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Timing invariances in toddlers' gait
The Development of T h i n Control and Temporal Or anization in 800rdhatei-lAction J. Fagard an%PH.Wolff (Editors) 8 Ekvier Science Publishers B.V., 1991
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Timing invariances in toddlers' gait Blandine Bril & Yvon BrenKre Laboratoire de Physiologie du Mouvement, UA CNRS 631, UniversitC Paris XI, F-91405 Orsay (France)
INTRODUCTION There are many ways of considering the temporal structure of gait. Gait movement can be "divided up" into phases according to diverse parameters. Figure 1 clearly shows that gait movement appears, at the level on which behavioral observations are made, as a succession of unipodal and bipodal stance phases. A single step is then defined as the succession of a double support phase and a single stance phase. A step cycle is generally defined as the movement camed out between two successive foot contacts of the same foot; this is equivalent to two successive single steps. Many studies that focus on the gait of adults or children give the duration of phases in percentages, for double-support as well as for swing or stance. The authors implicitly consider the relative invariances of gait movement even if they do not openly discuss its temporal structure. Values for the relative duration of the different phases vary greatly from one study to the other. For example, Jansen, Vittas, Hellberg & Hansen (1981) find 36% for the duration of the double support phase at a fixed velocity (1.1 d s ) , whereas Kirtley, Whittle & Jefferson (1985) find an average of 8.5% for an average velocity of 1.45 m/s. When velocity is taken into account, most of these studies attribute smaller values (in relative terms) to double-support duration for higher velocities (Grieve and Gear, 1966; Larsson, Odenrick, Sandlund, Weitz & Oberg, 1980; Murray, Kory, Clarkson & Sepic, 1966). Some studies state that double-support decreases down to zero as speed increases - at which point walking switches on to running (Grieve & Gear, 1966; Larsson et al., 1980). Whereas many studies give information concerning the relative duration of the stance phases of gait, very few, to our knowledge, explicitly discuss the theoretical implications of the temporal structure of gait movement, and of its invariances in particular. Furthermore, when temporal patterns are analyzed, segmental kinematics of the lower limbs are chosen to determine the phases of gait rather than more global parameters such as unipodal or bipodal support (Shapiro, Zernicke, Gregor & Diestel, 1981; Clark & Phillips, 1987). These
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two studies place more emphasis on the temporal relative invariances than on the differences, even though the published data may question these invariances. The authors of these two studies each have completely different theoretical viewpoints. Shapiro et al. (1981) conclude that their data support the generalized motor program theory. According to this view, relative timing is an invariant of motor program which is "called up" prior to the execution of the movement. The opposite view is held by Clark & Phillips (1987). They favor an interpretation stemming from the dynamical perspective (Kugler et al., 1982) in which relative timing invariances result from the use of a given "coordinative structure". A coordinative structure is defined here as "a unit of motor control which governs a group of muscles as it operates over one or more body joints" (Clark, 1982: p 165). They state that step cycle organization in the infant gait is similar both in absolute and relative timing to that of the adult, and conclude that as early as three months after onset of independent walking, toddlers "exhibit step organization that is remarkably similar to that of the mature walkers" (Clark & Phillips, 1987: p43).
step cycle
1111111
l e f t foot
right foot
1111111
Figure 1. Descriptive schema of gait cycle and stick diagram of a child 12 months after onset of I.W. (On the rigth of the stick diagram, the Philippson step cycle defined from the flexion-extension of the knee: phase E2, from FC to deep knee flexion (DKF); E3 from DKF to T O F from TO to DKF, El from DKF to FC).
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However, both studies implicitly consider that the temporal structure of gait as defined by the Philippson phases (fig. 1) is a good way to describe the organization of adult and child gait. In a developmental study of another locomotor movement, hopping, Roberton & Halverson (1988) explore the question of relative timing in relation to developmental qualitative changes in segmental coordination. They find very few relative timing invariances which span the entire duration of the longitudinal study. Only the time elapsed between the ground-touching and the deepest knee flexion appears to stay invariant in relative values from 3 to 18 years of age. The interesting point is that the authors suggest that the same event exists in walking (E2 phase of Philippson). Different possible explanations are discussed, and the issue is far from been settled (see chapter 16 of this book). These three studies on locomotor skills are based on an analysis of the kinematics of the limbs. But many other ways of "dividing up" gait movement are also possible. They stem from another choice of cues such as the acceleration of the center of gravity (a global expression of the movement), the displacement of the center of foot pressure, or the onset of muscular activity of different muscles, among others. To confront data resulting from different ways of considering gait organization would add much complexity to theoretical interpretation. The important point, as suggested by Heuer (1988), concerns the "motor delay" which represents the time interval between a central command and its peripheral registration. The motor delay in turn depends on which peripheral effect is taken into account, i.e. forces, kinematics of limb segments, muscular activity, etc. In this chapter we will question and discuss the possible significance of some temporal characteristics of gait as they are observed at a peripheral level (issued from the displacement of the foot pressure and the acceleration of the center of gravity) during the first two years of independent walking. The focus will be on the absolute and relative invariances of gait movement in relation to changes of other postural or locomotor parameters during early walking. EXPERIMENTAL SETTING
The data presented here are issued from a longitudinal study of five children (4 boys and one girl). The gait sequences of each child were recorded once a month during the first six months after onset of independent walking, then every six months during the following 18 months. Data were recorded by means of a large force plate and synchronized with a video system described in detail in Brenibre, Bril & Fontaine (1989). In each session the child walked about 20 sequences of steps on the force plate and several steps on the walkway ahead of it. Each sequence began with the child standing still and unsupported, barefoot, at the upper edge of the force plate (see figure 2.a). The child was then asked to walk towards its mother to the other side of
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the walkway. Only sequences leading to a regular and steady-state gait were taken into account for analysis.
DEFINITION OF TEMPORAL PARAMETERS. The different phases of gait movement have been defined as follows: - The initiation of gait movement from the initial upright posture starts with the onset of dynamic phenomena (to) and ends at the end of the first step (tvl); - One step is the succession of a double support stance phase (hence referred to as DS) and a single support stance phase (or swing phase of the controlateral leg, hence referred to as SW).The double support phase starts at foot contact (FC) and ends with "toe off' (TO). Time of FC corresponds to the abrupt variation in the curve of Xp, which indicates that the swinging foot has just touched the ground and that the center of foot pressure starts to move toward this foot. The end of DS is not as easy to determine. For Yp, the "levelling off' phases correspond to the time when the center of foot pressure is situated under the supporting foot. The alternation of plateaus corresponds to the alternation of the feet on the ground while walking. The y!evelling off" phases of the Xp and Yp curves start at the precise time that YG shifts sign (the curve of YG crosses the baseline). Consequently, we consider that the change in sign of YG determines the time at which the swing phase begins, which is the time of "toe off". Dynamically speaking, it is the shift of sign of YG that indicates the alternate phases of acceleration toward one foot or the other. Taking into account these definitions, the following temporal parameters were used in the analysis ( see figure 2): - T : duration of a single step. It is the time elapsed between two FCs; - DS : duration of a double-support phase. It is the time elapsed between FC and TO of the controlateral foot. The relative duration of DS is the ratio of DS to total duration of the step; - v : velocity. It is the mean velocity of a sequence of steps computed as the total length walked on the total duration of the sequence of steps; - f : frequency. It is the number of steps walked per second. THE TEMPORAL STRUCTURE OF TODDLERS' GAIT AND ITS RELATION TO SPEED After the end of the first month of independent walking (hence referred to as I.W.) the duration of steps decreases significantly as speed increases. This result confirms those of a previous sample of children under six months of I.W. (Bril & Brenibre, 1989), and concords with data found in the literature on gait for children (Beck et al., 1981) and adults (Grieve and Gear,
Timing Invariances in Toddlers' Gait
Figure 2. A/Drawing of the force plate and measure of the experimental parameters.
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B1 Sequence of steps for a child showing 1) the transient phase between upright posture and steady state gait (in grey), 2) several steps at steady state velocity. XG gives the instantaneous velocity of the center of gravity along the antero-posterior axis; Xp and Yp respectively give the displacement of the center of foot pressure along the antero-postenor axis and the lateral axis; k,VG and XG give the accelerationof the center of gravity along the three axes. is the onset of dynamic phenomena and tv 1 the end of the first step. FC is the instant of foot contact and TO the time of "toe off'.
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1966; Kirtley et al., 1985; Murray et al., 1966; etc.). Figure 3 summarizes the data at different times: one month, 2 months, 3 months, 5 months, 12 months, 18 months after onset of I.W.The graphs clearly show the increasing range of speed displayed by children as walking experience increases (Bril & BreniBre, 1990; submitted). The duration of the double-support phase and swing phase 1 month
2 months
T
’
sw
O
O
7
DS
(msl
OC/’
7w-
0.b
0.b
0.io
3 months
0.b
1.io
1.b
v (mls)
OL’/ob
o b
oio
ob
1.io
1 L
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803..
Figure 3. Development of the covariation between the temporal parameters and speed,
during the first two years of I.W.:( m ) duration of step, ( H ) swing and ( A ) double support phases.
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Toddlers'Gait
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showed the same trend but the correlation became significant only during the second month of I.W. for DS and during the third month for the swing phase. Concerning the frequency of steps, data showed a value of 2.5 steps per second during the first two sessions of observation, then an increase at two months of I.W. to 3 steps per second. The average frequency remained stable up to five months of I.W., and then showed a slight but constant decrease (Bril & BreniCre , 1990). Now the main question remains: since the duration of step and of its two phases varies according to speed, do absolute or relative temporal invariances exist, and what are their significance?
ABSOLUTE TEMPORAL INVARIANCE: THE DURATION OF THE FIRST STEP The duration of the movement starting with the first dynamic phenomena on the antero-posterior axis (Q) and ending with the end of the first step (tvl) has been analyzed from the data of 8 children having between 100 and 200 days of I.W. (Brenibre et al., 1989). The sequences of steps chosen for the analysis were those in which the child was absolutely still before starting to walk. The mean value of this first step varies between 470 ms and 730 ms, depending on the child. These two values respectively correspond to a mean progression velocity of the sequence of steps of .70m/s and .87 m/s. There was no correlation between the duration of the first step and the progression velocity of the forthcoming sequence of steps. Nor did a correlation exist with the frequency of steps (fig. 4). The duration of the first step thus appears to be a temporal invariant of the initiation of gait when the child starts independent waking. This absolute invariance can be discussed in relation to what has been shown for the adult. The movement, which occurs during the transient phase between upright posture and gait, can be compared to an oscillating system which begins its oscillating movement at its natural frequency. As is the case for the adult (Brenibre & Do, 1986), and contrary to steady state gait, duration of this first step and progression velocity are independent. In addition, this value of natural frequency corresponds to the semi period of the oscillation of either an inverted single pendulum which depends only on the position of the center of gravity with respect to the ground ( T / 2 = x ( l / g ) 1/29 where "1" is the position of the center of gravity with respect to the ground), or an inverted compound that would have the same mass, the same moment of inertia and the same position of the center of gravity a s the child (T / 2 = x ( ( IG + m 1 2 ) / m g 1 ) 1'2, where "I(y is the moment of inertia of the body, and "m" the subject's mass; Breniere et ai., 1989).
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0
.25
.50
.75
1.
1.25
1.50
v(mn)
1.75
Figure 4. Duration of the first step in children, compared with adult data. For the children each dot ( 0 ) corresponds to the value of tvl for one sequence of steps. For the five adults who constitute a reference group, each dot (+)corresponds to a mean value calculated over 7 sequences of steps executed at the same speed (from Brenibe, Bril & Fontaine, Journal of Motor Behavior, 21, pp 20-37, 1989). In the first case corresponding to the smaller values of the duration of the first step, the child seems to behave as if he has integrated the vertical position only of hisher center of gravity, but not the body inertia. In the other case, it would appear that, as for the mature gait, the child has integrated not only the position of hisher center of gravity, but the body‘s mass and moment of inertia as well. In either situation, it appears that anatomical parameters have a dynamic implication in the transient phase of gait from the initial standing posture. The duration of the first step is a good example of an absolute timing invariant. We may infer from this result that in order to be able to initiate a sequence of steps, the child must have integrated anatomical parameters of his body.
RELATIVE TEMPORAL INVARIANCE: DURATION OF THE DOUBLE-SUPPORT PHASE DURING STEADY STATE GAIT Certain characteristics of children gait may stem, at least in part, from the difficulty for the child to master unipodal stance in a non static situation (BreniCre & Bril, 1988; Bril & Breniere, 1990). It is important therefore to consider a gait cycle as the succession of two single steps, meaning two occurences of a double stance phase and a single stance phase, whereas a cycle is commonly described as a stance phase followed by a swing phase. To describe gait movement only in terms of stance and swing observed from the kinema-
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tics of one lower limb masks the fact that gait is the result of the two lower limbs, and that one of the main constraints is the demand for equilibrium. Some authors have interpreted the shorter duration of swing in children (compared to adults) as an indication of instability (Sutherland, Olshen, Cooper & Woo, 1980). The same idea was developed by Bril & BreniCre (1988, 1989), who interpreted the greater relative duration of the doublesupport phase as a necessary time period for balance recovery. The longitudinal data confirm this interpretation. Figure 5 illustrates the development of the duration of DS during the first two years after onset of I.W.As for the development of postural and locomotor parameters (Bril & BreniCre, submitted), there was at first a large decrease in relative terms (from 38% at onset of I.W. to 28% in average after 5 months if I.W.), followed by a slighter decrease. After two years of I.W.the value of DS is still greater than for adults (figure 5 & 6). Individual data showed an important variability factor between children. One of the children had a very important decrease in the duration of DS, from 38 % at one month to 28 % at 5 months, and 20% at 18 months, while another one had a decrease of only 4% during the first 5 months of I.W. (from 31% to 27%).
0
5
10
15
20
25
months after onset of I.W. Figure 5. Development of the relative duration of the double-support phase in relation to walking experience. The main characteristic of the relative duration of DS is that it remains invariant whatever the walking velocity (figure 6). These data confirm Shapiro et al. (1981) results, as well as Clark & Phillips (1987), even though definition of the phases was based on different criteria. The proportional duration model (Gentner, 1987) applied to the DS data shows that there was a great variability at one month (the relative duration of DS varies from 20 to 45%). After that period the values were more gathered around the mean value (figure 7). The correlation between the relative duration of DS and the total
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duration of the step was not significant, except at five months of I.W. (x=-.5, ~ 4 0 1 ) This . value confirms the data obtained in a previous study (Bril & Brenibre, 1989) where this correlation was significantly negative for 5 children out of 11 observed between 140 and 172 days of I.W.
t/T4' ..
r I
0' 0
r .
.25
.50
.75
a
In0
125
Is0
l.75
v
a00
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Figure 6. Relative values of the double-support phase in relation to average progression velocity, for 10 children with 150 to 200 days of I.W. For the children, each dot ( 0 ) corresponds to the mean value of the parameters representing one sequence of steps. For the three adults, each dot (+)corresponds to a mean value calculated on 10 sequences of steps executed at the same speed (from Bril & Brenibre, 1988, Posture and Gait: Development Adaptation and Modulation. Amblard B., Berthoz A. and Clarac F. (eds.), Elsevier Science Publishers B.V., p 27). The interpretation of this data is not easy. If, after onset of I.W., the duration of the DS phase depends on the time needed to balance recovery, we can hypothesize that the duration of DS will decrease as walking experience increases. The great variation in DS duration observed before two months of I.W. can be interpreted in a similar way: increasing stability reduces variability (figure 7). The development of the child propelling strategy may explain, at least in part, the important changes in DS duration observed during the first 5 months of LW. as compared with the following months (see figure 5). In another study we have showed that at the time of foot contact, contrary to the adult, the young toddler is dynamically in the situation of a fall; the value of the vertical acceleration is negative (see figure 2B; Breniere & Bril, 1988, submitted). For the adult, the vertical acceleration is always positive at heel strike. This means that the adult is able to initiate a propulsing phase during the swing phase - that is during unipodal stance - which is not the case in children. Furthermore, the vertical acceleration is correlated with speed from the second month of I.W. to the 6-8 month period. The value of this correlation decreases from the fifth month on, and it is no longer significant
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Timing Invariances in Toddler' Gait
during the second year of I.W. (Brenikre & Bril, submitted). These characteristics of the propelling strategy of the child are interpreted as a lack of unipodal stance control that could be, in part, responsible for the two-phase development of the relative duration of double-support phase. t/T
0 50
1 month
050
2 months
0 40-
0 30-
OM
0 20-
T (ms)
12 months 0 40
O
'i
Figure 7. The proportional duration model: development of relative values of double-
support phase in relation to the total duration of steps at different periods after onset of independent walking.
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The results of the relative duration of DS for all values of the total duration of the step and at different periods after onset of I.W., is puzzling. The previous discussion established not only that toddlers and adults use different strategies to propel themselves, but that there is a change in the propelling strategy of children after approximately 5 months of I.W. The existence of temporal relative invariances in young walkers as well as in adults regardless of the propulsing strategy used suggests that the invariances in relative timing of children and adults could well result from the segmental organization which characterizes adult or child gait. For adults, the segmental kinematics show that joint angle patterns are invariant, and do not change with walking speed (Winter, 1983). As invariances in the relative duration of DS and SW have been found in children as well as in adults (figure 6 & 7) we can hypothezise that a given propulsing strategy leads to joint angle patterns which remain the same over a wide range of speed. In other words, different strategies could lead to similar relative temporal invariances in movement, as seems to be the case with handwriting (Wann & Jones, 1986). At this stage of the study we can only suggest that a detailed analysis of the segmental kinematics during the development of gait, compared with mature gait, could help to point out the analogies and differences of the segmental organization of movement. Since different propulsing strategies could lead to analogous relative timing invariances, we can hypothesize that the temporal characteristics of gait comes from the segmental kinematic organization, as would suggest the results of both Shapiro et al. (1981) and Clark and Phillips (1987).
CONCLUSION Our results on early walking show that absolute and relative timing can be found in gait movement as soon as a few weeks after onset of independent walking. We have suggested that absolute invariants in the initiation of gait are primarily set up by anatomical and body segment parameters. The developmental analysis of such invariances suggests that children have to learn to optimize the use of the biomecanical properties of their bodies. Relative invariants are more difficult to interpret. We have seen that for each age and regardless of the speed of walking, the relative duration of the double-support phase is constant. However, the relative duration of the double-support phase decreases with walking experience. A very important decrease appears during the first 5 months of independent walking, followed by a slighter decrease during the 18 following months. If the relative timing is, at least in part, set up by the kinematic of the limb segments, as suggested by Roberton and Halverson (1988), then its relative timing invariance would signify that for a given age the kinematic of the limbs is stable accross speed. Here further investigation is needed to test this hypothesis.
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However it is important to note that the similarity between the temporal structure of gait in toddlers and adults insofar as its relation to speed is concerned may mask the remarkable differences in propulsing strategies.
REFERENCES Beck R., Andriacchi T.P., Kuo K.N., Fermier R.W. & Galante J.O. (1981) Changes in the gait pattern of the growing children. The Journal of Bone and Joint Surgery, 63A(9), 1452-1456. Brenibre Y. & Do M.C. (1986) When and how does steady state gait movement induced from upright posture begin ? Journal of Biomechanics, 19, 1035-1040. Brenibre Y . & Bril B. (1988) Pourquoi les enfants marchent en tombant alors que les adultes tombent en marchant ? C.R. Acad. Sci. Paris, 307111, 617-622. Brenibre Y. & Bril B. (1991) Why do the children walk in falling during the first four years of independent walking? (submitted) Brenihe Y., Bril B. & Fontaine R. (1989) Analysis of the transition from upright stance to steady state locomotion for children under 200 days of autonomous walking. Journal of Motor Behavior, 21, 20-37. Bril B. & Brenibre Y. (1989) Steady state velocity and temporal structure of gait during the first six months of autonomous walking. Human Movement Science, 8, 99-122. Bril B. & Brenibre Y. (1990) How does the child modulate his progression velocity during the first 18 months of independent walking ? In T. Brandt, W Bles & M. Dietrich (eds.), Disorder of Posture and Gait, Stuttgart: Georg Thieme Verlag. Bril B. & Brenibre Y. (1991) Why does postural requirement restrain progression velocity in young walkers ? (submitted). Clark J.E. (1982) The role of response mechanisms in motor skill development. In The Development of Movement Control and Co-ordination, Kelso J.A.S. & Clark J.E., New York: J.Wiley & Sons. Clark J.E. & Phillips S.J. (1987) The step cycle organization of infant walkers. Journal of Motor Behavior, 19, 421-433. Gentner D.R. (1987) Timing of skilled motor performance: tests of the propotional duration model. Psychological Rewiev, 94, 255,276.
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Grieve D.W. & Gear R.J. (1966) The relationship between length of stride, step frequency, time of swing and speed of walking for children and adults. Ergonomics, 5, 379-399. Heuer H. (1988) Testing the invariance of the relative timing: Comment on Gentner (1 987). Psychological Review, 95, 552-557. Jansen E.C., Vittas D., Hellberg S & Hansen J. (1981) Normal gait of old and young men and women. Acta Orthop. Scand., 53, 193-196. Kirtley C., Whittle M.W. & Jefferson R.J. (1985) Influence of walking speed on gait parameters. Biomedical Engineering, 7, 282-288. Kugler P.N., Kelso J.A.S. & Turvey M.T. (1982) On the control and coordination of naturally developing systems. In Development of Movement Control and Co-ordination, Kelso J.A.S & Clark J. (eds.),New York: J. Wiley & Sons. Larsson L.E., Odenrick P., Sandlund B., Weitz P & Oberg P.A. (1980) The phases of the stride and their interaction in the human gait. Scand. J. Rehab. Med, 12, 107-112. Murray M.P., Kory R.C., Clarkson B.H. & Sepic S.B. (1966) Comparison of free and fast speed walking patterns of normal men American Journal of Physical Medecine, 45, 8-24. Roberton M.A. & Halverson L.E. (1988) The development of locomotor coordination: longitudinal change and invariance. Journal of Motor Behavior, 20, 197-241. Schmidt R.A. (1985) The search for invariance in skilled movement behavior. Research Quarterly for Exercice and Sport, 56, 188-200. Shapiro D.C., Zernicke R.F., Gregor R.J. & Diestel J.D. (1981) Evidence for the generalized motor programs using gait pattern analysis. Journal of Motor Behavior, 13, 33-47. Sutherland D.H., Olshen R., Cooper L. & Woo S.L. (1980) The development of mature gait. The Journal of Bone and Joint Surgery, 62A, 336-353. Wann J.P. & Jones J.G. (1986) Space-time invariances in handwriting: Constrasts between primary school children displaying advanced or retarded handwriting acquisition. Human Movement Science, 5, 275-296. Winter D.A. (1983) Biomechanical motor patterns in normal walking. Journal of Motor Behavior, IS,302-330.
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Timing invariances in toddlers' gait Blandine Bril & Yvon BrenKre Laboratoire de Physiologie du Mouvement, UA CNRS 631, UniversitC Paris XI, F-91405 Orsay (France)
INTRODUCTION There are many ways of considering the temporal structure of gait. Gait movement can be "divided up" into phases according to diverse parameters. Figure 1 clearly shows that gait movement appears, at the level on which behavioral observations are made, as a succession of unipodal and bipodal stance phases. A single step is then defined as the succession of a double support phase and a single stance phase. A step cycle is generally defined as the movement camed out between two successive foot contacts of the same foot; this is equivalent to two successive single steps. Many studies that focus on the gait of adults or children give the duration of phases in percentages, for double-support as well as for swing or stance. The authors implicitly consider the relative invariances of gait movement even if they do not openly discuss its temporal structure. Values for the relative duration of the different phases vary greatly from one study to the other. For example, Jansen, Vittas, Hellberg & Hansen (1981) find 36% for the duration of the double support phase at a fixed velocity (1.1 d s ) , whereas Kirtley, Whittle & Jefferson (1985) find an average of 8.5% for an average velocity of 1.45 m/s. When velocity is taken into account, most of these studies attribute smaller values (in relative terms) to double-support duration for higher velocities (Grieve and Gear, 1966; Larsson, Odenrick, Sandlund, Weitz & Oberg, 1980; Murray, Kory, Clarkson & Sepic, 1966). Some studies state that double-support decreases down to zero as speed increases - at which point walking switches on to running (Grieve & Gear, 1966; Larsson et al., 1980). Whereas many studies give information concerning the relative duration of the stance phases of gait, very few, to our knowledge, explicitly discuss the theoretical implications of the temporal structure of gait movement, and of its invariances in particular. Furthermore, when temporal patterns are analyzed, segmental kinematics of the lower limbs are chosen to determine the phases of gait rather than more global parameters such as unipodal or bipodal support (Shapiro, Zernicke, Gregor & Diestel, 1981; Clark & Phillips, 1987). These
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two studies place more emphasis on the temporal relative invariances than on the differences, even though the published data may question these invariances. The authors of these two studies each have completely different theoretical viewpoints. Shapiro et al. (1981) conclude that their data support the generalized motor program theory. According to this view, relative timing is an invariant of motor program which is "called up" prior to the execution of the movement. The opposite view is held by Clark & Phillips (1987). They favor an interpretation stemming from the dynamical perspective (Kugler et al., 1982) in which relative timing invariances result from the use of a given "coordinative structure". A coordinative structure is defined here as "a unit of motor control which governs a group of muscles as it operates over one or more body joints" (Clark, 1982: p 165). They state that step cycle organization in the infant gait is similar both in absolute and relative timing to that of the adult, and conclude that as early as three months after onset of independent walking, toddlers "exhibit step organization that is remarkably similar to that of the mature walkers" (Clark & Phillips, 1987: p43).
step cycle
1111111
l e f t foot
right foot
1111111
Figure 1. Descriptive schema of gait cycle and stick diagram of a child 12 months after onset of I.W. (On the rigth of the stick diagram, the Philippson step cycle defined from the flexion-extension of the knee: phase E2, from FC to deep knee flexion (DKF); E3 from DKF to T O F from TO to DKF, El from DKF to FC).
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However, both studies implicitly consider that the temporal structure of gait as defined by the Philippson phases (fig. 1) is a good way to describe the organization of adult and child gait. In a developmental study of another locomotor movement, hopping, Roberton & Halverson (1988) explore the question of relative timing in relation to developmental qualitative changes in segmental coordination. They find very few relative timing invariances which span the entire duration of the longitudinal study. Only the time elapsed between the ground-touching and the deepest knee flexion appears to stay invariant in relative values from 3 to 18 years of age. The interesting point is that the authors suggest that the same event exists in walking (E2 phase of Philippson). Different possible explanations are discussed, and the issue is far from been settled (see chapter 16 of this book). These three studies on locomotor skills are based on an analysis of the kinematics of the limbs. But many other ways of "dividing up" gait movement are also possible. They stem from another choice of cues such as the acceleration of the center of gravity (a global expression of the movement), the displacement of the center of foot pressure, or the onset of muscular activity of different muscles, among others. To confront data resulting from different ways of considering gait organization would add much complexity to theoretical interpretation. The important point, as suggested by Heuer (1988), concerns the "motor delay" which represents the time interval between a central command and its peripheral registration. The motor delay in turn depends on which peripheral effect is taken into account, i.e. forces, kinematics of limb segments, muscular activity, etc. In this chapter we will question and discuss the possible significance of some temporal characteristics of gait as they are observed at a peripheral level (issued from the displacement of the foot pressure and the acceleration of the center of gravity) during the first two years of independent walking. The focus will be on the absolute and relative invariances of gait movement in relation to changes of other postural or locomotor parameters during early walking. EXPERIMENTAL SETTING
The data presented here are issued from a longitudinal study of five children (4 boys and one girl). The gait sequences of each child were recorded once a month during the first six months after onset of independent walking, then every six months during the following 18 months. Data were recorded by means of a large force plate and synchronized with a video system described in detail in Brenibre, Bril & Fontaine (1989). In each session the child walked about 20 sequences of steps on the force plate and several steps on the walkway ahead of it. Each sequence began with the child standing still and unsupported, barefoot, at the upper edge of the force plate (see figure 2.a). The child was then asked to walk towards its mother to the other side of
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the walkway. Only sequences leading to a regular and steady-state gait were taken into account for analysis.
DEFINITION OF TEMPORAL PARAMETERS. The different phases of gait movement have been defined as follows: - The initiation of gait movement from the initial upright posture starts with the onset of dynamic phenomena (to) and ends at the end of the first step (tvl); - One step is the succession of a double support stance phase (hence referred to as DS) and a single support stance phase (or swing phase of the controlateral leg, hence referred to as SW).The double support phase starts at foot contact (FC) and ends with "toe off' (TO). Time of FC corresponds to the abrupt variation in the curve of Xp, which indicates that the swinging foot has just touched the ground and that the center of foot pressure starts to move toward this foot. The end of DS is not as easy to determine. For Yp, the "levelling off' phases correspond to the time when the center of foot pressure is situated under the supporting foot. The alternation of plateaus corresponds to the alternation of the feet on the ground while walking. The y!evelling off" phases of the Xp and Yp curves start at the precise time that YG shifts sign (the curve of YG crosses the baseline). Consequently, we consider that the change in sign of YG determines the time at which the swing phase begins, which is the time of "toe off". Dynamically speaking, it is the shift of sign of YG that indicates the alternate phases of acceleration toward one foot or the other. Taking into account these definitions, the following temporal parameters were used in the analysis ( see figure 2): - T : duration of a single step. It is the time elapsed between two FCs; - DS : duration of a double-support phase. It is the time elapsed between FC and TO of the controlateral foot. The relative duration of DS is the ratio of DS to total duration of the step; - v : velocity. It is the mean velocity of a sequence of steps computed as the total length walked on the total duration of the sequence of steps; - f : frequency. It is the number of steps walked per second. THE TEMPORAL STRUCTURE OF TODDLERS' GAIT AND ITS RELATION TO SPEED After the end of the first month of independent walking (hence referred to as I.W.) the duration of steps decreases significantly as speed increases. This result confirms those of a previous sample of children under six months of I.W. (Bril & Brenibre, 1989), and concords with data found in the literature on gait for children (Beck et al., 1981) and adults (Grieve and Gear,
Timing Invariances in Toddlers' Gait
Figure 2. A/Drawing of the force plate and measure of the experimental parameters.
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B1 Sequence of steps for a child showing 1) the transient phase between upright posture and steady state gait (in grey), 2) several steps at steady state velocity. XG gives the instantaneous velocity of the center of gravity along the antero-posterior axis; Xp and Yp respectively give the displacement of the center of foot pressure along the antero-postenor axis and the lateral axis; k,VG and XG give the accelerationof the center of gravity along the three axes. is the onset of dynamic phenomena and tv 1 the end of the first step. FC is the instant of foot contact and TO the time of "toe off'.
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1966; Kirtley et al., 1985; Murray et al., 1966; etc.). Figure 3 summarizes the data at different times: one month, 2 months, 3 months, 5 months, 12 months, 18 months after onset of I.W.The graphs clearly show the increasing range of speed displayed by children as walking experience increases (Bril & BreniBre, 1990; submitted). The duration of the double-support phase and swing phase 1 month
2 months
T
’
sw
O
O
7
DS
(msl
OC/’
7w-
0.b
0.b
0.io
3 months
0.b
1.io
1.b
v (mls)
OL’/ob
o b
oio
ob
1.io
1 L
5 months
803..
Figure 3. Development of the covariation between the temporal parameters and speed,
during the first two years of I.W.:( m ) duration of step, ( H ) swing and ( A ) double support phases.
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Toddlers'Gait
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showed the same trend but the correlation became significant only during the second month of I.W. for DS and during the third month for the swing phase. Concerning the frequency of steps, data showed a value of 2.5 steps per second during the first two sessions of observation, then an increase at two months of I.W. to 3 steps per second. The average frequency remained stable up to five months of I.W., and then showed a slight but constant decrease (Bril & BreniCre , 1990). Now the main question remains: since the duration of step and of its two phases varies according to speed, do absolute or relative temporal invariances exist, and what are their significance?
ABSOLUTE TEMPORAL INVARIANCE: THE DURATION OF THE FIRST STEP The duration of the movement starting with the first dynamic phenomena on the antero-posterior axis (Q) and ending with the end of the first step (tvl) has been analyzed from the data of 8 children having between 100 and 200 days of I.W. (Brenibre et al., 1989). The sequences of steps chosen for the analysis were those in which the child was absolutely still before starting to walk. The mean value of this first step varies between 470 ms and 730 ms, depending on the child. These two values respectively correspond to a mean progression velocity of the sequence of steps of .70m/s and .87 m/s. There was no correlation between the duration of the first step and the progression velocity of the forthcoming sequence of steps. Nor did a correlation exist with the frequency of steps (fig. 4). The duration of the first step thus appears to be a temporal invariant of the initiation of gait when the child starts independent waking. This absolute invariance can be discussed in relation to what has been shown for the adult. The movement, which occurs during the transient phase between upright posture and gait, can be compared to an oscillating system which begins its oscillating movement at its natural frequency. As is the case for the adult (Brenibre & Do, 1986), and contrary to steady state gait, duration of this first step and progression velocity are independent. In addition, this value of natural frequency corresponds to the semi period of the oscillation of either an inverted single pendulum which depends only on the position of the center of gravity with respect to the ground ( T / 2 = x ( l / g ) 1/29 where "1" is the position of the center of gravity with respect to the ground), or an inverted compound that would have the same mass, the same moment of inertia and the same position of the center of gravity a s the child (T / 2 = x ( ( IG + m 1 2 ) / m g 1 ) 1'2, where "I(y is the moment of inertia of the body, and "m" the subject's mass; Breniere et ai., 1989).
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0
.25
.50
.75
1.
1.25
1.50
v(mn)
1.75
Figure 4. Duration of the first step in children, compared with adult data. For the children each dot ( 0 ) corresponds to the value of tvl for one sequence of steps. For the five adults who constitute a reference group, each dot (+)corresponds to a mean value calculated over 7 sequences of steps executed at the same speed (from Brenibe, Bril & Fontaine, Journal of Motor Behavior, 21, pp 20-37, 1989). In the first case corresponding to the smaller values of the duration of the first step, the child seems to behave as if he has integrated the vertical position only of hisher center of gravity, but not the body inertia. In the other case, it would appear that, as for the mature gait, the child has integrated not only the position of hisher center of gravity, but the body‘s mass and moment of inertia as well. In either situation, it appears that anatomical parameters have a dynamic implication in the transient phase of gait from the initial standing posture. The duration of the first step is a good example of an absolute timing invariant. We may infer from this result that in order to be able to initiate a sequence of steps, the child must have integrated anatomical parameters of his body.
RELATIVE TEMPORAL INVARIANCE: DURATION OF THE DOUBLE-SUPPORT PHASE DURING STEADY STATE GAIT Certain characteristics of children gait may stem, at least in part, from the difficulty for the child to master unipodal stance in a non static situation (BreniCre & Bril, 1988; Bril & Breniere, 1990). It is important therefore to consider a gait cycle as the succession of two single steps, meaning two occurences of a double stance phase and a single stance phase, whereas a cycle is commonly described as a stance phase followed by a swing phase. To describe gait movement only in terms of stance and swing observed from the kinema-
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Timing Invariances in Toddlers’ Gait
tics of one lower limb masks the fact that gait is the result of the two lower limbs, and that one of the main constraints is the demand for equilibrium. Some authors have interpreted the shorter duration of swing in children (compared to adults) as an indication of instability (Sutherland, Olshen, Cooper & Woo, 1980). The same idea was developed by Bril & BreniCre (1988, 1989), who interpreted the greater relative duration of the doublesupport phase as a necessary time period for balance recovery. The longitudinal data confirm this interpretation. Figure 5 illustrates the development of the duration of DS during the first two years after onset of I.W.As for the development of postural and locomotor parameters (Bril & BreniCre, submitted), there was at first a large decrease in relative terms (from 38% at onset of I.W. to 28% in average after 5 months if I.W.), followed by a slighter decrease. After two years of I.W.the value of DS is still greater than for adults (figure 5 & 6). Individual data showed an important variability factor between children. One of the children had a very important decrease in the duration of DS, from 38 % at one month to 28 % at 5 months, and 20% at 18 months, while another one had a decrease of only 4% during the first 5 months of I.W. (from 31% to 27%).
0
5
10
15
20
25
months after onset of I.W. Figure 5. Development of the relative duration of the double-support phase in relation to walking experience. The main characteristic of the relative duration of DS is that it remains invariant whatever the walking velocity (figure 6). These data confirm Shapiro et al. (1981) results, as well as Clark & Phillips (1987), even though definition of the phases was based on different criteria. The proportional duration model (Gentner, 1987) applied to the DS data shows that there was a great variability at one month (the relative duration of DS varies from 20 to 45%). After that period the values were more gathered around the mean value (figure 7). The correlation between the relative duration of DS and the total
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duration of the step was not significant, except at five months of I.W. (x=-.5, ~ 4 0 1 ) This . value confirms the data obtained in a previous study (Bril & Brenibre, 1989) where this correlation was significantly negative for 5 children out of 11 observed between 140 and 172 days of I.W.
t/T4' ..
r I
0' 0
r .
.25
.50
.75
a
In0
125
Is0
l.75
v
a00
(m/s)
Figure 6. Relative values of the double-support phase in relation to average progression velocity, for 10 children with 150 to 200 days of I.W. For the children, each dot ( 0 ) corresponds to the mean value of the parameters representing one sequence of steps. For the three adults, each dot (+)corresponds to a mean value calculated on 10 sequences of steps executed at the same speed (from Bril & Brenibre, 1988, Posture and Gait: Development Adaptation and Modulation. Amblard B., Berthoz A. and Clarac F. (eds.), Elsevier Science Publishers B.V., p 27). The interpretation of this data is not easy. If, after onset of I.W., the duration of the DS phase depends on the time needed to balance recovery, we can hypothesize that the duration of DS will decrease as walking experience increases. The great variation in DS duration observed before two months of I.W. can be interpreted in a similar way: increasing stability reduces variability (figure 7). The development of the child propelling strategy may explain, at least in part, the important changes in DS duration observed during the first 5 months of LW. as compared with the following months (see figure 5). In another study we have showed that at the time of foot contact, contrary to the adult, the young toddler is dynamically in the situation of a fall; the value of the vertical acceleration is negative (see figure 2B; Breniere & Bril, 1988, submitted). For the adult, the vertical acceleration is always positive at heel strike. This means that the adult is able to initiate a propulsing phase during the swing phase - that is during unipodal stance - which is not the case in children. Furthermore, the vertical acceleration is correlated with speed from the second month of I.W. to the 6-8 month period. The value of this correlation decreases from the fifth month on, and it is no longer significant
24 1
Timing Invariances in Toddler' Gait
during the second year of I.W. (Brenikre & Bril, submitted). These characteristics of the propelling strategy of the child are interpreted as a lack of unipodal stance control that could be, in part, responsible for the two-phase development of the relative duration of double-support phase. t/T
0 50
1 month
050
2 months
0 40-
0 30-
OM
0 20-
T (ms)
12 months 0 40
O
'i
Figure 7. The proportional duration model: development of relative values of double-
support phase in relation to the total duration of steps at different periods after onset of independent walking.
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The results of the relative duration of DS for all values of the total duration of the step and at different periods after onset of I.W., is puzzling. The previous discussion established not only that toddlers and adults use different strategies to propel themselves, but that there is a change in the propelling strategy of children after approximately 5 months of I.W. The existence of temporal relative invariances in young walkers as well as in adults regardless of the propulsing strategy used suggests that the invariances in relative timing of children and adults could well result from the segmental organization which characterizes adult or child gait. For adults, the segmental kinematics show that joint angle patterns are invariant, and do not change with walking speed (Winter, 1983). As invariances in the relative duration of DS and SW have been found in children as well as in adults (figure 6 & 7) we can hypothezise that a given propulsing strategy leads to joint angle patterns which remain the same over a wide range of speed. In other words, different strategies could lead to similar relative temporal invariances in movement, as seems to be the case with handwriting (Wann & Jones, 1986). At this stage of the study we can only suggest that a detailed analysis of the segmental kinematics during the development of gait, compared with mature gait, could help to point out the analogies and differences of the segmental organization of movement. Since different propulsing strategies could lead to analogous relative timing invariances, we can hypothesize that the temporal characteristics of gait comes from the segmental kinematic organization, as would suggest the results of both Shapiro et al. (1981) and Clark and Phillips (1987).
CONCLUSION Our results on early walking show that absolute and relative timing can be found in gait movement as soon as a few weeks after onset of independent walking. We have suggested that absolute invariants in the initiation of gait are primarily set up by anatomical and body segment parameters. The developmental analysis of such invariances suggests that children have to learn to optimize the use of the biomecanical properties of their bodies. Relative invariants are more difficult to interpret. We have seen that for each age and regardless of the speed of walking, the relative duration of the double-support phase is constant. However, the relative duration of the double-support phase decreases with walking experience. A very important decrease appears during the first 5 months of independent walking, followed by a slighter decrease during the 18 following months. If the relative timing is, at least in part, set up by the kinematic of the limb segments, as suggested by Roberton and Halverson (1988), then its relative timing invariance would signify that for a given age the kinematic of the limbs is stable accross speed. Here further investigation is needed to test this hypothesis.
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However it is important to note that the similarity between the temporal structure of gait in toddlers and adults insofar as its relation to speed is concerned may mask the remarkable differences in propulsing strategies.
REFERENCES Beck R., Andriacchi T.P., Kuo K.N., Fermier R.W. & Galante J.O. (1981) Changes in the gait pattern of the growing children. The Journal of Bone and Joint Surgery, 63A(9), 1452-1456. Brenibre Y. & Do M.C. (1986) When and how does steady state gait movement induced from upright posture begin ? Journal of Biomechanics, 19, 1035-1040. Brenibre Y . & Bril B. (1988) Pourquoi les enfants marchent en tombant alors que les adultes tombent en marchant ? C.R. Acad. Sci. Paris, 307111, 617-622. Brenibre Y. & Bril B. (1991) Why do the children walk in falling during the first four years of independent walking? (submitted) Brenihe Y., Bril B. & Fontaine R. (1989) Analysis of the transition from upright stance to steady state locomotion for children under 200 days of autonomous walking. Journal of Motor Behavior, 21, 20-37. Bril B. & Brenibre Y. (1989) Steady state velocity and temporal structure of gait during the first six months of autonomous walking. Human Movement Science, 8, 99-122. Bril B. & Brenibre Y. (1990) How does the child modulate his progression velocity during the first 18 months of independent walking ? In T. Brandt, W Bles & M. Dietrich (eds.), Disorder of Posture and Gait, Stuttgart: Georg Thieme Verlag. Bril B. & Brenibre Y. (1991) Why does postural requirement restrain progression velocity in young walkers ? (submitted). Clark J.E. (1982) The role of response mechanisms in motor skill development. In The Development of Movement Control and Co-ordination, Kelso J.A.S. & Clark J.E., New York: J.Wiley & Sons. Clark J.E. & Phillips S.J. (1987) The step cycle organization of infant walkers. Journal of Motor Behavior, 19, 421-433. Gentner D.R. (1987) Timing of skilled motor performance: tests of the propotional duration model. Psychological Rewiev, 94, 255,276.
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Grieve D.W. & Gear R.J. (1966) The relationship between length of stride, step frequency, time of swing and speed of walking for children and adults. Ergonomics, 5, 379-399. Heuer H. (1988) Testing the invariance of the relative timing: Comment on Gentner (1 987). Psychological Review, 95, 552-557. Jansen E.C., Vittas D., Hellberg S & Hansen J. (1981) Normal gait of old and young men and women. Acta Orthop. Scand., 53, 193-196. Kirtley C., Whittle M.W. & Jefferson R.J. (1985) Influence of walking speed on gait parameters. Biomedical Engineering, 7, 282-288. Kugler P.N., Kelso J.A.S. & Turvey M.T. (1982) On the control and coordination of naturally developing systems. In Development of Movement Control and Co-ordination, Kelso J.A.S & Clark J. (eds.),New York: J. Wiley & Sons. Larsson L.E., Odenrick P., Sandlund B., Weitz P & Oberg P.A. (1980) The phases of the stride and their interaction in the human gait. Scand. J. Rehab. Med, 12, 107-112. Murray M.P., Kory R.C., Clarkson B.H. & Sepic S.B. (1966) Comparison of free and fast speed walking patterns of normal men American Journal of Physical Medecine, 45, 8-24. Roberton M.A. & Halverson L.E. (1988) The development of locomotor coordination: longitudinal change and invariance. Journal of Motor Behavior, 20, 197-241. Schmidt R.A. (1985) The search for invariance in skilled movement behavior. Research Quarterly for Exercice and Sport, 56, 188-200. Shapiro D.C., Zernicke R.F., Gregor R.J. & Diestel J.D. (1981) Evidence for the generalized motor programs using gait pattern analysis. Journal of Motor Behavior, 13, 33-47. Sutherland D.H., Olshen R., Cooper L. & Woo S.L. (1980) The development of mature gait. The Journal of Bone and Joint Surgery, 62A, 336-353. Wann J.P. & Jones J.G. (1986) Space-time invariances in handwriting: Constrasts between primary school children displaying advanced or retarded handwriting acquisition. Human Movement Science, 5, 275-296. Winter D.A. (1983) Biomechanical motor patterns in normal walking. Journal of Motor Behavior, IS,302-330.