three months after suffering a stroke , 25% 
 of surviving patients remain wheelchairbound , and in 60% of subjects , walking ability and 
 speed are markedly reduced2 .
one of the 
 main impairments after stroke is reduced muscle strength on the side contralateral to the 
 brain lesion3 . the relation between 
 paretic knee muscle strength on the contralateral side and gait ability after a stroke has 
 been investigated in many studies1 , 3,4,5,6,7,8,9,10,11,12,13,14 . 
 a moderate to strong relation
is generally observed between knee muscle strength in the 
 paretic limb and gait performance4,5,6,7,8,9,10,11,12,13 .
however , muscle strength on the side ipsilateral to the lesion can also be affected after 
 stroke3 , 15 .
harris et al.15 
 suggested that the development of ipsilateral muscle weakness was associated with immobility 
 after stroke and weight loss due to swallowing difficulty and nutritional insufficiency . in 
 addition , throughout the aging process , older people demonstrate an overall decline in 
 muscle mass caused not by stroke but by aging16,17,18 . 

this generalized loss of skeletal muscle is considered a major factor leading to the 
 development of impairment in muscle strength for older adults18 .
regardless of the occurrence of stroke , lower limb weakness has 
 been identified as an important risk factor for walking in older adults19,20,21,22 .
muscle weakness 
 in the bilateral lower limbs caused by aging may have already been increasing before a 
 stroke23 .
thus , paretic and nonparetic 
 lower limb weakness of older stroke patients is complex as a result of the 
 multidimensionality of the challenges caused both by stroke and aging24 , 25 .
this muscle 
 weakness associated with aging is most obvious in areas such as japan , the united states , 
 and europe , which have dramatically aging populations26,27,28 .
very few studies have assessed the contribution of strength in nonparetic lower limbs to 
 gait performance1 , 3 , 29,30,31,32 .
furthermore , the findings are controversial : three studies1 , 29 , 31 reported no significant relation between 
 knee muscle strength in the nonparetic lower limb and gait performance , whereas a further 
 three found a significant relation3 , 30 , 32 .
the association between strength and functions may be curvilinear ; a 
 critical amount of strength is needed for  normal  performance of specific activities33 . above this threshold level of strength
below the threshold , there 
 should , theoretically , be a stronger relation between strength change and change in 
 performance .
a major aim of stroke rehabilitation is optimization of the recovery of muscle strength to 
 regain walking ability34,35,36,37 .
however , the relation between strength in the nonparetic 
 lower limb and gait performance has attracted much less attention , and the results are 
 conflicting . as the threshold level of strength to predict walking independently is unknown 
 in older stroke patients , it is difficult to predict the level of muscle strength that 
 allows independent walking in older patients with hemiparesis . if bilateral knee muscle 
 strength could be used to predict independent walking , training to regain gait performance 
 would become more evidence - based in aging societies .
therefore , this study was designed to assess the relations between bilateral knee extension 
 strengths and gait performance in older subjects with poststroke hemiparesis and to predict 
 gait performance by both paretic and nonparetic knee extension strength .
taking into 
 consideration for previous studies on knee extension strength and walking ability3 , 30 , 32 , we hypothesized that there is a 
 significant relationship between bilateral knee extensor strength and gait performance and 
 that both paretic and nonparetic lower limb strength could be used to predict independent 
 walking in older stroke patients .
to our knowledge , this is the first study to demonstrate 
 the predictive values of both paretic and nonparetic lower limb strength with respect to 
 gait independency .
the eligibility criteria included hemiplegia of the lower extremities , absence of severe 
 consciousness disorder , ability to sit up with a backrest for more than 30 minutes , ability 
 to push against a dynamometer with the nonparetic lower limb after physical guidance , a 
 period of less than 2 months since the stroke event , absence of severe cardiorespiratory 
 insufficiency , and willingness to participate in the study .
the average value and standard deviation ( sd ) of normalized knee extensor strength in 20 
 patients with poststroke hemiplegia were assessed to determine the sample size .
there is a 
 strong relation between force as measured by equipment and body weight in strength 
 measurements23 .
the variability 
 ( relative dispersion ) of the force scores was reduced by normalization against body weight . 

thus , the torques ( nm ) determined by force ( n ) and lower leg length ( m ) were normalized by 
 the ratio of body weight ( nm / kg ) to predict gait ability by strength measurement .
the 
 average normalized knee extensor strength in the nonparetic lower limb of the 20 subjects 
 was 1.33 newton - meters / kg ( nm / kg ; sd , 0.37 nm / kg ) . for the 9 subjects who could walk 
 independently , it was 1.51 nm / kg ( sd , 0.37 nm / kg ) , and for the 11 subjects who required 
 assistance , it was 1.18 nm / kg ( sd , 0.40 nm / kg ) .
five percent of the average normalized knee 
 extensor strength for the 9 subjects who could walk was 0.08 nm / kg ( 8% difference ) , and the 
 standard effect size was 0.30 .
sample size was based on a desired 90% statistical power to 
 detect an 8% difference in normalized knee extensor muscle strength against body weight 
 ( nm / kg ) , with a two - sided  of 5% .
a sample size of 234 was derived by insertion of 1-power 
 ( 0.90 ) ,  ( 0.05 ) , and standard effect size ( 0.30 ) values into the hulley matrix38 .
the authors therefore planned to recruit 
 about 234 people with poststroke hemiplegia for this study .
the study was approved by the 
 kawasaki municipal tama hospital institutional committee on human research . all subjects and 
 their families
were briefed about the aims of the study and the testing procedure prior to 
 participation . written informed consent was obtained from each subject .
knee extension strength was assessed with a tas mt-1 handheld dynamometer ( anima , tokyo , 
 japan ) .
the dynamometer pad is 5555  mm , and its front side is curved to fit the shape of 
 the areas to be measured on the extremities .
the measurement range of this dynamometer is 
 0.1 to 999.9 n , with a recording interval of 0.1 n. a handheld dynamometer may be used to 
 quantify maximal strength and may offer several advantages over free weights , including ease 
 of transport , time efficiency , and low cost .
the intraclass correlation coefficients , used 
 to characterize the reliability of the strength tests using the handheld dynamometer , ranged 
 from 0.84 to 0.99 , which is considered good39 , 40 .
furthermore , use of a handheld 
 dynamometer provides a reliable and valid means of measuring muscle strength in patients 
 with brain damage41,42,43,44 .
prior to strength testing , the tester took the subject s leg and guided it in the 
 appropriate direction in accordance with the testing protocol to familiarize the subject 
 with the feeling of pushing against the dynamometer .
strength of the knee extensor muscles 
 was then assessed bilaterally using the tas mt-1 . for knee extensor assessment ,
subjects 
 were seated in a hard chair with their knees flexed 90 and their arms on their thighs .
the 
 dynamometer was placed perpendicular to the leg just above the malleoli . during all tests , 

the dynamometer was kept stable by the examiner using both hands and/or the subject s leg 
 and was fixed by a belt to keep the knee flexed 90. subjects were told to push against the 
 dynamometer by attempting to straighten their leg . they were asked to build force gradually 
 to a maximum voluntary effort .
gait ability was precisely defined by the functional independence measure ( fim ) locomotion 
 item45 .
the fim locomotion item was 
 chosen because of its widespread use at rehabilitation facilities and ease of scoring .
in 
 this study , when the fim locomotion item score of a subject was 6 points or more ( modified 
 independence , in which the use of a cane and orthosis was accepted for 50-m gait , or 
 complete independence ) , the subject was considered to be able to walk . to determine the association between normalized knee extensor muscle strength in paretic 
 and strength in the nonparetic lower limb ,
then , 
 patients were classified into 2 groups : those who scored 6 points or more for the fim 
 locomotion item and those who scored less than 6 points .
discriminant analysis was performed 
 to identify the combination of knee extension strength of both limbs that discriminates best 
 between possibility and impossibility of gait and to clarify the contribution of the paretic 
 and nonparetic lower limbs to gait performance .
after discriminant analysis , paretic and 
 nonparetic knee extension strengths , adjusted by the degree of a standardized discriminant 
 coefficient , were integrated in the strength index .
the strength index was modeled as a 
 simple regression , and parameter estimates were assessed for goodness of fit to the model : 
 strength index = 1 x+ 2 y 
 ( 1 , standardized discriminant coefficient of paretic lower 
 limb ; x , normalized knee extension strength of paretic lower limb ; 
 2 , standardized discriminant coefficient of nonparetic 
 lower limb ; y , normalized knee extension strength of nonparetic lower 
 limb ) . the threshold level for prediction of independence was judged as the point where both 
 the negative and positive predictive values were high46,47,48 .
between january 2005 and january 2009 , 238 consecutive stroke inpatients from kawasaki 
 municipal tama hospital ( kanagawa , japan ) were enrolled in the present study .
characteristics of patients who met the inclusion 
 criteria are presented in table 1table 1.characteristics of patients satisfying the eligibility criteria ( n=238)age ( y)70.9  10.5gender ( n)men138women100diagnosis ( n)infarction196hemorrhage42time post stroke at assessment ( d)8.2  6.9paralysis side ( n)right125left113sensory disturbance ( n)tactile sense87deep sense19ataxia ( n ) 37aphasia ( n ) 33unilateral spatial neglect ( n)24lower leg length ( m)0.39  0.04knee extensor muscle strength ( nm)52.4  40.7values are shown as the mean  sd . the mean age of participants was 70.9  years ( sd , 10.5  years ) .
196 and 42 were diagnosed with cerebral infarction and 
 cerebral hemorrhage , respectively , 125 patients had right hemiplegia , and 113 patients had 
 left hemiplegia .
the average time since stroke event was 8.2 days ( sd , 6.9 days ) .
mean body 
 weight was 57.6  kg ( sd , 11.6  kg ) .
strength of the knee extensor muscles in the paretic lower 
 limb of the 238 subjects in this study ranged from 0.00 to 321.0 nm ( average , 52.4 ; sd , 40.7 
 nm ) . that in the nonparetic lower limb ranged from 7.1 to 336.0 nm ( average , 72.6 ; sd , 39.9 
 nm ) .
strength of the normalized knee extensor muscles in the paretic lower limb ranged from 
 0.00 to 3.82 nm / kg ( average , 0.90 ; sd , 0.62 nm / kg ) . that in the nonparetic lower limb ranged 
 from 0.10 to 4.00 nm / kg ( average , 1.24 ; sd , 0.58 nm / kg ) . the correlation coefficient ( r ) 
 between normalized knee extensor muscle strength in the paretic lower limb and that in the 
 nonparetic lower limb was 0.73 ( pearson correlation coefficient , p < 0.0001 ) .
values are shown as the mean  sd discriminant analysis was carried out to determine which paretic and nonparetic knee 
 extension strength had a weighted impact on differentiating between the ability and 
 inability to walk .
the discriminant analysis classified the difference between the ability 
 and inability to walk ( eigenvalue , 0.49 ; wilks lambda , 0.67 ;  , 93.85 ; df , 2 ; p 
 < 0.0001 ) .
two variables contributed to classification of the ability of stroke patients 
 to walk , which was performed with a standardized discriminant coefficient ( knee extensor 
 muscle strength in the paretic lower limb , 1.32 ; that in the nonparetic lower limb , 0.55 ) . 

thus , paretic and nonparetic knee extension strengths were integrated in the strength index : 
 strength index = 1.32 x + 0.55 y , where x 
 is the normalized knee extension strength in the paretic lower limb and y 
 is the normalized knee extension strength in nonparetic lower limb .
after discriminant 
 analysis , the threshold level for prediction of independence was judged as the point where 
 both the negative and positive predictive values were high .
a threshold level of 2.0 
 provided the best balance between positive and negative predictive values for the strength 
 index ( fig . 1fig .
1.prediction of gait performance by predictive value curvethe threshold level for prediction of independence was judged as the point where both 
 the negative ( open symbols ) and positive predictive values ( filled symbols ) were high . 

the curve for the negative and positive predictive values indicated that a strength 
 index of 2.0 would provide the best balance for gait performance ( positive predictive 
 value , 0.74 ; negative predictive value , 0.69 ) . ) .
prediction of gait performance by predictive value curve the threshold level for prediction of independence was judged as the point where both 
 the negative ( open symbols ) and positive predictive values ( filled symbols ) were high . 

the curve for the negative and positive predictive values indicated that a strength 
 index of 2.0 would provide the best balance for gait performance ( positive predictive 
 value , 0.74 ; negative predictive value , 0.69 ) .
in the present study , a relation between both paretic and nonparetic lower limb strength 
 and gait performance was discovered .
our results indicated that ( a ) the paretic lower limb 
 strength was correlated with the nonparetic lower limb strength , ( b ) both the paretic and 
 nonparetic knee extension strengths were predictors of gait performance in older patients 
 with poststroke hemiparesis , ( c ) the paretic knee extension strength affected gait 
 performance more than the nonparetic strength , and ( d ) the strength indices of the paretic 
 and nonparetic strengths combined with the weighted impact for gait performance could 
 predict gait performance .
a strength index of 2.0 , meaning that the prediction of gait 
 performance was deduced from the bilateral knee extension strengths , provides the best 
 balance between positive and negative predictive values .
about 75% of patients with a 
 strength index of more than 2.0 could walk independently .
however , 70% of patients with a 
 strength index of 2.0 or less could not walk independently .
a previous study suggested that 
 there was a moderate to strong relation between paretic knee extension strength and gait 
 performance4,5,6,7,8,9,10,11,12,13 , whereas the relation between nonparetic knee extension strength 
 and gait performance was controversial1 , 3 , 29,30,31,32 .
however , the abovementioned studies 
 recruited subjects who could walk without supervision or physical assistance and assessed 
 gait speed as gait performance . an additional new observation in
the present study was that 
 both the paretic and nonparetic lower limb strengths affected the ability to walk 
 independently . in our study , the predictive value of combined bilateral knee extension 
 strength for gait independency was clearly demonstrated .
moreover , we provided evidence indicating that paretic lower limb strength is correlated 
 with nonparetic lower limb strength in this study . throughout the aging process , people 
 demonstrate an overall decline in muscle mass17 .
this generalized loss of skeletal muscle is considered a major 
 factor leading to the development of impairments in muscle strength for older adults18 .
this muscle weakness associated with 
 aging is obvious in regions such as japan , the united states , and europe , where society is 
 dramatically aging26,27,28 .
our results implied that 
 throughout the aging process , older people demonstrate an overall decline in muscle mass 
 caused not by stroke but by aging .
although progressive resistance training is an appropriate intervention and assessment for 
 improving gait performance and bilateral lower limb strength in older people with poststroke 
 hemiparesis , comparatively little research has focused on the training effect of combined 
 paretic and nonparetic lower limbs of older patients with stroke50 .
our study demonstrated the threshold level of the 
 strength index for subjects with poststroke hemiparesis who could ambulate independently . 

therefore , the period required to reach the threshold level in resistance training programs 
 may be estimated by further research . in the future ,
a prospective cohort study is necessary 
 to identify predictors of recovery of independent gait ability after stroke .
in addition , 
 isometric evaluation with a handheld dynamometer utilizes a mode of contraction different 
 from that used in training , as isotonic contraction is most commonly used for exercise 
 training .
thus , use of a handheld dynamometer is limited by lack of specific training . 

future studies need to assess whether handheld dynamometers can measure changes in strength 
 after resistance training with the same precision as those measured by isotonic testing .
engardt et al.51 noted that patients 
 learned to use the nonparetic leg to compensate for the weakness of the paretic leg in the 
 early phase of rehabilitation . in previous studies
, patients might have already learned to 
 use the nonparetic leg to compensate for the weakness of the paretic leg in their gait 
 because a long period had passed since the onset of stroke1 , 3 , 29,30,31,32 .
it is still difficult to 
 predict the contribution of both the paretic and nonparetic lower limb strengths to gait 
 performance in older patients with poststroke hemiparesis .
however , about 25% of patients with a strength index of more 
 than 2.0 could not walk independently .
when patients with a knee extension strength over the 
 threshold level are unable to walk independently , learning to use the nonparetic and paretic 
 legs might be a useful strategy for the patient to adopt .
activities of daily living are 
 considered behavioral chains of component actions ; such chains have been learned and 
 performed since childhood52 .
a patient 
 with hemiplegia can not walk by means of the behavioral chains used by a healthy person and 
 thus has to learn new behavioral chains to walk independently .
there is a growing body of 
 evidence indicating that locomotor treadmill training with partial body - weight support may 
 be an effective method of improving gait quality in the acute stage of stroke53 , 54 .
the intensity of resistance training and skill training can be 
 decided by the threshold level of strength determined in this study .
future studies are 
 needed to assess whether changes in muscle strength measured using a handheld dynamometer 
 can reflect the ability of a subject to perform activities of daily life after resistance 
 and skill training .
it has been reported that stroke patients can not perform at higher angular velocities due 
 to spastic antagonist restraints55 . 

however , isometric strength has been shown not to be affected by antagonist muscle 
 spasticity56 .
our investigation 
 evaluated the relationship between isometric bilateral knee extension strength and gait 
 performance ; as a result , antagonist muscle spasticity would have had little effect on 
 agonist muscle strength .
however , because spasticity of knee extensor and flexor muscles in 
 stroke patients was not examined in this study , further research is needed to investigate 
 the relationship between lower limb strength and spasticity and gait performance .
 [ purpose ] the purpose of this study was to assess the relationships between bilateral 
 knee extension strengths and gait performance in subjects with poststroke hemiparesis and 
 to predict gait performance by the paretic and nonparetic knee extension strength . 
 [ subjects and methods ] this was a correlational study in which 238 consecutive inpatients 
 with poststroke hemiparesis were enrolled . 
 knee extensor muscle strengths in paretic and 
 nonparetic lower limbs were measured with a handheld dynamometer , and the presence or 
 absence of impaired gait was also determined . 
 [ results ] the mean strength in the paretic 
 lower limb was 0.90 nm / kg , and that in the nonparetic lower limb was 1.24 nm / kg 
 . 
 discriminant analysis classified the difference between the possibility and impossibility 
 of gait by knee extensor muscle strength ( standardized discriminant coefficient : paretic , 
 1.32 ; nonparetic , 0.55 ) . 
 thus , paretic and nonparetic knee extension strengths were 
 integrated in the strength index . 
 a threshold level of 2.0 provided the best balance 
 between positive and negative predictive values for the strength index . 
 [ conclusion ] the 
 results indicated that both paretic and nonparetic knee extension strengths were related 
 to gait performance . 
 the strength index deduced from bilateral knee extension strengths 
 may serve as a clinically meaningful index for rehabilitation assessment and training . 