the human foot is composed of three arch structures , namely the medial longitudinal arch 
 ( mla ) , lateral longitudinal arch , and transverse arch .
these arch structures reduce pressure 
 on the soft tissue by dispersing the loading stress and increasing the efficiency of force 
 transmission by functioning as a spring during walking1 .
the mla has been measured to evaluate the role of arch structure in 
 a physical therapy setting , with the navicular bone being regarded as a landmark of the arch 
 apex , as it is palpable and deviates minimally .
some methods of mla measurement have been 
 previously described , including navicular drop ( nd ) , in which the difference in navicular 
 height between the standing and sitting positions is measured2 .
the height and general shape of the mla are maintained by the 
 plantar fascia , ligaments , and intrinsic and extrinsic muscles of the foot3 .
previous studies have reported that nd is 
 related to lower limb disability4 , 5 and that it can be decreased after toe 
 exercise6 ; taken together , these 
 findings suggest that toe muscle strength may relate to arch structure and lower limb 
 disability .
the 
 extrinsic muscles running across the ankle joint include the flexor hallucis longus ( fhl ) 
 and flexor digitorum longus . on the other hand
, the intrinsic muscles do not run across the 
 ankle joint and do not contribute to ankle movement .
both the intrinsic and extrinsic 
 muscles are stretched by dorsiflexion of the metatarsophalangeal ( mtp ) joints , whereas only 
 the extrinsic muscles are relaxed by plantar flexion of the ankle joint7 .
the exhibited maximal torque is affected by the joint 
 angle8 , and a relationship between joint 
 angle and plantar flexion torque of the mtp joints has been reported previously9 .
thus , these previous studies suggest that excessive nd can cause lower limb disability and 
 that this can be controlled by toe exercise
. however , the dynamometer used in the previous 
 studies measured only toe grip strength , i.e. , the plantar flexion force of all toes at the 
 plantar flexion position of the mtp joint10 .
moreover , the relationship between nd and the measurement position 
 of plantar flexion torque of the mtp joints has not been studied .
therefore , the aims of 
 this study were to clarify the relationship between nd and plantar flexion torque of the 
 first and second - fifth mtp joints and to determine the differences between neutral positions 
 of the mtp and ankle joints and stretching position of the intrinsic muscles .
in a previous 
 study , the mla was found to be raised by contraction of the intrinsic foot muscles11 .
accordingly , we hypothesized that the 
 relationship between nd and plantar flexion torque of the mtp joints would change with 
 different measuring positions , and we believe that the results of this study will provide 
 valuable information for exercise and risk management to prevent lower limb 
 disabilities .
the mean values  standard deviations ( sds ) for 
 their age , height , and body weight were 23.8  1.5  years , 1.69  0.04 m , and 58.4  8.1  kg , 
 respectively .
this study was 
 approved by the ethics committee on human research of waseda university ( approval number : 
 2013 - 195 ) .
the authors provided all subjects with an explanation of the purpose and methods 
 of this study and details of the study protocol , and written informed consent was obtained 
 from all subjects .
navicular height was defined as the distance from the floor to the tubercle of the 
 navicular bone , as measured with a caliper .
palpation of the tubercle of the navicular bone 
 was performed by a physical therapist who had more than 3  years of experience in orthopedic 
 physical therapy .
nd was calculated by subtracting the navicular height in the standing 
 position from that in the sitting position .
a custom - made mtp joint plantar flexion torque meter device was used to measure mtp joint 
 plantar flexion torque .
the subjects were seated on a chair , with their trunk , thighs , lower 
 thighs , and dominant foot fastened to the chair and the torque meter device .
after warming 
 up , each subject performed maximal voluntary isometric contraction of plantar exion of the 
 first mtp joint , followed by that of the second - fifth mtp joint for 3  s to determine the 
 maximal voluntary contraction ( mvc ) torque .
the plantar flexion torque was calculated as the 
 tensile force of a strain gauge ( tu - br 500n , teac , japan ) multiplied by the 0.10-m lever arm 
 of the force plate ( fig .
1.structure of the torque meter used to measure isometric plantar flexion torque at the 
 metatarsophalangeal ( mtp ) joints .
mtp joint plantar flexion torque was calculated 
 using the following formula : plantar flexion torque ( nm ) = strain  ( n )  moment arm 
 0.10 ( m ) . ) .
we converted the tensile force data from analog to digital ( power lab , ad 
 instruments , australia ) via an amplifier ( dpm-711b , kyowa electronics , japan ) using a 
 personal computer .
mvc torque was measured at two positions : at a neutral position of the 
 ankle and mtp joints and at 45 dorsiflexion of the mtp joints with 20 plantar flexion of 
 the ankle joint .
structure of the torque meter used to measure isometric plantar flexion torque at the 
 metatarsophalangeal ( mtp ) joints .
mtp joint plantar flexion torque was calculated 
 using the following formula : plantar flexion torque ( nm ) = strain  ( n )  moment arm 
 0.10 ( m ) .
further , we measured mvc torque again on a different day to determine the test - retest 
 repeatability of these measurements , which was accomplished by calculating the mean 
 coefficient of variance ( mean / sd ) and intraclass correlation coefficient ( icc ) . to 
 assess the iccs
, we used the criteria advocated by fleiss12 , in which an icc > 0.75 is defined as excellent reliability .
a 
 pearson correlation coefficient was used to test the correlation between the nd and mvc 
 torques . for all tests ,
the mean coefficients of variance of the mvc torques of the first mtp and second - fifth mtp 
 joints measures were 7.6% and 7.4% , respectively , and the corresponding iccs ( 1.1 ) were 0.81 
 and 0.87 , respectively .
significant negative correlations were seen between the nd and the mvc torques at 20 
 plantar flexion of the ankle joint with 45 dorsiflexion of the mtp joints of the first mtp 
 joint ( r = 0.78 , p < 0.01 ) and second - fifth mtp joints 
 ( r = 0.82 , p < 0.01 ) ( table 
 1table 1.relationship between navicular drop ratio and maximal voluntary contraction 
 torque ratio of the plantar flexion of the metatarsophalangeal jointsposition of the mtp and ankle jointsmeasured jointsmvc torque(n
/ kg)nds(mm)correlationcoefficientsneutralfirst mtp0.13  0.037.4  2.50.52second - fifth mtp0.09  0.030.3845 dorsiflexion of the mtp joints , 20 plantar flexion 
 of the ankle jointfirst mtp0.17  0.030.78*second - fifth mtp0.12  0.020.82*mean  sds ; mtp joint : metatarsophalangeal joint ; mvc torque : maximal voluntary 
 contraction torque ; nd : navicular drop ; * p < 0.01 ) .
however , no significant correlations were found between the nd and mvc 
 torques at the neutral position of the ankle and first mtp joint ( r = 0.52 , p > 0.05 ) 
 and second - fifth mtp joints ( r = 0.38 , p > 0.05 ) ( table 1 ) .
mean  sds ; mtp joint : metatarsophalangeal joint ; mvc torque : maximal voluntary 
 contraction torque ; nd : navicular drop ; * p < 0.01
the iccs ( 1.1 ) for both the first and second - fifth mtp joints were more than 0.75 in this 
 study and showed excellent reliability12 , 
 and the test - retest repeatability of the measurements of mvc torque were confirmed .
significant negative correlations were observed between nd and mvc torque at 45 
 dorsiflexion of the mtp joints with 20 plantar flexion of the ankle joint . on the other 
 hand
, there was no significant correlation between nd and mvc torque at the neutral 
 position , indicating that nd relates to intrinsic muscle strength .
mvc torque is affected by muscle length , and muscle length in turn is known to be affected 
 by the joint angle8,13 . in a previous study , the muscle length of the fhl was found to vary an 
 average of 0.22  mm by 1 plantar flexion or dorsiflexion of the first mtp joint and 0.50  mm 
 by 1 plantar flexion or dorsiflexion of the ankle joint7 .
furthermore , according to the same study , at 45 dorsiflexion of 
 the first mtp joint , the muscle length of the fhl increased approximately 10  mm from that in 
 neutral position , whereas at 20 plantar flexion of the ankle joint , the length of the fhl 
 decreased approximately 10  mm from that in neutral position . in the present study , the 
 length variation of the extrinsic muscle
was countered and the intrinsic muscles were 
 lengthened by 20 plantar flexion of the ankle joint and 45 dorsiflexion of the first mtp 
 joint . at this position ,
a higher torque can be exerted even though the length of the 
 extrinsic muscle remains constant8 . in 
 addition
, it has been reported that toe flexion exercises performed during plantar flexion 
 of the ankle joint are an effective method of intrinsic foot flexor strength training14 . according to these findings , it appears 
 as if the intrinsic muscles are capable of exerting force in this position .
furthermore , it 
 has been reported that the mla was raised upon inducing contraction of the intrinsic muscles 
 via electrical stimulation11 . at the neutral position of the ankle and mtp joints , both the intrinsic and extrinsic 
 muscles can produce similar force .
however , the produced force ratio of the extrinsic muscle 
 to the intrinsic muscles is relatively large at the neutral position of the ankle and mtp 
 joints as compared to at 20 plantar flexion of the ankle joint with 45 dorsiflexion of the 
 mtp joints , and this is likely the reason for the lack of a significant correlation between 
 mvc torque and nd in this condition . taken together , these results suggest that the 
 intrinsic foot muscles contribute greatly to the construction of the mla and that nd relates 
 to maximal plantar flexion torque of mtp joints at 20 plantar flexion of the ankle joint 
 with 45 dorsiflexion of the first mtp joint .
these results support a previous finding that 
 nd is correlated with electromyographic activity of the abductor hallucis muscle15 .
moreover , these results indicate that the strength of the intrinsic toe plantar flexion 
 muscles is related to nd , suggesting that exercises targeting the intrinsic muscles may not 
 only help improve excessive nd but also prevent sport - related disorders caused by excessive 
 nd .
the main limitation of this study was that the mla was affected not only by the toe flexor 
 muscle but also by the muscle that did not contribute to mtp joint plantar flexion ( e.g. , 
 the tibialis posterior and peroneus longus muscles ) .
furthermore , we did not investigate extrinsic muscle length according to 
 variations of the mtp joint angle .
therefore , we instead discussed the results based on the 
 length variation of the fhl .
future studies aimed at assessing the flexor digitorum longus 
 length according to variations of the second to fifth mtp joints are needed . in conclusion
, we found that nd relates to mtp joint muscle strength in plantar flexion 
 where the intrinsic toe plantar flexion muscles are capable of exerting force .
this result 
 suggests that exercises targeting the intrinsic muscles may help improve excessive nd .
 [ purpose ] the purpose of this study was to determine the relationship between navicular 
 drop and plantar flexion torque of the first and second - fifth metatarsophalangeal joints . 
 
 [ subjects ] ten healthy young men participated in this study . [ methods ] 
 the pearson 
 product - moment correlation coefficient was calculated to determine the relationship 
 between navicular drop and plantar flexion torque of the first and second - fifth 
 metatarsophalangeal joints . 
 [ results ] significant negative correlations were observed 
 between navicular drop and plantar flexion torques in the lengthened position of the 
 intrinsic toe plantar flexion muscles , but no correlations were found between navicular 
 drop and plantar flexion torques in the neutral position of the ankle and 
 metatarsophalangeal joints . 
 moreover , the intrinsic toe plantar flexion muscles were found 
 to contribute to the formation of the medial longitudinal arch . 
 [ conclusion ] navicular 
 drop correlates with metatarsophalangeal joint muscle strength in plantar flexion where 
 the intrinsic toe muscles are capable of exerting force . 
INTRODUCTION
SUBJECTS AND METHODS
RESULTS
DISCUSSION