Journal of Biomechanics 43 (2010) 2394–2399

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Journal of Biomechanics

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In vivo operational fascicle lengths of vastus lateralis during sub-maximaland maximal cycling

Neal Austin a, Rachel Nilwik b, Walter Herzog a,n

a KNB 402 Human Performance Laboratory, Faculty of Kinesiology, The University of Calgary, Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N IN4b Faculty of Health, Medicine and Life Sciences, Maastricht University, Maastricht, Netherlands

a r t i c l e i n f o

Article history:

Accepted 20 April 2010Instantaneous contractile characteristics of skeletal muscle, during movement tasks, can be determined

and related to steady state mechanical properties such as the force–length relationship with the use of

Keywords:

Force–length

Ultrasound

Vastus lateralis

Cycling

In vivo

90/$ - see front matter & 2010 Elsevier Ltd. A

016/j.jbiomech.2010.04.016

esponding author. Tel.: +403 220 8525; fax:

ail address: walter@kin.ucalgary.ca (W. Herzo

a b s t r a c t

ultrasound imaging. A previous investigation into the contractile characteristics of the vastus lateralis

(VL) during cycling has shown that fascicles operate on the ‘‘weak’’ descending limb of the force–length

relationship, thus not taking advantage of the ‘‘strong’’ plateau region. The purpose of this study was to

investigate if VL fascicle lengths change from sub-maximal to maximal cycling conditions, and if

maximal cycling results in VL fascicle lengths which operate across the plateau of the force–length

relationship. Fifteen healthy male subjects (age 20.971.8 yr, wt. 67.076.3 kg, ht. 176.777.2 cm) were

tested to establish the maximal force–length relationship for the VL through ten maximal isometric

contractions at various knee angles. Subjects then cycled on an SRM cycle ergometer at cadences of 50

and 80 revolutions per minute at 100 W, 250 W, and maximal effort. Fascicle lengths were determined

at crank angles of 0, 90, and 1801. Fascicles operated at or near the plateau of the maximal force–length

relationship for maximal cycling, while operating on the descending limb during sub-maximal

conditions for both cadences. However, when comparing the fascicle operating range for the sub-

maximal cycling conditions to the corresponding sub-maximal force–length relationships, the VL now

also operated across the plateau region. We concluded from these results that regardless of cycling

effort, the VL operated through the ideal plateau region of the corresponding force–length relationship,

hence always working optimally. We hypothesize that this phenomenon is due to the coupling of series

elastic compliance and length dependent calcium sensitivity in the VL.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Knowledge of in vivo skeletal muscle fibre function hasincreased substantially with the advances in ultrasound imaging.Ultrasonography has allowed researchers to quantify skeletalmuscle architecture for static (Henriksson-Larson et al., 1992) anddynamic (Herbert and Gandevia, 1995) conditions, and todetermine the mechanical properties of skeletal muscles, suchas the force–length (Gordon et al., 1966) and force–velocityrelationships (Hill, 1938). Ichinose et al. (1997), Finni et al. (2001),and Maganaris et al. (2001, 2003) were among the first to useultrasound imaging to determine the force–length (Gordon et al.,1966) properties for human vastus lateralis (VL), tibialis anterior,and soleus, while Finni et al. (2001, 2003) and Ichinose et al.(2000) measured the corresponding force–velocity relationships.

It is appealing to think that the mechanical properties ofmuscles have evolved to best satisfy everyday function. Lutz andRome (1994) found that the mechanical properties of the

ll rights reserved.

+403 284 3553.

g).

semimembranosus muscle of the frog, Rana pipiens, were perfectlysuited for maximizing power output during jumping. Specifically,they showed that semimembranosus operated on the plateau ofthe force–length relationship and was shortening at optimalspeed for power production during jumping (Fig. 1).

In a study investigating in vivo muscle function, Herzog et al.(1991) determined the force–length properties of human rectusfemoris muscles in high performance runners and cyclists. Thesetwo groups of athletes use the rectus femoris at distinctlydifferent lengths; thus, optimal function for one group wouldseem to imply non-optimal function for the other group.However, they found that the rectus femoris was strongest atshort lengths for the cyclists and strongest at long lengths for therunners, suggesting that the force–length properties of thismuscle had adjusted to meet the chronic requirements of dailytraining in these specialized groups of athletes.

In contrast to the above findings, Muraoka et al. (2001)reported that the human VL, a major knee extensor muscle (Nariciet al., 1989), operated exclusively on the descending limb of theforce–length relationship during cycling, thereby working over arange that is clearly not optimal. Their study was performed fora single, sub-maximal condition (98 W) using a low pedaling rate

Fig. 1. Operational lengths and contraction velocities of the semimembranosus

sarcomeres of the frog, Rana pipiens, with relation to the corresponding force–

length and stress–velocity relationships during maximal jumping. (A) Sarcomeres

operate at lengths during maximal jumping that correspond to lengths that allow

for maximal force production on the force–length relationship. (B) The average

velocity of shortening during maximal jumping corresponds to contraction

velocities that result in maximal power production. (Adapted from Lutz and

Rome, 1994; with permission).

N. Austin et al. / Journal of Biomechanics 43 (2010) 2394–2399 2395

(40 revolutions per minute; RPM), and therefore is not appro-priate for comparison with typical race cycling conditions.Training or racing conditions would be performed at higherpedaling resistances (Vogt et al., 2006) and pedaling rates (Luciaet al., 2001). Muraoka et al. (2001) suggested that greater pedalingresistance is achieved with higher VL forces. In turn, higher VLforces would stretch series elastic elements, thereby causing VLfascicles to shorten for a given pedal position, thus approachingand possibly even covering the optimal plateau region of thismuscle for realistic cycling conditions.

In order to gain better insight into the relationship betweenthe force–length properties of muscles and the associated every-day function, in vivo quadriceps force–VL fascicle length proper-ties were determined and compared to the operating range of VLfascicles during cycling. Cycling conditions of 50 and 80 revolu-tions per minute (RPM) at sub-maximal (100 and 250 W) andmaximal power outputs were performed. Specifically, we wantedto test the hypothesis that human knee extensors, and VL as arepresentative of that group, work over a range covering optimalfascicle lengths on the force–length relationship, thereby allowingfor maximal force production (Lutz and Rome, 1994) during sub-maximal and maximal cycling.

2. Methods

Ethics approval for this study was obtained from the University of Calgary’s

Conjoint Health Research Ethics Board.

2.1. Subjects

Fifteen male subjects [age 20.971.8 (SD) yr, mass 67.076.3 kg, and height

176.777.2 cm] were recruited for this study. The inclusion criteria were that they

were healthy and active but did not train or compete in cycling, and that they had

no prior injury that might compromise the experimental testing. Prior to testing,

the experimental protocol was carefully explained to all subjects and written

informed consent was obtained.

To obtain the maximal quadriceps force–VL fascicle length relationship,

subjects were seated and secured on a dynamometer (System 3, Biodex, Shirley,

USA). The subject’s hip angle was set to 701 and their backs rested against the back

rest so that the knee hung just slightly over the edge of the seat, which allowed for

a full range of knee flexion. The knee center of rotation was carefully aligned with

the axis of rotation of the dynamometer and subjects were asked to perform a light

warm-up of 20–30 sub-maximal knee extensions/flexions. An ultrasound probe

(7.5 MHz linear array, Phillips EnVisor HD, Eindhoven, Netherlands) was then

placed, and secured, perpendicular to the skin over the VL, midway (�50%)

between the greater trochanter and lateral epicondyle of the right femur. Subjects

then performed 10 maximal isometric contractions at knee flexion angles ranging

from 101 to 1001 at 101 increments (full knee extension¼01). Ramp style isometric

contractions were performed, starting from zero force until they reached maximal

efforts over the course of 5 s (Ichinose et al., 1997). The order of knee angles was

randomized and a minimum of 2 min of rest was given to prevent fatigue. For each

trial, ultrasound images of the VL (49 Hz), knee extensor torque (1000 Hz), and

knee angle (1000 Hz) were synchronized, measured and stored on a computer for

off line analysis. Synchronization of the ultrasound images with the signals

recorded by computer was achieved with a wave form generator (1000 Hz) that

sent wave pulses simultaneously to the ultrasound images and computers. Fascicle

lengths at distinct instants in time were obtained by linear interpolation of the

fascicle length obtained from the two ultrasound frames that enclosed the instant

of interest. Prior to the cycling trials, subjects were given a minimum of 10 min of

rest to reduce any effects of fatigue.

Subjects then moved, with the ultrasound probe still secured over their VL, to a

cycle ergometer (SRM Julich, Germany) which they fit to their personal preference.

Subjects were tasked to cycle at each of the four sub-maximal conditions (50 and

80 RPM at power outputs of 100 and 250 W) until steady state cycling was

achieved. Steady state cycling was defined when the subjects maintained a

consistent cadence (72 RPM), and the power output was within 10 W of the

target value. Once steady state cycling was achieved, data collection was started

and maintained for a minimum of 16 pedal cycles. For the maximal conditions (50

and 80 RPM), subjects were asked to cycle at full effort for approximately 16 s and

a minimum of 16 pedal cycles were recorded. The pedaling frequencies of 50 and

80 RPM were chosen as 50 RPM has been associated with near minimal metabolic

cost (Coast and Welch, 1985) and 80 RPM is an average training and racing

frequency for long distance cyclists (Lucia et al., 2001). For each cycling condition,

ultrasound images of the VL (49 Hz), pedaling frequency (10 Hz) and power output

(10 Hz) were continuously monitored. A minimum of 2 min of rest was given

between the sub-maximal conditions, while a minimum of 5 min of rest was given

between the maximal conditions in an attempt to minimize fatigue, although the

achievement of true maximal power was not crucial for the measurement and

interpretation of the results.

2.2. Fascicle length

VL fascicles could not always be seen in their entirety; therefore, fascicle

lengths were measured using linear extrapolation (Finni et al., 2001) and dividing

muscle thickness (MT) by the angle of pennation (a) as illustrated in Fig. 2. Fascicle

lengths were measured at the point of maximal torque during the isometric

contractions, and at the 01, 901, and 1801 crank angle for all cycling conditions

using ImageJ software (National Institute of Health, USA). The 01 and 1801 crank

angles represent the start and end of the power phase, while the 901 crank angle is

the angle of maximal power production (Coyle et al., 1991). VL fascicle lengths

were also measured for entire pedal revolutions, for a single representative

subject, at both sub-maximal and maximal cycling efforts at 50 RPM.

Within and between subject comparisons of fascicle lengths, for cycling and

the isometric contractions, were made after normalizing fascicle lengths to the

length obtained for the maximal isometric knee extension trial.

2.3. Force, torque, and power measurements

Maximal knee extension torques for the maximal voluntary isometric

contractions were determined as the mean torque for a 7100 ms interval around

the point of maximal torque. All torques were corrected for gravity and any

passive forces. Quadriceps forces were then calculated by dividing the knee

extension torques by the angle-dependent moment arm of the quadriceps muscles

(Herzog and Read, 1993). Cycling power was averaged over the duration of each

test condition.

Fig. 2. Calculation of vastus lateralis fascicle length. A line (AB) is drawn from the

insertion point of a fascicle on the deep aponeurosis to where it can no longer be

seen on the ultrasound image. The angle between line AB and the deep

aponeurosis (line AC) is denoted as a and is the pennation angle. A line (DE) is

then drawn along the superficial aponeurosis of the vastus lateralis. The equations

of lines AB and DE are determined and their intersection point (F) is calculated.

Muscle thickness (MT) is then obtained as the shortest distance from point F to the

deep aponeurosis (point C). Using MT and the pennation angle (a), fascicle length

(FL) can be determined as: FL¼(MT/Sin(a)).Fig. 3. Mean (71 SE) quadriceps force–fascicle length relationship for all 16

subjects for knee angles ranging from 101 to 1001. Note the long ascending and

short descending limb of the relationship with peak forces occurring at a mean

knee angle of 701.

N. Austin et al. / Journal of Biomechanics 43 (2010) 2394–23992396

2.4. Statistics

A one way repeated measures ANOVA (a¼0.05) was used to determine

differences in fascicle lengths across the varying cycling efforts (100 W, 250 W,

and maximal effort), for a given cadence (50 or 80 RPM) and given crank angle

(01, 901, or 1801). Paired t-tests were used, (a¼0.05), to determine differences in

fascicle length between cadences (50 and 80 RPM) for a given cycling effort

(100 W, 250 W, and maximal effort) and a given crank angle (01, 901, or 1801).

3. Results

3.1. Force–length relationship

The maximal quadriceps force–VL fascicle length relationshiphad a long ascending limb, a plateau region and a shortdescending limb for knee angles ranging from 101 to 1001(Fig. 3). The shortest fascicle lengths were obtained at 101 ofknee flexion (mean71 SD; 5.370.6 cm), while maximal fasciclelengths were obtained at the most flexed, 1001, knee angle(11.171.3 cm). The maximal active isometric force(47797798 N) was obtained at an average knee flexion angle of701, which corresponded to an optimal VL fascicle length of9.371.7 cm. The corresponding normalized quadriceps force–VLfascicle length relationship is shown in Figs. 4a and 5a with alinearly extrapolated descending limb (Gordon et al., 1966) forpurposes of comparison with the functional fascicle lengthsencountered for the different cycling conditions.

3.2. Functional fascicle length ranges for cycling

Fascicle lengths continuously decreased during the powerphase of cycling for the 50 RPM (Fig. 4a; Tables 1 and 2) and the80 RPM conditions (Fig. 5a; Tables 1 and 2). Fascicle lengths for agiven pedaling frequency (either 50 or 80 RPM) tended todecrease with increasing power production. However, statisticalsignificance was only obtained for the 901 crank angle at 80 RPMs(p¼0.001) and the 1801 crank angle at the 50 (p¼0.01) and80 RPM (p¼0.04) conditions, for which the maximal effort fasciclelengths were shorter than those obtained for the sub-maximalefforts (100 and 250 W; Figs. 4a and 5a; Tables 1 and 2). Fig. 6illustrates the fascicle length–crank angle curve for an entirepedal revolution, of a representative subject, for sub-maximal(combined 100 and 250 W conditions) and maximal (610 W)pedaling conditions. Fascicle lengths continuously decrease from

01 to 1801 of crank angle for both sub-maximal and maximalconditions, and are substantially shorter for the maximalcompared to the sub-maximal conditions throughout the powerphase (0–1801), while they are approximately the same in therecovery phase (about 220–3201) when the quadriceps musclesare not activated.

Together, these results illustrate that fascicle lengths for themaximal effort cycling conditions cover a large portion of theplateau region of the maximal force–length relationship, whilethe sub-maximal conditions cover primarily the descending limb,just reaching the plateau towards the very end of the power phase(Figs. 4a and 5a).

Fascicle lengths were significantly shorter at crank angles of 01(maximal effort only) and 901 (sub-maximal efforts only) for the50 compared to the 80 RPM conditions (Table 2).

4. Discussion

Fascicle lengths for the VL were longest for the 100 W,intermediate for the 250 W, and shortest for the maximal effortconditions at crank angles of 901 and 1801 for both the 50 and80 RPM conditions (Tables 1 and 2). Although not necessarilystatistically significant in each case, this shortening of the fasciclelengths with increasing power output demonstrates that VLfascicle lengths are not only dependent on the crank angle, andthus knee angle (Muraoka et al., 2001), but also on the forceexerted by the knee extensor muscles, as knee extensor forcesincrease with increasing cycling power (Shinohara et al., 1997).

When superimposing the excursions of VL fascicle lengths ontothe maximal quadriceps force–VL fascicle length relationship, forthe power phase of cycling, it becomes apparent that they coverprimarily the descending limb for the sub-maximal effortconditions (100 and 250 W), while they cover a large portion ofthe plateau region for the maximal effort conditions for both 50and 80 RPM pedaling frequencies (Figs. 4a and 5a, respectively).This result suggests that when cycling at maximal effort, peopletake advantage of the plateau region of the quadriceps force–VLlength relationship, and therefore, cycling at maximal effort isoptimal from a force–length perspective. In contrast, whencycling at sub-maximal efforts, fascicle excursions are primarilyrestricted to the descending limb of the maximal force–length

Fig. 4. Mean (71 SE; shaded grey) fascicle length at the 01 and 1801 crank angle for the maximal (546 W) and sub-maximal (100 and 250 W) bicycling conditions at

50 RPM superimposed on the quadriceps force–VL fascicle length relationships. (A) Fascicle lengths superimposed on the maximal and (B) fascicle lengths superimposed on

the sub-maximal quadriceps force–VL fascicle length relationships. The sub-maximal quadriceps relationships were derived based on data presented by Ichinose et al.

(1997), and were fit to the corresponding sub-maximal cycling condition.

Fig. 5. Mean (71 SE; shaded grey) fascicle length at the 01 and 1801 crank angle for the maximal (750 W) and sub-maximal (100 and 250 W) bicycling conditions at

80 RPM superimposed on the quadriceps force–VL fascicle length relationships. (A) Fascicle lengths superimposed on the maximal and (B) fascicle lengths superimposed on

the sub-maximal quadriceps force–VL fascicle length relationships. The sub-maximal quadriceps relationships were derived based on data presented by Ichinose et al.

(1997) and were fit to the corresponding sub-maximal cycling condition.

Table 1Mean (71 SD, n¼15) fascicle lengths at crank angles of 01, 901, and 1801 for all

cycling conditions.

Fascicle length (cm)

01 901 1801

50 RPM 100.373.1 W 13.272.5 12.071.9 9.371.5

50 RPM 251.5710.7 W 13.373.2 11.872.0 8.771.2

50 RPM 546.1761.9 W 13.872.9 11.372.7 7.671.3

80 RPM 96.7713.3 W 13.272.7 12.972.2 9.371.2

80 RPM 256.279.1 W 13.072.8 12.472.5 8.971.2

80 RPM 750.1796.5 W 11.071.0 9.971.0 8.071.0

N. Austin et al. / Journal of Biomechanics 43 (2010) 2394–2399 2397

relationship, therefore not taking advantage of the strong plateauregion, thus working sub-optimally. The result for the sub-maximal effort conditions is supported by Muraoka et al. (2001)who showed that VL fascicle excursions were exclusively locatedon the descending limb of the force–length relationship for theirsubjects cycling at 40 RPM and 98 W.

It is well known that force–length relationships for sub-maximal activations differ in magnitude and shape from thoseobtained for maximal activation. Of specific interest for this studyis the observation that the plateau of sub-maximal force–lengthrelationships is shifted towards longer fibre (sarcomere) lengths(e.g., Rack and Westbury, 1969). In agreement with these

Table 2Mean (71 SD) normalized fascicle lengths at crank angles of 01, 901, and 1801

crank angles for all cycling conditions. Fascicles were normalized with respect to

the fascicle length corresponding to the maximal quadriceps force during maximal

voluntary isometric contraction, L0. Differences in fascicle length for different

power outputs (100 W, 250 W, and maximal effort) at a constant cadence (50 or

80 RPM) and constant crank angle (01, 901, or 1801) are indicated by (n

). Differences

in fascicle length for the different pedaling rates (50 and 80 RPM), at a constant

power output (100 W, 250 W, or maximal effort) and constant crank angle (01, 901,

or 1801) are denoted by (y).

Fascicle length [� L0]

01 901 1801

50 RPM 100.373.1 W 1.4670.23 1.3370.18y 1.0470.21

50 RPM 251.5710.7 W 1.4970.34 1.3070.23y 0.9770.18

50 RPM 546.1761.9 W 1.5370.31y 1.2270.29 0.8570.15n

80 RPM 96.7713.3 W 1.4770.31 1.4370.21y 1.0470.20

80 RPM 256.279.1 W 1.4570.31 1.3670.23y 1.0070.18

80 RPM 750.1796.5 W 1.2470.18y 1.1170.15n 0.9070.13n

Fig. 6. Normalized (mean71 SD) fascicle length–crank angle curve for a single

representative subject, cycling at sub-maximal (combined data from 100 and

250 W power outputs) and maximal (611 W power output) cycling conditions at

50 RPM. Six pedal revolutions were averaged for each condition. 01 and 3601 crank

angles correspond to the top dead center, and 1801 to the bottom dead center

position of the pedal.

N. Austin et al. / Journal of Biomechanics 43 (2010) 2394–23992398

observations, Ichinose et al. (1997) found that the plateau of theforce–length relationship for human VL was shifted by as much as30% for sub-maximal effort contractions. In order to compare thefascicle excursions for the sub-maximal efforts of cycling with thecorresponding sub-maximal quadriceps force–VL length relation-ships, we calculated the percent effort for the 100 and 250 Wconditions relative to the maximal effort power output obtainedfor the 50 RPM (546 W) and the 80 RPM (750 W) conditions. Oncethe level of effort was determined, we interpolated the data byIchinose et al. (1997) to the appropriate level and calculated thecorresponding sub-maximal quadriceps force–VL fascicle lengthrelationships. As expected, this resulted in decreased quadricepsforces and a shift of the relationship towards longer VL fasciclelengths (Figs. 4b and 5b). When superimposing the fascicleexcursions for the maximal and sub-maximal cycling conditionsat 50 RPM (Fig. 4b) and 80 RPM (Fig. 5b) on their correspondingmaximal and sub-maximal quadriceps force–VL fascicle lengthrelationships, the fascicle excursions are nearly centered on the‘‘strong’’ plateau for all conditions. These results suggest thatfascicle excursion, for maximal and sub-maximal cycling efforts,cover the ideal plateau region when due account is taken of theshift in sub-maximal force–length relationships. Therefore, it

appears that the interaction between muscle and tendon, in thisspecific case, increases force production potential for sub-maximal and maximal cycling conditions.

Limitations of our study should be kept in mind wheninterpreting these results. Developing the force–length relation-ship for VL requires some non-trivial assumptions. For example,misalignment of the knee axis with regards to the dynamometerhas been associated with errors in torque measurement rangingbetween 3.5% and 7.3% (Arampatzis et al., 2004). We wereextremely careful to align the knee and dynamometer axes, butcannot exclude absolute errors in the knee joint moments.However, since any knee axis misalignment for a subject wouldhave resulted in a systematic error, this should not have affectedthe shape of the force–length relationship or the location of theplateau region.

Furthermore, we reported data pertaining to the quadricepsforce–VL fascicle length relationship rather than the force–lengthrelation of the VL, thereby implicitly assuming that the contribu-tion of VL to the total knee extensor moment was constant acrossthe range tested. Although, this assumption has been made onmany other occasions in the published literature (e.g., Finni et al.,2001; Ichinose et al., 1997, 2000; Kawakami et al., 1995;Maganaris, 2003), it has not been proven correct. Nevertheless,the rare data on this topic suggest that muscles in an agonisticgroup tend to have similar force–length properties (Herzog et al.,1992) thereby supporting this particular assumption.

Obtaining accurate, absolute fascicle lengths with ultrasoundimaging is not trivial. If the ultrasound probe is not placed exactlyalong the plane of the fascicles, fascicle lengths will be distorted(Benard et al., 2009). However, misalignment of the probe wouldresult in a systematic error that would be eliminated for allpractical purposes when we calculate differences in fasciclelengths and when fascicle lengths are normalized for comparisonacross subjects. Also, our length measurements did not accountfor any possible fascicle curvatures which have been associatedwith VL fascicles. There are several reasons for our choice: first,absolute fascicle length were not as important in this study asfascicle length changes; second, entire fascicles could not alwaysbe traced as they often extended beyond the field of view of theultrasound probe; third, not accounting for fascicle curvaturewould result in systematic underestimations of fascicle length,and thus would not bias the shape or location of the force–lengthrelationship, and finally, errors associated with ignoring VLfascicle curvature would be less than 6% (Muramatsu et al., 2002).

5. Conclusion

Fascicle lengths and excursions for cycling enclosed theplateau of the quadriceps force–VL length relationship for allconditions, indicating that independent of the cycling effort, VLappears to be used optimally for cycling. This result was obtainedbecause the increased fascicle lengths with decreasing efforts ofcycling were closely matched with the shift in the force–lengthrelationship towards longer fascicle lengths. We conclude fromthis observation that the shift in force–length properties ofskeletal muscles, for different levels of activation, may accom-modate the force-dependent shifts of fascicle excursions whenmovements are performed at different efforts. If our novelobservation of matched fascicle length excursion with shifts inforce–length properties holds true in general, then we mayhypothesize that a functional coupling exists between the passiveproperties of the series elastic element and the shift of the force–length properties caused by the length-dependent calciumsensitivity of muscle (Moisescu and Theileczek, 1979; Stephensonand Willliams, 1982). Therefore, the mechanics (series

N. Austin et al. / Journal of Biomechanics 43 (2010) 2394–2399 2399

compliance) and physiology (calcium sensitivity) of muscles mayallow for optimal use of the force–length relationship at any levelof effort. This truly exciting proposal needs further testing withdifferent muscles and other sports activities or activities of dailyliving.

Conflict of interest statement

There are no commercial relationships for any of the authorsthat have biased the process of data collection and/or datareporting.

Acknowledgements

This project was supported through grants from the NaturalSciences and Engineering Research Council of Canada and theCanada Research Chair Programme.

References

Arampatzis, A., Karamanidis, K., De Monte, G., Stafilidis, S., Morey-Klapsing, G.,Bruggemann, G.P., 2004. Differences between measured and resultant jointmoments during voluntary and artificially elicited isometric knee extensioncontractions. Clinical Biomechanics 19, 277–283.

Benard, M.R., Becher, J.G., Harlaar, J., Huijing, P.A., Jaspers, R.T., 2009. Anatomicalinformation is needed in ultrasound imaging of muscle to avoid potentiallysubstantial errors in measurement of muscle geometry. Muscle and Nerve 39,652–665.

Coast, R.J., Welch, H.G., 1985. Linear increase in optimal pedal rate with increasedpower output in cycle ergometry. European Journal of Applied Physiology 53,339–342.

Coyle, E.F., Feltner, M.E., Kautz, S.A., 1991. Physiological and biomechanical factorsassociated with elite endurance cycling performance. Medicine and Science inSports and Exercise 23, 93–107.

Finni, T., Ikegawa, S., Lepola, V., Komi, P.V., 2001. In vivo behavior of vastus lateralismuscle during dynamic performances. European Journal of Sport Science 1,1–13.

Finni, T., Ikegawa, S., Lepola, V., Komi, P.V., 2003. Comparison of force–velocityrelationships of vastus lateralis muscle in isokinetic and in stretch-shorteningcycle exercises. Acta Physiologica Scandinavica 177, 483–491.

Gordon, A.M., Huxley, A.F., Julian, F.J., 1966. The variation in isometric tensionwith sarcomere length in vertebrate muscle fibres. Journal of Physiology 184,170–192.

Henriksson-Larsen, K., Wretling, M.L., Lorentzon, R., Oberg, L., 1992. Do musclefibre size and fibre angulation correlate in pennated human muscles. EuropeanJournal of Applied Physiology 64, 68–72.

Herbert, R.D., Gandevia, S.C., 1995. Changes in pennation with joint angle andmuscle torque: in vivo measurements in human brachialis muscle. Journal ofPhysiology 496, 287–297.

Herzog, W., Guimaraes, A.C., Anton, M.G., Carter-Erdman, K.A., 1991. Moment–length relations of rectus femoris muscles of speed skaters/cyclists andrunners. Medicine and Science in Sports and Exercise 23, 1289–1296.

Herzog, W., Leonard, T.R., Renaud, J.M., Wallace, J., Chaki, G., Bornemisza, S., 1992.Force–length properties and functional demands of cat gastrocnemius, soleus,and plantaris muscles. Journal of Biomechanics 25, 1329–1335.

Herzog, W., Read, I.J., 1993. Lines of action and moment arms of the major force-carrying structures crossing the human knee joint. Journal of Anatomy 182,213–230.

Hill, A.V., 1938. The heat of shortening and the dynamic constants of muscle.Proceedings of the Royal Society of London 126, 136–195.

Ichinose, Y., Kawakami, Y., Ito, M., Fukunaga, T., 1997. Estimation of active force–length characteristics of human vastus lateralis muscle. Acta Anatomica 159,78–83.

Ichinose, Y., Kawakami, Y., Ito, M., Kanehisa, H., Fukunaga, T., 2000. In vivoestimation of contraction velocity of human vastus lateralis muscle during‘‘isokinetic’’ action. Journal of Applied Physiology 88, 851–856.

Kawakami, Y., Abe, T., Kuno, S., Fukunaga, T., 1995. Training-induced changes inmuscle architecture and specific tension. European Journal of AppliedPhysiology 72, 37–43.

Lucia, A., Hoyos, J., Chicharro, J.L., 2001. Preferred pedaling cadence in professionalcycling. Medicine and Science in Sports and Exercise 33, 1361–1366.

Lutz, G.J., Rome, L.C., 1994. Built for jumping: the design of the frog muscularsystem. Science 263, 370–372.

Maganaris, C.N., 2001. Force–length characteristics of in vivo human skeletalmuscle. Acta Physiologica Scandinavica 172, 279–285.

Maganaris, C.N., 2003. Force–length characteristics of the in vivo humangastrocnemius muscle. Clinical Anatomy 16, 215–223.

Moisesce, D.G., Thieleczek, R., 1979. Sarcomere length effects on the Sr2+- andCa2 +-activation curves in skinned frog muscle fibres. Biomchimica etBiophysica Acta 546, 64–76.

Muramatsu, T., Muraoka, T., Kawakami, Y., Shibayama, A., Fukunaga, T., 2002. Invivo determination of fascicle curvature in contracting human skeletalmuscles. Journal of Applied Physiology 92, 129–134.

Muraoka, T., Kawakami, Y., Tachi, M., Fukunaga, T., 2001. Muscle fiber and tendonlength changes in the human vastus lateralis during slow pedaling. Journal ofApplied Physiology 91, 2035–2040.

Narici, M.V., Roi, G.S., Landoni, L., Minetti, A.E., Cerretelli, P., 1989. Changes in force,cross-sectional area and neural activation during strength training anddetraining of the human quadriceps. European Journal of Applied Physiologyand Occupational Physiology 59, 310–319.

Rack, P.M.H., Westbury, D.R., 1969. The effects of length and stimulus rate ontension in the isometric cat soleus muscle. Journal of Physiology 204, 443–460.

Shinohara, M., Kouzaki, M., Yoshihisa, T., Fukunaga, T., 1997. Mechanomyographyof the human quadriceps muscle during incremental cycle ergometry.European Journal of Applied Physiology 76, 314–319.

Stephenson, D.G., Williams, D.A., 1982. Effects of sarcomeres length on the force-pCa relation in fast and slow-twitch skinned muscle fibres from the rat. Journalof Physiology 333, 637–653.

Vogt, S., Heinrich, L., Schumacher, Y.O., Blum, A., Roecker, K., Dickhuth, H.,Schmid, A., 2006. Power output during stage racing in professional roadcycling. Medicine and Science in Sports and Exercise 38, 147–151.