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Open Access

Peer-reviewed

Research Article

A comparative analysis of co-contraction indices using synthetic EMG data: Implications for selection and interpretation

  • Hannah D. Carey,

    Roles Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing

    Affiliation Department of Kinesiology and Nutrition, University of Illinois Chicago, Chicago, Illinois, United States of America

    ⨯
  • Friedl De Groote,

    Roles Methodology, Writing – review & editing

    Affiliation Department of Movement Sciences, KU Leuven, Leuven, Vlaams-Brabant, Belgium

    ⨯
  • Andrew Sawers

    Roles Conceptualization, Funding acquisition, Methodology, Project administration, Resources, Supervision, Visualization, Writing – review & editing

    asawers@uic.edu

    Affiliation Department of Kinesiology and Nutrition, University of Illinois Chicago, Chicago, Illinois, United States of America

    ⨯

Abstract

Co-contraction—the simultaneous activation of opposing muscles—influences movement efficiency, joint stability, and motor learning. While consensus exists for EMG acquisition and processing, comparable guidance for quantifying co-contraction is lacking. This study evaluated the behavior and interrelationships of six commonly used co-contraction indices (CCIs) to develop practical recommendations for their selection, calculation, and interpretation. Synthetic EMG-like signals were generated and used to evaluate CCI behavior across a range of conditions that would be difficult to achieve experimentally. Based on their formulas and observed behavior, CCIs were sorted into three categories: shape-based, amplitude-driven, and temporal indices. Shape-based CCIs increase when two EMG signals have similar shapes, regardless of amplitudes. Amplitude-driven CCIs increase when activation is high in both muscles. Temporal CCIs increase as the duration of EMG overlap increases, regardless of signal shape or amplitude. Correlation analyses showed stronger associations within-category than between-category, supporting the proposed classification scheme. CCI behavior yielded three principal findings, each paired with a practical recommendation. First, EMG amplitude normalization techniques altered co-contraction estimates, and the effect varied by index. Researchers should therefore test whether their conclusions hold across normalization methods. Second, because CCIs differ in scale and theoretical maxima, their values are not directly comparable across indices. Comparisons should instead focus on relative trends interpreted within each index’s bounds. Third, each CCI category was sensitive to different EMG features (e.g., amplitude versus shape). The choice of CCI should therefore align with hypothesized differences in EMG signals—use shape-based CCIs when waveform similarity is of interest, and amplitude-driven CCIs when differences in activation magnitude are expected. These results provide initial guidance for selecting, calculating, and interpretating CCIs, and they establish a framework for testing the robustness of these theoretical findings using experimental EMG from diverse tasks, muscle pairs, and populations.

Citation: Carey HD, De Groote F, Sawers A (2026) A comparative analysis of co-contraction indices using synthetic EMG data: Implications for selection and interpretation. PLoS One 21(5): e0343081. https://doi.org/10.1371/journal.pone.0343081

Editor: Andrea Tigrini, Polytechnic University of Marche: Universita Politecnica delle Marche, ITALY

Received: January 31, 2026; Accepted: May 12, 2026; Published: May 29, 2026

Copyright: © 2026 Carey et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data for this study are publicly available from the Zenodo repository (https://doi.org/10.5281/zenodo.20058872).

Funding: The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Research reported in this publication was supported by the Department of Defense under Award No. HT9425-24-1-0212. The content is solely the responsibility of the authors and does not necessarily represent the official views of the Department of Defense. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

1. Introduction

Muscle co-contraction—the simultaneous activation of agonist and antagonist muscles crossing the same joint and acting in the same plane [1,2]—is central to understanding and controlling human movement. Co-contraction has been associated with movement inefficiency [3,4], early motor learning [5–8], robust resistance to mechanical disturbances [9], altered reflex responses [10–13], increased joint stiffness and stability [14–18], and reduced stress on joint ligaments [19]. Although there is extensive consensus on EMG collection, processing, and analysis [2,20–24], best practices for quantifying and interpreting co-contraction have received comparatively less attention. Systematic and scoping reviews document substantial diversity in co-contraction indices (CCI) and suggest that heterogeneity in populations, tasks, and methods impedes cross-study synthesis and clear guidance on index selection [25–27]. Experimental comparisons of CCIs have yielded valuable insights [18,28–30], but most evaluate only two indices, limiting their scope. The generalizability of these experimental findings is further constrained by study-specific EMG recordings and the noise inherent to EMG data. Synthetic EMG helps address these limitations by enabling targeted simulations of specific signal features and more precise evaluation of CCI behavior than are feasible with experimental data. For example, synthetic (i.e., simulated) datasets have been used to test how signal-to-noise ratio and preprocessing steps influence CCI outcomes [31]. A comprehensive assessment of CCI behavior under well-defined, controlled conditions using synthetic data is needed to develop actionable recommendations for CCI selection and interpretation. The purpose of this study was to characterize the behavior and interrelationships of six commonly used CCIs and develop practical guidance for their selection, calculation, and interpretation.

2. A brief description, comparison, and categorization of common co-contraction indices

Before reviewing, analyzing, and comparing six common co-contraction indices (CCI) [1,32–34], we first define some basic nomenclature. EMG1(t) and EMG2(t) represent the amplitude normalized electromyography (EMG) signals recorded from an agonist—antagonist muscle pair at time t. At each time point t, the higher and lower values of EMG1(t) and EMG2(t) are denoted as EMGhigh(t) and EMGlow(t), respectively.

2.1. The Simple ratio Co-Contraction Index (CCISR)

One of the earliest and simplest methods for quantifying co-contraction is the ratio of antagonist to agonist EMG activity (Eq. 1; Fig 1A) [35]. Simple ratio CCIs can be calculated using any number of EMG metrics derived from each muscle, including the peak, root mean squared, or integral of agonist and antagonist activity [36]. Because we often consider EMG signals with more complex shapes than those that can be characterized by a single data point (i.e., peak EMG), here we express the CCISR based on the integrated area of two EMG signals:

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Fig 1. Visualizing the Simple Ratio (A) and Falconer-Winter (B) co-contraction indices (CCIs).

Solid and dashed lines represent EMG1 and EMG2, respectively. At each time point, the blue and orange lines correspond to the low and high EMG signals, respectively, while the solid green line in panel B shows the total EMG (i.e., EMG1 + EMG2). The blue shaded area represents the integral of EMGlow, which serves as the numerator in both indices (see Eqn. 1–2). In panel (A), the gray hatched region denotes the integral of EMGhigh, used as the denominator in the Simple Ratio CCI (Eqn. 1). In panel (B), the grey hatched region represents EMGtotal, which serves as the denominator in the Falconer-Winter CCI (Eqn. 2).

https://doi.org/10.1371/journal.pone.0343081.g001

(1)

The simple ratio also does not consider the general amplitude of activation or provide an indication of when or how co-contraction varies over time, which may lead to inaccurate or inflated estimates of co-contraction. The simple ratio is therefore best suited for tasks with relatively invariant EMG amplitudes, such as isometric contractions, rather than more dynamic movements, especially if the antagonist is unclear.

2.2. The Falconer and Winter Co-Contraction Index (CCIFW)

Falconer and Winter [1] quantified co-contraction between two antagonist ankle muscles during gait using the ratio of the overlapping area between EMG1 and EMG2 (i.e., the integral of EMGlow) to the area of total EMG activity (i.e., integral of the sum of EMG1 and EMG2) (Eq. 2; Fig 1B). Multiplying the numerator (EMGlow) by two allows values of CCIFW to vary between 0 and 1. Although the original formula designated EMGhigh as the agonist and EMGlow as the antagonist, explicitly defining the antagonist is not necessary when using CCIFW.

(2)

The Falconer-Winter CCI is among the most widely cited co-contraction indices and has been used to study gait-related co-contraction in older adults [37,38], individuals with cerebral palsy [39], and stroke survivors [28]. Like the simple ratio, the Falconer-Winter CCI does not consider activation amplitude and was not originally intended to indicate when or how co-contraction varies over time. These characteristics suggest it is best applied to tasks with relatively constant EMG amplitudes or to short, quasi-stationary analysis windows. Historically reported as a single value integrated over brief time windows [1,38–40], the CCIFW has recently been computed sample-by-sample to produce a time-series [30].

2.3. The Thoroughman and Shadmehr Co-Contraction Index (CCITS)

To identify EMG correlates of sensorimotor adaptation, Thoroughman and Shadmehr [33] quantified muscle co-contraction using two EMG-derived time-series: the “wasted contraction” (Eq. 3) and the “effective contraction” (Eq. 4). At each time point, the smaller of the two EMG signals (i.e., EMGlow) is labeled the “wasted contraction” because it is considered to be cancelled by the larger, opposing activation signal (i.e., EMGhigh).

(3)

Subtracting the “wasted contraction” from the EMGhigh yields the “effective contraction” time-series.

(4)

The level of co-contraction can be quantified as the “wasted contraction” divided by the maximum of the “effective contraction”, and either left as a time series for analysis [41] or expressed as a single index by taking the mean (Eq. 5; Fig 2) [28,33].

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Fig 2. Visualizing the Thoroughman-Shadmehr co-contraction index (CCI).

In both panels, solid and dashed lines represent EMG1 and EMG2, respectively. At each time point, the orange line corresponds to the EMGhigh signal, while the blue line corresponds to the EMGlow signal (i.e., the “wasted” contraction). The solid green line represents EMGhigh— EMGlow, termed the “effective” contraction. The “wasted” and the “effective” contraction are then used to calculate the value of the Thoroughman-Shadmehr CCI (Eqn. 5).

https://doi.org/10.1371/journal.pone.0343081.g002

(5)

Notably, the Thoroughman-Shadmehr CCI has no upper bound. When EMG1 and EMG2 have very similar amplitudes the “effective contraction” (i.e., EMGhigh—EMGlow) becomes very small. As a result, dividing by the max effective contraction—a very small number—produces co-contraction values that can become arbitrarily large, approaching infinity. If the two EMG signals are identical, the maximum “effective contraction” is zero and the CCI becomes undefined. The Thoroughman-Shadmehr CCI has been used primarily to study co-contraction in the upper [7,33,41,42] rather than lower limb [28]. In some studies the wasted contraction is not scaled by the maximum effective contraction. The CCI is instead expressed as the average wasted contraction [7,42], which is equivalent to the Unnithan-Frost CCI described below.

2.4 The Unnithan and Frost Co-Contraction Index (CCIUF)

Unnithan et al., and Frost et al. [34,43] quantified co-contraction between agonist-antagonist muscle pairs in typically developing children and those with cerebral palsy using the ratio of the overlapping area between EMG1 and EMG2 (i.e., the integral of EMGlow) to the total number of data points (N) (Eq. 6; Fig 3A).

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Fig 3. Visualizing the Unnithan (A) and Rudolph (B) co-contraction indices (CCIs).

In both panels, solid lines represent EMG1 and dashed lines represent EMG2. At each time point, the blue and orange lines correspond to the EMGlow and EMGhigh signals. In panel (B) the solid green line represents EMGtotal (i.e., EMG1 + EMG2).

https://doi.org/10.1371/journal.pone.0343081.g003

(6)

The Unnithan-Frost CCI is equivalent to the mean of EMGlow and can therefore be thought of as the average amplitude of the overlap between two antagonist EMG signals (see Fig 3A). CCIUF and CCITS are equivalent if there is at least one time point where the difference between EMGhigh and EMGlow is exactly one. In that scenario, the maximum “effective contraction”—which serves as the denominator of the Thoroughman-Shadmehr index (Eq. 5)—is equal to 1, and CCITS becomes the same as the mean of EMGlow (i.e., CCIUF).

2.5 The Rudolph Co-Contraction Index (CCIR)

While investigating knee stability after ACL injury, Rudolph et al. [32] quantified co-contraction between an agonist-antagonist muscle pair by computing the ratio of the less active muscle’s amplitude (i.e., EMGlow) to the more active muscle’s amplitude (i.e., EMGhigh), multiplied by the sum of both muscles’ activity at each time point t during the time period of interest (Eq. 7; Fig 3B).

(7)

Unlike other CCIs, the Rudolph index is traditionally calculated as a time-series. By treating co-contraction as a function of time—rather than collapsing it into a single integrated, summed, or averaged value—this approach can reveal meaningful information about the magnitude and timing of peak co-contraction. This is particularly valuable for longer duration movements (e.g., over the course of a full gait cycle rather than during a single gait event or period), or when the timing of peak co-contraction is unknown. A single value for CCIR can be obtained by integrating the time-series, as originally proposed by Rudolph et al. [32]. Some researchers have instead used the sum [44] or average [45] of the CCIR time-series. In alignment with the original method, we report the integral throughout this paper. We discourage the use of the sum, as it produces co-contraction estimates that are both artificially large [44] and dependent on the number of data points, thereby limiting comparisons across subjects or studies.

2.6 The temporal co-contraction index (CCIT)

All of the CCIs described above incorporate both the amplitude and duration of the agonist and antagonist EMG signals. Co-contraction indices can also be derived solely from the temporal features of two EMG signals [46]. In a study of ankle muscle co-contraction after stroke, Lamontagne et al., [46] quantified temporal co-contraction between an agonist-antagonist muscle pair as the percentage of time that both muscles were active—that is, the ratio of their overlap time to the total observation time (Eq. 8; Fig 4). Here, toverlap represents the number of time points when both muscles are simultaneously active, and ttotal is the total number of time points within the period of interest.

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Fig 4. Visualizing the temporal co-contraction index (CCI).

Solid lines represent EMG1 and dashed lines represent EMG2. Blue lines denote the low EMG signal at each time point. The shaded bar below the x-axis indicates the time points during which EMG1 and EMG2 overlap relative to the total time (black outline).

https://doi.org/10.1371/journal.pone.0343081.g004

(8)

The magnitude of a temporal CCI can vary from 0% to 100% of the observation period. A temporal CCI may be appropriate when only the duration of simultaneous activation is of interest, or when working with populations in which EMG amplitude is unreliable. Unlike each of the other indices described above, CCIT is sensitive to the methods chosen to identify EMG onset and offset [47,48]. Other indices may therefore be preferable to CCIT if EMG onsets and offsets are difficult to identify. A further limitation of temporal CCIs is that they do not account for activation magnitude—co-contraction is treated the same whether both muscles are minimally or maximally active. CCIT is therefore insensitive to differences in EMG intensity.

3. A proposed co-contraction index classification scheme

We propose that the six CCIs reviewed above can be grouped into three categories: shape-based, amplitude-driven, and temporal CCIs. This classification scheme is based on the mathematical formula and general behavior of each index, as illustrated by 3D surface plots depicting all possible co-contraction values between two EMG signals varying from 0 to 1 (Fig 5) [49].

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Fig 5. 3D surface plots depicting all possible values of each co-contraction index (CCI) for any combination of EMG1 and EMG2.

Note the differences in shape, and thus behavior, of the CCIs. Panels A-C exhibit a dark blue “ridge” of high co-contraction whereas panels D and E possess a “sharp point” or peak of high co-contraction. The Simple Ratio (A), Falconer-Winter (B), and Thoroughman-Shadmehr (C) CCIs all return high co-contraction values when the two EMG signals have a similar value or shape, even when their amplitude is low (hence the “ridge”). These three indices are therefore termed shape-based CCIs. In contrast, the Unnithan-Frost and Rudolph CCIs both require high amplitude to produce high levels of co-contraction (hence the distinct peak-like feature in their surface plots). Because these two CCIs are primarily influenced by signal amplitude and require high activation in both muscles to produce large co-contraction values, they are termed amplitude-based CCIs. The temporal CCI is not included in the 3D surface plots because it does not vary with EMG amplitude. As CCI formulas do not all have the same maximum, y-axis limits in the surface plots vary.

https://doi.org/10.1371/journal.pone.0343081.g005

A central difference among the six CCIs emerges from the shapes of their 3D surface plots (Fig 5). The simple ratio [36], Falconer-Winter [1], and Thoroughman-Shadmehr [33] CCIs all display a prominent “ridge” along the diagonal where EMG1 and EMG2 are similar (shown in dark blue, Fig 5A-C). This ridge indicates that co-contraction estimates from these indices are primarily influenced by the similarity in the shape of the two EMG signals, producing higher co-contraction values when the signals are similar, regardless of their amplitude (Fig 5A-C). Because these three indices share this characteristic “ridge” and are all computed as the ratio of the less active muscle (i.e., EMGlow) to another quantity (e.g., total EMG activity), we propose grouping them into a single category collectively referred to as shape-based CCIs. Except for the Thoroughman-Shadmehr index [33], which ranges from zero to infinity, shape-based CCIs generally range from 0 to 1. A value of 0 indicates no co-contraction and occurs when EMGlow is zero, while a value of 1 typically reflects complete co-contraction—when the two EMG signals are identical, though not necessarily high in amplitude. Shape-based CCIs can also be expressed as percentages when multiplied by 100.

While all shape-based CCIs share the characteristic “ridge”, they also exhibit distinct features. Fig 6 illustrates the relationship between the three shape-based CCIs and EMGlow, assuming a fixed value for EMGhigh, (i.e., taking a “slice” through each surface plot). The simple ratio CCI increases linearly with EMGlow, reflecting a steady increase in co-contraction as the amplitude of the two EMG signals become more similar. CCIFW exhibits a more convex profile, whereas the Thoroughman-Shadmehr CCI exhibits an asymptotic response, with values rising rapidly from zero towards infinity (Fig 6). These differences demonstrate that, even within the same CCI category, identical inputs can yield different co-contraction values. Here EMGhigh was set equal to 1, but the general patterns observed in Fig 6 hold for different values of EMGhigh.

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Fig 6. Shape-based CCI values with EMGhigh fixed at 1.

Co-contraction values are presented for increasing values of EMGlow while the value for EMGhigh is fixed at 1. Co-contraction values derived from the three shape-based indices increase at different rates as the amplitude of EMGlow increases, suggesting that each index may yield distinct estimates of co-contraction, especially at moderate levels of EMGlow (e.g., 0.5). Similar results are obtained if different values of EMGhigh are used. Abbreviations: CCISR: Simple Ratio; CCIFW: Falconer-Winter; CCITS: Thoroughman-Shadmehr.

https://doi.org/10.1371/journal.pone.0343081.g006

In contrast to shape-based CCIs, the surface plots of the Unnithan-Frost [34,43] and Rudolph [32] indices each display a single peak when both EMG signals reach their maximum amplitude (Fig 5D-E). This pattern illustrates that these indices are primarily influenced by signal amplitude and require high activation in both muscles to produce large co-contraction values. Based on this shared behavior, we propose grouping these two indices into a single category: amplitude-driven CCIs. Although amplitude-driven CCIs have no theoretical upper bound, when EMG signals are amplitude normalized to range from zero to one, the maximum possible values of CCIUF and CCIR are 1 and 2, respectively. Amplitude-driven CCIs yield values near zero when there is little or no antagonist muscle activity. In addition to their common dependence on amplitude, both amplitude-driven indices display distinct behavioral characteristics. For example, the Unnithan-Frost index increases linearly with increases in EMGlow (Fig 5D), whereas the Rudolph index is more concave, reflecting a more “conservative” estimate of co-contraction (Fig 5E). Among all indices described here the Rudolph CCI is the most stringent: requiring high activation in both muscles before producing large co-contraction values.

Because temporal CCIs are based on the simultaneous activation of two muscles regardless of their amplitude, they produce binary values (0 or 1) at each time point, making them poorly suited for visualization with a 3D surface plot.

Comparing shape-based, amplitude-driven, and temporal CCI behaviors raises a central question: what constitutes co-contraction? Must both the agonist and antagonist muscles be highly active, as emphasized by amplitude-driven CCIs? Or is it sufficient that their activation levels are similar, regardless of amplitude, as assumed by shape-based methods? Alternatively, can co-contraction be quantified independent of both signal amplitude and similarity, as is implied by temporal CCIs? These questions highlight the importance of recognizing that different methods for estimating co-contraction may yield divergent results under similar conditions. For instance, during sustained low-amplitude activation of an agonist-antagonist muscle pair, shape-based CCIs would identify high co-contraction, while amplitude-driven CCIs would not. One could argue that amplitude-driven methods may underestimate co-contraction in such scenarios, potentially overlooking small but meaningful contributions to joint stabilization or movement inefficiency. Ultimately, shape-based, amplitude-driven, and temporal CCIs likely capture distinct, rather than redundant, aspects of co-contraction—each offering unique insights into human movement—an idea explored in greater detail below.

4. Do the groups hold up? Testing the proposed CCI classification scheme

The initial validity of the proposed CCI classification scheme was evaluated using correlation analyses of CCIs calculated using synthetic EMG data. Stronger correlations among CCIs within rather than between groups (i.e., shape-based, amplitude-driven, or temporal) would provide initial evidence supporting the proposed classification. Synthetic data were used to enable a more precise evaluation of CCI behavior than would be possible with experimental EMG data. Three thousand pairs of synthetic EMG signals—each ranging in amplitude from 0 up to 1—were generated to represent amplitude normalized EMG data from two muscles. The synthetic EMG data was generated as sinusoids (N = 1000), first- (N = 1000), and second-order (N = 1000) polynomials, in order to capture a large range of signals with varying shapes. Polynomials were created using randomly generated coefficients between −1 and 1 and intercepts between 0 and 1 for each muscle. Sinusoids were generated in the form:

(9)

where c2 and c6 are random numbers between 0 and 10, and all other ci are random numbers between 0 and 1. All synthetic EMG signals were rectified to eliminate negative values. Signals with a maximum amplitude greater than 1 were scaled to range from 0 to 1 (Fig 7). An activation threshold of 0.1 was used to define onset and offset for the temporal CCI only (for all other indices, nonzero EMG is considered active). While arbitrary, varying the threshold level was found to have minimal effect on the results.

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Fig 7. Samples of randomly generated synthetic EMG signals used to quantify correlations between co-contraction indices.

https://doi.org/10.1371/journal.pone.0343081.g007

Values for all six CCIs were calculated for each of the 3000 pairs of synthetic EMG signals. The relationship between co-contraction estimates from each of the six CCIs were visualized with scatterplots and quantified by calculating Chatterjee’s correlation coefficients [50]. Unlike Pearson’s correlation coefficient—which only detects linear relationships—and Spearman’s rho—which can capture nonlinear relationships for monotonic functions (i.e., always increasing or decreasing)—Chatterjee’s coefficient can identify both nonlinear and nonmonotonic relationships (e.g., a parabola) [50,51], making it well suited for evaluating the strength of the relationships between CCIs. Matlab scripts used to generate and evaluate the synthetic EMG data are available on GitHub (DOI: 10.5281/zenodo.20058872).

Except for correlations involving the temporal CCI, Chatterjee correlation coefficients were positive and greater than 0.4 (Fig 8). Consistent with our hypothesis, the strongest correlations occurred within each of the proposed CCI groups, i.e., > 0.7 for shape-based and > 0.9 for amplitude-driven). This pattern lends support to the proposed classification scheme. However, correlations among all five shape-based and amplitude-driven CCIs were consistently > 0.5, suggesting some degree of similarity between shape-based and amplitude-driven indices. Although shape-based and amplitude-driven CCIs produce different absolute values, their moderate correlations suggest that relative trends may be comparable across studies. However, this holds only when the underlying EMG features (i.e., amplitude, shape)—and nature of co-contraction being studied—are similar across studies.

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Fig 8. Pairwise correlations among six CCIs, derived from randomly generated pairs of synthetic EMG data, were quantified using Chatterjee’s correlation coefficient and visualized with scatterplots.

Axis limits differ across scatterplots but remain consistent within each row and column. Histograms along the diagonal illustrate the distribution of co-contraction values for each index, with co-contraction values on the x-axis and incidence on the y-axis (0-2500). Correlations were strongest among CCIs within the same group (i.e., shape-based or amplitude-based indices), supporting the proposed classification scheme. With the exception of the temporal CCI, moderate correlations were also observed between CCIs from different groups, a pattern which suggests that relative trends but not absolute values may be cautiously compared across studies that use indices from different groups. Abbreviations: CCISR: Simple Ratio; CCIFW: Falconer-Winter; CCITS: Thoroughman-Shadmehr; CCIUF: Unnithan-Frost; CCIR: Rudolph; CCIT: Temporal.

https://doi.org/10.1371/journal.pone.0343081.g008

To this point, we have characterized the behavior and relationships among commonly cited CCIs and grouped each index into one of three categories: (i) shape-based CCIs, which quantify similarity in shape between EMG signals; (ii) amplitude-driven CCIs, which capture periods of simultaneously high activation; and (iii) temporal CCIs, which quantify the duration of simultaneous activation. Within-category correlations were strong and behaviors similar, whereas between-category correlations were weaker, suggesting that these indices capture complimentary, rather than redundant aspects of co-contraction. Next we present three practical, data-driven recommendations that address common methodological and conceptual challenges in selecting, calculating, and interpretating CCIs.

5. Recommendations for the selection, calculation, and interpretation of co-contraction indices

To inform each of the recommendations below, synthetic EMG data were generated to create controlled and well-defined conditions that would be difficult to achieve with experimental data. Distinct from the correlation analysis, these synthetic signals were specifically designed to reflect common features of experimental EMG—such as low-level activation and varying degrees of overlap—that could be used to test each index’s response to specific signal characteristics. Eight pairs of synthetic EMG signals were generated using linear or piecewise linear functions, each ranging in value from 0 to 1, to reflect EMG data normalized to a within-task maximum and evaluated over 100 time points. The Matlab scripts used to generate and analyze these signals are provided on GitHub (DOI: 10.5281/zenodo.20058872).

  1. Proposal 1: Different amplitude normalization techniques alter the magnitude and interpretation of co-contraction indices

Amplitude normalization of EMG signals to a maximum reference value enables meaningful comparisons across muscles, participants, and measurement sessions or conditions [21]. The choice of amplitude normalization technique depends on the intended analysis and interpretation [21,52]. While most studies apply some form of amplitude normalization prior to calculating co-contraction values [26–28,53], the effects of different normalization techniques on co-contraction estimates remain unclear. Several studies have investigated how select normalization techniques influence co-contraction, yielding mixed results [28,54,55]. One study found that in the paretic limb of individuals with chronic stroke, co-contraction estimates between the soleus and tibialis anterior differed significantly between maximum M-wave and within-task normalization techniques across multiple shape-based CCIs [28]. Most evidence to date, however, suggests that amplitude normalization has little to no effect on co-contraction values [28,54,55]. These conclusions are based exclusively on shape-based CCIs [28,54,55], have been made without reference to non-normalized data [21], and in some cases, rely on EMG collected from neurologically impaired adults (e.g., post-stroke) [28]. An evaluation that incorporates amplitude-driven CCIs and comparisons to non-normalized data is needed to clarify the impact of amplitude normalization on co-contraction estimates.

To assess how different amplitude normalization techniques affect each CCI, three pairs of synthetic EMG signals, described above, were modified to reflect the peak amplitudes typically produced by three common amplitude normalization methods [21]: i) amplitudes ranging from 0 to 0.6, consistent with normalization to a maximum voluntary contraction (MVC) or M-wave; ii) amplitudes ranging from 0 to 1, representing normalization to a within-task maximum; and iii) amplitudes ranging from 0 to 1.4, simulating non-normalized EMG data. These differences in signal amplitude were then evaluated for their effect on co-contraction estimates calculated using the indices reviewed above.

EMG amplitude normalization techniques appear to affect shape-based and amplitude-driven CCIs differently (Fig 9). Amplitude-driven CCIs (e.g., CCIR, CCIUF) were most sensitive to normalization methods that altered both the amplitude of EMGlow and the total EMG activity (Fig 9A & C). Compared to non-normalized EMG data (dotted line, Fig 9A), decreases in the amplitude of EMG2 following within-task (dot-dashed line) and MVC-based amplitude normalization (dashed line) reduced the overlap between EMG1 and EMG2 while also slightly reducing the total EMG activity. The decrease in EMG2, which serves as EMGlow for the first half to two-thirds of Fig 9A, reduces the numerator of amplitude-driven CCIs (see Fig 3), thereby decreasing their overall magnitude (Fig 9C). Although the numerator of shape-based CCIs (e.g., Falconer-Winter, Fig 1) is slightly influenced by the decrease in EMGlow, a simultaneous reduction in total EMG activity—the denominator in shaped-based CCIs - offset this effect. As a result, the ratio of EMGlow to EMGhigh, and thus shape-based CCIs would remain relatively unchanged if both the amplitude of EMGlow and the total EMG activity are altered by amplitude normalization.

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Fig 9. Amplitude normalization influences each CCI in distinct ways.

In panels A and B, the amplitude of EMG1 (solid black lines) is fixed, while that of EMG2 varies to represent three amplitude normalization conditions: non-normalized (dotted line, maximum amplitude 1.4), within-task normalization (dash-dotted line, maximum amplitude 1), and MVC normalization (dashed line, maximum amplitude 0.6). Panels C and D show bar plots of co-contraction values for all six CCIs, calculated from the three EMG1 and EMG2 combinations in panels A and B. Amplitude-driven CCIs (i.e., Rudolph and Unnithan-Frost) are most affected when amplitude normalization reduces both EMGlow and total EMG (panel C). In contrast, shaped-based CCIs, like Falconer-Winter, are most sensitive when normalization alters only one of EMGlow and total EMG (panel D). Abbreviations: CCISR: simple ratio; CCIFW: Falconer-Winter; CCITS: Thoroughman-Shadmehr; CCIR: Rudolph; CCIUF: Unnithan-Frost; CCIT: temporal.

https://doi.org/10.1371/journal.pone.0343081.g009

In contrast, when only one of either total EMG activity or EMGlow is altered by amplitude normalization, the ratio of EMGlow to EMGhigh changes, producing a large increase in the magnitude of shaped-based CCIs (Fig 9B & D). For example, in Fig 9B, a decrease in the amplitude of EMG2, which serves as EMGhigh throughout, due to within-task (dot-dashed line) and MVC-based normalization (dashed line) reduces the total EMG activity without affecting the overlap between EMG1 and EMG2. This selective reduction in the denominator of shape-based CCIs (e.g., CCISR, CCIFW, CCITS; Figs 1 and 2) increases the co-contraction values (Fig 9D). Amplitude-driven CCIs are largely unaffected in such cases because they are more sensitive to changes in signal overlap, which depends on the amplitude of EMGlow (Fig 9D).

Amplitude normalization is largely irrelevant to temporal CCIs (e.g., Lamontagne) [46], which are based on EMG onset and offset times rather than signal amplitude or shape. In theory, normalizing EMG data to an extremely low reference value could increase the signal-to-noise ratio, complicate onset and offset detection, and potentially influence temporal CCI values. Such scenarios are unlikely in practice and the choice to normalize—or not—is generally not applicable to the calculation or interpretation of temporal CCIs.

These findings highlight the importance of considering the amplitude normalization method used [21], the type of CCI to which it is applied, and whether the method affects signal overlap (i.e., EMGlow), total EMG activity, or both. These factors determine whether—and in which direction—amplitude normalization alters estimates of muscle co-contraction.

  1. Recommendation: Because the effect of amplitude normalization on co-contraction varies by index, studies should assess the sensitivity of their results to different normalization techniques when possible.
  1. Proposal 2: Co-contraction estimates calculated from different indices are not directly comparable.

The wide range of behaviors (Fig 5) and different theoretical maximum values across CCIs (e.g., CCIFW_max = 1, CCIR_max = 2) suggest that estimates calculated from different CCIs should not be directly compared. Fig 10 illustrates how co-contraction estimates vary across indices under three well defined conditions: none (A), maximal (B), and partial (C) overlap between two synthetic EMG signals.

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Fig 10. Under identical conditions, different indices yield different co-contraction values.

Panels A-C illustrate three levels of overlap between two synthetic EMG signals plotted as a solid grey line and a dashed black line (A: none, B: complete, C: partial). Overlap is shown by the shaded blue regions, with corresponding bar graphs presenting the co-contraction values derived from each index for the three conditions. Light gray shading indicates periods of co-contraction identified by the temporal CCI. (A): In the absence of overlap, all CCI correctly return a value of zero. (B): Under complete overlap, all CCIs indicate “maximum” co-contraction, but the Thoroughman-Shadmehr (CCITS) and Rudolph (CCIR) indices return higher numerical values. Because indices have different theoretical maximums, these higher values should not be misinterpreted as “more” co-contraction than the other indices, but rather as “full” co-contraction. (C): Under partial overlap co-contraction values differ across indices. Subsequently, direct comparisons of indices’ absolute values should be avoided. Abbreviations: CCISR: Simple Ratio; CCIFW: Falconer-Winter; CCITS: Thoroughman-Shadmehr; CCIR: Rudolph; CCIUF: Unnithan-Frost; CCIT: Temporal.

https://doi.org/10.1371/journal.pone.0343081.g010

In Fig 10A, EMG signals do not overlap, only one muscle is active at a time, and all CCIs correctly return values of zero. From this example we can infer that none of the six reviewed CCIs are prone to identifying co-contraction when none exists. In Fig 10B, both muscles are maximally active throughout. Under these conditions the temporal and shape-based indices (e.g., CCISR, CCIFW), along with CCIUF, return a value of 1, but CCIR yields a value of 2 and CCITS is undefined. In the absence of an awareness for the different theoretical maximum values of each CCI, comparing CCIFW and CCIR in this scenario would falsely suggest that a study using CCIR observed “more co-contraction” than one using CCIFW, when the difference is purely mathematical—not physiological. Between these two extremes, when EMG1 and EMG2 partially overlap (Fig 10C), the calculated co-contraction values vary across indices (e.g., CCISR = 0.33; CCIFW = 0.50; CCITS = 0.25; CCIUF = 0.25; CCIR = 0.39; CCIT = 0.77). Consistent with prior studies [18,28] these results show substantial variation in co-contraction values across CCIs, even when computed from identical EMG signals. Such differences hinder cross-study comparisons when different indices are used [56], complicating the interpretation of systematic reviews [25,27,56].

  1. Recommendation: Avoid direct comparisons of co-contraction values derived from different indices. Instead, evaluate relative trends with respect to each index’s theoretical maximum to ensure fair, meaningful comparisons across CCIs.
  1. Proposal 3: The choice of co-contraction index should be aligned with hypothesized change (or difference) in EMG signals.

As discussed above and illustrated in Fig 5, each category of CCIs are sensitive to different characteristics of EMG signals and arguably represent different concepts of co-contraction. CCIs should therefore be selected based on the EMG features expected to differ across tasks or groups that are relevant to the research question (i.e., amplitude or shape). Amplitude-driven CCIs reflect high simultaneous activation; they are sensitive to changes in EMG signal amplitude and will therefore detect condition-dependent differences in co-contraction when amplitude changes occur without meaningful changes in EMG shape. In contrast, shape-based CCIs reflect waveform similarity; they are sensitive to signal shape and largely insensitive to amplitude differences. Selecting a CCI that does not reflect the hypothesized concept of co-contraction could limit detection of experimental differences.

As an example consider a study examining whether co-contraction differs between walking on level and uneven terrain. Prior work suggests that walking on uneven terrain increases EMG amplitude in both agonist and antagonist muscles while producing little change in signal shape [57]. In this case, differences in co-contraction are most likely to be detected with an amplitude-driven CCI that captures simultaneous increases in EMG magnitude. Fig 11 illustrates this point. The shape-based CCI (e.g., CCIFW) yields similar values for level terrain (Fig 11A) and uneven terrain (Fig 11B), consistent with minimal waveform changes. In contrast, the higher EMG amplitude (and longer activation) on uneven terrain increases the amplitude-driven and temporal CCIs (e.g., CCIR, CCIT). Choosing a shape-based CCI in this context could mask meaningful differences between walking conditions.

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Fig 11. Align the choice of CCI with the EMG feature expected to change or differ.

Synthetic EMG signals are plotted as solid gray and dashed black lines, with overlapping regions shaded blue. Light gray shading indicates periods of co-contraction identified by the temporal CCI. Corresponding bar graphs display the co-contraction values calculated from each index under each condition. Because of their sensitivity to signal similarity, shape-based CCIs (i.e., CCISR, CCIFW, CCITS)—but not amplitude-driven (e.g., CCIR, CCIUF) or temporal CCIs—return identical values in panels A and B, indicating “complete” co-contraction despite differences in signal amplitude. In contrast, amplitude-driven, but not shape-based CCIs reveal their sensitivity to signal amplitude by producing smaller co-contraction values in panel A than in B. Variations in co-contraction due to signal similarity are best detected with shape-based CCIs, whereas differences in co-contraction arising from changes in signal amplitude are better captured with amplitude-based CCIs. Abbreviations: CCISR: simple ratio; CCIFW: Falconer-Winter; CCITS: Thoroughman-Shadmehr; CCIR: Rudolph; CCIUF: Unnithan-Frost; CCIT: temporal.

https://doi.org/10.1371/journal.pone.0343081.g011

This example is not intended to represent all possible situations; rather, it illustrates that no single CCI captures all signal features that influence co-contraction estimates. Instead, each index emphasizes different EMG features (i.e., amplitude or shape), and their suitability depends on the task- and condition-specific determinants of co-contraction. The theoretical sensitivity of shape-based and amplitude-driven CCIs to different features of EMG was demonstrated experimentally by Harrington et al., (2025). In both typically developing children and those with cerebral palsy, co-contraction was higher during fast versus slow walking, and during overground versus aquatic treadmill walking—but only when calculated using amplitude-driven CCIs (i.e., CCIUF and CCIR). Shape-based CCIs (e.g., CCIFW) did not capture these differences [30]. That only amplitude-driven, not shape-based, CCIs detected these task-specific difference in co-contraction is attributable to the observed differences in EMG amplitude and the absence of any notable differences in signal shape between experimental conditions [30]. These results support both our proposed classification scheme and the broader recommendation to select CCIs based on expected or observed differences in EMG signal amplitude and/or shape.

  1. Recommendation: Match the co-contraction index to the co-contraction concept and thus EMG feature of interest—use a shape-based index (e.g., Falconer-Winter) when signal similarity is prioritized, and an amplitude-driven index (e.g., Rudolph) when differences in signal magnitude and duration are expected.

6. Final thoughts and next steps

We have shown that formulas for common co-contraction indices fall into one of three categories: i) shape-based CCIs, which define high co-contraction based on signal similarity regardless of amplitude, ii) amplitude-driven CCIs, in which simultaneous high activation in the agonist and antagonist muscles is required to yield high co-contraction, and iii) temporal CCIs, which defines co-contraction as the duration of simultaneous activation regardless of signal shape or amplitude. CCIs within each category—and, to a lesser extent, between categories—behave similarly. Due to differences in formula behavior and sensitivities to different features of EMG signals, we propose that researchers should: i) when possible, assess the sensitivity of their results to different amplitude normalization techniques, ii) assess relative trends rather than directly compare absolute co-contraction values derived from different indices, and iii) consider using a CCI sensitive to expected changes or differences in EMG signals. The current results also emphasize the importance of initial descriptive and visual analyses of EMG data so that researchers can carefully select indices in accordance with the features of their EMG data and specific research question.

Here we focused on six commonly used CCIs. Many other indices have been proposed and may be better suited for some research questions. The time-varying multi-muscle co-activation function developed by Ranavolo et al., is an amplitude-driven CCI that can incorporate more than two muscles to provide a more global estimate of co-contraction [49,58]. The Vector Coding Technique [59], which determines if EMG signals are in-phase [31], and the correlation coefficient technique, which quantifies the direction and strength of a linear relationship between two muscle signals [29,60,61], may be better suited for questions related to shared input to agonist-antagonist muscle pairs involved in co-contraction.

Our analyses used synthetic EMG data to create controlled scenarios, enabling more precise evaluation of CCI behavior over a wider range of conditions than would be feasible with experimental EMG. An important next step is to test the robustness of these theoretical findings using experimental EMG from diverse tasks, muscle pairs, and clinical populations.

Acknowledgments

We used the scientific colormaps oslo (for 3D surface plots) and lipari (for synthetic EMG) [62], which prevents visual distortion and is interpretable to readers with color-vision deficiencies [63].

References

  1. 1. Falconer K, Winter DA. Quantitative assessment of co-contraction at the ankle joint in walking. Electromyogr Clin Neurophysiol. 1985;25(2–3):135–49. pmid:3987606
  2. 2. McManus L, Lowery M, Merletti R, Søgaard K, Besomi M, Clancy EA, et al. Consensus for experimental design in electromyography (CEDE) project: Terminology matrix. J Electromyogr Kinesiol. 2021;59:102565. pmid:34102383
  3. 3. Winter DA. Energy assessments in pathological gait. Physiother Can. 1978;30:183–91.
  4. 4. Peterson DS, Martin PE. Effects of age and walking speed on coactivation and cost of walking in healthy adults. Gait Posture. 2010;31(3):355–9. pmid:20106666
  5. 5. Heald JB, Franklin DW, Wolpert DM. Increasing muscle co-contraction speeds up internal model acquisition during dynamic motor learning. Sci Rep. 2018;8(1):16355. pmid:30397273
  6. 6. Osu R, Franklin DW, Kato H, Gomi H, Domen K, Yoshioka T, et al. Short- and long-term changes in joint co-contraction associated with motor learning as revealed from surface EMG. J Neurophysiol. 2002;88(2):991–1004. pmid:12163548
  7. 7. Darainy M, Ostry DJ. Muscle cocontraction following dynamics learning. Exp Brain Res. 2008;190(2):153–63. pmid:18584164
  8. 8. Hobart DJ, Kelley DL, Bradley LS. Modifications occurring during acquisition of a novel throwing task. Am J Phys Med. 1975;54(1):1–24. pmid:1111305
  9. 9. Armstrong DP, Deluzio KJ, Scott SH. Agonist-antagonist muscular co-contraction improves rapid corrective responses. iScience. 2025;28(8):113122. pmid:40799397
  10. 10. Akazawa K, Milner TE, Stein RB. Modulation of reflex EMG and stiffness in response to stretch of human finger muscle. J Neurophysiol. 1983;49(1):16–27. pmid:6827293
  11. 11. Carter RR, Crago PE, Gorman PH. Nonlinear stretch reflex interaction during cocontraction. J Neurophysiol. 1993;69(3):943–52. pmid:8385202
  12. 12. Nielsen J, Kagamihara Y. The regulation of presynaptic inhibition during co-contraction of antagonistic muscles in man. J Physiol. 1993;464:575–93. pmid:8229819
  13. 13. Lewis GN, MacKinnon CD, Trumbower R, Perreault EJ. Co-contraction modifies the stretch reflex elicited in muscles shortened by a joint perturbation. Exp Brain Res. 2010;207(1–2):39–48. pmid:20878148
  14. 14. Hogan N. Adaptive control of mechanical impedance by coactivation of antagonist muscles. IEEE Trans Automat Contr. 1984;29(8):681–90.
  15. 15. Kornecki S. Mechanism of muscular stabilization process in joints. J Biomech. 1992;25(3):235–45. pmid:1564059
  16. 16. Besier TF, Lloyd DG, Ackland TR. Muscle activation strategies at the knee during running and cutting maneuvers. Med Sci Sports Exerc. 2003;35(1):119–27. pmid:12544645
  17. 17. Benjuya N, Melzer I, Kaplanski J. Aging-induced shifts from a reliance on sensory input to muscle cocontraction during balanced standing. J Gerontol A Biol Sci Med Sci. 2004;59(2):166–71. pmid:14999032
  18. 18. Li G, Shourijeh MS, Ao D, Patten C, Fregly BJ. How Well Do Commonly Used Co-contraction Indices Approximate Lower Limb Joint Stiffness Trends During Gait for Individuals Post-stroke? Front Bioeng Biotechnol. 2021;8:588908. pmid:33490046
  19. 19. Baratta R, Solomonow M, Zhou BH, Letson D, Chuinard R, D’Ambrosia R. Muscular coactivation. The role of the antagonist musculature in maintaining knee stability. Am J Sports Med. 1988;16(2):113–22. pmid:3377094
  20. 20. Besomi M, Hodges PW, Van Dieën J, Carson RG, Clancy EA, Disselhorst-Klug C, et al. Consensus for experimental design in electromyography (CEDE) project: Electrode selection matrix. J Electromyogr Kinesiol. 2019;48:128–44. pmid:31352156
  21. 21. Besomi M, Hodges PW, Clancy EA, Van Dieën J, Hug F, Lowery M, et al. Consensus for experimental design in electromyography (CEDE) project: Amplitude normalization matrix. J Electromyogr Kinesiol. 2020;53:102438. pmid:32569878
  22. 22. Gallina A, Disselhorst-Klug C, Farina D, Merletti R, Besomi M, Holobar A, et al. Consensus for experimental design in electromyography (CEDE) project: High-density surface electromyography matrix. J Electromyogr Kinesiol. 2022;64:102656. pmid:35344841
  23. 23. Besomi M, Devecchi V, Falla D, McGill K, Kiernan MC, Merletti R, et al. Consensus for experimental design in electromyography (CEDE) project: Checklist for reporting and critically appraising studies using EMG (CEDE-Check). J Electromyogr Kinesiol. 2024;76:102874. pmid:38547715
  24. 24. J M Dick T, Tucker K, Hug F, Besomi M, van Dieën JH, Enoka RM, et al. Consensus for experimental design in electromyography (CEDE) project: Application of EMG to estimate muscle force. J Electromyogr Kinesiol. 2024;79:102910. pmid:39069427
  25. 25. Rosa MCN, Marques A, Demain S, Metcalf CD, Rodrigues J. Methodologies to assess muscle co-contraction during gait in people with neurological impairment—a systematic literature review. J Electromyogr Kinesiol. 2014;24(2):179–91. pmid:24295541
  26. 26. Mohammadyari Gharehbolagh S, Dussault-Picard C, Arvisais D, Dixon PC. Muscle co-contraction and co-activation in cerebral palsy during gait: A scoping review. Gait Posture. 2023;105:6–16. pmid:37453339
  27. 27. Woods S, O’Mahoney C, McKiel A, Natale L, Falk B. Child-Adult differences in antagonist muscle coactivation: A systematic review. J Electromyogr Kinesiol. 2023;68:102727. pmid:36525931
  28. 28. Banks CL, Huang HJ, Little VL, Patten C. Electromyography Exposes Heterogeneity in Muscle Co-Contraction following Stroke. Front Neurol. 2017;8:699. pmid:29312124
  29. 29. Van Can EAM, Houdijk H, Buurke TJW. Exploring walking-dependent co-activation of quadriceps and hamstrings muscles using an isolated leg-swinging paradigm. Gait Posture. 2025;122:204–10. pmid:40706299
  30. 30. Harrington JW, Knarr BA, Dutt V, Kingston DC. Differences in lower limb co-contraction calculations vary clinical interpretation of aquatic treadmill walking in typically developing and children with cerebral palsy. Front Neurol. 2025;16:1506326. pmid:40098685
  31. 31. Rinaldi M, D’Anna C, Schmid M, Conforto S. Assessing the influence of SNR and pre-processing filter bandwidth on the extraction of different muscle co-activation indexes from surface EMG data. J Electromyogr Kinesiol. 2018;43:184–92. pmid:30384220
  32. 32. Rudolph KS, Axe MJ, Snyder-Mackler L. Dynamic stability after ACL injury: who can hop? Knee Surg Sports Traumatol Arthrosc. 2000;8:262–9.
  33. 33. Thoroughman KA, Shadmehr R. Electromyographic correlates of learning an internal model of reaching movements. J Neurosci. 1999;19(19):8573–88. pmid:10493757
  34. 34. Unnithan VB, Dowling JJ, Frost G, Volpe Ayub B, Bar-Or O. Cocontraction and phasic activity during GAIT in children with cerebral palsy. Electromyogr Clin Neurophysiol. 1996;36(8):487–94. pmid:8985677
  35. 35. Seyedali M, Czerniecki JM, Morgenroth DC, Hahn ME. Co-contraction patterns of trans-tibial amputee ankle and knee musculature during gait. J Neuroeng Rehabil. 2012;9:29. pmid:22640660
  36. 36. Damiano DL, Martellotta TL, Sullivan DJ, Granata KP, Abel MF. Muscle force production and functional performance in spastic cerebral palsy: relationship of cocontraction. Arch Phys Med Rehabil. 2000;81(7):895–900. pmid:10896001
  37. 37. Deffeyes JE, Karst GM, Stuberg WA, Kurz MJ. Coactivation of lower leg muscles during body weight-supported treadmill walking decreases with age in adolescents. Percept Mot Skills. 2012;115(1):241–60. pmid:23033760
  38. 38. Lo J, Lo O-Y, Olson EA, Habtemariam D, Iloputaife I, Gagnon MM, et al. Functional implications of muscle co-contraction during gait in advanced age. Gait Posture. 2017;53:110–4. pmid:28129590
  39. 39. Hesse S, Brandl-Hesse B, Seidel U, Doll B, Gregoric M. Lower limb muscle activity in ambulatory children with cerebral palsy before and after the treatment with Botulinum toxin A. Restor Neurol Neurosci. 2000;17(1):1–8. pmid:11490071
  40. 40. DaSilva MM, Chandran VD, Dixon PC, Loh JM, Dennerlein JT, Schiffman JM, et al. Muscle co-contractions are greater in older adults during walking at self-selected speeds over uneven compared to even surfaces. J Biomech. 2021;128:110718. pmid:34474374
  41. 41. Hardesty RL, Boots MT, Yakovenko S, Gritsenko V. Computational evidence for nonlinear feedforward modulation of fusimotor drive to antagonistic co-contracting muscles. Sci Rep. 2020;10(1):10625. pmid:32606297
  42. 42. Gribble PL, Mullin LI, Cothros N, Mattar A. Role of cocontraction in arm movement accuracy. J Neurophysiol. 2003;89(5):2396–405. pmid:12611935
  43. 43. Frost G, Dowling J, Dyson K, Bar-Or O. Cocontraction in three age groups of children during treadmill locomotion. J Electromyogr Kinesiol. 1997;7(3):179–86. pmid:20719703
  44. 44. Nelson-Wong E, Appell R, McKay M, Nawaz H, Roth J, Sigler R, et al. Increased fall risk is associated with elevated co-contraction about the ankle during static balance challenges in older adults. Eur J Appl Physiol. 2012;112(4):1379–89. pmid:21811766
  45. 45. Knarr BA, Zeni JA Jr, Higginson JS. Comparison of electromyography and joint moment as indicators of co-contraction. J Electromyogr Kinesiol. 2012;22(4):607–11. pmid:22382273
  46. 46. Lamontagne A, Richards CL, Malouin F. Coactivation during gait as an adaptive behavior after stroke. J Electromyogr Kinesiol. 2000;10(6):407–15. pmid:11102843
  47. 47. Solnik S, Rider P, Steinweg K, DeVita P, Hortobágyi T. Teager-Kaiser energy operator signal conditioning improves EMG onset detection. Eur J Appl Physiol. 2010;110(3):489–98. pmid:20526612
  48. 48. Hodges PW, Bui BH. A comparison of computer-based methods for the determination of onset of muscle contraction using electromyography. Electroencephalogr Clin Neurophysiol. 1996;101(6):511–9. pmid:9020824
  49. 49. Ranavolo A, Mari S, Conte C, Serrao M, Silvetti A, Iavicoli S, et al. A new muscle co-activation index for biomechanical load evaluation in work activities. Ergonomics. 2015;58(6):966–79. pmid:25555042
  50. 50. Chatterjee S. A New Coefficient of Correlation. J Am Stat Assoc. 2021;116(536):2009–22.
  51. 51. Sadeghi B. Chatterjee Correlation Coefficient: A robust alternative for classic correlation methods in geochemical studies- (including “TripleCpy” Python package). Ore Geol Rev. 2022;146:104954.
  52. 52. Hug F, Tucker K. Surface Electromyography to Study Muscle Coordination. In: Müller B, Wolf SI, Brueggemann G-P, Deng Z, McIntosh A, Miller F, et al., editors. Handbook of Human Motion. Cham: Springer International Publishing; 2017. p. 1–21.
    • 53. Paredes R, Crasto C, Mesquita Montes A, Arias-Buría JL. Changes in co-contraction magnitude during functional tasks following anterior cruciate ligament reconstruction: A systematic review. Knee. 2024;48:243–56. pmid:38781829
    • 54. Chalard A, Belle M, Montané E, Marque P, Amarantini D, Gasq D. Impact of the EMG normalization method on muscle activation and the antagonist-agonist co-contraction index during active elbow extension: Practical implications for post-stroke subjects. J Electromyogr Kinesiol. 2020;51:102403. pmid:32105912
    • 55. Devaprakash D, Weir GJ, Dunne JJ, Alderson JA, Donnelly CJ. The influence of digital filter type, amplitude normalisation method, and co-contraction algorithm on clinically relevant surface electromyography data during clinical movement assessments. J Electromyogr Kinesiol. 2016;31:126–35. pmid:27810649
    • 56. Ford KR, van den Bogert J, Myer GD, Shapiro R, Hewett TE. The effects of age and skill level on knee musculature co-contraction during functional activities: a systematic review. Br J Sports Med. 2008;42(7):561–6. pmid:18308891
    • 57. Voloshina AS, Kuo AD, Daley MA, Ferris DP. Biomechanics and energetics of walking on uneven terrain. J Exp Biol. 2013;216(Pt 21):3963–70. pmid:23913951
    • 58. Fiori L, Castiglia SF, Chini G, Draicchio F, Sacco F, Serrao M, et al. The Lower Limb Muscle Co-Activation Map during Human Locomotion: From Slow Walking to Running. Bioengineering (Basel). 2024;11(3):288. pmid:38534562
    • 59. Yoo H-J, Sim T, Choi A, Park H-J, Yang H, Heo HM. Quantifying coordination between agonist and antagonist muscles during a gait. J Mech Sci Technol. 2016;30:5321–8.
    • 60. Maudrich T, Tapper P, Clauß M, Falz R, Lässing J, Kenville R. Motor control strategies differ between monoarticular and biarticular quadriceps muscles during bipedal squats. Scand J Med Sci Sports. 2022;32(11):1569–80. pmid:36086908
    • 61. Alessandro C, Barroso FO, Prashara A, Tentler DP, Yeh H-Y, Tresch MC. Coordination amongst quadriceps muscles suggests neural regulation of internal joint stresses, not simplification of task performance. Proc Natl Acad Sci U S A. 2020;117(14):8135–42. pmid:32205442
    • 62. Crameri F. Scientific colour maps. Zenodo; 2023. https://doi.org/10.5281/zenodo.8409685
      • 63. Crameri F, Shephard GE, Heron PJ. The misuse of colour in science communication. Nat Commun. 2020;11(1):5444. pmid:33116149