Jacob H Svendsen

Pascal Madeleine

Gender differences in force variability 1 Amount and structure of force variability during short, ramp and sustained contractions in males and females

Keywords: Force variability, motor control, gender differences, endurance contraction, sample entropy

The aim of this study was to investigate the effect of gender differences on force variability assessed by means of linear and nonlinear estimators during short duration, ramp and sustained isometric elbow flexions. Ten males and 10 females performed elbow flexion receiving visual feedback from the direction of force exertion. Isometric elbow flexions were performed during: maximum voluntary contraction (MVC before and after endurance test), short contraction at 10-90 %MVC with 10 % increment for 5 s, ramp contraction from 5 to 50 %MVC over 30 s, and endurance contraction at 20 %MVC.

Standard deviation (SD), coefficient of variations (CV), and sample entropy (SaEn) were computed from the force signals recorded in 3D. During short and ramp contraction, SD increased with contraction level while SaEn followed an inverted U-shape function (p < .01). During endurance test, SD and CV increased with contraction time (p < .01). SD and SaEn were consistently higher in males than females while it was opposite for CV (p < .05). Separate control and compensatory mechanisms could be responsible for the observed changes in the amount and structure of task-related and tangential forces variability. Moreover, gender differences most likely point towards gender-dependent force control mechanisms. The lower magnitude and structure of variability observed in females may increase the risk for muscle overload and damage.

Introduction

The study of gender differences with respect to for instance pain and motor control has attracted a lot of interest within the last decade [START_REF] Greenspan | Studying sex and gender differences in pain and analgesia: A consensus report[END_REF][START_REF] Semmler | Gender differences in the fatigability of human skeletal muscle[END_REF]. Differences in factors like muscle mass, muscle morphology, substrate utilization, and neuromuscular activation have been reported among males and females [START_REF] Hicks | Sex differences in human skeletal muscle fatigue[END_REF][START_REF] Krogh-Lund | Changes in conduction velocity, median frequency, and root mean square-amplitude of the electromyogram during 25% maximal voluntary contraction of the triceps brachii muscle, to limit of endurance[END_REF][START_REF] Sejersted | Intramuscular fluid pressure during isometric contraction of human skeletal muscle[END_REF]. A larger muscle mass concomitant to the increased strength [START_REF] Miller | Gender differences in strength and muscle fiber characteristics[END_REF] could result in larger increased intramuscular pressure in males compared with females. Thus, metabolic imbalance between supply and demand may occur, resulting in a greater rate of fatigue development in males [START_REF] Béliveau | Myoelectrical and metabolic changes in muscle fatigue[END_REF][START_REF] Sahlin | Repetitive static muscle contractions in humans -a trigger of metabolic and oxidative stress[END_REF]. Further, females are found to be more fatigue-resistant than males during relative endurance tasks at sub-maximal force level [START_REF] Maughan | Endurance capacity of untrained males and females in isometric and dynamic muscular contractions[END_REF][START_REF] Semmler | Gender differences in the fatigability of human skeletal muscle[END_REF]. Contradictory results are reported in studies testing gender difference in strengthmatched groups. For instance, no difference between genders is found in line with the hypothesis that intramuscular pressure and muscle mass play a role [START_REF] Clark | Gender differences in skeletal muscle fatigability are related to contraction type and EMG spectral compression[END_REF][START_REF] Hunter | Sex differences in the fatigability of arm muscles depends on absolute force during isometric contractions[END_REF], while other studies have shown opposite results arguing for a less potent effect of metabolic imbalance (Hunter, Critchlow, Shin, & Enoka, 2004b;[START_REF] Larivière | Gender influence on fatigability of back muscles during intermittent isometric contractions: A study of neuromuscular activation patterns[END_REF].

In addition to muscle mass and morphology, neuromuscular activation, and coordination have been suggested as important factors but only a few studies have examined this issue [START_REF] Beck | Gender comparisons of mechanomyographic amplitude and mean power frequency versus isometric torque relationships[END_REF][START_REF] Ge | Gender-specific differences in electromyographic changes and perceived pain induced by experimental muscle pain during sustained contractions of the upper trapezius muscle[END_REF][START_REF] Sung | Gender differences in spectral and entropic measures of erector spinae muscle fatigue[END_REF]). An altered neuromuscular activity is reported to lead to improved recovery period for the deactivated motor units during endurance contraction [START_REF] Fallentin | Motor unit recruitment during prolonged isometric contractions[END_REF][START_REF] Hunter | Changes in muscle activation can prolong the endurance time of a submaximal isometric contraction in humans[END_REF], and this mechanism could be more potent for females compared with males explaining difference in an endurance task [START_REF] Semmler | Limb immobilization alters muscle activation patterns during a fatiguing isometric contraction[END_REF]. Finally, both peripheral and central mechanisms are likely to explain gender differences during sustained contraction.

Fluctuation in a recorded signal has in general been perceived as noise and disturbance to the signal of interest [START_REF] Fitts | The information capacity of the human motor system in controlling the amplitude of movement[END_REF][START_REF] Schmidt | Motoroutput variability: A theory for the accuracy of rapid motor acts[END_REF]. In studies investigating force control, force fluctuation or variability can be a way to assess important aspects of the motor control [START_REF] Latash | Motor control strategies revealed in the structure of motor variability[END_REF][START_REF] Jordan | Task goal and grip force dynamics[END_REF]. As previous studies have indicated, variability is not random like noise, but exhibit a degree of order that can be attributed to the operation of an adaptive control system [START_REF] Slifkin | Noise, information transmission, and force variability[END_REF]. Nonlinear analysis derived from nonlinear dynamics and chaos theory, is a valuable approach to understand the underlying aspects of neurophysiological signals [START_REF] Heffernan | Complexity of force output during static exercise in individuals with Down Syndrome[END_REF][START_REF] Richman | Physiological time-series analysis using approximate entropy and sample entropy[END_REF][START_REF] Slifkin | Noise, information transmission, and force variability[END_REF]van Emmerik & van Wegen, 2002). The structure of variability is usually measured by computing for instance the approximate entropy of the force signal [START_REF] Heffernan | Complexity of force output during static exercise in individuals with Down Syndrome[END_REF][START_REF] Slifkin | Noise, information transmission, and force variability[END_REF][START_REF] Sosnoff | Independence between the amount and structure of variability at low force levels[END_REF]. [START_REF] Hong | Magnitude and structure of isometric force variability: Mechanical and neurophysiological influences[END_REF] have recently shown during short duration contractions that compensatory mechanisms are governing the amount and structure of variability between dimensions, i.e., task-related force and tangential forces. To our knowledge, no studies have investigated the amount and structure of force variability in task-related and tangential forces during discrete and continuous force production. Moreover, linear methods have mainly been used to assess variability in genders during, for instance, sustained contraction [START_REF] Hunter | Sex differences in the fatigability of arm muscles depends on absolute force during isometric contractions[END_REF] and only one study has reported unexpected higher entropy values for males than for females [START_REF] Sung | Gender differences in spectral and entropic measures of erector spinae muscle fatigue[END_REF]. This calls for further studies describing the structural changes of force variability in task-related and tangential forces in relation with respect to gender difference during short and continuous force production.

In the present study, we hypothesized gender differences in the magnitude and structure of force variability in task-related and tangential forces. For this purpose, we examined the effect of gender on force variability in 3D during short duration, ramp and endurance contractions. Gender comparison was assessed by means of linear and nonlinear methods during discrete and continuous isometric elbow flexion.

Materials and methods

Participants

Ten males and 10 females participated in the study after having given their informed consent. The participants' anthropometric information is shown in Table 1. All participants were healthy and without any known neurological disorders. The study was approved by the local ethics committee (N-20070004MCH) and conducted in conformity with the Declaration of Helsinki.

Experimental procedure

The participants performed isometric elbow flexion consisting of short duration contractions, ramp contraction, and endurance contraction. The forces were recorded in 3D: 1) Task-related force: Fx: mainly elbow flexion and wrist flexion. 2) Tangential forces: Fy: mainly shoulder flexion, and Fz: mainly external shoulder rotation and radial deviation of the wrist. During the recordings, participants were sitting on a chair and holding the force sensor with the palm towards the ceiling and the elbow flexed at 90° (Fig. 1). The wrist and the shoulder were maintained in neutral position and the arm was in contact with the chest (slight touch). The experimenter controlled the participant position throughout the experiment.

Fig. 1, here

The experiment consisted of:

1. Maximal voluntary contraction (MVC init ) of Fx was recorded three times to determine the participants' maximum elbow flexion force. Each trial lasted 3 s and was separated by a 2 min pause. MVC init of Fx was used as reference contraction to set sub-maximal levels. Verbal encouragement was given during MVC tests.

Participants rested for 2 min after MVC recordings.

2. Short duration contractions consisted of nine contractions ranged from 10% to 90% of MVC init of Fx with a 10% increment in between (Fig. 2). The order of the contractions was randomized to prevent a priori knowledge of the following contraction level. Each contraction lasted 5 s with a 30 s pause in between. The participants were asked to reach the desired contraction level as fast as possible.

Participants rested for 2 min after short duration contractions.

3. Ramp contraction lasted 30 s starting at 5% and reaching 50 %MVC init of Fx (slope of 1.5 %MVC/s; Fig. 2). Participants rested for 2 min after ramp contraction.

Endurance contraction:

The participants maintained a level corresponding to 20 %MVC init of Fx until task failure (Fig. 2). Task failure occurred when the participants were not able to maintain force at 20 ± 2 %MVC of Fx for more than 5 s. Verbal encouragement was also given during endurance test.

5. MVC final of Fx was recorded 30 s after endurance test to assess changes in maximum force with respect to MVC init of Fx.

For the short duration, ramp and endurance contraction, the task-related force Fx was visually fed back to the participants. The pixel/N ratio was 2.4±0.8 pixel/N. For MVC trials, the maximum force was computed over 1 s with 100 ms overlapping. The highest force was then considered as MVC of Fx.

The contributions of tangential forces (Fy and Fz) to the task-related force (Fx) were calculated as the percentage contribution of each tangential force compared to Fx.

The error of performance was calculated as the difference between the exerted force signal and the required force level in percent.

Linear analysis of the force signals was performed to quantify the amount of variability.

Standard deviation (SD) and coefficient of variation (CV) were calculated. SD reflects the amount of the variability, and CV is the relative variability. CV was derived from the absolute value of the mean and SD of the signal.

Nonlinear analysis of the force signals was performed to assess the structure of variability. Time dependent structure of force variability reveals deterministic and stochastic organization of the neurophysiological system and the degree of complexity of a signal is typically associated with the number of system elements and their functional interactions [START_REF] Jordan | Task goal and grip force dynamics[END_REF][START_REF] Heffernan | Complexity of force output during static exercise in individuals with Down Syndrome[END_REF]van Emmerik & van Wegen, 2002).

Sample entropy (SaEn) was computed for this purpose. SaEn expresses the complexity of the recorded signal [START_REF] Kuusela | Nonlinear methods of biosignal analysis in assessing terbutaline-induced heart rate and blood pressure changes[END_REF][START_REF] Richman | Physiological time-series analysis using approximate entropy and sample entropy[END_REF]. SaEn is the negative logarithm of the relationship between the probabilities that two sequences coincide for m+1 and for m points, where larger value indicates more complex structure or lower predictability. The embedding dimension, m, and the tolerance distance, r, were set to m = 2 and r = 0.2× SD of the force channel.

For the short duration contractions, SD, CV, and SaEn were calculated over 3 s epoch (discarding the 1 st and last s) for each contraction level. Similarly for the ramp contraction, linear and nonlinear parameters were calculated over 3 s epochs through the 30 s contraction. Similarly, for the endurance contraction, seven epochs of 3 s from 0 to 100% of contraction time (steps of 16.7%) were used.

Statistical analysis

A one-way analysis of variance (ANOVA) with factor gender and dependent variable endurance time, a two-way ANOVA with factors gender and time (before/after endurance test) and dependent variable MVC level/tangential force contribution, and a three-way ANOVA with factors gender, contraction level/contraction time, and force direction and dependent variables error of performance, SD, CV and SaEn, were performed using SPSS 16.0 (SPSS Inc., Chicago, Illinois, USA). A post-hoc test of Least Significant Difference was used for pair wise comparisons. Mean ± SD is reported. The level of significance was set at p < .05.

Results

Males had higher MVC of Fx than females (F = 70.9, p < .01), respectively 245.6 ± 61.2 vs. 134.6 ± 25.8 N. MVC of Fx decreased from MVC init to MVC final (F = 11.5, p < .01), respectively from 212.5 ± 76.1 to 167.8 ± 63.6 N.

Fig. 3, here

Contribution from tangential forces to the task-related force Fx

For the short duration contractions (Fig. 3a), the two-way ANOVA showed gender differences, males had larger contribution from tangential forces to Fx than females (F = 14.2, p < .01), respectively 19.2 ± 7.9 % vs. 11 ± 5.5 %. Fy contributed significantly more than Fz to Fx (F = 12, p < .01), respectively 18.8 ± 9.2 % vs. 11.3 ± 6.8 %.

For the ramp contraction (Fig. 3b), the two-way ANOVA showed gender differences, males had larger contribution from tangential forces to Fx than females (F = 5.2, p = .02), respectively 30.1 ± 35.1 % vs. 10.2 ± 7.6 %. For the endurance contraction (Fig. 3c), Fy contributed significantly more than Fz to Fx (F = 17, p < .01), respectively 31.2 ± 212 % vs. 10.7 ± 5.2 %.

Fig. 4, here

Short duration contractions

The error of performance increased with increasing contraction level for short duration contractions (Fig. 4a; F = 5.9, p < .01) but did not change with gender (F = 0.1, p = .76).

The three-way ANOVA showed gender differences or tendency towards differences, SD and SaEn were larger for males compared with females while it was the opposite for CV (Fig. 5; respectively F = 93.0, p < .01, F = 5.2, p = .05 and F = 12.1, p < .01). SD increased with increasing contraction level (F = 48.7, p < .01). SaEn also tended to increase and decrease with contraction level (F = 5.2, p = .05). SD was higher for Fx compared with Fy and Fz while it was the opposite for CV and SaEn (respectively, F = 54.5, p < .01, F = 101, p < .01 and F = 25.9, p < .01). Moreover, there was a significant Gender × Contraction Level interaction for SD (F = 10.8, p < .01). SD was higher for males compared with females at 10-20-30-40-50-70-80-90 %MVC of Fx (p < .01). There was a significant Gender × Force Direction interaction for CV (F = 7.5, p < .01). CV was higher for females compared with males in Fy (p < .01). Finally, there was significant Contraction Level × Force Direction interaction for SaEn (F = 1.9, p = .02). SaEn was higher for Fz than Fx at 10-20-30-60-70-80-90 %MVC of Fx (p < .05). SaEn was also higher for Fz than Fy at 10-20 %MVC of Fx (p < .02) and for Fy than Fx at 60-70-80-90 %MVC of Fx (p < .01).

Ramp contraction

The error of performance increased with increasing contraction level during the ramp contraction (Fig. 4b; F = 4.0, p < .01) but did not change with gender (F = 0.6, p = .44).

The three-way ANOVA showed gender differences, SD and SaEn were larger for males compared with females while this pattern of results was the opposite for CV (Fig. 6; respectively, F = 217.4, p < .01, F = 12.6, p < .01, and F = 26.2, p < .01). SD and SaEn increased with increasing contraction level, while CV decreased (respectively, F = 15.9, p < .01, F = 31.2, p < .01, and F = 3.4, p < .01). SD was higher for Fx compared with Fy and Fz while it was the opposite for CV and SaEn (respectively, F = 61.2, p < .01, F = 61.1, p < .01 and F = 136, p < .01). There was a significant Gender × Contraction Level interaction for SD (F = 2.5, p < .01). SD was higher for males compared with females for all contraction levels (p < .01).

There was also a significant Gender × Force Direction interaction for CV (F = 6.5, p < .01). CV was higher for females compared with males in Fy (p < .01). There was a significant Contraction Level × Force Direction interaction for SaEn (F = 2.0, p = .01).

SaEn was higher for Fy than Fx at 5-15-20-25-30-35-40-45-50 %MVC of Fx (p < .05).

SaEn was higher for Fz than Fx at all contraction levels (p < .01) and than Fy at 5-10-15-20 %MVC of Fx (p < .01).

Fig. 6, here

Endurance contraction

The error of performance did not change during the sustained contraction (Fig. 4c; F = 0.9, p = .50) and nor with gender (F = 0.01, p = .91). Females had longer endurance duration than males, respectively 682.8 vs. 344.8 s (F = 7.5, p = .01). The three-way ANOVA showed gender differences, SD and SaEn were higher for males than females while it was the opposite for CV (Fig. 7; respectively F = 186.2, p < .01, F = 5.0, p = .02 and F = 4.5, p = .03). Both SD and CV increased with contraction time (respectively, F = 34.1, p < .01 and F = 8.5, p < .01). SD was higher for Fx compared with Fy and Fz while it was the opposite for CV and SaEn (respectively, F = 30.0, p < .01, F = 141, p < .01 and F = 23.4, p < .01). Moreover, there were significant Gender × Contraction Time, Gender × Force Direction and Contraction Time × Force Direction interactions for SD (respectively, F = 4.1, p < .01, F = 3.3, p = .04, and F = 2.5, p < .01). SD was higher for males compared with females throughout the contraction (p < .01). SD was also higher for males compared with females in all force directions (p < .01). SD was higher in Fx and Fy compared to Fz at 50-66.7-88.3-100 % of contraction time. There was also a significant Contraction Time × Force Direction interaction for CV (F = 2.2, p = .01). CV was higher for Fy and Fz compared with Fx throughout the contraction time (p < .01) and CV was higher for Fz compared with Fy at 50-66.7-83.3-100 % contraction time (p < .01).

Fig. 7, here

Discussion

The primary goal of this study was to investigate the effect of gender differences in variability of task-related and tangential forces by means of linear (amount of variability) and nonlinear (structure of variability) analysis during voluntary short duration, ramp and endurance isometric elbow flexions. The findings revealed for the first time that gender played a role in force variability during short, ramp and sustained contractions. Females were characterized by lower amount (SD) and structural complexity (SaEn) than males.

Further, the amount of variability increased with contraction level while the structure of variability changed according to an inverted U-shape function in the task-related force and tangential force Fy during discrete contractions. Finally, the amount of variability also increased with contraction time in the task-related force and tangential force Fy.

Effect of contraction level and gender on force variability

For short duration and contractions, the observed changes in the amount and structure of variability are in line with previous results reporting an exponential increase in SD and a decrease in CV in the direction of force exertion [START_REF] Hong | Magnitude and structure of isometric force variability: Mechanical and neurophysiological influences[END_REF][START_REF] Slifkin | Noise, information transmission, and force variability[END_REF][START_REF] Tracy | The amplitude of force variability is correlated in the knee extensor and elbow flexor muscles[END_REF]. Similar to that, SD increased for both taskrelated and tangential forces during short and continuous contractions. CV remained low most likely due to failure in reaching the required level for the high sub-maximal contractions as depicted by the increase in error of performance. Moreover, CV decreased slightly during ramp contraction as expected due to the exponential increase in SD with linearly increasing forces [START_REF] Hong | Magnitude and structure of isometric force variability: Mechanical and neurophysiological influences[END_REF][START_REF] Sosnoff | Independence between the amount and structure of variability at low force levels[END_REF]. SD was larger for males than for females in the direction of force exertion but also in the tangential directions even though there were no differences in the error of performance. As expected, the results were opposite for CV. This confirmed that the variability in discrete force production is non proportional to force level [START_REF] Carlton | Force variability and characteristics of force production[END_REF]. Moreover, the contributions of tangential forces to the task-related force were larger for males than for females during short duration and ramp contractions due to higher absolute force in males. This can in turn have influenced the magnitude of force variability [START_REF] Hong | Visual information gain and the regulation of constant force[END_REF][START_REF] Vaillancourt | Time-dependent structure in the discharge rate of human motor units[END_REF] as there were gender differences in the pixel/N ratio. Furthermore, the larger amount of variability (SD) found in males compared with females could also indicate that males had an elevated activity in the biceps brachii muscle compared with females due to higher force level [START_REF] Hunter | Sex differences in the fatigability of arm muscles depends on absolute force during isometric contractions[END_REF] and that muscle activation pattern could be different among genders [START_REF] Ge | Gender-specific differences in electromyographic changes and perceived pain induced by experimental muscle pain during sustained contractions of the upper trapezius muscle[END_REF]Yoon, Delap, Griffith, & Hunter, 2007).

With respect to the changes in the structure of variability, our results in the direction of force exertion are also in line with [START_REF] Slifkin | Noise, information transmission, and force variability[END_REF] and [START_REF] Hong | Magnitude and structure of isometric force variability: Mechanical and neurophysiological influences[END_REF]. The sample entropy increased up to approximately 50 %MVC of Fx during short duration contractions and then decreased, following an inverted U-shape [START_REF] Hong | Magnitude and structure of isometric force variability: Mechanical and neurophysiological influences[END_REF][START_REF] Slifkin | Noise, information transmission, and force variability[END_REF]. Compensatory synergistic mechanisms are likely to explain the similar changes in the task-related force and tangential force (Fy) seen during both discrete and continuous force production in line with a recent study [START_REF] Hong | Magnitude and structure of isometric force variability: Mechanical and neurophysiological influences[END_REF]. The sample entropy was higher for tangential forces than for task-related force. This confirmed recent results showing that the changes in approximate entropy values differ between task-related and tangential forces [START_REF] Hong | Magnitude and structure of isometric force variability: Mechanical and neurophysiological influences[END_REF]. Further, the present study emphasizes that the amount and structure of force variability during discrete and continuous contractions could be governed by separate control processes [START_REF] Sosnoff | Independence between the amount and structure of variability at low force levels[END_REF].

Similar to the magnitude of variability, the complexity of the task-related and tangential forces were also higher for males than for females arguing for potential gender dependent force control strategies. This would imply that the forces generated by males arise from a higher number of attractors or neural oscillators than females [START_REF] Heffernan | Complexity of force output during static exercise in individuals with Down Syndrome[END_REF][START_REF] Lipsitz | Dynamics of stability: The physiologic basis of functional health and frailty[END_REF][START_REF] Slifkin | Noise, information transmission, and force variability[END_REF][START_REF] Sosnoff | Aging and rhythmical force output: Loss of adaptive control of multiple neural oscillators[END_REF]van Emmerik & van Wegen, 2002). Finally, the observed changes in the amount and structure of variability occurring in the task-related and tangential forces can be explained by a lack of control of the participants' dominant arm position and/or compensatory mechanisms like co-contraction and changes in agonist/antagonist relationship aiming at maintaining the same force output [START_REF] Ervilha | The effect of muscle pain on elbow flexion and coactivation tasks[END_REF][START_REF] Hong | Magnitude and structure of isometric force variability: Mechanical and neurophysiological influences[END_REF][START_REF] Reeves | Trunk antagonist coactivation is associated with impaired neuromuscular performance[END_REF][START_REF] Rudroff | Electromyographic measures of muscle activation and changes in muscle architecture of human elbow flexors during fatiguing contractions[END_REF]. More studies assessing force variability in 3D are warranted to investigate neuromotor function.

Effect of endurance time and gender on force variability

The present study confirmed the presence of gender differences in endurance time (Hunter et al., 2004b;[START_REF] Maughan | Endurance capacity of untrained males and females in isometric and dynamic muscular contractions[END_REF][START_REF] Sato | Sex differences in static muscular endurance[END_REF] even though similar endurance time have also been reported in strength-matched groups [START_REF] Hunter | Sex differences in the fatigability of arm muscles depends on absolute force during isometric contractions[END_REF]Hunter, Critchlow, Shin, & Enoka, 2004a). The amount of force variability increased in taskrelated and tangential forces with contraction time while the level in error of performance did not change. The tangential force Fy contributed more than Fz to the task-related force showing that the exerted force was not kept purely mono-directional during the endurance test. Similar to what we observed during discrete and continuous contractions, the amount (SD) and structure (SaEn) were larger for males than for females during fatiguing isometric contraction while opposite results were obtained for CV. The results concerning gender effects are corroborated by recent studies from Yoon et al. (2007) and [START_REF] Sung | Gender differences in spectral and entropic measures of erector spinae muscle fatigue[END_REF].

Muscle fatigue is found to alter biomechanical movement patterns [START_REF] Selen | Fatigue-induced changes of impedance and performance in target tracking[END_REF]. The present gender-dependency in the amount and structure of force variability during endurance contraction could be due to the discrepancies in muscle activation pattern [START_REF] Ge | Gender-specific differences in electromyographic changes and perceived pain induced by experimental muscle pain during sustained contractions of the upper trapezius muscle[END_REF]Hunter et al., 2004a,b;Yoon et al., 2007). The level of muscular fatigue assessed by the decrease in MVC of Fx, immediately following endurance test was similar for males and females in line with Yoon et al. (2007). During sustained contraction, the CNS compensate for the decrease in the force generated by individual motor units by additional recruitment of motor units, changes in motor unit discharge rate and motor unit substitution [START_REF] Gandevia | Spinal and supraspinal factors in human muscle fatigue[END_REF]. These mechanisms are likely to account for the difference in size and structure of force variability among genders during an endurance test. Similarly to our findings during short duration and ramp contractions, the control mechanisms influencing the amount and structure of force variability could be gender dependent.

Moreover, the lower complexity or higher predictability found in females compared with males corresponding to a higher degree of regularity may not be favourable. Indeed, it may not allow appropriate adaptation to changes in sensory afferent feedback and may increase the risk for muscle overload and damage in females [START_REF] Ge | Gender-specific differences in electromyographic changes and perceived pain induced by experimental muscle pain during sustained contractions of the upper trapezius muscle[END_REF][START_REF] Lipsitz | Dynamics of stability: The physiologic basis of functional health and frailty[END_REF][START_REF] Madeleine | Changes in the degree of motor variability associated with experimental and chronic neck-shoulder pain during a standardised repetitive arm movement[END_REF][START_REF] Slifkin | Noise, information transmission, and force variability[END_REF]. While among males, the CNS may be better to take benefit of the redundancy of the motor system [START_REF] Latash | What are normal movements in atypical populations?[END_REF].

In summary, the analysis variability of task-related and tangential forces showed that the changes in the amount and structure of force variability differed with increasing contraction level and increased similarly with contraction time. This could be due to separate control processes and compensatory mechanisms influencing variability in taskrelated and tangential forces. Furthermore, the amount and structure of force variability was higher in males compared with females arguing for possible gender-dependent force control mechanisms.

Fig

  Fig. 2, here

Fig

  Fig. 5, here

  Fig. 1: Experimental setup depicts a participant performing an isometric elbow flexion

Fig. 2 :

 2 Fig.2: Examples of 3D force traces for one male and one female. Task-related forces (Fx;

Fig. 3 :

 3 Fig. 3: Mean + SE force (N) for task-related force (Fx) and tangential forces (Fy and Fz)

Fig. 4 :

 4 Fig. 4: Mean + SE error of performance (%) during a) short duration contractions, b) ramp

Fig. 5 :

 5 Fig. 5: Mean + SE standard deviation (SD, N), coefficient of variation (CV, %) and sample

Fig. 6 :

 6 Fig. 6: Mean + SE standard deviation (SD, N), coefficient of variation (CV, %) and sample

Fig. 7 :

 7 Fig. 7: Mean + SE standard deviation (SD, N), coefficient of variation (CV, %) and sample

Table 1 , here

 1

Table 1 :

 1 Participants information (mean ± SD).

		Females	Males
	Age (yrs)	24.7 ± 3.9	25.8 ± 2.5
	Weight (kg)	65.8 ± 9.3	80.2 ± 7.0
	Height (cm)	170 ± 7.7	188.9 ± 7.2
	Body Mass Index (kg/m 2 )	22.6 ± 2.4	22.5 ± 1.2

Acknowledgements

The authors want to thank Afshin Samani for his contribution to data collection. This work was financially supported by the Finale project (grant from Arbejdsmiljøforskningsfond), Det Obelske Familiefond and the Danish National Research Foundation.