Journal of Biomechanics 48 (2015) 621–626

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Increase in joint stability at the expense of energy efficiency correlates with force variability during a fatiguing task Joshua G.A. Cashaback a,n, Tyler Cluff b a b

Department of Kinesiology, McMaster University, Hamilton, Ont., Canada L8S 2K1 McMaster Integrative Neuroscience Discovery & Study (MiNDS), McMaster University, Hamilton, Ont., Canada L8S 2K1

art ic l e i nf o

a b s t r a c t

Article history: Accepted 26 December 2014

Empirical evidence suggests that our nervous system considers many objectives when performing various tasks. With the progression of fatigue, researchers have noted increase in both joint moment variability and muscular cocontraction during isometric force production tasks. Muscular cocontraction increases joint stability, but is metabolically costly. Thus, our nervous system must select a compromise between joint stability and energy efficiency. Interestingly, the continuous increase in cocontraction with fatigue suggests there may be a shift in the relative weighting of these objectives. Here we test the notion of dynamic objective weightings. Using multi-objective optimization, we found a shift in objective weighting that favoured joint stability at the expense of energy efficiency during fatigue. This shift was highly correlated with muscular cocontraction (R2 ¼ 0.78, po0.001) and elbow moment variability in the time (R2 ¼ 0.56, p o0.01) and frequency (R2 ¼0.57, po0.01) domains. By considering a dynamic objective weighting we obtained strong correlations with predicted and collected muscle activity (R2 ¼0.94, po 0.001). & 2015 Elsevier Ltd. All rights reserved.

Keywords: Multi-objective optimization Stiffness Energy Fatigue Muscle

1. Introduction Despite the relative ease with which we interact with our environment, the nervous system is faced with the difficult task of choosing muscle activity patterns that allow for the performance of everyday tasks. Since our joints are redundant, meaning there are more muscles than movement degrees-of-freedom, there is an infinite number of muscle activity patterns that balance joint loads. This redundancy provides the nervous system with the flexibility to consider several task objectives. There is evidence that the nervous system considers many objectives when selecting muscle activity patterns, including energy efficiency (Anderson and Pandy, 2001), joint stability (Stokes and Gardner-Morse, 2001; Brown and Potvin, 2005), joint loading (Seireg and Arvikar, 1973; Yettram and Jackman, 1982), joint discomfort (Marler et al., 2009), and muscle stress (Crowninshield and Brand, 1981; An et al., 1984; Hughes et al., 1995). These objectives often vary with properties of the task or environment (Milner and Cloutier, 1993; Burdet et al., 2001; Selen et al., 2006), and compete with one another for some motor tasks (Stokes and Gardner-Morse, 2001). The key challenge is to determine what n Correspondence to: Western University, 1151 Richmond Street, London, Ont., Canada N6A 3K7. Tel.: þ 1 519 661 2111x86185; fax: þ 1 519 661 3613. E-mail address: [email protected] (J.G.A. Cashaback).

http://dx.doi.org/10.1016/j.jbiomech.2014.12.053 0021-9290/& 2015 Elsevier Ltd. All rights reserved.

objectives are important for a given task, and how their relative weighting affects muscle activity and force production (Rosenbaum, 1991; Stokes and Gardner-Morse, 2001; Todorov and Jordan, 2002; Todorov, 2004). During fatiguing isometric contractions, many researchers have noted increases in force variability (Reeves et al., 2008; Singh et al., 2010) and muscle cocontraction (Psek and Cafarelli, 1993; O'Brien and Potvin, 1996; Potvin and O'Brien, 1998; Reeves et al., 2008). There is evidence that cocontraction may help stabilize our joints during load-bearing tasks (Lee et al., 2006; Potvin and O'Brien, 1998; Reeves et al., 2008), but is energetically costly and increases the rate of fatigue (Hogan, 1984; Cholewicki and McGill, 1996). Theoretically, if the nervous system considered only joint stability during isometric force production there would be maximal cocontraction. Conversely, if the nervous system considered only energy efficiency there would be minimal cocontraction. However, there seems to be a tradeoff between joint stability and energy efficiency because the amount of observed cocontraction lies somewhere between these extremes. Interestingly, the increase in cocontraction noted during fatigue suggests that the balance may shift continuously from reducing energy consumption to increasing stability. It is still unclear how these conflicting objectives change during muscular fatigue. Here, we investigate whether the nervous system shifts the balance between energy efficiency and joint stability during fatiguing isometric

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contractions. We addressed this question by formulating a cost function with two competing objectives–one that promotes joint stability (maximize stiffness) and another that promotes energy efficiency (minimize muscle stress). Based on evidence that cocontraction increases with fatigue (Psek and Cafarelli, 1993; O'Brien and Potvin, 1996; Potvin and O'Brien, 1998; Granata et al., 2004; Reeves et al., 2008), we hypothesized that the nervous system would increasingly favor joint stability (increase in cocontraction) at the expense of energy efficiency. Further, given the reported link between muscular cocontraction and force variability (Reeves et al., 2008), we hypothesized that the objective weighting would increase (indicating an increase in joint stability) with an increase in cocontraction and force variability in the time domain. We also explored the relationship between the weighting objective and force variability in the frequency domain.

2. Methods 2.1. Participants Twelve healthy males participated in the experiment (age 24.87 2.0 years, height 180.5 7 5.7 cm, and weight 79.7 7 10.1 kg). Participants were briefed on experimental protocol and provided written consent to procedures approved by the McMaster University Research Ethics Board.

the first intersection of force output and the 30% maximal elbow flexion moment criterion, or when participants stopped the exertion due to discomfort. We removed 2 s of data from the onset and termination of each trial to avoid altered force and sEMG recordings while subjects attempted to attain the force target (target overshooting and undershooting). Average trial durations were 152.4 s (7 14.8), 69.4 s ( 7 4.1), and 56.3 s ( 74.8) for the 40%, 70%, and 100% moment conditions, respectively. 2.4.1. Surface electromyography and force filtering Both whitening and extreme highpass filtering ( Z 140 Hz highpass cutoff) of sEMG removes low frequency signal content (Potvin and Brown, 2004) associated with fatigue (Bigland-Ritchie, 1981; Petrofsky et al., 1982; Kuorinka, 1988) and electrocardiogram artifact (Redfern et al., 1993; Drake and Callaghan, 2006). Compared to traditional filtering (e.g., 10–20 Hz highpass cutoff), whitening and extreme highpass filtering improve muscle sEMG-to-force estimates during rested (Potvin and Brown, 2004; Staudenmann et al., 2007; Riley et al., 2008) and fatiguing contractions (Cort et al., 2006; Potvin et al., 2010; La delfa et al., 2014). Importantly, Cort et al. (2006) showed that the ratio between whitened sEMG amplitude and elbow moment was relatively constant during fatiguing isometric elbow flexor contractions. We whitened the raw sEMG signals with a 5th order, autoregressive model to obtain better estimates of muscle forces (Clancy and Hogan, 1994; Potvin and Brown, 2004). Each whitened sEMG signal was rectified, low-pass filtered (Butterworth, 1st order, single-pass, 2 Hz cutoff), and normalized to peak activity from the maximum voluntary exertion trials. These processed biceps and tricep brachii sEMG signals were used to represent overall elbow flexor (sEMGflex) and extensor (sEMGext) activity, respectively. Force outputs were low-pass filtered to remove extraneous noise (Butterworth, 1st order, dual-pass, 30 Hz effective cutoff). Time series for each trial was then divided into ten windows of equal length (W1, W2, …, W10).

2.2. Instrumentation and data acquisition The forces generated by participants against a wrist cuff were recorded with a force transducer (MLP-300-C0, A-Tech Instruments, Scarborough, Canada) and amplified (S7DC, RPD Electronics). Electrode sites were first cleansed with alcohol. Surface electromyography (sEMG) was then recorded from the biceps brachii, brachioradialis, and triceps brachii muscles with bipolar electrode pairs (diameter¼ 2.5 cm; Medi-Trace 130, Kendall, Mansfield, MA). A ground electrode was fixed over the lateral epicondyle of the humerus. Only the biceps and triceps brachii were considered in the analysis because they are the primary elbow moment generators (Holzbaur et al., 2005). Some of the data were reported in another paper focused on how fatigue and contraction intensity influence the complexity of sEMG (Cashaback et al., 2013). Here, we describe methodology relevant to the current analysis. Force and sEMG signals were collected at 1000 Hz (LabVIEW v8.2, National Instruments, Austin, TX), converted to a digital signal (12-bit A/D converter; National Instruments, Austin, TX), amplified (gain¼ 500–1000, Zin ¼ 10 GΩ, CMRR¼115 dB at 60 Hz; Octopus, Bortec Biomedical Ltd., AB, Canada), and stored to disk for further processing. The target force and normalized force generated by the participant were displayed in real-time on an LCD monitor (IBM 6655-HG0). 2.3. Experimental protocol Participants sat with their upper limb in the horizontal plane and palm facing their chest. This was accomplished by maintaining 901 of shoulder flexion, shoulder internal rotation, and elbow flexion. We strapped the participants' wrist to a padded cuff, which was attached to a force transducer that measured the elbow flexor moment. After the participants were properly positioned in the apparatus, they performed two maximal isometric elbow flexion and extension exertions. Each contraction lasted  6 s (2 s ramp up, 3 s hold, 1 s ramp down) and was followed by 10 s of rest. We then calculated the maximal sEMG and elbow flexion moment by smoothing subjects' muscle activity and force-time profiles with a 1 s movingaverage filter (dual-pass, 0.999 s overlap). Individual subjects' peak sEMG and force values were determined from these 3 maximal exertion trials, and used to normalize each participant's force output during the fatiguing contractions. Participants rested for 5 min after the maximal voluntary exertion trials. For each of their visits, separated by at least three days, participants performed a series of exhausting isometric elbow flexion contraction at 40%, 70%, or 100% of their maximal elbow flexor moment. We instructed participants to match their normalized elbow flexion moment with the target moment (either 40%, 70%, or 100% of their recorded maximum elbow joint moment) displayed on the computer screen. Trials were terminated when participants were unable to maintain 30% of their maximal elbow flexor moment or were unable to continue due to discomfort. Separate sessions were used for different contraction intensities. We controlled for potential ordering effects by counterbalancing the order of contraction intensities across participants. 2.4. Data analysis Trial onset was defined as the first intersection of force output and target force (MATLAB r2009b; The Mathworks, Natick, MA). Trial termination was defined as

2.4.2. Co-contraction index We used the following cocontraction index (CI) to quantify the relative activity of the elbow flexors and extensors for each time window (Kellis et al., 2003) R t2 t 1 sEMGext ðtÞdt CI ¼ R t2 100; ð1Þ t 1 ½sEMGf lex þ sEMGext ðtÞdt where sEMGext and sEMGflex represent the processed and normalized activity of the elbow extensors and flexors respectively, and t1 and t2 are the start and end time of each time window respectively. 2.4.3. Force coefficient of variation and mean power frequency The force coefficient of variation (FCV) was calculated as the average force standard deviation divided by the average force, multiplied by 100. The mean power frequency of force (FMPF) was calculated as the centroid of the force power spectrum. We calculated FCV and FMPF for each time window.

2.4.4. Lumped musculotendon force, stiffness, and stress Using muscle architecture and coordinates from OpenSim (Musculographics Inc.; Holzbaur et al., 2005), we created a simplified lumped flexor and extensor musculoskeletal model of the elbow joint. The maximum force generating capacity (fmaxj) of some individual musculotendon unit (i) is f maxi ¼ CSAi  θ i  T i  AðxÞi þ PðxÞi ;

ð2Þ

where CSAi is an individual musculotendon's cross-sectional area, θi is pennation angle, Ti ¼ 140 N/cm2 is the muscle tension, and A(x)i, and P(x)i are the active and passive force– length corrections based on normalized muscle length (x). All these parameters were taken from Holzbaur et al. (2005). The maximum force generating capacity of the lumped flexor and extensor musculotendon (fmaxj) was calculated with f maxj ¼

n X

f maxi ;

ð3Þ

i¼1

where j corresponds to the lumped flexor or extensor musculotendon group, and n with the number of musculotendon units in that group. For simplicity, we modeled lumped musculotendon forces (fj) to change proportionally with the normalized activity of its corresponding muscles, such that f j ¼ aj  f maxj :

ð4Þ

We used the following weighted average to calculate the lumped flexor and extensor moment arms rj ¼

n X i¼1

ri 

f maxi ; f maxj

ð5Þ

where rj is the lumped flexor or extensor moment arm and ri are the individual muscle moment arms. By weighting a muscle's moment arm according to its relative force contribution in a lumped muscle group, we produced a more accurate lumped muscle moment arm that favors muscles by their ability to generate an elbow moment.

J.G.A. Cashaback, T. Cluff / Journal of Biomechanics 48 (2015) 621–626 Maximal individual muscle contributions to elbow rotational stiffness (Kmaxαi) was estimated with the following equation (Potvin and Brown, 2005; Pfeifer et al., 2012; Cashaback et al., 2013b):   dri ð6Þ þ kmaxi  r 2i ; Kmaxai ¼ f maxi da

2.4.5. Multi-objective optimization We considered two competing objectives for our optimization analysis: maximizing musculotendon stiffness and minimizing musculotendon stress. However, it is necessary to frame the optimization such that both objectives are maximized or minimized. To maximize the cost function while finding an equivalent solution that minimizes muscle stress, we found the maximum of the negative muscle stress. This concept is best demonstrated with a parabola. The minimum of a function f(x)¼x2 is equivalent to finding the maximum of its negative (i.e., f(x)¼–x2), where the solution for both is x¼0. We used the following cost function to estimate the lumped flexor and extensor activations in each time window

where α represents a rotational displacement about the flexion-extension degreeof-freedom and kmaxi is the maximal inline musculotendon stiffness. We approximated kmaxi by kmaxi ¼ q 

f maxi ; Li

623

ð7Þ

2

12

0

12 3

0

where q¼ 10 (Crisco III and Panjabi, 1991) is a dimensionless proportionality constant relating musculotendon force and length (Li) to inline musculotendon stiffness (Bergmark, 1989). Thus, the maximal individual musculotendon contribution to elbow rotational stiffness is   dri q  r 2i Kmaxai ¼ f maxi þ : ð8Þ da Li

n B n B C C 7 6 X X K αj σj C C 7 6 B B Max6w C  ð1  wÞ C 7; B n B n A A 5 4 j¼1@ P @P j ¼ 1 Kmaxαj σ maxj

Maximal and instantaneous rotational stiffness of each lumped musculotendon (Kmaxαj) can be calculated by

i¼j

Kmaxαj ¼

n X i¼1

j¼1

n X

i¼1

ð11Þ

CSAi

and

σj ¼ P n

fj

i¼1

;

ð13cÞ

where M is the average participant generated elbow flexion moment and w is the weighting coefficient that determines the relative influence of each objective. For example, a w of 1 or 0 favours the musculotendon stiffness or stress objective, respectively, leading to maximal or minimal co-contraction (Fig. 1). However, as it has been empirically observed (Reeves et al., 2008), the amount of cocontraction lies between these theoretical extremes. Thus, the nervous system is likely concerned with finding a balance between joint stability and energy efficiency that maintains an acceptable level of force variability while avoiding fatigue. To quantify that balance, we varied w from 0 to 1, in increments of 0.001, to find the 1001 different solutions of lumped flexor and extensor activities that match M. From these solutions, we found the w that produced the lowest root-mean-square error between the estimated and sEMG muscle activities. Numerical optimizations were performed in Mathematica 7.0 (2008, Wolfram Research Inc.).

ð10Þ

f maxj

ð13bÞ

0r aj r 1;

respectively, where the latter assumes a linear relationship between joint rotational stiffness and muscle activation (Brown and Potvin, 2007; Cashaback and Potvin, 2012; Cashaback et al., 2013a). Maximal and instantaneous muscular stress (σj) of a lumped musculotendon group was calculated as

σ maxj ¼ P n

f j  rj ¼ M

and

and K aj ¼ aj  Kmaxaj ;

j¼1

with the constraints

ð9Þ

Kmaxαi

ð13aÞ

ð12Þ

2.5. Statistical analysis

CSAi

We performed a 3 (moment)  10 (window) repeated-measures ANOVA with the objective weighting, w, as the dependent measure. Greenhouse-Geisser

respectively (Crowninshield and Brand, 1981; An et al., 1984; Stokes and GardnerMorse, 2001).

0.0 0.5 1.0

Cost Function Output (arbitrary units)

0.6

0.35

0.1

-0.25

-0.4 0.0

0.25

0.5

0.75

1.0

Extensor Activity (%) Fig. 1. The upper, middle, and lower blue surfaces show the cost function output (vertical axis) with various amounts of elbow flexor (depth axis) and extensor (horizontal axis) activations with the weighting (w) set to 0.2, 0.5, and 0.8, respectively. The orange plane is the moment constraint (40% of maximum shown) that the muscle activation solutions must lie along. With an increase in w, representing an increased emphasis of the muscular stiffness objective, it can be seen that the maximum of the cost function shifts from zero (black circle) to full (black square) extensor activity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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corrections were made to avoid sphericity violations and Tukey's HSD was used for mean comparisons. Pearson's product–moment correlation coefficient (R) and the coefficient of determination (R2) were found between w and each of the following: CI, FCV, and FMPF. We then used linear regression, which was forced to have a y-intercept of zero, to find the R and R2 between the estimated and processed sEMG muscle activities. All statistical significance was set to p ¼0.05.

3. Results The objective weighting, w, for each combination of moment (40%, 70%, and 100%) and time window (W1, W2, …, W10) are shown in Fig. 2. As hypothesized, we found that the objective weighting significantly increased with fatigue. From the ANOVA we found a significant interaction between moment and window (F(2.8, 30.4) ¼3.0, p ¼0.049), as well as significant main effects of window (F(1.6, 17.4) ¼6.1, p¼ 0.014) and moment (F(1.9, 20.9) ¼ 6.8, p ¼0.006). For the 100% moment condition, we found that w was significantly greater in W8, W9, and W10 compared to W1. At 40% and 70% moments, we found that w was greater in W9 and W10, but these changes did not reach statistical significance. For the main effect of window, we found that w started to increase at W7, but was only significantly different from W1 at W10. For the main effect of moment, 70% and 100% were significantly greater than 40% moment. As hypothesized, we found that w significantly increased with cocontraction (Fig. 4; R¼ 0.88, R2 ¼ 0.78, po0.001). As expected, we found that w was positively correlated with force variability in the time domain (Fig. 5; R¼0.75, R2 ¼0.56, po0.01). We also found that w was negatively correlated with force variability in the frequency domain (Fig. 6; R¼  0.75, R2 ¼ 0.57, po0.01). A very strong correlation also existed between estimated (aj) and collected sEMG muscle activations (Fig. 6; R¼ 0.97, R2 ¼0.94, po0.001).

4. Discussion Using a fatiguing task, we found that the nervous system shifts the relative influence of its objectives. Specifically, we found the objective weighting shifted to favor joint stability at the expense of energy efficiency when participants were highly fatigued. Importantly, the objective weighting was strongly correlated with the level of muscle cocontraction, as well as time and frequency domain measures of force variability. Further, estimated muscle activations were highly correlated with sEMG recorded from human subjects.

Muscular cocontraction has been observed at several major joints (Granata et al., 2005; Cashaback and Potvin, 2012; Brookham and Dickerson, 2013), and has been shown to increase with contraction intensity (Yang and Winter, 1983; Hebert et al., 1991; Clancy and Hogan, 1997; Reeves et al., 2008) and fatigue (Psek and Cafarelli, 1993; O'Brien and Potvin, 1996; Potvin and O'Brien, 1998; Reeves et al., 2008). Our results agree well with these findings. In the first time window (W1), when muscles were the least fatigued, we observed an increase in cocontraction with contraction intensity. We also found that the CI increased with each progressive window for the 70% and 100% moment conditions, but stayed relatively constant for the 40% moment condition. Despite the constant CI during the 40% moment condition, we still found slight increases in biceps and triceps brachii sEMG. This increase in cocontraction caused a modest increase in w that did not reach statistical significance (see W10 in Fig. 2). Regardless of whether changes in CI were linked to contraction intensity or fatigue, there was a strong relationship between CI and an increase in the objective weighting, w (Fig. 3). We believe increases in w and muscular cocontraction reflect a shift in muscle activity patterns that prioritizes joint stability at the expense of energy efficiency. Reeves et al. (2008) demonstrated that increases in force variability in the time domain are associated with greater muscle cocontraction and joint stiffness. The authors suggested that the nervous system may increase cocontraction to stabilize the joint and limit kinematic displacements caused by force variability. Increases in muscular cocontraction and stiffness with force variability spurred us to examine the relationship between w and force variability. Similar to Reeves et al. (2008) and Singh et al. (2010), we found that force variability measures in the time domain (FCV) increased with fatigue for all contraction intensities. Furthermore, we found that greater FCV corresponded with increased cocontraction intensity for 8 of the 10 windows. Both force variability (time domain) and cocontraction (discussed above) generally increased with fatigue and contraction intensity, which may explain the strong positive relationship between FCV and w. This relationship provides further evidence that the nervous system may modulate joint stiffness in response to force variability. In addition to examining force variability in the time domain, we examined the mean frequency content of force produced during fatigue (FMPF). We found that FMPF decreased with fatigue and contraction intensity. Singh et al. (2010) also noted a decrease

0.3

0.3

0.29

70% Moment

0.29

Weighting (unitless)

Weighting (unitless)

100% Moment

40% Moment 0.28

0.27

0.28

0.27

0.26

0.26

0.25 5

7.5

10

12.5

15

17.5

Cocontraction Index (%) 0.25 W1

W2

W3

W4

W5

W6

W7

W8

W9

W10

Window Fig. 2. Average weighting (w) for each normalized moment condition (40%, 70%, and 100%) and window (W1, W2, …, W10). Standard error bars are shown (n¼ 12).

Fig. 3. Relationship between mean weighting (w) and the cocontraction index (CI). The orange circles are the ensemble-average across participants (n ¼12) and the blue line represents the least-squares line of best fit. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

0.3

1

0.29

0.8

Predicted Muscle Activation

Weighting (unitless)

J.G.A. Cashaback, T. Cluff / Journal of Biomechanics 48 (2015) 621–626

0.28

0.27

0.26

625

0.6

0.4

0.2

0

0.25 1

2.5

4

5.5

7

8.5

10

0

0.2

Force Coefficient of Variation (%)

0.4

0.6

0.8

1

Collected Muscle Activation

Fig. 4. Relationship between mean weighting (w) and the coefficient of variation of force (FCV). The orange circles are the ensemble-average across participants (n¼ 12) and the blue line represents the least-squares line of best fit. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 6. Relationship between the predicted (aj) and collected sEMG activity. The orange circles are the ensemble-average across participants (n¼ 12) and the blue line represents the least-squares line of best fit. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

0.3

Weighting (unitless)

0.29

0.28

0.27

0.26

0.25 2.5

3

3.5

4

4.5

5

5.5

6

Force Mean Power Frequency (Hz) Fig. 5. Relationship between mean weighting (w) and the mean power frequency of force (FMPF). The orange circles are the ensemble-average across participants (n¼ 12) and the blue line represents the least-squares line of best fit. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

in FMPF with contraction intensity, but found that FMPF increased with fatigue. Differences between our studies include the examined joint (elbow vs. knee) and tested contraction intensities (40%, 70%, and 100% vs. 15% and 20%). There are some advantages of using force variability to predict muscle activations. First, despite muscular cocontraction being a better predictor of w, force variability may be the mechanism that elicits a change in objective weighting during fatigue (Reeves et al., 2008). Second, force data is comparatively easier to collect than sEMG, making it an attractive variable to measure in field studies. For the elbow, we found that both time and frequency domain measures of force variability were very good predictors of muscular cocontraction and w. We used two competing objectives, lumped muscle groups, and a single joint to predict muscle activation levels. In future investigations, it would be beneficial to develop a comprehensive musculotendon model that includes multiple joints, as well as both mono and bi-articular muscles. Numerical musculoskeletal models and accounting for interaction stiffnesses would improve

musculotendon stiffness estimates (Cashaback et al., 2013b), but were not feasible in our iterative multi-objective optimization due to their intensive computation requirements. Future work may benefit from examining individual characteristics, such as fatigue tolerance, and their influence on objective weightings. As stated above, there are many objectives that correlate with muscle activation. To robustly predict muscle activations, future work should examine different permutations of these objectives while considering that the objective weightings may be dynamic. Another interesting concept that should be further explored is the potential hierarchical structure of objectives (Bernstein, 1967; Pierrynowski, 1982; Todorov, 2004; Li et al., 2004). Improving anatomical fidelity in musculoskeletal models and choosing the correct objectives, including their weightings and hierarchal structure, will improve our understanding of how the nervous system controls movement. Using empirical data, we found that the multi-objective weighting shifted to increase joint stability at the expense of energy efficiency. This shift was significantly correlated with cocontraction and force variability in the time and frequency domains. Multi-objective optimization is becoming more prominent in biomechanics and motor control research. It has been used to predict muscle activity and force patterns (Stokes and Gardner-Morse, 2001; Todorov, 2002), joint loading (Stokes and Gardner-Morse, 2001), posture (Yang et al., 2006; Marler et al., 2009; Xiang et al., 2010), ground reaction forces (Xiang et al., 2010), and hand motion patterns during upper limb reaching movements (Todorov, 2005). Selecting the correct weighting in a multi-objective optimization is essential for accurate predictions. We suggest that it is also important to consider that these weighting may be dynamic and change over time.

Contributions T.C. and J.G.A.C contributed equally in all aspects of this manuscript.

Conflict of interest The authors report no conflict of interest.

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