Coactivation Index in Neuromuscular Control

• Coactivation Index (CI) is an operational measure of the simultaneous activation of antagonistic muscles, capturing both stiffness-setting and neural preparatory roles.
• It employs task-specific EMG processing and normalization—such as integrated EMG ratios or torque equivalence—to assess neuromuscular balance.
• CI findings vary with task demands, offering insights in contexts like visuo-haptic tracking and cycling to optimize motor control and feedback responses.

Searching arXiv for the papers on arXiv and directly related coactivation work. Coactivation Index (CI) denotes an operational measure of simultaneous activation of antagonistic muscle groups, used to summarize how strongly a neuromuscular system coactivates flexor–extensor or agonist–antagonist muscles during a task. In the recent motor-control literature, CI is not a single standardized quantity. Instead, it appears as task-specific quantification of coactivation derived from electromyographic data, torque-equivalent activation estimates, or integrated EMG over mechanically relevant movement phases. This variability is itself a central point: one perspective paper explicitly states that it does not introduce a single formal “Coactivation Index (CI)” definition or formula, while experimental studies operationalize CI in distinct ways depending on whether the goal is to estimate wrist stiffness in visuo-haptic interaction or flexor–extensor balance during cycling (Maurus et al., 2024, Borner et al., 2022, Ahmadi et al., 25 Jul 2025).

1. Conceptual definition and scope

Muscle coactivation is defined as “the simultaneous activation of agonist and antagonist muscles - muscles that act in opposite direction at a given joint” (Maurus et al., 2024). Within this framework, CI functions as a compact descriptor of the extent to which opposing muscle groups are concurrently active. In the cooperative wrist-tracking study, the index is explicitly tied to simultaneous activation of antagonistic wrist muscles as a means of stiffening the arm during a visuo-haptic task (Borner et al., 2022). In the cycling study, CI is used as one of three complementary descriptors of lower-limb neuromuscular coordination and is intended to capture how strongly flexor and extensor muscles around a joint are coactive during the mechanically demanding parts of the pedal cycle (Ahmadi et al., 25 Jul 2025).

A central conceptual distinction in the literature is between coactivation as a biomechanical stiffening strategy and coactivation as a neural preparatory state. The perspective on fast feedback control argues that muscle coactivation is not just a way to stiffen joints or raise mechanical impedance. Instead, it is presented as a way to prime the nervous system for fast, flexible, task-dependent feedback control. In that view, simultaneous activation of agonist and antagonist muscles can prepare the motor system so that, when a disturbance or sensory error occurs, the nervous system can rapidly generate excitation of agonists, inhibition of antagonists, or a combination of both (Maurus et al., 2024).

This suggests that CI should not be interpreted solely as a surrogate for joint stiffness. In some studies it is used precisely for that purpose, but in the broader sensorimotor literature coactivation is also treated as a state variable relevant to reflex gain, sensory processing, and feedback routing.

2. Mathematical formulations and operational definitions

No single cross-study CI equation is established in the papers considered here. The most direct consequence is that any technical use of CI must be read together with the task model, signal model, and normalization convention of the specific study.

Paper	Operationalization of CI	Core interpretation
"Physically interacting humans regulate muscle coactivation to improve visuo-haptic perception" (Borner et al., 2022)	Normalized average of $u(t)=\min\{\tau_f(t),\tau_e(t)\}$ over a 20 s trial	Antagonistic wrist coactivation / stiffness-setting strategy
"Quantifying lower-limb muscle coordination during cycling using electromyography-informed muscle synergies" (Ahmadi et al., 25 Jul 2025)	Ratio of integrated flexor EMG to total flexor-plus-extensor EMG in joint-specific critical phases	Joint-specific flexor–extensor balance during cycling
"Muscle coactivation primes the nervous system for fast and task-dependent feedback control" (Maurus et al., 2024)	No formal CI formula introduced	Coactivation as a neural preparatory state rather than a purely mechanical quantity

In the wrist-tracking study, instantaneous muscle coactivation is defined as

$u(t)\equiv \min\{\tau_f(t),\tau_e(t)\},$

where $\tau_f(t)$ and $\tau_e(t)$ are torque-equivalent activations inferred from the flexor and extensor EMG signals, respectively. Trial-level average coactivation is then

$$\overline{u}\equiv \frac{1}{T}\int_0^T u(t)\,dt,\qquad T=20\text{ s},$$

and the population-comparison quantity is the within-participant normalized value

$$u_n\equiv \frac{\overline{u}-\overline{u}_{\min}}{\overline{u}_{\max}-\overline{u}_{\min}}.$$

In that paper, the CI corresponds to this normalized average coactivation $u_n$ (Borner et al., 2022).

In the cycling study, CI is instead defined as a ratio of integrated EMG from flexor muscles to the total integrated EMG from flexors and extensors at a joint: $$CI_{\text{hip}}=\frac{iEMG_{RF}}{iEMG_{RF}+iEMG_{BF}},$$

$$CI_{\text{knee}}=\frac{iEMG_{BF}+iEMG_{GM}}{iEMG_{BF}+iEMG_{GM}+iEMG_{RF}+iEMG_{VM}+iEMG_{VL}},$$

$$CI_{\text{ankle}}=\frac{iEMG_{TA}}{iEMG_{TA}+iEMG_{GM}+iEMG_{SOL}}.$$

The authors state that a $u(t)\equiv \min\{\tau_f(t),\tau_e(t)\},$0 indicates relatively greater flexor activity, whereas $u(t)\equiv \min\{\tau_f(t),\tau_e(t)\},$1 indicates relatively greater extensor activity, and that these values are computed during critical phases of pedaling in which each joint experiences at least $u(t)\equiv \min\{\tau_f(t),\tau_e(t)\},$2 of its maximum net moment (Ahmadi et al., 25 Jul 2025).

The perspective paper on feedback control does not define a CI, but it does provide a related mechanical expression,

$u(t)\equiv \min\{\tau_f(t),\tau_e(t)\},$3

to illustrate how simultaneous activation of both muscle groups constrains and enables corrective output (Maurus et al., 2024). This is not labeled as a coactivation index, but it clarifies why coactivation matters for net torque production.

3. Measurement frameworks, preprocessing, and normalization

CI measures in these studies are derived from surface EMG and depend strongly on preprocessing and calibration. In the visuo-haptic wrist study, surface EMG was recorded from the antagonist wrist-muscle pair flexor carpi radialis (FCR) and extensor carpi radialis longus (ECRL). Raw EMG was high-pass filtered at 20 Hz using a second-order Butterworth filter, rectified, and low-pass filtered at 5 Hz using a second-order Butterworth filter to obtain the EMG envelope. Calibration required wrist flexion and extension torques at $u(t)\equiv \min\{\tau_f(t),\tau_e(t)\},$4 Nm, plus a maximal co-contraction condition while resisting a 3 Hz, $u(t)\equiv \min\{\tau_f(t),\tau_e(t)\},$5 sinusoidal disturbance. A linear regression was then used to map the EMG envelope to torque, for example

$u(t)\equiv \min\{\tau_f(t),\tau_e(t)\},$6

with an analogous relation for the extensor (Borner et al., 2022).

In the cycling study, EMG was recorded bilaterally from seven muscles using a wireless Delsys Trigno system at 2.2 kHz: vastus medialis, rectus femoris, vastus lateralis, biceps femoris long head, tibialis anterior, gastrocnemius medialis, and soleus. EMG was normalized to a dynamic MVC defined as the average of the top 10% of EMG magnitudes recorded during the test. CI was then computed from signals integrated over crank angle rather than from full-trial time averaging (Ahmadi et al., 25 Jul 2025).

The choice of normalization is not a minor implementation detail. In the wrist study, $u(t)\equiv \min\{\tau_f(t),\tau_e(t)\},$7 is explicitly normalized within each participant across that participant’s trials, which allows comparison across individuals despite different absolute EMG amplitudes, but also means that CI values are relative rather than absolute across people (Borner et al., 2022). In the cycling study, the ratio form embeds a different normalization logic: CI represents a joint-specific balance between flexor and extensor contributions during defined high-demand phases rather than the magnitude of simultaneous activation in absolute units (Ahmadi et al., 25 Jul 2025).

This suggests that “CI” can refer either to a co-contraction quantity in the narrow sense of concurrent antagonistic activity or to a joint-specific flexor–extensor EMG ratio. The distinction is methodological and interpretive, not merely terminological.

4. Functional interpretation in motor control and feedback regulation

The traditional interpretation of coactivation is that it increases the intrinsic viscoelastic properties of muscle, especially stiffness and damping, thereby resisting limb motion. The feedback-control perspective explicitly acknowledges that coactivation may increase mechanical impedance and that some perturbation behavior could reflect passive or intrinsic muscle properties. Its central claim, however, is that this explanation is incomplete (Maurus et al., 2024).

That perspective argues that coactivation may prime the nervous system for fast and task-dependent responses to sensory feedback by enabling excitation of agonist muscles, inhibition of antagonist muscles, or shared contributions of both. A key implication is that if the antagonist is already inactive, it cannot be further inhibited; coactivation preserves the possibility of rapid bidirectional modulation. The same paper further argues that coactivation may help exploit automatic gain scaling of stretch reflexes, motor unit recruitment principles, muscle spindle sensitivity changes via $u(t)\equiv \min\{\tau_f(t),\tau_e(t)\},$8-$u(t)\equiv \min\{\tau_f(t),\tau_e(t)\},$9 coactivation or $\tau_f(t)$0-motor neurons, and possibly arousal or neuromodulatory systems that alter excitability across the nervous system. It also proposes that increases in muscle coactivation may shift feedback responses from fast transcortical feedback pathways to even faster spinal proprioceptive and subcortical visual circuits (Maurus et al., 2024).

The visuo-haptic study gives a complementary interpretation. There, higher CI means greater wrist stiffness, better mechanical filtering or shaping of interaction forces, more resistance to unwanted perturbations from the partner, and more ability to exploit haptic information when the partner’s motion is informative; lower CI means lower stiffness, less energetic cost, and a more compliant arm (Borner et al., 2022). The authors argue that coactivation is not just error minimization. The experimentally observed CI pattern did not match the tracking error minimization model

$\tau_f(t)$1

but was instead better explained by an optimal information and effort model with cost

$\tau_f(t)$2

where

$\tau_f(t)$3

In that interpretation, CI reflects a compromise between minimizing prediction error in target estimation and minimizing metabolic effort (Borner et al., 2022).

In the cycling study, CI is interpreted in explicitly joint-specific terms. Reduced knee CI with increasing power is taken as a sign of more efficient neuromuscular control, because the central nervous system reduces unnecessary antagonist activity at the knee to maximize net knee torque. Increased ankle CI with increasing power is interpreted as a strategy to improve joint stiffness and stability under higher force demands, whereas stable hip CI suggests maintenance of the hip’s agonist–antagonist balance across workloads (Ahmadi et al., 25 Jul 2025).

5. Empirical patterns across tasks

In cooperative visuo-haptic tracking, normalized coactivation decreased with own visual noise,

$\tau_f(t)$4

and increased with haptic noise from the partner,

$\tau_f(t)$5

The effect of visual noise was much larger than the effect of partner noise. The four interaction conditions were SS, SF, FS, and FF, and the authors reported significant differences across the combinations of visual and haptic noise except for FS vs FF ($\tau_f(t)$6) (Borner et al., 2022). The qualitative result is that participants coactivated less when their own visual feedback was fuzzy and more when the partner’s guidance was noisier.

In cycling, the main CI result was a joint-specific divergence across power levels. Hip CI remained relatively stable across power levels and showed no significant power-level differences ($\tau_f(t)$7). Knee CI decreased significantly as power increased: for the non-dominant knee, $\tau_f(t)$8 at low power level to $\tau_f(t)$9 at medium power level and $\tau_e(t)$0 at high power level; for the dominant knee, $\tau_e(t)$1 to $\tau_e(t)$2 to $\tau_e(t)$3, with the reported changes significant at $\tau_e(t)$4. Ankle CI increased significantly with power: for the non-dominant ankle, $\tau_e(t)$5 to $\tau_e(t)$6 to $\tau_e(t)$7; for the dominant ankle, $\tau_e(t)$8 at low power level to $\tau_e(t)$9 at high power level, with significant between-limb differences at the ankle across all power levels ($$\overline{u}\equiv \frac{1}{T}\int_0^T u(t)\,dt,\qquad T=20\text{ s},$$0) (Ahmadi et al., 25 Jul 2025). The headline finding is that higher cycling power reduced knee coactivation but increased ankle coactivation, while the hip stayed comparatively stable.

The feedback-control perspective does not report a single CI dataset, but it specifies recurrent experimental signatures by which coactivation is inferred: increased baseline EMG in both muscles before a perturbation; paired excitation of agonists and inhibition of antagonists after the perturbation; changes in short-latency and long-latency EMG responses; and behavioral consequences such as faster return to target or improved correction success. Examples discussed include biofeedback-induced coactivation in arm posture tasks, standing balance with coactivation, novel or variable mechanical environments, and novel visuomotor rotations without physical limb displacement. A recurring pattern is that higher pre-perturbation coactivation is associated with stronger corrective responses in both muscles after sensory disturbance (Maurus et al., 2024).

6. Limitations, ambiguities, and acronym disambiguation

Several limitations recur across the literature. First, CI is an indirect estimate of stiffness rather than a direct mechanical measurement in the visuo-haptic study, because it is inferred from EMG-derived torques rather than mechanically measured joint stiffness (Borner et al., 2022). Second, the cycling paper emphasizes that surface EMG is susceptible to crosstalk and cannot directly quantify muscle force; synergy- and CI-based interpretations are therefore only approximations of underlying neuromuscular output (Ahmadi et al., 25 Jul 2025). Third, the feedback-control perspective stresses that coactivation is not identical to stiffness, that in vivo impedance estimates are confounded by neural feedback circuits, and that antagonist forces are often ignored even though they are not negligible (Maurus et al., 2024).

Task dependence introduces a further interpretive constraint. The perspective paper explicitly notes that the biceps and triceps were defined arbitrarily as agonist and antagonist muscles in its illustrative figure and that, depending on the movement direction or corrective response to a disturbance, the role of the agonist and antagonist muscles can change (Maurus et al., 2024). This means that coactivation is not an intrinsic property of a specific muscle pair; it is a property of their functional relation in the task. The cycling paper makes a related point by using joint-specific flexor–extensor groupings, so that its CI is “really a joint-specific flexor-extensor EMG ratio rather than a simple agonist-antagonist pair co-contraction measure” (Ahmadi et al., 25 Jul 2025).

A common misconception is that “CI” has a unique meaning across disciplines. The arXiv record shows the opposite. In industrial human-robot collaboration, CI means “Comfortability Index” rather than coactivation index (Savur et al., 2023). In atomic-structure theory, CI denotes “Configuration Interaction” (Ruiz, 2013). In graph theory, a CI-group is a Cayley-isomorphism group (Dobson et al., 2012, Dobson et al., 9 Feb 2026). In bibliometrics, the CI-index is a Choquet-integral-based citation index (Yin et al., 2019). In multisensory neuroscience, the paper on dependent probability summation proposes a coactivation index for integration beyond race-model probability summation, written as $$\overline{u}\equiv \frac{1}{T}\int_0^T u(t)\,dt,\qquad T=20\text{ s},$$1 for spike counts and $$\overline{u}\equiv \frac{1}{T}\int_0^T u(t)\,dt,\qquad T=20\text{ s},$$2 for reaction times (Colonius et al., 2015). These usages are terminologically homographic but conceptually unrelated.

For the neuromuscular literature specifically, the most defensible generalization is therefore limited and precise: Coactivation Index is best understood as a family of task-dependent operational measures that quantify simultaneous antagonistic activation or flexor–extensor balance from EMG-derived quantities, with interpretation contingent on the underlying biomechanical and sensorimotor framework. The recent literature further suggests that CI should be read not only as a descriptor of stiffness-setting but also, in some contexts, as an indicator of a neural preparatory state for fast, flexible, task-dependent feedback control (Maurus et al., 2024).