## 2 Materials and Methods
### Data Collection and Analysis Methods  
In the pilot study, ultrasound echo (SonImage MX1; KONICA MINOLTA, Tokyo, Japan) was used to measure changes in muscle cross-sectional area due to acute muscle swelling [26; 27] in AbH, FHB, and FDB before and after each intervention condition. Immediate effects were validated with ImageJ software (ImageJ 1.53t; National Institutes of Health, Baltimore, MD, USA) [28]. The region of interest was calculated by enclosing it along the fascial boundary. The mean of each muscle cross-sectional area was calculated from three images of each muscle of each participant. Toe grip strength was measured using a toe grip dynamometer (T.K.K.3362; Takei Scientific Instruments, Niigata, Japan). The reliability of this device has been reported [29]. Participants were seated on a 40 cm high chair, with the pelvis in the mid-pelvic position and the hip and knee joints in 90\({}^{\circ}\) flexion, according to the methods of previous studies [29]. Figure 2: Toe tube training in a sitting position, with the tube placed between the great toe and the second toe, and plantar flexion and dorsiflexion of the ankle joint. The ankle joint was placed in a neutral position and strapped to minimize movement. After the heel stopper was adjusted to fit each participant's heel, the first proximal phalanx was aligned with the grip bar. Measurements were taken twice each, alternating left and right, and the average of the maximum values was adopted. Participants received verbal encouragement while performing the test. The toe gap strength was measured using a toe gap dynamometer (Checker-kun; Nissinsangyo, Saitama, Japan) to measure the pinching strength between the great toe and the second toe [30]. This device has a structure similar to that of a grip dynamometer. The toe gap strength was measured twice each, alternately on the left and right side, in the same posture as the toe gap strength, taking care not to lift the heel, and the average value of the maximum values was adopted. Participants received verbal encouragement during the test. RSI measures how quickly an athlete can exert strength when moving from a single downward sinking movement (centrifugal movement) to an immediate jumping movement (centripetal movement). This can be measured by the movement of jumping down from a high place and immediately jumping back up, as in a drop jump, and is expressed as the ratio of the height of the jump to the time the athlete was in contact with the ground [31]. In other words, the higher the RSI, the more efficiently you can utilize the rebound from the ground, which is one of the most important factors for the running economy. Previous research has shown a correlation coefficient of 0.58 between the strength of the toe flexors and the rebound jump index [32]. In this study, RSI was calculated using the My Jump2 application (My Jump2 v.6.1.7; [PERSON], Madrid, Spain) with the drop jump test filmed on an iPhone XR (Apple, Cupertino, CA, USA) at 1080p/240 fps [33]. This uses the high-frame-rate and high-screen-resolution video recording on the iPhone to derive the jump behavior [33]. The time of flight and all subsequent variables were calculated from the participant's leg length and weight. RSI variables were provided from the output jump height (cm) and time of flight (ms). Total flight time was measured by manually selecting the first video frame in which the participant took off after the drop and the second frame in which they landed after the jump. My Jump 2 App calculates jump height from flight time using the following equation from [PERSON] et al. : h = t\({}^{2}\)\(\times\) 1.22625 or h = (g \(\times\) t\({}^{2}\))/8. Here, h is the total displacement of the center of gravity in meters (height jumped), is the total flight time in seconds, and g is the acceleration due to gravity (9.81 m/s\({}^{2}\)) [34].