Relationship Between Foot Flexibility and Leg Muscle Stiffness After Running: a Cross-sectional Study

Background Deformation of the foot is related to the development of running injuries. The prevention of running injuries requires the management of changes in leg muscle stiffness after running. However, the relationship of muscle stiffness and the structure and exibility of the foot arch is unclear. The purpose of this study was to investigate differences in muscle stiffness and exibility of the arch before and after running. Twenty lower limbs of 10 healthy volunteers were enrolled. All of the subjects performed the same running task on a treadmill set at an incline of 7%, running at a speed of 8 km/h for 60 min. The shear elastic modulus of the longitudinal axis of the medial and lateral gastrocnemius (MG, LG), exor digitorum longus (FDL), and abductor hallucis muscles were measured both before and after running using ultrasound shear wave elastography. Arch height index (AHI) and arch height exibility (AHF) were measured at 10, 50, and 90% of the body weight loaded position, respectively. The correlation of AHI, AHF, and alterations in each muscle stiffness before and after running was assessed using Spearman’s rank correlation coecient.


Abstract Background
Deformation of the foot is related to the development of running injuries. The prevention of running injuries requires the management of changes in leg muscle stiffness after running. However, the relationship of muscle stiffness and the structure and exibility of the foot arch is unclear. The purpose of this study was to investigate differences in muscle stiffness and exibility of the arch before and after running.

Methods
Twenty lower limbs of 10 healthy volunteers were enrolled. All of the subjects performed the same running task on a treadmill set at an incline of 7%, running at a speed of 8 km/h for 60 min. The shear elastic modulus of the longitudinal axis of the medial and lateral gastrocnemius (MG, LG), exor digitorum longus (FDL), and abductor hallucis muscles were measured both before and after running using ultrasound shear wave elastography. Arch height index (AHI) and arch height exibility (AHF) were measured at 10, 50, and 90% of the body weight loaded position, respectively. The correlation of AHI, AHF, and alterations in each muscle stiffness before and after running was assessed using Spearman's rank correlation coe cient.

Results
The FDL, LG, and MG were signi cantly harder after running than before running. The AHI and AHF had no signi cantly difference between before and after running. There were signi cant moderate correlations between AHF50 before running and stiffness of the FDL after running.

Conclusion
Increased stiffness of the FDL is related to medial tibial stress syndrome. Our results indicate that stiffness of the arch is associated with greater stiffness of the FDL, which restricts performance of the dynamic function of stretching the muscle and tendon complex of the toe exor with weight loading on the foot.
1. The stiffness of exor digitroum longus is increased after running.
2. Arch exibility is decreased after running, although arch height shows no change.

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The development of running injuries is multifactorial, with passive range of motion, muscle strength, biomechanics of the running, gender and body weight [1] [2,3] [4]. During running, muscle stiffness due to malalignment and overuse increases mechanical stress at the insertion of the skeletal muscles to the bone. Several authors demonstrated that the exor digitorum longus (FDL), and soleus muscles originated from the medial tibial border, and the medial tibial stress syndrome (MTSS) Increase in the stiffness of the exor digitorum longus (FDL), and traction-induced injury, related to muscles of the super cial and deep posterior compartments, has been implicated as the cause of medial tibial stress syndrome (MTSS) with symptoms commonly occurring in the distal third of the posteromedial tibia.
soleus muscles originated from the medial tibial border is related to medial tibial stress syndrome [5] [6,7]. In addition, Achilles tendinopathy is related to stiffness of the medial and lateral heads of the gastrocnemius (MG, LG) [8]. During physical therapy, these muscles are treated by stretching and strength training [9]. However, in many cases, the symptoms recur with a return to activity. Therefore, during physical therapy for running injuries, it is important to control for changes in the stiffness of key muscles after running.
Malalignment of the foot is a well-known cause of running injuries [10][11][12]. In particular, atfoot is reported to be a risk factor for patella-femoral pain syndrome [11] and low back pain [11,12]. Many studies demonstrate the relationship between running injuries and the static foot posture, although arch exibility plays a role in buffering loading stress by attening during weight loading. Recently, Zifchock et al. [13]proposed that most atfeet are very exible, with only a small proportion being associated with stiffness. Therefore, it is important for the treatment of running injuries to understand the role of not only static foot posture, but also the exibility of the arch. However, the relationship between running injuries and exibility of the arch is unclear.
Long distance running tends to decrease the height of the medial longitudinal arch, and to reduce arch exibility [14,15]. Moreover, the stiffness of the dynamic stabilizers of the arch, such as the tibialis posterior and the FDL, is increased after running [16,17]. However, the effects of the structure and exibility of the arch on changes in muscle stiffness after running are unclear. The arch of the foot is maintained by both a static stabilizer and a dynamic stabilizer as extrinsic and intrinsic foot muscles. We hypothesize that patients with greater alteration of both structure and exibility of the foot show an increase in stiffness of both the leg and foot muscles that maintain arch structure. Therefore, the purpose of this study was to investigate changes in muscle stiffness and the structure and the exibility of the arch of the foot before and after running.

Participants
Twenty lower limbs of 10 healthy university students who habitually participated in recreational sports activity more than 2 days per week were enrolled in this study. Inclusion criteria were subjects without any history of pain in the leg and foot while running. Two of the subjects could not nish the running task and were excluded from the study. Thus, 16 lower limbs of the remaining 8 subjects (age, 21.4±0.5 years; height, 162.4±9.2 cm; body weight, 54.1±8.3 kg; 5 males) were analyzed. The study was approved by the Medical Ethics Committee of the authors' institution (2018-103), and all the subjects provided informed consent for study participation.

Procedure
All subjects performed the same running task on a treadmill (Adventure3, Johnson Health Tech, Tokyo, Japan) set at an incline of 7% and a running speed of 8 km/h for 60 min after 3 min of warm up. Warm up started with level walking (4 km/h) for 90 s, followed by level jogging (6 km/h) for 90 s. After the warm up period, the incline was set at 7% and the running task was commenced (8 km/h). The foot contact pattern of the runners was not restricted.
Muscle stiffness was assessed using ultrasound shear wave elastography (Aplio 300, Canon Medical Systems, Tokyo, Japan) and a 5-14 MHz linear probe. A higher shear elastic modulus indicates an increase in the stiffness of the tissue. The shear elastic modulus (kPa) of each muscle was calculated automatically from 3 circular regions of interest (ROI) in the color mapped area of elastographic images of each muscle. Assessment of the shear elastic modulus after running was completed within 10 min after the running task. The shear elastic modulus of the longitudinal axis of the MG, LG, FDL, and abductor hallucis (AH) muscles were measured both before and after running for 60 min.
The LG and MG were measured at the proximal 30% of the lower leg (from the popliteal crease to the lateral malleolus). The FDL was measured at the proximal 50% of the area between the cleavage line of the knee and the medial malleolus [16,17]. The AH was measured at the medial border of the foot below the navicular bone. The FDL muscle was identi ed using a B-mode ultrasound image during passive motion of the toe. In addition, we marked the measurement site with cotton bandages so that measurements both before and after running could be recorded at the same site.
Ten lower limbs of 5 participants were included in a reliability study. Muscle stiffness was assessed by a single tester who had practiced ultrasound imaging for 2 h per week for 2 months before the study. The tester performed assessments 3 times as the rst session, and repeated the evaluations 3 times on another day as the second session. Assessment of intra-tester reliability of the measurement of muscle stiffness was performed using the intra-tester correlation coe cient [ICC (1,k)], and the standard error of the mean (SEM) was calculated from the mean value of the rst and second sessions. Minimum detectable change with 95% con dence intervals (MDC 95 ) was calculated using equation (1).
The structure and exibility of the medial longitudinal arch was assessed using the modi ed arch height index (AHI) [18] and arch height exibility (AHF) [13], respectively. Images of the medial side of the foot at 10%, 50%, and 90% body weight (BW) loading were captured by a digital camera (EOS Kiss X7i, Canon Inc., Tokyo, Japan) positioned at a constant distance (90 cm) from the foot. The dorsal arch height (DH) at 50% of the foot length divided into the truncated foot length in the 10%, 50%, and 90% body weightloaded positions were calculated as AHI 10 , AHI 50, and AHI 90 , respectively. The differences between AHI 50 and AHI 10 , and AHI 90 and AHI 10 were assessed as AHF 50 and AHF 90 by equations (2) and (3): Difference in AHI and difference in AHF (DAHI, DAHF) were de ned as the difference in each parameter before and after running. A higher DAHI indicated a decrease in arch height after running, and a higher DAHF indicated an increase in arch exibility after running.

Analysis
Muscle stiffness, arch structure, and arch exibility before and after running were compared using the Wlicoxon test, and the correlation of arch structure, arch exibility, and the difference in each parameter with muscle stiffness before and after running were assessed using Spearman's rank correlation coe cient. All statistical tests were performed using SPSS statistics version 25.0 (IBM Corp., Armonk, NY, USA), with p < 0.05 considered signi cant.

Results
The shear elastic modulus of each muscle is shown in Table 1. ICCs (1,k) of all the muscles were considered to have high reliability (> 0.7). LG, lateral gastrocnemius; MG, medial gastrocnemius; FDL, exor digitorum longus; AH: abductor hallucis The shear elastic modulus of each muscle before and after running for 60 min is shown in Table 2. The FDL, LG, and MG were signi cantly harder after running than before running. The hardness of the AH was not signi cantly different between before and after running. LG, MG, and FDL stiffness after running was signi cantly higher than before running.
LG: lateral gastrocnemius, MG: medial gastrocnemius, FDL: exor digitorum longus, AH: abductor hallucis The structure and exibility of the arch before and after running are shown in Table 3. The structure of the arch was not signi cantly different before and after running. In the assessment of arch exibility, AHF 50 indicated a signi cant decrease in the exibility of the arch after running. AHF 50 and 90 is arch height exibility for the 50 and 90% weight loading, respectively.
The correlation coe cients between AHI and AHF before running and the muscle stiffness after running are shown in Table 4. There were signi cant moderate correlations between AHF 50 before running and stiffness of the FDL after running. Thus, subjects with lesser exibility of the arch before running demonstrated harder FDLs after running. LG, lateral gastrocnemius; MG, medial gastrocnemius; FDL, exor digitorum longus; AH, abductor hallucis. AHI 10 , 50, and 90 is the arch height index for the 10, 50, and 90% weight loading, respectively. AHF 50 and 90 is the arch height exibility for the 50 and 90% weight loading, respectively.

Discussion
The purpose of this study was to investigate changes in muscle stiffness and the structure and the exibility of the arch of the foot before and after running. As results, decreased shear elastic modulus of the FDL, MG, and LG was observed after 60 min of uphill running, but there was no affect on arch height. Furthermore, after running, there was an increase in arch exibility with 50% weight loading. Subjects with lower exibility of the arch after running demonstrated greater stiffness of both the LG and FDL after running. Moreover, subjects with lesser exibility of the arch before running had a greater increase in stiffness of the FDL after running than those with greater exibility of the arch. Swanson et al. reported that uphill running increased plantar exion of the ankle during the propulsive phase [19]. Further, uphill running requires the generation of greater ankle power than that required during level and downhill running [20][21][22]. The resultant increased compartment pressure of the plantar exor muscles by the repetitive overload stress during running leads to greater stiffness of both the gastrocnemius and FDL.
Stiffness of the gastrocnemius reportedly has a strong correlation with plantar fasciitis [23]. Moreover, patients with a history of medial tibial stress syndrome had stiff FDLs [17] and increased stiffness of the FDL after running [16]. These results are similar to those of the our study, which show an increase in the stiffness of muscles related to running injuries. The arch height did not have any difference between before and after running, although, we hypothesize the lower arch is shown after running. Because, the long distance runners showed to decrease the arch height after half and full marathon [14] [15]. These differences of the in uence the arch structure is due to the level of distance, therefore, it has a possibility to decrease the arch height after longer distance than current study. In the other hand, there was shown to decrease the arch exibility after running. Despite the overwhelming focus on arch height as a predictor of overuse injury, there is evidence to suggest that arch stiffness might also be a key factor in predicting overuse injury [13] [24] [25] [26]. However, relationship arch exibility and muscle stiffness after running remind uncleared. This is a rst study, the subject with low exible arch before running has been demonstrated greater stiffness of both the LG and FDL after uphill running.
The FDL inverts the ankle and elevates the arch of the foot. LG muscle fascicles are reported to have a twisted structure in the Achilles tendon [27], resulting in stretching of the MG, LG, and soleus when the subtalar joint is pronated, and shortening with supination [28]. Thus, subjects with greater stiffness of both the FDL and LG demonstrate decreased arch exibility, because these muscles restrict pronation of the calcaneus.
Yamauchi et al [29] showed that toe exor strength was related to arch exibility in the weight-loaded position and that there is a greater increase in toe exor strength when changing from the sitting to standing position in subjects with a exible arch as compared to those with a stiff arch. Thus, a stiff arch restricts performance of the dynamic function of stretching of the muscle and tendon complex of the toe exor when weight is loaded on the foot. This function is known as stretch shortening cycle, which demonstrates the higher e ciency of the skeletal muscle tension. Our study demonstrated that subjects with low exible arch before running show greater stiffness of the FDL than those with high exible arch after repetitive weight loading, as during running. The foot with low exible arch has di culty participating in the stretch shortening cycle of the FDL, which leads to overuse of the FDL.
There are three limitations to this study. First, although we assessed foot alignment before and after running, we did not assess kinematics during running. Thus, the effects of kinematics during running on arch height and muscle activity are unclear.
The Achilles tendon is a tough band of dense connective tissue that connects both the gastrocnemius and soleus muscles to the calcaneal tendon. Further, the tibialis posterior muscle plays a big role in maintenance of arch structure. However, in this study, these muscles were not tested because of their deep position, di culty in assessment of the stiffness of deep muscles, and the presence of a hard aponeurosis super cial to the muscle. Further, muscle stiffness needs to be assessed less than 10 min after running for consideration of muscle fatigue. the subjects in this study did not have any symptoms of overuse injury in the lower limbs. Further studies will need to assess the altered arch stiffness and muscle stiffness after running in patients with running injuries.

Conclusions
Muscle stiffness related to running injuries was increased after 60 min of uphill treadmill running (8 km/h, 7% incline). Further, although arch height did not change, arch exibility was increased after running. Stiffness of the arch before running was associated with greater stiffness of the FDL after running, which restricted performance of the dynamic function of the stretching shortening cycle of the