In this randomized, double-blinded, parallel-controlled trial, participants were randomly assigned to either the TI group (TI stimulation) or the sham group (sham stimulation). At the first visit, we collected the participants’ anthropometric data (age, height, weight, and leg length) and baseline assessments of lower limb motor abilities (Y-balance, countermovement jump [CMJ], squat jump [SJ], and continuous jump [CJ]). Subsequent visits involved a continuous 5-day intervention followed by completion of a questionnaire on blinding efficacy and side effects. On the second day following the completion of all stimulation sessions, participants revisited the laboratory for re-evaluation of lower limb motor abilities (study design, see Fig. 1). This study was conducted at the Biomechanics Laboratory of Shanghai University of Sport from September 2021 to November 2022. The study successfully achieved the anticipated sample size, and all scheduled interventions and assessments were conducted according to the predetermined plan.

Forty-six healthy adult males were recruited; among them, forty participants completed this study (participant flow diagram, see Fig. 2). The inclusion criteria were as follows: (1) good physical condition, and ability to complete a 60-s continuous vertical jump test; (2) right-handedness with the right leg as the dominant leg; and (3) no lower limb injuries within the past 3 months. The exclusion criteria were as follows: (1) personal or family history of neurological diseases; (2) participation in another experiment involving non-invasive brain stimulation or strength training; (3) history of lower limb injuries; (4) presence of metallic implants in the head; and (5) receipt of invasive treatment within the past 6 weeks.

Before enrollment, all participants were required to understand the study’s purpose, experimental procedures, and precautions. All participants provided written informed consent during the first visit. Ethical approval was granted by the Institutional Review Board of the Shanghai University of Sport (102772022RT051).

The custom-made Temporal Interference Stimulation System utilized in this study was developed based on a study conducted by Grossman et al. [6]. It comprised multiple components, including MATLAB programs, converters, and isolators [6]. The MATLAB program tailored for this study generated digital signals for TI stimulation. Subsequently, these signals were output through a converter (USB-6361, National Instruments Inc., America) and delivered as electrical currents via an A395 linear stimulus isolator (A395, World Precision Instruments Inc., America) [17].

The TI stimulation electrodes were placed at F3, P3, F4, and P4 (based on the International 10–10 Electroencephalography System [20], Fig. 3A). Specifically, F3 and P3 were designated as one alternating current, whereas F4 and P4 were allocated as another, with frequencies set at 2 kHz and 2.02 kHz (resulting in a frequency difference of 20 Hz). The target region for this stimulation paradigm was the lower limb motor control area of the primary motor cortex (the M1 leg area). The electric field simulation diagrams are shown in Fig. 3B and C. The peak-to-peak amplitude of the current was set at 2 mA. Stimulation was continuously administered twice daily for 5 consecutive days, with a 20-min interval between sessions. Each session of stimulation lasted for a total of 20 min. For the Sham group, the electrode placement, current intensity, and frequencies were identical to those of the TI group. However, the current of sham stimulation was applied only at the beginning and end of the stimulation, with a 30-s ramp-up and ramp-down, and no current input during the intervening 19 min [21].

Electrode placement and the distribution of the envelope electric field. A The red and blue circles represent the stimulation points for two alternating currents; red represents one channel of alternating current, while blue represents the other channel. B, C Illustrates the envelope electric field distribution on the cortical surface and coronal plane, respectively. The shades of red and blue denote different electric field intensities, with a stronger intensity being indicated by a shift toward the red color

Participants remained seated, refrained from using mobile devices, and minimized their head movements during the stimulation sessions. The experimenters closely monitored the participants and immediately interrupted the stimulation if any unusual sensations were reported. The study strictly adhered to double-blinded experimental requirements, with only one experimenter being aware of the stimulation type. The participants and assessors remained blinded to the intervention.

Vertical jump performance data were collected using a three-dimensional force platform (9287C, Kistler, Switzerland) at a sampling frequency of 1000 Hz. Participants were assessed for three types of vertical jumps: countermovement jump (CMJ), squat jump (SJ), and continuous jump (CJ) with a fixed order. For CMJ, the participants were instructed to rapidly move downward upon hearing a command, followed by a maximal vertical jump. After landing, the participants were required to flex their knees to absorb the impact and return to their starting position. The SJ required participants to reposition themselves in a squat and then perform a maximal jump after holding the position statically for at least 3 s. Both jumps were completed three times, and the height, ground reaction force, and impulse indices were calculated. The CJ involved participants performing CMJ for 1 min. The participants were instructed to keep their hands on their hips to eliminate the influence of upper-limb movements on jump performance. The average heights of the initial 15 s (Hfirst15s) and last 15 s (Hlast15s) during CJ were calculated separately. These two measurements were used to calculate the fatigue index.

MATLAB was employed for the preprocessing and analysis of the kinetic signals. The ground reaction force was filtered at a cut-off frequency of 50 Hz. Key metrics, including jump height, impulse, and fatigue index, were calculated using the following formulae:

Jump Height: Jump height was calculated using the formula \(H=\frac g^\) proposed by Yamashita et al. [22]. Based on flight time, this approach demonstrated low internal heterogeneity among participants, providing a reliable measure for assessing individual changes before and after the intervention.

Ground Reaction Force: Maximum ground reaction force during the concentric phase of the vertical jump.

Impulse: Calculated using the formula \(I=_F(t)dt\) where F(t) represents the resultant external force, and t is the ground contact time.

Fatigue Index (FI): Calculated as \(FI=\frac_-_}_}\times 100\%\), where Hfirst15s is the average height of the initial 15 s and Hlast15s is the average height of the last 15 s.

The Y-balance test was used to assess the dynamic postural stability of the dominant leg (all participants were right-legged) [23, 24]. The participants stood barefoot on their dominant leg (right leg) with their toes positioned at a marked line on a fixed platform. While maintaining a stable single-leg stance, the participants pushed a movable platform sequentially in the anterior, posteromedial, and posterolateral directions. During the test, participants were instructed to keep their hands on their hips facing forward with the non-supporting foot elevated. If the non-supporting foot touched the ground midway, the trial was considered unsuccessful and was repeated. Three successful attempts were made in each direction, and the distance (cm) was recorded. The Push Distance (% of leg length) was calculated using the following formula to standardize the data: Push Distance (%) = Distance/Leg Length × 100%, where Leg Length represents the distance from the greater trochanter to the lateral malleolus (cm).

The random allocation sequence was generated using the SPSS (version 26.0; IBM, Armonk, NY, USA) random number generator, assigning participants to the TI group or sham group with a 1:1 allocation ratio. All data were stored on a password-protected computer; additionally, the stimulation procedure was named words unrelated to the stimulation. Recruitment personnel, data collectors, statistical analysts, and participants were blinded to the group allocation, with a designated researcher being responsible for intervention based on the group assignments.

Participants were not informed of any differences between TI and sham stimulation. Sham stimulation involve a 30-s ramp-up and ramp-down, which created an itching sensation similar to the real stimulation for the participants. To ensure successful blinding, participants were asked to guess whether the stimulation was real or sham at the end of the stimulation. Information regarding side effects, including tingling, itching, burning, skin redness, drowsiness, inattention, and mood swings, was collected using a side-effect questionnaire [25]. Participants rated the severity of each side effect as none, mild, moderate, or severe.

The primary statistical model was a two-way repeated measures ANOVA based on the research design. The desired statistical power was set at 0.80, a significance level of 0.05, and an effect size of 0.40, resulting in a minimum sample size of 16 per group. Considering potential dropout rates, 46 participants were included in the study.

The normality of distribution was assessed using the Shapiro–Wilk normality test. Normally distributed data are presented as mean ± standard deviations (SD). Independent sample t-tests were used for between-group comparisons of anthropometric data. When the data met the assumptions of normality and homogeneity of variances, two-way repeated measures ANOVA was used to investigate the effects of group (TI vs. sham) and time (pre-test vs. post-test) on vertical jump performance and dynamic postural stability. Paired t-tests were used to assess within-group differences before and after stimulation. The significance level (α) was set at 0.05, and the effect size was represented by η2. Statistical analyses were performed using SPSS (version 26.0; IBM, Armonk, NY, USA).