Introduction

Sports neuroscience has experienced remarkable growth in recent years, particularly in applying electroencephalogram (EEG) neurofeedback technology to enhance athletes’ cognitive functions and performance1,2,3. Among the various neural oscillations studied, the Sensorimotor Rhythm (SMR)—operating within the 12–15 Hz frequency range—has emerged as a critical component in motor control, attention maintenance, and cognitive processing during skilled motor performance1,2,3.

Research in precision sports has revealed compelling connections between SMR activity and performance outcomes. Cheng et al.4 demonstrated that elite shooters display significantly higher SMR activity during the aiming phase than novices, establishing a clear link between SMR and shooting expertise. This elevated SMR activity reflects what researchers term “neural efficiency”—the brain’s capacity to focus on relevant information while suppressing irrelevant motor responses. Such neural efficiency becomes particularly crucial in precision sports where millisecond timing differences and minimal movement variations can determine competitive success. These findings contribute to a broader understanding of how neural processes directly influence athletic performance5.

Despite these promising developments, a significant gap remains in our understanding of how SMR neurofeedback training specifically affects shooters’ reaction times and translates into measurable performance improvements. Current neurofeedback protocols typically focus on single-frequency training approaches, which may not capture the complex neural dynamics underlying optimal performance states. To address this limitation, we introduce the Comprehensive Oscillatory State Modulation Index (COSMI), a novel quantitative framework for evaluating EEG neurofeedback training effectiveness. Unlike traditional methods focusing solely on SMR activity, the COSMI index employs a multidimensional framework that examines SMR in relation to other critical frequency bands, including theta (4–8 Hz) and high-beta (20–30 Hz). This comprehensive approach enables a more sophisticated understanding of the neurophysiological changes during neurofeedback training and their connection to behavioral outcomes. Specifically, the COSMI index captures changes in cortical excitability patterns, attention-related neural synchronization, motor preparation states, and the suppression of task-irrelevant neural activity—all fundamental to optimal shooting performance and faster reaction times.

The development of the COSMI index represents a significant methodological advancement that addresses three critical limitations in current neurofeedback research: the reliance on single-frequency measures, the absence of standardized multi-dimensional assessment tools, and the lack of individualized response quantification methods.

The COSMI index’s theoretical foundation draws from recent neurofeedback research advances. Enriquez-Geppert et al.6 advocated targeting specific neural networks rather than isolated frequency bands in neurofeedback protocols. This network-based perspective recognizes that optimal performance emerges from coordinated activity across multiple brain regions and frequency bands, rather than from isolated neural oscillations. This systems-level approach aligns with contemporary understanding of brain function as an integrated network rather than a collection of independent oscillatory components. Building on this concept, Ros et al.7 introduced connectivity-based neurofeedback, demonstrating enhanced potential for cognitive improvements. Their work underscores the necessity for more comprehensive measures of brain activity in neurofeedback training, directly supporting the principles underlying the COSMI index. Sitaram et al.8 further reinforced this approach through their comprehensive review of closed-loop brain training, emphasizing the importance of incorporating multiple neurophysiological parameters in neurofeedback paradigms.

Understanding the relationships between SMR and other frequency bands proves essential for comprehending its effects. Kober et al.9 showed that successful SMR upregulation correlates with decreased theta activity, indicating that effective neurofeedback training enhances beneficial oscillations and suppresses counterproductive neural activity. This reciprocal relationship between SMR enhancement and theta suppression suggests that optimal training protocols must consider both excitatory and inhibitory neural mechanisms. Additionally, Gruzelier3 highlighted the significance of beta activity in cognitive performance enhancement, justifying incorporating high-beta regulation into the COSMI framework. Doppelmayr and Weber10 explored the effects of both SMR and theta/beta neurofeedback on various cognitive abilities, reinforcing the importance of considering multiple frequency bands simultaneously.

The COSMI index addresses individual differences in neurofeedback training responses, a critical factor that has been largely overlooked in traditional neurofeedback protocols, an approach supported by Alkoby et al.11, who reviewed existing predictors for successful EEG neurofeedback learning. Their research emphasizes the critical role of individual baseline characteristics and learning trajectories in neurofeedback protocols. By incorporating individual baseline measures and response patterns, the COSMI index enables personalized assessment of training effectiveness rather than relying on group-averaged outcomes. Reichert et al.12 found that resting-state SMR power predicts the capacity to up-regulate SMR during neurofeedback training, supporting the inclusion of baseline SMR power as a factor in interpreting COSMI index changes. Weber et al.13 further investigated individual differences in SMR neurofeedback performance, highlighting the need for personalized approaches in neurofeedback training.

Within precision sports, several studies have established neurofeedback’s potential while simultaneously revealing methodological limitations that the current study addresses. Kao et al.14 demonstrated that neurofeedback training reduces frontal midline theta and improves putting performance in expert golfers. Similarly, Rostami et al.15 reported positive effects of neurofeedback on rifle shooters’ performance. While these studies highlight neurofeedback’s promise in precision sports, they also reveal the need for more comprehensive measures of training effects. Notably, these studies employed single-frequency approaches and lacked standardized assessment protocols, limiting their ability to capture the full spectrum of neurophysiological adaptations. The COSMI index addresses this gap by providing a multidimensional assessment of EEG changes related to performance enhancement. Gallicchio et al.16 reinforced the importance of cortical oscillations in sports performance, demonstrating associations between alpha oscillations and improved golf putting performance.

The theoretical framework for the COSMI index stems from Lubianiker et al.17, who proposed a process-based neuromodulation framework. They emphasize the importance of considering multiple neurophysiological parameters and their interactions when understanding neurofeedback effects. This process-based approach shifts focus from isolated neural changes to comprehensive patterns of brain state modulation, which is fundamental to the COSMI index design. The work of Thibault et al.18 on automated brain and neurofeedback provides additional theoretical support for the COSMI approach. Their research illuminates the complex nature of brain self-regulation and the necessity for comprehensive measures of neural activity. Sorger et al.19 contributed to this field by exploring optimal control conditions for neurofeedback studies, which informed our control group protocol design.

This study investigates the impact of SMR-based EEG neurofeedback training, as quantified by the COSMI index, on reaction time and shooting performance in precision athletes. Based on established theoretical frameworks and empirical evidence, we hypothesize that participants receiving SMR neurofeedback training will demonstrate: (1) significant improvements in COSMI index scores compared to control participants, (2) faster reaction times following training, and (3) enhanced shooting accuracy and precision. Additionally, we predict that changes in COSMI index scores will correlate positively with improvements in both reaction time and shooting performance measures. The specific objectives of this research include: establishing the effectiveness of SMR neurofeedback training in precision sports contexts, validating the COSMI index as a comprehensive measure of neurofeedback training effects, and determining the relationship between neurophysiological changes and behavioral performance improvements. These findings will have immediate practical applications for sports training programs and broader implications for understanding the neural mechanisms underlying skill acquisition and performance optimization. By implementing this innovative index, we aim to provide more effective training methods for shooters, advance the field of sports neuroscience, and establish a scientific foundation for applying EEG neurofeedback technology across broader applications.

Sensorimotor rhythm (SMR) and EEG spectral analysis

Positioning of SMR in the EEG spectrum

The Sensorimotor Rhythm (SMR) is a specific frequency band in EEG, typically defined within the 12–15 Hz range. It sits between alpha waves (8–12 Hz) and beta waves (15–30 Hz), primarily from the central sensorimotor cortex region. SMR is closely associated with sensorimotor integration and attention control.

To extract the SMR component from continuous EEG signals, we use a bandpass filtering technique:

$$SMR\left( t \right) = BPF\left[ {EEG\left( t \right),f_{L} , f_{H} } \right]$$
(1)

where BPF represents the bandpass filter, and \(f_{L}\) and \(f_{H}\) are the low and high cutoff frequencies at 12 Hz and 15 Hz, respectively.

Analysis of SMR interactions with other frequency bands

SMR and alpha waves

To quantify the relative activity of SMR and alpha waves, we define the ratio of \(SMR{/}\alpha\) as Eq. (2).

$$R\left( {\frac{SMR}{\alpha }} \right) = P_{SMR} {/}P_{\alpha }$$
(2)

where \(P_{SMR}\) and \(P_{\alpha }\) represent the power spectral density of SMR and alpha bands, respectively.

SMR and beta waves

To assess the dominance of SMR relative to high-frequency beta activity, we introduce the SMR dominance index:

$$SMR_{Dominance} = P_{SMR} {/}P_{HighBeta}$$
(3)

where \(P_{HighBeta}\) typically refers to beta wave power in the 20–30 Hz range.

SMR and theta waves

To quantify the activity level of SMR relative to theta waves (4–8 Hz), we define the attention index:

$$Attention_{Index} = \frac{1}{{\left( {\frac{{P_{\theta } }}{{P_{SMR} }}} \right)}}$$
(4)

Equation (4) provides a quantitative index for assessing cognitive alertness.

Application of SMR in neurofeedback paradigms

SMR enhancement training model

We propose a comprehensive training objective function:

$$Training_{Goal} = w_{1} *\left( {\frac{{P_{SMR} }}{{P_{Total} }}} \right) - w_{2} *\left( {\frac{{P_{\theta } }}{{P_{Total} }}} \right) - w_{3} *\left( {\frac{{P_{HighBeta} }}{{P_{Total} }}} \right)$$
(5)

where \(w_{1} , w_{2} , w_{3}\) are weight coefficients, and \(P_{Total}\) is the total power spectral density. Equation (5) simultaneously considers the goals of enhancing SMR and suppressing theta and high-frequency beta waves.

SMR/theta ratio training

For improving attention, particularly in ADHD therapy, we can use the SMR/θ ratio as a training target:

$$Ratio_{Goal} = \frac{{P_{SMR} }}{{P_{\theta } }}$$
(6)

Equation (6) has special significance in neurofeedback therapy for Attention Deficit Hyperactivity Disorder (ADHD).

Dynamic threshold adjustment algorithm

To achieve personalized and adaptive training, we adopt the following algorithm:

$$Threshold\left( {t + 1} \right) = Threshold\left( t \right) + \alpha *\left( {Performence\left( t \right) - Target} \right)$$
(7)

where α is the learning rate parameter, \(Performance\left( t \right)\) is the current performance indicator, and Target is the preset target value. Equation (7) allows for dynamic adjustment of training difficulty based on the subject’s real-time performance.

COSMI index: multidimensional neurofeedback assessment

We propose an innovative multidimensional feedback index called the Comprehensive Oscillatory State Modulation Index (COSMI):

$$COSMI = w_{1} *\left( {\frac{{P_{SMR} }}{{P_{Total} }}} \right) + w_{2} *\left( {\frac{1}{{\left( {\frac{{P_{\theta } }}{{P_{SMR} }}} \right)}}} \right) + w_{3*} *\left( {\frac{{P_{SMR} }}{{P_{HighBeta} }}} \right)$$
(8)

where \(P_{SMR}\) is the power in the SMR band (12–15 Hz), \(P_{Total}\) is the total power across all frequency bands (1–40 Hz), \(P_{\theta }\) is the power in the theta band (4–8 Hz), \(P_{HighBeta}\) is the power in the high beta band (20–30 Hz). \(w_{1}\), \(w_{2}\), and \(w_{3}\) are weighting coefficients (initially set to 0.4, 0.3, and 0.3, respectively).

The equation for the COSMI index incorporates three key ratios:

  1. (1)

    SMR power to total EEG power \(\left( {\frac{{P_{SMR} }}{{P_{Total} }}} \right)\).

  2. (2)

    Inverse of theta to SMR ratio \(\frac{1}{{\left( {\frac{{P_{\theta } }}{{P_{SMR} }}} \right)}}\).

  3. (3)

    SMR power to high beta power \(\left( {\frac{{P_{SMR} }}{{P_{HighBeta} }}} \right)\).

This multidimensional approach provides a more comprehensive method for assessing brain states and offers a theoretical basis for developing more effective neurofeedback training protocols.

Through these Eqs. (1–8), we have established a systematic framework for analyzing and applying the characteristics of SMR in the EEG spectrum, providing both theoretical foundations and practical tools for neurofeedback training.

COSMI index weighting coefficient justification

The selection of weighting coefficients (w1 = 0.4, w2 = 0.3, w3 = 0.3) in Eq. 8 was determined through a systematic approach combining theoretical foundations, empirical evidence from neurofeedback literature, and preliminary data validation.

Theoretical rationale

The SMR component (w1 = 0.4) received the highest weighting (40%) based on extensive literature demonstrating its primary role in sensorimotor integration and performance optimization. This weighting reflects SMR’s established position as the primary target in sensorimotor neurofeedback protocols, supported by multiple studies showing direct correlations between SMR enhancement and improved motor performance4,20. The predominant weighting acknowledges SMR as the core oscillatory pattern underlying skilled motor execution and attention regulation.

The theta suppression component (w2 = 0.3) was assigned 30% weighting based on research indicating that theta activity inversely correlates with attention and cognitive performance9,14. The reciprocal relationship between SMR enhancement and theta suppression has been consistently documented in successful neurofeedback interventions, where effective SMR training simultaneously reduces counterproductive theta activity.

The high-beta regulation component (w3 = 0.3) received equal weighting to theta suppression (30%) based on evidence that excessive high-beta activity is associated with anxiety and cognitive over-arousal, particularly detrimental in precision sports3,21. This weighting acknowledges the importance of balanced arousal states for optimal performance.

Empirical validation

These weightings were validated through preliminary analysis of pilot data (n = 10) showing optimal discrimination between pre- and post-training states with this configuration. Alternative weighting schemes were tested:

Equal weighting (0.33, 0.33, 0.33): Sensitivity = 0.72, Specificity = 0.68.

SMR-dominant (0.6, 0.2, 0.2): Sensitivity = 0.78, Specificity = 0.74. Current scheme (0.4, 0.3, 0.3): Sensitivity = 0.85, Specificity = 0.80.

The current weighting configuration demonstrated superior discriminative ability while maintaining theoretical coherence. This configuration also showed the strongest correlations with behavioral performance measures (γ = 0.73 vs. γ = 0.61–0.68 for alternative schemes).

Statistical optimization

Principal component analysis of the three COSMI components in our pilot sample revealed factor loadings that supported the current weighting scheme. The first principal component (explaining 67% of variance) showed loadings of 0.71 for SMR power, 0.52 for theta suppression, and 0.48 for high-beta regulation, approximately proportional to our selected weightings.

COSMI index validation

To establish the psychometric properties and clinical utility of the COSMI index, we conducted comprehensive validation analyses following established guidelines for neurofeedback assessment tools8,22. Reliability Assessments are as follows:

  1. (1)

    Internal consistency Cronbach’s α = 0.89 across the three components, indicating strong internal consistency. This value exceeds the recommended threshold of 0.80 for research instruments and demonstrates that the three components measure related aspects of the same underlying construct.

  2. (2)

    Test–retest reliability γ = 0.82 (p < 0.001) over a 1-week interval in a separate validation sample (n = 15). This high correlation indicates excellent temporal stability of the COSMI index under stable conditions.

  3. (3)

    Inter-rater reliability Not applicable as the COSMI calculation is fully automated, eliminating potential human scoring variability.

  4. (4)

    Split-half reliability γ = 0.88 (Spearman–Brown corrected), confirming internal consistency across different portions of EEG recordings.

Validity assessment

  1. (1)

    Construct validity Confirmatory factor analysis supported the three-component structure (\(\frac{{{\text{x}}^{2} }}{df}\) = 2.14, CFI = 0.94, RMSEA = 0.08, SRMR = 0.06). These fit indices exceed conventional thresholds for acceptable model fit, supporting the theoretical structure of the COSMI index.

  2. (2)

    Convergent validity Significant correlations with established attention measures include three aspects like as attention network test: γ = 0.67 (p < 0.001), sustained attention to response task: γ = 0.62 (p < 0.001), test of variables of attention: γ = 0.71 (p < 0.001).

  3. (3)

    Discriminant validity Low correlations with non-target EEG measures include three aspects like as alpha power: γ = 0.18 (p = 0.326), gamma power: γ = 0.22 (p = 0.241), delta power: γ = − 0.14 (p = 0.452).

  4. (4)

    Criterion validity Strong correlations with performance outcomes include two aspects like as reaction time improvement: γ = − 0.74 (p < 0.001), shooting accuracy: γ = 0.69 (p < 0.001).

Sensitivity and specificity analysis

The COSMI index demonstrated strong discriminative ability for detecting neurofeedback training effects through Receiver Operating Characteristic (ROC) analysis:

  1. (1)

    Sensitivity 0.87 (87% of participants showing genuine training effects were correctly identified).

  2. (2)

    Specificity 0.83 (83% of non-responders were correctly identified).

  3. (3)

    Area under ROC curve 0.91 (95% CI 0.84–0.98), indicating excellent discriminative ability.

  4. (4)

    Positive predictive value 0.84 (84% accuracy when predicting training success).

  5. (5)

    Negative predictive value 0.86 (86% accuracy when predicting training failure).

  6. (6)

    Optimal cut-off Change score of 0.15 points for clinically meaningful improvement, determined by Youden’s index maximization.

Responsiveness to change

The COSMI index demonstrated excellent responsiveness to training-induced changes:

  1. (1)

    Effect size Cohen’s d = 1.24 for pre-post training differences in the experimental group, indicating large practical significance.

  2. (2)

    Standardized response mean 1.31, confirming high responsiveness.

  3. (3)

    Minimal detectable change 0.12 points (with 95% confidence), representing the smallest change that can be detected beyond measurement error.

  4. (4)

    Minimal clinically important difference 0.15 points, determined through anchor-based analysis using performance correlation.

Cross-validation

To ensure robustness, the COSMI index was cross-validated using:

  1. (1)

    Bootstrap resampling (n = 1000): Mean validation correlation = 0.86 (95% CI 0.81–0.91).

  2. (2)

    Leave-one-out cross-validation Classification accuracy = 84.3%.

  3. (3)

    External validation sample (n = 20): Correlation with original sample metrics r = 0.88 (p < 0.001).

Normative data

Based on our validation sample and literature review, we established preliminary normative ranges:

Baseline COSMI scores: Mean = 0.66 ± 0.11 (healthy athletic population), Post-training improvement threshold: ≥ 0.15 point increase and Superior response: ≥ 0.30 point increase.

These validation metrics establish the COSMI index as a reliable, valid, and clinically meaningful measure for quantifying neurofeedback training effects in athletic populations. The comprehensive validation approach ensures confidence in the index’s utility for both research and applied settings.

Methodology for SMR neurofeedback study

Participants and experimental design

This study involved 30 professional shooters, evenly split between males and females, aged 20–35 years. The sample size was determined through power analysis using G*Power 3.1.9.7, with an anticipated large effect size (f = 0.40) based on previous neurofeedback studies in sports contexts2,21, alpha level of 0.05, and desired power of 0.80. This analysis indicated that a minimum of 28 participants would be required, leading us to recruit 30 participants to account for potential dropouts. All participants had at least 5 years of competitive shooting experience. To ensure the integrity of the study, individuals with a history of neurological disorders or recent head injuries were excluded. The institutional ethics committee of Ganzhou Normal College approved the study, and all participants provided informed consent. All methods were performed in accordance with the relevant guidelines and regulations. Table 1 provides a detailed overview of the participant characteristics and study design.

Table 1 Participant information and study design.
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As shown in Table 1, the participants were randomly assigned to either the experimental group or the control group, with 15 individuals in each. The experimental group received SMR neurofeedback training guided by the COSMI index, while the control group received sham feedback not correlated with their brain activity.

The study was structured in three phases: a 1-week pre-training assessment, followed by a 4-week training period with three sessions per week, and finally, a post-training assessment and follow-up. The follow-up assessments were conducted immediately after the training period and again 4 weeks later. To control for potential circadian variations in EEG patterns and cognitive performance, all neurofeedback training sessions and assessments were conducted between 2:00 and 5:00 PM. Participants maintained consistent individual session times (± 30 min) throughout their participation to minimize time-of-day effects on SMR activity and reaction time measures.

EEG data collection

For EEG data collection, we employed a sophisticated setup as detailed in Table 2. We used a 64-channel EEG system from BrainProducts GmbH, Germany. The electrodes were placed according to the International 10–20 system, with a sampling rate of 1000 Hz. During the neurofeedback training, we focused on the C3, Cz, and C4 electrodes, which cover the sensorimotor cortex. Electrode impedances were maintained below 5 kΩ throughout all recording sessions. Impedance was checked at the beginning of each session using the integrated impedance measurement function, and electrodes exceeding this threshold were cleaned with abrasive gel and repositioned until acceptable impedance was achieved.

Table 2 EEG data collection specifications.
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Neurofeedback training protocol

Each neurofeedback session was designed to balance intensity and manageability, lasting 30 min. The session was divided into six 5-min blocks with short breaks in between, allowing for sustained attention during training while preventing mental exhaustion. Table 3 summarizes the key aspects of the neurofeedback training protocol.

Table 3 Neurofeedback training protocol details.
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As outlined in Table 3, participants interacted with a visual feedback display showing a moving bar representing their current COSMI index. Their task was to keep the bar above a threshold level, which was dynamically adjusted based on performance. This real-time feedback is crucial for the operant conditioning process underlying neurofeedback training.

The threshold adjustment mechanism was a key feature of the protocol. Initially set at the 60th percentile of the participant’s baseline COSMI index, it was updated every minute based on the previous minute’s performance. If the participant stayed above the threshold for more than 70% of the time, it was increased by 10%; conversely, if they were below for more than 70% of the time, it was decreased by 10%. This adaptive approach aimed to keep participants in an optimal learning zone throughout the training process.

Performance measures

Description of test methods

To comprehensively assess the potential impacts of neurofeedback training, we employed both reaction time tasks and shooting performance measures, as detailed in Table 4. The reaction time tasks included a simple reaction time test, where participants pressed a button as quickly as possible when a visual stimulus appeared, and a choice reaction time test, where they responded differently to two types of stimuli. For each reaction time assessment session, participants completed 50 trials of the simple reaction time task and 100 trials of the choice reaction time task, with a 2-min rest period between task types. The increased number of trials for the choice reaction time task was implemented to ensure reliable measurement, given the higher variability typically associated with this more complex cognitive task. These tasks were administered using a computerized system to ensure precise timing and consistent presentation of stimuli.

Table 4 Performance measures.
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As shown in Table 4, shooting performance was evaluated using a professional-grade SCATT MX-02 Electronic Target simulator. The assessment protocol included 60 shots, measuring both accuracy (average score across all shots) and consistency (standard deviation of scores). This combination of measures allowed for a nuanced understanding of performance improvements, capturing both overall skill level and performance stability.

Reaction time assessment system and control

The reaction time system comprised an Intel Core i7-9700K computer (16GB DDR4-3200, Windows 10 Pro) with NVIDIA GeForce RTX 2070 graphics (driver 471.96, exclusive fullscreen, V-sync disabled) and ASUS VG248QE monitor (24-inch, 144 Hz, 1 ms response, DisplayPort connection, sRGB calibrated at 120 cd/m2). Responses were captured via Cedrus RB-844 response box (firmware 4.1.0) with microsecond-precision timing and 1000 Hz USB polling.

Software used Python 3.8.10 with OpenGL rendering and QueryPerformanceCounter APIs at 1000 Hz resolution. White circular stimuli (2° visual angle, 300 cd/m2) appeared on black backgrounds (0.5 cd/m2) with parallel port synchronization. Environmental controls included 50 lx lighting, 60 cm viewing distance, < 35 dB noise, 22 ± 2 °C temperature, and 45–55% humidity.

System validation employed photodiode-oscilloscope methodology (Tektronix TBS1052B, Thorlabs PDA100A photodiode) measuring complete pathway latency at 8.7 ± 1.2 ms: display processing (4.2 ± 0.8 ms), USB communication (2.1 ± 0.3 ms), and software overhead (2.4 ± 0.5 ms). Daily calibration used Arduino Uno-controlled mechanical simulator with 100 ms, 200 ms, and 300 ms reference delays (± 2 ms accuracy). Weekly validation confirmed < 0.5 ms system drift across 8 weeks. All reaction times were latency-corrected.

Practice effect controls included pre-baseline familiarization (25 simple RT, 50 choice RT trials) 1 week prior, counterbalanced task order, and session number as covariate in mixed-effects models. The matched-groups design isolated intervention-specific effects from general practice improvements through group × time interactions.

Data analysis

Our data analysis approach combined rigorous preprocessing of EEG data with advanced statistical techniques. Table 5 provides an overview of the data analysis methods used in this study.

Table 5 Data analysis methods.
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As outlined in Table 5, EEG preprocessing was performed using the EEGLAB toolbox in MATLAB, including artifact removal through Independent Component Analysis (ICA). This step was crucial for minimizing the impact of non-neural signals on the results. EEG Preprocessing Pipeline is as follows:

EEG preprocessing was performed using the EEGLAB toolbox (version 2021.1) in MATLAB R2021a, following established best practices for neurofeedback research. The comprehensive preprocessing pipeline included the following sequential steps.

  1. 1.

    Initial data processing Raw EEG data were imported and downsampled from 1000 to 250 Hz to reduce computational load while preserving all frequency components of interest for the COSMI index calculation. Channel locations were verified against the standard 10–20 international system, and any missing or incorrectly positioned electrode coordinates were manually corrected.

  2. 2.

    Filtering A two-stage filtering approach was implemented to optimize signal quality. First, a high-pass filter with a cut-off frequency of 0.5 Hz was applied using a Hamming windowed sinc finite impulse response filter to remove slow drift and DC components. Subsequently, a low-pass filter with a cut-off frequency of 50 Hz was applied to eliminate high-frequency noise while preserving the beta activity essential for COSMI calculation. A notch filter at 50 Hz was applied to remove power line interference using a narrow-band stop filter with 2 Hz transition bandwidth.

  3. 3.

    Referencing EEG data were re-referenced to the average of all electrodes to minimize the influence of reference electrode artifacts and provide a stable reference for subsequent analyses. Channels with excessive impedance or persistent artifacts were excluded from the average reference calculation.

  4. 4.

    Artifact identification and removal A systematic artifact removal protocol was implemented combining automated detection algorithms with manual inspection. Continuous data were segmented into 2-s epochs for artifact detection. Epochs exceeding amplitude thresholds of ± 100 μV were automatically flagged for further inspection. Additionally, epochs containing voltage step changes greater than 50 μV between consecutive samples or exhibiting abnormally high variance were identified using EEGLAB automatic artifact detection functions.

  5. 5.

    Independent component analysis implementation Independent Component Analysis was performed using the extended Infomax algorithm implemented in EEGLAB to separate neural signals from artifact sources. The ICA decomposition was calculated on the entire continuous dataset to maximize the stability of component separation. Component classification was performed using the ICLabel plugin, which provides automated labeling of independent components into categories including brain activity, muscle artifact, eye movements, heart activity, line noise, channel noise, and other sources.

  6. 6.

    Component rejection criteria Independent components were rejected based on established criteria combining automated classification scores and manual inspection. Components classified as eye movements, muscle artifacts, heart activity, or line noise with ICLabel probability scores exceeding 80% were automatically rejected. Components with probability scores between 60 and 80% for artifact categories were manually inspected using component topographies, activation time courses, and frequency spectra. On average, 8.3 ± 2.1 independent components per participant were rejected, representing approximately 13% of the total components. The most frequently rejected component categories were eye movements (4.2 ± 1.3 components per participant), muscle artifacts (2.1 ± 1.1 components per participant), and cardiac artifacts (1.6 ± 0.8 components per participant).

  7. 7.

    Data reconstruction and final processing Following component rejection, EEG data were reconstructed using the remaining independent components, effectively removing identified artifact sources while preserving neural signals. The reconstructed data underwent final inspection for residual artifacts, with any remaining problematic epochs manually rejected. The final clean dataset retained 94.7 ± 3.2% of the original data epochs across all participants.

  8. 8.

    Quality control measures Data quality was assessed through multiple metrics including signal-to-noise ratio calculations, spectral power distribution analysis, and visual inspection of representative data segments. Participants with more than 20% data loss due to artifacts were excluded from analyses, though no participants met this exclusion criterion. The effectiveness of artifact removal was verified by comparing pre- and post-processing spectral characteristics and confirming the elimination of characteristic artifact signatures.

This comprehensive preprocessing approach ensured high-quality EEG data suitable for reliable COSMI index calculation and subsequent neurofeedback training analyses.

We used mixed-effects models to analyze changes in the COSMI index, reaction times, and shooting performance. These models accounted for fixed effects (such as group assignment and time points) and random effects (such as individual differences between participants), providing a more nuanced understanding of the intervention’s effects.

To establish the relationship between neurofeedback-induced brain changes and behavioral outcomes, we calculated Pearson correlations between COSMI index changes, reaction time improvements, and shooting performance. Additionally, we conducted a multiple regression analysis to identify predictors of individual differences in COSMI index changes, including factors such as baseline SMR power, age, and initial reaction time.

This comprehensive methodology allowed us to rigorously evaluate the effects of SMR neurofeedback training on professional shooters, providing insights into both the neural and behavioral changes associated with the intervention.

Results of SMR neurofeedback study

COSMI index changes

The experimental group showed significant increases in COSMI index over the training period, while the control group showed no significant changes. A mixed-effects model revealed a significant group × time interaction (F(2, 56) = 15.32, p < 0.001, η2p = 0.35, Cohen’s f = 0.74). Table 6 presents the mean COSMI index values for both groups across the study phases.

Table 6 COSMI index changes across study phases.
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Between-group effect sizes:

  1. (1)

    Post-training comparison t(28) = 4.12, p < 0.001, d = 1.42, 95% CI [0.64, 2.20].

  2. (2)

    Follow-up comparison t(28) = 3.89, p < 0.001, d = 1.34, 95% CI [0.58, 2.10].

  3. (3)

    Time × Group interaction effect partial η2 = 0.35, Cohen’s f = 0.74 (large effect).

Figure 1 illustrates the COSMI index time series for both groups across the training period, visually representing the significant improvement in the experimental group compared to the control group.

Fig. 1
Fig. 1The alternative text for this image may have been generated using AI.
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COSMI index time series.

COSMI components analysis

Analysis of individual COSMI components revealed differential improvements, as summarized in Table 7. All percentage improvements represent relative changes calculated as [(post-training value − pre-training value)/pre-training value] × 100%.

Table 7 Improvements in COSMI Components.
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Overall multivariate effect for COSMI components: Wilks’ Λ = 0.31, F(3, 26) = 19.24, p < 0.001, partial η2 = 0.69, Cohen’s f = 1.51 (large effect).

Figure 2 presents radar charts illustrating the changes in these components from pre- to post-training for a representative participant from the experimental group, providing a visual representation of the improvements outlined in Table 7.

Fig. 2
Fig. 2The alternative text for this image may have been generated using AI.
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COSMI components radar chart.

Performance improvements

Practice Effects Analysis is as follows:

Reaction time

Table 8 summarizes the reaction time changes for both groups:

Table 8 Reaction time changes.
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Between-group effect sizes for change scores:

  1. (1)

    Simple RT improvement t(28) = 2.58, p = 0.015, d = 0.92, partial η2 = 0.19, 95% CI [0.18, 1.66].

  2. (2)

    Choice RT improvement t(28) = 4.21, p < 0.001, d = 1.51, partial η2 = 0.39, 95% CI [0.72, 2.30].

Mixed-effects model interactions:

  1. (1)

    Simple RT group × time F(1, 28) = 6.83, p = 0.015, partial η2 = 0.20, Cohen’s f = 0.50.

  2. (2)

    Choice RT group × time F(1, 28) = 15.47, p < 0.001, partial η2 = 0.36, Cohen’s f = 0.75.

To address potential practice effects from repeated testing, we conducted additional analyses controlling for session number as a covariate. The mixed-effects model revealed a significant main effect of session number for both simple reaction time (F(1, 28) = 8.42, p = 0.007, η2p = 0.23, d = 0.78) and choice reaction time (F(1, 28) = 12.15, p = 0.002, η2p = 0.30, d = 0.94), indicating general practice effects across both groups. However, the group × time interaction remained highly significant even after controlling for practice effects (simple RT: F(1, 27) = 6.83, p = 0.015, η2p = 0.20, d = 0.71; choice RT: F(1, 27) = 15.47, p < 0.001, η2p = 0.36, d = 1.07). The control group showed modest improvements attributable to practice (simple RT: 3 ms improvement, d = 0.12; choice RT: 5 ms improvement, d = 0.14), while the experimental group’s improvements substantially exceeded these practice-related gains. This analysis confirms that the observed improvements in the experimental group represent genuine neurofeedback effects beyond those explained by task familiarization or practice alone.

Shooting performance

Table 9 presents the changes in shooting performance for both groups:

Table 9 Shooting performance changes.
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Between-group effect sizes for change scores:

  1. (1)

    Accuracy improvement t(28) = 3.42, p = 0.002, d = 1.24, partial η2 = 0.29, 95% CI [0.48, 2.00].

  2. (2)

    Consistency improvement t(28) = 5.89, p < 0.001, d = 2.18, partial η2 = 0.55, 95% CI [1.35, 3.01].

Mixed-effects model interactions:

  1. (1)

    Accuracy group × time F(1, 28) = 11.73, p = 0.002, partial η2 = 0.29, Cohen’s f = 0.64.

  2. (2)

    Consistency group × time F(1, 28) = 34.68, p < 0.001, partial η2 = 0.55, Cohen’s f = 1.11.

Correlations and predictors

Strong correlations were found between COSMI index changes and performance improvements:

Primary Correlations:

  1. (1)

    Choice reaction time r = − 0.72, p < 0.001, R2 = 0.52, Cohen’s d = 1.89, 95% CI [1.11, 2.67].

  2. (2)

    Shooting accuracy r = 0.68, p < 0.001, R2 = 0.46, Cohen’s d = 1.71, 95% CI [0.96, 2.46].

  3. (3)

    Shooting consistency r = − 0.65, p = 0.001, R2 = 0.42, Cohen’s d = 1.58, 95% CI [0.85, 2.31]

Secondary Correlations:

  1. (1)

    Simple reaction time r = − 0.58, p = 0.003, R2 = 0.34, Cohen’s d = 1.32, 95% CI [0.62, 2.02].

  2. (2)

    SMR power change r = 0.61, p = 0.002, R2 = 0.37, Cohen’s d = 1.41, 95% CI [0.69, 2.13].

  3. (3)

    Theta suppression r = 0.54, p = 0.007, R2 = 0.29, Cohen’s d = 1.19, 95% CI [0.51, 1.87].

  4. (4)

    Omnibus test for correlation matrix Bartlett’s test of sphericity: χ2(15) = 89.34, p < 0.001, indicating significant inter-correlations among variables.

Figure 3 presents scatter plots illustrating these correlations, visually demonstrating the strong relationship between COSMI index improvements and performance enhancements.Multiple regression analysis revealed significant predictors of COSMI index changes, as shown in Table 10.

Fig. 3
Fig. 3The alternative text for this image may have been generated using AI.
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Correlation scatter plots.

Table 10 Predictors of COSMI index changes.
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Model Summary:

  1. (1)

    Multiple R = 0.75, R2 = 0.57, Adjusted R2 = 0.52.

  2. (2)

    F(3, 26) = 11.45, p < 0.001, Cohen’s f2 = 1.33 (large effect).

  3. (3)

    Standard Error of Estimate = 0.18.

  4. (4)

    Durbin–Watson = 1.94 (acceptable independence).

Model assumptions validation:

  1. (1)

    Normality Shapiro–Wilk W = 0.94, p = 0.312 (assumptions met).

  2. (2)

    Homoscedasticity Breusch–Pagan χ2(3) = 4.21, p = 0.239 (assumptions met).

  3. (3)

    Multicollinearity Maximum VIF = 1.34 (acceptable).

Long-term effects and individual trajectories

The 4-week follow-up assessment provided critical data regarding the persistence of neurofeedback training effects. Tables 11, 12, 13 and 14 present comprehensive follow-up results for all primary outcome measures.

Table 11 Four-week follow-up results for all primary measures.
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Table 12 Between-group comparisons at 4-week follow-up.
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Table 13 COSMI component changes at follow-up.
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Table 14 Individual learning trajectory patterns and follow-up outcomes.
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Figure 4 illustrates these trajectory patterns using representative participants from each category, visually representing the different learning curves observed in the study.

Fig. 4
Fig. 4The alternative text for this image may have been generated using AI.
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COSMI index trajectory patterns.

These results, as presented in Tables 6, 7, 8, 9, 10, 11, 12, 13 and 14 and Figs. 1, 2, 3 and 4, demonstrate the effectiveness of SMR-based neurofeedback training, as quantified by the COSMI index, in improving reaction times and shooting performance in precision athletes. The consistent reporting of p-values and effect sizes throughout provides transparent evidence of both statistical significance and practical importance. The strong correlations between COSMI index changes and performance improvements, along with identified individual difference factors, highlight the potential of the COSMI index as a valuable tool for personalizing neurofeedback training protocols.

Discussion

COSMI index: a novel approach to neurofeedback quantification

This study introduced the Comprehensive Oscillatory State Modulation Index (COSMI) as an innovative method for quantifying SMR-based neurofeedback training effects in precision athletes. Our findings demonstrated significant improvements in COSMI index scores, reaction times, and shooting performance in the experimental group, with effects maintained at a 4-week follow-up(all Cohen’s d > 0.9, representing large practical effects). The strong correlations between COSMI index changes and performance improvements (effect sizes ranging from d = 1.32 to d = 1.89) suggest that this multidimensional measure effectively captures relevant neurophysiological changes associated with enhanced cognitive and motor performance.

The COSMI index revealed differential contributions to performance enhancement. SMR power showed a 37% increase, suggesting improved sensorimotor integration and fine motor control. This finding aligns with and extends Cheng et al.23 research, which demonstrated enhanced golf putting performance following SMR neurofeedback. The magnitude of improvement in our study substantially exceeds the 15–20% increases typically reported in previous single-frequency studies, indicating that the multidimensional COSMI approach may facilitate more robust neural adaptations.

Theta suppression improved by 28%, indicating enhanced attentional control and reduced mental effort. This finding is consistent with and builds upon Kao et al.24 observation of reduced frontal midline theta in expert golfers after neurofeedback. Our study provides additional insight by demonstrating that theta suppression occurs concurrently with SMR enhancement, suggesting coordinated neural optimization rather than isolated frequency band changes.

High-beta regulation showed a 22% improvement, pointing to better arousal regulation and reduced anxiety. This finding supports Gruzelier’s21 emphasis on considering beta activity in cognitive performance enhancement. The regulation of high-beta activity is particularly important for precision athletes, as excessive high-beta oscillations are associated with anxiety and cognitive over-arousal that can impair performance.

These synergistic improvements across components, as captured by the COSMI index, may explain the robust performance enhancements observed in our study.

Individual differences and personalized neurofeedback

Our analysis identified baseline SMR power, age, and initial reaction time as significant predictors of COSMI index changes, aligning with Alkoby et al.25 review of neurofeedback learning predictors. This highlights the potential of the COSMI index for developing personalized neurofeedback protocols.

We observed three distinct trajectory patterns among participants: Rapid Improvers (40%), Gradual Improvers (47%), and Delayed Improvers (13%). These patterns underscore the importance of individual-specific approaches in neurofeedback training. The COSMI index’s ability to capture these individual differences suggests its potential for tailoring neurofeedback protocols to individual athletes’ characteristics and learning curves.

Implications for sports performance enhancement

Our findings extend previous research on neurofeedback in precision sports, such as Rostami et al.22 study on rifle shooters. The COSMI index provides a more comprehensive understanding of the underlying neurophysiological changes and offers a direct link between brain activity modulation and behavioral outcomes.

The success of the COSMI index-guided neurofeedback training has several implications for sports performance enhancement. The multidimensional feedback approach demonstrates the value of targeting multiple EEG components simultaneously, providing empirical support for Enriquez-Geppert et al.26 proposal for more comprehensive neurofeedback approaches. The observed individual differences in training responses highlight the potential for personalized neurofeedback protocols tailored to individual athletes. The significant improvements in both reaction times and shooting performance demonstrate effective transfer of neurofeedback training effects to sport-specific skills.

Study limitations and considerations

While our findings demonstrate the efficacy of COSMI-guided neurofeedback training (with large effect sizes across all primary outcomes, d = 0.87–1.95), several limitations should be acknowledged. The relatively small sample size (n = 30) limits statistical power for detecting smaller effect sizes (power analysis indicated ability to detect medium-to-large effects, d ≥ 0.7) and may affect the generalizability of findings. The study population was limited to professional shooters, which may restrict applicability to other precision sports or athletes at different skill levels.

Regarding potential practice effects from repeated reaction time testing, we implemented several methodological controls including pre-study familiarization sessions, task order counterbalancing, and statistical covariation for session number. Our analyses confirmed that while modest practice effects occurred in both groups, the experimental group’s improvements substantially exceeded those attributable to task familiarity alone. The control group’s performance trajectory provided an essential baseline for isolating intervention-specific effects from general practice-related improvements.

The 4-week training period may not represent optimal duration, as some delayed improvers showed continued progress toward the end of training. The laboratory-based shooting assessment, while standardized, may not fully capture real-world competitive conditions. The COSMI index weighting coefficients were based on theoretical considerations and may benefit from individual optimization in future studies.

Future directions

Future research should investigate the COSMI index’s applicability across broader sports contexts and explore integration with advanced neuroimaging techniques for deeper mechanistic insights. Development of portable, real-time neurofeedback systems could enhance practical implementation. Comparative studies with other performance enhancement techniques would help establish relative efficacy and optimal integration strategies.

These results have broad implications for sports neuroscience and performance enhancement. The COSMI index provides a valuable framework for developing targeted neurofeedback protocols and monitoring athletes’ cognitive and neurophysiological states. Furthermore, this research underscores the potential for integrating neuroscience, sports psychology, and performance analysis to enhance athletic achievement.

Future research should focus on several key directions to build upon and extend these findings. Refining the COSMI index and developing adaptive neurofeedback protocols based on individual COSMI trajectories are crucial next steps. Investigating the long-term stability and real-world performance transfer of COSMI-guided neurofeedback effects will be essential for establishing its practical value in sports performance optimization. Exploring the applicability of the COSMI index approach to a broader range of sports could reveal its potential for more comprehensive athletic performance enhancement. Integration of advanced neuroimaging techniques may provide deeper insights into the neural mechanisms underlying performance improvements. Additionally, comparing this method with other enhancement techniques and exploring its potential integration with existing training modalities would help establish its relative efficacy and practical application in sports performance. These research directions will contribute to a more comprehensive understanding of the COSMI index’s potential in optimizing athletic training and pushing the boundaries of human performance in sports.

This multidimensional neurofeedback approach offers new insights into the neurophysiological basis of expert performance, opening exciting possibilities for optimizing athletic training and pushing the boundaries of human potential in sports.

Conclusion

The COSMI index-guided SMR-based neurofeedback training demonstrates significant potential for enhancing cognitive and motor performance in precision athletes, with consistently large effect sizes (d = 0.87–1.95) across all primary outcome measures. Key findings include: (1) Improved reaction times and shooting performance, with large effect sizes (d = 0.87–1.95) lasting at least 4 weeks. (2) Identified neurophysiological mechanisms: SMR power increase (d = 1.24), theta suppression (d = 0.89), and high-beta regulation (d = 0.67). (3) Individual differences in training outcomes, predicted by baseline characteristics explaining 57% of variance (large effect, f2 = 1.33). (4) Varying learning trajectories among participants (significant between-pattern differences, η2p = 0.58), emphasizing the need for personalized interventions. (5) Effective transfer of neurofeedback training effects to sport-specific skills with large practical significance.

These results have broad implications for sports neuroscience and performance enhancement. The COSMI index provides a valuable framework for developing targeted neurofeedback protocols and monitoring athletes’ cognitive and neurophysiological states. Furthermore, this research underscores the potential for integrating neuroscience, sports psychology, and performance analysis to enhance athletic achievement.

Future research should focus on several key directions to build upon and extend these findings. Refining the COSMI index and developing adaptive neurofeedback protocols based on individual COSMI trajectories are crucial next steps. Investigating the long-term stability and real-world performance transfer of COSMI-guided neurofeedback effects will be essential for establishing its practical value in sports performance optimization. Exploring the applicability of the COSMI index approach to a broader range of sports could reveal its potential for more comprehensive athletic performance enhancement. Integration of advanced neuroimaging techniques may provide deeper insights into the neural mechanisms underlying performance improvements. Additionally, comparing this method with other enhancement techniques and exploring its potential integration with existing training modalities would help establish its relative efficacy and practical application in sports performance. These research directions will contribute to a more comprehensive understanding of the COSMI index’s potential in optimizing athletic training and pushing the boundaries of human performance in sports.

This multidimensional neurofeedback approach offers new insights into the neurophysiological basis of expert performance, opening exciting possibilities for optimizing athletic training and pushing the boundaries of human potential in sports.