## 4 Discussion
### Interpretation of Results
On the other hand, it has been reported that the extrinsic muscles, the flexor hallucis longus and the flexor digitorum longus, contribute to strengthening toe-off [40]. In addition, the fibular muscles of the extrinsic muscles have been shown to contribute to ankle stability and to be activated during the late stance phase of running [41]. These extrinsic muscles are correlated with toe strength and have been shown to contribute to the generation of greater metatarsophalangeal joint flexion moments during exercise [7]. These studies suggest that both extrinsic and intrinsic muscles contribute to the generation of the metatarsophalangeal joint flexion moment, and that the coordinated activity of both is important. The advantage of tube training is the ability to train with a predominance of extrinsic muscles in the dorsiflexion position of the ankle joint, and with a predominance of the IFM in the plantar flexion position. After 10 weeks of jump rope training, the RSI increased by 13%, which was associated with improved performance in the 3 km time trial [42]. In this study, the baseline overall RSI was slightly high at 2.37 because the participants were competitive runners in the 40 cm drop jump. And, in the 5-week intervention, the RSI increased by 9.5% in the tube training and 4.2% in the SF-ex. The jump height is the most common and practical indicator for evaluating an athlete's explosive power [31]. A positive correlation exists between the strength of the toe flexors, including the IFM, and vertical jump performance [32]. In the vertical jump, the force generated by the hip extensors, knee extensors, plantar flexors, and toe flexors pushes against the ground, accelerating the body upwards. The flexor digitorum brevis helps to transmit the force of the lower limbs to the forefoot, and propels the body upwards in the trajectory of the jump [43; 44]. This also has the effect of lifting the heel off the ground during a vertical jump, increasing the plantar flexion moment at the ankle joint [45]. Extrinsic toe flexor activity tends to increase in conjunction with an increase in triceps surae muscle activity, suggesting that the energy generated at the ankle joint is transmitted to the metatarsophalangeal joint [46]. From these results, it can be concluded that the toe flexors are important for controlling the generation of force during the push-off phase of the vertical jump, and tube training can strengthen the toe flexors in the plantar flexion position of the ankle joint. The improvement in the toe grip strength, toe grip strength, and RSI indicates that tube training is an effective training method that promotes coordinated activity of both extrinsic and intrinsic muscles. Medial tibial stress syndrome is a common disorder among runners. In particular, approximately 15% of high school cross-country athletes develop the disorder during the three-month competition season, and approximately 44% develop it over a three-year follow-up period [47; 48]. Recovery from this injury takes between six and eleven weeks to return to the original competitive level [49]. These research results suggest the importance of introducing effective programs for prevention and early recovery for runners. In this study, tube training was able to show improvements in toe function equivalent to SF-ex through a 5-week intervention. Tube training does not rely on gravity as resistance [50]. Therefore, the load can be adjusted, enabling the exercise to be performed even during the period of unweighting due to lower limb injury. Tube-training may also be an effective training method for runners who are unable to run due to injury and are recovering the injured area.