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Effect of prolonged free-walking fatigue on gait and physiological rhythm
ARTICLE IN PRESS
Journal of Biomechanics 37 (2004) 1271–1280
Effect of prolonged free-walking fatigue on gait and physiological rhythm Kohzoh Yoshinoa,*, Tomoko Motoshigeb, Tsutomu Arakib, Katsunori Matsuokaa a
Human Stress Signal Research Center, National Institute of Advanced Industrial Science and Technology (AIST), 1-8-31 Midorigaoka, Ikeda, Osaka 563 8577, Japan b Department of Mechanical Science and Bioengineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560 8531, Japan Accepted 6 November 2003
Abstract This study examined the ways in which gait patterns and physiological rhythms such as those of muscle activity (tibialis anterior (TA) and biceps femoris (BF)) and cardiac activity are affected by the fatigue induced by prolonged free walking. Twelve normal subjects who walked for 3 h at their preferred pace were divided into two groups according to whether their mean gait cycle time (reciprocal of stride rate) during the second 90 min was higher (Group A: n=8) or lower (Group B: n=4) than that during the first 90 min. For Group A, the level of subjective fatigue during the walking task was significantly higher and the heart rate at rest was significantly lower than Group B. In Group A, prolonged walking significantly decreased the mean power frequency of the electromyography from TA, increased the variability of gait rhythm, decreased the largest Lyapunov exponent of the vertical component of back-waist acceleration, and decreased the amplitude of the vertical component of back-waist acceleration. Taking the onset timings of these changes into account, we propose that subjects who tire easily during prolonged walking first show local muscle fatigue at TA followed by instability of gait rhythm and then they slow their gait rhythm to enhance local dynamic stability. For both groups we constructed a physical fatigue index described by linear regression of gait and physiological variables. When we compared the subjective fatigue level with the fatigue level predicted using the index, we obtained a relatively high correlation coefficient for both groups (r=0.77). r 2003 Elsevier Ltd. All rights reserved. Keywords: Fatigue; Prolonged walking; Electromyography; Lyapunov exponent; Heart rate
1. Introduction Fatigue is recognized as a serious social problem, and an important step in overcoming it is the development of indices for evaluating fatigue during daily life (Cohen et al., 1995; Hancock and Desmond, 2000). Several studies have shown how physiological electric signals change their features in the time and frequency domains as a result of the physical fatigue induced by movement. The mean power frequency (MPF) of an electromyography (EMG) signal, for example, is known to be shifted downward by the muscle fatigue induced by static isometric contraction (Merletti et al., 1991) and by dynamic movements such as running (Mizrahi et al., 2000a), cycling (Bonato et al., 1996; Kiryu et al., 1998), *Corresponding author. Tel.: +81-727-51-8243; fax: +81-727-519961. E-mail address: [email protected] (K. Yoshino). 0021-9290/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2003.11.031
and skiing (Kiryu et al., 1999). Mizrahi et al. (2000a) and Voloshin et al. (1998) used accelerometers to measure the amplitude of the shock waves induced by heel strikes and found that the amplitude measured at the shank and sacrum increased during long-distance treadmill running. This indicates that fatigue reduces the ability of the musculoskeletal system to attenuate the shock waves. Heart rate variability (HRV) analysis is often used to evaluate autonomous nerve activity indirectly (Akselrod et al., 1981). The heart rate (HR) and the ratio of lowfrequency (LF; 0.04–0.15 Hz) power to high-frequency (HF; over 0.15 Hz) power (index of sympathetic nerve activity, although it is not fully accepted during exercise (Oida et al., 1997)), increase with exercise intensity (Nakamura et al., 1993). Saito et al. (1997) showed that HR increases during prolonged cycling at a constant low intensity. Our goal is to develop an index for assessing fatigue during daily life using physiological electric signals. Gait
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acceleration, EMG, and HRV were selected for the signals, since these signals can be measured during daily life by wearable sensor technology. Although locomotion is one of the most frequent events in our daily life, no other study has shown how the physiological electric signals measured during locomotion are affected by the fatigue induced by long-term walking. Moreover, since other studies related to prolonged exercise fatigue focused on the constant exercise intensity protocol, little is known about the preferred gait pattern people select under fatigue conditions. One study showed that stride rate of treadmill running at a given speed decreases by prolonged running fatigue (Mizrahi et al., 2000b). In this study, we examined how long-term free walking affects gait pattern and physiological rhythms such as those of muscle activity, back-waist acceleration, and cardiac activity. Using the results, we constructed a physical fatigue index for young (age 18–29) males described by linear regression of the gait and physiological variables. The purpose of the proposed index is for predicting subjective fatigue automatically using objective indices measured during preferred pace walking in daily life.
2. Methodology Twelve normal male subjects (age 19–26) participated in this study after having provided their informed written consent as approved by the Ethical Committee on Human Research at AIST Kansai. Subjects were instructed to walk 3 h continuously at their self-determined preferred pace on level ground. Subjects reported their subjective fatigue level (10-point linear scale) every 30 min. The lowest level (1) and the highest level (10) represent ‘not fatigued at all’ and ‘more fatigued than ever’, respectively. Each subject sat on a chair for 15 min before and after the walking task. The surface EMGs of the tibialis anterior (TA; dorsiflexor of the ankle) and biceps femoris (BF; flexor of the knee) of the right leg were recorded from a pair of Ag–AgCl electrodes (interelectrode distance 3 cm) after cleansing the skin by alcohol. A strain-gauge-type triaxial accelerometer (AS-5TG, Kyowa, Japan) was clipped tightly on a belt tightened around subjects’ waist, and was located around the center of L5-S1 intervertebal disk to measure back-waist accelerations in the anterior–posterior (Ax), medio-lateral (Ay), and vertical (Az) directions. The reproducibility of the accelerometer was assessed by comparing the mean value (baseline level) of the back-waist acceleration during the beginning period (0–15 min) and during the ending period (165–180 min) of the walking task. The difference between the two periods in each direction was less than 1% of the mean amplitude during walking. This verifies the reproducibility of the accelerometer.
The ECG was recorded from a pair of Ag–AgCl electrodes placed on the chest. All analog signals were amplified and digitized at 1 kHz sampling rate and stored on a compact flash card placed inside a portable recorder (DR-C2, TEAC, Japan) (analog band-pass filter: EMG:10–500 Hz, ECG:0.05–200 Hz). The data collected during the 3-h walking tasks were divided into 12 non-overlapping data sets 15 min long, and the subjects were divided into two groups according to whether the mean gait cycle time (reciprocal of the stride rate) in the second 90 min was longer (Group A) or shorter (Group B) than that in the first 90 min. The following physiological and gait variables were calculated for each 15-min set for each subject and averaged among subjects in their corresponding group. (i) MPF of EMG signal: MPF ¼
fH X f ¼fL
ðfPðf ÞÞ=
fH X
ðPðf ÞÞ;
ð1Þ
f ¼fL
where f denotes frequency, P(f) is 215 points averaged fast Fourier transform (FFT) power spectrum of EMG signals, fL=20 Hz, and fH=300 Hz. (ii) Mean gait cycle time (reciprocal of stride rate): To compute the gait cycle time, we first extracted the minimum peaks of the Ax signals by detecting minimum points after the downward threshold crossing. Since acceleration was measured at the center part of the back waist, Ax shows the effect of both right and left steps. The gait cycle time was therefore obtained as the length of the interval between alternate minimum peaks of Ax. The mean value of the gait cycle time series in each 15min set was calculated. (iii) Coefficient of variation (CV) of gait cycle time: The CV of the gait cycle time is the ratio of the standard deviation of the gait cycle time to the mean gait cycle time. (iv) Largest finite-time Lyapunov exponent of backwaist acceleration signal: The Lyapunov exponent is the mean exponential rate of divergence of initially nearby points, thus quantifying local dynamical stability (Dingwell and Cusumano, 2000; Dingwell et al., 2000, 2001; Yokoi et al., 1998). We estimated the largest finite-time Lyapunov exponent of down-sampled (100 Hz) Ax, Ay, and Az by using the algorithm proposed by Rosenstein et al. (1993) as follow. The attractor dynamics was reconstructed by taking embedding delayed samples (Takens, 1980). The time lag was determined by the time at which the autocorrelation dropped to 1/e of the value at time zero. The embedding dimension was set to five from the result of false nearest neighbor analysis (Kennel et al., 1992). The largest Lyapunov exponent was estimated by calculating the slope of linear fits to the log-scaled curve of the divergence distance between neighboring trajectories in the reconstructed phase space. To exclude the
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effect of different gait cycle times among data, the time axis for the divergence curve was rescaled by dividing by the mean gait cycle time. The range of the region calculating the slope was from 0.5 to 4 gait cycle times. (v) Mean amplitude of back-waist acceleration: The amplitude of back-waist acceleration in each gait cycle was obtained by subtracting the maximum value from the minimum value. The mean value of the amplitude sequence in each 15-min set was calculated. Variables (i)–(v) derived from acceleration signals represent fundamental properties of gait rhythm. Those are associated with oscillatory frequency, static stability (variability), dynamical stability, and amplitude of the gait rhythm. Before the analysis, we considered that these fundamental properties of gait rhythm have a possibility to be modulated by fatigue. (vi) Heart rate (HR): R-waves were detected from each ECG waveform, and then time intervals between two successive R-waves (RR interval) were calculated. The mean RR interval was calculated for each 15-min set during the walking task and for the rest task. HR (beats/min) was obtained by dividing 60 by the mean RR interval. HR was obtained in order to investigate how sympathetic nerve activity during exercise is modified by fatigue. (vii) LF/HF of RR-interval fluctuation: The sympathetic nerve activity was also evaluated by calculating LF/HF, the ratio of the LF component (0.04–0.15 Hz) to the HF component (0.15–0.7 Hz) of the 27 points averaged FFT power spectrum of RRinterval fluctuation. Two-factor (set (time) group) ANOVA with Tukey’s honestly significant difference test was applied to these data, and statistical significance was determined at po0.05. To develop a technology using physiological electric signals to assess fatigue during daily life, we constructed
a physical fatigue index by using multiple linear best subsets regression model analysis for each group. The dependent variable of the model was the subjective level of fatigue and the candidates for independent (predictor) variables of the model were MPF of EMG from TA, CV of gait cycle time, mean gait cycle time, the largest Lyapunov exponent of Az, mean amplitude of Az, and LF/HF of RR-interval fluctuation. We calculated Akaike Information Criterion (AIC) (Akaike, 1974) for all possible combinations of predictor variables. The combination which gives the minimum AIC was selected for the optimal model for each group.
3. Results Eight of the 12 subjects constituted Group A, and the other four subjects constituted Group B. Group A (age 23.1271.55) was significantly older than Group B (age 20.7571.25) (p=0.02). For both groups the mean subjective levels of fatigue increased monotonically with time, but from 60 min onwards those of Group A were significantly higher than those of Group B (Fig. 1). The MPF of EMG signal recorded from the TA decreased significantly (compared with the first 15 min) from 105 min onwards in Group A (Fig. 2(a)). It did not change significantly with time in Group B (Fig. 2(b)). The MPF of EMG signal recorded from the BF did not change significantly with time in either group (figures not shown). The CV of the gait cycle time increased significantly (compared with the first 15 min) from 120 min onwards in Group A (Fig. 3(a)), whereas it tended to decrease gradually with time in Group B (Fig. 3(b)). Mean gait cycle time increased significantly (compared with the first 15 min) from 135 min onwards in
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Fig. 1. Time courses of the subjective level of fatigue. Mean values with standard deviation bars are shown. (a) Group A; (b) Group B. Significant differences (po0.05) from the first 30 min are indicated by asterisks. From 60 min onwards the values for Group A are significantly higher than those for Group B.
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The mean amplitude of Az decreased significantly, compared with the 30–45 min, from 150 to 165 min in Group A (Fig. 6(e)). The mean amplitude of Ay increased significantly, compared with the first 15 min, from 105 min onwards in Group B (Fig. 6(d)). To obtain more precise onset timing of the changes in these variables, we divided the walking-task data into shorter time increments, each 1.8 min long (thus 100 sets), and recalculated the variables for each set. We used 1.8 min long intervals because it is difficult to
Group A (Fig. 4(a)), whereas it tended to decrease gradually with time in Group B (Fig. 4(b)). The largest finite-time Lyapunov exponent of Az decreased significantly (compared with the 15–30 min) from 150 min onwards in Group A (Fig. 5(e)). In Group B, however, the largest finite-time Lyapunov exponent of back-waist accelerations in all three directions Ax, Ay, and Az increased significantly, compared with the first 15 min, respectively, from 135 to 165 min, from 150 min onwards, and from 120 to 165 min (Figs. 5(b), (d), (f)).
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Fig. 4. Time courses of mean gait cycle time. Mean values with standard deviation bars are shown. (a) Group A; (b) Group B. Significant differences (po0.05) from the first 15 min are indicated by asterisks.
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Fig. 5. Time courses of largest finite-time Lyapunov exponent of back-waist acceleration signals in (a), (b) anterior–posterior direction (Ax), (c), (d) medio-lateral direction (Ay), and (e), (f) vertical direction (Az). (a), (c), (e) Group A; (b), (d), (f) Group B. Mean values with standard deviation bars are shown. Significant differences (po0.05) from the first 15 min are indicated by asterisks, and those from 15 to 30 min are indicated by diamonds.
calculate Lyapunov exponents from data sets shorter than this. The results for Group A are shown in Fig. 7, where it can be seen that (a) the MPF of EMG signal recorded from the TA changed from the beginning, (b) the CV of the gait cycle time followed it after about 15 min, and (c) the mean gait cycle time, (d) the largest Lyapunov exponent of Az, and (e) the mean amplitude of Az all began to change after various time lags 30– 50 min after the beginning of the walking task. To confirm this, we calculated the cross-correlation function between each combination of two variables X and Y in Fig. 7 and compared the area of the function the negative lag region (50 to 0 min) and that the positive lag region (0 to +50 min). If the area in the negative lag region is larger than that in the positive lag region, this implies that the changes in the variable X preceded those in variable Y. We used the area instead of the peak lag because clear monopeaks were not observed in several
cross-correlation functions. The results are shown in Table 1 and implies the following order: (decreased MPF of EMG from tibialis anterior) - (increased CV of gait cycle time) - (increased mean gait cycle time) (decreased largest Lyapunov exponent of Az) and (decreased mean amplitude of Az). The mean HR during the walking task was almost constant until 120 min from the beginning, and it tended to increase gradually during the last 60 min in both groups (Figs. 8(a),(b)). The LF/HF of RR-interval variability tended to increase gradually in Group A (Fig. 8(c)), but it did not either increase or decrease in Group B (Fig. 8(d)). The mean HR of Group A subjects at rest before the walking task was significantly lower than that of Group B subjects (p=0.02) (Fig. 8(e)). We applied best subsets regression analysis to the data in order to construct a physical fatigue index described by multiple linear regression of gait and physiological
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Fig. 6. Time courses of mean amplitude of back-waist acceleration signals in (a), (b) anterior–posterior direction (Ax), (c), (d) medio-lateral direction (Ay), and (e), (f) vertical direction (Az). (a), (c), (e) Group A; (b), (d), (f) Group B. Mean values with standard deviation bars are shown. Significant differences (po0.05) from the first 15 min are indicated by asterisks, and those from 15 to 30 min are indicated by diamonds.
variables for each group. The optimal combination of predictor variables was MPF of EMG from TA, CV of gait cycle time, mean gait cycle time, mean amplitude of Az, and LF/HF in Group A, and MPF of EMG from TA, CV of gait cycle time, and mean amplitude of Az in Group B. The values of regression coefficients of each variable are summarized in Table 2. The correlation coefficient between the predicted fatigue level using the index and the subjective fatigue level was r=0.77 for both groups.
4. Discussion We examined the gait and physiological variables whose values changed with time during the prolonged walking task, since the level of subjective fatigue
increased with elapsed time (Fig. 1). We divided the subjects into two groups according to whether the mean gait cycle time during the second half of the walking task was longer (Group A) or shorter (Group B) than that in the first half. Group A subjects reported subjective fatigue levels significantly higher than those reported by Group B subjects (Fig. 1). Main results are summarized as follow. 1. Group A subjects reported subjective fatigue levels significantly higher than those reported by Group B subjects (Fig. 1). 2. Group A showed significant decrease in MPF of EMG from TA (Fig. 2(a)) with elapsed time, whereas no significant change was observed in Group B (Fig. 2(b)). 3. Group A showed significant increase in stride-tostride variability (Fig. 3(a)), mean gait cycle time
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Fig. 7. For Group A subjects, shorter-time-increment (1.8 min) time courses of (a) MPF of EMG recorded from TA, (b) CV of gait cycle time, (c) mean gait cycle time, (d) largest Lyapunov exponent of Az, and (e) mean amplitude of Az.
Table 1 Area in negative lag region (50 min to 0 min) and in positive lag region (0 to +50 min) of the cross correlation function between two variables X and Y Variable X MPF of EMG from TA MPF of EMG from TA MPF of EMG from TA MPF of EMG from TA CV of gait cycle time CV of gait cycle time CV of gait cycle time Mean gait cycle time Mean gait cycle time Largest Lyap. exp. (Az)
Variable Y CV of gait cycle time Mean gait cycle time Largest Lyap. exp. (Az) Mean amplitude (Az) Mean gait cycle time Largest Lyap. exp. (Az) Mean amplitude (Az) Largest Lyap. exp. (Az) Mean amplitude (Az) Mean amplitude (Az)
Area (negative) 1
2.27 10 2.36 3.81 101 4.01 7.87 103 1.29 103 1.33 102 1.13 102 1.15 101 1.22 103
Area (positive) 2.00 101 1.73 1.78 101 2.89 6.40 103 6.64 104 1.06 102 7.45 103 1.14 101 1.87 103
If the area in negative lag region is larger than that in positive lag region, then it implies that the changes in the variable X preceded that in the variable Y.
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Fig. 8. Time courses of (a), (b) mean HR and (c), (d) LF/HF of HRV during the walking task. (a), (c) Group A; (b), (d) Group B. Mean values with standard deviation bars are shown. (e) Mean HR at rest before the walking task. Vertical bars indicate the standard deviations. Group A showed a significantly lower mean HR at rest than Group B (p=0.02). Table 2 Values of coefficients of each predictor variable in multiple linear regression model for physical fatigue index, and the correlation coefficient between the subjective fatigue level and the fatigue level predicted using the model
MPF of EMG from TA CV of gait cycle time Mean gait cycle time Largest Lyap. exp. (Az) Mean amplitude (Az) LF/HF Correlation coefficient (r)
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0.06 139.90 7.48 — 4.77 0.05 0.77
0.24 161.29 — — 5.45 — 0.77
(Fig. 4(a)), and mean amplitude of vertical acceleration signal (Az) (Fig. 6(e)) and significant decrease in the largest Lyapunov exponent (local dynamical unstability) of Az (Fig. 5(e)) with elapsed time.
4. Group B showed significant increase in the largest Lyapunov exponent (local dynamical unstability) of acceleration signals in all three directions (Figs. 5(b), (d), (f)) and mean amplitude of medio-lateral acceleration signal (Ay) (Fig. 6(d)). 5. Group A showed significantly lower HR at rest before the walking task than Group B (Fig. 8(e)). 6. LF/HF of HRV tended to increase in Group A, whereas it did not tend to either increase or decrease in Group B. The objection will be raised that shifts in these variables were too small as compared with betweensubject variance (Figs. 2–6). However, most of the subjects showed clear monotonous increases or decreases from their own baseline level with time and this resulted in the statistical significance.
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Previous studies showed that the MPF of EMG signals is decreased by the muscle fatigue induced by static isometric exercises (Merletti et al., 1991) and relatively high-intensity dynamic movement such as running, cycling, and skiing (Bonato et al., 1996; Kiryu et al., 1998, 1999; Mizrahi et al., 2000a, b). In the present study, MPF of EMG recorded from TA decreased with elapsed time in Group A (Fig. 2(a)). This suggests that the MPF of EMG can be used to assess local muscle fatigue induced by even relatively low-intensity dynamic movement such as walking. Group B did not show significant decrease in MPF of EMG from TA (Fig. 2(b)). This suggests that Group A showed higher local muscle fatigue at TA than Group B. MPF of EMG recorded from BF did not show any significant change with time. This suggests that long-term walking more strongly affects those muscles that act at the ankle than those that act at the knee. We mainly discuss the result for Group A in this paper, since Group A showed significantly higher level of subjective fatigue and local muscle fatigue at TA than Group B. In Group A subjects, changes in several gait and physiological variables reached the 5% significant level in the following order (Figs. 2–6(a)): (decreased MPF of EMG from TA) - (increased CV of gait cycle time) - (increased mean gait cycle time) - (decreased largest Lyapunov exponent of Az) and (decreased mean amplitude of Az). This order was also observed in the onset timing of the shorter-time-increment time courses (Fig. 7) and was confirmed by cross correlation analysis (Table 1). Dingwell et al. (2000) showed that (i) peripheral neuropathy patients walk slower with higher stride-tostride variability and with better local dynamic stability than control normal subjects, and (ii) strong negative correlation between walking speed and local dynamic stability in both peripheral neuropathy patients and control normal subjects, which supports the hypothesis that decreases in walking speed are a compensatory strategy to enhance local dynamical stability in order to keep from falling. Since the phenomenon (i) is similar to that observed in Group A subjects with higher subjective fatigue in our study (Figs. 3–5), Group A subjects with higher subjective fatigue might take the same compensatory strategy as the peripheral neuropathy patients, although the similarity might come only from a biomechanical point of view. Mizrahi et al. (2000a, b) and Voloshin et al. (1998) suggested that the fatigued musculoskeletal system is less able to attenuate heel strike-initiated shock waves, which could be observed as increase in the amplitude of the acceleration measured at the shank and sacrum. Since the mean gait cycle time in their study increased significantly with elapsed running time, subjects in their study can be classified as Group A in our terminology. In our study, the acceleration amplitude at the back-
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waist near the sacrum decreased in Group A subjects (Fig. 6(e)), while in Mizrahi et al.’s study (2000a, b) it increased. This difference might be due to the fact that the subjects in Mizrahi et al.’s study (2000a, b) ran on a treadmill with a pre-determined constant velocity, whereas the subjects in our study walked on the ground at their self-determined preferred speed and therefore had more options to select optimal gait patterns as they became fatigued. It is therefore natural to think the following three possibilities for the factors making the difference. Those are (i) decrease in walking speed in our study, (ii) decrease in initial intensity of the heel-strike impact intensity in our study, and (iii) difference between running and walking. From these observations and arguments, we propose the following hypothetical model of the gait and physiological response to physical fatigue by the Group A subjects. That is, muscle fatigue at the TA is followed by instability of the gait rhythm, after which subjects slowed the gait rhythm in order to enhance local dynamical stability in the vertical direction to keep from falling. The HR during the walking task was almost constant for the first 120 min, after which it tended to increase gradually in both groups (Fig. 8(a),(b)). Saito et al. (1997) showed that long-term cycling at a constant low intensity (40% maximum oxygen uptake) would cause an increase in HR with exercise time. Although exercise intensity was not constant during the walking task in our study, the result of HR change was consistent with theirs. In Group A in the present study, the LF/HF of RR-interval variability tended to increase gradually suggesting that sympathetic nerve activity tended to increase during prolonged walking (Fig. 8(c)). To apply these results to practical problems, such as assessing fatigue during daily life, we constructed a physical fatigue index for young (age 18–29) male described by multiple linear regression of the gait and physiological variables. The types of independent variables for linear regression selected by best subsets regression analysis varied depending on the groups. Mean gait cycle time and LF/HF of HRV were not selected for the parameters for linear regression in Group B. This suggests that oscillatory frequency of gait rhythm and sympathetic nervous activity in Group B were less affected by fatigue and more stable throughout the long-term walking than Group A. We consider that underlying mechanisms (which are unknown at the moment) between Groups A and B are different, and this leads to the different types of independent variables. Since we do not compare the values of fatigue indices between Groups A and B and use them separately, defining two types of indices has little problem. The correlation coefficient between the fatigue level predicted and the subjective fatigue level obtained was relatively high for both groups (r=0.77) (Table 2).
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We close our argument after discussing the possible factors dividing subjects into two groups. Subjects were asked to answer their self-confidence level (10-point linear scale) on long-distance walking before the experiment. Group B tended to show higher selfconfidence level than Group A (Group A: 5.472.7, Group B: 7.173.2). Moreover, three subjects from Group B play sports more frequently than three times a week or run marathons. These facts suggest that Group B has relatively higher level of stamina than Group A. This might be the main factor causing the differences between the two groups on gait and physiological rhythm during the long-term walking task. Those are (i) Group B did not slow down their gait rhythm and showed more stable gait rhythm than Group A, (ii) Group B did not show significant muscular fatigue, and (iii) the level of sympathetic nerve activity evaluated by LF/HF of HRV was more stable throughout the longdistance walking than Group A. Group B subjects showed higher HR before the walking task than Group A (Fig. 8(e)). If we assume that the maximum HR does not differ among age-matched subjects (Fox et al., 1971), this result suggests that (maximum HR reserve)=(maximum HR)(resting HR) of Group A subjects is greater than that of Group B subjects. This contradicts with the former discussion that Group B might have higher level of stamina than Group A. More detailed analysis on physiological differences between the two groups is left for future work. References Akaike, H., 1974. A newlook at the statistical accuracy. IEEE Transactions on Automatic Control AC-19, 716–723. Akselrod, S., Gordon, D., Ubel, F.A., Shannon, D.C., Barger, A.C., Cohen, R.J., 1981. Power spectrum analysis of heart rate fluctuation: a quantitative probe of beat-to-beat cardiovascular control. Science 213, 220–222. Bonato, P., Gagliati, G., Knaflitz, M., 1996. Analysis of myoelectric signals recorded during dynamic contractions: a time-frequency approach to assessing muscle fatigue. IEEE Magazine of Medicine and Biology 15, 102–111. Cohen, S., Kessler, R.C., Gordon, L.U., 1995. Measuring Stress, A Guide for Health and Social Scientists. Oxford University Press, Oxford. Dingwell, J.B., Cusumano, J.P., 2000. Nonlinear time series analysis of normal and pathological human walking. Chaos 10, 848–863.
Dingwell, J.B., Cusumano, J.P., Sternad, D., Cavanagh, P.R., 2000. Slower speeds in patients with diabetic neuropathy lead to improved local dynamic stability of continuous overground walking. Journal of Biomechanics 33, 1269–1277. Dingwell, J.B., Cusumano, J.P., Cavanagh, P.R., Sternad, D., 2001. Local dynamic stability versus kinematic variability of continuous overground and treadmill walking. Journal of Biomechanical Engineering 123, 27–32. Fox, S.M., Naughton, J.P., Haskell, W.L., 1971. Physical activity and the prevention of coronary heart disease. Annals of Clinical Research 3, 404–432. Hancock, P.A., Desmond, P.A. (Eds.), 2000. Stress, Workload, and Fatigue. Lawrence Erlbaum Associates, London. Kennel, M.B., Brown, R., Abarbanel, H.D.I., 1992. Determining embedding dimension for phase-space reconstruction using a geometric construction. Physical Review A 45, 3403–3411. Kiryu, T., Takahashi, K., Ogawa, K., 1998. Multivariate analysis of muscular fatigue during bicycle ergometer exercise. IEEE Transactions on Biomedical Engineering 45 (10), 1194–1204. Kiryu, T., Motomiya, N., Ushiyama, Y., Okada, M., 1999. Evaluation of fatigue using heart rate variability and myoelectric signals during skiing. Proceedings of the 21th Annual International Conference of the IEEE/EMBS, Atlanta, p. 585. Merletti, R., Lo Conte, L.R., Orizio, C., 1991. Indices of muscle fatigue. Journal of Electromyography and Kinesiology 1, 20–33. Mizrahi, J., Verbitsky, O., Isakov, E., 2000a. Fatigue-related loading imbalance on the shank in running: a possible factor in stress fractures. Annals of Biomedical Engineering 28, 463–469. Mizrahi, J., Verbitsky, O., Isakov, E., Daily, D., 2000b. Effect of fatigue on leg kinematics and impact acceleration in long distance running. Human Movement Science 19, 139–151. Nakamura, Y., Yamamoto, Y., Muraoka, I., 1993. Autonomic control of heart rate during physical exercise and fractal dimension of heart rate variability. Journal of Applied Physiology 74, 875–881. Oida, E., Moritani, T., Yamori, Y., 1997. Tone-entropy analysis on cardiac recovery after dynamic exercise. Journal of Applied Physiology 82, 1794–1801. Rosenstein, M.T., Collins, J.J., De Luca, C.J., 1993. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65, 117–134. Saito, M., Sone, R., Ikeda, M., Mano, T., 1997. Sympathetic outflow to the skeletal muscle in humans increases during prolonged light exercise. Journal of Applied Physiology 82, 1237–1243. Takens, F., 1980. Detecting strange attractors in turbulence. In: Rands, D.A., Young, L.S. (Eds.), Dynamical Systems and Turbulence. Springer, Berlin, Heidelberg, New York, pp. 366–381. Voloshin, A.S., Mizrahi, J., Verbitsky, O., Isakov, E., 1998. Dynamic loading on the human musculoskeletal system—effect of fatigue. Clinical Biomechanics 13, 515–520. Yokoi, T., Takahashi, A., Kizuka, T., 1998. Kinematic description of self-organized leg motion transition in human locomotion learning. Journal of Robotics and Mechatronics 10, 333–337.
Journal of Biomechanics 37 (2004) 1271–1280
Effect of prolonged free-walking fatigue on gait and physiological rhythm Kohzoh Yoshinoa,*, Tomoko Motoshigeb, Tsutomu Arakib, Katsunori Matsuokaa a
Human Stress Signal Research Center, National Institute of Advanced Industrial Science and Technology (AIST), 1-8-31 Midorigaoka, Ikeda, Osaka 563 8577, Japan b Department of Mechanical Science and Bioengineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560 8531, Japan Accepted 6 November 2003
Abstract This study examined the ways in which gait patterns and physiological rhythms such as those of muscle activity (tibialis anterior (TA) and biceps femoris (BF)) and cardiac activity are affected by the fatigue induced by prolonged free walking. Twelve normal subjects who walked for 3 h at their preferred pace were divided into two groups according to whether their mean gait cycle time (reciprocal of stride rate) during the second 90 min was higher (Group A: n=8) or lower (Group B: n=4) than that during the first 90 min. For Group A, the level of subjective fatigue during the walking task was significantly higher and the heart rate at rest was significantly lower than Group B. In Group A, prolonged walking significantly decreased the mean power frequency of the electromyography from TA, increased the variability of gait rhythm, decreased the largest Lyapunov exponent of the vertical component of back-waist acceleration, and decreased the amplitude of the vertical component of back-waist acceleration. Taking the onset timings of these changes into account, we propose that subjects who tire easily during prolonged walking first show local muscle fatigue at TA followed by instability of gait rhythm and then they slow their gait rhythm to enhance local dynamic stability. For both groups we constructed a physical fatigue index described by linear regression of gait and physiological variables. When we compared the subjective fatigue level with the fatigue level predicted using the index, we obtained a relatively high correlation coefficient for both groups (r=0.77). r 2003 Elsevier Ltd. All rights reserved. Keywords: Fatigue; Prolonged walking; Electromyography; Lyapunov exponent; Heart rate
1. Introduction Fatigue is recognized as a serious social problem, and an important step in overcoming it is the development of indices for evaluating fatigue during daily life (Cohen et al., 1995; Hancock and Desmond, 2000). Several studies have shown how physiological electric signals change their features in the time and frequency domains as a result of the physical fatigue induced by movement. The mean power frequency (MPF) of an electromyography (EMG) signal, for example, is known to be shifted downward by the muscle fatigue induced by static isometric contraction (Merletti et al., 1991) and by dynamic movements such as running (Mizrahi et al., 2000a), cycling (Bonato et al., 1996; Kiryu et al., 1998), *Corresponding author. Tel.: +81-727-51-8243; fax: +81-727-519961. E-mail address: [email protected] (K. Yoshino). 0021-9290/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2003.11.031
and skiing (Kiryu et al., 1999). Mizrahi et al. (2000a) and Voloshin et al. (1998) used accelerometers to measure the amplitude of the shock waves induced by heel strikes and found that the amplitude measured at the shank and sacrum increased during long-distance treadmill running. This indicates that fatigue reduces the ability of the musculoskeletal system to attenuate the shock waves. Heart rate variability (HRV) analysis is often used to evaluate autonomous nerve activity indirectly (Akselrod et al., 1981). The heart rate (HR) and the ratio of lowfrequency (LF; 0.04–0.15 Hz) power to high-frequency (HF; over 0.15 Hz) power (index of sympathetic nerve activity, although it is not fully accepted during exercise (Oida et al., 1997)), increase with exercise intensity (Nakamura et al., 1993). Saito et al. (1997) showed that HR increases during prolonged cycling at a constant low intensity. Our goal is to develop an index for assessing fatigue during daily life using physiological electric signals. Gait
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acceleration, EMG, and HRV were selected for the signals, since these signals can be measured during daily life by wearable sensor technology. Although locomotion is one of the most frequent events in our daily life, no other study has shown how the physiological electric signals measured during locomotion are affected by the fatigue induced by long-term walking. Moreover, since other studies related to prolonged exercise fatigue focused on the constant exercise intensity protocol, little is known about the preferred gait pattern people select under fatigue conditions. One study showed that stride rate of treadmill running at a given speed decreases by prolonged running fatigue (Mizrahi et al., 2000b). In this study, we examined how long-term free walking affects gait pattern and physiological rhythms such as those of muscle activity, back-waist acceleration, and cardiac activity. Using the results, we constructed a physical fatigue index for young (age 18–29) males described by linear regression of the gait and physiological variables. The purpose of the proposed index is for predicting subjective fatigue automatically using objective indices measured during preferred pace walking in daily life.
2. Methodology Twelve normal male subjects (age 19–26) participated in this study after having provided their informed written consent as approved by the Ethical Committee on Human Research at AIST Kansai. Subjects were instructed to walk 3 h continuously at their self-determined preferred pace on level ground. Subjects reported their subjective fatigue level (10-point linear scale) every 30 min. The lowest level (1) and the highest level (10) represent ‘not fatigued at all’ and ‘more fatigued than ever’, respectively. Each subject sat on a chair for 15 min before and after the walking task. The surface EMGs of the tibialis anterior (TA; dorsiflexor of the ankle) and biceps femoris (BF; flexor of the knee) of the right leg were recorded from a pair of Ag–AgCl electrodes (interelectrode distance 3 cm) after cleansing the skin by alcohol. A strain-gauge-type triaxial accelerometer (AS-5TG, Kyowa, Japan) was clipped tightly on a belt tightened around subjects’ waist, and was located around the center of L5-S1 intervertebal disk to measure back-waist accelerations in the anterior–posterior (Ax), medio-lateral (Ay), and vertical (Az) directions. The reproducibility of the accelerometer was assessed by comparing the mean value (baseline level) of the back-waist acceleration during the beginning period (0–15 min) and during the ending period (165–180 min) of the walking task. The difference between the two periods in each direction was less than 1% of the mean amplitude during walking. This verifies the reproducibility of the accelerometer.
The ECG was recorded from a pair of Ag–AgCl electrodes placed on the chest. All analog signals were amplified and digitized at 1 kHz sampling rate and stored on a compact flash card placed inside a portable recorder (DR-C2, TEAC, Japan) (analog band-pass filter: EMG:10–500 Hz, ECG:0.05–200 Hz). The data collected during the 3-h walking tasks were divided into 12 non-overlapping data sets 15 min long, and the subjects were divided into two groups according to whether the mean gait cycle time (reciprocal of the stride rate) in the second 90 min was longer (Group A) or shorter (Group B) than that in the first 90 min. The following physiological and gait variables were calculated for each 15-min set for each subject and averaged among subjects in their corresponding group. (i) MPF of EMG signal: MPF ¼
fH X f ¼fL
ðfPðf ÞÞ=
fH X
ðPðf ÞÞ;
ð1Þ
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where f denotes frequency, P(f) is 215 points averaged fast Fourier transform (FFT) power spectrum of EMG signals, fL=20 Hz, and fH=300 Hz. (ii) Mean gait cycle time (reciprocal of stride rate): To compute the gait cycle time, we first extracted the minimum peaks of the Ax signals by detecting minimum points after the downward threshold crossing. Since acceleration was measured at the center part of the back waist, Ax shows the effect of both right and left steps. The gait cycle time was therefore obtained as the length of the interval between alternate minimum peaks of Ax. The mean value of the gait cycle time series in each 15min set was calculated. (iii) Coefficient of variation (CV) of gait cycle time: The CV of the gait cycle time is the ratio of the standard deviation of the gait cycle time to the mean gait cycle time. (iv) Largest finite-time Lyapunov exponent of backwaist acceleration signal: The Lyapunov exponent is the mean exponential rate of divergence of initially nearby points, thus quantifying local dynamical stability (Dingwell and Cusumano, 2000; Dingwell et al., 2000, 2001; Yokoi et al., 1998). We estimated the largest finite-time Lyapunov exponent of down-sampled (100 Hz) Ax, Ay, and Az by using the algorithm proposed by Rosenstein et al. (1993) as follow. The attractor dynamics was reconstructed by taking embedding delayed samples (Takens, 1980). The time lag was determined by the time at which the autocorrelation dropped to 1/e of the value at time zero. The embedding dimension was set to five from the result of false nearest neighbor analysis (Kennel et al., 1992). The largest Lyapunov exponent was estimated by calculating the slope of linear fits to the log-scaled curve of the divergence distance between neighboring trajectories in the reconstructed phase space. To exclude the
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effect of different gait cycle times among data, the time axis for the divergence curve was rescaled by dividing by the mean gait cycle time. The range of the region calculating the slope was from 0.5 to 4 gait cycle times. (v) Mean amplitude of back-waist acceleration: The amplitude of back-waist acceleration in each gait cycle was obtained by subtracting the maximum value from the minimum value. The mean value of the amplitude sequence in each 15-min set was calculated. Variables (i)–(v) derived from acceleration signals represent fundamental properties of gait rhythm. Those are associated with oscillatory frequency, static stability (variability), dynamical stability, and amplitude of the gait rhythm. Before the analysis, we considered that these fundamental properties of gait rhythm have a possibility to be modulated by fatigue. (vi) Heart rate (HR): R-waves were detected from each ECG waveform, and then time intervals between two successive R-waves (RR interval) were calculated. The mean RR interval was calculated for each 15-min set during the walking task and for the rest task. HR (beats/min) was obtained by dividing 60 by the mean RR interval. HR was obtained in order to investigate how sympathetic nerve activity during exercise is modified by fatigue. (vii) LF/HF of RR-interval fluctuation: The sympathetic nerve activity was also evaluated by calculating LF/HF, the ratio of the LF component (0.04–0.15 Hz) to the HF component (0.15–0.7 Hz) of the 27 points averaged FFT power spectrum of RRinterval fluctuation. Two-factor (set (time) group) ANOVA with Tukey’s honestly significant difference test was applied to these data, and statistical significance was determined at po0.05. To develop a technology using physiological electric signals to assess fatigue during daily life, we constructed
a physical fatigue index by using multiple linear best subsets regression model analysis for each group. The dependent variable of the model was the subjective level of fatigue and the candidates for independent (predictor) variables of the model were MPF of EMG from TA, CV of gait cycle time, mean gait cycle time, the largest Lyapunov exponent of Az, mean amplitude of Az, and LF/HF of RR-interval fluctuation. We calculated Akaike Information Criterion (AIC) (Akaike, 1974) for all possible combinations of predictor variables. The combination which gives the minimum AIC was selected for the optimal model for each group.
3. Results Eight of the 12 subjects constituted Group A, and the other four subjects constituted Group B. Group A (age 23.1271.55) was significantly older than Group B (age 20.7571.25) (p=0.02). For both groups the mean subjective levels of fatigue increased monotonically with time, but from 60 min onwards those of Group A were significantly higher than those of Group B (Fig. 1). The MPF of EMG signal recorded from the TA decreased significantly (compared with the first 15 min) from 105 min onwards in Group A (Fig. 2(a)). It did not change significantly with time in Group B (Fig. 2(b)). The MPF of EMG signal recorded from the BF did not change significantly with time in either group (figures not shown). The CV of the gait cycle time increased significantly (compared with the first 15 min) from 120 min onwards in Group A (Fig. 3(a)), whereas it tended to decrease gradually with time in Group B (Fig. 3(b)). Mean gait cycle time increased significantly (compared with the first 15 min) from 135 min onwards in
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The mean amplitude of Az decreased significantly, compared with the 30–45 min, from 150 to 165 min in Group A (Fig. 6(e)). The mean amplitude of Ay increased significantly, compared with the first 15 min, from 105 min onwards in Group B (Fig. 6(d)). To obtain more precise onset timing of the changes in these variables, we divided the walking-task data into shorter time increments, each 1.8 min long (thus 100 sets), and recalculated the variables for each set. We used 1.8 min long intervals because it is difficult to
Group A (Fig. 4(a)), whereas it tended to decrease gradually with time in Group B (Fig. 4(b)). The largest finite-time Lyapunov exponent of Az decreased significantly (compared with the 15–30 min) from 150 min onwards in Group A (Fig. 5(e)). In Group B, however, the largest finite-time Lyapunov exponent of back-waist accelerations in all three directions Ax, Ay, and Az increased significantly, compared with the first 15 min, respectively, from 135 to 165 min, from 150 min onwards, and from 120 to 165 min (Figs. 5(b), (d), (f)).
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Fig. 5. Time courses of largest finite-time Lyapunov exponent of back-waist acceleration signals in (a), (b) anterior–posterior direction (Ax), (c), (d) medio-lateral direction (Ay), and (e), (f) vertical direction (Az). (a), (c), (e) Group A; (b), (d), (f) Group B. Mean values with standard deviation bars are shown. Significant differences (po0.05) from the first 15 min are indicated by asterisks, and those from 15 to 30 min are indicated by diamonds.
calculate Lyapunov exponents from data sets shorter than this. The results for Group A are shown in Fig. 7, where it can be seen that (a) the MPF of EMG signal recorded from the TA changed from the beginning, (b) the CV of the gait cycle time followed it after about 15 min, and (c) the mean gait cycle time, (d) the largest Lyapunov exponent of Az, and (e) the mean amplitude of Az all began to change after various time lags 30– 50 min after the beginning of the walking task. To confirm this, we calculated the cross-correlation function between each combination of two variables X and Y in Fig. 7 and compared the area of the function the negative lag region (50 to 0 min) and that the positive lag region (0 to +50 min). If the area in the negative lag region is larger than that in the positive lag region, this implies that the changes in the variable X preceded those in variable Y. We used the area instead of the peak lag because clear monopeaks were not observed in several
cross-correlation functions. The results are shown in Table 1 and implies the following order: (decreased MPF of EMG from tibialis anterior) - (increased CV of gait cycle time) - (increased mean gait cycle time) (decreased largest Lyapunov exponent of Az) and (decreased mean amplitude of Az). The mean HR during the walking task was almost constant until 120 min from the beginning, and it tended to increase gradually during the last 60 min in both groups (Figs. 8(a),(b)). The LF/HF of RR-interval variability tended to increase gradually in Group A (Fig. 8(c)), but it did not either increase or decrease in Group B (Fig. 8(d)). The mean HR of Group A subjects at rest before the walking task was significantly lower than that of Group B subjects (p=0.02) (Fig. 8(e)). We applied best subsets regression analysis to the data in order to construct a physical fatigue index described by multiple linear regression of gait and physiological
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Fig. 6. Time courses of mean amplitude of back-waist acceleration signals in (a), (b) anterior–posterior direction (Ax), (c), (d) medio-lateral direction (Ay), and (e), (f) vertical direction (Az). (a), (c), (e) Group A; (b), (d), (f) Group B. Mean values with standard deviation bars are shown. Significant differences (po0.05) from the first 15 min are indicated by asterisks, and those from 15 to 30 min are indicated by diamonds.
variables for each group. The optimal combination of predictor variables was MPF of EMG from TA, CV of gait cycle time, mean gait cycle time, mean amplitude of Az, and LF/HF in Group A, and MPF of EMG from TA, CV of gait cycle time, and mean amplitude of Az in Group B. The values of regression coefficients of each variable are summarized in Table 2. The correlation coefficient between the predicted fatigue level using the index and the subjective fatigue level was r=0.77 for both groups.
4. Discussion We examined the gait and physiological variables whose values changed with time during the prolonged walking task, since the level of subjective fatigue
increased with elapsed time (Fig. 1). We divided the subjects into two groups according to whether the mean gait cycle time during the second half of the walking task was longer (Group A) or shorter (Group B) than that in the first half. Group A subjects reported subjective fatigue levels significantly higher than those reported by Group B subjects (Fig. 1). Main results are summarized as follow. 1. Group A subjects reported subjective fatigue levels significantly higher than those reported by Group B subjects (Fig. 1). 2. Group A showed significant decrease in MPF of EMG from TA (Fig. 2(a)) with elapsed time, whereas no significant change was observed in Group B (Fig. 2(b)). 3. Group A showed significant increase in stride-tostride variability (Fig. 3(a)), mean gait cycle time
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CV of gait cycle time
MPF (Hz)
93
90
0.03
0.02 87 0
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Largest Lyapunov Exponent
Mean gait cycle time (sec)
0.16 1.2
1.1
0.13
0.1 0
30
60
Mean amplitude of Ay (G)
(c)
90 120 Time (min)
150
90 120 Time (min)
150
180
(d)
1.2
1 0
(e)
30
60
180
Fig. 7. For Group A subjects, shorter-time-increment (1.8 min) time courses of (a) MPF of EMG recorded from TA, (b) CV of gait cycle time, (c) mean gait cycle time, (d) largest Lyapunov exponent of Az, and (e) mean amplitude of Az.
Table 1 Area in negative lag region (50 min to 0 min) and in positive lag region (0 to +50 min) of the cross correlation function between two variables X and Y Variable X MPF of EMG from TA MPF of EMG from TA MPF of EMG from TA MPF of EMG from TA CV of gait cycle time CV of gait cycle time CV of gait cycle time Mean gait cycle time Mean gait cycle time Largest Lyap. exp. (Az)
Variable Y CV of gait cycle time Mean gait cycle time Largest Lyap. exp. (Az) Mean amplitude (Az) Mean gait cycle time Largest Lyap. exp. (Az) Mean amplitude (Az) Largest Lyap. exp. (Az) Mean amplitude (Az) Mean amplitude (Az)
Area (negative) 1
2.27 10 2.36 3.81 101 4.01 7.87 103 1.29 103 1.33 102 1.13 102 1.15 101 1.22 103
Area (positive) 2.00 101 1.73 1.78 101 2.89 6.40 103 6.64 104 1.06 102 7.45 103 1.14 101 1.87 103
If the area in negative lag region is larger than that in positive lag region, then it implies that the changes in the variable X preceded that in the variable Y.
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Mean Heart Rate (beats/min)
Mean Heart Rate (beats/min)
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90 120 Time (min)
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100
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(b)
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LF/HF
LF/HF
(a)
120
20
10
20
10
0
30
60
(c)
90 120 Time (min)
150
180
(d)
Mean Heart Rate (beats/min)
p=0.02
(e)
100
50
0 Group A
Group B
Fig. 8. Time courses of (a), (b) mean HR and (c), (d) LF/HF of HRV during the walking task. (a), (c) Group A; (b), (d) Group B. Mean values with standard deviation bars are shown. (e) Mean HR at rest before the walking task. Vertical bars indicate the standard deviations. Group A showed a significantly lower mean HR at rest than Group B (p=0.02). Table 2 Values of coefficients of each predictor variable in multiple linear regression model for physical fatigue index, and the correlation coefficient between the subjective fatigue level and the fatigue level predicted using the model
MPF of EMG from TA CV of gait cycle time Mean gait cycle time Largest Lyap. exp. (Az) Mean amplitude (Az) LF/HF Correlation coefficient (r)
Group A
Group B
0.06 139.90 7.48 — 4.77 0.05 0.77
0.24 161.29 — — 5.45 — 0.77
(Fig. 4(a)), and mean amplitude of vertical acceleration signal (Az) (Fig. 6(e)) and significant decrease in the largest Lyapunov exponent (local dynamical unstability) of Az (Fig. 5(e)) with elapsed time.
4. Group B showed significant increase in the largest Lyapunov exponent (local dynamical unstability) of acceleration signals in all three directions (Figs. 5(b), (d), (f)) and mean amplitude of medio-lateral acceleration signal (Ay) (Fig. 6(d)). 5. Group A showed significantly lower HR at rest before the walking task than Group B (Fig. 8(e)). 6. LF/HF of HRV tended to increase in Group A, whereas it did not tend to either increase or decrease in Group B. The objection will be raised that shifts in these variables were too small as compared with betweensubject variance (Figs. 2–6). However, most of the subjects showed clear monotonous increases or decreases from their own baseline level with time and this resulted in the statistical significance.
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Previous studies showed that the MPF of EMG signals is decreased by the muscle fatigue induced by static isometric exercises (Merletti et al., 1991) and relatively high-intensity dynamic movement such as running, cycling, and skiing (Bonato et al., 1996; Kiryu et al., 1998, 1999; Mizrahi et al., 2000a, b). In the present study, MPF of EMG recorded from TA decreased with elapsed time in Group A (Fig. 2(a)). This suggests that the MPF of EMG can be used to assess local muscle fatigue induced by even relatively low-intensity dynamic movement such as walking. Group B did not show significant decrease in MPF of EMG from TA (Fig. 2(b)). This suggests that Group A showed higher local muscle fatigue at TA than Group B. MPF of EMG recorded from BF did not show any significant change with time. This suggests that long-term walking more strongly affects those muscles that act at the ankle than those that act at the knee. We mainly discuss the result for Group A in this paper, since Group A showed significantly higher level of subjective fatigue and local muscle fatigue at TA than Group B. In Group A subjects, changes in several gait and physiological variables reached the 5% significant level in the following order (Figs. 2–6(a)): (decreased MPF of EMG from TA) - (increased CV of gait cycle time) - (increased mean gait cycle time) - (decreased largest Lyapunov exponent of Az) and (decreased mean amplitude of Az). This order was also observed in the onset timing of the shorter-time-increment time courses (Fig. 7) and was confirmed by cross correlation analysis (Table 1). Dingwell et al. (2000) showed that (i) peripheral neuropathy patients walk slower with higher stride-tostride variability and with better local dynamic stability than control normal subjects, and (ii) strong negative correlation between walking speed and local dynamic stability in both peripheral neuropathy patients and control normal subjects, which supports the hypothesis that decreases in walking speed are a compensatory strategy to enhance local dynamical stability in order to keep from falling. Since the phenomenon (i) is similar to that observed in Group A subjects with higher subjective fatigue in our study (Figs. 3–5), Group A subjects with higher subjective fatigue might take the same compensatory strategy as the peripheral neuropathy patients, although the similarity might come only from a biomechanical point of view. Mizrahi et al. (2000a, b) and Voloshin et al. (1998) suggested that the fatigued musculoskeletal system is less able to attenuate heel strike-initiated shock waves, which could be observed as increase in the amplitude of the acceleration measured at the shank and sacrum. Since the mean gait cycle time in their study increased significantly with elapsed running time, subjects in their study can be classified as Group A in our terminology. In our study, the acceleration amplitude at the back-
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waist near the sacrum decreased in Group A subjects (Fig. 6(e)), while in Mizrahi et al.’s study (2000a, b) it increased. This difference might be due to the fact that the subjects in Mizrahi et al.’s study (2000a, b) ran on a treadmill with a pre-determined constant velocity, whereas the subjects in our study walked on the ground at their self-determined preferred speed and therefore had more options to select optimal gait patterns as they became fatigued. It is therefore natural to think the following three possibilities for the factors making the difference. Those are (i) decrease in walking speed in our study, (ii) decrease in initial intensity of the heel-strike impact intensity in our study, and (iii) difference between running and walking. From these observations and arguments, we propose the following hypothetical model of the gait and physiological response to physical fatigue by the Group A subjects. That is, muscle fatigue at the TA is followed by instability of the gait rhythm, after which subjects slowed the gait rhythm in order to enhance local dynamical stability in the vertical direction to keep from falling. The HR during the walking task was almost constant for the first 120 min, after which it tended to increase gradually in both groups (Fig. 8(a),(b)). Saito et al. (1997) showed that long-term cycling at a constant low intensity (40% maximum oxygen uptake) would cause an increase in HR with exercise time. Although exercise intensity was not constant during the walking task in our study, the result of HR change was consistent with theirs. In Group A in the present study, the LF/HF of RR-interval variability tended to increase gradually suggesting that sympathetic nerve activity tended to increase during prolonged walking (Fig. 8(c)). To apply these results to practical problems, such as assessing fatigue during daily life, we constructed a physical fatigue index for young (age 18–29) male described by multiple linear regression of the gait and physiological variables. The types of independent variables for linear regression selected by best subsets regression analysis varied depending on the groups. Mean gait cycle time and LF/HF of HRV were not selected for the parameters for linear regression in Group B. This suggests that oscillatory frequency of gait rhythm and sympathetic nervous activity in Group B were less affected by fatigue and more stable throughout the long-term walking than Group A. We consider that underlying mechanisms (which are unknown at the moment) between Groups A and B are different, and this leads to the different types of independent variables. Since we do not compare the values of fatigue indices between Groups A and B and use them separately, defining two types of indices has little problem. The correlation coefficient between the fatigue level predicted and the subjective fatigue level obtained was relatively high for both groups (r=0.77) (Table 2).
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We close our argument after discussing the possible factors dividing subjects into two groups. Subjects were asked to answer their self-confidence level (10-point linear scale) on long-distance walking before the experiment. Group B tended to show higher selfconfidence level than Group A (Group A: 5.472.7, Group B: 7.173.2). Moreover, three subjects from Group B play sports more frequently than three times a week or run marathons. These facts suggest that Group B has relatively higher level of stamina than Group A. This might be the main factor causing the differences between the two groups on gait and physiological rhythm during the long-term walking task. Those are (i) Group B did not slow down their gait rhythm and showed more stable gait rhythm than Group A, (ii) Group B did not show significant muscular fatigue, and (iii) the level of sympathetic nerve activity evaluated by LF/HF of HRV was more stable throughout the longdistance walking than Group A. Group B subjects showed higher HR before the walking task than Group A (Fig. 8(e)). If we assume that the maximum HR does not differ among age-matched subjects (Fox et al., 1971), this result suggests that (maximum HR reserve)=(maximum HR)(resting HR) of Group A subjects is greater than that of Group B subjects. This contradicts with the former discussion that Group B might have higher level of stamina than Group A. More detailed analysis on physiological differences between the two groups is left for future work. References Akaike, H., 1974. A newlook at the statistical accuracy. IEEE Transactions on Automatic Control AC-19, 716–723. Akselrod, S., Gordon, D., Ubel, F.A., Shannon, D.C., Barger, A.C., Cohen, R.J., 1981. Power spectrum analysis of heart rate fluctuation: a quantitative probe of beat-to-beat cardiovascular control. Science 213, 220–222. Bonato, P., Gagliati, G., Knaflitz, M., 1996. Analysis of myoelectric signals recorded during dynamic contractions: a time-frequency approach to assessing muscle fatigue. IEEE Magazine of Medicine and Biology 15, 102–111. Cohen, S., Kessler, R.C., Gordon, L.U., 1995. Measuring Stress, A Guide for Health and Social Scientists. Oxford University Press, Oxford. Dingwell, J.B., Cusumano, J.P., 2000. Nonlinear time series analysis of normal and pathological human walking. Chaos 10, 848–863.
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