Force Generation of the Hallux is More Sensitive to the Ankle and Metatarsophalangeal Joint Angle Than the Lesser Toes

Background: Because the structure of the hallux is independent of that of the lesser toes and it uses different muscles to move, the force generation characteristics of the hallux could be independent of those of the lesser toes. The purpose of this study is to clarify the torque–angle relationships in the rst and second–fth metatarsophalangeal joints (MTPJs). Methods: Ten healthy young men served as volunteers in this study. The maximal voluntary contraction (MVC) of the plantar- ﬂ exion torques of the rst and second–fth MTPJs were measured at 0°, 15°, 30°, and 45° dorsiexed positions of the MTPJs and 20° plantar-exed, neutral, and 20° dorsiexed positions of the ankle. The Friedman test and the Wilcoxon signed-rank test with a Holm correction was used for the ankle and MTPJ angles. Results: When the rst MTPJ was 0° to DF30°, the MVC torque of the rst MTPJ at DF20° of the ankle was higher than at PF20°of the ankle. On the other hand, no signicant difference existed between the MVC torques of the second–fth MTPJs at any ankle position. When the ankle was in a neutral position, the MVC of the rst MTPJ torque increased as the MTPJ was dorsiexed. However, the MVC torques of the second through fth MTPJs did not signicantly differ for the 15°, 30°, and 45° dorsiexed positions of the MTPJ. Conclusion: The MVC torque of the rst MTPJ is more sensitive to the MTPJ and ankle positions than the second–fth MTPJs.


Background
The toe exor muscles are activated during walking and holding a single-leg stance [1,2]. It has been reported that toe grip strength is associated with functional mobility in the older people [3]. Consequently, the weakness of the toe grip is a risk factor for falls in the older people [4]. In addition, in healthy young people, the cross-sectional area of the intrinsic foot muscles affects their performance during the singleleg stance [5]. Thus, the toe exor muscle function affects the balance ability for all ages, and the assessment of the toe exor muscle strength is important for the improvement of the balancing ability in humans.
The joint angle alters the maximum force generated by the muscle [6]. Additionally, it affects the muscle length and internal moment arm [7,8], which further affect the force generation capacity. The length of the extrinsic toe exor muscles is altered by the metatarsophalangeal joint (MTPJ) as well as the ankle joint angle [7]. The plantar exion torque of the MTPJ is in uenced by the force-length relationship of the intrinsic and extrinsic muscles of the foot when the MTPJ angle is changed, and it is in uenced by the relationship with the extrinsic muscles when the ankle joint angle is changed. During the plantar-exion of the ankle, the soleus muscle is activated selectively at the knee exion position [9]. Measuring muscle strength at various joint angles helps us determine the measurement positions of the maximal voluntary contraction (MVC) torque according to the muscle that needs to be assessed.
A previous study reported the relationship between the MVC torque and joint angle (torque-angle relationship) of an MTPJ for all toes [10]. However, the structure of the rst toe (hallux) is independent of that of the other toes and it is moved using different muscles in most primates, including humans [11].
Our previous study reported that runners with a history of medial tibial stress syndrome exhibit higher plantar-exion strength in their rst MTPJ [12]. Regarding adaptation in sports, this study suggests that it is important to consider the strengths of the hallux and lesser toes separately. Moreover, the composition ratio of the intrinsic and extrinsic muscles is different between the plantar-exion muscle of the rst and second-fth MTPJs [13]. Consequently, there is a possibility that the sensitivity of the plantar-exion muscle to the joint angle is different in case of rst and second-fth MTPJs.
Recently, we developed a device that could measure the plantar-exion torque of the rst MTPJ and a unit of the second-fth MTPJs [14]. It is possible to measure the plantar-exion torque of the rst MTPJ and second-fth MTPJs at various MTPJ and ankle positions. The purpose of this study was to determine the relationship between the MVC of the plantar-exion torque and joint angle in the rst and secondfth MTPJs using this device. We hypothesized that the plantar-exion of the rst MTPJ is sensitive to the joint positions due to the large composition ratio of the extrinsic muscles.

Participants
Ten healthy young men voluntarily participated in this study. The mean ± standard deviations of their age, height, and mass were 23.2 ± 1.9 years, 169.2 ± 3.7 cm, and 58.4 ± 8.1 kg, respectively. The individual values are detailed in Table 1. The required sample size for a repeated analysis of variance [effect size = 0.25, α error = 0.05, power = 0.80, correlation among repeated measures = 0.6] was calculated using a statistical power analysis software (G*power 3.1, Heinrich Hein University, Germany), and the value obtained was 10. This study was approved by institutional human research ethics committee and was carried out in accordance with the declaration of Helsinki.

Measurement of MVC torque
The MVC torque was measured using a custom-made torque-measuring device. This device recorded the tensile force data from the strain gauge (TU-BR, TEAC, Japan), and converted it from analog to digital using an A/D converter (Power Lab, AD instruments, Australia) via an ampli er (DPM-711B, Kyowa Electronics, Japan). The torque values were calculated as the corresponding tensile forces multiplied by the 0.10 m lever arm of the force plate.
Each subject was sat back in a dedicated chair and their trunk was secured to the chair using non-elastic straps. Their right foot (dominant side) was secured to the torque-measuring device (Fig. 1). Additionally, it was con rmed that the bottom of the toes and foot of the subject did not oat from the device in all measurements. After a warming-up session with subjective 60% contractions, each subject performed the MVC torques of the rst and the second-fth MTPJs at each position for approximately 3 s. The results thus obtained were used to determine the highest torque. The subjects were verbally instructed to avoid counter movement. The MVC torque was calculated as the highest torque minus the lowest torque obtained during contraction (Fig. 2). To avoid the effects of muscle fatigue, the resting period was set as at least 2 min. For analysis, the average torque between the two measurements conducted at each position was chosen. The reliability of the measurements was previously reported [14].

Statistical Analysis
The descriptive data are presented as means ± SDs. Shapiro-Wilk tests were used to verify a normal distribution, and the results showed that some components did not follow a normal distribution.
Therefore, the Friedman test was used for the ankle and MTPJ angles. When signi cant differences were found in the Friedman test, the Wilcoxon signed-rank test with a Holm correction was used for multiple comparisons. The same method was used to examine the differences in the torque-angle relationships of the rst and second-fth MTPJs. For all the MTPJ and the ankle positions, the MVC torque values were compared between the rst and second-fth MTPJs using the Mann-Whitney U test. Statistical analyses were performed using a statistical software (SPSS Statistics 26, IBM, USA). For all the tests, the statistical signi cance was set as p < 0.05.

Results
There were signi cant variations in the ankle positions at 0°, DF15°, and DF30° of the rst MTPJ in the Friedman test (p < 0.01, < 0.01, and 0.01, respectively). In contrast, there was no signi cant difference in the ankle positions at DF45°of the rst MTPJ (p = 0.15). When the rst MTPJ was at 0° to DF30°, the MVC torques at PF20° of the ankle were smaller than those at DF20° of the ankle. There were signi cant variations in the rst MTPJ positions at PF20°, 0°, and DF20° of the ankle in the Friedman test, t (p < 0.01, < 0.01, and 0.01, respectively). When the ankle was at PF20°, the MVC torques were signi cantly different from all other torques and increased as the MTPJ dorsi exed (Fig. 3). When the ankle was at 0°, the MVC torques increased signi cantly as the MTPJ dorsi exed in four comparisons (0° and DF30°, 0° and DF45°, DF15° and DF45° as well as DF30° and DF45°). When the ankle was at DF20°, the MVC torque at 0° of the MTPJ was signi cantly lower than that at DF15° and DF45°. In contrast, there was no signi cant difference in the MVC torques at DF15°, DF30°, and DF45°.
There was no signi cant variation in the ankle positions at all second-fth MTPJ positions in the Friedman test (p = 0.12, 0.06, 0.06, and 0.20, respectively). There were signi cant differences in the second-fth MTPJ angles at PF20°, 0°, and DF20° of the ankle in the Friedman test (p < 0.01, < 0.01, and 0.03, respectively). When the ankle was at PF20°, the MVC torques increased signi cantly as the MTPJ dorsi exed in four comparisons (0° and DF15°, 0° and DF45°, DF15° and DF45° as well as DF30° and DF45°) (Fig. 4). When the ankle was at 0°and DF20°, the MVC torques at 0° of each MTPJ were signi cantly lower than those at the other MTPJ angles.

Discussion
This study demonstrated the torque-angle relationships for the rst and second-fth MTPJs. The main ndings of the present study were 1) the force generation of the rst MTPJ was sensitive to the ankle position and 2) the force generation of the rst MTPJ was sensitive to the MTPJ angle when the ankle was at DF0°. To the best of our knowledge, this is the rst study to show each force generation characteristic of the rst MTPJ and second-fth MTPJs. To the best of our knowledge, this is the rst study to show each force generation characteristic of the rst MTPJ and second-fth MTPJs.
When the rst MTPJ was 0°, DF15°, and DF30°, the MVC torque of the rst MTPJ at DF20° of the ankle was higher than at PF20°of the ankle. However, there was no signi cant variation in the ankle positions at all second-fth MTPJ positions. These results supported our hypothesis. The plantar-exion moment arm of the ankle is larger in the exor hallucis longus muscle compared to the exor digitorum longus muscle [8]. As a result, the exor hallucis longus muscle is varies more in length compared to the exor digitorum longus muscle during the plantar-exion/dorsi exion of the ankle. Therefore, we considered that the extrinsic muscles make a large contribution to the plantar-exion torque of the MTPJ in the dorsi exion position of the ankle, and the muscle activity of the rst MTPJ becomes relatively large at the dorsi exed position of the ankle.
The MVC torques of the rst MTPJ increased as the MTPJ was dorsi exed when the ankle was at PF20°a nd 0°. However, we observed no signi cant difference between the MVC torques measured at DF15° to DF45° of the rst MTPJ when the ankle was at DF20°. The force capacity generated by a muscle ber is altered by the muscle ber length (force-length relationships) [17]. These results suggested that the ranges of MTPJ and ankle correspond to the ascending arm of the torque-angle relationship at 0° to DF45° of the rst MTPJ, when the ankle was at PF20° and 0°, and the plateau region (i.e., optimum angle zone) at DF15° to DF45° of the rst MTPJ, when the ankle was at DF20°. The maximal torque is generated at DF20° of rst MTPJ during sprinting [16]. In addition, the ankle lies in the neutral to plantarexed position when maximal torque is generated at the rst MTPJ during sprinting [15,18]. The obtained results indicate that plantar-exion torque of the MTPJs was generated in ascending limb of the torqueangle relationship during sprinting. Therefore, to generate the higher torque, it could be advantageous not to limit the dorsi exion of the MTPJ during running and sprinting.
The MVC torques of the second-fth MTPJs increased as the MTPJ was dorsi exed when the ankle was at PF20°. However, no signi cant difference could be observed between the MVC torques at DF15° to DF45° of the second-fth MTPJs when the ankle was at 0° and DF20°. The force generation characteristics are different between the rst and the second-fth MTPJs. The torque-angle relationship of the extrinsic and intrinsic muscles was found to be in the optimum angle zone between DF15° to DF45° when the ankle was at 0° in the second-fth MTPJs. In contrast, the torque-angle relationship was in the ascending arm at 0° in the rst MTPJ. A previous study reported that the fth MTPJ was less dorsi exed than the rst MTPJ in human walking [19]. We considered that the optimum muscle lengths of the second-fth MTPJs could be shorter than that of the rst MTPJ. Therefore, the muscle activity of the rst MTPJ becomes relatively large at the dorsi exed position of the MTPJ.
The highest torques were 11.4 ± 2.3 and 7.8 ± 1.7 N m on the rst and second-fth MTPJs, respectively.
The MVC torque of the rst MTPJ was larger than second-fth MTPJ at all positions. The torques measured in the present study were higher than those estimated in a previous study [13], wherein, the productivity of the torque was calculated from the anatomical cross-sectional area and estimated muscle tensions reported in a study of cadavers. However, physiological cross-sectional area has been reported to be more suitable for predicting functional properties than anatomical cross-sectional area [20]. In addition, the force that a muscle can generate per unit area is altered by the number and ring rate of a motor unit [21], and varies from muscle to muscle [22]. Thus, an estimated value may be different from the measured value. Consequently, the in vivo measured torques of this study were higher than the estimated values reported in the previous study. In the present study, the MVC torque was particularly greater in the rst MTPJ. During walking, humans push off from an axis between the rst and second MTPJ [23]. In such cases, the rst MTPJ was greatly dorsi exed [19]. These walking characteristics possibly contribute to the development of the motor unit of the hallux.
The MVC torque in the present study was lower than the plantar-exion torque of the MTPJ during running [24]. A previous study reported that the intrinsic foot muscle lengthens and recoils rapidly during the later stance in accordance with the recoil of the foot arch during running [25]. It is considered that this recoil action causes the stretch shortening cycle [26], which results in an increased torque production. Some limitations should be noted. The sample size was small, and the subjects were limited to young men and normal structure of their foot in this study. Hence, the applicable range of the results may be limited. Previous studies have shown that arch height is not correlated to toe grip strength [27]. Additionally, the optimal angle for force production is independent of age or gender [28]. However, there is room to investigate the behavior of the torque-angle relationship among the wide population to understand the toe function.

Conclusions
This study demonstrated the torque-angle relationships for the rst and second-fth MTPJs. When ankle was at 0°, the MVC torque of the rst MTPJ increased with the MTPJ dorsi exion, but the MVC torques of the second-fth MTPJ were not signi cantly different at DF15° to DF45° of the MTPJ when the ankle was at 0°. Furthermore, when the rst MTPJ was 0° to DF30°, the MVC torque of the rst MTPJ at DF20° of the ankle was higher than at PF20°of the ankle. On the other hand, no signi cant difference existed between the MVC torques of the second-fth MTPJs at any ankle position. Thus, the present study suggested that the force generation characteristic of the rst MTPJ is more sensitive to the MTPJ and ankle position than the second-fth MTPJs.

Availability of data and materials
The data that support the ndings of this study are available from the corresponding author upon reasonable request.

Competing interests
The authors declare that they have no competing interests.  Structure of the metatarsophalangeal joint (MTPJ) plantar-exion torque-mater for measuring the isometric torque. The plantar-exion torque was calculated from the tensile force (ε) and lever arm of the foot plate (0.10 m).

Figure 2
Typical data of the measured maximal voluntary isometric plantar-exion torque of each metatarsophalangeal joint (MTPJ). Maximal voluntary isometric plantar-exion torque was de ned as the difference between the maximal torque during maximal voluntary isometric contraction (MVC) and passive torque at rest.