Participants

The study included nine patients with a clinical diagnosis of muscle spasticity secondary to neurological conditions such as cerebral palsy or stroke. The spasticity level was classified using the MTS, under the supervision of a trained physiotherapist independent from the physiotherapist responsible for conducting the evaluation procedure

Participants were prospectively recruited from the neuromuscular rehabilitation unit of a public healthcare institution in southwestern Colombia between November and December 2023. Inclusion criteria included clinically documented spasticity, age ≥ 18 years, ability to cooperate during the evaluation protocol, and overall medical stability. Exclusion criteria included recent orthopedic surgery (within the past six months), active infections, and the use of muscle relaxants or botulinum toxin within seven days prior to assessment.

Demographic data including sex, age, height, weight, body mass index (BMI), diagnosis, and type of spasticity were collected through a structured interview conducted prior to evaluation and recorded using a standardized study form. These variables are detailed in Table 3. All participants or their legal guardians, when applicable, signed a written informed consent form prior to enrollment.

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Table 3. Individual participant characteristics (n = 9).

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The study was approved by the Ethics Committee of the Health Care Unit of Mercaderes (Approval No. 02–2023, Minutes No. 09), and all procedures were carried out in accordance with the ethical principles set forth in the Declaration of Helsinki, the Belmont Report, and the U.S. Code of Federal Regulations.

Surface electromyography (sEMG)

The Myo Armband (Thalmic Labs), a portable device equipped with eight Ag/AgCl electrodes (10 mm diameter, 20 mm inter-electrode distance), was used to record neuromuscular activity from the belly of the biceps brachii on the affected limb. The signal was acquired at 1 kHz, within a ± 5 mV range and 16-bit resolution. A third-order Butterworth filter (20–500 Hz) was then applied, followed by signal rectification and smoothing using a 100 ms moving window. Synchronization with other devices was achieved via external time stamps.

Inertial measurement unit (IMU)

The WT901BLECL sensor (WitMotion) was fixed to the distal segment of the forearm to capture kinematic variables. The system integrates a triaxial accelerometer (±16 g), triaxial gyroscope (±2000^◦/s), and magnetometer (±4900 µT), operating at a sampling rate of 100 Hz. Calibration procedures were applied to compensate for drift and offset. The data were used to compute angular velocity (rad/s), linear acceleration (m/s²), and joint angles via the Madgwick sensor fusion algorithm.

Sensorized glove

A custom glove was designed with nine resistive force sensors (FSR 402, Interlink Electronics; range: 0.1–10 N; resolution: ± 0.05 N) distributed across the distal phalanges and palm of the evaluator’s hand. The FSRs were connected to an Arduino Nano microcontroller (50 Hz) via voltage divider circuits. Each sensor was individually calibrated using reference weights (0.5–10 N) and fitted with a third-order polynomial model (R² > 0.98) to convert voltage outputs into force values.

Experimental protocol

An experimental protocol was implemented based on the synchronized integration of Q_j, ω, and sEMG recordings during standardized passive mobilizations according to the MTS. This approach enabled simultaneous and objective characterization of both mechanical stiffness and neuromuscular excitability associated with spasticity. Signal acquisition was carried out under controlled conditions, applying slow (V1) and fast (V3) stretches sequentially, as established by the MTS.

During the protocol, a trained physiotherapist, equipped with the sensorized glove and IMU sensor performed passive mobilizations of the participant’s elbow, ensuring full joint range under both conditions. The Fig 1 illustrates the practical implementation of the multimodal system in the clinical setting. It shows the evaluator’s position and sensor arrangement: the glove on the physiotherapist’s dominant hand and an IMU sensor on the wrist for monitoring movement velocity an IMU on the patient’s distal forearm, and the sEMG electrodes aligned on the belly of the spastic biceps muscle. This setup enabled simultaneous, non-invasive, and structured capture of the key domains involved in the spastic phenomenon.

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Fig 1. Implementation of the multimodal system during clinical spasticity assessment in the upper limb.

The physiotherapist is shown using the FSR-equipped sensorized glove and wears an IMU on the wrist, while the patient is instrumented with an IMU on the distal forearm and sEMG electrodes placed over the biceps brachii muscle.

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Evaluation procedure

Each participant was evaluated in a seated position, with the shoulder in neutral adduction and the affected elbow initially in maximum passive flexion. All assessments were performed by the same trained physiotherapist equipped with the sensorized glove on the dominant hand, performed standardized passive elbow mobilizations in accordance with MTS guidelines. The protocol included two passive stretch conditions. First, a slow stretch (V1) was applied at a controlled angular velocity of approximately 5◦/s, covering the full joint range from maximal flexion to full extension to identify the R2 angle, corresponding to the passive elongation limit without reflex activation. Then, a fast stretch (V3) was applied at approximately 100◦/s, intended to elicit the muscle’s reflex response and determine the R1 angle, defined as the initial point of spastic resistance or “catch.” To minimize potential evaluation bias, manual clinical classification using the MTS was independently performed by a different physiotherapist, ensuring separation between clinical assessment and instrumented evaluation. Although formal blinding was not implemented during the assessment, the use of objective sensor-based measurements reduces the influence of observer-related bias.

Fig 2 shows the procedure sequence. Fig 2A represents the initiation of the slow stretch (V1) from maximum flexion to determine R2. Fig 2B illustrates the transition toward full extension, while Fig 2C shows the fast stretch phase (V3), during which the R1 angle is identified through the spastic reflex.

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Fig 2. Schematic sequence of the passive elbow evaluation protocol.

(A) Slow stretch (V1) from maximal flexion to determine R₂. (B) Transition phase toward joint extension. (C) Fast stretch (V3) to elicit the spastic reflex and determine the R₁ or “catch” angle. The system includes FSR sensors in the evaluator’s glove, an IMU on the forearm, and an sEMG system over the biceps brachii.

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The order of application was kept constant, with V1 followed by V3, including a 10-second interval between both conditions to reduce the effect of reflex preactivation.

Each condition was repeated three consecutive times to ensure measurement consistency. During fast stretches, the sensorized glove recorded in real time the generalized force Qj applied by the physiotherapist on the patient’s forearm. A sudden increase in this force was interpreted as the onset of spastic resistance (R1). Simultaneously, an IMU fixed on the distal forearm recorded the angular velocity ω, verifying that predefined kinematic criteria were met. Additionally, an sEMG system captured neuromuscular reflex activity in the biceps brachii, complementing the objective analysis with neurophysiological data. This configuration enabled the synchronized acquisition of biomechanical and neuromuscular signals, including generalized force, angular velocity, and neuromuscular excitability. These signals were subsequently processed to derive simple indicators, which were then integrated into the Composite Index.

Data processing

All collected data were processed offline using MATLAB R2023a (MathWorks Inc., Natick, MA, USA) to extract quantitative biomechanical and neurophysiological measures.

Signals from the sensorized glove were converted into force units (Newtons) using third-order polynomial calibration curves fitted with standard weights ranging from 0.5 to 10 N. The signals were then smoothed to eliminate high-frequency noise and obtain a continuous temporal profile of the resistance force exerted during each stretch cycle.

IMU data were filtered by using a 5 Hz low-pass filter and processed to extract elbow joint kinematics, including sagittal plane angular position, instantaneous angular velocity, and acceleration. From these signals, the R₂ angle (maximum elongation without reflex activation) and R₁ angle (onset of the spastic “catch”) were determined according to the MTS protocol. The difference between these angles, expressed as ∆R = R₂ − R₁, was used as a differential clinical parameter to characterize spasticity severity.

The Q_j was estimated by using a spatial transformation based on a 3D glove model, incorporating specific angles and distances of each FSR sensor relative to the estimated hand center of mass. This transformation enabled calculation of linear (Q_T) and rotational (Q_R) force moments for each recorded sample, providing a more accurate biomechanical interpretation of the therapeutic interaction.

Simultaneously, sEMG signals were preprocessed with a third-order bidirectional Butterworth filter with a 20–500 Hz passband. The signals were then rectified and smoothed using a 100 ms moving window to obtain the linear envelope of neuromuscular activation. Activation latency was calculated as the time interval between the onset of the fast stretch (V3 condition) and the significant increase in the EMG signal, along with peak amplitude and the integral following the reflex response, as representations of the excitability of the spastic muscle.

To integrate sEMG and biomechanical signals, a cross-correlation analysis was performed between the sEMG envelope and the Q_j signal, enabling synchronization and highlighting the reflex delay between mechanical stimulus and muscle activation (see Fig 3).

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Fig 3. Temporal synchronization between the filtered sEMG signal of the biceps and the generalized force (Q_j) during fast stretching.

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Additionally, a three-dimensional visualization of Q_j, angular position (θ), and mean angular velocity (ω) was generated, as shown in Fig 4. This representation allowed the observation of biomechanical response patterns and relevant kinetic events during passive stretch, supporting the visual validation of the signal processing and subsequent analysis.

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Fig 4. Three-dimensional mapping of the generalized force(Q_j), angular position (θ), and mean angular velocity (ω).

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Simple indicators for spasticity assessment

The accuracy and effectiveness of a CI directly depends on the methodological robustness and clinical relevance of the selected simple indicators. These indicators must meet criteria such as high quality, sensitivity to change, adequate sampling frequency, and reliable data availability [40]. In this study, three fundamental domains were identified for spasticity assessment: generalized force (via FSR sensors), joint angular velocity (via IMU), and surface electromyographic activity (sEMG).

For these signals, the Area Under the Curve (AUC) was adopted as the primary approach to quantitatively estimate the neuromuscular response to stretch. AUC provides an integrated measure that combines magnitude and temporal duration, which is particularly relevant in spasticity where both reflex response and passive resistance depend on the intensity and time evolution of the stimulus [41–43]. This approach allows differentiation between passive movement phases, such as the angle at which the spastic reflex appears (R1) and the maximum elongation without reflex (R2), enabling a more precise characterization of muscle dynamics.

The validity of AUC is not limited to clinical contexts. In sports science, it has been used to analyze neuromuscular efficiency during eccentric and concentric contractions, and to assess load management under fatigue or explosive effort conditions [44,45]. To illustrate, it has proven useful in characterizing hamstring and quadriceps performance during sprinting and direction changes, where stride stiffness and ground contact time are influenced by the muscle’s load-absorbing capacity [46].

From an instrumental standpoint, AUC also offers computational advantages. Its implementation is efficient and less susceptible to artifacts or high-frequency noise, as temporal integration smooths out irregularities without requiring aggressive filtering. This makes it a reliable metric in high-variability clinical settings and real-time applications [47].

In this study, six simple AUC-based indicators were computed: two for each signal type (FSR, IMU, sEMG) under R1 and R2 conditions. These variables were normalized by using min-max scaling and Z-score standardization, then subjected to correlation and principal component analysis (PCA) to verify independence and reduce informational redundancy.

For reference, the derived simple indicators are summarized in Table 1, which specifies each metric’s origin and corresponding condition. These indicators serve as the foundation for the CI integration described in the next section.

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Table 1. Simple indicators for spasticity assessment.

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Composite Index integration

The CI was developed to synthesize six biomechanical and neuromuscular simple indicators into a single, quantitative measure of spasticity severity. These variables, derived from the area under the curve (AUC) of signals recorded during the MTS protocol and represent different physiological aspects of spasticity, including passive stiffness, reflex activation, and dynamic resistance. Data were acquired using FSR (force), sEMG (muscle activity), and IMU (angular velocity) sensors during both slow (R2) and fast (R1) stretches.

A structured four-step methodology was implemented to ensure the internal validity of the CI, encompassing normalization, redundancy analysis, weight refinement and final aggregation, as visually summarized in Fig 5.

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Fig 5. Methodological framework for Composite Index (CI) construction.

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1. (1). Normalization: All six AUC-based indicators were first normalized using min–max scaling to ensure comparability and remove unit dependency. Those where higher raw values indicated lower spasticity (e.g., force at R1) were inverted to maintain interpretability. After normalization, all features were aligned so that higher values reflect greater spasticity.
2. (2). Independence analysis: To reduce redundancy and preserve the unique contribution of each feature, statistical independence was assessed via pairwise Pearson correlation tests. Table 2 presents the corresponding p-values. A p-value < 0.05 was considered statistically significant.

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Table 2. P-values between simple indicators.

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Notably:

• AUC sEMG (R2) was significantly correlated with AUC sEMG (R1) (p = 0.0045) and AUC Velocity (R2) (p = 0.0033).
• AUC sEMG (R1) also showed correlation with AUC Velocity (R1) (p = 0.0062).
• These findings revealed partial redundancy, particularly among the neuromuscular and kinematic simple indicators during fast stretches. In contrast, AUC Force (R1) and AUC Force (R2) showed weaker correlations (p > 0.5), suggesting higher informational independence.

1. (3). Weight refinement: The weighting strategy used in the CI was designed to be transparent, mathematically justified, and internally valid. Initially, each of the six normalized indicators was assigned an equal weight (1/6), following the principle of uniform importance when no clear hierarchy is established [40]. To quantify the degree of redundancy, we computed a significant correlation count for each indicator. This was defined as the number of pairwise correlations (out of the five possible) with a p-value < 0.05, based on Pearson correlation tests (see Table 2). This count was used as a proxy for feature overlap:
   • Indicators with more significant correlations were considered more redundant and were softly penalized in the final weighting.
   • Indicators with fewer or no significant correlations were deemed more independent and were favored with higher weights.
   • For example, AUC sEMG (R2) exhibited two statistically significant correlations one with AUC sEMG (R1) and one with AUC Velocity (R2) while AUC Force (R1) showed no significant correlation with any other indicator. As a result, the former received a moderate weight, and the latter was prioritized.

This approach reflects a quantitatively motivated heuristic, inspired by methods of correlation-based feature weighting often applied in composite indices and machine learning contexts [48,49]. It minimizes multicollinearity and reinforces the contribution of informationally distinct indicators, thereby improving the robustness and interpretability of the CI. Within this framework, it should be acknowledged that the weighting scheme is derived from statistical relationships identified within a limited sample and is therefore inherently sensitive to cohort specific patterns. Consequently, the assigned weights represent an internally consistent configuration specific to this study, rather than a universally established or generalizable weighting structure. The stability and generalizability of this weighting approach should be further examined through cross-validation and external validation.

The refined weights assigned to each normalized metric were as follows:

p₁ = 0.20 (AUC Force (R2))

p₂ = 0.20 (1 – AUC Force (R1))

p₃ = 0.20 (AUC sEMG (R2))

p₄ = 0.10 (1 - AUC sEMG (R1))

p₅ = 0.10 (AUC Vel. (R2))

p₆ = 0.20 (1 – AUC Vel. (R1))

It is important to note that although AUC sEMG (R2) presented moderate statistical redundancy, it was retained with a balanced weight due to its distinct physiological significance. Specifically, this feature captures baseline muscle activation during slow passive stretch, which reflects non-reflex hypertonia, a clinically relevant manifestation of spasticity not accounted for by reflex mediated variables alone. This sustained neuromuscular activity, often linked to increased muscle tone at rest, plays a crucial role in functional limitations and treatment response. Therefore, the influence of AUC sEMG (R2) in the CI despite its correlation with other variables was preserved to ensure coverage of this important physiological dimension.

1. (4). Aggregation: Once all six indicators were normalized and assigned refined weights, the CI was calculated through a weighted linear aggregation, a standard method used in multi-criteria assessment frameworks and composite index construction [40,48]. This approach enables a transparent and interpretable synthesis of multidimensional data into a single score that reflects the severity of spasticity.

The final expression of the CI is as follows:

CI = p₁ AUC Force (R2) + p₂· (1 − AUC Force (R1))

+ p₃· AUC sEMG (R2) + p₄· (1 − AUC sEMG (R1))

+ p₅· (1 − AUC Vel. (R2)) + p₆· (1 − AUC Vel. (R1))

This formulation ensures that higher CI values correspond to greater severity of spasticity. The metric integrates contributions from both neural (e.g., reflexive sEMG, force responses) and non-neural (e.g., passive stiffness, baseline tone) sources of resistance. The weighting scheme reflects the statistical independence and informational value of each component, as established in the previous steps.

Linear aggregation was chosen due to its interpretability, additive transparency, and sensitivity preservation meaning that improvements or deteriorations in one component (e.g., reduced AUC sEMG) directly translate to proportional changes in the overall CI, provided all other components remain constant. This property is particularly important for clinical monitoring and longitudinal comparison.

Demographic data from the pilot study

Of the nine participants, five were diagnosed with cerebral palsy and four with stroke, all of whom presented upper limb spasticity and were evaluated using the MTS. The mean age was 27 with a standard deviation of 7.9 years. Three of the nine participants were female. The demographic details are outlined in Table 3.

Multivariate analysis of simple indicators via PCA

To assess redundancy and complementarity among the simple indicators used in the construction of the CI, principal component analysis (PCA) was performed. This procedure enabled the identification of latent dimensions that explain most of the variance in the dataset and allowed visualization of the metric distribution in a reduced three-dimensional space.

Fig 6 shows the 3D biplot resulting from the PCA applied to the six AUC simple indicators, corresponding to generalized force, surface electromyography, and angular velocity under the R1 and R2 conditions of the MTS. The first three principal components explained a combined 83.85% of the total variance: 46.82% for the first dimension (Dim1), 22.36% for the second (Dim2), and 14.67% for the third (Dim3).

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Fig 6. Three-dimensional representation of the principal component analysis (PCA) applied to the normalized indicators.

The three dimensions explain 83.85% of the total variance.

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The orientation of the vectors in the multivariate space provides insight into the functional grouping of the indicators. The variables AUC Velocity (R1) and AUC Velocity (R2) had marked negative projections on Dim1, aligned with AUC Force (R1), indicating an association between reflex mechanical response and angular velocity patterns. In contrast, AUC sEMG (R2) and AUC sEMG (R1) were grouped in the opposite direction, emphasizing their distinct contribution to neuromuscular activation.

Notably, AUC Force (R2) showed a high loading on Dim3, with a value of 0.656, as shown in the factor loading matrix in Table 4. This indicates that the variable captures a distinct dimension of variability, supporting its inclusion as a non-redundant metric in the CI synthesis.

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Table 4. Factor loading matrix for the simple indicators.

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Sensitivity analysis

Validation of the proposed system was conducted on a cohort of patients with clinically diagnosed spasticity by analyzing both the simple indicators and the CI to evaluate sensitivity, relevance, and discrimination capability. The aim was to determine each metric’s contribution to CI variability, thereby enhancing clinical interpretability of spasticity.

Fig 7 shows the analysis estimates of each metric’s relative impact on total index variability, reflecting its discriminative power.

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Fig 7. Sensitivity coefficients for each simple indicator contributing to the CI: AUC Force (R2), AUC Force (R1), AUC sEMG (R2), AUC sEMG (R1), AUC Velocity (R2), and AUC Velocity (R1).

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Results indicate that AUC sEMG (R2) has the highest sensitivity coefficient (≈ 0.33), making it the most influential metric in characterizing spastic behavior. Similarly, AUC sEMG (R1) and AUC Velocity (R2) also displayed relatively high sensitivity values, suggesting that both early reflex activation and angular velocity during full stretch are relevant in objectively describing spasticity.

Conversely, AUC Force (R1) showed the lowest sensitivity value, suggesting a reduced influence on the CI. This may be attributed to the tendency of spasticity to manifest more intensely at higher elongation and velocity conditions rather than during initial resistance.

Fig 8 presents individual CI values for each evaluated subject. Each patient has two records: one for the spastic limb and one for the contralateral side, identified with the suffix “s.” This coding enables intra-individual comparison of neuromuscular behavior between limbs, facilitating detection of spastic asymmetries and possible compensatory mechanisms.

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Fig 8. Composite Index values for evaluated patients.

The suffix “s” denotes the contralateral non-spastic side.

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Considerable variability in CI values was observed across participants. For example, patients P1 and P7 exhibited high CI values on the spastic side, indicating greater passive resistance and heightened reflex activation, typical of increased muscle tone. In contrast, patients P9 and P8 showed lower CI values, suggesting either lower spasticity or effective neuromuscular adaptation.

In most cases, significant differences were noted between body sides, confirming the CI’s utility in detecting unilateral alterations characteristic of neurological lesions.

Correlation analysis between simple indicators and the Modified Tardieu Scale

To assess the relationship between the biomechanical and neurophysiological simple indicators obtained during the R1 and R2 conditions of the assessment protocol, a cross-correlation analysis was conducted. Fig 9 shows the scatter plots for all pairwise combinations of AUC values in generalized force, angular velocity, and surface EMG, coded by MTS level.

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Fig 9. Scatter plots between pairs of simple indicators (AUC values for force, velocity and sEMG) for the spastic limb.

Key findings from the analysis include.

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• AUC Force (R2) vs. AUC sEMG (R2): A moderate positive correlation was observed (r = 0.58), indicating that increased reflex activation (sEMG) is associated with greater passive resistance during rapid stretch.
• AUC Force (R2) vs. AUC sEMG (R1): No significant correlation was found, suggesting that low-speed neuromuscular activity does not directly predict passive resistance under rapid conditions.
• AUC Force (R2) vs. AUC Velocity (R2): A moderate negative correlation was found (r = −0.46), indicating that higher angular stretch velocities are associated with lower measured resistance.
• AUC Velocity (R2) vs. AUC sEMG (R2): A moderate inverse trend was noted (r = −0.48), suggesting that higher velocities may correspond to decreased reflex activity.
• AUC sEMG (R2) vs. AUC sEMG (R1): High consistency in neuromuscular response was observed between fast and slow stretches (r = 0.81, p < 0.01).

Combinations such as AUC Force (R1) vs. AUC Velocity (R2) and AUC sEMG (R1) vs. AUC Velocity (R2) showed no significant correlations, suggesting that each metric captures complementary aspects of spasticity.

Table 5 summarizes the ANOVA results comparing CI scores across clinically stratified spasticity groups. The between-group sum of squares was 0.11, the within-group (residual) sum was 0.05, yielding a total variance of 0.16. The resulting F-statistic was 6.38 with a corresponding p-value of 0.03, indicating a statistically significant difference between group means (p < 0.05).

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Table 5. One-way ANOVA results applied to the CI.

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This confirms that the CI reflects not only individual biomechanical and neurophysiological characteristics but is also sensitive to clinical classification of spasticity. This discrimination is attributable to the influence of key contributing indicators identified earlier, such as AUC sEMG (R2), AUC sEMG (R1), and AUC Velocity (R2), which showed high sensitivity in the integration model.

Fig 10 shows the descriptive comparison of composite performance scores (I_d) across clinical spasticity levels based on body regions affected by abnormal tone, as per the MTS. In this horizontal error-bar plot, each point represents the mean I_d for MTS levels 2, 3, and 4, with standard error of the mean (SEM), facilitating intra-group variability interpretation.

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Fig 10. Descriptive comparison of composite performance (I_d) across clinical levels of the MTS, considering only body regions affected by muscle tone abnormalities.

Each point indicates the mean for levels 2 (blue), 3 (gray), and 4 (red), with corresponding standard error of the mean (SEM).

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Results reveal that the highest average Id occurred in level 2 spasticity (mean = 0.47, 95% Confidence Interval: 0.39–0.55), followed by level 4 (mean = 0.45, 95% Confidence Interval: 0.31–0.60), and level 3 (mean = 0.42, 95% Confidence Interval: 0.36–0.48). This trend suggests that in muscle tone–affected regions, lower clinical spasticity grades are associated with better biomechanical and neuromuscular performance.

The observed effect size (η² = 0.68) indicates a strong association between Composite Index scores and spasticity severity, with 68% of the total variance explained by differences between spasticity levels. While the statistical analysis yielded a significant F-value (p = 0.03), the small sample size may limit the precision of variance estimates. A post hoc power analysis based on the observed η² suggests adequate power to detect large effects; however, the limited number of participants per group may increase the risk of a Type II error failing to identify smaller, yet clinically meaningful differences

While mean values for levels 2 and 4 are close, the wider dispersion in level 4 may reflect greater functional heterogeneity among patients with severe spasticity. These findings highlight the CI’s capacity to sensitively reflect functional differences associated with spastic tone severity.