## 2 Material and Methods
### K-VRRS Technologies and Intervention  
K-VRRS (depending on the technological components used) allows the implementation of both immersive and non-immersive virtual reality-based treatments. In this study, we implemented non-immersive virtual reality-based treatments. The first phase of the treatment was conducted during the participants' hospitalization at our facility, using the K-VRRS-EVO system. K-VRRS-EVO consists of a PC station connected to a high-resolution touchscreen LCD monitor, which displays virtual activities, and a 3D motion tracking system. This motion tracking system includes a series of sensors placed on the subject to detect and reproduce their movements in real time within a three-dimensional virtual environment. The sensor technologies used include K-sensors, inertial sensors for measuring acceleration and angular velocity, and passive 3D magnetic sensors. These sensors are attached to anatomical bands or gloves and, in conjunction with a low-intensity electromagnetic field generator, allow for real-time kinematic tracking and motion detection. The VRRS software (version 5.2.32.16055) processes data collected by magnetic sensors, which capture the spatial coordinates (\(\kappa\), \(y\), \(z\)) of a joint segment, and by inertial sensors (IMUs), which measure angular velocities and linear accelerations. These data are analyzed using algorithms for signal integration and processing. This computational pipeline extracts kinematic descriptors (e.g., velocity, path length), movement smoothness indices (e.g., jerk), and temporal metrics (e.g., movement execution time), providing information concerning the spatiotemporal dynamics of motion. During the first phase of the treatment, participants underwent both standard physiotherapeutic treatment and intensive K-VRRS-based neuromotor rehabilitation. Standard physiotherapy intervention primarily focused on functional training of one or both arms, emphasizing activities oriented toward specific functions and guided by principles of motor learning and control. The K-VRRS-based treatment included two in-person rehabilitation sessions per day, six days a week, with each session lasting approximately 45 min, throughout the hospitalization period. Each session involved the patients performing 3D virtual games and tasks, such as controlling a diver to collect fish and seahorses or moving an object vertically and horizontally along simple or complex trajectories within the virtual environment. Additionally, participants performed Catching (gripping) and Reaching (reaching) exercises, which required them to execute flexion/extension movements, shoulder internal/external rotation, and elbow flexion/extension across three planes: frontal, sagittal, and transverse. The second phase of the treatment was conducted via TR. The K-VRRS system facilitates TR through two distinct workstations: one located at the patient's home and the otherat the rehabilitation hospital. The home workstation, referred to as the VRRS-Home Kit, includes a tablet, a motion detection camera, and wearable sensors for movement tracking. Two types of sensors were used in the Home Kit: the K-Sensor and the K-Wand, which together enable tele-motor rehabilitation. The K-Wand is an innovative device designed for the tele-motor rehabilitation of the upper limb and trunk. It features exclusive light recognition technology, allowing it to detect movements in depth. The K-Sensor consists of a set of inertial sensors placed on the upper limb using anatomical bands. The hospital workstation, known as the TeleCockpit, is a technological setup equipped with an integrated videoconferencing system that allows therapists to control the home device and monitor the patient's actions via the Home Kit. TR sessions can be conducted in two ways: (i) online, with real-time interaction between the patient and therapist via videoconference, or (ii) offline, where the patient performs exercises independently with the guidance of a Smart Virtual Assistant.