This study is a double-blind randomized controlled pilot trial and was designed according to the Consolidated Standards of Reporting Trials (CONSORT) extension to pilot trials . The study flowchart is shown in Fig. 1. Twenty-four stroke patients will be enrolled and randomly allocated to an active or sham tDCS group. This study will be conducted in Fujita Health University Hospital, Aichi, Japan. All participants will provide written informed consent before participation according to the Declaration of Helsinki of 1964, as revised in 2013. This study has been approved by the Certified Review Board at Fujita Health University (approval No. CR21-029) and registered at the Japan Registry of Clinical Trials (jRCTs042200078).
The inclusion criteria are as follows: (1) age 40–79 years, (2) first-ever unilateral supratentorial ischemic or hemorrhagic stroke, (3) time exceeding 6 months after stroke onset, (4) mild to moderate upper limb hemiparesis [able to perform at least one component of the Action Research Arm Test (ARAT) in the grasp, grip, or pinch subscales; score of 10–51 on ARAT], and (5) independent walking ability [score of > 6 on the Functional Independence Measure (FIM) for walk]. The exclusion criteria are as follows: (1) unstable physical condition, (2) inability to communicate due to severe language impairment, (3) neurological disorders other than stroke, (4) facial sensory deficits, (5) inability to perform training because of psychological disorders or cognitive dysfunction, (6) cognitive impairments [Mini-Mental State Examination (MMSE) < 24] [38,39], (7) inability to perform training because of musculoskeletal disorders, (8) botulinum toxin injections into the arm within the last 6 months, and (9) any contraindications to tDCS, TMS, and MRI such as a history of epilepsy, metallic implants, cardiac pacemaker, drug or alcohol abuse, or pregnancy.
Potential participants will be identified from the outpatient clinic of the University Hospital and the local community. The advertisement for the study is open to the public via our department website to allow patients in the local community to access relevant information. Individuals who are interested in this study will be required to make an appointment for screening. The eligibility of potential participants will first be carefully assessed by a physician. They will then be screened for motor and cognitive functions using the ARAT and MMSE by a trained occupational therapist. Written informed consent will be obtained from those who fulfill the criteria and are willing to take part in this study.
Participants will be stratified according to age and ARAT score, and randomly allocated to either the active tDCS or sham tDCS group using a computer-generated, permuted block randomization method with permuted block sizes of 2 and 4. The random allocation will be conducted using the Research Electronic Data Capture (REDCap) tools  by independent researchers who will not be involved in any intervention and assessments.
A time schedule of this study is shown in Fig. 2A. The participants will be admitted to Fujita Health University Hospital. The participants will undergo intensive upper limb training for 4 hours per day (2 hours per half-day) and receive cerebellar tDCS (active or sham) for 20 min at the beginning of the intensive training (Fig. 2B), considering that the effects of tDCS on the neural excitability of a targeted brain region last for 30–120 min [2,5–7]. This will be repeated for 5 consecutive days per week for 2 weeks (i.e., 10 days of intervention). During the intervention period, botulinum toxin injections and any changes of medications that could affect spasticity will not be allowed.
The stimulation will be delivered using DC STIMULATOR PLUS (NeuroConn, GmbH, Ilmenau, Germany). The anode (5 × 5 cm) will be placed on the cerebellar hemisphere on the contralesional side. Specifically, lobule VI, one of the subregions contributing to motor control of the upper limb , will be a focal target of the stimulation. Conventionally, the anode is placed at the fixed position 3 cm lateral to the inion ; however, in the present study, the optimal location for targeting the lobule VI will be determined for each individual using computational simulation (see Computational modeling subsection). The cathode (5 × 5 cm) will be placed on the cheek on the contralesional side.
The detailed time course of active and sham tDCS is shown in Fig. 2C. The ‘study mode’ of the NeuroConn stimulator will be used to successfully implement double-blinding using 5-digit codes that activate the active or sham stimulation. Only the independent researchers that conduct the random allocation can access the code list. The experimenter will remain blinded to the information regarding which code belongs to the active or sham stimulation. In the active tDCS group, 1 mA constant current will be delivered for 20 min, whereas in the sham tDCS group, 1 mA constant current will be delivered for 40 s to induce similar scalp sensations. In both groups, the current will be ramped up to 1 mA and ramped down over 15 s at the start and end of the stimulation . During the sham tDCS condition, only a weak current of 110 μA will be delivered every 550 ms after the ramped-down periods to test the electrode impedance. Only the impedance level and stimulation duration will be displayed in both conditions, which facilitates the blinding of the experimenter. The sham procedure is commonly used in tDCS research and at least 30-s active stimulation with slow ramp up and down are recommended for effective blinding during sham sessions . The participants will not be given any information about stimulation parameters.
Intensive upper limb training
Intensive upper limb training based on the concept of CIMT will be provided by trained occupational therapists who will be blinded to the intervention allocation. CIMT is a therapeutic package that consists of repetitive and task-oriented training, behavioral methods for transferring the use of the affected arm in life situations, and constraining the use of the less affected arm to achieve participants’ specific goals . Since previous studies have reported that physical restraint has no significant effects on the outcome of CIMT [46,47], no restraints will be applied to the unaffected arm of the participants in this study. Another difference compared to the original CIMT is with respect to the training hours per day, with 4 hours in this study compared to 6 hours in the original . To accomplish sufficient training, participants will be encouraged to use their affected arm in activities of daily living. Additionally, the participants will engage in self-training programmed by the occupational therapists for 2 hours per day (Fig. 2B). If necessary, functional electrical stimulation will be provided to enhance muscle contractions and perform functional tasks, but rehabilitative robots will not be allowed.
Fig. 3 shows the method that will be used to optimize the location of the tDCS montage at the individual level. First, the head model will be treated as a passive volume conductor constructed from 3D T1- and T2-weighted MRI of each participant before the experiment. The computational method has been reported in detail in a previous report [48,49]. It involves using the scalar potential finite difference method with fast computational techniques to accelerate the computational assessment before the intervention [50,51]. The computational model estimates the individualized electric field intensity and distribution on the cerebellar region applying a bipolar montage throughout the electrodes (5 × 5 cm) with an injection current of 1 mA, as used in the experiment. The cathode will be fixed on the buccinator muscle on the cheek on the contralesional side to avoid high electric currents flowing on the cerebrum. The anode will be placed on a grid (13 × 11, size of grid = 10 mm) centered on the inion to identify the position that generates the highest electric field strength (maximum and average values), with lobule VI as the target area. The optimal electrode location will be determined based on a reference landmark (10–20 system) and the Montreal Neurological Institute coordinates for confirmation.
The schedule of data collection is summarized in SPIRIT figure (Fig. 4). Clinical assessments of the upper limb and neurophysiological and neuroanatomical assessments will be conducted prior to the intervention (baseline, t0), at the middle of the intervention [middle, t1 (ARAT only)], immediately after the intervention (post, t2), and 1 month after the intervention (follow-up, t3).
The primary outcome in this study is the ARAT score. ARAT is a clinical measurement that consists of 19 tests with 4 subscales: grasp, grip, pinch, and gross movement, which assess upper limb motor function [52,53]. The quality of movement is scored on an ordinal 4-point scale, ranging from 0 to 3 in each test, with a maximum score of 57 . ARAT is classified as an outcome measurement of activity capacity [54,55] based on the International Classification of Functioning framework , and it shows excellent validity and reliability in chronic stroke patients .
Secondary outcomes include the Fugl-Meyer Assessment for the upper extremity (FMA) and Motor Activity Log-14 (MAL-14). FMA is classified as an outcome measurement of body functions  based on the International Classification of Functioning framework . FMA for the upper extremity consists of 33 items including reflex testing, movement observation, grasp testing, and coordination assessment. The score ranges from 0 to 66. FMA shows excellent validity and reliability in chronic stroke patients [58,59]. MAL-14 is a structured interview to assess how much (amount of use: AOU) and how well (quality of movement: QOM) a patient uses the paretic hand and arm during activities of daily living [60,61]. For the AOU assessment, the score ranges from 0 (never uses the arm) to 5 (uses the arm as often as before the stroke), while for the QOM assessment, the score ranges from 0 (never uses the arm) to 5 (uses the arm as well as before the stroke). MAL-14 is classified as an outcome measurement of activity performance [54,55] based on the International Classification of Functioning framework , and it shows excellent validity and reliability in chronic stroke patients .
ARAT and FMA will be video-recorded , and video-based assessments will be conducted by two trained occupational therapists who will be blinded to the allocation and will not be involved in the interventions. In addition, the following participant baseline characteristics will be collected: age, affected side of the brain, time since onset, and FIM and MMSE scores.
As an index of cerebellar excitability, we will assess the magnitude of cerebellar inhibition (CBI) to the contralateral M1 using a paired-pulse TMS paradigm (Magstim 2002, Magstim Company, Whitland, UK) (Fig. 5). CBI will be measured by delivering a conditioning stimulus (CS) over the cerebellum for 5 ms prior to a test stimulus (TS) over M1, resulting in the reduction of motor evoked potential (MEP) elicited by TS over M1. CBI is thought to be driven by inhibitory outputs from the cerebellar cortex to the deep cerebellar nuclei that have excitatory outputs to the contralateral M1 . Therefore, changes in CBI magnitude can be interpreted as cerebellar excitability changes [66,67]. We will assess the cerebellar excitability changes with the assumption that cerebellar plasticity may underlie the intervention effects.
The CS will be delivered to the contralesional side of the cerebellum using a double-cone coil which will be centered at the same location determined by the computation modeling, while the TS will be delivered to the ipsilesional side of M1 using the figure-of-eight coil over the optimal stimulation site (“hot spot”) of the first dorsal interosseous (FDI) muscle (Fig. 5). To determine the intensity of the cerebellar CS, we will first test the brainstem active motor threshold for the pyramidal tract by delivering stimuli over the inion using a single pulse with the double-cone coil. The brainstem active motor threshold is defined as the nearest 5% maximum stimulator output (MSO) that elicits MEPs exceeding 50 μV from the FDI muscle in the affected hand in at least 5 of 10 successive stimuli . The cerebellar CS intensity will be set at 5% below the brainstem active motor threshold [64,69,70]. If the threshold is not observed below 80% of MSO, 70% of MSO will be used for the cerebellar CS. For the intensity of TS over M1, we will first assess the resting motor threshold (rMT) of the FDI muscle which is determined as the lowest intensity that evokes an MEP amplitude greater than 50 μV in at least 5 of 10 successive stimuli . Thereafter, the TS intensity will be set at 125% of rMT. For the CBI assessment, in a set of 30 TS, 15 TS will be combined with the preceding CS (conditioned TS), while the other 15 TS will be delivered without CS (unconditioned TS). The inter-stimulus interval for TS will be 4–6 s, and the order of conditioned and unconditioned TS will be randomized. The position of the TS over M1 will be tracked using a neuronavigation system (Brainsight, Rogue Research, Montreal, Canada). CBI will be calculated as the ratio of the mean amplitude of conditioned MEP over the unconditioned MEP.
We will also assess M1 excitability by delivering single-pulse TMS over the ipsilesional M1 as a separate measurement set to confirm that potential CBI changes will not be accompanied by M1 excitability changes. For this purpose, 15 stimuli with an intensity of 125% of rMT will be applied with the inter-stimulus interval of 4–6 s. The mean amplitude will be used as a proxy for M1 excitability.
Surface electromyography will be recorded using a biosignal recording system (Nuropack X1 MEB-2312; Nihon Kohden Corporation, Tokyo, Japan) at the frequency of 5 kHz, with a bandpass filter of 10 Hz to 10 kHz. Recorded analog data will be digitized with a micro 1401 AD converter (Cambridge Electronic Design, Cambridge, UK) and stored on a computer (Signal Software, Cambridge Electronic Design, Cambridge, UK) for offline analysis.
To identify structural characteristics of the individual brain, MR images will be acquired prior to the intervention (baseline, t0) and after the intervention (post, t2). The brain MRI will be conducted using a 3-T scanner (Vantage Centurian 3T; Canon Medical Systems, Tochigi, Japan). For brain tissue segmentation, 3D T1- and T2-weighted images with high resolution (voxel size: 0.8 × 0.8 × 0.8 mm3) will be acquired . In addition, to identify functional and structural connectivity between widespread brain areas, resting-state functional MRI and diffusion tensor imaging will be obtained . The 3D T1- and T2-weighted images will be used for the computational modeling (see Computational Modeling subsection).
To evaluate the safety of the intervention and overall protocol, we will record adverse events such as burns to the skin, prolonged abnormal cutaneous sensation, dizziness, fatigue, pain related to overuse of the affected arm, etc. To monitor the existence of the temporary side effects, especially of the tDCS, we will provide participants with a questionnaire  after every 20 min of active or sham tDCS intervention. The questionnaire consists of 14 items regarding symptoms which will enable us to determine if the participants are experiencing severe symptoms. The score ranges from 1 to 10, from absent to severe symptoms.
We created the feasibility criteria based on the suggested reasons for conducting a pilot study [74,75]. We adapted the criteria to our study settings as follows: (1) rates of eligible participants during the screening, (2) retention and follow-up rates throughout the study, (3) adherence rate to the study protocol (amount of total training hours of each participant), and (4) validity of the data collection schedule.
A previous study proposed the rules of thumb for estimating the sample size of a pilot study based on the anticipated effect size of the future main trial . According to the proposal, if the future main trial is designed around medium to large effect with 80% power and a two-sided 5% significance, a sample size for the pilot trial is set at 10 in each group . Allowing for a 20% of drop-out rate, we will recruit 12 participants in each group.
Participants, assessors, occupational therapists providing intensive upper limb training, experimenter applying the tDCS, and a researcher analyzing the data will be all blinded to group allocation. Independent researchers who will conduct the random allocation will not be blinded. A researcher who is in charge of patients’ safety and risk management can access the group allocation via the REDCap if necessary.
The active and sham tDCS groups will be compared with regard to demographic variables to assess group differences using the Student t-test or Mann-Whitney U-test for continuous variables and the χ2 test for categorical variables. Group differences of the primary (ARAT score) and secondary (FMA, MAL-14, and neurophysiological measures) outcomes will be analyzed using multivariable regression analyses and compared at each assessment time point. Furthermore, adverse events and their frequency and the questionnaire score will be reported to evaluate the safety of the procedure.