INTRODUCTION

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RECENTLY A PAPER EMPHASIZED that to calculate mechanical efficiency during knee-extension exercise there is a need for estimating internal power (IP) generated to overcome inertial and gravitational forces related to the movement of the lower limb when external power (EP) during such exercise was delivered to an ergometer at different contraction rates (11). This is an important aspect that for various forms of locomotion has been debated for many years, and various biomechanical models have been developed for estimating IP (1, 8, 18, 23, 27, 33, 35-37). The methods and criteria for calculation of IP are manyfold, resulting in highly diverse values of IP, and the taxonomy used regarding the terms external and internal work or power is inconsistent. It is generaly agreed that work done on a load external to the body (e.g., a cycle ergometer) corresponds to EP, and IP during such activity has been suggested to include all potential energy (E_pot) and kinetic energy (E_kin) changes due to movement of all body segments (33, 37). However, during various forms of locomotion such as walking and running, the energy changes of the whole body center of gravity are considered as "external work" and only the kinetic energy changes of the body segments relative to the whole body center of gravity are considered as "internal work" (8, 23, 36). These conflicting conventions are probably due to the difference in nature of these activities: during running and walking horizontally on a treadmill, no power in strictly mechanical sense is performed external to the body, when calculated as a mean across one or more strides. However, because the muscles do perform power at each push-off that results in a lift of the body center of gravity, this power output has been considered as EP. Of note is that such EP is also performed during exercise such as cycling and knee extension, but it has not been included in the EP that during such activities is measured exclusively as work done against a load external to the body. The division of the work into internal and external as calculated during horizontal running and walking has been criticized as being based on an "imaginary" resultant force acting on a fictitious point (39), and the legitimacy or sense of computing total work as the sum of internal and external work has been questioned (32, 39). Therefore, there is a need to reevaluate whether the computation of total power (TP) from IP and EP is justified from the physiological responses such as heart rate, muscle blood flow, oxygen uptake (O₂), and efficiency.

With the use of a "novel model" for calculating IP, mechanical efficiency during knee extension was reported to be lower at 100 than at 60 contractions/min (cpm) (11). However, such finding is fully dependent on the model used for calculating IP, which may vary widely as emphasized above. Therefore, the aim of the present study was to 1) use an established kinematic model for estimation of IP during knee extension performed at several contraction rates, 2) validate this kinematic model and compare it with the "novel model," and 3) analyze the relationship between TP and physiological responses for evaluating the legitimacy of IP estimates.

	METHODS

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Subjects. Eight men volunteered to participate in this study. Subjects provided informed, written consent for the investigation, which was approved by the local Ethics Committee. All subjects were physically active, but none was specifically trained. Their age was 24 ± 0.8 (SE) yr, height was 1.82 ± 0.03 m, and weight was 82 ± 4 kg.

Exercise model. Single-leg, dynamic knee-extension exercise (2) was performed in sitting position (backrest 30° inclined) with the subjects secured to the seat with straps around torso, hip, and thighs. The heel was connected to an aluminum brace (weight 0.7 kg) that via a rod was connected to the pedal arm (length 0.22 m) of a friction-braked modified cycle ergometer (Monark, Varberg, Sweden) for the determination of EP. Special precision weights were manufactured that allowed to adjust the resistance with 1-g accuracy, resulting in a precision of 0.1 W or better for all contraction rates, and care was taken that these weights were always hanging free and unsupported to result in the corresponding friction. With the subjects sitting on a horizontal surface and the lower leg vertical, the knee angle was 107 ± 1° (180° = fully extended knee). During each contraction, the knee was extended to 150 ± 2° (knee angle range of movement was 43 ± 2°). The subjects were instructed to contract only the knee-extensor muscles during the extension phase and to relax during flexion. All subjects participated in training sessions before the actual experiments to become fully familiarized with the exercise. Furthermore, they had their maximal knee-extension performance measured at 60 cpm, and the values obtained ranged from 60 to 80 W. On the day of experimental series for this study, the subjects performed single-leg dynamic knee-extension at 20 and 40 W of EP at contraction rates of 45, 60, 75, 90, and 105 cpm in randomized order. Each bout was performed until steady state was attained before all simultaneous recordings were made (see below: IP, O₂, Heart rate, and Leg blood flow), and each bout lasted 5-7 min in all.

IP. IP corresponding to the changes in E_pot and E_kin of the exercising leg during the movements was quantified from a biomechanical model (37) based on anthropometric (19) and kinematic measurements. Kinematic data were obtained from two-dimensional (2D) video recordings (50 Hz) in the sagittal plane of the leg. Round reflective markers were attached to the skin or brace of the exercising leg over the top point of trochanter major, epicondylus lateralis on femur, malleolus lateralis on tibia, and caput ossa metatarsalia 5, and also on three points of the aluminum brace, allowing the identification of its center of mass. Five knee extensions were digitized by using Peak Motus 2000 (Peak Performance Technologies Englewood, CO). The coordinates were filtered by fourth-order Butterworth low-pass filter. A 2D position file containing the x and y coordinates for each marker was used as input for the software program ERGILA (developed in Matlab from The MathWorks, South Natick, MA), implementing the model as suggested by Winter (37). For the present study a two-segment model was used consisting of 1) thigh and 2) lower leg including foot and brace. In short, the model assumes instantaneous energy transfer between segments as well as between E_pot and E_kin: total energy (E_tot) = E_pot + E_kin. IP is calculated as the sum of the positive E_tot changes per second as mean from five knee extensions. Only the summed positive energy changes are included, with the summed negative energy changes being disregarded. TP was calculated by summing EP as measured on the modified cycle ergometer and IP as calculated from the kinematic model. Muscle mechanical efficiency was calculated as (EP + IP) divided by the corresponding rate of energy expenditure. Energy expenditure was estimated from O₂ for each subject and exercise bout after subtraction of resting O₂, which was assumed to be 0.00333 l/s, and applying the oxygen energy equivalent (OE) in joules per liter of oxygen determined from the respiratory exchange ratios (RER) according to Coyle et al. (10).

O₂. Pulmonary O₂ was measured by using a breath-by-breath gas analysis system (CPX/D Metabolic Cart, Medical Graphics). The gas analyzers were routinely calibrated against certified calibration gases of known concentrations, and the ventilation sensor was calibrated with a 3-liter syringe. After 3 min of knee-extension exercise, recordings were sampled over 15 s, and the mean of eight such successive values was taken to represent the O₂ for each exercise bout. RER was also calculated from these data.

Heart rate. Heart rate (HR) was recorded continuously by using the Finapres (Ohmeda 2300).

Leg blood flow. Leg blood flow (LBF) was recorded simultaneously with O₂ during steady state by using the ultrasound Doppler technique. LBF was measured as femoral artery blood flow, and the procedure used to obtain these measurements has previously been validated and shown to produce accurate absolute values at rest and during exercise (28). In our hands, 105 cpm was the highest contraction rate at which proper LBF measurements could be attained. The equipment used was an ultrasound Doppler (model CFM 800, Vingmed Sound, Horten, Norway) equipped with an annular phased array transducer (APAT, Vingmed Sound) probe (11.5-mm diameter), operating at an imaging frequency of 7.5 MHz and variable Doppler frequencies of 4.0-6.0 MHz (high-pulsed repetition mode 4-36 kHz). The site for vessel diameter determination and blood velocity measurements in the common femoral artery was always distal to the inguinal ligament but above the bifurcation into the superficial and profound femoral branch. The blood velocity measurements were performed with the probe in as low insonation angle as physically possible, always below 60° (15). The mean vessel diameter was calculated in relation to the duration of the blood pressure curve according to the following formula: diameter = (systolic diameter/3) + 2 (diastolic diameter/3) (28). The diameter measurements were obtained under perpendicular insonation. LBF was calculated by multiplying the cross-sectional area of the femoral artery by the angle-corrected, time- and space-averaged, and amplitude (signal intensity)-weighted mean blood velocity (in m/s) (28). For further details, see Osada and Rådegran (26).

Validation of the kinematic model. Validation of the kinematic model for calculation of IP was based on independent estimations of IP from the metabolic data only (IP_met)

(1)

where EP is 20 and 40 W, respectively, "O_2 exercise" is measured directly (in l/s), "O_2 rest" is set to ~0.00333 l/s, OE (in J/l) is determined from RER (10) (corresponding to ~20 kJ/l as a mean), and DE is delta efficiency for each particular knee-extension rate. DE was calculated as the difference in EP between the 20- and 40-W bouts (= 20 W) divided by the corresponding difference in the rate of energy expenditure determined from O₂, by again accounting for the RER. The basic assumption for calculating IP_met is that DE reflects a generic, movement-specific DE that is independent of EP (i.e., represents net efficiency at 20 W as well as at 40 W when performed with the same contraction rate).

Statistics. ANOVA was used followed by Fisher's post hoc least significant diffference test. Linear regression and curve fitting (third-degree polynomial) were made in EXEL 2000 (Microsoft, WA) and GraphPad PRISM (version 2.0, San Diego, CA), respectively. A Bland-Altman analysis was used to evaluate IP calculated from the kinematic model against IP_met (5). Data are presented as means ± SE or (range), and P < 0.05 was considered statistically significant.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The major movement was the knee angular displacement as expected, but also the thigh showed some angular displacement relative to horizontal, although the energy changes of the lower leg were by far larger than those of the thigh (Fig. 1). The changes in E_pot occurred in synchrony with the movement of the lower leg, whereas the changes in E_kin occurred at twice that frequency. Of note is the observation that the amplitude (peak  nadir) for the changes in E_kin increased in a curvilinear mode with contraction frequency, whereas for the changes in E_pot the amplitude remained rather constant (Fig. 1). The timewise changes of these energies were partially out of phase; i.e., peak E_pot corresponded to nadir E_kin, and this attenuated the summed positive E_tot because of the assumption of instantaneous energy transfer in the model. IP increased significantly with increasing contraction rate (45, 60, 75, 90, and 105 cpm): 5 ± 0.2, 7 ± 0.2, 13 ± 0.5, 21 ± 0.7, and 36 ± 1.4 W at 20 W of EP, and 5 ± 0.4, 8 ± 0.4, 13 ± 0.4, 21 ± 0.6, and 32 ± 1.7 at 40 W, respectively (Fig. 2). There was no difference in IP between the two different levels of EP, in accordance with all the angular displacements showing highly similar time histories during 20 and 40 W (Fig. 1). A third-order polynomial fit (y = ax + bx³), including the coordinate (0, 0), resulted in the following equation: IP = 0.0299x + 0.00002617x³ (R² = 0.996), where IP is the mean value for 20 and 40 W, and x is contraction rate.

View larger version (39K): [in this window] [in a new window]   Fig. 1.   Sample plot from a representative subject of the changes in knee angle and thigh angle relative to horizontal in combination with energy changes estimated from a kinematic model during knee-extension exercise. Results are from exercise bouts at 20 W (thin lines) and 40 W (thick lines) of external power (EP) performed at the 5 different contraction rates (2-s periods shown). Estimated contributions of the sum of the positive total energy changes from thigh (Etot thigh) and lower leg (Etot lower leg) are presented separately, and also the potential (Epot) and kinetic (Ekin) energy changes are shown separately. Finally, the instantaneous sum of all energy changes (Etot) is shown. deg, Degrees; cpm, contractions/min.

View larger version (15K): [in this window] [in a new window]   Fig. 2.   Internal power (IP) vs. contraction rate. , Data from the present study shown as means ± SE. Symbol size exceeds ±1 SE for the low contraction rates. Solid line is drawn according to the following equation: IP = 0.0299x + 0.00002617x3 (R2 = 0.996), where x is contraction rate. , Data from Ferguson et al. (11). Dashed line is the best fit to those data including (0,0).

When the subject's individual anthropometric differences are taken into account, IP tended to increase with body mass at the highest contraction rates (Fig. 3). However, R² values were 0.5 and nonsignificant. Thus the effect of body mass (within 65-100 kg) on IP could be disregarded by taking into account the interindividual variation relative to the difference in IP between contraction rates, a finding that is in concert with that of Ferguson et al. (11). Therefore, independent of the subject's body mass, the IP during knee extension may be calculated from the formula for the polynomial fit above.

View larger version (16K): [in this window] [in a new window]   Fig. 3.   IP vs. body mass presented as individual data for the various contraction frequencies. , 45 cpm; , 60 cpm; , 75 cpm; , 90 cpm; , 105 cpm. IP is for each subject taken as the mean value of 20 and 40 W.

LBF, pulmonary O₂, and HR increased when constant EP was performed with increasing contraction rate and were consistently higher at 40 W compared with 20 W of EP (Fig. 4). DE calculated from these data ranged from 16 to 23% between contraction rates but showed no significant differences, with the overall mean for DE being 20 ± 1%. The RER values used in these calculations for estimation of OE ranged from 0.85 to 1.01 for the different exercise bouts. The subsequent calculation of IP_met on the basis of Eq. 1 (as mean of 20 and 40 W) resulted in the following values: 5 ± 3.3, 7 ± 1.5, 10 ± 2.3, 19 ± 4.7, and 28 ± 6.6 W at the contraction rates of 45, 60, 75, 90, and 105 cpm, respectively. The above IP values calculated from the kinematic model were validated against these IP_met values by using the Bland-Altman analysis. Inclusion of all individual data sets (n = 74, because of 6 missing data sets) in one analysis showed that the estimated bias, calculated as the overall mean difference between IP_met and IP based on kinematics, was 2 W and that 93% of the differences between IP_met and IP based on kinematics were within ±2 SD of all these differences (Fig. 5). When the same analysis was used for each of the 10 exercise bouts (n = 8 or 7 in each bout), the overall difference ranged from 0 to 8 W, and corresponding differences within ± 2 SD of all differences ranged from 86 to 100%. Also, Bland-Altman analysis performed for each of the eight subjects (n = 10 exercise bouts for each subject) showed that 88-100% of the differences between IP_met and IP were within ± 2 SD of all these differences. The slopes of the regression lines for each of these plots ranged from 0.94 to 0.71 with a mean of 0.04. Thus assessment of the slope for the Bland-Altman analyses did not indicate a systematic relationship between the differences between IP_met and IP (on the basis of kinematics) vs. the average of these two variables.

View larger version (13K): [in this window] [in a new window]   Fig. 4.   Values (means ± SE) of leg blood flow (A), pulmonary oxygen uptake (O2) (B), and heart rate (C) during exercise performed at 5 different contraction rates.

View larger version (17K): [in this window] [in a new window]   Fig. 5.   Bland-Altman plot of the difference between IP calculated from metabolic variables (IPmet) and IP calculated from the kinematic model (IPkinematic) vs. the average of these 2 values. The overall mean value of differences was 2 W and is depicted as the solid horizontal line together with the 2 dashed lines at difference ± 2 SD.

When the physiological variables LBF, O₂, and HR were plotted vs. TP (= IP + EP), where IP was calculated from the kinematic data, they fell on the same lines independent of contraction rate (Fig. 6). This was supported by the three linear regression lines calculated for the respective mean values (all R²  0.92 and significant). We also calculated regression lines and R² values for each subject for each of the three variables. The R² values ranged from 0.52 to 0.99, except for one subject's LBF data, where a large variability was seen and the R² value was only 0.05. The correlations were reanalyzed excluding this subject, but this did not significantly affect our results and we decided to retain the subject in all data sets. The largest variability was seen for the LBF data at the highest contraction frequencies of 105 cpm, and these data tend to be on the high side of the regression line but did not deviate significantly.

View larger version (13K): [in this window] [in a new window]   Fig. 6.   Leg blood flow (A), pulmonary O2 (B), and heart rate (C) vs. total power output estimated as EP + IP, where IP is calculated according to a kinematic model. Values are means ± SE.

Muscle mechanical efficiency at the five contraction rates was 22 ± 1.6, 23 ± 1.5, 24 ± 1.8, 23 ± 1.4, and 20 ± 1.3% at 20 W of EP, and 20 ± 1.1, 23 ± 1.0, 22 ± 0.9, 21 ± 1.3, and 18 ± 1.3% at 40 W of EP, respectively. The overall muscle mechanical efficiency was 22 ± 0.5% with no significant differences between working conditions.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The use of an established kinematic model for the calculation of IP during knee-extension exercise showed a curvilinear relationship between IP and contraction rate. This was expected because the E_kin of a movement increases with the velocity squared, which in turn corresponds to the contraction rate squared (21), and, therefore, the timewise E_kin changes during the movements should increase with a third-order polynomial in relation to contraction rate (13, 24). Because E_pot per contraction is independent of the movement velocity it follows from a corresponding argument that the timewise E_pot changes should increase proportionally with contraction rate, leading to the third-order polynomial fit applied for the present data: IP = ax + bx³, where x is the contraction rate. Surprisingly, some movement of the thigh occurred, which added a small but significant amount to the total IP during knee-extension exercise. This may be due to soft tissue compression of the thigh, e.g., during lifting of the lower leg against a resistance such that the posterior thigh will be compressed against the horizontal surface. In all, IP amounted to between 12 and 180% of the EP depending on contraction rate and magnitude of EP. The model used in the present study assumes instantaneous exchange of energy between all energy components (potential as well as kinetic translational and rotational) within each body segment and also between body segments (37). Only the summed positive energy changes are the basis for the power calculations here, and thus the minimum IP is reperesented, because energy changes in opposite directions will attenuate the sum. Storage of elastic energy during an eccentric work phase and release during a subsequent concentric work phase may further reduce the muscular work performed to overcome the TP but could be ignored during knee-extension exercise, because the knee extensors are almost completely relaxed in the eccentric phase and therefore unlikely to store elastic energy (2). The present kinematic model is based on theoretical considerations and has proven empirically to be valid in a number of studies with widely different movement patterns (20, 25, 33). In the present study, the validity of this model was further evaluated from metabolic data. The estimated bias of IP based on the kinematic model was only 2 W compared with IP_met, and the lack of agreement seemed not to depend on the magnitude of IP.

The novel use of DE for estimating IP from metabolic variables is a method fundamentally different from kinematic model calculations, whether these are based on video recordings as in this study or on goniometer recordings as in a previous study (11). Thus the metabolic based calculation of IP_met may be used as "a gold standard" for validation of the kinematic estimation of IP. Previous studies have introduced "metabolic counterparts of internal power but not combined this with independent estimates of the mechanical power (13, 22). DE was taken as a movement specific efficiency being independent of EP and was calculated from aerobic metabolism only. This is justified from the experimental conditions in which healthy young men exercised at EP up to 40 W, which previously was shown to elicit only minor lactate changes (31). Furthermore, in the present study EP only up to 70% of maximum working capacity was performed and all the RER values were <1, which was in support of a prevailing aerobic metabolism. Importantly, for the conversion of O₂ to total energy turnover rate in watts, the RER value was used for estimation of the oxygen energy equivalent (10). The present estimates of IP_met from metabolic data were highly similar to IP estimates from kinematic data during knee extension, which is in support of the kinematic model assumptions used in this study.

However, our data on IP were not in concert with those in a previous study because our data were generally lower than those reported by Ferguson et al. (11). This may in part be due to differences in the setup because the knee angular displacement in each contraction in the present study was ~45°, but it was reported to be 80° in the study by Ferguson et al., although Ferguson et al. ignored movement of the thigh, which was shown to be significant in our setup and would have predicted our values to become higher (11). Surprisingly, Ferguson et al. reported IP to be lower at higher workloads than at lower workloads during high contraction rates, but not during low contraction rates, without giving any explanation for this finding (11). Of note is that in our calculation of IP no difference was found when the same contraction rate was performed with different external loads. This was expected because in these two conditions the same movement of the leg is performed in terms of timewise displacement of the lower leg (Fig. 1). Thus velocities and accelerations are similar, which in turn implies that the same muscular work has to be performed to move the leg. However, our finding of nonlinearity between IP and contraction rate is the most essential difference compared with the data by Ferguson et al. This relationship is of crucial importance in the comparison of muscle mechanical efficiency at different contractions rates. If IP increases proportional with contraction rate, as implicated by the data of Ferguson et al. (Fig. 1), then this may be the reason for their finding of lower muscle mechanical efficiency at high compared with low contraction rates. Importantly, the present study design with several different contraction rates allowed us to describe the dependency of IP on contraction rate.

In the present study, no differences in muscle mechanical efficiency were found between contraction rates, neither when estimated as DE nor when based on the kinematic model. These two fully independent calculations of efficiency resulted in remarkably similar values, and in particular DE, or apparent efficiency, has previously been suggested as the most valid measure of muscular efficiency (34). Thus our findings are considered to be convincing evidence for the independency of muscle mechanical efficiency relative to contraction rate during the present contraction velocities. Studies on single fibers have demonstrated efficiency to depend on contraction velocity despite a wide spread in most data (16, 38). Delicate data on single human muscle fibers show fiber type-specific efficiencies relative to contraction velocity (6). The curves drawn to fit the data showed for type I fibers peak efficiency to occur at a velocity of ~0.2 fiber lengths/s and for type IIA fibers at ~0.3 fiber length/s at 20°C. On the basis of these single-fiber data, it is often implied that efficiency changes with contraction rate in voluntary movements also; however, scrutinizing the literature reveals contradictory findings. In the early studies of Asmussen (4), DE during bicycling seemed to be greater at higher contraction rates (68 vs. 102 cpm). This was confirmed in a number of later studies (7, 9, 22, 30), whereas another study was in support of a decrease in DE with increasing pedal rate (40-100 rpm) (14), and still another study presented data fitting an U-shaped curve (13). Finally, some studies do discuss efficiency to be independent of contractions velocity within a wide range of velocities (6, 29). Our knowledge on muscle mechanical efficiency during different voluntary contraction velocities is still limited, and changes in fiber-type recruitment occurring with changes in contraction intensity or velocity during human voluntary contractions may mask possible relationships between efficiency and contraction rate. This is because the fiber types show maximum efficiency at different contractions velocities, as pointed out above and discussed previously (40). Therefore, functionally constant efficiencies may exist during a wide range of voluntary activity. Of note is that the interpretation of data during varying contraction rates may not be comparable when differences in angular displacements or velocities are not accounted for.

The contradictions regarding IP and mechanical efficiency during knee extension in the present study and the earlier study by Ferguson and co-workers (11) emphasize that the model assumptions for estimating IP are crucial. Ferguson and co-workers (11) stated that their model allowed IP to be determined accurately on the basis of test-retest reliability analysis, but they did not validate their model. Direct measurement of IP is not possible, and mechanistic discussions on the topic have come to a "dead end" (32). Nonetheless, the inclusion of IP is justified if, from human voluntary exercise, we can gain information on the muscular level. This was essentially the aim when the knee-extension model was introduced (2), and therefore it is equally essential to adopt a model for IP calculation that will not distort data on TP in a physiologically nonsensical way.

This brings us back to the legitimacy or justification for estimating IP, which is that it contributes to a generic understanding of physiological responses to muscle contractile work. For this reason, we studied not only HR and O₂ but also blood flow of the exercising muscle group during the performance of various magnitudes of EP in combination with different magnitudes of IP due to different contraction rates. We measured LBF, which previously has been shown to reflect the increases in blood flow of the contracting knee-extensor muscles (3). Interestingly, LBF increased not only with increasing EP but also with increasing IP (Fig. 4), and when plotted against TP (= EP + IP), LBF fell on the same line independent of the relative contribution of EP and IP (Fig. 6), when IP was calculated based on kinematic model assumptions (37). This is at variance with the most recent paper by Ferguson at al. (12) in which they applied their previously published model for estimation of IP and showed LBF to be higher when the same TP (54 W) was performed at 100 cpm compared with 60 cpm. This may be exclusively due to their model for IP calculations, but also the experimental setup may play a role. Thus knee extension performed with an angular range of only 20° showed LBF to be similar when the same EP (<15 W) was performed at 60 and 80 cpm (17). This finding implies LBF to be relatively higher at 60 cpm compared with 80 cpm had the same TP been performed, which is in contradiction to Ferguson et al. (12). Interestingly, in our study, LBF was proportional to TP independent of contraction rate, and our experimental setup comprised both angular exertions and EP values between those applied in the studies of Ferguson et al. (12) and Hoelting et al. (17), respectively. In combination, these three studies suggest a U-shaped curve relationship between LBF and constant TP performed with increasing shortening velocities. Comprehensive studies covering a wide range of muscle contraction ranges and velocities as well as EPs are necessary to reveal the muscle blood flow dependency on contraction intensity and contraction rate to bridge the controversies and increase our generic understanding of physiological responses to muscular contractions, including validated models for estimation of TP.

In conclusion, a novel metabolic validation of an established kinematic model for calculating IP supports the model assumptions for knee-extension exercise. The present polynomial fit (IP = 0.0299x + 0.00002617x³, where x is contraction rate) accurately estimates IP for subjects having a body mass within 65-100 kg when exercising with knee angle displacements of ~45° from a vertical lower leg position. When this model was applied, the physiological responses LBF, O₂, and HR were closely related to TP, supporting the legitimacy of IP estimates. Muscular mechanical efficiency (20 ± 1%) as well as DE (22 ± 0.5%) remained remarkably constant across contraction rates. A range of knee angular displacements and velocities as well as EPs have to be addressed in future studies for establishing a comprehensive data set for IP estimates to be used in the variety of knee-extension studies in which the knowledge of TP is pertinent.