The aim of the study is to evaluate the changes induced by a course of Transcutaneous Electrical Nerve Stimulation (TENS) treatment on the perception of phantom limb pain.

In particular, we want to evaluate the changes induced by a course of TENS treatment on posture, balance, and gait.

For each patient, the study will consist of a total of 20 sessions (4 mapping sessions, 3 Stimulus Intensity Discrimination sessions, 10 rehabilitation treatments, and 3 evaluation sessions).

One session will be carried out each day. Each session will last 60 minutes, except for the evaluation sessions, which are expected to last approximately 90 minutes.

For the patient, the study ends with the last evaluation, voluntary withdrawal from the study, or the patient's death.

All patients enrolled in the study will receive the same treatment as no randomization is planned. For each patient, the study will consist of two 60-minute sessions per day, except for the evaluation ones which are expected to last approximately 90 minutes, five days per week for a total duration of 4 weeks. The rehabilitation will imply both a TENS treatment and a conventional one.

1. Mapping sessions: Four Mapping sessions performed at the beginning of each week. The aim of these sessions will be to manually re-tune the perceptual thresholds and characterize the elicited sensation's location and quality on both limbs.

   The patients will be asked to lie prone on a sterile medical bed in order to use an electromyography device to detect the distal end of the nerve trunk and determine the ideal electrode position for nerve stimulation (i.e., the tibial nerve in patients with Transtibial Amputation (TTA) and the sciatic one in those ones with Transfemoral Amputation (TFA)). Using anatomical landmarks, the skin surface will be identified, cleaned with an alcohol pad and the stimulation electrodes will be positioned.

   The session will consist of the three following phases:

   • Perceptual thresholds identification. The PW, PF, stimulus duration and rest between two consecutive stimuli will be kept constant to 500 µs, 500 Hz, 1 s and 5 s, respectively. The PA will be incremented between one stimulus and the following one from 1 mA with a step of 0.1 mA until both the sensory and motor thresholds were reached. The sensory and motor thresholds will be defined as the lowest current intensity values needed to evoke a well-defined, referred tactile sensation in the phantom limb and a visible muscle contraction, respectively. Subsequently, two different pulse amplitude values (i.e., PAmin and PAmax) will be identified respectively as the minimum and maximum current value able to evoke a well-defined and painless referred tactile sensation in the phantom limb without inducing muscular contraction. The total number of stimulus provided to the participants in this phase will be variable since perceptual thresholds values are patient-specific;
   • Charge modulation. The PA, PF, stimulus duration and rest between two consecutive stimuli will be kept constant to PAmax, 150 Hz, 1 s and 5 s, respectively. The PW will be varied in the range 100-500 µs with a step of 40 µs for a total of 11 stimuli. At the end of the modulation, the PW value at which the participant can feel a well-defined and comfortable sensation will be selected;
   • Frequency modulation. The PA, PW, stimulus duration and rest between two consecutive stimuli will be kept constant to PAmax, the selected value in the previous phase, 1 s and 5 s, respectively. The PF will be varied in the range 50-500 Hz with a step of 50 Hz for a total of 10 stimuli.

   For each delivered stimulus, the patient will be asked to indicate the location of the evoked sensation adopting pictures representing the missing foot and leg and then to describe them. The descriptors included: a five-point scale for the naturalness ranging from unnatural to natural, a metric of the location of the sensation (i.e., superficial and/or deep), a scale from 0 to 10 for the intensity and pain of the sensation and multiple choices for the quality (touch/pression, pinch, vibration, tugging, tingling, burning, hot, cold, ankle flexion, ankle extension, toes flexion, toes extension and nothing). The Mapping protocol will be administered to the patients' both limbs randomly.

2. Stimulus Intensity Discrimination sessions: Three Stimulus Intensity Discrimination sessions will be conducted over three consecutive days during the first week.

   The aim of these sessions will be to evaluate the participant's ability to differentiate between stimuli of varying intensity levels. This assessment will be particularly relevant since, during in a real-world application of the proposed device, the electrical stimulation delivered to the participant will vary based on the load exerted on the ground during walking. Therefore, training the participant to distinguish between different intensity levels may enhance the capacity to identify distinct phases of the gait cycle solely through TENS, thereby potentially improving overall ambulatory performance. In accordance with the results obtained in the first mapping session, three levels of intensity will be settled: PAmin, PAmax and their middle value. The protocol will include a familiarization phase in which the levels (low, medium, high) will be presented in order three times each; then a validation phase in which 45 stimuli (15 for each level) will be provided in random way. The patient, lying in a prone position on a sterilized medical bed blindfolded and acoustically shielded, will be required to recognize each stimulus, discriminate the intensity and refer it. Throughout the whole session, the PW, PF, stimulus duration and rest between a stimulus and the following one will be kept constant to 500 µs, 500 Hz, 1 s and 5 s, respectively.

3. Rehabilitative sessions: Ten rehabilitative sessions will be conducted to retrain gait under controlled and repeatable experimental conditions. During these sessions, participants will use a custom-developed electrical stimulation device, combined with either technological solutions or proprioceptive exercises.

   In the former case, the auto-adaptive treadmill Walker View (TecnoBody, Dalmine, BG, IT) will be used: the robot will support the patients' body weight and will adapt the speed according to the patient's residual motor capabilities. In addition, the patient will be immersed in a virtual reality environment that could enhance the engagement during the session and potentially the rehabilitative efficacy. During task execution, the electrical stimulation of the residual nerve will be triggered and modulated by the instrumented insole em- bedded in participant's own prosthesis. The patient kinematics and load applied to the ground will be monitored through the 3D camera and force platforms embedded in the system.

   In the latter case, the patients will undergo proprioceptive exercises under the support and supervision of a physiotherapist to train different terrain texture recognition via TENS;

4. Evaluation sessions: Three evaluation sessions will be performed at the beginning (T0), in the middle (T1) and at the end (T2) of the experimental protocol. Each session will consist of:

   • Phantom limb perception. The patient's phantom limb perception will be quantified in terms of accuracy in discriminating among the three terrain textures (i.e., tiles, grass and thermoplastic modules with ridges and valleys). The experimenter will wear the instrumented insole while the patient, blindfolded and acoustically shielded, will assume a prone position on a sterilized medical bed with electrodes placed on the amputated limb at the previously identified sites. The experimenter will perform five walking trials for each of the three textures at a self-selected speed along a straight 10 m walkway. The data acquired from the instrumented insole will be used to modulate the electrical stimulation delivered to the patient, who will be required to identify the terrain.
   • Instrumented evaluation of lower limb biomechanics. The patients's performance during ambulation on the different terrain textures with and without electrical stimulation will be monitored.

Gait analysis will be performed with the optoelectronic marker-based system BTS Smart D 500 (BTS Bioengineering, Milan, IT): eight cameras will be geometrically calibrated and mounted on tripods to capture twenty-two photo-reflective spherical (diameter of 10 mm) markers' motion placed on specific body anatomical landmarks according to Davis protocol. The patients will be asked to perform, for each terrain, ten walking trials (five with stimulation and five without it in a random order) at a self-selected speed along a straight path of 10 m. Whether at T0 the patients will be not able to ambulate autonomously but exclusively with the use of an aid (e.g., crutch, cane or a walker), the same aid will be employed in the other evaluating sessions too to ensure consistency in experimental conditions.

• Clinical survey. The aforementioned clinical survey composed of Numerical Rating Scale, NPSI and DN4 questionnaires will be submitted to the patients to evaluate the post-amputation neuropathic pain.

In accordance with Italian standards on patients rehabili- tation, the proposed approach will not be limited to TENS treatment but will also incorporate traditional one where the ambulation without weight bearing on the operated limb or with partial bearing and ambulation with gradual weight bearing with or without aid will be performed or assisted by physical therapists, mostly in one-to-one sessions.

Inclusion Criteria:

• Age between 18 and 80 years;
• unilateral TTA or TFA at least two months prior the study;
• stable clinical conditions;
• skin integrity;
• absence of cognitive deficits;
• able to walk using the prosthesis;
• no previous experience with TENS.

Exclusion Criteria:

• Bilateral amputation;
• open wounds or sores on the residual limb;
• cognitive deficits;
• pregnancy;
• presence of implanted medical device (e.g., cardiac defibrillators, pacemakers or infusion pumps);
• refusal to sign the informed consent.