Neuropathic pain is frequent and drugs relieves only 50% of the patients. Repetitive transcranial magnetic stimulation (rTMS) at high frequency (HF, usually 10Hz) applied on the primary motor cortex (M1) is an effective treatment of neuropathic pain. For the treatment of chronic pain, the 'classical' HF-rTMS protocol (CHF-rTMS) include one daily session for one or two weeks as an induction phase of treatment followed by a weekly session to produce analgesic effects. However, another type of protocol is based on a more spaced repetition of HF-rTMS sessions (SHF-rTMS), including intervals of several days or weeks between two sessions, but also resulting in a significant pain relief. However, CHF-rTMS and SHF-rTMS have never been compared regarding their analgesic efficacy.

Alongside with pain, depression is the other clinical condition for which HF-rTMS is proposed as an effective therapeutic strategy. Another type of rTMS paradigm, called "accelerated intermittent theta burst stimulation" (ACC-iTBS) protocol has been recently proposed for the treatment of depression, combining a high number of pulses delivered per session and a high number of short-duration sessions grouped into a few days of stimulation. However, this type of protocol has never been applied for the treatment of chronic pain patients.

Thus, for the first time we propose to compare in a pilot study the efficacy of three different rTMS protocols for the treatment of chronic neuropathic: CHF-rTMS, SHF-rTMS, and ACC-iTBS. In this study, two protocols two rTMS protocols (CHF-rTMS and ACC-iTBS) will share the same high total number of TMS pulses (i.e. 30 000 pulses) versus an rTMS protocol (SHF-rTMS) based on a lower total number of TMS pulses (i.e. 6 400 pulses), while one protocol (CHF-rTMS) will include a higher number of days of stimulation (i.e. 10 days) compared to the two other protocols (ACC-iTBS and SHF-rTMS) (i.e. 4 days). In all cases, the motor cortical target and the intensity of stimulation will the same.

Thus, this study will be able to appraise the respective influence of the number of pulses delivered (the higher the number, the greater the effect) and the number of sessions (the higher the number, the more restrictive the implementation of treatment). That is to say that the new ACC-iTBS protocol could be an optimal compromise of a more efficacious and more easy-to-perform rTMS protocol for the treatment of patients with chronic pain.

Description of the research proceedings and study design This is a 3-parallel-group monocentric randomized study, in which 36 patients, aged between 18 and 80 years, suffering from painful peripheral neuropathy (DN4 and NRS pain scores ≥4/10), will be randomly assigned to one of three rTMS protocols: CHF-rTMS, SHF-rTMS, and ACC-iTBS. The group allocation of the patients will be performed by one investigator not involved in the experimental task or clinical assessment. Patients will be recruited in the Clinical Neurophysiology department of the Henri Mondor University Hospital, Créteil, France, where the research will take place

Screening and inclusion visits During a routine medical visit, the study will be explained and proposed to the eligible patients and a letter of information about the protocol will be given to them. The list of the patients receiving the letter of information will be collected to determine the ratio between the number of patients definitively included and the number of patients screened. After a delay of reflection of at least a week, patients who agree to perform this research will be convened for an inclusion visit. After checking the inclusion/exclusion criteria, the informed consent form will be completed and signed by the participant and duly countersigned by the investigator.

During this inclusion visit, performed two weeks after the rTMS intervention, information regarding demographic data (age, gender), medical history and the list of drug treatments will be collected. A pain diary of 13 pages will be given to the patient with one page per week presenting a 0-10 numeric pain intensity rating scale (NRS) per day and a box to indicate the number of pain attacks and analgesic pills taken in addition to the usual treatment for each day of the week (cf. Appendix). Finally a code will be assigned to the patient (first 3 letters of the surname and the inclusion number) and this code will be sent to the person responsible for the randomization between the three types of stimulation protocol (CHF-rTMS / SHF-rTMS / ACC-iTBS).

First assessment visit One week after the inclusion visit (i.e. one week before the rTMS intervention), the first complete assessment visit will be managed to record all the clinical and neurophysiological outcome measures assessed in this study.

Clinical outcome measures: Scales and questionnaires

In addition to the report of all the daily NRS scores from the patient's pain diary, the following questionnaires (annexes) will be filled by the patients, based on the overall assessment of the preceding week:

• 7-item Interference Scale of the Brief Pain Inventory (BPI) [48] to assess the impact of pain on the patient's daily functioning; this scale rates from 0 (does not interfere) to 10 (complete interference) the degree to which pain interfered with general activity, mood, walking ability, normal work, relations with other people, sleep and enjoyment of life (max score 70)
• 0-5 pain Verbal Rating Scale (VRS) to assess the global painful feeling with adjectives reflecting pain intensity
• Neuropathic Pain Symptom Inventory (NPSI) [49] based on 10 questions to quantitatively assess pain intensity according to various sensory descriptors (max total score 100), five subscores (burning (superficial) and pressing (deep) spontaneous pain, paroxysmal pain, evoked pain, paresthesia/dysesthesia), and 2 questions to assess the duration of spontaneous pain and the number of pain paroxysms on categorical scales
• Pain Catastrophizing Scale (PCS) [50] based on 13 questions to quantitatively assess various types of negative feelings and emotions that can be associated with the tendency to catastrophizing (irrational thinking by the patient with the belief that her/his health condition is or will be worse than it actually is) and rated from 0 (not present) to 4 (permanent) (max score 52)
• Hospital Anxiety and Depression scale (HAD) [51] based on 14 questions to quantitatively assess symptoms of anxiety or depression rated from 0 (not present) to 3 (maximal impairment) (max score 21 for each anxiety and depression dimension subscores)
• Fatigue Severity Scale (FSS) [52] based on 9 questions to quantitatively assess the physical aspect of fatigue and its influence on daily functioning, especially related to medical illness (max score 63)
• Leeds Sleep Evaluation Questionnaire (LSEQ) [53] based on 10 questions to quantitatively assess various aspects of sleep quality and early morning behavior, leading to four subscores: getting to sleep (items 1-3), quality of sleep (items 4-5), awakening following sleep (items 6-7), and behavior following awakening (items 8-10) (max score 100).

Neurophysiological outcome measures (1): Resting-state Electroencephalography (rsEEG)

• One period of 5 min of EEG will be recorded in the patients remaining calm and relaxed (resting state) without any particular task to perform and with eyes closed. The rsEEG will be recorded using a cap with 60 scalp electrodes and a 60-channel EEG machine (eXimia, Nexstim, Helsinki, Finland). Electrode impedance will be maintained below 5 kΩ.
• EEG signal will be analyzed offline using MATLAB software (The MathWorks, Inc., Natick, MA, USA) and EEGLab Toolbox. Following an initial sampling frequency of 1,450 Hz, the EEG signal will be down-sampled to 256 Hz and bandpass filtered (1-97Hz, with a zero-phase 3rd-order Butterworth filter and the application of a 50 Hz (± 2 Hz) notch filter) using EEGLAB plugin Cleanline. Once the data reconstructed, continuous data will be segmented into 4 second, non-overlapping epochs. Independent Component Analysis (ICA) decomposition will be used to identify and reject blink artifacts. Amplitude-based automatic rejection ± 80 μV will be applied to reject epochs with eye movement activities. After visual inspection, channels with a rejection rate superior to 20% across trials will be rejected and will be interpolated with non-artifacted neighboring channels.
• Analysis of the power spectral density (PSD) will be carried out using a Welch's method, with a 2-s window size, 50% overlapping Hamming window. PSD analysis will be performed by dividing the EEG signal into three frequency bands, according to what is known about how chronic pain affects the EEG signal [54]: the θ band (theta: 4-7 Hz), the α-β1 band (alpha: 8-12 Hz; beta1: 13-20 Hz), and the β2 band (beta2: 21-35 Hz). EEG signal power is thought to be increased in the θ band and possibly in the β2 band, but decreased in the α-β1 band in the presence of ongoing neuropathic pain. For each of these three frequency bands, the absolute (aPSD, μV2) and relative (rPSD, %) PSD values will be calculated, rPSD being defined as the ratio of the aPSD in a given frequency band to the overall aPSD value in the entire 4-35 Hz frequency band.
• Also according to what is known about how chronic pain affects the EEG signal [54], the dominant peak frequency (DPF, Hz) will be determined for two different frequency bands of interest: the θ-α band (4-13 Hz) and the β1-β2 band (13-35 Hz). The DPF is thought be decreased in the θ-α band and increased in the whole β1-β2 band in neuropathic pain patients.
• PSD and DPF will be computed on each of the 60 scalp recordings and a grand-averaging will be performed for 11 brain regions defined as follows according to EEG electrode sites: right Frontal (FP2, AF2, F2, F4, F6), left Frontal (FP1, AF1, F1, F3, F5), right Central (FC2, FC4, FC6, C2, C4, C6), left Central (FC1, FC3, FC5, C1, C3, C5), right Parietal (CP2, CP4, CP6, P2, P4, P6, P8), left Parietal (CP1, CP3, CP5, P1, P3, P5, P7), right Occipital (PO4, O2), left Occipital (PO3, O1), right Temporal (FT8, FT10, T8, TP8, TP10), left Temporal (FT7, FT9, T7, TP7, TP9), and midline (FPZ, AFZ, FZ, FCZ, CZ, CPZ, PZ, POZ, OZ).
• Four metrics of EEG Functional Connectivity (FC) will be analyzed: magnitude square coherence (MSC), lagged coherence (LC), phase locking value (PLV), and phase lag index (PLI) [55-58]. The MSC is a function of the PSD of two electrodes x (Pxx) and y (Pyy), and the cross PSD (Pxy) of electrodes x and y in frequency f. The MSC is calculated as follows: MSCxy(f)=∣Pxy(f )∣²/(Pxx(f )Pyy(f)). The LC allowed to avoid the impact of volume conduction of the EEG signal and takes into account the imaginary part of the cross-spectrum coherence. LC is calculated as follows: LC(f)=imag(C(f))/square(1-real(C(f))²), where imag(C(f)) and real(C(f)) are the imaginary part and the real part of the cross-spectrum in a frequency f. The PLV characterizes the phase synchronization between two narrow-band signals for two time-series. The PLV is calculated as follows: PLV(t) ≜ |E[ejΔφ(t)]|, where Δφ(t) is the phase difference of two signal (using Hilbert transform). PLV range from 0 for a random phase relationship to 1 for a fixed phase relationship. However, when computing synchrony between pairs of electrodes or cortical locations, nonzero PLVs can arise from a single source contributing to both signals because of volume conduction or limited spatial resolution (linear mixing) and not corresponding to a "true" phase locking between two distinct signals. To distinguish between these two conditions, the PLI will be measured, which is equal to zero in the case of linear mixing (completely symmetric phase distribution) and nonzero when there is a consistent phase difference (phase lag) between two time-series (maximum 1 for completely asymmetric phase distribution). The PLI is calculated as follows: PLI(t) ≜ |E(sign(Δφ(t)|.
• The FC metrics (MSC, LC, PLV, PLI) will be assessed between all pairs of scalp electrodes (pairwise measures, resulting in a 60x60 FC matrix) for each frequency band (θ, α, β1, β2). Averaged values of the FC metrics will also be computed between the 10 right and left brain regions (as defined above), resulting in a 10x10 FC matrix to assess intrahemispheric and interhemispheric FC.
• Finally, we will perform a graph analysis of the FC metrics to extract the following variables: clustering coefficient (CC), modularity (MOD), characteristic path length (CPL), and global efficiency (GE) [59,60]. The CC and MOD are thought to reflect the functional segregation properties of a complex network. On the other hand, CPL and GE are thought to reflect functional integration of a complex network. An increase vs. decrease in CC and CPL defines a 'regular' vs. 'random' organization typology, respectively. Finally, the Eigenvector centrality (EC), or nodal centrality, will be determined to quantify the importance of a single node within the entire network |61]. All FC graph variables will be calculated on the weighted connectivity matrices for each band and for each FC metric.

Neurophysiological outcome measures (2): TMS-EEG evoked potentials (TEPs)

• Following the 5 minutes of rsEEG recording, using the same EEG electrode montage, TMS-EEG evoked potentials (TEPs) will be recorded to TMS pulses delivered with a focal figure-of-eight coil (mean/outer winding diameter 50/70 mm, biphasic pulse shape, pulse length 280 ms, focal area of the stimulation 0.68 cm² ) connected to an eXimia TMS Stimulator (Nexstim). All participants will be seated in an armchair in a relaxed position with eyes open, visually fixating on a cross 1 m in front of them to reduce eye movement. The primary motor cortex contralateral to pain (or of the left hemisphere) will be stimulated with the coil centered over the hand knob (hand motor cortical representation). At this stimulation site, the resting motor threshold (RMT) will be measured (as the minimum intensity of stimulation producing at least 5 motor evoked potentials (MEPs) of more than 50 µV amplitude in a series of 10 stimuli). Then, 60 pulses will be delivered at an intensity of 120% of RMT with a random interstimulus interval around 2 seconds (total examination time: less than 5 minutes). The precision and reproducibility of the TMS pulse location will be guaranteed by means of a Navigated Brain Stimulation (NBS) system (Nexstim). During all TMS-EEG recordings, a masking sound will be played via earphones and a thin layer of foam will be placed between the coil and the scalp for abolishing auditory and somatosensory inputs associated with TMS coil discharge.
• Raw EEG signal will be initially filtered between 0.1 and 350 Hz and sampled at 1,450 Hz. Then, TMS-EEG data will be down-sampled to 725 Hz, band-pass filtered (1-45 Hz with a zero-phase 3rd-order Butterworth filter), and segmented in a time window of ± 500 ms around the stimulus. To remove the high-amplitude TMS pulse artifact, time segments from -10 to 20 ms around the TMS pulse will be edited using linear interpolation. ICA will be performed and components related to blink and eye-movement artifacts will be removed. Major remaining artifacts (e.g., movements) will be rejected manually by visual inspection. TMS-EEG data recorded from the 40 trials will be averaged separately for each scalp EEG recording site and each stimulation site of the mapping grid. From this averaging, the TMS-EEG evoked potentials (TEPs) will be obtained. The TEPs to motor cortex stimulation include the following peaks: N15, P30, N45, P55, N100, P180 and N280. The N45 and N100 are among the most reliable responses and considered to be modulated by GABA-A and GABA-B receptors, respectively, reflecting the GABA/glutamate balance [62-65]. In this study, the N45 and N100 peaks will be defined as the most negative peak recorded in the time window from 40 to 50 ms and 80 to 120 ms, respectively and the peak amplitude of these two components will be measured at each EEG recording site and the averaged values for the 11 brain regions defined on rsEEG recordings. In addition, the global mean field power (GMFP) will be calculated in the time windows (40-50 ms and 80-120 ms) as the standard deviation across all the electrodes.
• The signal propagation (TEP spreading) in the same time windows will be assessed by a topographical technique using a quadratic interpolation method between neighboring electrodes. All these assessments were in the time domain. A frequency domain method will be combined for the analysis of the event-related spectral perturbation (ERSP), which estimates the evolution of EEG power over frequency and time, using a wavelet transform averaged across trials [66]. The ERSP expresses the magnitude (in decibels) of EEG oscillations.

Neurophysiological outcome measures (3): Threshold-tracking of Short Intracortical Cortical Inhibition (T-SICI)

• For this test, paired TMS pulses will be delivered with a focal D70 alpha figure-of-eight coil connected to by two monophasic Magstim 200² stimulators in BiStim configuration (Magstim, Whitland, UK) and positioned over the hand knob of the primary motor cortex contralateral to pain (or of the left hemisphere). The MEPs will be recorded at the first dorsal interosseus (FDI) hand muscle contralateral to TMS side using pre-gelled disposable surface electrodes (Ref. 9013S0242, Natus-Dantec, Skovlunde, Denmark) in a tendon-belly montage. All the stimulation sequences will be controlled automatically by the QTMSG-12 protocol of the QtracW software (UCL, London, UK). First, the stimulation intensity threshold to produce MEPs of 200µV amplitude in the FDI at rest (RMT200) will be determined. For T-SICI recording [67-70], the intensity of the conditioning stimuli will be set to 70% of RMT200 and the intensity of the test stimuli will track the 200 µV target with steps varying by 1% of maximum stimulator output (MSO). The paired stimuli will be delivered 6 times at 9 interstimulus intervals (ISIs) from 1 to 7 ms in a pseudo-randomized order mixed with test stimuli alone every four trials, making a total of 72 stimuli (total examination time: less than 10 minutes).
• The maximum amount of threshold increase (maximum MEP inhibition), the ISI value corresponding to this value and the area under the T-SICI curve from 2 to 6 ms ISI will be retained for analyses.

Overall, the duration of the neurophysiological tests will be about 30-45 minutes (10-15 minutes to place EEG cap, 5 minutes for rsEEG recording, 5-10 minutes for TEP recording, 10-15 minutes for T-SICI recording).

rTMS interventions The first rTMS session will be performed one week after the first assessment visit. In addition to the report of all the daily NRS scores from the patient's pain diary of the preceding week, the impact of pain and pain intensity during this week will be scored on the BPI and VRS before the rTMS session.

Then, according to the randomization, one of the 3 rTMS protocols will be applied: CHF-rTMS / SHF-rTMS / ACC-iTBS using a focal figure-of-eight coil connected to an eXimia TMS Stimulator (Nexstim). In all cases, the coil will be centered over the hand knob of the primary motor cortex contralateral to pain (or of the left hemisphere) under neuronavigation (NBS) guidance. The RMT (as defined above) will be determined before each session, and all stimulation will be performed at 80% of RMT.

Follow-up assessments and final visit Assessment will be performed every week for 11 consecutive weeks. In addition to the report of all the daily NRS scores from the patient's pain diary of the preceding week, the impact of pain and pain intensity during this week will be scored on the BPI and VRS. In addition, the 7-item patients' clinical global impression (PGIC) will be used to evaluate the subjective improvement or deterioration (from very much improved to very much deteriorated) during this week [71]. Finally, the occurrences of side effects will be collected if rTMS session(s) was (were) performed during the preceding week.

At the end of the week 7 after the first rTMS intervention (during which the last CHF-rTMS and SHF-rTMS session and the last two days of ACC-iTBS sessions will take place), the second complete assessment visit will be managed to record all the clinical and neurophysiological outcome measures assessed in this study (including clinical questionnaires, rsEEG, TEPs, and T-SICI).

At the end of the week 11 after the first rTMS intervention, a final visit will be managed, during which the patients will be asked for two questions to determine: (i) whether or not they think they benefited significantly from the rTMS therapy; (ii) whether or not they wish to continue the rTMS therapy.

Thus, the patients will be asked to come to our hospital center for the inclusion visit, for all days of rTMS sessions (4 or 10 days), for the two complete assessment visits, and for the final visit. All other intermediate evaluations will be done by phone call during the follow-up.

Inclusion Criteria:

• (1) existence of a definite peripheral neuropathy on both clinical and neurophysiological grounds, present for at least 6 months;
• (2) neuropathic pain clearly related to the neuropathy, as defined by a score ≥ 4/10 on the questionnaire "Douleur Neuropathique en 4 Questions" (DN4) ;
• (3) a score ≥ 4/10 on a 0-10 numerical rating scale (NRS) concerning the average intensity of daily ongoing pain;
• (4) age between 18 and 80 years;
• (5) affiliation with the social security system;
• (6) ability to provide signed informed consent.

Exclusion Criteria:

• (1) concomitant neurological (neurodegenerative disorders, migraine, epilepsy, stroke, tumor) or psychiatric illness;
• (2) contraindications related to TMS (intracranial ferromagnetic material);
• (3) drug-resistant or active epilepsy.