Abstract
D uring a step the body falls until caught by the swing lim b as it returns to the ground. This suggests a relationship between swing foot and body position/velocity at heel- strike. The ballistic hypothesis predicts that body (CoM ) position/velocity at heel- strike will depend on its position/velocity at toe-off and on the step duration. Thus determ ining the CoM toe-off position/velocity requires that w here and w hen the stepping foot is to be placed back down on the ground is determ ined in advance. This study investigates these ideas by asking subjects to step forw ards (to the sam e place) at a range o f speeds. In addition, the tem poral structure o f the m ovem ent sequence is analysed. As before, CoM motion data w ere calculated from ground reaction forces, and foot contact events were determ ined electrically. The preparation and execution o f the step w ere divided into a num ber o f phases according to ground reaction and foot contact events. Subjects varied their M L CoM position at toe-off w ith step duration in a m anner consistent with the ballistic hypothesis suggesting that they w ere taking into account the intended duration o f the step. H ow ever M L CoM velocity was constant across the range of m ovem ent speeds, not only at toe-off but at any given fraction through the movement. The durations o f the phases o f the step w ere found to be fixed fractions o f the overall m ovem ent time. This suggests the presence o f som e sort o f tim ing tem plate w hich can be ‘ru n ’ at various speeds but w hich keeps the relative tim ing o f the sequence o f events constant. This in turn suggests that the duration of the step is determ ined in advance. These findings are consistent with the idea that not only the ‘go al’ (new foot position) but also the duration o f the step are determ ined in advance and used to ju dge the toe-off conditions of the body-m ass required for the body to fall appropriately during the step.
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Introduction
The previous study suggested that during a step the body falls in the frontal plane m ore or less freely, and that therefore its m otion is largely controlled by bringing it to a certain position and velocity at the start o f the step. The discussion assum ed that different trajectories o f the body-m ass are required or at least desirable for different directions o f step. This seems reasonable since, if the swing foot as it returns to the ground catches the fall o f the body, there is presum ably some relationship at heel- strike betw een 1) foot position and 2) body position and velocity w hich (for exam ple) allows the body to be caught m ost easily or securely. The study described in chapter 6 tests directly the prediction of a relationship betw een foot and body position/velocity at heel-strike.
If the b o d y ’s m otion during the step is determ ined by its position and velocity at toe- off, then these two variables together w ith the step duration determ ine its position and velocity at heel-strike. From this, and the suggested relationship betw een foot and body position/velocity at heel-strike, a num ber o f predictions are indicated. The study in the last chapter (im plicitly) tested one o f these, that CoM position and velocity at toe-off will vary predictably with the swing foot position (at heel strike) w hen step duration is approxim ately constant. The study described in this chapter tests another, that CoM position and velocity at toe-off will vary predictably w ith step duration w hen the swing foot position at heel-strike is held approxim ately constant.
A nother issue investigated here is w hether the step duration is determ ined in advance. If the aim or ‘g oal’ o f a step is thought to be w here the swing foot is to be placed then the preparatory m ovem ents o f the body m ass m ust be seen as being determ ined by this goal. In fact these preparatory m ovem ents are often ‘relegated’ to the status o f ‘anticipatory postural adjustm ents’ (M assion, 1991), although this does not necessarily seem helpful since both posture and equilibrium are being changed rather than m aintained. H owever, the issue here is that w here the swing foot is to be placed does not alone specify the required preparatory m ovem ent o f the body mass, or m ore particularly the CoM position and velocity at toe-off. It is also necessary to know (in advance) the intended duration o f the step.
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A motor programme fo r stepping
It has previously been suggested that the sequence o f m ovem ents w hich com prise hum an gait initiation is controlled using a ‘m otor program m e’ (Brunt et a l , 1991). The notion o f a m otor program m e is o f a stored sequences o f m uscle com m ands that can be ‘run o f f at will and w ithout the need for feedback from the periphery
(Lashley, 1917; Henry, 1960; Keele 1968; Schm idt, 1975). The discovery o f central pattern generators (see chapter 6) has been seen as direct evidence for the existence o f such program m es. Schm idt (1975) suggested that m otor program m es m ight exist only in general form and, prior to being used, a num ber o f param eters such as overall speed or force o f the m ovem ent must be decided upon. Thus for exam ple a
program m e m ay exist for throw ing a ball, but before using it the subject gauges how hard or fast to throw it. A num ber o f studies have looked for evidence o f m otor program m es in hum an gait and gait initiation. Shapiro et a l (1981) postulated the existence in hum ans o f a m otor program m e for locom otor lim b m ovem ents. They studied subjects w alking and running at a range o f speeds on a treadmill. U sing records o f jo in t angle w ith time they divided the step cycle into 4 phases after the schem e proposed by Philippson (1905; cited in Shapiro et a l, 1981). They found that in both w alking and running, w hile the absolute tim e spent in each o f these phases varied w ith the overall m ovem ent speed, the fraction o f the step cycle spent in each was approxim ately constant. (The fraction o f the cycle spent in each phase was different for w alking and running.) The authors suggest that these findings betray the existence o f a generalised limb m ovem ent m otor program m e w hich specifies the tem poral relationship between the various changes in jo in t angle, but w hich can be ‘run o f f at a range o f speeds. M elvill Jones & W att (1971) in a study o f long-latency stretch reflexes in the triceps surae during stepping concluded that “It w ould seem that the entire act is program m ed and dispatched from higher centres as a single e n t ity the correct tim ing and sequence o f m uscle contractions having been learned through previous experience.”
B runt et a/. (1991) divided the initiation o f gait (from cue to m ove, to second toe-off) into a num ber o f periods using EM G and foot contact events. They found that over a wide range o f speeds each o f these periods rem ained a constant fraction o f the
Chapter 4
initiation period as a whole, and took this as evidence o f an underlying gait initiation m otor program m e. H ow ever B renière et a l (1987) considered that, as the speed o f gait initiation increased, the duration o f the ‘anticipation p hase’ (up to heel-off o f initial swing limb) increased while that o f the ‘execution phase’ (from sw ing heel-off to m axim um forw ard CoM velocity) decreased. Curiously, they found that the sum of these two periods rem ained approxim ately constant over the range o f gait initiation speeds studied. This stedy* m easures the duration o f the constituent parts o f the step sequence over a range o f movem ent speeds in an effort to resolve this conflict and to assess w hether there is evidence that step duration is determ ined in advance.
Finally, this study com pares the way in w hich the M L and A P CoM velocities vary w ith m ovem ent speed. The free-fall ballistic m odel o f the last chapter m ight predict that M L velocity should decrease with increasing speed {i.e. with decreasing step duration), whereas the A P velocity, as m ight be predicted, has been shown to increase (Cook & Cozzens, 1976).
M ethods
The experim ental procedure was sim ilar to that described in the previous study and only the differences are described here.
Six norm al subjects (five fem ale and one male) w ith ages ranging from 23 to 32 (m ean = 26.3) years gave their inform ed consent to participate in the study, w hich was approved by the local ethics com mittee. Subjects stood w ith an interm alleolar distance o f 15cm, and on an auditory cue stepped forw ards first w ith one foot and then w ith the other so that they ended each trial as they started it, in norm al quiet stance. Tw o lights placed in front o f the subject, one o f w hich illum inated at the sam e tim e as the auditory cue, indicated w ith w hich foot to begin the m ovem ent. E ach subject took a total o f 60 steps divided into 3 blocks o f 20. In one o f the blocks subjects w ere instructed to step at their norm al speed, in another to step faster than norm al, and in the other to step slow er than norm al. The order in w hich these speed conditions were presented was random ised across subjects.
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As before, the m otion o f subjects’ CoM as they stepped was calculated using ground reaction forces and num erical integration techniques (see chapter 2).
Results
Figure 4.1 shows single right-foot trials taken from 2 representative subjects. The traces show the AP (red) and M L (blue) com ponents o f acceleration and velocity o f the CoM for fast, norm al and slow steps. Only the first 3 seconds o f each trial is shown. The 4 vertical dotted lines associated with each set o f traces show 1) the tim e o f onset o f lateral acceleration 2) peak preparatory lateral acceleration 3) toe- o ff 4) heel-strike. N ote that here and in all that follows, the term ‘preparatory’ refers to the period up to toe-off of the first step, that is up to the 3"^^ vertical line in figure 4.1. The deflections in the traces after the 4 ‘^ vertical line are associated w ith the step o f the left foot, w hich is being brought forw ards to be alongside the right.
The m axim um forw ards velocity occurs in all cases soon after heel-strike (4^^ vertical line) and can be seen to increase from the slow through the norm al to the fast step speeds. This was the case in all subjects. The left bar chart o f figure 4.2A shows the means (+SEM ) o f m axim um forwards velocity across all subjects and trials for the 3 step speeds (F(1.4,7.2) =23.1, p=0.001; A N O V A w ith repeated m easures: fractional degrees o f freedom result from adjustm ents using the Huynh- F eldt epsilon to correct for departures from the assum ption o f circularity (Hays,
1988)/. From figure 4.1, the overall duration o f the step (F^ to 4^*^ vertical line) can be seen to decrease w ith increasing step speed. This too was the case in all subjects (right panel, figure 4.2A; F(2,10) =28.0, p<0.001). These results show that subjects w ere able to com ply well with the instructions to step forw ards at norm al, faster than norm al and slow er than norm al speeds.
S u b je c t 5 (S C ) a c c e le r a tio n Slow v e lo c ity 0 .5 m /s - 0 .2 m /s Normal 1 ^ Fast S u b je c t 2 (A S ) a c c e le ra tio n v e lo c ity Figure 4.1
AP (red) and ML (blue) components o f acceleration and velocity for single right- foot steps taken from 2 representative subjects. One fast, one normal and one slow step from each subject is shown. Upwards
deflection indicates
forwards acceleration in AP traces, and leftwards
(towards support side) in ML. Vertical dotted lines indicate 1) time o f onset of lateral acceleration 2) peak preparatory lateral
acceleration 3) toe-off 4) heel-strike.
r \
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A Max. forwards velocity Total step duration
B Absolute duration Relative duration
Figure 4.2
A Means (+SE) across subjects o f maximum forwards velocity and step duration (force onset to heel-strike) for the 3 stepping-speed conditions, slow (red), normal (blue), and fast (green).
B Means (+SE) across subjects of durations o f the 3 component periods o f the step (as depicted in cartoons at the right-hand side). Left column shows absolute duration, right shows duration o f period divided by total step duration (relative duration).
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Durations o f each o f the phases o f the step
The events m arked by the vertical dotted lines in figure 4.1 divide each o f the steps into 3 periods or phases. In each o f the trials illustrated the first and third periods appear to be o f approxim ately equal duration w hilst the second is noticeably shorter. This was m ore apparent in some subjects than others, but in all cases, over the range o f step speeds, the durations o f the each o f the 3 phases appeared to vary together. To investigate this, the duration o f each phase was m easured in all trials. The results are shown in figure 4.2B. The absolute duration o f each period reduces w ith increase in step speed (left colum n - respectively, F( 1.5,7.6)= 17.5, p=0.002; F(1.7,8,7)=26.9, p<0.001; F(1.9,9.4)=24.2, p<0.001). H owever, w hen the duration o f each phase is expressed as a fraction o f the total step duration (lateral acceleration onset to heel- strike), there is no significant difference across step speeds (right-hand colum n; F(1.7,8.5)=1.6, p=0.26; F(2,10)=1.5, p=0.27; F(2,10)=1.8, p=0.22). Thus, as step speed increases, the durations o f each o f these periods reduce by the sam e proportion.
Medio lateral motion o f the CoM
The traces in figure 4.3 show the M L velocity and displacem ent o f the CoM plotted against time. Single trials have been aligned to toe-off (vertical broken line) and then averaged by condition across all subjects. Right foot trials show an initial deviation upw ards (towards the subjects’ left side), left foot trials dow nw ards (tow ards the subjects’ right). A fter reflection about the midline, right and left foot trials appear very similar. As in the previous study, this was confirm ed statistically, the effect of stepping foot or any o f its interactions not reaching significance in any o f the
m easurem ents made. M L velocity and position o f the CoM at toe-off w ere m easured in all trials and the results are shown in the bar charts in figure 4.3. The position changed across step speed, w ith the CoM being m ore displaced tow ards the support side the slow er the step (F(1.9,9.3)=37.5, p<0.001). In contrast, the velocity at toe off was very constant across the range o f stepping speeds (F(2,10)=0.37, p=0.70).
Chapter 4