AMERICAN JOURNAL OF PHYSICAL AN'FHROPOLOGY 89:19-27 (1992)
Can We Really Walk Straight? TERUO U E T m Department of Health and Physical Education, Faculty of General Education, Tokyo University of Agriculture and Technology, Fuchu, Tokyo 183, Japan
KEY WORDS Footprint, Fourier analysis, Meandering walk, Gait asymmetry ABSTRACT Twenty healthy men were asked to walk as straight as possible t o a target SO m away a t normal speed. A series of footprints was recorded for each subject by having him wear socks soaked with red ink and walk on white paper fixed flat to the floor. Fourier analysis was applied to determine whether the subjects actually were able to walk straight, and the results revealed that all walked in a sinuous line rather than a straight line. Periodicity and amplitude of the meandering differed from subject to subject. These facts suggest that none of us can walk in a strictly straight line; rather, we meander, primarily due to a slight structural or functional imbalance of our limbs, which produces a gait asymmetry, and secondarily due to feedback from our sense of sight, which acts to correct the shifted walking course. 0 1992 Wiley-Liss, h e .
Because bipedal walking is the most common form of human locomotion and is a distinctive human characteristic, it has been the subject of many studies. Chodera and Level1 (1973) reported that the change in pattern of a walking course under different conditions fell into one of three basic shapes: a curve to the left, a curve to the right, or an S-shaped curve, the latter found more frequently at slow walking speed. Nigorikawa f 1988)reported that a man whose sight was obstructed did not walk straight but instead veered to the left or the right. The purpose of the present paper is to clarify whether people can really walk straight or not, and, if not, how the path of a walking person deviates from a straight line. This was undertaken by applying Fourier analysis to the tracks left by subjects walking to a target approximately 60 m away at normal speed. MATERIALS AND METHODS Subjects
The subjects were 20 healthy Japanese men aged 18-45 years. None of them had any history of lower limb problems. Their 0 1992 WILEY-LISS, INC.
mean height was 172.0 cm (SD = 5.55 cm) and their mean weight 65.5 kg (SD = 6.12 kg). The only significant difference between left and right limbs was in forearm length (Table 1). Seventeen of the subjects kicked a ball better with the right foot, the rest with the left (Table 2). Method of recording footprints A piece of white paper 0.8 x 50 m in size
was fixed flat on the floor. The subject, wearing socks soaked with red ink and with pedal switches attached just beneath the heel and the great toe of both feet, was asked to walk at his normal speed in a straight line to a target SO m away. The pedal switch used in this experiment was designed to be as small as possible (-8 mm in diameter and 2 mm thick) so that it might not affect the experimental walking. The pedal switch was made of two fine wires separated by a rubber mat containing fine-grained iron, which was compressed enough under body weight to permit current to flow from one wire to
Received November 8,1990; accepted March 3,1992.
T. UETAKE
20 TABLE 1 , Means for anthropometrical measurement icmi
Right
..._.___ - Left
_-________-____X__ SD Arm length Forearm length2 Hand length Biepicondyle of arm Bistvloid uorc. of forearm Hand breadth Arm girth Forearm girth Thigh length3 Leg length Foot length Foot height Biepicondyle of thigh Bieuicondvle of leg Fooi breadth .Thigh girth Leg girth
31.8 23.0 19.2 6.7 5.6 8.3 27.5 25.6 468 36 2 252
1.43 1.32 0.36 0.29 0.38 1.54 1,34 183 2 55 104
75
0 50
94 74 10.3 52.7 36.8
065 038 0.60 3.37 1.94
SD 30.9 24.2 19.3 6.7 5.7 8.4 27.9 26.2 468 36 o 252 75 95 74 10.2 52.9 36.9
1.87 1.14
putting on the pedal switch and the soaked socks. The subject was instructed to stand in the middle of one end of the paper, to start with his left foot, and to walk at normal speed to the other end of the paper. Subjects following these directions left an average of 72.8 footprints (SD = 6.47). The time (seconds) elapsed from the first heel contact to the last w a s determined from the pedal switch record, and - - the -cadence (strides per second) was calculated as the number of strides divided by the time.
:::; 0.27 0.40 1.49 1.18 173 2 57 100 0 50 071 037 0.58 3.48 1.55
Anthropometrical measurements were taken following the procedures of Martin and Seller (1957). 'The lateral difference is statistically significant iP < 0.01). 3Thigh length = (iliac height - tibia1 height) x 0.93.
the other. During the experimental walking, the pedal switch was covered with a n adhesive vinyl tape so as not to short circuit. An open circuit, made with the pedal switch, a small battery, and a data recorder set apart from the experimental walking course, closed whenever the pedal switch contacted the floor, and the moment of contact was recorded. Before the experiment, a few practice steps were taken by the subject before
Fourier analysis of the pattern of change of the two heel positions
Because the walking cycle during the first four steps was erratic, only steps 5-68 were usually analyzed in this study. However, if a subject did not leave more than 68 steps, his steps from the fifth to the last were analyzed. The distance from the most posterior point of the heel impression to the center line of the paper, referred to here as step width, was measured with a digitizer (Fig. 1).Measurements to the left of the center line of the paper were indicated by a plus symbol, those to the right side by a minus. A n indeterminate form or pattern can be easily quantified using Fourier analysis, which has been used to analyze a variety of biological forms, from crania (Lestrel and Roch, 1986; Lestrel, 1989; Inoue, 1990) and
TABLE 2. Cadrnre and step uidth (em! Cadence
X
0.95 0.85 0.92 0.95 0.93 0.86 1.00 0.92 0.85 0.81 0.78 0.93 0.93 1.05 0.93 1.06 1.06 0.96 0.81 0.96
5.6 0.2 6.3 4.5 0.6 - 5.2 1.5 1.9 - 2.0 3.2 0.3 6.4 11.5 4.5 1.9 1.5 2.2 2.1 12.4 - 1.3
~.
Subj. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
BFS' __ R R R L R R R R R R R R R R L R L R R R
BFS, better font. side for kicking a ball.
~
Left SD
cv
2.91 4.19 3.28 2.25 3.43 6.76 2.24 1.95 1.78 2.52 2.30 2.49 2.87 1.32 1.91 2.23 1.86 1.52 1.58 2.63
2095.0 52.1 50.0 571.7 130.0 149.3 102.6 89.0 78.8 766.7 38.9 25.0 29.3 100.5 148.7 84.5 72.4 12.7 202.3
X _________ 52.0 - 3.8 3.5 0.7 - 3.2 - 2.8 - 2.8 - 4.3 - 5.2 -- 6.0 - 0.5 - 4.7 - 1.1 7.1 - 2.5 - 4.2 3.4 - 4.9 0.8 5.9 - 9.9 -
-
Right _~
.~.
SD 2.61 3.95 3.82 2.01 3.17 2.24 2.29 1.29 2.05 3.09 1.91 2.59 2.64 1.24 1.99 2.10 2.17 1.89 1.72 2.29
CV
__._
68.7 112.9 545.7 62.8 113.2 80.0 53.3 24.8 34.2 618.0 40.6 235.5 37.2 49.6 47.4 61.8 44.3 236.3 29.2 23.1
21
FOOTPRINTS IN NORMAL WALKING I
0
target right and l e f t s t e p w i d t h Fig. 1. Schematic presentation of the walking experiment. TABLE 3. SLW widtt? tor theoretrcal pattern of stey, width change immi
____ Case ____A St, No.'
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Left 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00
Case B
Case C __
~
Right
Left
Right
Left
Right
25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 29.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00
50.00 48.10 42.68 34.57 25.00 15.43 7.32 1.90 0.00 1.90 7.32 15.43 25.00 34.56 42.67 48.10 50.00 48.10 42.68 34.57 25.01 15.44 7.33 1.91 0.00 1.90 7.32 15.43 24.99 34.56 42.67 48.09
- 0.48 - 4.21 - 11.11 - 20.12
50.00 42.68 25.00 7.32 0.00 7.32 25.00 42.67 50.00 42.68 25.01 7.33 0.00 7.32 25.00 42.67 50.00 42.68 25.01 7.33 0.00 7.31 25.00 42.67 50.00 42.69 25.01 7.33 0.00 7.31 25.00 42.66
- 1.90 - 15.43
-
- 29.88 - 38.89 - 45.79 49.52 49.52 45.79 38.89 29.88 - 20.13 - 11.11 - 4.22 - 0.48 - 0.48 -- 4.21 - 11.11 - 20.12 - 29.87 - 38.88 - 45.78 - 49.52 - 49.52 45.79 - 38.90 - 29.88 - 20.13 - 11.12 - 4.22 - 0.48 -
34.57 48.10 48.10 34.57 15.44 - 1.90 - 1.90 - 15.43 - 34.56 - 48.09 - 48.10 - 34.57 - 15.44 -- 1.91 - 1.90 - 15.42 - 34.56 - 48.09 -- 48.10 - 34.58 - 15.44 ---
-
1.91 1.90
- 15.42 34.55 48.10 - 48.10 - 34.58 - 15.45 - 1.91 --
'Step number
mandibles (Halazonetis et al., 1991) to the waveshape of electronystagmograms (Reccia et al., 1990). In this study, taking the step width distance of 64 sequential steps as the axis of the ordinate and step number as the abscissa, Fourier analysis was used to examine patterns of step width change. These data were fed into a Fourier analysis program developed by Hino (1977) for a microcomputer, which yielded coefficients of
cosine and sine and amplitudes in each harmonic as output. If one could walk straight (case A, Table 3), coefficients of cosine or sine and amplitudes would appear only in the 32nd harmonic (Fig. 2A, Table 4). On the other hand, if one walked meanderingly (case B or C, Table 31, that would be reflected not only in the value of the 32nd harmonic but in other harmonics (Fig. 2B,C, Table 4).Because appearance of amplitude in
22
T. U E T m
C
Fig. 2. Theoretical pattern of step width change: Straight walking (A) and meandering walking (B, C). WidtMength ratio of each step is exaggerated by a factor of 7 to display meandering more clearly.
and the number in parentheses indicates the magnitude of amplitude of each harmonic relative to that of the 32nd harmonic. Fifteen subjects among the 20 had the highest amplitude at the 32nd harmonic. The next highest amplitude fell into four groups: 11 (Nos. 1, 4, 8, 9, 11-16, 19) at the first RESULTS harmonic, two (Nos. 7,17)at the second harmonic, one (No. 5) at the fourth harmonic, Cadence and step width Table 2 shows the cadence and the mean and one (No. 20) at the 24th harmonic. In for the step width of both left and right contrast, the remaining five subjects had sides. It is clear that there is a difference the highest amplitude at the first harmonic. from subject to subject; cadences ranged Three of these (Nos. 3, 6, 10) had the next from 0.78 to 1.06, and step width ranged highest harmonic at the 32nd harmonic and from -4.0 cm to over 12 cm on the left side two (Nos. 2,181 at the second harmonic. and from -9.9 cm to over 6.5 cm on the right Typical pattern of step width change side. A common finding was that each subFigure 3 shows some typical patterns of ject had a large coefficient of variation value change in step width. Figure 3A shows one for both step widths. case in which the subject walked relatively Results of Fourier analysis straight (No. 14). The results of Fourier Table 5 outlines the results of Fourier analysis for this case indicated that the analysis, in which the number of harmonics highest amplitude was at the 32nd haris listed in order of magnitude of amplitude, monic, but the next one was only a small other than the 32nd harmonic (especially a low harmonic number) will demonstrate that an individual walked meanderingly rather than straight, the magnitude of amplitude of each harmonic was used to assess each subject's manner of walking.
23
FOOTPRINTS IN NORMAL WALKING
TABLE 4. Amplitudes oftheoretical pattern
H' 1 2 3 4 5 6 7 8 9 10 11 12 13
i4 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
For case A .____ Cosine 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 25.00
of step
width change
For case B ________-____ Cosine
Sine-____
Cosine ___
0.00 0.00
0.00 25.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0 00
0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 25.00
6.uu 0.00 0.00
0.00 0.00 0.00 25.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 25.00
Sine 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
For case C
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Sine ___ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
n on
0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
'Harmonic
by the activities of the entire body and can therefore provide us with a wide range of interesting information. For example, the Pliocene footprints at Laetoli in northern Tanzania have been used to infer the stature of the individual who left them (White, 1980; Robbins, 1987; Tuttle, 1987) and the number of steps per minute (Charteris et al., 1981, 1982; Alexander, 1984; Tuttle, 1987) as well as the contour pattern of individual footprints (Day and Wickens, 1980; White and Suwa, 1987). Footprints have also been used t o diagnose abnormal walking. From studies of footprints, Dougan (1924) and Patek (1926) observed an inconstancy in the foot angle on the same side during successive steps, even in normal walking. Despite this inconstancy, it was clear that the foot angle (i.e., toeing out) increased as the walkDISCUSSION ing speed decreased (Morton, 1932)and that The trail of footprints made by the plantar there were significant differences among surface of the feet during walking is affected age groups, with those over 60 years old
percentage of the first harmonic. Figure 3B shows a case of walking with long periodic meandering (No. 6); the results of Fourier analysis indicated that the highest amplitude was a t the first harmonic and the next, which had an amplitude equivalent to that of the first, was at the 32nd harmonic. Figure 3C shows a case with moderate periodic meandering (No. 171, for which the results of fourier analysis indicated that the highest amplitude was at the 32nd harmonic and the next was at the second harmonic. Finally, Figure 3D shows a case of walking with relatively short periodic meandering (No. 5), for which Fourier analysis revealed that the highest amplitude was at the 32nd harmonic and the next was a t the fourth harmonic.
T. UETAKE
24
TABLE 5. Order in amplitude _ _ _ ~ _ _ _ _ _ Subj. ____________
1 2 3 4
5 6 7 8 9 10 11 12 13
14 15 16 17 18 19 20
of
harmonics analyzed by FFT Harmonic
1st
2nd
3rd
32 (100.0) l(189.6) l(125.1) 32 (100.0) 32 (100.0) l(107.7) 32 (100.0) 32 (100.0) 32 (100.0) l(155.8) 32 (100.0) 32 (100.0) 32 (1 00 0) 32 (100.0) 32 (100.0) 32 (100.0) 32 (100.0) l(166.6) 32 (100.0) 32 (100.0)
l(49.1) 2 (111.4) 32 (100.0) l(35.3) 4 (95.5) 32 (100.0) 2 (71.6) l(39.0) l(78.7) 32 (100.0) l(68.5) l(65.8) li9)R.l) l(18.9) l(47.0) l(53.9) 2 (46.8) 2 (130.8) l(47.5) 24 (32.9)
2 (35.6) 32 (100.0) 2 (60.6) 9 (24.4) l(90.1) 30 (46.1) 3 (34.6) 15 (27.8) 3 (40.2) 3 (64.2) 2 (45.1) 30 (42.3) 3 (80.9) 21 (15.0) 6 (29.8) 3 (45.3) l(28.7) 23 (103.7) 2 (24.7) 23 (25.0)
_____
___
.-
4th---__-________-5th 4 (25.5) 26 (18.0) 3 (89.2) 20 (58.5) 7 (48.6) 3 (45.9) 10 (18.1) 5 (19.4) 6 175.4) 2 (72.1) 10 (45.8) 22 (33.5) 11 (29.6) 23 (28.2) 6 (22.0) 31 (25.4) 4 (33.8) 17 (33.5) 2 (43.7) 20 (31.5) 7 (26.1) 22 (24.6) 2 (37.9) 4 (35.5) 26 (55.3) 2 (53.5) 24 (14.6) 23 (13.3) 12 (27.5) 4 (24.3) 5 (37.8) 13 (32.4) 19 (20.1) 3 (20.0) 32 (100.0) 4 (80.1) 3 (20.2) 5 (18.2) 4 (20.0) 14 (20.1)
'Parentheses show the rate of amplitude for the 32nd harmonic.
showing a more pronounced angle than those younger (Murray et al., 1964). These facts indicate that increase in the foot angle has to do with maintaining lateral body balance, as Morton (1932) suggested. Another way of keeping lateral body balance while walking, which has not been examined extensively in previous studies, is the separation of the two feet. When we are walking and want to turn in another direction, we usually change both the angulation of the foot and the distance between the heel and the center line of the walking course. If deviations in the foot angle and the heel position relative to the center line of the walking course are correlated with each other, meandering walking will necessarily result, even in an experiment in which the subject is told to keep to as straight a path as possible. The secondary first-harmonic amplitude peak evinced in case No. 14 (Fig. 3A) shows that even an exceptionally straight-looking trail of footprints may exhibit a pronounced meander. These findings confirm that we cannot walk exactly straight but always meander to some degree. To seek the reason for this phenomenon, we must refer to earlier studies on structural and functional asymmetry in the lower limbs. Published studies of asymmetry of
tibial torsion (Staheli and Engel, 1972; Malekafzali and Wood, 1979; Clernentz, 1988) and lower limb length (Rush and Steiner, 1946; Ingelmark and Lindstrom, 1963; Friberg, 1983; Friberg and Kvist, 1988) have concluded that a lateral difference or side dominance exists even in normal individuals and that a great many people have more tibial torsion on the right side and greater lower limb length on the left side. Studies of lower limb preference have been numerous, all finding a functional asymmetry in our lower limb behaviors (Nachshon et al., 1983; Plato et al., 1985; Chapman et al., 1987). Table 1 shows the means of the present subjects' anthropometrical measurements of upper and lower limbs. As stated, a significant lateral difference was observed only in forearm length ( P < 0.01). However, as has been found in many other studies on lower limb length, the left lower limb was usually slightly longer than the right, and right girth measurements of both upper and lower limbs were slightly larger than left. Many (17 of 20) of the subjects showed a right side preference in kicking a ball. It is clear from these facts that there is a structural and functional asymmetry in the lower limbs of the present subjects.
25
FOOTPRINTS IN NORMAL. WALKING
A I
1
D r
1
I
-Fig 3 Typical pattern of step width change in relatively straight walking (A),long periodic meandering (B), moderate periodic meandering (C), and relatively short periodic meandering (D). WidthAength ratios exaggerated as in Figure 2
It seems likely that these lateral differ- larger right foot angle than left foot angle. ences, side dominances, or lower limb pref- As has been found in other studies, genererences inevitably produce a gait asymme- ally the left stance phase lasted signifitry. For example, Chatinier and Rozendal cantly longer than the right, and the right (1970) reported that stance phase in walk- swing phase lasted significantly longer than ing lasted longer for the left foot than for the the left. These results indicate that the right, and they surmized that this asymme- present subjects also had a gait asymmetry. As stated above, all subjects in this study try reflects a functional lateral dominance of our limbs. Holden et al. (1985)reported that walked meanderingly to a greater or lesser over 90% of their subjects had a signifi- degree. It was thought that there were two cantly greater right foot angle, correspond- main and inseparable reasons for this, One ing to the asymmetry of tibia1 torsion. Table is that a slight structural or functional im6 shows the foot angle, stance duration, and balance in our body shifts our walking swing duration of the present subjects in the course, and the other is that there is feedwalking experiment. A significant lateral back from the sense of sight, which acts difference was observed in almost all indi- to correct a shifted walking course to a viduals in a t least one of the three measure- straight one. As Schaeffer (1928) demonments. For the foot angle, 13 of 20 had a strated, blindfolded subjects walk spirally to significant lateral difference, and further the left or right, presumably because they observation revealed that ten of them had a lack this visual feedback. Shifting the walk-
T. UETAKE
26
TABLE 6. Foot angle, stance duration, and swing duration
Subj. 1
2 3 4 5 6 7 8 9
Foot angle' (degrees)___-.___ Left Right _____SD X SD ~
x
10.5 19.1 9.2 14.5 13.5 15.4 7.5 16.3 15.5
1.75 2.24 1.92 1.72 1.80 2.43 1.44 2.23 1.66 1.88
10 ~.
14.2
1: 12 13 14 15
10.6
1.m
12.7 20.1 4.2 16.5 10.7 3.0 9.3 6.3 14.4
2.41 1.76 1.35 2.02 1.56 1.20 1.68 1.73 1.80
16
17 18 19 20
13.1 18.0 9.1 21.0 21.8 20.0 8.1 15.6 11.9 15.0 13.9 18.7 28.0 3.6 10.6 6.8 6.9 13.1 13.6 13.9
Stance duration ~
__ _ X_ 2.12"" 531.8 4.37 692.7 2.61 637.4 1.58"" 532.4 2.90"" 599.5 2.39"" 656.1 1.80 585.6 3.95 607.4
.
Swing duration
(rnsec) _ _
Left
__-_
Right
566.1
_ SD_ 16.41 18.85 20.24 39.25 16.45 25.29 18.59 19.58 21.58 108.42
747x
3462
556.0 663.4 701.9 658.1 652.8 639.2 610.8 614.4 579.5
28.59 190.38 56.49 41.63 15.00 24.27 34.21 98.13 21.97
2 . 5 P 666.6
3.68 2.96"" 4.05*" 4.17** 1.70 2.26"" 1.67"" 1.60"" 1.97"" 3.34"" 3.34
_
hS€.C)
Left
Right -
._ - .~
X
562.6 653.0 615.9 627.1 581.2 639.2 565.1 603.6 674.3 706.8 666 4 576.2 670.8 567.7 546.9 492.5 473.6 547.5 700.1 571.1
22.18"" 23.73"" 20.74*" 12.88"" 14.19"" 18.61"" 15.80"" 19.05 21.44 32.37"* 46.25"* 18.1Xr*
92.17 73.07*" 22.38"" 87.05"" 55.35"" 19.00"" 19.01"" 23.82
479.0 484.1 454.3 518.7 478.1 508.9 417.6 485.8 496.2 646.4 542.8 512.0 402.5 245.0 426.5 285.7 298.3 436.1 605.0 475.8
18.91 13.65 11.78 50.59 17.53 28.12 13.42 17.90 17.21 112.51 19.40 23.2'7 162.07 34.18 39.08 36.28 31.78 63.35 100.19 12.96
510.6
524.8 477.8 419.0 497.9 522.5 439.9 488.9 487.9 507.3 628.5 497.4 389.1 322.0 413.6 243.9 247.4 409.7 516.2 464.1
__ SD 19.92"" 20.28"" 15.85"" 20.21"" 19.12"" 16.37" 8.75"" 15.83 20.07 18.95"" 33.77"" 27.27 66.47 70.60"" 33.88 43.22"" 24.10** 47.86 18.82"" 12.65""
Foot angle: The angle made by the line of progression and the longitudinal axis that equally divides t h e angle made by the inner and outer tangential lines of a footprint. *"The lateral difference is statistically significant ( P c.05, P < 0.01, respectively).
ing course and visually compensating for those shifts by turns may thus cause the meandering walking observed in this study. Further studies are needed t o elucidate the factors causing differences between individuals. ACKNOWLEDGMENTS Grateful acknowledgment is made ho Prof. Ohtsuki of the Tokyo University of Agriculture and Technology for his suggestions and advice. LITERATURE CITED Alexander RM (1984) Stride length and speed for adults, children, and fossil hominids. Am. J . Phys. Anthropol. 63:23-27. Chapman JP, Chapman U,and Allen JJ (1987) The measurement of foot preference. Neuropsychologia 25:579-584. Charteris J , Wall JC, and Nottrodt JW (1981) Functional reconstruction of gait from the Pliocene hominid footprints a t Laetoli, northern Tanzania. Nature 290.496498. Charteris J , Wall JC, and Nottrodt JW (1982) Pliocene hominid gait: New interpretations based on available footprint data from Laetoli. Am. J . Phys. Anthropol. 58.133-144. Chatinier KD, and Rozendal RH (1970) Temporal symmetry of p i t of selected normal human subjects. Proc.
Koniklijke Nedarlandse Akad. Weternschappen, Seriese C 74.353461. Chodera JD, and Level1 RM (1973) Footprint Patterns During Walking. Baltimore: University Park Press, pp. 81-90. Clement2 BG (1988) Tibia1 torsion measured in normal adults. Acta Orthop. Scand. 59r441-442. Day MH, Wickens EH (1980) Laetoli Pliocene hominid footprints and hipedalism. Nature 286:385-387. Dougan S (1924) The angle of gait. Am. J. Phys. Anthropol. 7:275-270. Friberg 0 (1983:Clinical symptoms and biomechanics of lumbar spine and hip joint in leg length inequality. Spine 8:643451. Friberg 0 , and Kvist M (1988) Factors determining the preference of takeoff leg in jumping. Int. J . Sports Med. 9:349-352. Halazonetis DJ, Shapiro E, Gheewalla RK, and Clark RE (1991) Quantitative description of the shape of the mandible. Am. J. Orthod. Dentofac. Orthop. 99:49-56. Wino M (1977) Spectrum Analysis. Tokyo: Asakura (in Japanese). Holden JP, Cavanagh PR, Williams KR, and Bednarski KN (1985) Foot Angles During Walking and Running. Biomechanics IXA. Human Kmetics Pub., pp. 451456. Ingelmark BE, and Lindstrom J (1963) Asymmetries of the lower extremities and pelvis and their relations. Acta Morphol. Scand. 5:221-234. Inoue M (19901Fourier analysis of the forehead shape of skull and sex determination by use of computer. J. Forensic Sci. 47:lOl-112.
FOOTPRINTS IN NORMAL WALKING
Lestrel PE (1989) Some approaches toward the mathematical modeling of the craniofacial complex. J . Craniofac. Genet. Dev. Biol. 9:77-91. Lestrel PE, and Roche AF (1986) Cranial base shape variation with age: A longitudinal study of shape using Fourier analysis. Hum. Biol. 58r527-540. Malekafzali S, and Wood MB (1979) Tibial torsion-A simple clinical apparatus for its measurement and its application to a normal adult population. Clin. Orthop. Rel. Res. 145:154-157. Martin R, and Seller K (1957) Lehrbuch der Anthropologie. Stuttgart: G. Fischer. Morton DJ (1932) The angle of gait: A study based upon examination of the feet of Central African natives. J. Bone Joint Surg. 30:741-754. Murray MP, DrGught izc,and Kury RC tj.964, Waiking patterns of normal men. J. Bone Joint Surg. 46A:335360. Nachshon I, Denno D, and Aurand S (1983) Lateral preferences of hand, eye and foot: relation to cerebral dominance. Int. J. Neurosci. 18:l-10. Nigorikawa T (1988) A preliminary study of walking bias phenomenon which is related to ring-wandering. Ann. Physiol. Anthropol. 7:99-106. Patek SD (1926) The angle of gait in women. Am. J. Phys. Anthropol. 9:273-291. Plato CC, Fox KM, and Garruto RM (1985)Measures of
27
lateral functional dominance: Foot preference, eye preference, digital interlocking, arm folding and foot overlapping. Hum. Biol. 57r327-334. Reccia R, Roberti G, and Russo P (1990) Computer analysis of ENG spectral features from patients with congenital nystagmus. J . Biomed. Eng. 12:3945. Robbins LM 11987) Hominid footprints from site G. In MD Leakey and JM Harris (eds.): Laetoli: A Pliocene Site in Northern Tanzania. Oxford: Clarendon Press. pp. 497-502. Rush WA, and Steiner HA (1946) A Study of Lower Extremity Length Inequality. Am. J. Roentgenol. 56: 616-623. Schaeffer AA (19281 Spiral movement in man. J. Morphol. Physiol. 45r293-398. Staheli LT, and Engel GM (1972) Tibial torsion. Clin. Orthop. Rel. Res. 86r183-186. Tuttle RH (1987) Kinesiological inferences and evolutionary implications from Laetoli bipedal trails G-1, G-2/3, and A. In MD Leakey and JM Harris (eds.): Laetoli: A Pliocene Site in Northern Tanzania. Oxford: Clarendon Press, pp. 503-523. White TD (1980) Evolutionary implications of Pliocene hominid footprints. Science 208:175-176. White TD, and Suwa G (1987) Hominid footprints at Laetoli: Facts and interpretations. Am. J. Phys. Anthropol. 72r485-514.
Can We Really Walk Straight? TERUO U E T m Department of Health and Physical Education, Faculty of General Education, Tokyo University of Agriculture and Technology, Fuchu, Tokyo 183, Japan
KEY WORDS Footprint, Fourier analysis, Meandering walk, Gait asymmetry ABSTRACT Twenty healthy men were asked to walk as straight as possible t o a target SO m away a t normal speed. A series of footprints was recorded for each subject by having him wear socks soaked with red ink and walk on white paper fixed flat to the floor. Fourier analysis was applied to determine whether the subjects actually were able to walk straight, and the results revealed that all walked in a sinuous line rather than a straight line. Periodicity and amplitude of the meandering differed from subject to subject. These facts suggest that none of us can walk in a strictly straight line; rather, we meander, primarily due to a slight structural or functional imbalance of our limbs, which produces a gait asymmetry, and secondarily due to feedback from our sense of sight, which acts to correct the shifted walking course. 0 1992 Wiley-Liss, h e .
Because bipedal walking is the most common form of human locomotion and is a distinctive human characteristic, it has been the subject of many studies. Chodera and Level1 (1973) reported that the change in pattern of a walking course under different conditions fell into one of three basic shapes: a curve to the left, a curve to the right, or an S-shaped curve, the latter found more frequently at slow walking speed. Nigorikawa f 1988)reported that a man whose sight was obstructed did not walk straight but instead veered to the left or the right. The purpose of the present paper is to clarify whether people can really walk straight or not, and, if not, how the path of a walking person deviates from a straight line. This was undertaken by applying Fourier analysis to the tracks left by subjects walking to a target approximately 60 m away at normal speed. MATERIALS AND METHODS Subjects
The subjects were 20 healthy Japanese men aged 18-45 years. None of them had any history of lower limb problems. Their 0 1992 WILEY-LISS, INC.
mean height was 172.0 cm (SD = 5.55 cm) and their mean weight 65.5 kg (SD = 6.12 kg). The only significant difference between left and right limbs was in forearm length (Table 1). Seventeen of the subjects kicked a ball better with the right foot, the rest with the left (Table 2). Method of recording footprints A piece of white paper 0.8 x 50 m in size
was fixed flat on the floor. The subject, wearing socks soaked with red ink and with pedal switches attached just beneath the heel and the great toe of both feet, was asked to walk at his normal speed in a straight line to a target SO m away. The pedal switch used in this experiment was designed to be as small as possible (-8 mm in diameter and 2 mm thick) so that it might not affect the experimental walking. The pedal switch was made of two fine wires separated by a rubber mat containing fine-grained iron, which was compressed enough under body weight to permit current to flow from one wire to
Received November 8,1990; accepted March 3,1992.
T. UETAKE
20 TABLE 1 , Means for anthropometrical measurement icmi
Right
..._.___ - Left
_-________-____X__ SD Arm length Forearm length2 Hand length Biepicondyle of arm Bistvloid uorc. of forearm Hand breadth Arm girth Forearm girth Thigh length3 Leg length Foot length Foot height Biepicondyle of thigh Bieuicondvle of leg Fooi breadth .Thigh girth Leg girth
31.8 23.0 19.2 6.7 5.6 8.3 27.5 25.6 468 36 2 252
1.43 1.32 0.36 0.29 0.38 1.54 1,34 183 2 55 104
75
0 50
94 74 10.3 52.7 36.8
065 038 0.60 3.37 1.94
SD 30.9 24.2 19.3 6.7 5.7 8.4 27.9 26.2 468 36 o 252 75 95 74 10.2 52.9 36.9
1.87 1.14
putting on the pedal switch and the soaked socks. The subject was instructed to stand in the middle of one end of the paper, to start with his left foot, and to walk at normal speed to the other end of the paper. Subjects following these directions left an average of 72.8 footprints (SD = 6.47). The time (seconds) elapsed from the first heel contact to the last w a s determined from the pedal switch record, and - - the -cadence (strides per second) was calculated as the number of strides divided by the time.
:::; 0.27 0.40 1.49 1.18 173 2 57 100 0 50 071 037 0.58 3.48 1.55
Anthropometrical measurements were taken following the procedures of Martin and Seller (1957). 'The lateral difference is statistically significant iP < 0.01). 3Thigh length = (iliac height - tibia1 height) x 0.93.
the other. During the experimental walking, the pedal switch was covered with a n adhesive vinyl tape so as not to short circuit. An open circuit, made with the pedal switch, a small battery, and a data recorder set apart from the experimental walking course, closed whenever the pedal switch contacted the floor, and the moment of contact was recorded. Before the experiment, a few practice steps were taken by the subject before
Fourier analysis of the pattern of change of the two heel positions
Because the walking cycle during the first four steps was erratic, only steps 5-68 were usually analyzed in this study. However, if a subject did not leave more than 68 steps, his steps from the fifth to the last were analyzed. The distance from the most posterior point of the heel impression to the center line of the paper, referred to here as step width, was measured with a digitizer (Fig. 1).Measurements to the left of the center line of the paper were indicated by a plus symbol, those to the right side by a minus. A n indeterminate form or pattern can be easily quantified using Fourier analysis, which has been used to analyze a variety of biological forms, from crania (Lestrel and Roch, 1986; Lestrel, 1989; Inoue, 1990) and
TABLE 2. Cadrnre and step uidth (em! Cadence
X
0.95 0.85 0.92 0.95 0.93 0.86 1.00 0.92 0.85 0.81 0.78 0.93 0.93 1.05 0.93 1.06 1.06 0.96 0.81 0.96
5.6 0.2 6.3 4.5 0.6 - 5.2 1.5 1.9 - 2.0 3.2 0.3 6.4 11.5 4.5 1.9 1.5 2.2 2.1 12.4 - 1.3
~.
Subj. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
BFS' __ R R R L R R R R R R R R R R L R L R R R
BFS, better font. side for kicking a ball.
~
Left SD
cv
2.91 4.19 3.28 2.25 3.43 6.76 2.24 1.95 1.78 2.52 2.30 2.49 2.87 1.32 1.91 2.23 1.86 1.52 1.58 2.63
2095.0 52.1 50.0 571.7 130.0 149.3 102.6 89.0 78.8 766.7 38.9 25.0 29.3 100.5 148.7 84.5 72.4 12.7 202.3
X _________ 52.0 - 3.8 3.5 0.7 - 3.2 - 2.8 - 2.8 - 4.3 - 5.2 -- 6.0 - 0.5 - 4.7 - 1.1 7.1 - 2.5 - 4.2 3.4 - 4.9 0.8 5.9 - 9.9 -
-
Right _~
.~.
SD 2.61 3.95 3.82 2.01 3.17 2.24 2.29 1.29 2.05 3.09 1.91 2.59 2.64 1.24 1.99 2.10 2.17 1.89 1.72 2.29
CV
__._
68.7 112.9 545.7 62.8 113.2 80.0 53.3 24.8 34.2 618.0 40.6 235.5 37.2 49.6 47.4 61.8 44.3 236.3 29.2 23.1
21
FOOTPRINTS IN NORMAL WALKING I
0
target right and l e f t s t e p w i d t h Fig. 1. Schematic presentation of the walking experiment. TABLE 3. SLW widtt? tor theoretrcal pattern of stey, width change immi
____ Case ____A St, No.'
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Left 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00
Case B
Case C __
~
Right
Left
Right
Left
Right
25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00 - 29.00 - 25.00 - 25.00 - 25.00 - 25.00 - 25.00
50.00 48.10 42.68 34.57 25.00 15.43 7.32 1.90 0.00 1.90 7.32 15.43 25.00 34.56 42.67 48.10 50.00 48.10 42.68 34.57 25.01 15.44 7.33 1.91 0.00 1.90 7.32 15.43 24.99 34.56 42.67 48.09
- 0.48 - 4.21 - 11.11 - 20.12
50.00 42.68 25.00 7.32 0.00 7.32 25.00 42.67 50.00 42.68 25.01 7.33 0.00 7.32 25.00 42.67 50.00 42.68 25.01 7.33 0.00 7.31 25.00 42.67 50.00 42.69 25.01 7.33 0.00 7.31 25.00 42.66
- 1.90 - 15.43
-
- 29.88 - 38.89 - 45.79 49.52 49.52 45.79 38.89 29.88 - 20.13 - 11.11 - 4.22 - 0.48 - 0.48 -- 4.21 - 11.11 - 20.12 - 29.87 - 38.88 - 45.78 - 49.52 - 49.52 45.79 - 38.90 - 29.88 - 20.13 - 11.12 - 4.22 - 0.48 -
34.57 48.10 48.10 34.57 15.44 - 1.90 - 1.90 - 15.43 - 34.56 - 48.09 - 48.10 - 34.57 - 15.44 -- 1.91 - 1.90 - 15.42 - 34.56 - 48.09 -- 48.10 - 34.58 - 15.44 ---
-
1.91 1.90
- 15.42 34.55 48.10 - 48.10 - 34.58 - 15.45 - 1.91 --
'Step number
mandibles (Halazonetis et al., 1991) to the waveshape of electronystagmograms (Reccia et al., 1990). In this study, taking the step width distance of 64 sequential steps as the axis of the ordinate and step number as the abscissa, Fourier analysis was used to examine patterns of step width change. These data were fed into a Fourier analysis program developed by Hino (1977) for a microcomputer, which yielded coefficients of
cosine and sine and amplitudes in each harmonic as output. If one could walk straight (case A, Table 3), coefficients of cosine or sine and amplitudes would appear only in the 32nd harmonic (Fig. 2A, Table 4). On the other hand, if one walked meanderingly (case B or C, Table 31, that would be reflected not only in the value of the 32nd harmonic but in other harmonics (Fig. 2B,C, Table 4).Because appearance of amplitude in
22
T. U E T m
C
Fig. 2. Theoretical pattern of step width change: Straight walking (A) and meandering walking (B, C). WidtMength ratio of each step is exaggerated by a factor of 7 to display meandering more clearly.
and the number in parentheses indicates the magnitude of amplitude of each harmonic relative to that of the 32nd harmonic. Fifteen subjects among the 20 had the highest amplitude at the 32nd harmonic. The next highest amplitude fell into four groups: 11 (Nos. 1, 4, 8, 9, 11-16, 19) at the first RESULTS harmonic, two (Nos. 7,17)at the second harmonic, one (No. 5) at the fourth harmonic, Cadence and step width Table 2 shows the cadence and the mean and one (No. 20) at the 24th harmonic. In for the step width of both left and right contrast, the remaining five subjects had sides. It is clear that there is a difference the highest amplitude at the first harmonic. from subject to subject; cadences ranged Three of these (Nos. 3, 6, 10) had the next from 0.78 to 1.06, and step width ranged highest harmonic at the 32nd harmonic and from -4.0 cm to over 12 cm on the left side two (Nos. 2,181 at the second harmonic. and from -9.9 cm to over 6.5 cm on the right Typical pattern of step width change side. A common finding was that each subFigure 3 shows some typical patterns of ject had a large coefficient of variation value change in step width. Figure 3A shows one for both step widths. case in which the subject walked relatively Results of Fourier analysis straight (No. 14). The results of Fourier Table 5 outlines the results of Fourier analysis for this case indicated that the analysis, in which the number of harmonics highest amplitude was at the 32nd haris listed in order of magnitude of amplitude, monic, but the next one was only a small other than the 32nd harmonic (especially a low harmonic number) will demonstrate that an individual walked meanderingly rather than straight, the magnitude of amplitude of each harmonic was used to assess each subject's manner of walking.
23
FOOTPRINTS IN NORMAL WALKING
TABLE 4. Amplitudes oftheoretical pattern
H' 1 2 3 4 5 6 7 8 9 10 11 12 13
i4 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
For case A .____ Cosine 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 25.00
of step
width change
For case B ________-____ Cosine
Sine-____
Cosine ___
0.00 0.00
0.00 25.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0 00
0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 25.00
6.uu 0.00 0.00
0.00 0.00 0.00 25.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 25.00
Sine 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
For case C
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Sine ___ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
n on
0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
'Harmonic
by the activities of the entire body and can therefore provide us with a wide range of interesting information. For example, the Pliocene footprints at Laetoli in northern Tanzania have been used to infer the stature of the individual who left them (White, 1980; Robbins, 1987; Tuttle, 1987) and the number of steps per minute (Charteris et al., 1981, 1982; Alexander, 1984; Tuttle, 1987) as well as the contour pattern of individual footprints (Day and Wickens, 1980; White and Suwa, 1987). Footprints have also been used t o diagnose abnormal walking. From studies of footprints, Dougan (1924) and Patek (1926) observed an inconstancy in the foot angle on the same side during successive steps, even in normal walking. Despite this inconstancy, it was clear that the foot angle (i.e., toeing out) increased as the walkDISCUSSION ing speed decreased (Morton, 1932)and that The trail of footprints made by the plantar there were significant differences among surface of the feet during walking is affected age groups, with those over 60 years old
percentage of the first harmonic. Figure 3B shows a case of walking with long periodic meandering (No. 6); the results of Fourier analysis indicated that the highest amplitude was a t the first harmonic and the next, which had an amplitude equivalent to that of the first, was at the 32nd harmonic. Figure 3C shows a case with moderate periodic meandering (No. 171, for which the results of fourier analysis indicated that the highest amplitude was at the 32nd harmonic and the next was at the second harmonic. Finally, Figure 3D shows a case of walking with relatively short periodic meandering (No. 5), for which Fourier analysis revealed that the highest amplitude was at the 32nd harmonic and the next was a t the fourth harmonic.
T. UETAKE
24
TABLE 5. Order in amplitude _ _ _ ~ _ _ _ _ _ Subj. ____________
1 2 3 4
5 6 7 8 9 10 11 12 13
14 15 16 17 18 19 20
of
harmonics analyzed by FFT Harmonic
1st
2nd
3rd
32 (100.0) l(189.6) l(125.1) 32 (100.0) 32 (100.0) l(107.7) 32 (100.0) 32 (100.0) 32 (100.0) l(155.8) 32 (100.0) 32 (100.0) 32 (1 00 0) 32 (100.0) 32 (100.0) 32 (100.0) 32 (100.0) l(166.6) 32 (100.0) 32 (100.0)
l(49.1) 2 (111.4) 32 (100.0) l(35.3) 4 (95.5) 32 (100.0) 2 (71.6) l(39.0) l(78.7) 32 (100.0) l(68.5) l(65.8) li9)R.l) l(18.9) l(47.0) l(53.9) 2 (46.8) 2 (130.8) l(47.5) 24 (32.9)
2 (35.6) 32 (100.0) 2 (60.6) 9 (24.4) l(90.1) 30 (46.1) 3 (34.6) 15 (27.8) 3 (40.2) 3 (64.2) 2 (45.1) 30 (42.3) 3 (80.9) 21 (15.0) 6 (29.8) 3 (45.3) l(28.7) 23 (103.7) 2 (24.7) 23 (25.0)
_____
___
.-
4th---__-________-5th 4 (25.5) 26 (18.0) 3 (89.2) 20 (58.5) 7 (48.6) 3 (45.9) 10 (18.1) 5 (19.4) 6 175.4) 2 (72.1) 10 (45.8) 22 (33.5) 11 (29.6) 23 (28.2) 6 (22.0) 31 (25.4) 4 (33.8) 17 (33.5) 2 (43.7) 20 (31.5) 7 (26.1) 22 (24.6) 2 (37.9) 4 (35.5) 26 (55.3) 2 (53.5) 24 (14.6) 23 (13.3) 12 (27.5) 4 (24.3) 5 (37.8) 13 (32.4) 19 (20.1) 3 (20.0) 32 (100.0) 4 (80.1) 3 (20.2) 5 (18.2) 4 (20.0) 14 (20.1)
'Parentheses show the rate of amplitude for the 32nd harmonic.
showing a more pronounced angle than those younger (Murray et al., 1964). These facts indicate that increase in the foot angle has to do with maintaining lateral body balance, as Morton (1932) suggested. Another way of keeping lateral body balance while walking, which has not been examined extensively in previous studies, is the separation of the two feet. When we are walking and want to turn in another direction, we usually change both the angulation of the foot and the distance between the heel and the center line of the walking course. If deviations in the foot angle and the heel position relative to the center line of the walking course are correlated with each other, meandering walking will necessarily result, even in an experiment in which the subject is told to keep to as straight a path as possible. The secondary first-harmonic amplitude peak evinced in case No. 14 (Fig. 3A) shows that even an exceptionally straight-looking trail of footprints may exhibit a pronounced meander. These findings confirm that we cannot walk exactly straight but always meander to some degree. To seek the reason for this phenomenon, we must refer to earlier studies on structural and functional asymmetry in the lower limbs. Published studies of asymmetry of
tibial torsion (Staheli and Engel, 1972; Malekafzali and Wood, 1979; Clernentz, 1988) and lower limb length (Rush and Steiner, 1946; Ingelmark and Lindstrom, 1963; Friberg, 1983; Friberg and Kvist, 1988) have concluded that a lateral difference or side dominance exists even in normal individuals and that a great many people have more tibial torsion on the right side and greater lower limb length on the left side. Studies of lower limb preference have been numerous, all finding a functional asymmetry in our lower limb behaviors (Nachshon et al., 1983; Plato et al., 1985; Chapman et al., 1987). Table 1 shows the means of the present subjects' anthropometrical measurements of upper and lower limbs. As stated, a significant lateral difference was observed only in forearm length ( P < 0.01). However, as has been found in many other studies on lower limb length, the left lower limb was usually slightly longer than the right, and right girth measurements of both upper and lower limbs were slightly larger than left. Many (17 of 20) of the subjects showed a right side preference in kicking a ball. It is clear from these facts that there is a structural and functional asymmetry in the lower limbs of the present subjects.
25
FOOTPRINTS IN NORMAL. WALKING
A I
1
D r
1
I
-Fig 3 Typical pattern of step width change in relatively straight walking (A),long periodic meandering (B), moderate periodic meandering (C), and relatively short periodic meandering (D). WidthAength ratios exaggerated as in Figure 2
It seems likely that these lateral differ- larger right foot angle than left foot angle. ences, side dominances, or lower limb pref- As has been found in other studies, genererences inevitably produce a gait asymme- ally the left stance phase lasted signifitry. For example, Chatinier and Rozendal cantly longer than the right, and the right (1970) reported that stance phase in walk- swing phase lasted significantly longer than ing lasted longer for the left foot than for the the left. These results indicate that the right, and they surmized that this asymme- present subjects also had a gait asymmetry. As stated above, all subjects in this study try reflects a functional lateral dominance of our limbs. Holden et al. (1985)reported that walked meanderingly to a greater or lesser over 90% of their subjects had a signifi- degree. It was thought that there were two cantly greater right foot angle, correspond- main and inseparable reasons for this, One ing to the asymmetry of tibia1 torsion. Table is that a slight structural or functional im6 shows the foot angle, stance duration, and balance in our body shifts our walking swing duration of the present subjects in the course, and the other is that there is feedwalking experiment. A significant lateral back from the sense of sight, which acts difference was observed in almost all indi- to correct a shifted walking course to a viduals in a t least one of the three measure- straight one. As Schaeffer (1928) demonments. For the foot angle, 13 of 20 had a strated, blindfolded subjects walk spirally to significant lateral difference, and further the left or right, presumably because they observation revealed that ten of them had a lack this visual feedback. Shifting the walk-
T. UETAKE
26
TABLE 6. Foot angle, stance duration, and swing duration
Subj. 1
2 3 4 5 6 7 8 9
Foot angle' (degrees)___-.___ Left Right _____SD X SD ~
x
10.5 19.1 9.2 14.5 13.5 15.4 7.5 16.3 15.5
1.75 2.24 1.92 1.72 1.80 2.43 1.44 2.23 1.66 1.88
10 ~.
14.2
1: 12 13 14 15
10.6
1.m
12.7 20.1 4.2 16.5 10.7 3.0 9.3 6.3 14.4
2.41 1.76 1.35 2.02 1.56 1.20 1.68 1.73 1.80
16
17 18 19 20
13.1 18.0 9.1 21.0 21.8 20.0 8.1 15.6 11.9 15.0 13.9 18.7 28.0 3.6 10.6 6.8 6.9 13.1 13.6 13.9
Stance duration ~
__ _ X_ 2.12"" 531.8 4.37 692.7 2.61 637.4 1.58"" 532.4 2.90"" 599.5 2.39"" 656.1 1.80 585.6 3.95 607.4
.
Swing duration
(rnsec) _ _
Left
__-_
Right
566.1
_ SD_ 16.41 18.85 20.24 39.25 16.45 25.29 18.59 19.58 21.58 108.42
747x
3462
556.0 663.4 701.9 658.1 652.8 639.2 610.8 614.4 579.5
28.59 190.38 56.49 41.63 15.00 24.27 34.21 98.13 21.97
2 . 5 P 666.6
3.68 2.96"" 4.05*" 4.17** 1.70 2.26"" 1.67"" 1.60"" 1.97"" 3.34"" 3.34
_
hS€.C)
Left
Right -
._ - .~
X
562.6 653.0 615.9 627.1 581.2 639.2 565.1 603.6 674.3 706.8 666 4 576.2 670.8 567.7 546.9 492.5 473.6 547.5 700.1 571.1
22.18"" 23.73"" 20.74*" 12.88"" 14.19"" 18.61"" 15.80"" 19.05 21.44 32.37"* 46.25"* 18.1Xr*
92.17 73.07*" 22.38"" 87.05"" 55.35"" 19.00"" 19.01"" 23.82
479.0 484.1 454.3 518.7 478.1 508.9 417.6 485.8 496.2 646.4 542.8 512.0 402.5 245.0 426.5 285.7 298.3 436.1 605.0 475.8
18.91 13.65 11.78 50.59 17.53 28.12 13.42 17.90 17.21 112.51 19.40 23.2'7 162.07 34.18 39.08 36.28 31.78 63.35 100.19 12.96
510.6
524.8 477.8 419.0 497.9 522.5 439.9 488.9 487.9 507.3 628.5 497.4 389.1 322.0 413.6 243.9 247.4 409.7 516.2 464.1
__ SD 19.92"" 20.28"" 15.85"" 20.21"" 19.12"" 16.37" 8.75"" 15.83 20.07 18.95"" 33.77"" 27.27 66.47 70.60"" 33.88 43.22"" 24.10** 47.86 18.82"" 12.65""
Foot angle: The angle made by the line of progression and the longitudinal axis that equally divides t h e angle made by the inner and outer tangential lines of a footprint. *"The lateral difference is statistically significant ( P c.05, P < 0.01, respectively).
ing course and visually compensating for those shifts by turns may thus cause the meandering walking observed in this study. Further studies are needed t o elucidate the factors causing differences between individuals. ACKNOWLEDGMENTS Grateful acknowledgment is made ho Prof. Ohtsuki of the Tokyo University of Agriculture and Technology for his suggestions and advice. LITERATURE CITED Alexander RM (1984) Stride length and speed for adults, children, and fossil hominids. Am. J . Phys. Anthropol. 63:23-27. Chapman JP, Chapman U,and Allen JJ (1987) The measurement of foot preference. Neuropsychologia 25:579-584. Charteris J , Wall JC, and Nottrodt JW (1981) Functional reconstruction of gait from the Pliocene hominid footprints a t Laetoli, northern Tanzania. Nature 290.496498. Charteris J , Wall JC, and Nottrodt JW (1982) Pliocene hominid gait: New interpretations based on available footprint data from Laetoli. Am. J . Phys. Anthropol. 58.133-144. Chatinier KD, and Rozendal RH (1970) Temporal symmetry of p i t of selected normal human subjects. Proc.
Koniklijke Nedarlandse Akad. Weternschappen, Seriese C 74.353461. Chodera JD, and Level1 RM (1973) Footprint Patterns During Walking. Baltimore: University Park Press, pp. 81-90. Clement2 BG (1988) Tibia1 torsion measured in normal adults. Acta Orthop. Scand. 59r441-442. Day MH, Wickens EH (1980) Laetoli Pliocene hominid footprints and hipedalism. Nature 286:385-387. Dougan S (1924) The angle of gait. Am. J. Phys. Anthropol. 7:275-270. Friberg 0 (1983:Clinical symptoms and biomechanics of lumbar spine and hip joint in leg length inequality. Spine 8:643451. Friberg 0 , and Kvist M (1988) Factors determining the preference of takeoff leg in jumping. Int. J . Sports Med. 9:349-352. Halazonetis DJ, Shapiro E, Gheewalla RK, and Clark RE (1991) Quantitative description of the shape of the mandible. Am. J. Orthod. Dentofac. Orthop. 99:49-56. Wino M (1977) Spectrum Analysis. Tokyo: Asakura (in Japanese). Holden JP, Cavanagh PR, Williams KR, and Bednarski KN (1985) Foot Angles During Walking and Running. Biomechanics IXA. Human Kmetics Pub., pp. 451456. Ingelmark BE, and Lindstrom J (1963) Asymmetries of the lower extremities and pelvis and their relations. Acta Morphol. Scand. 5:221-234. Inoue M (19901Fourier analysis of the forehead shape of skull and sex determination by use of computer. J. Forensic Sci. 47:lOl-112.
FOOTPRINTS IN NORMAL WALKING
Lestrel PE (1989) Some approaches toward the mathematical modeling of the craniofacial complex. J . Craniofac. Genet. Dev. Biol. 9:77-91. Lestrel PE, and Roche AF (1986) Cranial base shape variation with age: A longitudinal study of shape using Fourier analysis. Hum. Biol. 58r527-540. Malekafzali S, and Wood MB (1979) Tibial torsion-A simple clinical apparatus for its measurement and its application to a normal adult population. Clin. Orthop. Rel. Res. 145:154-157. Martin R, and Seller K (1957) Lehrbuch der Anthropologie. Stuttgart: G. Fischer. Morton DJ (1932) The angle of gait: A study based upon examination of the feet of Central African natives. J. Bone Joint Surg. 30:741-754. Murray MP, DrGught izc,and Kury RC tj.964, Waiking patterns of normal men. J. Bone Joint Surg. 46A:335360. Nachshon I, Denno D, and Aurand S (1983) Lateral preferences of hand, eye and foot: relation to cerebral dominance. Int. J. Neurosci. 18:l-10. Nigorikawa T (1988) A preliminary study of walking bias phenomenon which is related to ring-wandering. Ann. Physiol. Anthropol. 7:99-106. Patek SD (1926) The angle of gait in women. Am. J. Phys. Anthropol. 9:273-291. Plato CC, Fox KM, and Garruto RM (1985)Measures of
27
lateral functional dominance: Foot preference, eye preference, digital interlocking, arm folding and foot overlapping. Hum. Biol. 57r327-334. Reccia R, Roberti G, and Russo P (1990) Computer analysis of ENG spectral features from patients with congenital nystagmus. J . Biomed. Eng. 12:3945. Robbins LM 11987) Hominid footprints from site G. In MD Leakey and JM Harris (eds.): Laetoli: A Pliocene Site in Northern Tanzania. Oxford: Clarendon Press. pp. 497-502. Rush WA, and Steiner HA (1946) A Study of Lower Extremity Length Inequality. Am. J. Roentgenol. 56: 616-623. Schaeffer AA (19281 Spiral movement in man. J. Morphol. Physiol. 45r293-398. Staheli LT, and Engel GM (1972) Tibial torsion. Clin. Orthop. Rel. Res. 86r183-186. Tuttle RH (1987) Kinesiological inferences and evolutionary implications from Laetoli bipedal trails G-1, G-2/3, and A. In MD Leakey and JM Harris (eds.): Laetoli: A Pliocene Site in Northern Tanzania. Oxford: Clarendon Press, pp. 503-523. White TD (1980) Evolutionary implications of Pliocene hominid footprints. Science 208:175-176. White TD, and Suwa G (1987) Hominid footprints at Laetoli: Facts and interpretations. Am. J. Phys. Anthropol. 72r485-514.
