INTRODUCTION

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LOCOMOTION IS AN ACTION THAT is executed by repeating the same movement cyclically. It was suggested that a specific neural system, a pattern generator, located in the spine, contributes to the generation of the cyclical motor command automatically (9, 10, 13, 17). However, this pattern generator is not the only determinant of walking movements. Walking movements emerge as a consequence of the interaction, or self-organizing process, of neural and mechanical dynamic systems, including musculoskeletal dynamics, the pattern generator, modulation from the supraspinal neural system, and afferent modulation (1, 25). These multiple modulations in the neuromuscular locomotor (NML) system may induce variability in walking movements.

However, excess variability could be one factor involved in falling and could at least prevent smooth walking, because, according to system theory, excess variability implies system instability in general. Therefore, gait variability should be as small as possible. Actually, a healthy NML system suppresses gait variability well, whereas gait variability is high when parts of the NML system lose function, as in gait-disabled patients (5, 11, 14, 21). In addition, high gait variability is related to fall risk in older adults (15, 20). Thus, with regard to the gait system, low gait variability suggests that the NML system is well stabilized, and, inversely, high gait variability suggests that the NML system is poorly stabilized. Therefore, it is possible to evaluate the stability of the NML system by measuring gait variability (12, 15, 20, 21, 24).

Numerous studies have suggested that the metabolic cost per unit distance walked is minimized at usual walking speeds (6, 16, 26, 31, 32) and that mechanical efficiency is maximized at usual walking speeds (2, 7). These phenomena are generally known as gait optimization. According to this concept, it is also hypothesized that the NML system is best stabilized at the usual walking speed, that is to say, gait variability is also minimized at the usual walking speed. There have been a few studies that have addressed the minimization of gait variability. Yamasaki et al. (30) reported that the variability of step length was minimum at the usual walking speed during a treadmill walking task; the same result was confirmed by Sekiya et al. (24), who studied normal ground walking.

However, no study to date has analyzed the variability of the ground reaction force (GRF) to evaluate gait performance. The GRF is regarded as a representative measurement of gait, because it is the external force involved in walking and it affects the acceleration of the body's center of mass (29). The goal of locomotion is to drive the center of mass stably in the desired direction. It is at the kinetic level that we can see the cause of movement rather than at the kinematic level, and, therefore, GRF may be a more appropriate global parameter to characterize gait than kinematics such as step length or step width. However, it is difficult to obtain the GRF for a number of steps at constant speed by using a standard ground-mounted measurement system. In recent years, several types of force platforms mounted on treadmills have been developed (3, 4, 8, 18, 19). We are now able to obtain three-dimensional GRF data easily for an adequate number of steps by using the most recent model (3, 4).

Therefore, the purpose of this study was to investigate whether or not the NML system is optimized at a unique speed with respect to the variability of the GRF during treadmill walking.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Subjects. Ten healthy male subjects who were well experienced in treadmill walking (age 28.8 ± 5.2 yr, height 170.2 ± 6.6 cm, weight 65.2 ± 7.9 kg; mean ± SD) volunteered for the experiment. Subjects were asked to be free from pathologies likely to affect gait. They gave informed consent before taking part in the experiment, and this study was approved by the ethics committee of this university.

Materials. GRF was measured with a treadmill ergometer (ADAL, Tecmachine) specially equipped with four three-dimensional piezoelectric sensors (3, 4). The apparatus had two walking belts that were virtually two independent treadmills placed side by side and separated by 4 mm. The treadmills were mechanically independent to allow for separate measurements of the GRF induced by each lower limb during the support phase. For that purpose, each treadmill was built on a metallic frame and driven by its own motor, which was also fixed on the same support. All of the treadmill components, including the motors, were tightly fixed to the ground through four crystal transducers (type KI 9067, Kistler). The natural frequency of this measurement system was >120 Hz, and the linearities were ensured by the manufacturer from 0 to 3,000 N for the vertical components and 500 N for the horizontal components. In addition, Belli et al. (3) recently examined the same kind of treadmill in detail. The maximum nonlinearity was 0.2-0.7%, except for a 1.45% nonlinearity of the anterioposterior force (F_y). We also tested nonlinearity, and it was sufficiently <1%, similar to the level given by the manufacturer.

Procedure and data analysis. Subjects were required to walk on the treadmill at 3.0, 4.0, 5.0, 6.0, 7.0, and 8.0 km/h after adequate practice (1-2 min) walking at each speed. Each trial executed successively after practice was 60 s, and, therefore, we could obtain the GRF for >40 steps for each leg per each trial. Three orthogonal GRF components were recorded: vertical force (F_z), horizontal-mediolateral force (F_x), and horizontal-anteroposterior force (F_y). Signals from crystal force transducers were sampled at 100 Hz and stored on a personal computer via a 12-bit analog-to-digital converter. All data were low-pass filtered [cutoff frequency = 8 Hz, according to Winter (27)] with a fourth-ordered Butterworth filter by using a zero-phase lag (29).

View larger version (13K): [in this window] [in a new window]   Fig. 1.   Representative examples of vertical (Fz; A), mediolateral (Fx; B), and anteroposterior (Fy; C) ground reaction force (GRF) of a right foot during treadmill walking. Vertical bar, one-half body weight (BW); horizontal bar, 0.2 s. Analyzed indexes in this study are defined by arrows. Fzp1, first peak of Fz; Fzp2, second peak of Fz; Fxp, Fx peak; Fyp1, first peak of Fy; Fyp2, second peak of Fy.

	RESULTS

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Figure 2 shows examples of GRF variability over 20 steps at three different speeds in one subject. We can see that the variability of F_z and F_x increased with increments in walking speed. However, with respect to F_y, variability at the middle speed (5.0 km/h) was smallest compared with those at both the low (3.0 km/h) and high (8.0 km/h) speeds.

View larger version (28K): [in this window] [in a new window]   Fig. 2.   Qualitative visualization of GRF variability. Twenty GRF curves from 1 subject for right leg at 3 different speeds are superimposed on each graph. Nos. near each peak indicate the coefficient of variation (CV) for each index of these 20 steps. Superimposed vertical scale bar, 0.1 BW; horizontal scale bar, 0.1 s.

Figure 3 shows CVs of GRF indexes in relation to walking speed for all subjects and for both legs. The effects of speeds on CV were significant for all GRF indexes, except for the left F_yp1. In addition, Tukey's test indicated that there were increment trends of CV with speed for F_z and F_x, whereas, for F_y, CVs at middle speeds (6.0 and 7.0 km/h for right F_yp1, and 5.0 and 6.0 km/h for both F_yp2) were significantly lower than those at both the slowest and fastest speeds. These statistical results indicated that kinetic variability increased with speeds for F_z and F_x, whereas there was a speed at which variability was minimum for F_y.

View larger version (21K): [in this window] [in a new window]   Fig. 3.   Relationship between the CVs of GRF indexes and speed of walking. A: Fzp1; B: Fzp2; C: Fxp; D: Fyp1; E: Fyp2. Each bar indicates group average ± SD. * Significantly different from CV at 3.0 km/h for corresponding leg;  significantly different from CV at 8.0 km/h for corresponding leg: P < 0.05.

To obtain the minimum variability speeds for the F_y indexes, we applied quadratic regression analyses by the least squares method to each CV of the F_y index. The results of these regression analyses were as follows: right F_yp1, y = 37.2  10.7x + 0.912x², R² = 0.864; left F_yp1, y = 24.8  6.18x + 0.528x², R² = 0.948; right F_yp2, y = 23.8  6.99x + 0.623x², R² = 0.900; left F_yp2, y = 29.1  8.94x + 0.810x², R² = 0.991, where x is walking speed and y is CV. According to these equations, the minimum variability speeds were 5.8, 5.6, 5.8, and 5.5 km/h for right F_yp1, left F_yp1, right F_yp2, and left F_yp2, respectively.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Before we turn to our main result, a few remarks should be made concerning measurement errors. Belli et al. (3) reported a measurement error due to running belts above the 17-Hz frequency region. We removed this noise with a low-pass filter (see METHODS). There was also measurement error <1% due to nonlinearity of this force plate, as mentioned in METHODS. This level of error was low compared with the range of CVs in this paper (from 1.76% for left F_zp1 at 3 km/h to 20.8% for right F_xp at 8 km/h). We also emphasize here that this small error did not critically affect the speed dependency of CV, because the error mixed in indexes equally for all speeds. Therefore, we consider our CV data to be reliable for the speed dependency of GRF variability during treadmill walking.

The main finding of this study was that there was a speed dependency for GRF variability. For F_z and F_x, there was an increasing trend in variability with speed from 3 to 8 km/h. However, there was a speed at which the variability of GRF was minimum for F_y. The minimum variability speeds of 5.5-5.8 km/h were within the limits of usual walking speeds. This result indicates that the NML system was most stabilized at usual walking speed, that is to say, there was an optimum speed for the NML system. This result is similar to those of previous studies, which revealed that there was an optimum speed for walking in terms of energetics (2, 6, 7, 16, 26, 31, 32) and that these optimum speeds were also within the limits of usual walking speeds. These optimization phenomena suggest that we usually choose the most energetically efficient speed when we walk, and our result also suggests that, at this usual speed, the gait control system is most stable.

It should be noted that an optimum speed was found only for F_y and that the variability of F_x and F_z increased with speed. Whereas F_y affects the propulsion of the body, F_x affects lateral sway, and F_z affects the vertical sway of the body. Therefore, the variability of F_x and F_z can be regarded as representing the stability of the balance control mechanism. Thus our results suggest that optimization for the NML system is only observed in the case of the propulsion control mechanism, whereas the instability in the balance control mechanism increases with speed.

It was already reported that variability in step length was minimum at around the usual speed (90-100 m/min) during treadmill walking (30) and that variability in step length was also minimum at a preferred speed during overground walking (24). The step length and F_y values may interactively relate to each other, because, as the push-off force, F_yp2 is estimated to be the main force moving the leg forward, and F_yp1, as a braking force, may be strongly affected by the magnitude of step length. Actually, both step length and F_y increased linearly with increments in walking speed (22, 23), suggesting that there is a linear relationship between the two. In addition, Sekiya et al. (24) also reported that variability of step width increased linearly with speed. F_x and step width may also be related to each other, because kinetics would be the source of kinematics, as mentioned above. Therefore, it is possible that our major results and the results of the kinematic studies were attributable to the same mechanism.

However, the previously reported kinematic variability was comparatively smaller than kinetic variability observed in this study. From Fig. 5 in the previous study by Yamasaki et al. (30), the minimum CV of step length was ~2.5% for male subjects at 100 m/min, and CVs for the slowest speed and the fastest speed were ~4.9% at 60 m/min and ~3.8% at 130 m/min, respectively. These values were considerably smaller than our CVs for F_y, i.e., the minimum value was 4.0% for right F_yp2 at 5 km/h, and CVs for the slowest speed and the fastest speed were 12.6% for right F_yp1 at 3 km/h and 11.3% for right F_yp1 at 8 km/h, respectively (Fig. 3). Winter (28) investigated kinematic and kinetic variabilities simultaneously, although he measured only one subject and nine steps, and concluded that kinetic variability was larger than kinematic variability. Therefore, our speculation that our results and the results of kinematics were attributable to the same mechanism is not rejected. However, further work with simultaneous recording of kinematics and kinetics for populations is needed to test this matter.

In conclusion, we quantified the variability of the GRF during treadmill walking at different walking speeds. We discovered that the variability of the F_y was minimized at the usual walking speed, whereas those of the other two components increased with increments in walking speed. This finding suggests that there is an optimum speed for the NML control system but only for the propulsion control mechanism. In general, a system that is designed for a specific condition does not necessarily work well for other conditions. Our results suggest that the gait system is adapted to execute walking at the usual speed. However, it remains unclear how this optimization occurs or why the optimization occurs only for the propulsion control mechanism. Further investigation is needed to clarify these points.