abnormal knee kinematics are considered to be an important factor influencing the long - term 
 outcomes after cruciate ligament injuries1,2,3 . in 
 order to improve long - term outcomes of treatments for the patients with cruciate ligament 
 injuries ,
therefore , it is important to 
 precisely evaluate the kinematics of knees with cruciate ligament injuries .
the motion of a 
 knee joint with ligament injury is commonly evaluated by static methods such as the lachman 
 test , posterior drawer test , valgus stress test , and arthrometric measurements , e.g. 
 kt-1000 .
however , patients with knee ligament deficiencies usually complain about their 
 symptoms under dynamic conditions .
therefore , there is a possibility that the instability of 
 the knee joint evaluated in static conditions does not reflect the functional disabilities 
 of its ligament injury1 , 3,4,5 .
three - dimensional motion analysis using optical skin marker systems has been widely used as 
 an evaluation method of body kinematics in dynamic conditions with muscular activations . 

this approach provides six - degrees - of - freedom motion of the kinematics of the knee during 
 activities of daily living without restricted conditions in vivo .
andriacchi et al . 
 developed a point cluster technique ( pct ) , which employs an overabundance of markers ( a 
 cluster ) placed on each segment to minimize the effects of skin movement artifacts6 .
the pct can be extended to minimize skin 
 movement artifact by optimal weighting of the markers according to their degree of 
 deformation .
the criteria of the normal range of three - dimensional knee kinematics during 
 walking remain uncertain . side - to - side difference in the range of knee motion
is widely used 
 as a criterion of the normal range of knee motion1 . to detect an abnormal knee motion during walking ,
it is useful to 
 determine the normal range of the side - to - side difference in knee kinematics during walking 
 based on the data using the pct . to the best of our knowledge , however , no study has 
 examined this ; therefore , the purpose of the present study was to determine the normal range 
 of the side - to - side difference in knee kinematics using pct during walking based on three 
 dimensional kinematics of the knee of healthy subjects .
the study was approved by the research ethics committee of hakodate national college of 
 technology and informed consent was obtained from each subject before the test .
twenty - one 
 healthy normal volunteers without knee pain or an episode of injury to the legs were 
 recruited for the study .
the subjects were 11 males and 10 females with an average age of 
 27.0 ( sd 7.2 ) years , and ranging from 21 to 47  years , and an average body mass index of 20.6 
 ( sd 2.4 )  kg / m , ranging from 16.8 to 27.7  kg / m .
the subjects were 
 tested bilaterally at a self - selected normal walking speed during their walking for 8  m 
 after the first four strides .
the subjects walked 
 barefoot on a hard surface at an average walking speed of 1.25 m / s .
the 
 subjects took a rest before each trial until they had recovered from fatigue .
the kinematic data were collected by a three - dimensional motion analysis system using four 
 infrared light cameras ( rrorflex , qualisys ab inc . ,
ground reaction 
 forces during the tests were also measured using two multi - component force plates ( or6 , 
 advanced mechanical technology inc . ,
three - dimensional motion data were processed using 
 qualisys track manager ( qualisys track manager 3d , qualisys ab inc . ,
force data were used to identify the time of heel strike in each gait cycle .
a gait cycle 
 was defined as the interval between heel strike to heel strike on the ipsilateral side . 

light - reflective markers were placed by physical therapists well - trained in the pct and body 
 surface anatomy6 .
kinematic measurements 
 were made of 21 light - reflective markers arranged on two limb segments , creating separate 
 cluster groups of 11 markers on the thigh and 10 markers on the shank .
the pct employs an overabundance of markers ( a cluster ) placed on each segment to minimize 
 the skin motion artifact due to segmental form change by muscle contraction and 
 marker - oscillation6 .
the pct is based on 
 a cluster of points uniformly distributed on the limb segment .
each point is assigned an 
 arbitrary mass , which can be varied at each time step .
the center of mass and the inertia 
 tensor of the cluster of points are calculated as described below .
the eigenvalues and the 
 eigenvectors of the inertia tensor are the principal moments of inertia and the principle 
 axes of the point cluster .
the eigenvalues are invariant to movement if the segment 
 is behaving as a rigid body .
if the eigenvalues change from their value in the rest 
 position , then the segment where the markers are placed has deviated from rigid body 
 movement .
the individual weighting is adjusted by redistributing the weight factors at each 
 time step to minimize the eigenvalue changes .
examined the pct using simulation trials with 
 systematic and random components of deformation error introduced into marker position 
 vectors7 .
they also tested the pct in 
 vivo with a subject fitted with an external fixation device ( ilizarov ) .
the average location 
 and orientation measurement errors of the pct were 0.6  mm ( sd 0.6  mm , maximum approximately 
 3  mm ) and 0.5 degrees ( sd 0.5 degrees , maximum approximately 4 degrees ) respectively7 .
another study has also reported an accuracy 
 of 0.79 degrees ( sd 0.48 degrees ) for flexion - extension , 1.79 degrees ( sd 0.93 degrees ) for 
 internal - external rotation , and 0.40 degrees ( sd 0.12 degrees ) for abduction - adduction8 .
intra - class correlations coefficients ( 1 , 
 5 ) and standard errors of measurement of the pct have been calculated using the data of a 
 previous study and indicate substantial or almost perfect reliability9 . in the present study ,
the position 
 coordinate data were converted to flexion - extension ( fe ) , abduction - adduction ( aa ) , 
 internal - external ( ie ) rotation , and the anterior - posterior ( ap ) , medial - lateral ( ml ) , 
 superior - inferior ( si ) translation of the tibia with respect to a gait cycle6 .
data from three trials were averaged and 
 the average was used for the analysis of each limb .
the value of the right leg subtracted 
 from that of the left leg was defined as the side - to - side difference in rotation / translation 
 in each stage of the gait cycle .
we then determined the average side - to - side differences and 
 their 95% confidence intervals ( cis ) . for statistical analysis , one - way analysis of variance and post - hoc bonferroni tests
were 
 performed to compare the average side - to - side difference of each motion among 0% , 20% , 40% , 
 60% and 80% of the time of a gait cycle .
differences were considered statistically 
 significant at p < 0.05 with bonferroni adjustment for post - hoc multiple comparisons .
based on the ground reaction forces of the force plates , the stance and swing phases during 
 walking were determined . as a result , 0% to mean 61.6% ( sd 1.3% ) of the gait cycle was 
 regarded as the stance phase . therefore , 0% ,
20% , 40% , 60% and 80% of the gait cycle were 
 considered as the early stance phase , the middle stance phase , the late stance phase , the 
 early swing phase and the late middle swing phase , respectively .
the average knee kinematics pattern of the right and left legs during a gait cycle are 
 shown in fig .
1.the average knee kinematics pattern of the right and left legs during a gait 
 cyclea ) flexion - extension ; b ) adduction - abduction ; c ) internal - external rotation of the 
 tibia .
regarding fe of the knee during walking , the average values ( 95% cis ) of 
 side - to - side differences at each time frame of normal walking were 4.3 degrees ( 3.0 to 5.7 
 degrees ) , 4.9 degrees ( 3.5 to 6.3 degrees ) , 4.4 degrees ( 2.9 to 5.9 degrees ) , 7.4 degrees 
 ( 5.2 to 9.6 degrees ) and 5.4 degrees ( 3.4 to 7.3 degrees ) at 0% , 20% , 40% , 60% , and 80% of 
 the gait cycle , respectively ( fig .
2.the 95% confidence intervals ( cis ) of side - to - side differences of the normal 
 subjectsa ) flexion - extension ( fe ) ; b ) abduction - adduction ( aa ) ; c ) internal - external ( ie ) 
 rotation ; d ) anterior - posterior ( ap ) translation ; e ) medial - lateral ( ml ) translation ; 
 f ) superior - inferior ( si ) translation , table 1table 1.the average of side - to - side differences and their 95% confidence intervals in 
 each stage of the gait cyclewalking cycle0%20%40%60%80%rotation ( degrees)flexion - extension4.3 ( 3.05.7)4.9 ( 3.56.3)4.4 ( 2.95.9)7.4 ( 5.29.6)5.4 ( 3.47.3)abduction - adduction3.8 ( 2.65.1)4.5 ( 2.76.4)3.2 ( 2.14.3)5.4 ( 3.67.2)8.9 ( 5.911.9)internal - external7.4 ( 5.59.4)5.7 ( 3.77.8)4.7 ( 3.36.1)6.2 ( 4.08.4)7.4 ( 4.710.2)translation ( mm)anterior - posterior9.7 ( 6.712.7)7.7 ( 4.510.9)6.8 ( 4.19.6)9.2 ( 5.013.4)12.8 ( 6.818.8)medial - lateral6.3 ( 3.79.0)5.3 ( 3.47.1)5.5 ( 3.77.3)6.7 ( 4.98.5)5.9 ( 3.78.1)superior - inferior7.7 ( 4.510.8)8.1 ( 4.211.9)8.2 ( 4.112.4)8.9 ( 4.413.5)9.8 ( 9.818.8)(mean , 95% ci ) . a : post - hoc bonferroni tests ( vs. 0% : p<0.001 , vs. 20% : 
 p<0.001 , vs. 40% : p<0.001 , vs. 60% : p<0.001 ) .
b : post - hoc bonferroni test 
 ( vs. 40% p<0.001 ) ) . there were no significant differences in the side - to - side differences of fe 
 among 0% , 20% , 40% , 60% , and 80% of the gait cycle ( p=0.086 ) .
the average side - to - side 
 differences ( 95%cis ) of aa were 3.8 degrees ( 2.6 to 5.1 degrees ) , 4.5 degrees ( 2.7 to 6.4 
 degrees ) , 3.2 degrees ( 2.1 to 4.3 degrees ) , 5.4 degrees ( 3.6 to 7.2 degrees ) and 8.9 degrees 
 ( 5.9 to 11.9 degrees ) at 0% , 20% , 40% , 60% , and 80% of the gait cycle , respectively ( fig .
the side - to - side difference of aa at 80% of the walking cycle was significantly 
 greater than those at 0% , 20% , 40% and 60% of the gait cycle ( vs. 0% : p<0.001 , vs. 20% : 
 p<0.001 , vs. 40% : p<0.001 , vs. 60% : p<0.001 ) .
the average side - to - side differences 
 ( 95%cis ) of ie rotation were 7.4 degrees ( 5.5 to 9.4 degrees ) , 5.7 degrees ( 3.7 to 7.8 
 degrees ) , 4.7 degrees ( 3.3 to 6.1 degrees ) , 6.2 degrees ( 4.0 to 8.4 degrees ) and 7.4 degrees 
 ( 4.7 to 10.2 degrees ) at 0% , 20% , 40% , 60% , and 80% of the gait cycle , respectively ( fig .
there were no significant differences in the side - to - side differences of ie 
 rotation among 0% , 20% , 40% , 60% , and 80% of the gait cycle ( p=0.332 ) . at 0% , 20% , 40% ,
60% , 
 and 80% of the gait cycle , the average values ( 95% cis ) of side - to - side differences of ap 
 translation were 9.7  mm ( 6.7 to 12.7  mm ) , 7.7  mm ( 4.5 to 10.9  mm ) , 6.8  mm ( 4.1 to 9.6  mm ) , 
 9.2  mm ( 5.0 to 13.4  mm ) and 12.8  mm ( 6.8 to 18.8  mm ) , respectively ( fig .
the 
 side - to - side difference of ap translation at 80% of the gait cycle was significantly greater 
 than that at 40% of the gait cycle ( p=0.001 ) .
the average side - to - side differences ( 95%cis ) 
 of ml translation were 6.3  mm ( 3.7 to 9.0  mm ) , 5.3  mm ( 3.4 to 7.1  mm ) , 5.5  mm ( 3.7 to 
 7.3  mm ) , 6.7  mm ( 4.9 to 8.5  mm ) and 5.9  mm ( 3.7 to 8.1  mm ) , respectively ( fig . 2-e , table 
 1 ) .
there were no significant differences in the side - to - side differences of ml 
 translation among 0% , 20% , 40% , 60% , and 80% of the walking cycle ( p=0.875 ) .
similarly the 
 average side - to - side differences ( 95%cis ) of si translation were 7.7  mm ( 4.5 to 10.8  mm ) , 
 8.1  mm ( 4.2 to 11.9  mm ) , 8.2  mm ( 4.1 to 12.4  mm ) , 8.9  mm ( 4.4 to 13.5  mm ) and 9.8  mm ( 9.8 to 
 18.8  mm ) , respectively ( fig .
there were no significant differences in 
 the side - to - side differences of sl translation among 0% , 20% , 40% , 60% , and 80% of the 
 walking cycle ( p=0.947 ) .
the average knee kinematics pattern of the right and left legs during a gait 
 cycle a ) flexion - extension ; b ) adduction - abduction ; c ) internal - external rotation of the 
 tibia the 95% confidence intervals ( cis ) of side - to - side differences of the normal 
 subjects a ) flexion - extension ( fe ) ; b ) abduction - adduction ( aa ) ; c ) internal - external ( ie ) 
 rotation ; d ) anterior - posterior ( ap ) translation ; e ) medial - lateral ( ml ) translation ; 
 f ) superior - inferior ( si ) translation ( mean , 95% ci ) . a : post - hoc bonferroni tests ( vs. 0% : p<0.001 , vs. 20% : 
 p<0.001 , vs. 40% : p<0.001 , vs. 60% : p<0.001 ) .
b : post - hoc bonferroni test 
 ( vs. 40% p<0.001 ) for clinical application , the knee kinematics of a case with the posterior cruciate 
 ligament injury ( pcl ) were also evaluated .
a 37  year - old male suffered a knee injury while 
 playing rugby football .
the case showed grade-3 positive in the posterior drawer test , and 
 posteromedial rotatory instability11 .
the 
 mri images indicated a pcl injury . at two months after injury , evaluation of 3-d kinematics 
 during walking
based on the 
 side - to - side differences of kinematic data during each stage of gait , the tibia of the 
 injured leg was shifted posteriorly in ap translation during 20% to 60% walking cycle , and 
 shifted internally in ie rotation during 0% to 60% gait cycle ( fig . 3fig .
3the side - to - side difference of the femur relative to the tibia in the case with pcl 
 and pms injuries with the 95% confidence intervals ( cis ) of the normal subjects .
a ) 
 anterior - posterior ( ap ) translation ; b ) internal - external ( ie ) rotation ) .
the side - to - side difference of the femur relative to the tibia in the case with pcl 
 and pms injuries with the 95% confidence intervals ( cis ) of the normal subjects .
a ) 
 anterior - posterior ( ap ) translation ; b ) internal - external ( ie ) rotation
the present study investigated the side - to - side differences in kinematics of the knee joint 
 during walking by healthy subjects .
the side - to - side differences in adduction - abduction 
 rotation and anterior - posterior translation of the tibia were found to be highly dependent 
 on the stage of gait , and they were significantly larger in the swing phase than in the 
 stance phase .
therefore , our findings suggest that it is important to know the normal ranges 
 of the side - to - side differences in knee kinematics in each stage of the gait cycle , in 
 particular those of adduction - abduction and anterior - posterior translation of the knee , in 
 order to evaluate the knee kinematics of subjects during walking .
the reason why the 
 side - to - side differences of adduction - abduction rotation and anterior - posterior translation 
 of the tibia during walking are larger in the swing phase than in the stance phase remain 
 unknown .
one possible reason is mechanical restraint of the motion of the tibia during 
 walking .
the leg is not subject to weight bearing in the swing phase , and the tibia can move 
 with less mechanical restraint in the swing phase than in the stance phase . without weight 

bearing , the knee is relaxed and the joint kinematics are likely to be influenced by 
 ligament balance , rather than joint morphology .
the knee kinematics during walking of a pcl injury case are also presented . for this case , 

an abnormal side - to - side difference in internal rotation of the tibia during walking as well 
 as an abnormal side - to - side difference in posterior translation of the tibia were found .
li 
 et al . reported that pcl deficiency significantly increases posterior translation of the 
 tibia during knee flexion under a weight - bearing condition using a dual - orthogonal 
 fluoroscopic system12 .
however , there was 
 no significant difference in internal - external rotation between pcl - injury and normal knees 
 throughout the range of flexion . in our present study
, the case might have had associated 
 injuries of posteromedial structures of the knee .
previous cadaver studies have shown that 
 additional injuries of posteromedial structures significantly increase internal rotation of 
 the tibia as well as posterior translation of the tibia in pcl deficient knees13,14,15 . regarding clinical relevance ,
our findings indicate that the evaluation of the side - to - side 
 difference of knee - joint kinematics provides useful information for clinical practice . 

however , caution is required in the clinical application of the evaluation of the 
 side - to - side difference of knee - joint kinematics during walking because , there is a 
 possibility that the contralateral leg would functionally adapt to the condition after 
 trauma or disease .
some investigators have reported that the contralateral leg as well as 
 the injured leg functionally adapt to the condition after the injury of the acl and show the 
 so - called quadriceps - avoidance gait16,17,18,19 .
therefore , the evaluation of the 
 side - to - side difference of knee joint kinematics may underestimate the knee kinematics of an 
 injured leg .
while 
 this approach can measure in vivo kinematics of the knee in a dynamic condition , namely in a 
 more physiological condition , it has been reported to have low accuracy due to skin movement 
 artifacts20 , 21 .
the recently described pct employs an overabundance of markers ( a 
 cluster ) placed on each segment to minimize the effects of skin movement artifact6 .
the pct can be extended to minimize skin 
 movement artifacts by optimal weighting of the markers according to their degree of 
 deformation6 .
furthermore pct permits 
 direct in vivo measurement of the complete six - degrees - of - freedom motion of the kinematics 
 of the knee during activities of daily living .
pct has , therefore , recently attracted 
 attention , since the data of three dimensional kinematics of the knee during activities of 
 daily living including walking are considered to reflect function of the knee joint .
walking speed , surface condition , and shoes presumably influence the results of gait 
 analysis .
the 
 knee kinematics measured in this study during walking and gait speed were similar to those 
 reported by other investigators22,23,24,25,26 .
first , since the point cluster technique is based 
 on skin makers , the accuracy of the relative positions of the femur with respect to the 
 tibia depends on the marker attachment technique of the examiner .
second , the sample size of 
 the present study , 21 , was not large enough to determine the normal range of the 
 side - to - side - difference of the knee kinematics during walking .
third , the effect of age or 
 gender differences was not investigated in the present study .
however , no significant 
 differences have been reported between age groups and gender in previous knee kinematics 
 studies27,28,29 , suggesting their effects 
 in this study would have been small . despite the above - noted limitations , the mean 
 side - to - side differences and their 95% cis as objective criteria of normal knee kinematics 
 are useful information for the functional evaluation of subjects with disorders of the knee 
 joint . in conclusion
, the knee kinematics of healthy subjects during walking were measured using 
 the pct , and the normal range of side - to - side differences in knee kinematics were determined 
 for five stages of the gait cycle .
the side - to - side differences in aa rotation and ap 
 translation were highly dependent on the stage of gait ; therefore , the normal ranges of the 
 side - to - side differences in knee kinematics of each stage of gait , in particular aa rotation 
 and ap translation of the tibia , are useful information for the evaluation of the normal and 
 pathological knee kinematics during walking .
 [ purpose ] the purpose of this study was to determine the normal range of the side - to - side 
 difference in three dimensional knee kinematics measured by the point cluster technique 
 ( pct ) . 
 [ subjects ] the subjects were twenty - one healthy normal volunteers without knee pain 
 or an episode of injury to the legs . [ methods ] the subjects were tested bilaterally at a 
 self - selected normal walking speed and six degrees of freedom knee kinematics were 
 measured using the pct , and the 95% confidence intervals of the average side - to - side 
 differences in flexion - extension ( fe ) , adduction - abduction ( aa ) , internal - external ( ie ) 
 rotation , and anterior - posterior ( ap ) , medial - lateral ( ml ) , superior - inferior ( si ) 
 translation in each stage of the gait cycle were determined . 
 [ results ] the average 
 side - to - side differences and their 95% confidence intervals in rotation / translation in 
 each stage of the gait cycle were determined . 
 the side - to - side differences in aa rotation 
 and ap translation of the tibia were significantly larger in the swing phase than in the 
 stance phase . 
 [ conclusion ] the side - to - side differences in aa rotation and ap translation 
 were highly dependent on the stage of the gait cycle . 
 therefore , the normal ranges of the 
 side - to - side differences in knee kinematics in each stage of the gait cycle , in particular 
 aa rotation and ap translation of the tibia , is useful information for evaluating knee 
 kinematics during walking . 
INTRODUCTION
SUBJECTS AND METHODS
RESULTS
DISCUSSION