walking speed is calculated by multiplying the step length by cadence , for which infinite 
 combinations exist at a certain speed .
however , a single ratio of step length and cadence is 
 selected based on the minimal cost of transfer1 .
this walk ratio2 
 remains constant within a certain range of speeds , including the preferred speed3 , 4 . at 
 fast speeds ,
however , details 
 of change in the walk ratio at slow speeds remain to be explored .
sekiya et al . demonstrated 
 that as walking speed decreases , the walk ratio increases and becomes more variable5 .
they hypothesized a boundary at which the 
 walk ratio constancy would be broken during slow walking ; however , they did not identify a 
 specific speed .
it is necessary to explore how walking behavior changes at a low speed to 
 understand the slow walking observed in various conditions such as aging and pathological 
 conditions such as stroke .
herein , the basic characteristics of slow walking at various 
 speeds were examined , and the lower walking speed boundary was estimated at which the walk 
 ratio constancy is broken in healthy adults .
the mean age , height , and 
 weight (  standard deviation ) were 24.5  3.3  years , 166.7  8.2  cm , and 59.2  10.2  kg , 
 respectively .
the study protocol was approved by the ethics committee of tokyo bay rehabilitation 
 hospital , and informed consent was obtained from all participants .
participants were verbally instructed to walk in a straight line on a flat walkway at five 
 different speeds ( fast , preferred , slightly slow , slow , and very slow ) .
speed conditions 
 were such that participants could walk at their preferred speed as a reference before 
 increasing or decreasing the speed : 1 ) preferred , 2 ) fast , 3 ) preferred , 4 ) slightly slow , 
 5 ) preferred , 6 ) slow , and 7 ) very slow . participants were instructed to walk comfortably , 
 and they were given no instructions regarding the step length or cadence .
three 
 experimenters ( a , b , and c ) participated in the measurements .
experimenters a and b visually 
 observed and marked the fifth and fifteenth heel strikes after walking was initiated .
experimenter c recorded the time 
 required to walk 10 steps using a stopwatch with 1/100-second precision .
the step length , cadence , speed , and walk ratio ( step length / cadence ) at each speed 
 condition were calculated individually using the distance walked and time required . for the 
 preferred speed , the mean of three measurements was used . to exclude the influence of height 
 differences ,
gait parameters were adjusted using the following equations5 : adjusted step length = step length  ( mean 
 height / individual height ) ; adjusted cadence = cadence  ( individual height / mean 
 height ) ; adjusted speed = adjusted step length  adjusted cadence ; and 
 adjusted walk ratio = adjusted step length / adjusted cadence . a k - means algorithm
based non - hierarchal cluster analysis was used to divide all the data 
 for the two variables ( speed and walk ratio ) into two clusters ( normal walk and slow walk ) , 
 enabling us to evaluate the lower walking speed boundary .
pearson correlation coefficients 
 with bonferroni correction were used to examine the relationships between each gait 
 parameter in each cluster .
all statistical analyses were performed using stata / se 13.1 
 ( statacorp , college station , tx , usa ) .
gait parameters at each speed condition with or without height adjustment are shown in 
 table 1table 
 1.gait parameters and number of participants classified in the 
 slow - walk cluster for each speed conditiongait 
 parameterspeed 
 conditionvery slowslowslightly slowpreferredfaststep length ( m)0.43  0.160.47  0.150.58  0.0890.70  0.0710.87  
 0.094cadence ( steps / min)24.8 
  13.442.0  17.783.2  13.2112.1  7.37135.9  12.5speed ( m / min)11.4  8.1420.9  12.549.1  13.079.0  
 9.88118.2  18.6walk ratio 

( m / steps / min)0.027  0.0290.015  
 0.0120.0071  0.00120.0063  
 0.000710.0064  0.00081adjusted step length ( m)0.43  0.160.47  0.150.58
 0.0910.70  0.0710.87  0.070adjusted cadence ( steps / min)24.8  13.341.9  17.683.2  13.3112.0  6.33135.7  12.1adjusted speed ( m / min)11.4  8.1420.9  12.649.1  13.179.0  10.0118.2  17.6adjusted walk ratio ( m / steps / min)0.027  
 0.0290.015  0.0120.0071  
 0.00120.0069  0.000470.0064
 
 0.00053participants classified in the slow - walk 
 cluster , n ( % ) 21 ( 100%)19 
 ( 90.5%)4 ( 19.0%)0 ( 0%)0 ( 0%)data are shown as 
 means  standard deviations unless otherwise indicated . *
a non - hierarchal cluster 
 analysis successfully divided the data of the two variables ( speed and walk ratio ) into two 
 clusters ( fig .
1.relationships between the velocity and walk ratio ( a ) , and 
 between the step length and cadence ( b ) . ) . the maximum speed in the slow - walk cluster 
 was 61.1 m / min , and the minimum speed in the normal - walk cluster was 63.6 m / min
; thus , the 
 clusters were divided at approximately 62 m / min without overlap ( fig .
each gait parameter is 
 adjusted for height relationships between the velocity and walk ratio ( a ) , and 
 between the step length and cadence ( b ) .
figure 1-b shows the relationship between the 
 step length and cadence ; these variables were clearly correlated in the normal - walk cluster 
 but not in the slow - walk cluster . despite a slight overlap , the clusters could be clearly 
 separated in terms of cadence .
the average of these overlapping values ( six values , three 
 per cluster ) was 98.0 m / steps / min .
however , the data could not be clearly divided into two 
 clusters in terms of the step length .
table 2table 
 2.pearson correlation coefficients between each gait parameter 
 in each clusteradjusted 
 speedadjusted step lengthadjusted 
 cadenceadjusted walk ratio(a ) 
 slow - walk clusteradjusted speed1.00adjusted step length0.711.00adjusted cadence0.950.501.00adjusted walk ratio0.470.160.581.00(b ) normal - walk clusteradjusted speed1.00adjusted step 
 length0.951.00adjusted 
 cadence0.950.801.00adjusted walk ratio0.030.350.291.00*bonferroni corrected p values 
 < 0.001 shows the correlation coefficients 
 between each gait parameter in each cluster . in the normal - walk cluster ,
the walk ratio was 
 independent ( i.e. , it had no correlation with other gait parameters ) .
in contrast , the walk 
 ratio correlated negatively with speed ( r=0.47 ; p<0.001 ) and cadence ( r=0.58 ; 
 p<0.001 ) in the slow - walk cluster . the step length , cadence , and speed significantly 
 correlated with each other in both clusters .
this is the first investigation of walking characteristics over several speeds , including a 
 very slow speed ( < 20 m / min ) .
this study s results showed an initial break in walk ratio 
 constancy at approximately 62 m / min in healthy adults ; this loss of constancy subsequently 
 increased as speed decreased .
additionally , the findings suggested that the walk ratio 
 boundary was defined by cadence not by step length .
accordingly , a cadence boundary was 
 estimated at approximately 98 m / steps / min .
on the basis of scatter plot observations , sekiya et al . suggested that the walk ratio 
 tended to increase and vary more at 60 m / min5 , which was consistent with our results .
furthermore , the disrupted 
 walk ratio constancy at slow speeds may be explained by a model - based assumption in which 
 the physical constraints for optimizing energetic efficiency are no longer preserved at slow 
 walking speeds .
a physics - based model with an energy efficiency of 100% proposed that an 
 upper swing phase limit was 0.50.6 seconds6 , resulting in a lower cadence limit of approximately 100120 
 m / steps / min without consideration of the double - support phase .
this model - based lower 
 boundary of energy - efficient walking is consistent with our results .
a few reports have pointed out that the behaviors of the walk ratio in patients with 
 pathological conditions are different from that of healthy person .
a stroke is the 
 representative condition of slow walking , as stroke patients walk at decreased speeds ( 648 
 m / min)7 .
demonstrated that 
 although the walk ratio of patients with hemiparetic stroke with a slow walking speed 
 ( < 60 m / min ) was approximately one - half of the walk ratio of healthy subjects , this ratio 
 remained constant regardless of speed8 . 

their report suggests that patients with hemiparetic stroke differ from healthy subjects in 
 terms of incorporating a slow walking strategy .
examined the walk ratio in 
 patients with multiple sclerosis ; the walk ratio was significantly lower in these patients 
 than in control patients , and it was related to the severity of disability9 .
they suggested that the walk ratio is a 
 disability - sensitive index of gait control , and thus a promising outcome measure for 
 treatments .
further studies are needed to clarify the difference between walk ratios 
 corresponding to normal and various pathological gaits , and the clinical meaning of 
 them .
first , a visual method was used to identify the point 
 of heel strike .
although the findings drawn from this study may be robust even with a 
 several  cm bias , this may have caused slight differences in our boundary calculations . 

second , as only temporal - distance factors were investigated in this preliminary study , 
 further studies are required to explore the true mechanism that defines the lower walking 
 boundary . finally , a relatively small sample size of patients with a narrow age range was 
 used . a larger sample size and wide age range of patients
are needed to explore whether 
 there is a difference between age groups and between genders . in conclusion , this study confirmed that the walk ratio constancy was broken at slow speeds 
 in healthy adults .
the gait speed at which the walk ratio constancy was broken was estimated 
 as 62 m / min , suggesting that walking at less than approximately 60 m / min may be regulated 
 with somewhat different control strategies than those used at the higher walking speed in 
 healthy adults .
the present study s findings offer valuable information for understanding 
 slow walking observed in individuals with various pathological conditions .
 [ purpose ] the ratio of step length to cadence ( walk ratio ) is invariant over a wide range 
 of speeds . however , no studies have investigated details of the change in the walk ratio 
 at slow speeds . 
 it is necessary to explore how walking behavior changes at a low speed to 
 understand the slow walking observed in various conditions such as aging and pathological 
 conditions . in this study , 
 changes in the walk ratio at slow speeds were investigated , and 
 a lower boundary was estimated at which the walk ratio constancy is broken . [ subjects and 
 methods ] twenty - one healthy adults were instructed to walk along a flat , straight walkway 
 at five different speeds ( fast , preferred , slightly slow , slow , and very slow ) . 
 the walk 
 ratio was calculated from the step length and cadence . 
 [ results ] as the walking speed 
 decreased , the walk ratio and variance began to increase abruptly . 
 the initial break in 
 the walk ratio constancy was at approximately 62 m / min . 
 in addition , the boundary of 
 cadence was approximately 98 m / steps / min . 
 [ conclusions ] the study successfully determined 
 a lower boundary at which the walk ratio constancy was broken , suggesting that different 
 control strategies are used when walking at less than the gait speed at which constancy is 
 broken in healthy adults . 
 the finding provides valuable information for understanding slow 
 walking observed in individuals with various pathological conditions . 
INTRODUCTION
SUBJECTS AND METHODS
RESULTS
DISCUSSION
Conflicts of interest and source of funding