**4. Discussion**

Compared with the control group, the female athletes with dominant-leg CAI improved in the SEBT, the active repositioning portion of the joint position sense test, and 30◦/s of CON and ECC of the ankle invertor in the isokinetic strength test after completing a 6-week WVB or balance training program. However, very small to small effect sizes for the assessed outcomes were observed between the exercise programs and control groups.

Sixty-three female athletes (50 basketball players and 13 volleyball players) with CAI participated in the study. Some prospective studies have reported that 19%–20% of ankle sprain rates occur in female basketball players [26,27]. Compared with male athletes, female athletes often experience greater laxity in the ankle joint and its ligaments. These sex-specific differences are caused by variations in hormone levels [28]. In addition, because the dominant leg is preferentially used for jumping and landing in basketball and volleyball, 80% of CAI in the dominant ankle is due to participation in sports [26]. Balance exercise programs have been designed specifically for female athletes, and the resulting improvements in balance and stability after completing such programs could reduce the risk of contact ankle sprains [29]. To our knowledge, the current study is the first to compare two exercise training programs with a control group. After 6 weeks, the WVB training group performed better than the balance training group did, and both groups exhibited improvements in dynamic balance, joint position sense, and isokinetic muscle strength after assessment. However, compared with the control group, both groups contributed to very small or small effect sizes of the assessed variables.

Balance deficit is the main cause of increased risk of recurring ankle sprain [30]. The exercise training programs, i.e., WBV and balance training, also play a decisive role in the rehabilitation process after an ankle sprain [31,32]. Some studies have suggested that balance training, especially by using the BOSU Balance Trainer, effectively reduces the balance deficit in patients with CAI [33,34]. WBV training is a popular method used for CAI rehabilitation and mitigating ankle instability. WBV training can increase α and γ neuron excitability and improve muscle spindle sensitivity, resulting in decreased muscular reaction time [8,9]. Therefore, the effects of WBV training on CAI could enhance ankle posture control during the SEBT, a dynamic balance measurement tool. Compared with the control group, female athletes with CAI experienced enhanced dynamic balance through WBV training and by using the BOSU Balance Trainer, both of which resulted in similar effects. However, both training programs contributed to very small or small effect sizes for CAI. Rendos et al. observed that WBV training does not cause acute dynamic balance improvements in patients with CAI [35]. Sierra-Guzmán et al. observed that compared with a control group, athletes with CAI exhibited moderate effect sizes (d = 0.54) in a composite score of SEBT after 6-week programs combining WBV training and the BOSU Balance Trainer [36]. Cloak et al. also observed a significant increase in the SEBT and revealed that 6-week programs combining WBV and a wobble board were effective for athletes with CAI [7]. Established programs combined with WBV may be a potential rehabilitation strategy for athletes with CAI, and should be studied in the future.

The joint position sense test measures joint kinesthesia and is used to measure the sensorimotor deficit of CAI [37]. Compared with the control group, athletes who underwent 6-week programs incorporating WBV training and the BOSU Balance Trainer showed improvement in the active repositioning of joint position sense at an ankle inversion of 15◦, neutral ankle position, and an ankle eversion of 10◦, but no significant improvement in passive repositioning (*p* > 0.05). Sousa et al. indicated that CAI could cause a decrease in joint position sense during ankle inversion, consequently affecting functional ankle movement [38]. In the current study, the reduced joint position error in ankle inversion and eversion is the contraction that was improved by both balance training programs. During active repositioning, the detection of movement sensation is markedly enhanced by ankle muscle contraction. We observed that the enhancement in active repositioning was better than that in passive repositioning because of the increase in spindle afferent activity and muscle strength [39]. Otzel et al. applied WBV at 35 Hz for CAI rehabilitation and reported no improvement in joint position accuracy or proprioception [40]. In the current study, the WBV training with a frequency of 5 Hz could improve the joint kinesthesia ability of ankle inversion and eversion in active repositioning for CAI, and the effects were the same as the balance training program. Baumbach et al. indicated that the frequency of WBV may be a key factor in CAI rehabilitation [41]. A frequency of <10 Hz is used for relaxing muscles; a frequency between 10 Hz and 20 Hz is used for coordination exercises, and a frequency >20 Hz is used for enhancing muscle contractions in WBV training [42]. However, the effects of various WBV frequencies on joint position sense in CAI are unknown, and additional research on this issue is warranted.

Regarding ankle strength, Wilkerson et al. reported significantly greater deficits in inversion strength than in eversion strength by using an isokinetic dynamometer [43]. Concentric invertor strength deficits are commonly found in patients with CAI, resulting in deep peroneal nerve dysfunction or selective neuromuscular inhibition after ankle sprain [44]. Ko et al. analyzed isokinetic ankle invertor and evertor muscle strength at angular velocities of 30◦/s and 120◦/s in patients with CAI and observed a severe invertor strength deficit at an angular velocity of 30◦/s [45]. In our findings, the ECC and CON invertor strengths at 30◦/s of angular velocity in the WBV and balance training group were significantly higher than those in the control group (*p* < 0.05). However, no significant differences in ECC and CON at angular velocities of 30◦/s and 120◦/s were observed in both groups before and after assessment (*p* > 0.05). Three exercise movements (double-leg stance, one-legged stance, and tandem stance) were applied in our training program, which consisted of 6-week programs incorporating static balance training exercises on a vibration platform or balance ball. During the exercises, the athletes (who had CAI) were instructed to maintain their balance on an unstable surface. The low frequency of 5 Hz of WBV in addition to static posture control exercises improved the ankle invertor strengths in ECC and CON at an angular velocity of 30◦/s. This strategy can be used as ankle invertor strength training for mitigating strength deficits in patients with CAI. The resultant increase in invertor isokinetic strength at a low angular velocity could be applied to reduce the capacity of control lateral postural sway during weight-bearing activities and to alleviate CAI symptoms [46].

Some studies have suggested that patients with CAI possess limited evertor isokinetic strength in injured ankles [47,48] and that an increase in evertor strength could assist the lateral ligaments in supporting a sudden ankle inversion movement [49]. The ECC of eversion/CON of inversion strength ratio, which is a functional agonist/antagonist strength ratio, is focused on outcome measurements for patients with CAI. Because normal movement patterns of lower extremities and gait patterns involve the interaction of agonist and antagonist strength, the strength ratio was used as an indicator of rehabilitation training for patients with CAI [50]. Brent et al. used the ankle eversion/inversion strength ratio to assess the outcomes of a 6-week strength training program for CAI and indicated that the balance of ankle eversion and inversion strength can support injured ligaments and improve ankle stability [49]. In the current study, the ankle eversion isokinetic strength and eversion/inversion isokinetic strength ratio at 30◦/s and 120◦/s angular velocities and the ECC of eversion/COM of inversion strength ratio did not exhibit significant differences within and between the groups (*p* > 0.05). Brent et al. reported that ankle invertor and evertor strength was significantly increased in college students with CAI after a 6-week strength training program [49]. Mohd Salim et al. also observed that the ankle eversion/inversion strength ratio improved in the ankles of patients with CAI after a 1-week standard physiotherapy program [51]. These studies suggest that ankle eversion or inversion strength in the ankles of patients with CAI could be increased compared with those with healthy ankles after specific exercise training for mitigating CAI [49,51]. However, we are the first to further examine the ECC and CON of eversion and inversion strengths at various angular velocities and compare training and nontraining groups in the context of the ankles of patients with CAI. Research on this topic is rare, and comparing the effects of ankle eversion or inversion on isokinetic strength after a balance training program specific to patients with CAI remains challenging.

This study had several limitations. First, the participants with CAI self-reported their symptoms and ankle sprain history, which could be misleading when determining CAI status. Second, dorsiflexion and plantar flexion movements were not involved in the measurement of joint position sense and isokinetic strength. The anterior and posterior kinetic chain involving ankle stability was not discussed after the training programs. Third, lack of long-term follow-up could not confirm the cure of CAI or long-term effects. Four, our exercise training programs may be of insufficient duration and exercise implementation as normal fitness training. Our results revealed that there were very small or small effect

sizes for CAI in dynamic balance, joint kinesthesia ability, and muscle strength of the ankle invertor and evertor after 6-week WBV or balance training. We researched the effects of the 20-min exercise comprised of three exercise movements performed on a balance ball or vibration platform. The variability of movement design may be inadequate, and the progress of training intensity maybe also insufficient, resulting in a very small or small effects on improvement of muscle strength, proprioception and balance ability. Investigation on the effects on different program designs of WBV or balance training in future studies is recommended.
