise and that lower muscular efficiency could be caused by higher O2 cost with increasing pedal rate.

The purpose of this study was to investigate the muscular efficiency during cycling exercise under certain P tot or P ext experimental conditions that required a large range of pedal rates from 40 to 120 rpm.

Methods

Subjects

Seven healthy male subjects (age 22.4 ± 0.4 years; height 169.6 ± 1.9 cm; mass 64.1 ± 2.9 kg, \(\dot V{\text{O}}_{2\max } ;\) 43.6 ± 2.9 ml kg−1 min−1) volunteered to participate in experiment 1 (Exp. 1) and nine healthy male subjects (age 20.7 ± 0.8 years; height 170.3 ± 1.6 cm; mass 62.6 ± 1.6 kg, \(\dot V{\text{O}}_{2\max } ;\) 47.8 ± 2.1 ml kg−1 min−1) in experiment 2 (Exp. 2). All subjects were physically active, but none was specifically trained. They were all informed of the purpose and procedure of this study, and gave their informed, written consent prior to testing. The experimental protocol used in this study was approved by the Ethics Committee for Human Subjects of the Kyushu Institute of Technology.

Experimental protocol

This study consisted of two experiments with different cycling conditions; Exp. 1 and Exp. 2 were carried out at the same levels of P tot and P ext, respectively (Table 1). In each experiment the subjects performed three exercise tests with different pedal rates (40, 80 and 120 rpm) on a friction-braked cycle ergometer (Monark 818E, Crescent AB, Sweden). The load during cycling at each pedal rate was adjusted to maintain the same P tot level in Exp. 1 and the same P ext level in Exp. 2, since P int and P ext were expected to alter with the changes in pedal rates. The exercise tests were composed of 3-min rest and unloaded cycling for 2 min followed by 5-min loaded cycling in Exp. 1, and 3-min rest and unloaded cycling for 3 min followed by 4-min loaded cycling in Exp. 2. An electrical metronome was set to assist subjects in maintaining the target pedal rates. The three exercise tests in each experiment were carried out in randomized order separated from a recovery period (∼30 min) within 1 day.

Table 1 Target power outputs at three target pedal rates in two experiments
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Measurements

Breath-by-breath pulmonary gas exchange parameters were measured continuously throughout the exercise tests using a metabolic analysis system (A-E 300S, Minato Medical Science, Japan). Inspired and expired gas volumes were measured using a hot-wire respiratory-flow system. The expired fractions of oxygen (O2) and carbon dioxide (CO2) were analyzed using a paramagnetic oxygen-analyzer and an infrared carbon dioxide analyzer, respectively. The system was calibrated prior to each test according to the manufacturer’s instructions. The volume was calibrated before each test by manually pumping a 2-l syringe. The O2 and CO2 analyzers were calibrated using a standard gas of known concentration (O2 15.01%, CO2 5.020% in N2 balance) before each test. Breath-by-breath minute ventilation \( \left( {\dot V_{\text{E}} } \right), \) O2 uptake \(\left( {\dot V{\text{O}}_2 } \right),\) CO2 output \(\left( {\dot V{\text{CO}}_2 } \right)\) and respiratory exchange ratio \(\left( {R;{\text{ }}{{\dot V{\text{CO}}_2 } \mathord{\left/ {\vphantom {{\dot V{\text{CO}}_2 } {\dot V{\text{O}}_2 }}} \right. \kern-\nulldelimiterspace} {\dot V{\text{O}}_2 }}} \right)\) were determined, and the data were stored on a hard disk for future analyses. Heart rate (HR) was recorded telemetrically with a Polar heart rate monitor (S610i, Polar Electro Oy, Finland). Pulmonary gas exchange parameters and HR data were averaged for 1 min (from first to second min) in a sitting position on the ergometer and during unloaded cycling exercise, and for 2 min (last 2 min) during loaded cycling exercise.

Arterialized capillary blood samples were taken from the fingertip immediately before and after each exercise test, and blood lactate concentration was analyzed by a semi-automated lactate analyzer (YSI-1500 Sport, Yellow Springs Ins., USA).

Flywheel frequency during cycling was measured by an IC hall sensor attached to the cycle ergometer to analyze pedal frequency.

Calculations

Total energy expenditure \( \left( {\dot E_{{\text{tot}}} } \right) \) was calculated as the sum of aerobic energy expenditure \(\left( {\dot E_{{\text{aerobic}}} } \right)\) plus anaerobic energy expenditure \(\left( {\dot E_{{\text{anaerobic}}} } \right).\) \(\dot E_{{\text{aerobic}}} \) was calculated using the R and \(\dot V{\text{O}}_2 \) at a steady state level from the following equation based on a table developed by Lusk (1924):

$$ \dot E\;\left( {\text{W}} \right) = \left( {1.232R + 3.815} \right)\;\dot V{\text{O}}_2 {{\left( {1\;{\text{min} ^{- 1}} } \right)} \mathord{\left/ {\vphantom {{\left( {1\;{\text {min}}^{- 1} } \right)} {0.0143}}} \right. \kern-\nulldelimiterspace} {0.0143}}. $$

\(\dot E_{{\text{anaerobic}}} {\text{ }}({\text{W}})\) was estimated by substitution of \(\dot V{\text{O}}_2 \) derived from blood lactate accumulation ([ΔLa]) into the above equation. The \(\dot V{\text{O}}_2 \) was estimated from conversion of the [ΔLa] (mmol l−1) calculated as the difference between pre- and post-exercise lactate concentration from the following equation (Di Prampero and Ferretti 1999):

$$ \dot V{\text{O}}_2 \left( {{\text{ml}}\,{\text{min}}^{ - 1} } \right) = 3.3\;\left[ {\Delta {\text{La}}} \right]\;{\text{BM}}\;\left( {{\text{body mass}};{\text{ kg}}} \right). $$

The exercising muscle performs both P ext and P int (Cavagna and Kaneko 1977). P ext was estimated from external (pedal) force and pedal frequency (f; Hz) that was calculated by actually measured flywheel frequency and the ratio of pedal to flywheel rotations (3.64).

$$ P_{{\text{ext}}} \;\left( {\text{W}} \right) = {\text{load}}\;\left( {{\text{kp}}} \right)9.8\;\left( {{\text{m}}\;{\text{s}}^{ - 2} ;{\text{gravitational acceleration}}} \right)6\;\left( {{\text{m}}\;{\text{rev}}.^{ - 1} } \right)f\;\left( {{\text{Hz}}} \right). $$

According to Minetti et al. (2001), P int was estimated from BM and f as follows:

$$ P_{{\text{int}}} \;\left( {\text{W}} \right) = 0.153\;{\text{BM}}\;\left( {{\text{kg}}} \right)f^3 \;\left( {{\text{Hz}}} \right). $$

Muscular efficiency was calculated by dividing the total power output (P tot = P int + P ext) by the energy expenditure above a resting state (Kaneko et al. 1979; Ferguson et al. 2002; Hansen and Sjøgaard 2006). In this study the P tot was used as an index of power output generated by exercising muscle, because our main purpose was to investigate the effect of muscular efficiency under different levels of pedal rates and/or P int during cycling. We used the following equation:

$$ {\text{Muscular efficiency}}\left( \% \right) = {{\left( {P_{\text{int} } + P_{{\text{ext}}} } \right)} \mathord{\left/ {\vphantom {{\left( {P_{\text{int} } + P_{{\text{ext}}} } \right)} {\left( {\dot E_{{\text{tot}}} - \dot E_{{\text{rest}}} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\dot E_{{\text{tot}}} - \dot E_{{\text{rest}}} } \right)}} \times 100\% $$

where \(\dot E_{{\text{tot}}} \) was total energy expenditure during loaded cycling and \(\dot E_{{\text{rest}}} \) energy expenditure at a resting state.

Statistics

All data are presented as means ± SEM. A one-way ANOVA with repeated measures was used to test the differences in physiological variables between the three exercise tests in each experiment. If a significant F ratio was obtained, then a Student–Newman–Keuls post hoc test was performed to obtain the differences in the selected variables. A Pearson’s correlation coefficient was employed to test the relationship between two variables. Statistical significance was accepted at P < 0.05.

Results

Cardio-respiratory variables (\(\dot V{\text{O}}_2 ,\) R and HR), [ΔLa], actually measured pedal rates, power output (P int, P ext and P tot) and energy expenditures \(\left( {\dot E_{{\text{aerobic}}} {\text{ and }}\dot E_{{\text{anaerobic}}} } \right)\) during unloaded and loaded cycling exercise at three levels of pedal rates in two experiments are given in Table 2. In two experiments \(\dot V{\text{O}}_2 \) during unloaded cycling revealed the highest values (1,560–1,600 ml min−1) at 120 rpm compared with 40 rpm (370–430 ml min−1) and 80 rpm (630–640 ml min−1). As a result of the increased P int, \(\dot V{\text{O}}_2 \) was observed to rise with increasing pedal rate regardless of P ext = 0. Similarly, [ΔLa] at 120 rpm was also significantly higher than 80 rpm for Exp. 1, and 40 and 80 rpm for Exp. 2, respectively (P < 0.05). The estimated P int at 120 rpm (∼90 W) was markedly increased with increasing pedal rate (∼3 W at 40 rpm and ∼25 W at 80 rpm) in the two experiments.

Table 2 Cardio-respiratory variables, blood lactate accumulation, measured pedal rate, power outputs and energy expenditures during cycling exercise at three levels of pedal rates under two experimental conditions
Full size table

In Exp. 1 under the same level of P tot, the difference between the measured and target pedal rates was found to be larger at 120 rpm than at the other two pedal rates. Consequently, the P int showed a higher value at 120 rpm for Exp. 1 than that for Exp. 2, and thus P tot calculated as the sum of P int and P ext was significantly higher at 120 rpm (121 ± 4.1 W) in a comparison with 40 rpm (113 ± 3.2 W) and 80 rpm (110 ± 4.7 W) (P < 0.05). \(\dot E_{{\text{tot}}} \) calculated during cycling at 80 rpm (418 ± 23 W) was significantly lower compared to that at 40 rpm (502 ± 20 W) and 120 rpm (584 ± 39 W) (P < 0.05). Due to the lower levels of P tot and \(\dot E_{{\text{tot}}} ,\) muscular efficiency estimated at 80 rpm (26.5 ± 0.8%) was significantly higher than that at 40 rpm (22.6 ± 0.8%) and at 120 rpm (21.1 ± 1.0%) (P < 0.05, Fig. 1, upper panel).

Fig. 1
figure 1

Muscular efficiency as a function of pedal rate during cycling exercise at three levels of pedal rates in experiment 1 (upper panel) and 2 (lower panel). a Significantly different from 40 rpm, b significantly different from 120 rpm

Full size image

In Exp. 2 under the same level of P ext, the actually measured P ext showed a similar value in three exercise tests at three levels of pedal rates. However, muscular efficiency at 120 rpm (20.9 ± 0.9%) was significantly lower than that at 40 (23.5 ± 0.5%) and 80 rpm (25.6 ± 0.9%) (P < 0.05, Fig. 1, lower panel).

Discussion

The main finding obtained in the present study was that there was an inverted U shaped relationship between pedal rate and muscular efficiency and that the highest muscular efficiency (approximately 26%) was found at 80 rpm and the lowest muscular efficiency at 120 rpm in both experiments (Fig. 1). Luhtanen et al. (1987) have demonstrated that efficiency values assessed from the same experimental data, based on several definitions of efficiency, were 19.7–17.4% for gross efficiency \(\left( {{{P_{{\text{ext}}} } \mathord{\left/ {\vphantom {{P_{{\text{ext}}} } {\dot E_{{\text{tot}}} }}} \right. \kern-\nulldelimiterspace} {\dot E_{{\text{tot}}} }}} \right),\) 21.8–17.5% for net efficiency \(\left[ {{{P_{{\text{ext}}} } \mathord{\left/ {\vphantom {{P_{{\text{ext}}} } {\left( {\dot E_{{\text{tot}}} - \dot E_{{\text{rest}}} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\dot E_{{\text{tot}}} - \dot E_{{\text{rest}}} } \right)}}} \right]\) and 29.7–21.0% for muscular efficiency \( \left[ {{{\left( {P_{{\text{int}}} + P_{{\text{ext}}} } \right)} \mathord{\left/ {\vphantom {{\left( {P_{{\text{int}}} + P_{{\text{ext}}} } \right)} {\left( {\dot E_{{\text{tot}}} - \dot E_{{\text{rest}}} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\dot E_{{\text{tot}}} - \dot E_{{\text{rest}}} } \right)}}} \right] \) in a cycling exercise from light to heavy exercise intensities. This finding would imply that the estimation of efficiency is influenced by how energy expenditure consumed by and power output generated by exercising muscle itself are evaluated. Therefore, the evaluations for these variables during exercise must be precisely made under various exercise conditions such as different pedal rates. In both experiments of the present study the estimated P int was markedly increased with increasing pedal rate (Table 2).

An estimation of P int in this study was made using the equation proposed by Minetti et al. (2001). Although various models have been developed for estimating P int, consistent methods and criteria for the assessment of P int have not yet been obtained. Sjøgaard et al. (2002) proposed an independent estimation of P int based on metabolic data to reevaluate whether the computation of P int is justified. We found that the calculation from pedal rate and body mass proposed by Minetti et al. (2001) could be easily applied for the estimation of P int in cycling. Hansen et al. (2004) compared P int from the different models and showed that P int from Minetti’s model (2001) was lower than that from other models. We therefore inferred that P int evaluated by the model of Minetti et al. (2001) in this study might be underestimated. However, when considering small differences of P int between physiological and biomechanical models, it seems unlikely that the slightly lower estimation of P int in this study could affect significantly the present results of muscular efficiencies. Ferguson et al. (2002) estimated P int from the model of Minetti et al. (2001) to investigate the influence of pedal rate and muscle temperature on muscular efficiency. A correlation coefficient between P int estimated from the present data using both the Minetti et al. (2001) and Sjøgaard et al. (2002) models was 0.95 (P < 0.001), indicating that the estimated P int level would be adequate. Furthermore, the muscular efficiency obtained in our two experiments was observed to range from 20.9 to 26.5%, which is consistent with the values reported by the previous studies using similar methods for estimation of muscular efficiency as we used in this study (Ferguson et al. 2002; Hansen and Sjøgaard 2006; Luhtanen et al. 1987).

A possible explanation for the present result is that \(\dot V{\text{O}}_2 \) exponentially increases with increasing pedal rate. In fact, we observed that \(\dot V{\text{O}}_2 \) and P int increased remarkably with increasing pedal rate during unloaded cycling, as shown in Table 2. The magnitude of \(\dot V{\text{O}}_2 \) appears to change depending on the levels of P int. This is supported by previous studies that examined \(\dot V{\text{O}}_2 \) as a function of optimal pedal rate. \(\dot V{\text{O}}_2 \) at a given power output (P ext) during cycling was minimized at a unique pedal rate (60–80 rpm) and exponentially increased from the pedal rate (Coast and Welch 1985; Foss and Hallén 2004; Seabury et al. 1977), while MacIntosh et al. (2000) illustrated the same feature with electromyogram (EMG) data. This means that optimal muscular effciency could exist in a unique pedal rate and decrease with increasing pedal rate, which is consistent with the present results that higher muscular efficiency existed at 80 rpm and decreased with increasing pedal rate.

Our results raised a question about why O2 cost would be larger at higher pedal rates. This would be due to extra energy related to energy turnover by the Ca2+-ATPase for noncontractile processes at higher cycling pedal rates (Abbate et al. 2001; Baker et al. 1994). Energy released from ATP is converted into power outputs including P int and P ext, and is also used by various ion pumps, particularly the Ca2+ pump of the sarcoplasmic recticulum (SR) (Barclay 1994). Blinks et al. (1978) demonstrated that Ca2+ reabsorption into the SR further increased at higher contraction frequencies. On the other hand, it has been reported that a large proportion (∼43%) of ATP is used by noncontractile processes, with more ATP derived from anaerobic rather than aerobic metabolism (Baker et al. 1994). This notion is consistent with the present data that larger [ΔLa] was observed at 120 rpm compared with 40 and 80 rpm (Table 2), which would lead to more anaerobic energy at 120 rpm, resulting in lower muscular efficiency. Hogan et al. (1998) demonstrated that muscle contractions of short duration resulted in a significantly higher calculated rate of ATP utilization, a threefold increase in glycolysis and greater fatigue related to the increased intracellular [La−] and [H+], compared with muscle contractions of long duration in canine muscle. It is possible that the lower muscular efficiency as a consequence of higher energy expenditure at the higher pedal rate might be related to noncontractile processes such as excessive energy consumption related to the reaccumulation of Ca2+ by the SR.

The muscular efficiency at 40 rpm was significantly lower than that at 80 rpm in Exp. 1, but there was no significant difference in Exp. 2 compared with efficiency at 80 rpm. Human skeletal muscle is composed mainly of type I and type II muscle fibers. Furthermore, the ratio of the two fiber types in the recruited muscle fibers is altered by tension exerted in exercising muscle or by exercise intensity (Sargeant 1994). Type II muscle fibers are more inefficient than type I muscle fibers in humans (Coyle et al. 1992; Jones et al. 2004; Hansen et al. 2002; Horowitz et al. 1994; Mogensen et al. 2006). Ahlquest et al. (1992), using the same experimental condition as our Exp. 1, demonstrated that at the same metabolic rate glycogen depletion in type II muscle fibers at 50 rpm was greater than that at 100 rpm during cycling. This means that a greater recruitment of type II muscle fibers at the lower pedal rate could be induced due to higher muscle force required to overcome the higher resistance per cycle at the same metabolic rate. The lower muscular efficiency at the lower pedal rate with higher pedal force may result from the greater recruitment of low-efficiency type II muscle fibers, presumably owing to the higher muscle force exerted. This supports the results of Exp. 1 that muscular efficiency at a lower pedal rate (40 rpm) with higher pedal force (250%↑) was significantly lower than that at 80 rpm under the same P tot condition.

In conclusion, there was an inverted U shaped relationship between pedal rate and muscular efficiency during cycling exercise under certain P tot or P ext experimental conditions that required a large range of pedal rates. Muscular efficiency could be affected by the differences in O2 cost and P int due to the levels of pedal rates.