walking is an action with an extremely low energy cost . from the perspective of energy 
 conversion of the center of mass ( com ) ,
the trajectory of the com in the sagittal plane is 
 similar to the motion of a pendulum , and this movement in known as the inverted pendulum 
 model1 , 2 . in this model , kinetic energy in the direction of progress reaches 
 its peak at the time of heel strike , and gradually decreases in the first half of the stance 
 phase as kinetic energy is converted to potential energy of the com .
the potential energy 
 shows its peak at the midpoint of the stance phase . during the latter half of the stance 
 phase ,
when the com goes down , potential energy gradually decreases , as it is converted into 
 kinetic energy . in order to achieve an efficient gait ,
this has been shown by passive walking robots3 achieving ambulation with relatively low 
 energy cost .
although the free gait speed of hemiplegic patients is less than half of that 
 of healthy individuals , their oxygen consumption cost is about 25% larger4 .
the cause of the increased energy cost of 
 hemiplegic gait is closely related to the increase of external work by the muscles involved 
 in moving the com5 .
furthermore , it is 
 thought that inefficiency in the energy conversion described above is one of the 
 characteristics of hemiplegic gait6 .
the rocker function proposed by perry7 is 
 said to play an important role in reproducing the inverted pendulum model and achieving 
 efficient energy conversion .
a plantar flexion resistive ankle - foot orthosis ( pf - afo ) is an 
 afo which assists the rocker function8,9,10
. 
 the pf - afo directly assists the initial turnover period , and wearers also show an 
 improvement in the second turnover period after continuous use of the pf - afo11 , 12 .
the objective of this study was to investigate the change in 
 mechanical energy of the com in hemiplegic gait after continuous use of a pf - afo .
the subjects were 5 maintenance - phase hemiplegics who used afos without a plantar 
 flexion - resistive function in their daily lives ( table 
 1table 1 .
subject characteristicscase 1case 2case 3case 4case 5sexfemalemalefemalemalemaleage ( years)3337506765diagnosiscerebral infarctioncerebral hemorrhagecerebral hemorrhagecerebral infarctioncerebral infarctionparetic sideleftrightleftrightrightperiod from onset ( months)202812420244lower limb brsiiiiviiiiiiiiilower limb fma9 ( 41%)20 ( 91%)15 ( 68%)15 ( 68%)17 ( 77%)ankle joint mas2121 + 2independencesupervision requiredindependentindependentindependentindependentsubject s own orthosisafo with metal uprightsplastic leaf springplastic leaf springplastic leaf springplastic leaf springheight ( cm)160175151164163weight ( kg)5775516865brs : brunnstrom recovery stage ; fma : fugl - meyer assessment ; mas : modified ashworth 
 scale ) . the participation criteria for the study were : cerebrovascular disease 
 hemiplegia with unilateral pathology at onset ; no rehabilitation treatment during the 
 experimental period ; no marked higher brain dysfunction or difficulty understanding 
 commands ; no marked limitation in joint mobility of the lower limbs or trunk ; being able to 
 walk unassisted ; and being able to walk forward by means of a heel strike .
the subjects 
 received a thorough explanation about the study content and methods both orally and in 
 writing , and their written consent to participation was received .
the study content 
 conformed to the principles of the declaration of helsinki and received approval from the 
 hokkaido institute of technology graduate school research ethics committee .
brs : brunnstrom recovery stage ; fma : fugl - meyer assessment ; mas : modified ashworth 
 scale the experimental schedule was as follows .
on the first day , a 3d - motion analysis device was 
 used to measure the gait of the patients while wearing their own afo , and their gait after 
 the first fitting of the pf - afo .
after subjects had consented to continuous use of the 
 pf - afo , the same gait measurements were performed after 34 weeks of pf - afo use .
each pf - afo 
 was manufactured from a cast of the foot of each subject . at the first fitting ,
the plantar flexion movement of the ankle joint of the pf - afo was 
 confirmed in stance .
after subjects had consented to use the pf - afo , the amount of resistive 
 moment and the initial ankle joint angle of the pf - afo were adjusted for each subject s 
 condition .
touch the ground with the heel of the side with 
 paralysis first .  in the measurement of pf - afo gait on the first day , sufficient walking 
 practice time was provided to familiarize subjects with the new orthosis .
then , 3d - motion 
 analysis was performed on a flat walking pathway 7.5  m in length , and 6 one - way trial walks 
 were performed under two conditions , with subjects own afos and with the pf - afo .
data after 
 the fourth step from the start of ambulation was used in order to extract a steady state . 

the apparatus used for measurement was a 3d - motion analysis device ( vicon - nexus , vicon 
 motion system inc . , ltd . ,
sixteen reflective markers were placed on the subjects : on the left and 
 right sides of the acromion , one - third of the distance from the greater trochanter and the 
 anterior superior iliac spine , the lateral center of the knee joint cleft , the external 
 malleolus , the head of the fifth metatarsal , the calcaneal region , the anterior superior 
 iliac spine , and the posterior superior iliac spine . the sampling frequency was 120  hz . a 
 seven - link segmental model was used to calculate the com using the anthropometric data of 
 typical japanese men and women .
the conversion efficiency of com potential energy to kinetic energy was calculated using 
 the method of cavana et al13,14,15,16,17,18,19,20,21,22,23 . in the present 
 study ,
the mechanical energy was calculated as described below based on the com information 
 measured and calculated from the 3d - motion analysis data . in this study ,
thus , there were four kinds of 
 power : the power used to accelerate in the travel direction of the com ( power - y ) , the power 
 for lifting the com in the vertical direction com ( power - z ) , the power generated by muscles 
 ( power - ext ) , and the rate of exchange of kinetic energy to potential energy ( % 
 recovery ) . to calculate the com energy changes during ambulation , it is necessary to have information 
 about the peak value of the vertical com position ( com - z ) .
the motion of com - z is described 
 by a sinusoidal curve ( fig .
separate phases of the mechanical energy of com ) . in order to know the rise and fall of the inverted pendulum on both the paretic and 
 non - paretic sides ,
it is necessary to know the highest and lowest points of com - z during 
 gait .
therefore , knowledge of the range between the peak values of com - z on the paretic side 
 and non - paretic side is necessary . to find this ,
gait data of more than one gait cycle was 
 extracted , from the heel contact of the paralyzed limb to the foot contact of the 
 ipsilateral limb , to have information about the highest and lowest positions of the com .
to 
 calulate the kinetic energy and potential energy during ambulation , the kinetic energy 
 ( ek.y ) in the direction of progress of the body com was calculated using formula 1 , the 
 kinetic energy ( ek.z ) in the vertical direction by formula 2 , the potential energy ( ep ) by 
 formula 3 , the total kinetic energy ( ek ) by formula 4 , and the total energy ( etot ) by 
 formula 5.ek.y=1/2mvy 
 ( 1)ek.z=1/2mvz 
 ( 2)ep = mgz 
 ( 3)ek = ek.y+ek.z 
 ( 4)etot = ek+ep 
 ( 5)were , m is the body mass , g is the acceleration due to 
 gravity ( 9.8 m / s ) , vz is the vertical velocity of com , and vy is the velocity 
 in the direction of com progress .  
separate phases of the mechanical energy of com the external work for accelerating the com in the direction of progress was calculated 
 using formula 6 , the external work of raising the com in the vertical direction against 
 gravity by formula 7 , and the external work generated by the muscles to move the com was 
 calculated using formula 8.wy=ek.y 
 ( 6)wz= 
 ( ek.z+ep ) 
 ( 7)wext=etot 
 ( 8)were ,  is the amount of energy increase or decrease and  
 is the summation of the data of . by dividing the external work by time , it was possible to determine the external power 
 ( power - y ) use to accelerate the com in the direction of progress , the external power 
 ( power - z ) for raising the com , and the external power ( power - ext ) generated by the muscles . 

conversion efficiency ( % recovery16 ) was 
 calculated using formula 
 9.%recovery=(wy+wz-wext ) 
  ( wy+wz )  100 
 ( 9)%recovery is the rate of mutual exchange of the kinetic 
 energy and potential energy of the com in walking .
meaning the value of % recovery in 
 walking with efficient use of gravity is high .
the % recovery value was calculated for each 
 phase shown in fig . 1 , and
the averages of one whole gait cycle , and the stance phases of 
 the paretic and the non - paretic sides were calculated .
the data of gait speed , power - y , 
 power - z , power - ext of each phase , and % recovery , were compared among the three conditions 
 of : gait with patients own afos , with the pf - afo at the first fitting , with the pf - afo 
 after continuous use .
r 2.8.1 software was used for statistical analysis , and the 
 steel - dwass method was applied .
no significant changes were noted in gait speed for gait with the pf - afo on the first day 
 in all cases , but a significant increase was seen in four cases after continuous use of the 
 pf - afo ( table 2table 2 .
changes in gait speed[m / sec]mean ( sd)(1 ) subject s own orthosis(2 ) before continuous use of pf - afo(3 ) after continuous use of pf - afo(1)vs.(2)(1)vs.(3)(2)vs.(3)case 10.39 ( 0.03)0.41 ( 0.05)0.50 ( 0.02)***case 20.75 ( 0.03)0.76 ( 0.02)0.85 ( 0.04)****case 30.62 ( 0.04)0.55 ( 0.04)0.69 ( 0.02)****case 40.28 ( 0.02)0.28 ( 0.01)0.29 ( 0.02)case 50.21 ( 0.01)0.21 ( 0.02)0.25 ( 0.02)*****p<0.05 ; * * p<0.01 ) . an increase was also seen in power - y in all cases in the non - paretic side 
 downward phase after continuous use of the pf - afo ( table 3table 3 .
changes in power - y[w / kg]mean ( sd)paretic side elevation(1 ) subject s own orthosis(2 ) before continuous use of pf - afo(3 ) after continuous use of pf - afo(1)vs.(2)(1)vs.(3)(2)vs.(3)case 11.4 ( 0.4)0.2 ( 1.6)1.8 ( 0.8)*case 27.0 ( 3.3)6.5 ( 2.7)9.5 ( 2.9)*case 30.2 ( 1.6)2.2 ( 1.4)2.3 ( 0.7)**case 40.4 ( 0.3)0.5 ( 0.3)0.5 ( 0.1)case 50.4 ( 0.2)0.2 ( 0.2)0.1 ( 0.2)***paretic side drop(1 ) subject s own orthosis(2 ) before continuous use of pf - afo(3 ) after continuous use of pf - afo(1)vs.(2)(1)vs.(3)(2)vs.(3)case 10.4 ( 0.9)0.9 ( 0.5)1.0 ( 0.6)case 24.3 ( 1.0)5.5 ( 1.6)6.4 ( 2.4)case 33.6 ( 2.7)3.7 ( 1.2)5.5 ( 1.5)case 40.3 ( 0.1)0.8 ( 0.3)0.8 ( 0.2)****case 51.1 ( 0.3)1.6 ( 0.5)1.5 ( 0.2)***non - paretic side elevation(1 ) subject s own orthosis(2 ) before continuous use of pf - afo(3 ) after continuous use of pf - afo(1)vs.(2)(1)vs.(3)(2)vs.(3)case 13.5 ( 0.6)3.2 ( 0.6)4.5 ( 0.6)*case 27.6 ( 1.5)9.3 ( 1.7)13.0 ( 5.6)*case 37.7 ( 2.6)6.1 ( 1.2)8.3 ( 1.2)*case 41.1 ( 0.2)1.1 ( 0.2)1.5 ( 0.2)**case 52.0 ( 0.4)2.1 ( 0.5)2.1 ( 0.3)non - paretic side drop(1 ) subject s own orthosis(2 ) before continuous use of pf - afo(3 ) after continuous use of pf - afo(1)vs.(2)(1)vs.(3)(2)vs.(3)case 12.9 ( 0.3)3.9 ( 1.2)5.5 ( 0.8)*case 210.2 ( 1.6)9.3 ( 1.9)12.8 ( 2.1)***case 36.2 ( 1.3)5.5 ( 1.5)8.1 ( 0.9)****case 41.5 ( 0.1)1.4 ( 0.2)1.7 ( 0.1)**case 50.4 ( 0.1)0.4 ( 0.1)0.7 ( 0.1)*****p<0.05 ; * * p<0.01 ) .
power - z showed a significant change in all phases of both the paretic and 
 non - paretic sides after continuous use of the pf - afo in 3 cases ( table 4table 4 .
changes in power - z[w / kg]mean ( sd)paretic side elevation(1 ) subject s own orthosis(2 ) before continuous use of pf - afo(3 ) after continuous use of pf - afo(1)vs.(2)(1)vs.(3)(2)vs.(3)case 112.4 ( 2.7)14.1 ( 2.2)16.9 ( 0.7)**case 214.6 ( 1.8)14.2 ( 1.7)15.2 ( 3.9)case 35.8 ( 0.8)7.1 ( 1.5)7.9 ( 1.7)*case 410.5 ( 1.5)9.9 ( 1.6)9.3 ( 0.8)case 58.6 ( 2.8)10.1 ( 1.9)12.5 ( 1.3)**paretic side drop(1 ) subject s own orthosis(2 ) before continuous use of pf - afo(3 ) after continuous use of pf - afo(1)vs.(2)(1)vs.(3)(2)vs.(3)case 15.6 ( 0.3)6.6 ( 1.3)6.9 ( 1.3)case 214.5 ( 1.6)15.8 ( 1.9)21.7 ( 4.8)****case 32.5 ( 1.1)4.7 ( 1.3)7.4 ( 1.0)****case 410.1 ( 2.5)12.6 ( 1.5)10.3 ( 1.1)*case 58.2 ( 1.5)8.7 ( 1.8)10.4 ( 1.1)*non - paretic side elevation(1 ) subject s own orthosis(2 ) before continuous use of pf - afo(3 ) after continuous use of pf - afo(1)vs.(2)(1)vs.(3)(2)vs.(3)case 111.3 ( 1.6)11.3 ( 1.3)12.2 ( 0.8)case 223.9 ( 0.8)24.8 ( 2.3)28.0 ( 4.0)**case 327.3 ( 1.7)25.4 ( 0.9)21.5 ( 1.1)****case 415.4 ( 2.1)16.4 ( 1.1)14.6 ( 0.8)*case 519.3 ( 2.4)17.1 ( 1.9)14.7 ( 1.2)***non - paretic side drop(1 ) subject s own orthosis(2 ) before continuous use of pf - afo(3 ) after continuous use of pf - afo(1)vs.(2)(1)vs.(3)(2)vs.(3)case 119.0 ( 2.3)18.9 ( 2.4)22.6 ( 1.2)*case 223.6 ( 2.2)22.2 ( 1.6)25.0 ( 3.1)*case 328.8 ( 1.5)29.3 ( 2.3)22.9 ( 1.6)****case 414.6 ( 0.7)15.5 ( 0.5)14.9 ( 1.4)case 518.2 ( 1.3)17.1 ( 1.3)17.3 ( 2.4)*p<0.05 ; * * p<0.01 ) .
the results of power - ext showed some changes , but no clear trend was noted 
 ( table 5table 5 .
changes in power - ext[w / kg]mean ( sd)paretic side elevation(1 ) subject s own orthosis(2 ) before continuous use of pf - afo(3 ) after continuous use of pf - afo(1)vs.(2)(1)vs.(3)(2)vs.(3)case 113.9 ( 3.1)13.9 ( 3.8)15.1 ( 1.0)case 27.6 ( 2.9)7.7 ( 3.5)5.8 ( 3.5)case 35.5 ( 1.0)4.9 ( 1.9)5.6 ( 2.2)case 410.1 ( 1.6)9.4 ( 1.3)8.8 ( 0.7)case 59.0 ( 2.8)10.3 ( 1.9)12.4 ( 1.3)**paretic side drop(1 ) subject s own orthosis(2 ) before continuous use of pf - afo(3 ) after continuous use of pf - afo(1)vs.(2)(1)vs.(3)(2)vs.(3)case 15.3 ( 0.8)5.7 ( 1.6)5.8 ( 1.6)case 210.3 ( 2.0)10.4 ( 1.2)15.3 ( 3.0)****case 31.1 ( 14.9)1.0 ( 1.2)1.9 ( 1.4)case 410.5 ( 2.5)11.9 ( 1.6)9.6 ( 1.0)*case 57.1 ( 1.4)7.1 ( 1.3)8.9 ( 1.1)**non - paretic side elevation(1 ) subject s own orthosis(2 ) before continuous use of pf - afo(3 ) after continuous use of pf - afo(1)vs.(2)(1)vs.(3)(2)vs.(3)case 17.8 ( 1.9)8.0 ( 1.1)7.7 ( 0.7)case 216.3 ( 1.2)15.5 ( 2.5)15.0 ( 2.9)case 319.6 ( 1.4)19.3 ( 1.6)13.2 ( 1.1)****case 414.3 ( 1.9)15.3 ( 1.1)13.1 ( 0.8)*case 517.4 ( 2.2)15.0 ( 1.9)12.6 ( 1.2)***non - paretic side drop(1 ) subject s own orthosis(2 ) before continuous use of pf - afo(3 ) after continuous use of pf - afo(1)vs.(2)(1)vs.(3)(2)vs.(3)case 116.2 ( 2.6)14.9 ( 2.2)17.1 ( 1.4)case 211.8 ( 1.8)13.0 ( 1.2)12.2 ( 4.0)case 321.9 ( 1.4)23.8 ( 2.4)14.8 ( 0.9)****case 413.0 ( 0.7)14.2 ( 0.5)13.2 ( 1.3)*case 517.8 ( 1.2)16.7 ( 1.2)16.6 ( 2.3)*p<0.05 ; * * p<0.01 ) .
the average % recovery for one gait cycle after the continuous use of the 
 pf - afo increased in all cases .
the comparison of the averages of the non - paretic and paretic 
 stance phases , revealed increases in % recovery in the non - paretic stance phases of four 
 cases , and in the paretic stance phases of two cases ( table 6table 6 .
changes in % recovery[%]mean ( sd)average of the one cycle gait(1 ) subject s own orthosis(2 ) before continuous use of pf - afo(3 ) after continuous use of pf - afo(1)vs.(2)(1)vs.(3)(2)vs.(3)case 122.3 ( 5.7)28.1 ( 7.1)34.8 ( 2.5)*case 255.1 ( 6.9)56.0 ( 4.9)62.3 ( 3.9)**case 343.8 ( 14.5)49.5
( 5.4)59.5 ( 6.9)**case 410.2 ( 0.3)12.5 ( 1.1)15.5 ( 1.1)*****case 511.6 ( 1.3)14.2 ( 2.3)15.0 ( 1.3)**average of the paretic stance phase(1 ) subject s own orthosis(2 ) before continuous use of pf - afo(3 ) after continuous use of pf - afo(1)vs.(2)(1)vs.(3)(2)vs.(3)case 17.7 ( 9.5)17.1 ( 15.8)22.6 ( 7.5)case 253.2 ( 14.6)55.8 ( 9.9)60.4 ( 7.4)case 343.2 ( 21.9)64.1 ( 12.0)65.1 ( 13.6)case 43.6 ( 2.2)10.5 ( 2.3)12.0 ( 1.5)****case 511.5 ( 2.2)15.5 ( 1.8)13.8 ( 1.6)**average of the non - paretic stance phase(1 ) subject s own orthosis(2 ) before continuous use of pf - afo(3 ) after continuous use of pf - afo(1)vs.(2)(1)vs.(3)(2)vs.(3)case 137.0 ( 5.8)39.1 ( 4.2)46.5 ( 4.5)case 257.0 ( 3.0)56.3 ( 3.3)64.2 ( 6.3)****case 344.4 ( 11.3)35.0 ( 3.0)54.0 ( 2.5)**case 416.9 ( 1.1)14.5 ( 1.7)19.1 ( 1.3)***case 511.6 ( 1.4)12.9 ( 3.0)16.2 ( 1.8)****p<0.05 ; * * p<0.01 ) .
the most interesting result of this study was the increase of % recovery in one gait cycle 
 gait after the continuous use of the pf - afo .
since the pf - afo was worn only on the paretic 
 side , it had no direct effect on the non - paretic side . however , comparing the averages of 
 the non - paretic stance and paretic stance , four out of five subjects showed large increases 
 in the stance phase of the non - paretic side .
furthermore , only small changes were found just 
 after pf - afo adaptation , but many changes were found after its continuous use .
the present results happened because loading on the paralyzed limb became smooth due to the 
 use of the pf - afo , eliminating the need for excessive control of the non - paretic side24 .
the increase of power - y in the downward 
 phase on the non - paretic side of all cases , indicates that subjects made steps without 
 decreasing the speed of the com in the late stance phase of the non - paretic side . 

furthermore , the results suggest that the immediate effects at the time of first use of the 
 pf - afo were few , but many changes were found after its continuous use , indicating that time 
 was necessary to learn to control the non - paretic side in order to adapt to the pf - afo11 , 12 , 24 . taken together , the use of the pf - afo increased com energy conversion efficiency .
this 
 change was seen not only on the paretic side with the afo , but also on the non - paretic side , 
 and a certain amount of time was needed to adapt the pf - afo .
a limitation of this study was that the time series of mechanical energy was not 
 investigated in detail .
also , some parameters increased after 34 weeks use of the pf - afo , 
 but of the exact timing of these changes was not investigated .
a detailed study of the time 
 series of the adaptation to the pf - afo , and the development of an exercise program to 
 facilitate early adaptation of the pf - afo will be necessary in a future study .
   [ purpose ] the aim of this study was to investigate the changes in mechanical energy due 
 to continuous use of a plantar flexion resistive ankle - foot orthosis ( afo ) of subjects 
 with chronic hemiplegia . [ subjects and methods ] the subjects were 5 hemiplegic patients 
 using afos without a plantar flexion resistive function in their daily lives . 
 we analyzed 
 the gait of the subjects using a 3d motion capture system under three conditions : 
 patients use of their own afos ; after being fitted with a plantar flexion resistive afo ; 
 and after continuous use of the device . the gait efficiency was determined by calculating 
 the mutual exchange of kinetic and potential energy of the center of mass . 
 [ results ] an 
 increased exchange rate of the kinetic and potential energy was found for all subjects . a 
 larger increase of energy exchange was shown on the non - paralyzed side , and after 
 continuous use of the plantar flexion resistive afo . [ conclusion ] we found that continuous 
 use of a plantar flexion resistive afo increased the rate of mutual exchange between 
 kinetic energy and potential energy . 
 the change in the rate was closely related to the 
 role of the non - paretic side , showing that the subjects needed a certain amount of time to 
 adapt to the plantar flexion resistive afo . 
INTRODUCTION
SUBJECTS AND METHODS
RESULTS
DISCUSSION