Maturation of Gait Dynamics Stride to Stride Variability

8/19/2019 Maturation of Gait Dynamics Stride to Stride Variability

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Maturation of gait dynamics: stride-to-stride variabili tya nd i ts tempora l orga niza t ion in children

J . M. H AUS DORFF,1,2,3 L. ZEMANY, 1 C.-K. PENG,1,3 AND A. L . G OLDBERG ER1,31M argret H . A. Rey L abora tory fo r Nonl inear Dynamics in M edic ine, 2Gerontology Di vision a nd Departm ent of M edi cin e, B eth I srael Deaconess M edi cal Cent er, Boston 02215; and 3H ar var d M edi cal School, B oston, M assachusett s 02115

Hausdorff, J . M., L. Zemany, C.-K. Peng, and A. L.Goldberger. Maturat ion of ga i t dynam ics: s tr ide-to-str idevariability and its temporal organization in children. J . Appl .Physiol. 86(3): 1040–1047, 1999.—In very young children,immature cont ro l o f pos ture and ga i t resu l t s in uns teadylocomotion. In children of 3 yr of age, ga it a ppear s relativelymature ; however, i t i s unknown whether the dynamics ofwa lking change beyond th i s age . B ecause s t r ide dynamicsdepend on neural control, we hypothesized tha t m otor controlwould continue t o develop beyond a ge 3. To test this hypoth-esis, we measured t he ga it cycle dura tion on a str ide-by-strideba sis in 50 hea lthy 3-t o 14-yr-old children (25 girls). Measur e-ments of stride-to-stride variability were signicantly larger

both in the 3- an d 4-yr-old children, compar ed with the 6- an d7-yr-old children, and in the 6- and 7-yr-old children, com-pared wit h t he 11- to 14-yr-old children. Measur ements of th etemporal organizat ion of gai t also revealed signicant age-dependent changes. The effects of age persisted even afterad jus t ing for he igh t . These ndings ind ica te tha t maturestr ide dynamics may not be completely developed even inhealthy 7-yr-old children and that different aspects of stridedynam ics ma ture at different a ges.

age; wa lking; spectral a nalysis; fractal ana lysis

WHEN YOUNG CHILDREN r s t beg in to walk , immaturecontrol of posture and gai t resul ts in la rge s t r ide-to-s t r ide uctuat ions and frequent fa l ls (5 , 23) . By thet ime chi ldren are 3 yrs old, their gai t is re la t ivelymature (26) , and the visual ly apparent unsteadinesshas been replaced by a more s table walking pat tern.Nonetheless , subt le changes in the development ofneuromuscular contr ol a nd locomotor function con-tinue well beyond age 3 (2, 19, 23, 25, 26). Some studiessuggest a decrease in walking variability after this age(21, 24). However, a key una nsw ered quest ion is wh ethersubtle cha nges in gait unstea diness and st ride-to-str idedynamics also occur beyond this age.

Even in healthy young adults, the ga it cycle durat ion(the stride time) uctuates from one stride to the next

in an apparent ly random, ‘‘noisy’’ ma nner (11, 16).However, in young adul ts with intact neural control ,the magnitude of these uctuations is relatively small.Although th e str ide-to-str ide changes a ppea r to uctu-a te ra ndomly, wit h no correla tion betw een present a ndfuture str ide times, the healthy a dult locomotor systema ctua lly possesses ‘‘memory,’’s uch tha t t he cha nge from

one s t r ide to the nex t d isplays a subt le, ‘‘h idden’’temporal structure that has been associated with long-range, f ractal organizat ion (11, 12). In contra st , inpersons with neurological disease and in older persons,especially those w ith a history of fa lls, stride-to-stridevariability increases, and the temporal organization ofstride time dynamics is altered as well (3, 4, 7, 8, 10,14).

These studies suggest tha t a na lysis of the str ide timedyna mics may a lso provide a w indow into the develop-ment of neuromuscular control in children. Given theapparent para l lels betw een t he immat ure gai t of chil -dren and the unsteady gai t of older persons and per-sons with neurological impairment (23), along with thesubt le continued development of neura l cont rol beyondage 3, we hypothesized tha t s t r ide t ime dynam ics w illnot be ful ly ma tured at this a ge. In the present s tudy,we t ested this h ypothesis by m easuring stride-to-strideuctuat ions in the ga i t cycle durat ion of heal thy 3- to14-yr-old children. More specically, we sought 1 ) t ocharacterize the development of mature stride dynam-ics, 2 ) t o d et e rm in e a t w h a t a g es ch a n g es i n g a i tdynamics occur, and 3 ) to compar e the ga it dyn a mics ofchildren to those of adu lts.

METHODS

Subjects

Fifty boys and girls par ticipat ed in this study. P ar ents of 3-to 14-yr-old children were asked if they would be willing tohave the i r chi ld par t icipa te in th i s s tudy. I f the ch i ld andparen t were wi l l ing to par t ic ipa te , paren ts were asked toprovide informed w rit ten consent a nd t o ll out a quest ion-na ire describing th e child’s medical history. Most childrenwere attending a local day camp or day care center. Childrenwere excluded if they ha d a ny disorders likely to affect ga it, ifthey w ere unable to wa lk independently for 8 min, or i f theywere born prematurely. Children were classied into threeag e groups: 3- and 4-yr-old ( n 11), 6- and 7-yr-old ( n 20),

and 11- to 14-yr-old ( n

12) children. A few 5-yr-old ( n

3),8-yr -old ( n 1), a nd 10-yr-old ( n 3) children were alsos tud ied . Height and weight of the younges t , middle, andoldest age groups were 105 2, 125 1, and 155 10 cm a nd17.3 0.7, 25.3 0.9, 44.4 2.7 kg, respectively. There w ereequal numbers of boys and g i r l s , and there were s imi la rnumbers of boys and girls in each a ge group. For comparison,we used da ta from historical contr ols [speci cally, 10 healthyyoung adults (age, 18–29 yr) who walked for 1 h around alarge t rack under condit ions similar to those in t he presentstudy (12)] . All of the analysis methods performed on thechildren’s da ta were a pplied t o the rst 8 min of the longerdat a segment s in this adult control group.

The costs of publication of this article were defrayed in part by thepayment of page charges . The ar t ic le must therefore be herebymarked ‘‘advertisement ’’ in accordan ce with 18 U.S.C. Section 1734solely to indicate this fact.

8750-7587/99 $5.00 C opyr igh t 1999 the American Physiological Society1040 h t t p://w w w.ja p.org


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Protocol

Subjects w alked a t t heir self-determined, norma l pace for 8min around a 400-m running track. All subjects wore theirown shoes or sneakers. An invest iga tor wa lked s l igh t lybehind each subject during the test . A recently developedtechnique was used to measure the s t r ide t ime dynamicsduring this relatively long walk on level ground (9, 11, 12).Two force-sensit ive sw itches w ere placed in side th e subject’sright shoe: one underneath the heel of the foot and the otherundernea th the ba l l o f the foot . The output of these footswit ches, which provides a mea sure of the force applied to th e oor, wa s sampled at 300 Hz an d stored in a sma ll (5.5 2 9cm), l ightweight (0.1 kg), ankle-worn recorder. 1 Subse-quently, the recorded signal was automatical ly analyzed todetermine ini t ial conta ct t ime (heel s tr ike) of each st r idethroughout the walk, and, hence, the str ide t ime ( the t imefrom one heel strike to the next heel strike of the same foot)time series (9). The a verage w alking speed w as determined bymeasuring lap t ime.

St r i d eTi meDy n amics

To study the effects of ag e on t he int rinsic stride-to-stride

dynamics, some preprocessing was performed on each timeseries. The rst 60 s and t he last 5 s of each time series werenot included to eliminate a ny sta rt-up or ending effects a nd toal low the subject to become famil iar with the w alking tra ck.The t ime series were also processed to remove an y pauses(stride time 2 s and t he 5 s before and after a ny pauses) aswell as any large spikes or outl iers . These outl iers , whichoccurred infrequently, w ere removed so tha t the intr insicdyna mics of each time series could be more readily a na lyzed.This w as accomplished by using previously esta blished meth-ods (8, 10) by 1 ) determining the mean and SD of the str idet ime while excluding the 5%of the da ta with the lowest a ndhighest values and then 2 ) removing from the original t imeseries al l data tha t fel l 4.0 SD a wa y from this mean va lue.The number of pauses (typically 0) and the n umber of stridesexcluded (ty pically 2%) w ere simila r in all t hree a ge groups.

As shown in Table 1 and summarized below, we appliedseveral mea surements t o analyze the va riabil ity a nd tempo-ra l structure of the stride time dyna mics.

Stri de-to-Strid e Vari abil i ty M easur es

To est imate the overal l s tr ide-to-str ide variabil i ty, wecalculated the SD of each t ime series a nd the coefficient ofvar iat ion (CV) (100 SD/mean), a n index of variabil i tynormalized to each subject’s m ean cycle durat ion. B oth t heSD an d the CV provide a measure of overall var iat ions in gaitt iming dur ing the en t i re walk , i . e . , the ampl i tude of theuctua t ions in the t ime ser ies wi th respect to the mean .However, these measures may be inuenced by trends in thedat a (e.g. , due to a change in speed) and cannot dist inguish

betw een a wa lk with lar ge cha nges from one stride to the nextand a wa lk in which str ide-to-str ide variat ions are sma ll andmore long-term, global changes (e.g. , a change in average

value) result in a larg e SD. Therefore, to estima te var iabilityindependent of loca l changes in the mean , w e q uant iedsuccessive str ide-to-stride changes (i.e., the difference be-tw een the stride time of one stride a nd t he previous stride) bydetermining the rst difference of each time series. The rstdifference, a discrete a nalog of the rst derivat ive, is ones tandard method for removing s low vary ing t rends a nd i sca lcu la ted by subt rac t ing the prev ious va lue in the t imeseries from the current value. The SD of the rst-differencetime series provides a measure of variabil i ty a fter detrend-ing.

Temporal Str ucture M easur ements

To s tudy the tempora l organiza t ion , we applied th reemethods to ana lyze different aspects of the dyna mic structureof the time series of the stride t ime.

Spectr al anal ysis. Fourier spectral analysis is a s tandardmethod for examining the dynamics of a t ime ser ies . Toensure that these measures of the dynamics were indepen-dent of the a verage str ide t ime or the str ide t ime var iabil ity,we studied the rst 256 points of each subject’s time series(after the 60-s start-up period) by rst subtracting the meanan d dividing by the S D. This produces a t ime series centereda t 0 w i t h a S D of 1. 0. S u b se q ue nt l y, s t a n da r d F ou r ie rana lys i s, w i th the use of a rectangular window, was per-formed on each time series. To qua ntify an y differences in th espectra, w e calculated the percenta ge of power in th e high-frequency ba nd (0.25–0.50 strides 1 ) a n d t h e r a t i o o f t h elow-frequ ency (0.05–0.25 strid es 1 ) to high-frequency power.This ratio excludes the power in the lowest frequencies andthus is independent of very large-scale changes in the stridet ime. By computing the rat io of the uctuations over rela-t ively long t ime scales (i .e. , low frequencies) to short t imescales (i .e. , high frequencies), an index of the frequency‘‘balance’’ of the spectra is obtained. A large low-to-high ratiois indicative of nonstationarity. Therefore, to the extent thatthe ga i t of the younger children is more nonstat ionary, onewould expect this spectral ratio to decrease with maturation.

Au tocorr ela ti on decay. As a complementary method forana lyzing the temporal s tructure of gai t dyna mics, we exam-ined the autocorrelat ion propert ies of the str ide t ime. Theaut ocorrelation function estimat es how a time series is corre-la ted w i th i t sel f over d i fferen t t ime lags and provides ameasur e of the memory in th e system, i.e., for up to how ma nystrides is the present value of the stride time correlated w ithpast values? After direct calculat ion of the autocorrelat ionfunction in the time domain (20), we calculated two indexes ofaut ocorrelation decay : 37% a nd 67% , the num ber of strides forthe autocorrelation to decay to 37%(1/ e ) or 63%(1 1/e ) of i tsini t ial value, respectively. To minimize any effects of da talength, mean, or varian ce, we applied this ana lysis to the rst256 strides and normalized each time series with respect toi ts mean and SD. This a utocorrelat ion measure emphasizesthe correlat ion propert ies over a very short t ime scale, in

1 Pr evious studies have shown tha t lower-extremity loading on theorder of 1–2%of body weight can have subtle effects on gait. For thel ightes t ch i ld s tudied here , the ga i t m onitor w as 0.8% of bodyweight. For most 6- and 7-yr-old children (15 of 20) and all of theoldest children, the monitor wa s 0.5%of body weight. Thus a verysmal l loading effec t cannot be excluded in the 3- and 4-yr-o ldchildren. However, it seems unlikely that this inuenced the compari-sons between the tw o older groups, in w hich, as shown below, therewere still signicant age-related differences.

Ta ble 1. S t r ide t im e ana lysi s methods

Varia bility Mea sures: Fluctuat ion MagnitudeStandard deviation (SD)Coefficient of va ria tion (CV)SD of detrended (rst difference) time series

Temporal Structure Measures: Fluctuation D ynam icsFourier (spectral) analysisAutocorrelation decay time

Detrended uctuation analysisUnl ike var iabi l ity measures , t empora l s t ruc ture measures ar e

sensitive to the order of the data points in the time series.

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which the correlation decays most rapidly. If the memory ofthe system increases with maturity, one would expect to seelonger decay times in older children.

Str ide t ime corre la t ions . To further s tudy the temporalstructure of the str ide t ime dynamics ( independent of theovera ll varian ce), we also applied detrended uctuat ion a na ly-sis (DFA) (11, 18) to ea ch subject’s time series. DFA is amodied random walk analysis that can be used to quantifythe long-range, fra ctal propert ies of a relat ively long t imeseries or, in the case of shorter time series (i.e., the presentstudy), it can be used to measure how correlation propertieschange over different t ime scales or observation w indows (10,18). Methodological detai ls have been provided elsewhere(10–12, 18). Briey, the root-mean square uctuation of theintegra ted an d detrended time series is calculated at differentt ime scales, and the slope of the relat ionship between the uctuat ion ma gnitude and the time scale determines a fractalscal ing index ( ). To de te rmine the degree and na ture ofstride time correlations, we used previously validated meth-ods (10) an d calculated over the region 10 n 20 (wh ere n is the number of strides in the window of observation). Thisregion wa s chosen because i t provides a s tat is t ical ly robustest imate of s tr ide t ime correlat ion propert ies tha t are mostindependent of nite s ize effects ( length of data) (17) andbecause i t has been shown to be sensi t ive to the effects ofneurological disease and aging in older adults (10). Like theautocorrelat ion method, the DFA method q uanti es correla-t ion propert ies. H owever, t he D FA method a ssumes that ,wi th in the sca le of in terest , the cor re la t ion decays in apower-law manner and, therefore, a single exponent ( ) canquantify the scal ing. Whereas the autocorrelat ion methodwas applied to examine the dynamics over very short t imescales, the DFA method, a s applied here, examines scal ingover relat ively longer t ime periods. If the str ide-to-str ideuctuations are more random (less correlated) in youngerchildren, one would expect that w ould be closer to 0.5 (w hit enoise)in this group. In contra st, an va lue closer t o 1.5 wouldindicate uctuta t ions with a brown noise qua li ty, indicat ingthe dominance of low-frequency, slowly changing trends (18).

Stati st ical M ethods

The nonpara metric Kruska l-Wallis test wa s used to test forsta tistical differences among th e three age groups. If this testshowed signicant differences, multiple Wilcoxon rank sumtests w ere performed to compar e two groups at a t ime. Thesenonpara metric tests make no assum ptions about the underly-ing distr ibution of the data being compared. P 0 .05 wa sused as the level for s ta t i s t ica l s ign icance in de tect ingunivariate group differences. Stat is t ical analysis was per-formed by using SAS software release 6.12 (SAS, Cary, NC).Group results are reported as means S E .

RESULTS

Str ide Tim e-Vari abi l i ty Measur ements

Representa tive examples of the effects of age on t hes t r id e t i me u ct u a t i on s a r e s h ow n i n F ig . 1. Th estr ide-to-stride var iability is largest in the 4-yr-old,lower in the 7-yr-old, and smaller still in the 11-yr-oldchild . As summarized in Table 2 , t here wa s a highlysignicant effect of age on variability (P 0.0001). Boththe SD and CV were s ignicant ly lar ger in t he 3- and4-yr-old children compar ed wit h the 6- and 7-yr-oldchildren (P 0.0001). In a ddit ion, th ese measur es weresigni cant ly larger in the 6- and 7-yr-old compared

w ith th e 11- to 14-yr-old childr en ( P 0.005). O f n ote,the stride-to-str ide va riability of the 11- to 14-yr-oldchildren was closest to the values obtained in healthyyoung adults (CV 1.3 0.1%in the young adult s a nd2.1 0.1%in t he 11- t o 14-yr-old child ren ).

In the representative examples shown in Fig. 1, thelocal average of the s t r ide t ime of the oldest child isrelat ively constant throughout the walk. In contrast ,for t he tw o younger children, the loca l a verage a ppearsto change from t ime to t ime. Therefore , we next ad-dressed tw o questions. 1 ) Is t he increased va riability inthe younger children simply due to fatigue during t hiswalk? 2 ) Is t his increa sed varia bility d ue to a change inrate during the walk (e.g., long-term slowing down orspeeding up) a nd not indicat ive of short -term , stride-to-stride unst eadiness per se?

Fig. 1. Representative wa lking time series of 4-, 7-, and 11-yr-oldchildren. Str ide-to-str ide uctua tions ar e largest in 4-yr-old child an dsma llest in 11-yr-old child. C oefficient of va ria tion (CV), a measu re ofvar iability, w as 8.4, 4.3, an d 1.9% in 4-, 7-, a nd 11-yr-old children,respectively.

Ta ble 2. S t r i d e t i m e v ar i a bi l i t y

3–4 Yr O lds 6–7 Yr O lds 11–14 Yr O lds

SD, ms

O ri gi na l t im e s er ie s 55 5† 31 2 23 1*‡Aft er det ren din g 48 4† 28 1 22 1*‡Fir st 30 st r ides 47 5† 25 1 17 1*‡

CV, %Or ig ina l t ime s er i es 6. 1 0.5† 3.3 0.2 2.1 0.1†‡Lowest 30-strid e seg-

ment 3.1 0.2† 1.8 0.1 1.2 0.1†‡Fir st 30 st r ides 5.1 0.5† 2.6 0.1 1.6 0.1†‡

Values a re means SE ; n 11, 20, and 12 in 3- to 4-yr-old, 6- to7-yr-old, and 11-to 14-yr-old age groups, respectively. Kruskal-Wallistes ts de tected s ignicant d i fferences a mong the 3 groups for a l lmeasures ( P 0.0001). Signicant differences compared with 6- and7-yr-old group, * P 0.005; † P 0.0001. ‡ Signi cant differencebetween oldest and youngest groups, P 0.0001.

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To evaluat e these quest ions, w e detrended each t imeseries to minimize the effects of any local changes inaverage stride. Figure 2 shows the results for the timeseries shown in Fig. 1. Even aft er detrending, varia bil-ity is lar gest for the 4-yr-old child an d sma llest for t heoldest child. This inverse relat ionship betw een varia bil-ity a nd age aft er detrending wa s found in general for a llsubjects a s w ell. The SD of the detrended t ime series, ameasure of the dispers ion or var iabi l i ty, was s igni-cant ly lar ger in the 3- a nd 4-yr-old children compar edw ith t he 6-a nd 7-yr-old children ( P 0.0001)and in the6- and 7-yr-old children compared with the oldestchildren (P 0.004).

As a f ur t h er t e st of t h es e n d in gs , w e a n a l y zedsubsections of each subject’s t ime series to nd the 30con s ecu t i ve s t r i des w i t h t h e l ow e s t C V. (A d a t a -ana lysi s window wa s moved forwa rd ve s t r ides a t atime a cross the time series, and in ea ch window the CVw a s calculat ed.)Va ria bility during this segment shouldbe la rgely independent of a subject’s speeding up ors lowing down during the t r ia l and reects the ‘‘best-effort’’ of the neuromuscular control system. For thedat a shown in Figs . 1 and 2, the CV calculat ed in thismanner wa s 3.8, 1.9, and 1.1% for the 4-, 7-, and11-yr-old children, respectively. Figure 3 shows theresults of t his lowest var ia bi li ty t ime segment for a l lsubjects . Even during a re la t ively short t ime per iod,t h e u ct u a t i on s f rom on e s t r id e t o t h e n ex t w e r esignicantly increased in the 3- and 4-yr-old childrencompa red w ith t he 6-a nd 7-yr-old children ( P 0.0001)a nd in the 6- a nd 7-yr-old children compar ed w ith theoldest children ( P 0.0001). In fact, the CV of each ofthe oldest chi ldren wa s lower t han tha t of a l l of the 3-and 4-yr-old children.

Final ly, to conrm that the increased var iabi l i ty inthe younger children w a s not simply due to fa tigue or ach a n g e o f s peed d u ri ng t h e w a l k , w e s t u di ed t h evaria bi li ty of only t he rst 30 st r ides. As w as the casefor the ent i re walk, both the SD and CV were s igni-cantly larger in the 3- and 4-yr-old children comparedw ith t he 6-a nd 7-yr-old children ( P 0.0001)and in the6- and 7-yr-old chi ldren compared with the oldestchildren ( P 0.0003; Ta ble 2).

Temporal-Str ucture M easur ements

Spectr al analysis. The above resul ts demonstra tethat the magnitude of s t r ide- to-s t r ide var iabi l i ty de-crea ses with ma tur at ion in health y children. The ques-tion we next a ddress is w hether the tempora l structureof the s t r ide t ime dynamics i s a l so age dependen t .Figure 4 shows the resul ts of spectra l a nalysis for thetime series shown in Fig. 1. As expected, there appearsto be a change in the frequency spectrum with age. Thepower in the higher f requency ranges appears to beslightly larger in t he oldest child and sm a ller in the t woyounger children. C onversely, low-frequency power a p-pears to be reduced in the 11-yr-old child comparedwit h t he tw o younger children. For the entire group ingeneral, the percentage of high-frequency power was

increased and low-frequency power was decreased inthe oldest children compared with the other two groups(Table 3). Although these t rends were not signican t,there was a signicant dependence of the low-to-highrat io on t he age group (P 0.002). This spectral ratiowa s signican tly la rger in the oldest children compar edw ith th e 6- a nd 7-yr-old children ( P 0.02), and it alsotended to be la rger in the 6- and 7-yr-old childrencompared with the youngest chi ldren ( P 0.06). Inother w ords, the ra tio of the str ide time uctua tions onr el a t iv el y l a rge t i me s ca l es t o t h e u ct u a t i on s onshorter t ime scales decrea sed with a ge.

Fig. 2. Representative t ime series after detrending (for sa me dat asets shown in Fig. 1). Even after detrending, which minimizes effectsof local changes in mean value, stride-to-stride uctuations in stridetime a re still la rgest in 4-yr-old child a nd sm allest in 11-yr-old child.SD was 60, 27, and 20 ms for time series of these 4-, 7-, and 11-yr-oldsubjects, r espectively. (For gr aphin g purposes, 2 off-scale da ta pointswit h va lues between 0.2 an d 0.3 s are not sh own for 4-yr-old subject.)

F ig. 3. S t r i de t ime va r i abi li t y a s f unct i on o f age . Shown i s CVcalculated during 30-stride subsection of each subject’s time serieswi th the lowest var iabi li ty. Even dur ing th is per iod of re la t ivelysteady wa lking, gait va riabili ty decreases with age. I nset : data pointsreplotted on log-log axes. S lope of best- t l ine is close t o 1.0,indicating that CV decreases inversely with age (CV a ge 1 ). Notehow the s t r ide t ime va r iabi li ty observed in o ldest ch ildren ap-proaches tha t of healthy adults (12). Er or bars, mean SE for youngadul ts .



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To conr m tha t this difference in spectral balancewas no t due to any s imple l a rge-sca le t r ends in theda ta , we per formed spect ra l ana lysi s o f each t imeseries after detrending each time series (by taking therst difference). The results were similar to those forthe or iginal t ime ser ies (Table 3); this suggests tha tthere is a change in spectral balance independent oflar ge-scale trends in the da ta . Moreover, w e con rmed

tha t this effect persisted even if w e changed (somewh a tar bi t rar i ly) the w ay in w hich t he spectra were divided.For example, when the high-frequency ba nd w a s rede- ned as 0.3–0.4 str ide 1 a nd the low-frequency ba nd a s0.1 to 0.2 str ide 1, a similar effect of age on t he bala nceof spectra l pow er w a s observed (Ta ble 3 and Fig. 5).

Autocorrelation measurements. As expected, m eas ure-ments of the deca y of the a utocorrela tion function a lso

var ied with a ge. For t he younger children, 63% decayedrapidly (af ter 2 or 3 s t r ides), w hereas this decay t ime

wa s general ly larger in the t wo older groups. Speci-cally, 63% was 2.5 0.2 and 4.8 0.6 strides in t he 3-and 4-yr-old and the 6- and 7-yr-old children, respec-tively (P 0.0005). 63% was s l ight ly, but not s igni-cantly, larger in the 11- to 14-yr-old children (5.6 1.1strides) compared with the 6- and 7-yr-old children.Similar results were obtained for 37% . This m eas ure ofthe decay of the au tocor rela t ion funct ion wa s a l solowest in the 3-and 4-yr-old children (5.8 1.0 strides),larger (P 0.06) in th e 6- a nd 7-yr -old childr en (11.43.3 str ides), an d tended t o be slightly la rger in th e 11-t o14-yr -old childr en (19.0 9.8 str ides; P 0.01 com-pared w ith t he youngest children).

Str ide t i me corr elat i ons. The fractal-scaling index

wa s simila r in the tw o youngest a ge groups an d tendedto decrease in the oldest chi ldren ( 0.93 0.04,0.93 0.03, 0.88 0.04, in th e 3- and 4-yr-old, 6- a nd7-yr-old, a nd 11- to 14-yr-old children, respectively).When this analysis was performed on the rst differ-ence of the time series (i .e. , after removing any largetrends), the effect of age became more pronounced andsta t is t ical ly s igni cant (P 0.01 an d P 0.05 compar-ing th e 11- to 14-yr-old children to th e 6- an d 7-yr-olda nd t he 3- a nd 4-yr-old children, r espectively).

The D FA method a utoma tically ‘‘detrends’’ the da tab y d et e rm in in g t h e u ct u a t i on s a b ou t t h e l ea s t -squa res, best- t str a ight line in ea ch w indow of observa -tion. Nonstationarities (trends) that are not well char-

a cterized by a st ra ight line could possibly give rise to anina ccura te scaling exponent. Therefore, to furt her exam-ine the dynamical propert ies , we also computed thescaling index by using higher order DFA detrending.Specically, we detrended each window of box size n byusing second-order polynomials instead of the rst-order linea r det rending (12).

With second-order detrending of the time series, theage effect was apparent both before (see Fig. 6) andaf te r t ak ing the rs t d ifference of the t ime se r ies.Among the younger subjects ( 11-yr-old subjects), 10subjects ( 25%) ha d sca ling in dexes 1.0, whereas all

Fig . 4 . Representa t ive resul t s of spect ra l a nalys is ( for da ta se tsshown in Fig. 1). Time series w ere normalized so that total power issame in each of the spectra. Note subtle decrease in low-frequencypower and increase in h igh-f requency power wi th age . Ra t ios oflow-frequency power (0.05–0.25 stride 1 ) to high-frequency power(0.25–0.50 stride 1 ) were 9.0, 4.6, a nd 1.5 for th e 4-, 7-, a nd 11-yr-oldsubjects, respectively.

Ta ble 3. Spectral analysis

3–4 Yr O lds 6–7 Yr O lds 11–14 Yr O lds

%High -frequency pow er,0.25–0.5 stride 1 0.054 0.010 0.064 0.012 0.100 0.022

L ow -t o-h ig h r at io 6.8 1.2 4.1 0.5 2.3 0.5*†Low-to-high ratio afterdet rending 0.30 0.02* 0 .20 0. 03 0. 15 0.03†

%High -frequency pow er,0.3–0.4 stride 1 0.022 0.005 0.023 0.004 0.038 0.009

L ow -t o-h ig h r at io 6.8 1.1 4.5 0.7 2.3 0.3*†Low-to-high ratio after

det rending 0.41 0. 06 0. 29 0. 04 0. 18 0.02†

Values a re means SE ; n 11, 20, and 12 in 3- to 4-yr-old, 6- to7-yr-old, an d 11- to 14-yr-old groups, respectively. Kru skal-Wallistes ts de tected s ignicant d i fferences a mong the 3 groups for a l lmeasures except high-frequency power. Signicant differences be-tw een groups; * compared w ith 6- to 7-yr-old group, P 0.05; † oldestcompared with youngest group, P 0.005.

Fig . 5 . Rat io of power in the re la t ive ly low-frequency (0 .1–0.2stride 1 ) to relatively high-frequency (0.3–0.4 stride 1) bands de-creases with age. Note that this index of stride dynamics excludeshighest a nd lowest frequencies. In oldest children, ratio a pproachestha t of hea l thy a dul ts. Error bars , mean SE for young adults. Seeal so Ta ble 3.



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of the scaling exponents were 1.0 in the oldest sub-jects. Although the scaling properties were similar inthe 3- and 4-yr-old and the 6- and 7-yr-old subjects, w a s signica ntly lower in t he oldest children compar edwith the 6- and 7-yr-old children and compared withth e 3- a nd 4-yr-old children ( P 0.05). The mea n ofthe oldest chi ldren comes closest to the mean valueobta ined in young adu lts (Fig. 6).

Relat i onship of Str i de Dynam ics to Height

In children, ma ny a spects of gait depend on body size.For example, over cer ta in age ranges, s t r ide lengthincreases l inear ly with age, but the rela t ionship be-tween s t r ide l eng th and age becomes cons tan t a f t e r

adjust ing for height or leg length (2). Similar ly, w eobserved a signica nt increase (P 0.0001) in velocityin the 6- a nd 7-yr-old children (1.20 0.03 m/s)compa red w ith th e 3-a nd 4-yr-old children (1.00 0.03m/s). H owever, r elat ive velocity (velocity/height ) w a sessentia lly identica l in th ese two groups (P 0.92). Tobegin to eva luat e whether the changes in stride dyna m-ics were only a funct ion of changes in biomechanicsrelat ed to growt h, w e norma lized t he dynamical mea-surements w ith respect t o height. In t he present st udy,heigh t increased l inear ly wi th age (r 0.96; P 0.0001). Variability is inversely related to age (Fig. 3).Thus w e norma lized t he dyna mical va riables (either byappropriat ely dividing or mult iplying by height) a nd

reexa mined the r elationship with a ge. The a ge depen-dence pers is ted when the mea sures of va r iabi l ity anddynamics were adjusted for height or if leg length wasused instead of height as the normalizing factor. Forexample, the CV normalized wit h respect to leg lengthwa s 128 10, 83 5, and 67 3 in t he 3- a nd 4-yr-old,6- a nd 7-yr-old, and the 11- to 14-yr-old subjects ,respect ively. The difference betw een th e 6- a nd 7-yr -oldand the 11- to 14-yr-old children was signicant ( P 0.05). The CV in the 3- and 4-yr-old chi ldren wa ssigni cant ly increased (P 0.0005) compar ed wit hboth older groups.

Final ly, w e note tha t , consis tent with previous nd-ings (26), the a verage va lues of stride t ime and w a lkingve loc i ty were age dependen t . Mean s t r ide t ime was900 14 ms in t he 3-a nd 4-yr-old children, increa sed to955 12 ms in th e 6- a nd 7-yr-old children ( P 0.01),and increased fur ther in the 11- to 14-yr-old group(1.072 18 ms; P 0.0001). Wa lking velocity w a s1.00 0.03 m/s in t he 3- an d 4-yr -old childr en, 1.200.03 m/s in t he 6-a nd 7-yr old child ren, a nd 1.28 .0.03m/s in the 11- to 14-yr old children. The differencebetween the youngest and the two older groups wassignicant (P 0.0001); however, wa lking velocity w a snot signica ntly different in the 6- a nd 7-yr-old a nd t he11- t o 14-yr -old g roups.

DISCUSSION

This qua n t i t a t ive s tudy of s t r ide va r iab il ity anddynamics reveals several interest ing new ndings. 1 )Str ide- to-s t r ide var ia t ions in gai t cycle durat ion aresignican tly larger in hea lthy 3- an d 4-yr-old childrencompared with 6- and 7-yr-old children and in 6- and

7-yr-old children compared w ith children a ges 11 to 14.2 ) The temporal s t ructure of gai t uctuat ions is notfully developed in 7-yr-old children, whereas in olderchildren (11- to 14-yr-old children), str ide dyna micsapproach the values observed in adul ts . 3 ) Differentfeatur es of stride dyna mics do not develop at the sa metim e (Ta ble 4). Thus, w herea s visua l observa tion migh tsuggest that the s t r ide dynamics of chi ldren are notdifferent f rom those of adul ts , quant i ta t ive measure-ment of gai t dynamics indicates that s t r ide- to-s t r idecontr ol of w a lking is n ot fully ma ture even in 7-yr-oldchildren.

A number of similarities have been reported in thegait patterns of children and elderly adults (5, 6, 23).

This nding may reect a reappearance of pr imit ivereexes or simply diminished contr ol of ba lance (23).The p resent s tudy demons t ra tes tha t pa ra l l el s a l soexist w ith r espect t o st ride dyna mics. As we observed inchildren, alt erat ions of stride dyna mics have been seenin older adults and persons with neurological impair-men t (3, 4, 7, 8, 10, 14).

Al though the s t r ide dynamics of young ch i ld rensha re some cha ra cteristics of the unst a ble dynamics ofthe elder ly and those with neurological dysfunct ion,there a ppear to be importa nt differences a s wel l . For

Fig . 6 . Frac ta l sca l ing index ( ) decreases wi th age . This ndingsuggests an age-related change in stride-to-stride dynamics over therange of 10–20 strides. Scaling exponent shown here was determinedaft er 2nd-order detrendin g of each w indow of observation. Note how observed in oldest children approaches that of healthy a dults. Err orbars , means SE for young adults.

Ta ble 4. E ffects of age on str ide t i me dynami cs

3–4 Yr Olds 6–7 Yr Olds 11–14 Yr Olds

Variability >> > —Low-to high-frequency power >> > —Autocorrelation decay time < — —Fra ctal scaling exponent > > —

Arrows indicate comparisons with oldest children ( n 12), in whomstride tim e dynam ics ar e most like those of adu lts. Note how differentaspects of the tempora l s t ruc ture of the s t r ide dynamics tend tomat ure at different ages. The low- to high-frequency power ra tio wa snot statist ically different in the 2 youngest groups; however, thisrepresentation reects the observed trend toward a decreased ratioin 6- and 7-yr-old children ( n 20) compared with 3- and 4-yr oldchildren (n 11).



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example, the present ndings suggest t hat the fracta l-scal ing index changes monotonical ly throughout thel ifespan (h ighes t in ch i ld ren , lower in adu l t s , andlowest in the elder ly and persons with neurologicaldisease). In contrast, stride variability likely changesin a U -sha ped fa shion (high in children, low er in adult s,a n d h ig her w i t h d is ea s e a n d per h a ps a l s o i n v er yadvanced age) . Thus, f rom the perspect ive of s t r idetime dyna mics, the changes in ga it of older persons donot simply re ect a retur n to a n immat ure ga it patt ern.

The alt erat ions of the dyna mics of the st ride time inthe younger chi ldren may be caused by a number offactors . The increased var iabi l i ty may in par t be re-la ted to decreased wa lking veloci ty and decreasedpos tura l s t a b i li ty a t lower speeds (23). However,w hereas a djustment for height minimized the effects ofage on velocity, the age-related differences in both them a g n it u d e o f t h e v a r ia b il it y a n d i n t h e d y na m i cspersis ted af ter controll ing for height . A number offac tors a l so sugges t tha t the observed age-re la t edchanges in the temporal organization of stride dynam-

ics are most l ikely not simply attributable to reducedheight, ga it speed, cha nge in concentr a tion during th ewalk, or increased stride-to-stride variability (unsteadi-ness). For example, fractal scaling indexes were similarin the 3-a nd 4-yr-old children compar ed wit h the 6-a nd7-yr-old children, despi te s igni cant differences instride-to-stride variability, velocity, and height. Age-related differences in stride dynamics were evident indynamical metr ics even a f ter detrending to minimizethe effects of changes in speed or local average stridetime. Moreover, an age-related effect was observed int h e r a t i o of s pect r a l b a la n ce, a m ea s u r e t h a t w a sderived independently of st ride-to-stride va riabilityand very-low-frequency changes likely to be associated

w ith cha nge of speed or loss of concent ra tion.Fut ure study of children who ar e wa lking at differentspeeds may help elucidate the role of velocity on stridedynamics in children. In addition, studies that includeassessment o f motor con t ro l and ba lance as we l l a sother a spects of the locomotor contr ol syst em ma y a lsohelp to clar ify t he role of potential contr ibuting fa ctorsto the development of ma ture ga i t dynamics. Perha psdifferences in motor contr ol development a ccount forsome of t he observed heterogeneity in str ide dyna micswithin each age group (e.g ., Fig. 1). An intr iguingpossibility is th a t t hese dyna mical metrics may providea m ea n s of q u a n t if yi ng t h e s t a g e of m a t u r a t i on a ldevelopment. In any case, i t seems that 1 ) stride time

dynamics most l ikely depend on some aspect of theneuromuscular control system that is not merely re-lated to walking velocity or gait variability, and 2 ) theimmature ga i t dynamics in ch i ld ren may reec t thesubtle, ongoing development of more than one compo-nent of motor control . The dynamic act ion theory ofmotor cont rol postula tes t ha t locomotor function can beviewed as a complex system with multiple degrees offreedom, the collective beha vior of which is governed inpart by the principle of self-organization (13, 23, 27).P erha ps, therefore, ma tur e locomotion dyna mics emergeonly w hen a ll of the int eracting individual components

are fully developed. The change in scaling exponentswith age, a measure associated w ith a nonequil ibr iumdynamical system with multiple degrees of freedom (1,22), may reect th i s emergen t behav ior. C andida teelements tha t could a ffect s t r ide dyna mics includebiomecha nical and neura l properties tha t a re known t oma ture only in older children (e.g., electromyogra mrecruitment pa tt erns are more va riable in children whoa re 7 yr of a ge) (15, 23).

Addit ional s tudies wil l be needed to explain thesecomplex a ge-relat ed changes in the magnitude andtemporal s t ructure of s t r ide dynamics. Nonetheless ,the present ndings have potentially important impli-ca t ions for the unders tand ing a nd model ing of theintegrat ive control of locomotor funct ion and neura ldevelopment . Furthermore, t he resul ts suggest thepossibility that quantitative measures of stride dynam-ics may be useful in augmenting the early detection andclassication of gait disorders in children.

We thank J .-Y. Wei, D. Kaliton, and J .Mietus for valuable discus-sions and assistan ce.

This work was supported in part by National Insti tute on AgingGra nts AG-14100, AG-08812, AG-00294, and AG-10829 and byNational Insti tute of Mental Health Grant MH-54081. We are alsograt eful for pa rtial support from t he American Federation for AgingResearch, the G . Ha rold and Leila Y. Mathers C har itable Foundation,and the Nat ional Aeronautics and Spa ce Administrat ion.

Address for correspondence and reprint request s: J . M. Ha usdorff,Gerontology Division, Beth Israel Deaconess Medical Center, 330Br ookl ine Ave. , Boston, MA 02215 (E-mai l : [email protected]).

Received 9 J uly 1998; accepted in nal form 4 November 1998.

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Maturation of Gait Dynamics Stride to Stride Variability