Three chronic stroke survivors (age: 55.7 ± 8.1; months post-stroke: 67.7 ± 34.2; FM-UL: 38.0 ± 9.0, mean ± SD) participated in this pilot study. Data from seven healthy, right-handed individuals (mean age: 24.2 ± 2.4 years) with no history of neurological disorders were collected in our previous study (Berger et al., 2013) and were used as a healthy reference group. All participants gave written informed consent, and all procedures were conducted in conformance with the Declaration of Helsinki and were approved by the Ethical Review Board of Fondazione Santa Lucia, Rome (Italy) (CE/AG4-PROG. 222-34 and CE/PROG.899, dates of approval were 2009/03/09 and 2021/01/27, respectively).

During the experiment, participants were seated comfortably on a chair in front of a table with their UL secured in a hand-forearm orthosis immobilizing the hand, wrist, and forearm (Figure 1). The base of the splint was connected through a steel bar with a cylindrical post extension to a custom-made steel socket attached to the sensitive plate of a six-axis force/torque transducer (Delta F/T Sensor; ATI Industrial Automation), mounted underneath the table surface. This sensor recorded the isometric forces and torques generated by the participant during the execution of a virtual reaching task. The task involved applying force without any physical movement of the limb, enabling the control of a virtual object through isometric contractions.

Muscle activity was measured using surface electromyographic (EMG). Signals were recorded from 13 muscles acting on the shoulder and elbow, including the brachioradialis (BracRad), short and long heads of the biceps brachii (BicShort; BicLong), lateral and long heads of the triceps brachii (TriLat; TriLong), anterior, middle, and posterior deltoid (DeltA; DeltM; DeltP), infraspinatus (InfraSp), pectoralis major (PectMaj), teres major (TerMaj), latissimus dorsi (LatDorsi), and middle trapezius (TrapMid). EMG signals of the stroke patients were acquired using wireless active bipolar electrodes (Trigno Avanti Sensor, Delsys) and bandpass filtered (30–450 Hz). In contrast, signals from healthy subjects were recorded using active bipolar electrodes (DE 2.1, Delsys), bandpass filtered (20–450 Hz), and amplified (gain 1000, Bagnoli-16; Delsys). Both force and EMG signals were digitized at a sampling rate of 1 kHz using a National Instruments PCI-6229 data acquisition board installed in a workstation computer. To extract the muscle activation envelope, EMG signals recorded from stroke patients were rectified, low-pass filtered using a fourth-order Butterworth filter with a 1.5 Hz cutoff frequency, and averaged over non-overlapping 25 ms windows while EMG signals recorded from healthy subjects were rectified, low-pass filtered using a second-order Butterworth filter with a 5 Hz cutoff frequency, and averaged over non-overlapping 10 ms windows, see (Berger et al., 2013; Berger and d’Avella, 2014) for more details. The resulting signals were baseline-corrected and normalized to the maximum value recorded from each muscle during trials in which subjects were instructed to generate maximum force in each direction.

Healthy participants performed the task with their view of the arm occluded by a 21-inch LCD monitor, which displayed the rendering of a virtual table aligned with the real workspace (Berger et al., 2013). In contrast, stroke patients wore a Meta Quest 3s headset (Meta Platforms, Inc., CA, United States), which presented them with an immersive virtual environment (Figure 1). The virtual scene, developed using the Unity software platform (Unity Technologies, CA, United States), was designed to replicate the real laboratory setting, including a virtual table matching the dimensions of the physical one. At rest, a spherical cursor was displayed at the virtual location corresponding to the center of the participant’s palm. This cursor was constrained to move within a horizontal plane and could be used to reach spherical targets appearing within the same plane, see (Berger et al., 2013) for more details.

The computation of the cursor position was handled by the data acquisition workstation running a real-time operating system (Matlab XPC). This system processes the input signals and transmits the resulting position data to a separate workstation, generating the virtual environment. Cursor dynamics were simulated in real time using an adaptive mass-spring-damper (MSD) model, following the approach described by (Park and Meek, 1995). Depending on the control modality, the virtual mass will either be driven by the actual isometric force recorded by the transducer (force control, FC) or by an estimated force derived from the participant’s EMG signals (EMG control, EC), obtained through a linear mapping of rectified and filtered EMG data (as described below in the EMG-to-force mapping section).

EMG-to-force mapping for healthy participants: The isometric force generated at the hand is approximately a linear function of muscle activations: f = H   m where f is the generated two-dimensional force vector, m is the 13-dimensional vector of muscle activations, and H is a matrix mapping muscle activation to force (dimensions 2 × 13). The EMG-to-force mapping ( H ) was estimated using multiple linear regression of the low-pass filtered force (second-order Butterworth; 1 Hz cutoff) and the filtered EMG signals recorded during FC (dynamic phase, i.e., time from target go until the target has been reached). In healthy individuals, we have previously demonstrated that this mapping is well-structured, allowing for effective motor control in an isometric reaching task in healthy subjects (Berger et al., 2013; Berger and d’Avella, 2014; Berger and d’Avella, 2023b; Berger and d’Avella, 2023a).

EMG-to-force mapping for stroke patients: Myoelectric control relied on an individual-specific mapping matrix ( H ), which represents the relationship between the recorded EMG signals and the exerted force during FC blocks. While it is possible in principle to estimate such an H matrix for stroke patients as for healthy participants, we adopted a different approach. Stroke patients exhibit dysfunctional muscle activations characterized by co-contraction, defined as the synchronous activation of agonist and antagonist muscles (Silva et al., 2014), and spasticity, which refers to stiff or rigid muscles causing involuntary muscle contractions (Zhang et al., 2013). As a result, the H matrix derived from their muscle activity would also be dysfunctional, reflecting these abnormal activations. Using such a mapping matrix in myoelectric control may allow stroke patients to move the cursor correctly, but it would fail to induce proper motor re-learning. To overcome this limitation, we propose an alternative approach: replacing the patient-specific H matrix with a standardized functional one ( H s t d ) (see Figure 2). H s t d is obtained by averaging the individual H matrices of healthy participants, serving as a reference, ensuring a mapping matrix that reflects physiologically appropriate muscle activations.

To support the re-learning of functional muscle activation patterns, we combined the use of a standardized mapping matrix, i.e., H s t d , derived from neurologically intact individuals, with an adaptive assistive mechanism for myoelectric control implemented in a virtual reality environment. The idea is to provide patients with a training context that not only facilitates task execution but also encourages correction of dysfunctional motor strategies through continuous visual feedback. In this way, the system provides salient visual feedback on the quality of motor output and may thus help patients to improve their neuromuscular control. This approach is grounded in motor learning theory, where visual feedback (Krakauer et al., 2019) and error-based correction (Patton et al., 2006; Reisman et al., 2013) are essential to adaptation. However, rather than relying on error amplification, which may overwhelm or discourage the user (Sharp et al., 2011; Marchal-Crespo et al., 2017), we propose supporting patients’ voluntary movements within the EMG-controlled virtual reality environment by correcting, in real time, the effects of pathological muscle activations in the MAL. By reinforcing the components of functional activation patterns during task execution, this strategy is expected to guide patients toward healthier motor behaviors. We thus aim at promoting neural plasticity and functional recovery by combining voluntary effort with feedback from corrected and successful movements in VR. A central element of our approach is the ability to change visual feedback in real time based on the patient’s muscle activity. This is made possible by using a virtual reality environment, where the motion of a virtual cursor is controlled by EMG signals. When a patient’s muscle activation deviates from a healthy pattern, the system adjusts the virtual movement to correct for this, guiding the user toward a more functional strategy. This process allows us to create a form of assistance that is tailored to the individual. Instead of forcing the patient to follow a fixed path, we modify the effect of their muscle activity so that the movement remains goal-directed, even if the underlying activation is impaired. As a result, patients receive feedback that is based on their own EMG signals, helping them to better understand and gradually improve how to control their muscles. This is different from passive approaches, where the limb is simply moved by the system and the patient is not actively involved. In contrast, our method requires the patient to make voluntary efforts, which are essential for promoting brain plasticity and motor recovery. As patients get better, the level of assistance is progressively reduced. This keeps the task challenging but achievable, helping to maintain motivation and encouraging continuous improvement. With time, this feedback-based training may replace abnormal muscle patterns with healthier ones (Berger and d’Avella, 2024).

Based on these concepts, we developed an assistive-adaptive algorithm designed to enhance movement execution by projecting in real-time the recorded muscle activations m onto a reference muscle pattern m r e f for a specific target direction ( ϑ ) (Figure 3): m p r o j ϑ = P ϑ · m , with  P ϑ = m r e f ϑ · m r e f T ϑ m r e f ϑ 2

To define the direction-specific reference muscle activation pattern m r e f ϑ , we first calculated m m e d ϑ , the median muscle activation vector for each target direction ϑ across the healthy participants used to determine H s t d . Specifically, for each subject, the average EMG envelope across all repetitions of a given direction from target go until the target has been reached was calculated Then, the median vector across subjects of the direction-specific average activations was taken. This procedure provided a robust assessment of the typical activation pattern for each direction, capturing physiologically plausible features while reducing the influence of outliers or inter-subject variability. During stroke patients’ myoelectric control, muscle activations are translated into output forces via a linear mapping defined by the standardized EMG-to-force matrix ( H s t d , see 2.3). However, directly using m m e d ϑ as input to this mapping does not ensure that the resulting force H s t d · m m e d ϑ will align with the desired target. For this reason, we refined m m e d through a quadratic optimization procedure to obtain the final reference pattern m r e f ϑ . This optimization, implemented using the quadprog function in MATLAB, was subject to the constraints that the resulting force must exactly match the desired force to reach the target ( f t a r g e t ϑ = H s t d · m r e f ϑ ) and that m r e f must not have negative activations ( m r e f ≥ 0 ) . Within these constraints, the optimization aimed at maximizing the similarity between m r e f and m m e d to maintain the physiological meaning while minimizing the norm of m r e f to reduce co-contraction and promote efficient muscle activation. The objective function used for this optimization was formulated as: J m = m r e f T · m r e f − λ · m r e f T · m m e d where λ is a weighting parameter that balances the trade-off between minimizing co-contraction and preserving physiological similarity to the median activation pattern. The selection criterion was designed to ensure a stable solution. To this end, we analyzed how the norm of m r e f varied as a function of λ . The smallest value of λ at which further reductions led to changes smaller than 10 − 4 was chosen (Figure 4A). This approach identified an optimal λ value of 1.2 · 10 − 3 . At this value, the similarity between m r e f and m m e d exceeded 0.95, ensuring that the optimized activation patterns maintained a high degree of physiological plausibility while effectively reducing co-contraction. Following this optimization process, the reference muscle patterns m r e f were established for each target direction ϑ and their profiles are presented in Figure 4B.

Having defined m r e f , the assisted muscle activation m * ϑ for each target direction is determined as a weighted combination of the actual muscle pattern ( m and the muscle pattern projected on the reference pattern m p r o j : m * ϑ = 1 − α   m + α   m p r o j ϑ with α being the level of assistance that is adjusted during training. At full assistance ( α = 1 ), cursor movement aligns with the target direction, simulating optimal muscle activation. To promote active motor engagement, assistance is progressively reduced based on patient performance, ensuring a consistent level of task difficulty. As assistance decreases, deviations in cursor trajectory provide real-time feedback on the muscle activation adjustments required to achieve accurate control.

To ensure that the assisted muscle activation m * can effectively control the virtual cursor, the H s t d must be scaled to produce forces that allow to reach the target given the patient’s actual capabilities. To achieve this, an initial scaling procedure is applied based on the performance of the LAL, providing an individual measure of force generation capability in the context of the specific task. Before the first therapy session, data are collected from the LAL during isometric force control tasks, as described below in 2.6.1. Offline cursor trajectories are reconstructed using the H s t d and the m L A L *   ϑ with total assistance ( α = 1 . For each target direction, the maximum amplitude of the reconstructed force ( f L A L *   ϑ   max is computed, and a scaling factor γ ϑ is determined by dividing the force magnitude corresponding to the target distance d = f t a r g e t ϑ by this value: γ ϑ = d f L A L *   ϑ   max , with  f L A L *   ϑ = H s t d   m L A L *   ϑ

This factor ensures that the reconstructed trajectory accurately reaches the target. To obtain a single global scaling factor for H s t d the average value of γ ϑ across all the target directions is taken, and the scaled H s t d will be: H s t d s c a l e d = γ ¯   H s t d

To account for direction-specific motor impairment of the MAL, an additional scaling factor is required. In stroke patients, impairment levels may vary across movement directions and training sessions, necessitating individualized adjustments. To compute this additional scaling parameter for the MAL, the same approach used to determine γ is applied. However, instead of using data from the LAL, trajectories are reconstructed from the three force control blocks performed by the patient in the session with the MAL, as described below in 2.6.2. This reconstruction is carried out using the H s t d s c a l e d and the m M A L *    ϑ with total assistance α = 1 . Following the same procedure, the scaling parameter β ϑ is computed as: β ϑ = d f M A L *    ϑ   max , with  f M A L *    ϑ = H s t d s c a l e d   m M A L *    ϑ

A value of β = 1 indicates that the scaling for the MAL is identical to that of the LAL, providing an additional measure to assess the patient’s motor performance across different movement directions and sessions. Indeed, the scaling parameter β ϑ is updated at each session to account for potential changes in patient performance. This approach also facilitates the monitoring of parameter variations across each target direction, providing an additional metric for assessing motor learning. Now, integrating all the components described above, the final force applied to control the virtual cursor is given by: f ϑ = β ϑ   H s t d s c a l e d   m * ϑ

Each session has a maximum duration of 30 minutes, balancing therapeutic effectiveness with minimization of the patient’s fatigue. Each session consists of a series of blocks of eight trials, with each trial corresponding to one of the eight target directions spaced at 45° intervals.

Offline reconstruction of trajectories using H s t d : To investigate the feasibility of using the standardized mapping matrix H s t d , we performed offline trajectory reconstructions on data previously collected from healthy participants. EMG data recorded during the myoelectric control block were reprocessed using H s t d . Specifically, the vectors of EMG signals were multiplied by the standardized matrix to generate estimated force vectors, which were then passed through the same adaptive mass-spring-damper (MSD) filter used during real-time control. This allowed us to reconstruct the cursor trajectory that would have been generated as the subject used the standard matrix during the task.

Similarity Between Muscle Activation Patterns: To assess the effectiveness of the assistive-adaptive algorithm, we computed the similarity between the average filtered muscle activation pattern recorded during each trial and the reference activation pattern used for projection. As a measure of similarity, we computed the scalar product between the two muscle activation patterns. This measure indicates how closely the patient’s muscle activity aligns with the optimized reference pattern over the session. Higher similarity values indicate a successful adaptation to the reference functional muscle space.

Initial Direction Error: The Initial Direction Error (IDE) quantifies the angular deviation between a straight-line trajectory toward the target and the actual movement direction initiated by the participant. Specifically, the IDE is computed as the absolute angle between the target direction and the instantaneous trajectory vector measured 0.1 s after the target onset (target go). This metric provides a sensitive assessment of the accuracy of initial motor planning and the participant’s ability to generate a correct feedforward command. Lower IDE values reflect more accurate movement initiation, indicating improved motor planning and reduced neuromuscular deficits during the early phase of trajectory execution in myoelectric control.

Path Length: The Path Length (PL) quantifies the total distance traveled by the cursor during each trial and serves as a measure of movement efficiency. It is computed as the sum of the Euclidean distances between consecutive points along the cursor trajectory from movement onset to target acquisition. Formally, if the cursor trajectory is sampled at n time points with positions x 1 , x 2 , … , x N , the path length is calculated as: P L = ∑ i = 1 n − 1 x i + 1 − x i

Shorter path lengths indicate more direct and controlled movements toward the target, while longer paths suggest deviations, corrections, or hesitations. A reduction in PL over time is typically interpreted as a sign of improved motor coordination and growing familiarity with the myoelectric control system.

Initially, we tested the mapping between muscle activity and applied forces using H s t d in healthy participants. The offline-reconstructed trajectories (Figure 5) were directed towards the targets with a good directional accuracy (20.4° ± 15.3° IDE, mean ± SD, averaged across subjects), suggesting that H s t d preserves the general structure of the myoelectric control. For comparison, the same subjects achieved an average IDE of 8.02° ± 2.09° (mean ± SD, averaged across subjects) during online myoelectric control with their own subject-specific mappings. Although less precise, the performance with H s t d still demonstrates that the proposed standardized approach can support functional cursor control. It is important to note that these trajectories were reconstructed in post-processing and do not reflect the actual movements of the cursor during the original sessions. Nonetheless, we hypothesize that in a real-time scenario, the presence of visual feedback could support subjects in further refining their motor output when using H s t d , thereby improving accuracy and making the control physiologically meaningful. In addition, discrepancies in trajectory amplitude were observed, highlighting the need for subject-specific scaling to ensure accurate force magnitude representation.

Three stroke survivors participated in the study using the protocol outlined in 2.6. These pilot experiments consist of a single session and therefore do not provide a clear indication of the efficacy of therapy over multiple sessions. However, they do provide a preliminary assessment of the feasibility of the assistive-adaptive algorithm for assistive myoelectric control in stroke patients. All three stroke patients showed improved kinematic performances following the patient-tailored assistance (Figure 6), which will be explained in detail in the following subsections.

The preliminary data collected from three pilot cases offer encouraging yet limited insights into the short-term effects of the proposed assistive-adaptive control strategy. Each patient completed a single therapy session, during which we observed modest but consistent trends suggesting that the algorithm may support improved motor execution and coordination within the boundaries of a single exposure. Building on these initial observations and the theoretical hypothesis underlying the algorithm, we anticipate that repeated exposure to the training protocol will lead to progressive and more stable improvements. Across multiple training sessions, the combination of adaptive assistance, real-time feedback, and the use of a standardized functional mapping is expected to reinforce functional activation patterns, reduce pathological co-contractions, and enhance voluntary motor control. Patients are expected to progressively internalize more effective muscle strategies, improving both, movement quality and autonomy. We expect these neuromuscular improvements to translate into clinically meaningful functional gains. One of the primary anticipated outcomes is a significant increase in scores on the Fugl-Meyer Assessment for the Upper Extremity (FMA-UE), reflecting enhanced motor capacity and coordination of the MAL. A sustained improvement in FMA-UE would provide strong evidence that the proposed strategy is not only effective at guiding motor performance during the task but also capable of driving broader functional recovery. In summary, while these pilot data support the system’s capacity to induce short-term motor benefits, we expect a full multi-session therapy protocol to reinforce these effects over time, enabling durable neuroplastic changes and significant clinical improvements.