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Normative data of knee joint motion and ground reaction forces in adult level walking
NORMATIVE DATA OF KNEE JOINT MOTION AND GROUND REACTION FORCES IN ADULT LEVEL WALKING E. Y. CB.40, R. K. LACGHMAN, Btomechanics
Laboratory.
Department
E. SCHNEIDER
of Orthopedics.
and R. N. STAWFER
Mayo Clinic, Rochester.
MN 55905, U S.A.
Abstract-A normative data base of temporal distance factors, knee joint motion and ground reaction force patterns for 148 adults during levjel walking is reported. The data \sere studied using parametric and nonparametric (Fourier series) representations to facihrate statistical analyses. Key parameters were divided according to age and sex. Individual force and motton curves of each normal subject were averaged to establish the ‘typicat’ patterns. All typical patterns were combined to construct the ‘general‘ patterns. The essenttal number and most significant Fourier coefficients were determined. It was found that the sex-related variation is more signmcant than theage-related variation in adult gatt. Thisdata basecan serveasacommon reference for comparison.
INTRODL’CTION Human walking has been extensively studied by many investigators from various disciplines, including anatomy, kinesiology, neurophysiology and biomechanics. The historical development of this branch of biological science since the pre-renaissance era has been thoroughly reviewed (Contini and Drillis. 1954: Steindler, 1953; Pauwels, 1945). Although gait analysis. or assessment, has been pursued for a long period of time, our knowledge concerning human locomotion is far from complete. Normal walking is an extremely complex biomechanical process. It involves a three-dimensional motion of a multiple linkage system which demands coordinated control by the central nervous system far exceeding the sophistication of man-made machines. In spite of the attempts to model human gait, comprehensive data is still insufficient to put locomotion in quantitative terms. The inability to describe gait characteristics objectively and the lack of effective methods for data analysis to study a large population might have been some of the contributing factors. Although the attempt to describe human gait based on neurophgsiologic control principles is still in its developmental stage. the phenomenologica! aspects of locomotion have shown significant promise in associating the normal and abnormal gait patterns with the underlying musculoskeletal pathologies. Since the major aim of treating patients with arthritic diseases is to correct joint deformity and restore functional normality. the ability to quantitate any visible structural or functional changes in the limb segments atflicted by the pathology based on well-defined and clinically meaningful parameters is important. In addition, a carefully established normative data base from a broad spectrum of the population is essential to define anthropomorphic and physiologic variability. The ability to establish such a data base depends on an
efficient measurement technique and data analysis method. Normal knee joint kinematics in gait have been studied extensively with regard to sagittal motion (Murray rr al., 1964,197O; Murray, 1967; Eberhart and Inman. 1951; Liberson. 1965; Sutherland and Hagy. 1972; Kapovich and Herden, 1960; Winter er al., 1972, 1974; Bajd et al.. 1976; Milner er al.. 1973; Dommasch 1972) and three-dimensional rotation er al.. (Kettelkamp et al., 1970; Townsend rr 01.. 1977; Lamoreus. 1971: Morrison. 1969). Few studies have addressed the question of data variation among the normal population, which may be due to the insufficient sample size investigated. The existing reports also limit the results to some specific gait parameters with varying definitions. A number of the more recent studies compared abnormal knee function with that of normals, but without presenting extensive normal data (Andersson t’r (II.. 1981: Gyory ef ~1.. 1976; Chao and Stauffer. 1974: Stauffer et (II.. 1977, Chao et al., 1980). This paper reports data on knee joint motion. ground reaction forces, and fundamental temporal distance factors from a large normal population accumulated during the past 8 yr. A unified data collection reduction system and an effective analysis technique have been developed. The joint motion measurement technique may have certain disadvantages but the results produced can serve as a reference for comparison wi:h other data series, Although only a single joint was included in the evaluation, it may be possible that the systemic effects on other joints can be assessed indirectly from the temporal distance factors and the ground reaction patterns since these measurements represent a compounded effect of limb motion, POPULATION
STUDIED
Three groups of normal subjects, designated as I. II and III. with different age and sex distributions were studied with special emphasis on certain gait para219
E. Y. CHAO. R. K. LAUGHMAN,
220
E. SCHNEIDER
meters. Group I was the most complete in terms of the major gait variables included, but its mean age was older for the purpose of establishing normal data for the total knee replacement patients. Group II was designed to study joint motion in a younger age group with no information collected on ground reaction forces. Group III was primarily used for ground reaction force analysis. The age and sex distribution and the specific gait parameters studied for each group are summarized in Table 1. The subjects in groups I1 and III \vere used in the analysis of the essential number of Fourier coefficients required to reconstruct the motion and force patterns; such analysis was not performed for the subjects in group I. It was felt that this number of subjects should be sufficient to define the data variability of the normal population. The subjects were allowed to walk at their preferred speed and no attempt was made to study the effect of gait velocity on the key variables. Subjects were encouraged lo wear their ordinary walking shoes to avoid an additional variable. The subject’s body weight (BW)and lowerextremity length (LEL) were measured to normalize certain gait parameters. The entire normal population was recruited from local residents and Mayo Clinic employees, who were in good health
and R. N. STAUFFER
and had no prior history ofjoint disease in their lower extremities. BASIC GAIT PARAMETERS
Three groups of gait parameters were analyzed. Although some of these are well known, their definitions may vary among the different investigators. It is, therefore. necessary to briefly define all of them for future reference. Temporal distance factors
A typical footprint diagram, as shown in Fig. 1. illustrates the basic temporal distance factors studied. In order to compensate for anthropometric variations. stride length and step length were normalized against the lower estremity length (LEL). Cadence was defined as the number of strides min-‘, rather than the customary unit of step min- ‘. Walking speed was expressed in m min- ‘. Although left/right symmetry is generally assumed among the normals, this hypothesis was examined. Consequently, the basic temporal distance factors were defined separately for the left and right legs (Fig. 1). In certain gait patterns, the events of heel strike and toe off cannot be clearly identified. When this occurs, ‘ioot
Table 1. Normal population
groups used to establish the data base for knee joint motion and ground reaction force during gait
Type of parameters
Sub group
range
Age mean
men
Sex women Total
Temporal stride characteristics
II
32-85 19-32
53 25
32 21
37 20
69 41
Ground reaction forces
I III
32-85 21-67
58 42
32 20
37 18
69 38
I
32-85
58
32
37
69
19-32
25
21
20
41
Knee joint motion
II
Step w&h
Distance
I
--t
___
_
-
Stridk ianglh +
Fig.
1. Typical
-.. -Walk&
dmctvm
temporal distance factors used in gait analysis. Note that the single stance period of one leg is the same as the swing phase of the contralateral leg.
Normative
data of knee joint motion
and *foot off’ can be used as temporal markers for the stride parameters (Perry, 1974; Perry er 01. 1974).
strike’
Ground reaction force.5 Three basic components of ground reaction between the foot and the floor during stance phase of gait are defined as the vertical. fore-aft and mediolateral forces (Fig. 2). The entire pat tern of ground reaction force has been used as a descriptive criterion to study human gait (Hargreaves and Scales. 1975; Jacobs et nl., 1972). In addition, values can be identified from these curves for parametric analysis. A total of nine force parameters in percentage of body weight (F,-F,) and their chronological incidences of occurrence (Ti-T,) expressed in percent of stance phase period were defined. Additional variables. such as heel strike impulse (Simon tv cd.. 1982). foot-ground vertical impulse (Stott er al., 1973; Cavanagh and Lafortune, 19SO: Katoh er al.. 1981) and foot center of pressure distribution (Arcan and Brull. 1976; Cavanagh and Ae. 1980; Elftman. 1934: Grundy er nl., 1975; Scranton and McMaster, 1976;Katoh eta/., 1981),can bedetermined from the data curves. These specialized definitions are more suitable for the investigation of foot mechanics.
0
20
40 %
i
F
-lo
9
-15
j_
Of
60
60
221
and they were not studied
in the present
analysis.
Knee joint rotations Based on a convenient coordinate system established for joint relative motion (Grood et al., 1979; Chao. 1980), the three-dimensional rotation for the knee can be described simultaneously. If the relative joint rotation only occurs in one of the traditional planes (sagittal, frontal, transverse) from its neutral position, thecurrent definition would match with the traditional anatomical definitions of flexion-extension, abducand rotation tion-adduction internal-external (Fig. 3). Ten key parameters are defined from these motion curves (Fig. 4). The definitions of these parameters are summarized in Table 2 for reference. In general, the total stance flexion ($,) has a magnitude similar to the terminal stance flexion (4,). The total swing phase flexion (4s) and the total sagittal motion (#6) are also very close. For this reason. +3 and d5 were not measured. GAIT MEASURING TECHSIQCES
Temporal distancefactors A 10 m long walkway with two optical switches at either end was used for the gait analysis. Ample space at both ends of the walkway was available to allow the subject to walk at near constant velocity. The middle portion of the walking path had two sections of instrumented stainless steel tape mats to allow accurate
100
stance
T6
t
-20 i
Fig. 2. Basic parameters used to reaction forces. The force directions acting from the foot to the floor. magnitudes represent the aft components. BY I* : 1 c
+ii
F6
describe the foot-floor are defined as the forces Therefore, the negative and the medial force
% of gait tcycle +--
stance
-L
swing J
Fig. 4. Basic parameters defined in the study rotation in three dimensions.
of knee joint
E. Y.
222
CHAO.
Table 2.
R. K.
LAUGHMAN. E. SCHNEIDERand
Detinitions
Joint motion
R. N.
STAUFFER
used in describing the basic knee joint motion parameters Parameter
Definition
Knee flexion at heel strike (or foot contact)
(62 Flexion Extension
Total stance abd-add Total frontal motion
Abduction Adduction Rotation ::
measurement of step length and width (with a resolution of Zcm or + 1 cm) for either foot (Fig. 5). Walking speed was calculated from the signals produced by the optical switches (averaged speed) and verified by the tape mat measurements. Custom-made foot switches were placed underneath the soles of the shoes at the locations of the big toe, first and fifth metatarsal heads, and the heel (Fig. 6). The heel switches had a metal tag to allow direct contact with the tape mat for step length and width calculation. A self-contained electronic control unit was designed to provide the foot-ground contact pattern, as well as the step length/width calculation. Ground
reaction force
patterns
Two force plates located in the center of the walkway were used in the present study. One was a custom-designed transparent plate ivith seven quartz force transducers (Hagy et al.. 19751 and the other one. a commercially available Kistler* force platform. Both plates had a minimum resonant frequency of lOG200 Hz. adequate to record the main responses between the foot and ground during contact. These tbvo plates were placed in sequence along the walkway with a 20cm center line offset to facilitate a clean loading contact. Such an arrangement can also provide simultaneous observation of double support. The construction and the function of these plates have been previously described (Chao rr al.. 1980; Katoh et al.. 1981). Kner joint angular
Pre-stance flexion Total stance Aexion Terminal stance flexion Total swing Rexion Total sagittal motion
i-oration
Triaxial electrogoniometers were used to measure the three-dimensional knee joint rotations. The theoretical and experimental justification of this instrument has previously been presented (Chao et al.. 1970.1980; Chao and Hoffman, 1977). The advantages and disadvantages of this method. when compared against other techniques. werealso discussed (Stanic et (11..1976; Chao. 1978). The unique ability of providing
Total stance rotation Total transverse motion
instantaneous three-dimensional joint relative motion was the main reason for adopting this methodology IO manage our relatively large population sample. Although the placement of the goniometer can produce error, a trained evaluator. with the assistance of an instrument mounting guide, can reduce such error. The reproducibility of the data has been demonstrated by a test-retest experiment (Hoffman pr al., 1977). The variation of gait patterns for each test subject was found acceptable. Normal cross talk due to the external placement of the device can be corrected mathematically (Chao et al., 1970; Chao, 1978. 19801. The physical interference of the instrument did not seem to cause any significant change in normal gait function. DATA REDCCTION
Data samphg
ASD
ASaLYSIS
and reduction
Twenty-six channels of analog data were digitized through the A D convertor of a PDP 11134 digital computer. A 12-channel Beckman strip chart recorder was used to provide visual inspection of the analog data recorded by the goniometers. force plates. foot switches and tape mats. An instrument panel, capable of monitoring all test devices. \vas designed to check the test conditions before and durini each gait run. .L\ computer terminal (VT-55 monitor unit) was also used to provide immediate feedback of the data from the main computer to ensure correct data entry. The sampling rate of the A D conversion was set at 100 Hz. Thissampling rate is by no means optimal, but judging from our data acquisition system and the amount 01 data to be processed. the current rate was considered acceptable (Winter ct trl.. 1974). The entire analysis results were available one hour after completion of the evaluation. Flow-chart diagrams illustrating the b,tGc instrument organization. data collection. reduction and analysis schemes are sho\\n in Fig. 7.
-*Model 9281Al Switzerland.
I, Kistler
Instrumente.
AC.
Winterthur.
All parameters idenritied for the normal populatron were subjected to routine statistical an,tl\sis to obtall:
Fig. 3. The knee joint axes and planes of rotation as illustrated in a three-dimensional perspective view. The flexion-extension axis (l-l) is fixed to the femur, the internal-external rotation axis (3-3) is fixed to the tibia. The abduction-adduction axis is perpendicular to both of the other axes.
223
Fig. 5. Gait laboratory with instrumented walkway, including optical switches (S), stainless steel tape mats (T) and force platforms (F). The force plates are concealed in the ground, making them difficult to visualize.
Fig. 6. The foot-switch system used to measure the foot-floor contact sequences during level walking. Each switch is 1.5 mm thick, and the heel switch (H) has a metal tap to provide the measurement ofstep length and width when it is in contact with the instrumented mats. 224
__ “5
II = number
ol’par;imrtcrs
W, = weighting
Iliclur
In the prc\enl
(12
equal
similar expression
uf palt
determine
efficiency
(Kljajic
A/D
stud!.
selected among
walking
to cvlcul;~~c I,. ;jnd
rhe parameters
used.
\\eighrlng
MS
u~d.
A
hzs been
used
to
syrnmr~ry
;md energy
(11t/l.. 19751. A shghtly
dilt‘erent
con~umpt~on formukt
channel)
converter (64
channel)
.
::::::iFoot
~~ PDP
:‘. .::‘.:
11/34a
L
Synchromze
.
!r
Trlgger
POP 11/34a Computer Tekll 40 Tern -
(256kb) System
---,_-A,--,
Data
Aquisition Program
-
Printromx Lme/graphic Printer
rb)
Fig. 7 [a) Flow diagram for gait analysis inslrument organization and data reduction scheme. (b) Flow chart descnbing the computer system structure for gait data reduction. analysis display and storage
I’or I>
E. Y. CHAO.
226
R. K. LAUGHMAN, E.
has recently been suggested (Soudan, 1982). No attempt was made to compare the symmetry index values calculated from these two methods. Non-parametric
analysis
There were two main purposes in performing the following analyses. The first was to derive repeatable and reliable coefficients which can substitute the parameters defined previously. Additional important parameters may also be identified by combining the existing coefficients and time so that not only the magnitude but also the wave form ofgait signalscan be objectively studied. The second purpose was to present the data in closed-form expression so that all the individual curves could be averaged conveniently. In addition, raw data storage in the computer becomes more efficient. The method of Fourier analysis was adopted, since it has been successful in the past to study human gait, (Zarrugh and Radcliffe, 1979; Jackson, 1979; Sutherland er al., 1980; Jacobs er al., 1972; Alexander and Jayes, 1980). The theory behind this method can be found in standard texts (Brigham, 1974; Goertzel, 1968). Briefly stated, the ground reaction force or joint motion patterns can be expressed as a periodic function of time,f(t) with period T,;
2 (Ajcosjw,t+BjSinjw,t)
f(t) = A,+
j=
with w, as the sampling frequency. coeflicients are determined by; A,, = f
‘“f(t)dt 0 s0
(2)
1
The Fourier
= f(t),
(3)
(4)
s T. f(t)sinjw,tdr. 0I0
(5)
The method of selecting the essential number of
Table
3. Temporal
distance
harmonics depends upon the sampling rate and thaccuracy required to reconstruct the original dar.1 curve. Different objective criteria have been tried before (Capozzo et al., 1975; Jackson, 1979; Winter et al., 1974). The technique adopted here has been described elsewhere (Schneider and Chao, 1982). Using the Fourier analysis technique, three basic patterns of knee joint motion and ground reaction were determined. The ‘individual’ pattern stands fer the data curve recorded in one cycle of a gait run in .1 single subject. When all the individual patterns of J subject areaveraged, they form the ‘t!_pical’pattern ~LX that subject. When all the typical patterns for the normal population are combined, a ‘general’ pattern 15 defined for the normal group.
RESULTS
The normal subjects were divided according to as< and sex. The two groups (I and III) selected for ground reaction force analysis were studied at two differenr time periods and for varying objectives. Although thclr age ranges had an obvious overlap, the statistic21 result, based on student’s f-test, showed that these tao groups were significantly different (p < 0.001). For thlj reason, it was considered adequate to study the age and sex effects based on the population groups defined in Table 1. For convenience, the results of the parametric and non-parametric analyses are presented separateI>. Parametric
Aj =; o OTgf(t)cosjw, t dr,
Bj =f
SCHNEIDER and R. N. STAUFFER
analysis
The temporal-distance factors for population groups I and II are summarized in Table 3 according to sex. Both mean and standard deviation for each parameter are presented. The step length and doubls stance for the right leg were tabulated, but the corresponding data for the left leg are presented implicitly through the ratio values. It is interesting to find that step length is nearly symmetric in both men and women (group II only) but not their single and
factors in the normal population groups I (ages 32-85)and II (ages 19-32). Ths values and standard deviation are presented. (Refer to Fig. 1 for definitions) Women
Men (n = 53)
for the mean
(n = 57)
Parameter
I (n = 32)
II (n = 21)
Total
I (n = 37)
II (n = 20)
Total
Cadence (stride min- ‘) Stride Length, LEL’ Speed (m min- ‘)* Step length, right (cm)* Step length ratio (small/large) Step length/LEL, right Right stance ( “,, G.C.) Left stance ( a0 G.C.) Single stance, right (7, G.C.) Double stance. right ( “/, G.C.) Double stance ratio (small, large)
52+5 1.56+0.15 76.1 f 12.5 73+8 t 0.78 + 0.07 59i2 t 41+2 8.8 k 1.9 t
50+8 1.48kO.17 71.9 + 18.3 69k9 1.0*0 0.73 + 0.08 60+2 6Ok3 4Ok2 10.2 f 2.6 0.8 kO.1
51k6 1.53kO.16 74.4+ 15.1 71+8 t 0.76 +- 0.08 59+2 t 4lk2 9.4 f 2.3 t
56k5 1.40+0.14 69.4kll.O 61+8 t 0.70 + 0.07 60+2 t 40+2 10.0 f 5.5
5i ~5 1.39zo.17 63.9fll.l 6017 l.OrO 0.69 I 0.08 59r2 59r3 41*2 8.9 t 2.0 0.9 10.1
545 5 1.40+0.11 67.5+11 1 61+_7
1,G.C. = Percent of Gait Cycle *Significantly corrected with 10 or more parameters tThe stride characteristics were assumed symmetric
(p -C0.01). in this group.
t
t 0.70 f O.CI59k’ t 41+2 9.6 + 4.6 t
Normative
227
data of knee joint motion
double stance ratios (group I only). Among all temporal distance factors. only cadence was found to be slgmficantly different at the level of p < 0.01 in the female subjects between the two age groups (I and II). Houever, when the two age groups are combined, cadence, stride length LEL and step length are found to be different between men and women (p < 0.01). Therefore. within the age range studied here, dividmg the normative data on the temporal stride characteristics according to sex appears necessary. The single stance (single limb loading) of one leg is, by definition, identical to the swing phase of the contralateral limb. The double stance for the left leg can be easily calculated by subtracting the right swing phase and right double stance period from the left stance phase (Fig. 1). The key parameters for ground reaction force, as defined in Fig. 2, are tabulated in Tables 4 and 5 for men and women in each age group studied. The relative variations for the force components with higher magnitudes (f, , F2, F,, F, and F6) are smaller. The same relationship holds for the time factors. This reflects that the main features contained in ground reaction force patterns appear consistent, but they tend to vary on minute details. Men tend to have equal peaks (F, and F,) in the vertical force, while women appear to have a higher second peak (F3). However, this difference was insignificant statistically. The magnitudes for F,, T4 and T, were found to be different between groups I and III in men, while F, and
F, were different in women for p < 0.01. In subject group I, men and women were different (p < 0.01) in F, , F,, T, and T,. However, when the two groups were combined, sex only caused statistical differences in F, and T, Since F, and F, have higher magnitudes and are thus more sensitive in depicting variation caused by gait abnormalities, it appears that a separation based on sex is also necessary in presenting ground reaction force data. However. the age erect cannot be discounted and a more refined separation of age groups may be necessary before definitive conclusions can be drawn. Although the anticipated variation exists in nearly all parameters studied, total ranges of knee joint motion in each plane are surprisingly consistent (Table 6). To examine age and sex effects on knee joint motion, the results of groups I and II were compared statistically. It was found that joint motion in gait is age related in men (p < 0.01 for 41 and $1; p < 0.05 for @4r 46 and 6,) but not in women, except for knee flexion at heel strike (41, p < 0.05) which may be influenced by the type of footwear used by the female subjects. When the data for men and women were compared, regardless of age, only the total sagittal motion ( &6) and frontal motion (e,) were found to be different at the levels ofp < 0.05 and p < 0.01, respectively. Although the age factor seems important in describing knee motion in men, the variation in these parameters was large, which makes such division less reliable. Since sex separation has been shown necessary
Table 4. Basic parameters in ground reaction force. (See Fig. 2 for definitions) Men (n = 52)
Parameter
Women
(n = 55)
(O. B. W.)
I (n = 32)
III (n = 20)
Total
I (n = 37)
III (n = 18)
F,’ F2’
114*9 72f9 111+9 1.8 + 1.9 17.7 k4.0 20 + 3.9 4.2 &-1.4 5.1 f. 1.8 4.7 f 2.0
111*7 74+13 112+7 3.6 + 3.0 17.Ok4.6 19.9 + 2.9 5.2 + 2.9 4.4 * 2.8 4.6 f 2.4
113+Ei 72kll 112+8 2.5 k 2.4 17.4 + 4.2 19.9 + 3.5 4.6k2.1 4.8 + 2.2 4.7 + 2.1
107&S 7558 llOk6 1.7k2.0 15.1 + 5.0 16.7k4.1 3.6+ 1.7 4.6 f 2.3 4.2 + 1.7
110+7 74k8 116_+10 3.0 + 1.4 17.1 f 3.8 21.1 +4.0 4.3 + 2.8 4.7 * 2.1 3.9 * 2.2
F, F, f,* f,* FF, F, ‘Significantly
Table
correlated
with 10 or more parameters
5. Key time parameters
T,’ T, T3 T4 75 r, 7, T& 79 *Significantly
reaction
108i8 75k8 112k8 2.1 + 1.9 15.7 + 4.7 18.1 f4.5 3.8 k 2.1 4.6 + 2.2 4.1 + 1.8
(p < 0.01).
forces. (See Fig. 2 for definitions)
Women (n = 55)
Men (n = 52)
Parameter
( Q.stance)
in ground
Total
I (n = 32)
III (n = 20)
Total
I (n = 37) _
III (n = 18)
Total
25 + 3 47+6 79*4 3*1 20+3 87 k 2 8_+3 25L-4 73*4
24&4 46+4 77+2 4+2 19k2 86kl 7_+3
24+3 47 f 5 78+3 3+1 19+3 86&2 8+3 27+6 73 * 5
27k4 49*5 78k4 3+1 21k3 87+3 8+3 30+9 69+11
25+3 5oi9 78+3” 3+1 19+3 86kl 7+3 31+6 72+6
27+3 49k6 78 f 3 3+1 20+3 87 ) 3 8+3 31+8 70+10
correlated
31+7 72+6
with 10 or more parameters
(p < 0.01).
228
E. Y. CHAO,R. K.
LAUGHMAN,
E. SCHNEIDER and R. N. STAUFFER
Table 6. Key joint motion parameters at the knee during level walking. (See Fig. 4 for definitions) Parameter (degrees)
Men (n = 53) 1 (n = 32) -1+4 17+5 31*5 72+6 7+2 12+4 9*3 14*4
II (n = 21) 7+4 13k6 35+6 68k8 6+2 11*3 11*3 14+3
in other gait parameters, joint motion data should be treated in a similar manner. A total of41 gait parameters (two on joint isometric strength and two related to stair walking were not reported here) were subjected to linear correlation matrix analysis. Among the 37 parameters included in this paper, ten had significant correlation (p < 0.01) with ten or more of the remaining variables. These parameters, as marked by an asterisk in Tables 3-6, will assist in the selection of the most significant variables for future statistical analysis. It is interesting to note that no joint motion parameters appeared in this list, which tends to suggest that in the study of normal gait in adults, joint motion data could be redundant. However, such a relationship may not exist when abnormal gait is involved. Certain parameters did not have a normal distribution within the population analyzed, percentile distribution (10th and 90th percentile) was used to express the data. Since such presentation is less common in the literature, it is omitted here. When the normal range for each parameter is used to assess gait abnormalities in patients, such an expression may be more adequate. The symmetry index (I,) was calculated using equation (1) for the population group I based on a subset of eight significant parameters. These parameters are passive and standing knee flexion, percent of stance phase, 42, &, F,, F, and T, . A mean value of 0.93 + 0.03 was obtained, while a value of ‘1’ stands for a perfect symmetry between the two legs. These results signify that an average normal gait seems to have a slight asymmetry. Non-parametric anal_vsis
Figure 8 illustrates the ‘typical’ patterns of the three floor reaction force components in one subject and the ‘general’ patterns of a group of 26 normals. The men and women were combined, since there was no significant difference between the two sexes in the current subset of the normal population studied. The means, plus and minus one standard deviation, are plotted. The variation among each individual pattern can be significant (especially in the fore-aft and medial-lateral components), which indicates the need of studying the averaged patterns. Similarly, the variation among the normal sample can become substantial, but the ‘gen-
Women (n = 57) Total
1 (n = 37)
II (n = 20)
Total
2+6 15k6 32+6 71+7 7+2 12+3 10+3 14*4
o&-5 15k6 30+5 66k9 7+2 lot4 10+3 14+4
4*6 14+5 31+7 70+8 6*2 9*2 9_+2 13+3
1*5 15*6 30&6 68k8 7+2 10*3 9+3 13*4
eral’ pattern provides a good representation of the general wave form of these curves. The typical pattern is able to illustrate the subtle feature of the raw data, such as the impulse at the initial heel strike in the vertical force reaction (Simon et al., 1982). However. in the general pattern these minute features become obscure due to the averaging process. The Fourier coefficients (both the sine and cosine terms) for the first seven harmonics used to reconstruct the ‘general’ patterns are listed in Table 7 for thirteen men and thirteen women. The magnitude of the coefficients beyond the seventh harmonics decreases quickly to an insignificant level. The essential number of harmonics required to construct these patterns was found to be five for the vertical force, while up to the seventh harmonics were required for both the fore-aft and medial-lateral force components. The essential number of Fourier coefficients for the ‘typical’ pattern of each normal subject is slightly higher. A comparison of the ‘typical’ and the ‘general’ patterns for the three knee motion components are shown in Fig. 9. Again, the variation among the individual patterns was quite small. but it became substantial among the typical patterns in the normal population studied. This variation may be due to the baseline shift during motion evaluation. The mean curve, defined as the ‘general’ pattern. appears to be able to retain the basic features of the typical motion data and to provide reliable peak-to-peak measurements. The essential Fourier coefI%ents required to reconstruct the ‘general’ patterns are presented in Table 8 in terms of their mean and standard deviation. The number of terms needed for the typical pattern is slightly higher. DISCUSSION It has been suggested that in adult gait, significant deviation may occur at the sixth decade (Murray er al., 1964). To re-examine this hypothesis, the normal group I was further divided into two subgroups, separated at 55 years of age. Such a division allowed us to study three age groups in both sexes, i.e. younger than 32 yr (original group II), between 32 and 55 yr la subset of group I. 17 men and 15 women), and older than 55 yr of age (a subset of group 1. 15 men and 22
Normarive
data of knee joint motion
--e-tnmean
01 26normals
X8of stance
phase
Fig. 8. Normal ground reaction force patterns. (a) The mean and 1 standard deviation envelope of the ‘typical’ pattern of one normal subject based on 6 individual parterns. (b) The nean and 1 standard deviation envelope of the ‘general’ pattern of 26 normal subjects (a subset of group 111).
Table 7. The Fourier
coefficients
used to produce the ‘general’ pattern force components
Fourier coefficient
( “<,BW .A” AI A, A3 Al .A3 .4, A1 B, BL B, B, B, B, B-
of the ground
reaction
Subset of group III (n = 26) Vertical
Fore-aft
MedialLlateral
- 33.5 + 3.6 - 1l.S + 2.3 -2.3 f I.4 -0.9 f 1.2 - 0.4 f 0.9 -0.3 +0.7
-0.4rfo.s _ 1.7kO.7 -0.1 +0.8 0.8 kO.5 0.8 f0.5 0.3 + 0.3 0 * 0.2 -0.2 f 0.2
1.9 + 1.2 - 2.0 + 0.5 - 1.6 t 0.5 0.1 * 0.4 0.4 * 0.2 0.4 c 0.3 0.3 + 0.3 0. I _t0.1
- 2.3 f 2.9 1.5 + 3.7 2.6 f 1.9 3.3 + 1.4 1.8 + 1.2 0.9 +0.8 0.4 f 0.7
12.4 f I.7 4.4 f 1.2 -0.6+0.6 -1.5kO.5 - 1.1 +0.4 -0.6kO.3 - 0.4 f 0.2
OkO.6 -0.5kO.3 -0.3*0.3 -0.2kO.3 -0.1 kO.3 -0.1 +0.3 -02+02
78.1 f 2.9
- 22.6 + 3.7
women). The new results nearly paralleled our original tindings in that age difference seems to cause deviation in ground reaction force patterns in women, and it appears to affect knee joint motion only in men,
particularly between the groups separated at 55 yr. In general, sex variation was found more significant than the age effects. Therefore, in grouping normative data it appears more appropriate to divide it according to
E. Y.
230
P D
60.
5 ‘G
40.
CHAO,
R. K.
LAUGHMAN, E. SCHNEIDERand R. N. STACFFER
_meanof7lparfern m one sublecf
--+-
mean ol 65 normals
mean+lsd.
5 2
20.
.s 2
0.
2 201
’ 0
I. 20
GOgait
Fycle
80
100
%
-
-20+
‘I %
of gait
80
100
<3
I
2ot
Fig. 9. Knee joint rotation patterns. (a) The mean and 1 standard deviation envelope of the ‘typical’ patterr. ofone normal subject based on 11 individual patterns. (b) The mean and 1 standard deviation envelope of the ‘general’ pattern in 65 normals (a subset of group I).
Table 8. The essential Fourier coefficients used to produce the ‘general‘ pattern of knee joint motion during gait. Fourier coefficient (degrees) A0 A, A, A3 A, A,
Flexion/extension
Subset of group II (n = 37) Abduction/adduction Inr-ext. rotation
A7 A,
24.69 k 3.74 - 8.73 k 3.01 - 12.71 f 2.63 0.49 * 1.13 -0.97+1.12 0.78 + 0.84 0.48 f 0.49 0.50 f. 0.39 0.26 + 0.25
- 2.93 + 2.09 - 0.36 + 0.95 1.50 * 1.19 0.80 & 0.61 0.10 + 0.42 -0.07 f 0.32 0.21 kO.23 0.06kO.16 0.13 kO.15
B, B, B3 B, B, B, B, &
- 20.10 + 2.72 10.96 + 2.57 4.21 * 1.10 1.83f1.11 1.22 * 0.57 0.45 * 0.48 0.38 + 0.46 -0.06 _+0.33
0.78 + 1.93 0.23 + 0.92 - 0.66 + 0.64 - 0.33 * 0.49 0.17 +0.28 0.09 * 0.20 -0.01 kO.18 0.12kO.16
A6
sex. When age variation is to be considered, a separation at 55-60 yr seems to be adequate. The temporal4istance parameters involved in freespeed walking have shown surprising consistent!
-
-
I .24 k 3.60 1.56 It: 1.79 0.96 k I.63 0.50 f. 0.92 _ 0.09 k 0.61 * 0.35 f 0.69 0.11 kO.49 0.29 f 0.46 0.20 + 0.41
-0.55 & 1.95 -0.86 f 1.30 - 0.05 + 0.85 0.63 + 0.90 0.22 f 0.50 0.76 + 0.56 0.50 + 0.44 0.3 1 * 0.28
among the two groups (I and II) analyzed. .Although walking speed varied among the individuals. the range of variation was too small to study its effect on other gait parameters. Linear extrapolation of the current
Normative data of knee joint motion ddta IO the extreme ranges of walking would not be reasonable. Speed of walking was found to be an important parameter. as identified from the correlation study. The normalization of distance related factors with respect to the lower extremity length (l_EI_) appears to reduce intersubject variation (Table 3). Single and double stance periods are closely related to weight acceptance in each leg. These parameters are expected to have a significant contribution in studying pathological gait, since the normal load acceptance capability of the lower extremity joints will be predisposed by the specific disease involved. The joint motion and ground reaction force parameters are important in the assessment of the quality and characteristics of human gait. However, not all of them need to be identified due to their inherent relationship. When a specific class of abnormal gait is to be investigated. R’ analysis (multiple correlation) must be conduc’ted in order to identify the key parameters which can help to differentiate the joint functional changes caused by the underlying pathological conditions. The relative importance of these parameters must also be established through the USC’of discriminate analysis. so that they can be properly weighted to improve the sensitivity of data separation. Not all of the motion and force parameters can be identified easily and repeatedly, especially when abnormal patterns are involved. When these values are read directly from the raw data tracings, the entire process can be extremely tedious and human error due to subjective judgment becomes inevitable. These drawbacks can be prevented by augmenting an automated search program using a computer. However, in the event of data pattern changes, this program may become very complex. Fourier analysis may alleviate this problem, since most of the parameters defined previously can be determined accurately by the Fourier series expression. Nova. variables capable of detecting pattern variation in gait data can also be investigated. The use of Fourier analysis has other advantages. Raw data on the joint motion and ground reaction force patterns can be stored efficiently in the computer using a finite number of Fourier coeficients instead of the digitized discrete data points. Typical and general patterns can be easily reconstructed in their graphical form for display or phasic analysis. The averaging process involving numerous patternscan be performed and presented conveniently. TO handle large normal and patient populations. this method of data handling ‘tnd analysis is extremely helpful. The ‘individual’ joint motion and ground reaction force patterns for each normal subject exhibited certain variations among the gait cycles tested. These iartations may be due to the natural responses, en\,ironmental effects and/or experimental errors. It is important that these patterns be averaged so that a representative ‘typical’ pattern can be produced for a specific subject. When the normal population is studied as a whole, the ‘typical’ patterns for all the subjects vary mainly in magnitude, but not in their
231
general wave form,due to baseline shift. Consequently. the ‘general’ pattern is a good representation for the entire group studied. However, such an averaging process tends to obscure subtle features occurring in a short period of time. If gait analysis is performed with the intention ofcharacterizing these minute events. the averaging process should be avoided to allow the individual patterns to be dealt with separately by using a maximum number of Fourier coefficients for their description. The present results, both in their parametric form and their characteristic wave patterns, have compared favorably with most of the available data in the literature. Although the definitions used for various gait parameters may vary from one institution to another, as long as the general patterns of the variables can be reproduced, such as in the present case. objective comparison should still be possible. To establish a useful reference data base for normal subjects requires an enormous amount of time and cost. If our data can be matched with other available sources, a combination of similar data series will provide a data bank of large sample size available to all investigators for clinical and research applications. It is important to recognize that the triaxial goniometer technique may not be the best method for joint motion measurement. The cross talk effect due to possible misplacement ofthe instrument can introduce artifacts. Soft tissue involvement may also cause error. although this drawback is difficult to avoid, regardless of the instrument system used. Despite their large variation, baseline measurements of abduction-adduction and rotational motion at the knee during stance phase can be useful in the study of pathological gait. If these motion components become large in abnormal gait, they may reflect possible pathological conditions. Due to the general lack of such data in a sizeable sample. the present results in three-dimensional knee motion can certainly be used as a common reference for comparison. In the advent of modern technology with fast-paced development of sophisticated electronics and computerized video instruments. it is expected that a completely automated method of conducting gait evaluation will emerge. However. the adoption of new instrumentation must be balanced with effective data reduction and analysis smce human gait is a highly variable biological phenomenon, and its problems cannot all be dealt with by sophisticated equipment alone. It is advisable that more effort be devoted to data analysis and the present paper only represents one such attempt.
Acknowledgemenrs-The work reported in this paper was supported in its entirety by NIH Grant No. Am 18029. Many people havedevoted their timeand etforts to the development ofthe instrumentation and data analysis methodology used in this study. We wish to specifically acknowledge the contributions made by Fred Axmear. Ross Hoffman. Mitsuo Tanaka and Joanie Bechtold.
232
E. Y. CHAO,
R. K. LAUGHMAN, E. SCHNEIDER
REFERENCES Alexander, R. M. and Jayes, A. S. (1980) Fourier analysis of forces exerted in walking and running, J. Biomechrrnics 13, 383-390. Andersson. G. E. J.. Andriacchi.T. P.and Galante, J. 0. (1981) Correlation between changes in gait and in clinical status after knee arthroplasty. AC~A od~op. scond. 52, 569-573. Arcan, M. and Brull, M. A. (1976) A fundamental characteristic of the human body and foot. the foot-ground pressure pattern. J. Biomrchctnic.s 9, 453457. Bajd, T., Stanic, U., Kljajic, M. and Trnkoczy, A. (1976) Online electrogoniometric gait analysis. Camp. Biomrd. Re,. 9, 5. Brigham, E. 0. (1974) The F~sr Fourier Tru~rsj~rm. PrenticeHall, Englewood Cliffs, N.J. Capozzo, A., Leo, T. and Pedotti, A. (1975) A general computing method for the analysis of human locomotion. J. Biomechunics 8, 307-320. Cavanagh, P. R. and Ae, M. (1980) A technique for the display of pressure distributions beneath the foot. J. Biomechrmics 13, 69-75. Cavanagh, P. R., Lafortune, M. A. (1980) Ground reaction forces in distance running. J. Biomechnnics 13, 397406. Chao, E. Y., Rim, K., Smidt, G. L. and Johnston. R. C. (1970) The application of4 x 4 matrix method to the correction of the measurement of hip joint rotation. J. Biomrc~hcmics 3. 459471. Chao, E. Y. and Stauffer. R. N. (1974) Biomechanical evaluation of geometric and polycentric knee arthroplasty. In Tolo/ Knee Rep/acemenr. pp. 52-60. Institution of Mechanical Engineers, London. Chao. E. Y. and Hoffman, R. R. (1977) Instrumented measurement of human joint motion. ISATrans. 17,13-19. Chao, E. Y. (1978) Experimental methods for biomechanical measurement of joint kinematics. In CRC Handbook oj Bioengineeriny in Medicine and Biolog) (edited by Feinberg. B. N. and Fleming. D. G.). Vol. I, pp. 38541 I. CRC Press, West Palm Beach, FL. Chao. E. Y. (1980) Justification of triaxial goniometer for the measurement of joint rotation. J. Biomrchanics 13, 989-1006. Chao. E. Y.. Laughman. R. K. and Stauffer, R. N. (1980) Biomechanical gait evaluation of pre and postoperative total knee replacement patients. Arch. orrhop. Traum. Sury. 97. 309-317. Contini. R. and Drillis. R. (1954) Biomechanics. Agpl. Mech. Ret-. 7, 49-52. Dommasch, H. S.. Brandell, B. R. and Murray. E. B. (1972) Investigation into techniques of gait analysis. J. biol. phoroyr. 40, 106-l 16. Eberhart. H. D. and Inman, V. T. (1951) An evaluation of experimental procedures used in a fundamental study of human locomotion. Ann. iz’. 1: Acad. Sci. 51. 1213-1228. Elftman, H. A. (1934) A cinematic study of the distribution of pressure in the human foot. Anal. Res. 59, 481491. Goertzel, G. (1968) Fourier analysis. In ~AfhemAticA/ Mrrhodsfor Digital Computers, (Edited by Ralston, A. and Wilf, H.), pp. 258-262. John Wiley, New York. Grood, E. S., Suntay. W. J., Noyes, F. R., Butler, D. L., Miller. E. H. and Malek. M. (1979) Total motion measurement during knee laxity tests. In TrAnSAcfiOnS of‘ rhe 251h Orrhopcwdic Research Socier!. Vol. 4, p. 80. Grundy. M.. Tosh. P. A.. McLelsh. R. D. and Smidt, L. (1975) An investigation of the centers of pressure under the foot while walking. J. Bone Jr. Surg. 57B. 98-103. Gyiiry. A. N.. Chao, E. Y. and Stauffer, R. N. (1976) Functional evaluation of normal and pathologic knees during gait. Archs. ph.w. Med. Rehabil. 57, 571-577. Hagy, J. L.. Keller, C. W. and Musil, L. W. (1975) Load cell supports for a dynamic force plate. Proceedings of‘rhe Ninrh .4tmua/ Aerospwr Medicine Symposium, NASA Techniccrl .tfemorundum TMY 3274.
and R. N. STAUFFEH
Hargrales. P. and Scales. J. T. (1975) Clmical assessment of gait using load measuring footwear. ..lc,rtr orrhop. sc~tmd.46. 877-895. Hon‘man, R. R.. Laughman. R. K.. Stautt‘er. R. N. and Chao. E.Y.(1977lNormativedataofkneemotioningaitandstair actlvittes. Proc. o/ 1111’ 30111 Armuul Confcrcwt~ on Enyintvriny in Medicine cmtl Bioloy!.. Vol. 19, p. 186. Alliance for Engineermg in Medicine and Biology. Jackson, K. M. (1979) Fitting of mathematical function t<) biomechanical data. IEEE Trtrnr. hiwwll. Enyrlil BME. 26(2), 122-124. Jacobs. N. A.. Skorecki. J. and Charnle). J. (1972) Analysis ol the vertical component of force in normal and pathological gait. J. Biomrchtrnics 5, I I 31. Kapovich. P. V. and Herden. E. L. (1960) Electrogoniometric study of joints. U.S. Armed Forces Med. J. I I, 42-l 450. Katoh. Y.. Chao. E. Y.. Morre\. 8. F.. Laughman. R. K. and Schneider. E. (1981 I Objective evaluation of painful heel syndrome b) gait analysis. In Proc ctdim/.t o/ tht, I .///r/i /t1rrrmrriomr/ Cwlyre.u q! Bionlr‘,lr[r,lic..~. 20 2-l July. Nagoya. Japan. Human Klnrtics Publishers. Champaign. IL. Kettelkamp. D. B.. Johnson, R. J.. Smidt. G. L.. Chao. E. 1’. and Walker, M. (1970)Anelectrogoniometricstudy ofknee motion in normal gait. J. BIW JI. Surcq. 52A, 775. 790. KlJajic. M.. Bajd. T. and Stanic. U. (1975) Quantitative gait evaluation of hemiplegic patients using electrical stimulation orthoses. /EEE Trtrm. hiomrd. Enyruy 22, 43% 441. Lamoreus. L. (1971) Kinematic measurements in walking. Bull. Prosrhrt. Rr.\. 10-15, 3-84. Liberson. A’. T. (1965) Biomechanics of gait: a method ot study. .Arc,h.t. phy.5. .2fed. Reh
8: 2. Perry, J. (1974) Clinical gait analyzer. 8~11. Prosrhur. Rc.\. 10-12, 188-192. Perry. J.. Homer. M. M.. Giovan. P.. Antonelli. D. and Greenberg, R. (1974) Gait analysis ofthe-triceps surae in cerebral palsy. J. BOW Ji Sury. 56.4. >I l--520. Schneider. E. and Chao. E. Y. (1982) Fourier analysis: a valuable tool in gait analysis. 7rtmwcrion.s o/ rhc ZYrh Orthopedic Research Socier,v. Vol. 7. p. 221. Scranton, P. E. and McMastsr. J. H. (1976) Momcntarj distribution of forces under the foot. J. Biomechtmk.\ 9. 45-48. Simon. S. R.. Paul. I. L.. Mansour. J.. Munro. M.. Abernath. P. J. and Radin, E. L. (1982) Peak dynamic force in human gait. J. Bwmechtmics 14, 817-822. Soudan. K. (1982) Standardization of gait kinematic data using a gait symmetry index and Fourier analysis. In Biom&anics: Prmciplcs and .-lpplrcutions (EdIted b} Huiskes. R.. van Camp&. D. H. and de Wijn. J. R.). pp. 135-140. Martinus Niihoff. The Hague. The Netherlands. Stanic. U.. Bajd, T.. Valencic. V..cotm~rio,l c/ml rht,
Normative
data of knee Joint motion
c ;t,rrt ,r/ .I~IU/I \I, IJ/ (;‘III. pp. IO? 119. Phrladelphia. Sr,ruttir. R. N.. Chao. E Y. and Gyory. A. N. (19771 Bromechanlcal gait .IIIA~!.MS of thedrseased kneeJoint. Clip. L)rrIr~rp. rzl. Re\. 126. 2% 255. S~c~ndler. .4. 11953) Hrstorrcal rekieu of rhe studres and ~n\es,trgatrcns made rn relaIron 10 human gull. J. Bow ./I .s10I/. 3%. 54&542. Stntr. J. R. R.. Hurton. \V. C. and Stokes. 1. A. F. (1973) Forces under the foor. J. Bvrr~~Jr .Sary. 55B, 335-344. Sutherland. D. H.and Hag!. J. L. 119721 Measurement ot‘garr mo\emenl from molron pxrure tilm. J. Bmr Jr Sury. 5JA, ‘$7-797. Sutherland. D. H.. Olshen. R.. Cooper. L. and Wood. S. L.
233
(1980) The development of mature gall. J. tlorrr Jr .Sur~r. 62A, 336 353. Townsend. M. A., Izak. M. and Jackson. R. W. (19771 Total motion knee goniometry. J. B~omd~u~~ IO, I x3 193. Winrer, D. A., Greenlow. R. R and Hobson, D. A. (1972) Televisioncomputer analysis of kinemalics of humau gait. Conrp. hiorned. Ru.\. 5, 49&504. Winter, D. A.. Sidwall, H. G. and Hobson, D. A. (1974) Measurement and reduction of norse m kinematics of IocomoIion. J. Biomechonics 7, 157-159. Zarrugh, M. Y. and Radcliffe. C. W. (1979) Computer generation of human gait kinematics. J. BKVIW-/U& 12, 99-111.
Laboratory.
Department
E. SCHNEIDER
of Orthopedics.
and R. N. STAWFER
Mayo Clinic, Rochester.
MN 55905, U S.A.
Abstract-A normative data base of temporal distance factors, knee joint motion and ground reaction force patterns for 148 adults during levjel walking is reported. The data \sere studied using parametric and nonparametric (Fourier series) representations to facihrate statistical analyses. Key parameters were divided according to age and sex. Individual force and motton curves of each normal subject were averaged to establish the ‘typicat’ patterns. All typical patterns were combined to construct the ‘general‘ patterns. The essenttal number and most significant Fourier coefficients were determined. It was found that the sex-related variation is more signmcant than theage-related variation in adult gatt. Thisdata basecan serveasacommon reference for comparison.
INTRODL’CTION Human walking has been extensively studied by many investigators from various disciplines, including anatomy, kinesiology, neurophysiology and biomechanics. The historical development of this branch of biological science since the pre-renaissance era has been thoroughly reviewed (Contini and Drillis. 1954: Steindler, 1953; Pauwels, 1945). Although gait analysis. or assessment, has been pursued for a long period of time, our knowledge concerning human locomotion is far from complete. Normal walking is an extremely complex biomechanical process. It involves a three-dimensional motion of a multiple linkage system which demands coordinated control by the central nervous system far exceeding the sophistication of man-made machines. In spite of the attempts to model human gait, comprehensive data is still insufficient to put locomotion in quantitative terms. The inability to describe gait characteristics objectively and the lack of effective methods for data analysis to study a large population might have been some of the contributing factors. Although the attempt to describe human gait based on neurophgsiologic control principles is still in its developmental stage. the phenomenologica! aspects of locomotion have shown significant promise in associating the normal and abnormal gait patterns with the underlying musculoskeletal pathologies. Since the major aim of treating patients with arthritic diseases is to correct joint deformity and restore functional normality. the ability to quantitate any visible structural or functional changes in the limb segments atflicted by the pathology based on well-defined and clinically meaningful parameters is important. In addition, a carefully established normative data base from a broad spectrum of the population is essential to define anthropomorphic and physiologic variability. The ability to establish such a data base depends on an
efficient measurement technique and data analysis method. Normal knee joint kinematics in gait have been studied extensively with regard to sagittal motion (Murray rr al., 1964,197O; Murray, 1967; Eberhart and Inman. 1951; Liberson. 1965; Sutherland and Hagy. 1972; Kapovich and Herden, 1960; Winter er al., 1972, 1974; Bajd et al.. 1976; Milner er al.. 1973; Dommasch 1972) and three-dimensional rotation er al.. (Kettelkamp et al., 1970; Townsend rr 01.. 1977; Lamoreus. 1971: Morrison. 1969). Few studies have addressed the question of data variation among the normal population, which may be due to the insufficient sample size investigated. The existing reports also limit the results to some specific gait parameters with varying definitions. A number of the more recent studies compared abnormal knee function with that of normals, but without presenting extensive normal data (Andersson t’r (II.. 1981: Gyory ef ~1.. 1976; Chao and Stauffer. 1974: Stauffer et (II.. 1977, Chao et al., 1980). This paper reports data on knee joint motion. ground reaction forces, and fundamental temporal distance factors from a large normal population accumulated during the past 8 yr. A unified data collection reduction system and an effective analysis technique have been developed. The joint motion measurement technique may have certain disadvantages but the results produced can serve as a reference for comparison wi:h other data series, Although only a single joint was included in the evaluation, it may be possible that the systemic effects on other joints can be assessed indirectly from the temporal distance factors and the ground reaction patterns since these measurements represent a compounded effect of limb motion, POPULATION
STUDIED
Three groups of normal subjects, designated as I. II and III. with different age and sex distributions were studied with special emphasis on certain gait para219
E. Y. CHAO. R. K. LAUGHMAN,
220
E. SCHNEIDER
meters. Group I was the most complete in terms of the major gait variables included, but its mean age was older for the purpose of establishing normal data for the total knee replacement patients. Group II was designed to study joint motion in a younger age group with no information collected on ground reaction forces. Group III was primarily used for ground reaction force analysis. The age and sex distribution and the specific gait parameters studied for each group are summarized in Table 1. The subjects in groups I1 and III \vere used in the analysis of the essential number of Fourier coefficients required to reconstruct the motion and force patterns; such analysis was not performed for the subjects in group I. It was felt that this number of subjects should be sufficient to define the data variability of the normal population. The subjects were allowed to walk at their preferred speed and no attempt was made to study the effect of gait velocity on the key variables. Subjects were encouraged lo wear their ordinary walking shoes to avoid an additional variable. The subject’s body weight (BW)and lowerextremity length (LEL) were measured to normalize certain gait parameters. The entire normal population was recruited from local residents and Mayo Clinic employees, who were in good health
and R. N. STAUFFER
and had no prior history ofjoint disease in their lower extremities. BASIC GAIT PARAMETERS
Three groups of gait parameters were analyzed. Although some of these are well known, their definitions may vary among the different investigators. It is, therefore. necessary to briefly define all of them for future reference. Temporal distance factors
A typical footprint diagram, as shown in Fig. 1. illustrates the basic temporal distance factors studied. In order to compensate for anthropometric variations. stride length and step length were normalized against the lower estremity length (LEL). Cadence was defined as the number of strides min-‘, rather than the customary unit of step min- ‘. Walking speed was expressed in m min- ‘. Although left/right symmetry is generally assumed among the normals, this hypothesis was examined. Consequently, the basic temporal distance factors were defined separately for the left and right legs (Fig. 1). In certain gait patterns, the events of heel strike and toe off cannot be clearly identified. When this occurs, ‘ioot
Table 1. Normal population
groups used to establish the data base for knee joint motion and ground reaction force during gait
Type of parameters
Sub group
range
Age mean
men
Sex women Total
Temporal stride characteristics
II
32-85 19-32
53 25
32 21
37 20
69 41
Ground reaction forces
I III
32-85 21-67
58 42
32 20
37 18
69 38
I
32-85
58
32
37
69
19-32
25
21
20
41
Knee joint motion
II
Step w&h
Distance
I
--t
___
_
-
Stridk ianglh +
Fig.
1. Typical
-.. -Walk&
dmctvm
temporal distance factors used in gait analysis. Note that the single stance period of one leg is the same as the swing phase of the contralateral leg.
Normative
data of knee joint motion
and *foot off’ can be used as temporal markers for the stride parameters (Perry, 1974; Perry er 01. 1974).
strike’
Ground reaction force.5 Three basic components of ground reaction between the foot and the floor during stance phase of gait are defined as the vertical. fore-aft and mediolateral forces (Fig. 2). The entire pat tern of ground reaction force has been used as a descriptive criterion to study human gait (Hargreaves and Scales. 1975; Jacobs et nl., 1972). In addition, values can be identified from these curves for parametric analysis. A total of nine force parameters in percentage of body weight (F,-F,) and their chronological incidences of occurrence (Ti-T,) expressed in percent of stance phase period were defined. Additional variables. such as heel strike impulse (Simon tv cd.. 1982). foot-ground vertical impulse (Stott er al., 1973; Cavanagh and Lafortune, 19SO: Katoh er al.. 1981) and foot center of pressure distribution (Arcan and Brull. 1976; Cavanagh and Ae. 1980; Elftman. 1934: Grundy er nl., 1975; Scranton and McMaster, 1976;Katoh eta/., 1981),can bedetermined from the data curves. These specialized definitions are more suitable for the investigation of foot mechanics.
0
20
40 %
i
F
-lo
9
-15
j_
Of
60
60
221
and they were not studied
in the present
analysis.
Knee joint rotations Based on a convenient coordinate system established for joint relative motion (Grood et al., 1979; Chao. 1980), the three-dimensional rotation for the knee can be described simultaneously. If the relative joint rotation only occurs in one of the traditional planes (sagittal, frontal, transverse) from its neutral position, thecurrent definition would match with the traditional anatomical definitions of flexion-extension, abducand rotation tion-adduction internal-external (Fig. 3). Ten key parameters are defined from these motion curves (Fig. 4). The definitions of these parameters are summarized in Table 2 for reference. In general, the total stance flexion ($,) has a magnitude similar to the terminal stance flexion (4,). The total swing phase flexion (4s) and the total sagittal motion (#6) are also very close. For this reason. +3 and d5 were not measured. GAIT MEASURING TECHSIQCES
Temporal distancefactors A 10 m long walkway with two optical switches at either end was used for the gait analysis. Ample space at both ends of the walkway was available to allow the subject to walk at near constant velocity. The middle portion of the walking path had two sections of instrumented stainless steel tape mats to allow accurate
100
stance
T6
t
-20 i
Fig. 2. Basic parameters used to reaction forces. The force directions acting from the foot to the floor. magnitudes represent the aft components. BY I* : 1 c
+ii
F6
describe the foot-floor are defined as the forces Therefore, the negative and the medial force
% of gait tcycle +--
stance
-L
swing J
Fig. 4. Basic parameters defined in the study rotation in three dimensions.
of knee joint
E. Y.
222
CHAO.
Table 2.
R. K.
LAUGHMAN. E. SCHNEIDERand
Detinitions
Joint motion
R. N.
STAUFFER
used in describing the basic knee joint motion parameters Parameter
Definition
Knee flexion at heel strike (or foot contact)
(62 Flexion Extension
Total stance abd-add Total frontal motion
Abduction Adduction Rotation ::
measurement of step length and width (with a resolution of Zcm or + 1 cm) for either foot (Fig. 5). Walking speed was calculated from the signals produced by the optical switches (averaged speed) and verified by the tape mat measurements. Custom-made foot switches were placed underneath the soles of the shoes at the locations of the big toe, first and fifth metatarsal heads, and the heel (Fig. 6). The heel switches had a metal tag to allow direct contact with the tape mat for step length and width calculation. A self-contained electronic control unit was designed to provide the foot-ground contact pattern, as well as the step length/width calculation. Ground
reaction force
patterns
Two force plates located in the center of the walkway were used in the present study. One was a custom-designed transparent plate ivith seven quartz force transducers (Hagy et al.. 19751 and the other one. a commercially available Kistler* force platform. Both plates had a minimum resonant frequency of lOG200 Hz. adequate to record the main responses between the foot and ground during contact. These tbvo plates were placed in sequence along the walkway with a 20cm center line offset to facilitate a clean loading contact. Such an arrangement can also provide simultaneous observation of double support. The construction and the function of these plates have been previously described (Chao rr al.. 1980; Katoh et al.. 1981). Kner joint angular
Pre-stance flexion Total stance Aexion Terminal stance flexion Total swing Rexion Total sagittal motion
i-oration
Triaxial electrogoniometers were used to measure the three-dimensional knee joint rotations. The theoretical and experimental justification of this instrument has previously been presented (Chao et al.. 1970.1980; Chao and Hoffman, 1977). The advantages and disadvantages of this method. when compared against other techniques. werealso discussed (Stanic et (11..1976; Chao. 1978). The unique ability of providing
Total stance rotation Total transverse motion
instantaneous three-dimensional joint relative motion was the main reason for adopting this methodology IO manage our relatively large population sample. Although the placement of the goniometer can produce error, a trained evaluator. with the assistance of an instrument mounting guide, can reduce such error. The reproducibility of the data has been demonstrated by a test-retest experiment (Hoffman pr al., 1977). The variation of gait patterns for each test subject was found acceptable. Normal cross talk due to the external placement of the device can be corrected mathematically (Chao et al., 1970; Chao, 1978. 19801. The physical interference of the instrument did not seem to cause any significant change in normal gait function. DATA REDCCTION
Data samphg
ASD
ASaLYSIS
and reduction
Twenty-six channels of analog data were digitized through the A D convertor of a PDP 11134 digital computer. A 12-channel Beckman strip chart recorder was used to provide visual inspection of the analog data recorded by the goniometers. force plates. foot switches and tape mats. An instrument panel, capable of monitoring all test devices. \vas designed to check the test conditions before and durini each gait run. .L\ computer terminal (VT-55 monitor unit) was also used to provide immediate feedback of the data from the main computer to ensure correct data entry. The sampling rate of the A D conversion was set at 100 Hz. Thissampling rate is by no means optimal, but judging from our data acquisition system and the amount 01 data to be processed. the current rate was considered acceptable (Winter ct trl.. 1974). The entire analysis results were available one hour after completion of the evaluation. Flow-chart diagrams illustrating the b,tGc instrument organization. data collection. reduction and analysis schemes are sho\\n in Fig. 7.
-*Model 9281Al Switzerland.
I, Kistler
Instrumente.
AC.
Winterthur.
All parameters idenritied for the normal populatron were subjected to routine statistical an,tl\sis to obtall:
Fig. 3. The knee joint axes and planes of rotation as illustrated in a three-dimensional perspective view. The flexion-extension axis (l-l) is fixed to the femur, the internal-external rotation axis (3-3) is fixed to the tibia. The abduction-adduction axis is perpendicular to both of the other axes.
223
Fig. 5. Gait laboratory with instrumented walkway, including optical switches (S), stainless steel tape mats (T) and force platforms (F). The force plates are concealed in the ground, making them difficult to visualize.
Fig. 6. The foot-switch system used to measure the foot-floor contact sequences during level walking. Each switch is 1.5 mm thick, and the heel switch (H) has a metal tap to provide the measurement ofstep length and width when it is in contact with the instrumented mats. 224
__ “5
II = number
ol’par;imrtcrs
W, = weighting
Iliclur
In the prc\enl
(12
equal
similar expression
uf palt
determine
efficiency
(Kljajic
A/D
stud!.
selected among
walking
to cvlcul;~~c I,. ;jnd
rhe parameters
used.
\\eighrlng
MS
u~d.
A
hzs been
used
to
syrnmr~ry
;md energy
(11t/l.. 19751. A shghtly
dilt‘erent
con~umpt~on formukt
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converter (64
channel)
.
::::::iFoot
~~ PDP
:‘. .::‘.:
11/34a
L
Synchromze
.
!r
Trlgger
POP 11/34a Computer Tekll 40 Tern -
(256kb) System
---,_-A,--,
Data
Aquisition Program
-
Printromx Lme/graphic Printer
rb)
Fig. 7 [a) Flow diagram for gait analysis inslrument organization and data reduction scheme. (b) Flow chart descnbing the computer system structure for gait data reduction. analysis display and storage
I’or I>
E. Y. CHAO.
226
R. K. LAUGHMAN, E.
has recently been suggested (Soudan, 1982). No attempt was made to compare the symmetry index values calculated from these two methods. Non-parametric
analysis
There were two main purposes in performing the following analyses. The first was to derive repeatable and reliable coefficients which can substitute the parameters defined previously. Additional important parameters may also be identified by combining the existing coefficients and time so that not only the magnitude but also the wave form ofgait signalscan be objectively studied. The second purpose was to present the data in closed-form expression so that all the individual curves could be averaged conveniently. In addition, raw data storage in the computer becomes more efficient. The method of Fourier analysis was adopted, since it has been successful in the past to study human gait, (Zarrugh and Radcliffe, 1979; Jackson, 1979; Sutherland er al., 1980; Jacobs er al., 1972; Alexander and Jayes, 1980). The theory behind this method can be found in standard texts (Brigham, 1974; Goertzel, 1968). Briefly stated, the ground reaction force or joint motion patterns can be expressed as a periodic function of time,f(t) with period T,;
2 (Ajcosjw,t+BjSinjw,t)
f(t) = A,+
j=
with w, as the sampling frequency. coeflicients are determined by; A,, = f
‘“f(t)dt 0 s0
(2)
1
The Fourier
= f(t),
(3)
(4)
s T. f(t)sinjw,tdr. 0I0
(5)
The method of selecting the essential number of
Table
3. Temporal
distance
harmonics depends upon the sampling rate and thaccuracy required to reconstruct the original dar.1 curve. Different objective criteria have been tried before (Capozzo et al., 1975; Jackson, 1979; Winter et al., 1974). The technique adopted here has been described elsewhere (Schneider and Chao, 1982). Using the Fourier analysis technique, three basic patterns of knee joint motion and ground reaction were determined. The ‘individual’ pattern stands fer the data curve recorded in one cycle of a gait run in .1 single subject. When all the individual patterns of J subject areaveraged, they form the ‘t!_pical’pattern ~LX that subject. When all the typical patterns for the normal population are combined, a ‘general’ pattern 15 defined for the normal group.
RESULTS
The normal subjects were divided according to as< and sex. The two groups (I and III) selected for ground reaction force analysis were studied at two differenr time periods and for varying objectives. Although thclr age ranges had an obvious overlap, the statistic21 result, based on student’s f-test, showed that these tao groups were significantly different (p < 0.001). For thlj reason, it was considered adequate to study the age and sex effects based on the population groups defined in Table 1. For convenience, the results of the parametric and non-parametric analyses are presented separateI>. Parametric
Aj =; o OTgf(t)cosjw, t dr,
Bj =f
SCHNEIDER and R. N. STAUFFER
analysis
The temporal-distance factors for population groups I and II are summarized in Table 3 according to sex. Both mean and standard deviation for each parameter are presented. The step length and doubls stance for the right leg were tabulated, but the corresponding data for the left leg are presented implicitly through the ratio values. It is interesting to find that step length is nearly symmetric in both men and women (group II only) but not their single and
factors in the normal population groups I (ages 32-85)and II (ages 19-32). Ths values and standard deviation are presented. (Refer to Fig. 1 for definitions) Women
Men (n = 53)
for the mean
(n = 57)
Parameter
I (n = 32)
II (n = 21)
Total
I (n = 37)
II (n = 20)
Total
Cadence (stride min- ‘) Stride Length, LEL’ Speed (m min- ‘)* Step length, right (cm)* Step length ratio (small/large) Step length/LEL, right Right stance ( “,, G.C.) Left stance ( a0 G.C.) Single stance, right (7, G.C.) Double stance. right ( “/, G.C.) Double stance ratio (small, large)
52+5 1.56+0.15 76.1 f 12.5 73+8 t 0.78 + 0.07 59i2 t 41+2 8.8 k 1.9 t
50+8 1.48kO.17 71.9 + 18.3 69k9 1.0*0 0.73 + 0.08 60+2 6Ok3 4Ok2 10.2 f 2.6 0.8 kO.1
51k6 1.53kO.16 74.4+ 15.1 71+8 t 0.76 +- 0.08 59+2 t 4lk2 9.4 f 2.3 t
56k5 1.40+0.14 69.4kll.O 61+8 t 0.70 + 0.07 60+2 t 40+2 10.0 f 5.5
5i ~5 1.39zo.17 63.9fll.l 6017 l.OrO 0.69 I 0.08 59r2 59r3 41*2 8.9 t 2.0 0.9 10.1
545 5 1.40+0.11 67.5+11 1 61+_7
1,G.C. = Percent of Gait Cycle *Significantly corrected with 10 or more parameters tThe stride characteristics were assumed symmetric
(p -C0.01). in this group.
t
t 0.70 f O.CI59k’ t 41+2 9.6 + 4.6 t
Normative
227
data of knee joint motion
double stance ratios (group I only). Among all temporal distance factors. only cadence was found to be slgmficantly different at the level of p < 0.01 in the female subjects between the two age groups (I and II). Houever, when the two age groups are combined, cadence, stride length LEL and step length are found to be different between men and women (p < 0.01). Therefore. within the age range studied here, dividmg the normative data on the temporal stride characteristics according to sex appears necessary. The single stance (single limb loading) of one leg is, by definition, identical to the swing phase of the contralateral limb. The double stance for the left leg can be easily calculated by subtracting the right swing phase and right double stance period from the left stance phase (Fig. 1). The key parameters for ground reaction force, as defined in Fig. 2, are tabulated in Tables 4 and 5 for men and women in each age group studied. The relative variations for the force components with higher magnitudes (f, , F2, F,, F, and F6) are smaller. The same relationship holds for the time factors. This reflects that the main features contained in ground reaction force patterns appear consistent, but they tend to vary on minute details. Men tend to have equal peaks (F, and F,) in the vertical force, while women appear to have a higher second peak (F3). However, this difference was insignificant statistically. The magnitudes for F,, T4 and T, were found to be different between groups I and III in men, while F, and
F, were different in women for p < 0.01. In subject group I, men and women were different (p < 0.01) in F, , F,, T, and T,. However, when the two groups were combined, sex only caused statistical differences in F, and T, Since F, and F, have higher magnitudes and are thus more sensitive in depicting variation caused by gait abnormalities, it appears that a separation based on sex is also necessary in presenting ground reaction force data. However. the age erect cannot be discounted and a more refined separation of age groups may be necessary before definitive conclusions can be drawn. Although the anticipated variation exists in nearly all parameters studied, total ranges of knee joint motion in each plane are surprisingly consistent (Table 6). To examine age and sex effects on knee joint motion, the results of groups I and II were compared statistically. It was found that joint motion in gait is age related in men (p < 0.01 for 41 and $1; p < 0.05 for @4r 46 and 6,) but not in women, except for knee flexion at heel strike (41, p < 0.05) which may be influenced by the type of footwear used by the female subjects. When the data for men and women were compared, regardless of age, only the total sagittal motion ( &6) and frontal motion (e,) were found to be different at the levels ofp < 0.05 and p < 0.01, respectively. Although the age factor seems important in describing knee motion in men, the variation in these parameters was large, which makes such division less reliable. Since sex separation has been shown necessary
Table 4. Basic parameters in ground reaction force. (See Fig. 2 for definitions) Men (n = 52)
Parameter
Women
(n = 55)
(O. B. W.)
I (n = 32)
III (n = 20)
Total
I (n = 37)
III (n = 18)
F,’ F2’
114*9 72f9 111+9 1.8 + 1.9 17.7 k4.0 20 + 3.9 4.2 &-1.4 5.1 f. 1.8 4.7 f 2.0
111*7 74+13 112+7 3.6 + 3.0 17.Ok4.6 19.9 + 2.9 5.2 + 2.9 4.4 * 2.8 4.6 f 2.4
113+Ei 72kll 112+8 2.5 k 2.4 17.4 + 4.2 19.9 + 3.5 4.6k2.1 4.8 + 2.2 4.7 + 2.1
107&S 7558 llOk6 1.7k2.0 15.1 + 5.0 16.7k4.1 3.6+ 1.7 4.6 f 2.3 4.2 + 1.7
110+7 74k8 116_+10 3.0 + 1.4 17.1 f 3.8 21.1 +4.0 4.3 + 2.8 4.7 * 2.1 3.9 * 2.2
F, F, f,* f,* FF, F, ‘Significantly
Table
correlated
with 10 or more parameters
5. Key time parameters
T,’ T, T3 T4 75 r, 7, T& 79 *Significantly
reaction
108i8 75k8 112k8 2.1 + 1.9 15.7 + 4.7 18.1 f4.5 3.8 k 2.1 4.6 + 2.2 4.1 + 1.8
(p < 0.01).
forces. (See Fig. 2 for definitions)
Women (n = 55)
Men (n = 52)
Parameter
( Q.stance)
in ground
Total
I (n = 32)
III (n = 20)
Total
I (n = 37) _
III (n = 18)
Total
25 + 3 47+6 79*4 3*1 20+3 87 k 2 8_+3 25L-4 73*4
24&4 46+4 77+2 4+2 19k2 86kl 7_+3
24+3 47 f 5 78+3 3+1 19+3 86&2 8+3 27+6 73 * 5
27k4 49*5 78k4 3+1 21k3 87+3 8+3 30+9 69+11
25+3 5oi9 78+3” 3+1 19+3 86kl 7+3 31+6 72+6
27+3 49k6 78 f 3 3+1 20+3 87 ) 3 8+3 31+8 70+10
correlated
31+7 72+6
with 10 or more parameters
(p < 0.01).
228
E. Y. CHAO,R. K.
LAUGHMAN,
E. SCHNEIDER and R. N. STAUFFER
Table 6. Key joint motion parameters at the knee during level walking. (See Fig. 4 for definitions) Parameter (degrees)
Men (n = 53) 1 (n = 32) -1+4 17+5 31*5 72+6 7+2 12+4 9*3 14*4
II (n = 21) 7+4 13k6 35+6 68k8 6+2 11*3 11*3 14+3
in other gait parameters, joint motion data should be treated in a similar manner. A total of41 gait parameters (two on joint isometric strength and two related to stair walking were not reported here) were subjected to linear correlation matrix analysis. Among the 37 parameters included in this paper, ten had significant correlation (p < 0.01) with ten or more of the remaining variables. These parameters, as marked by an asterisk in Tables 3-6, will assist in the selection of the most significant variables for future statistical analysis. It is interesting to note that no joint motion parameters appeared in this list, which tends to suggest that in the study of normal gait in adults, joint motion data could be redundant. However, such a relationship may not exist when abnormal gait is involved. Certain parameters did not have a normal distribution within the population analyzed, percentile distribution (10th and 90th percentile) was used to express the data. Since such presentation is less common in the literature, it is omitted here. When the normal range for each parameter is used to assess gait abnormalities in patients, such an expression may be more adequate. The symmetry index (I,) was calculated using equation (1) for the population group I based on a subset of eight significant parameters. These parameters are passive and standing knee flexion, percent of stance phase, 42, &, F,, F, and T, . A mean value of 0.93 + 0.03 was obtained, while a value of ‘1’ stands for a perfect symmetry between the two legs. These results signify that an average normal gait seems to have a slight asymmetry. Non-parametric anal_vsis
Figure 8 illustrates the ‘typical’ patterns of the three floor reaction force components in one subject and the ‘general’ patterns of a group of 26 normals. The men and women were combined, since there was no significant difference between the two sexes in the current subset of the normal population studied. The means, plus and minus one standard deviation, are plotted. The variation among each individual pattern can be significant (especially in the fore-aft and medial-lateral components), which indicates the need of studying the averaged patterns. Similarly, the variation among the normal sample can become substantial, but the ‘gen-
Women (n = 57) Total
1 (n = 37)
II (n = 20)
Total
2+6 15k6 32+6 71+7 7+2 12+3 10+3 14*4
o&-5 15k6 30+5 66k9 7+2 lot4 10+3 14+4
4*6 14+5 31+7 70+8 6*2 9*2 9_+2 13+3
1*5 15*6 30&6 68k8 7+2 10*3 9+3 13*4
eral’ pattern provides a good representation of the general wave form of these curves. The typical pattern is able to illustrate the subtle feature of the raw data, such as the impulse at the initial heel strike in the vertical force reaction (Simon et al., 1982). However. in the general pattern these minute features become obscure due to the averaging process. The Fourier coefficients (both the sine and cosine terms) for the first seven harmonics used to reconstruct the ‘general’ patterns are listed in Table 7 for thirteen men and thirteen women. The magnitude of the coefficients beyond the seventh harmonics decreases quickly to an insignificant level. The essential number of harmonics required to construct these patterns was found to be five for the vertical force, while up to the seventh harmonics were required for both the fore-aft and medial-lateral force components. The essential number of Fourier coefficients for the ‘typical’ pattern of each normal subject is slightly higher. A comparison of the ‘typical’ and the ‘general’ patterns for the three knee motion components are shown in Fig. 9. Again, the variation among the individual patterns was quite small. but it became substantial among the typical patterns in the normal population studied. This variation may be due to the baseline shift during motion evaluation. The mean curve, defined as the ‘general’ pattern. appears to be able to retain the basic features of the typical motion data and to provide reliable peak-to-peak measurements. The essential Fourier coefI%ents required to reconstruct the ‘general’ patterns are presented in Table 8 in terms of their mean and standard deviation. The number of terms needed for the typical pattern is slightly higher. DISCUSSION It has been suggested that in adult gait, significant deviation may occur at the sixth decade (Murray er al., 1964). To re-examine this hypothesis, the normal group I was further divided into two subgroups, separated at 55 years of age. Such a division allowed us to study three age groups in both sexes, i.e. younger than 32 yr (original group II), between 32 and 55 yr la subset of group I. 17 men and 15 women), and older than 55 yr of age (a subset of group 1. 15 men and 22
Normarive
data of knee joint motion
--e-tnmean
01 26normals
X8of stance
phase
Fig. 8. Normal ground reaction force patterns. (a) The mean and 1 standard deviation envelope of the ‘typical’ pattern of one normal subject based on 6 individual parterns. (b) The nean and 1 standard deviation envelope of the ‘general’ pattern of 26 normal subjects (a subset of group 111).
Table 7. The Fourier
coefficients
used to produce the ‘general’ pattern force components
Fourier coefficient
( “<,BW .A” AI A, A3 Al .A3 .4, A1 B, BL B, B, B, B, B-
of the ground
reaction
Subset of group III (n = 26) Vertical
Fore-aft
MedialLlateral
- 33.5 + 3.6 - 1l.S + 2.3 -2.3 f I.4 -0.9 f 1.2 - 0.4 f 0.9 -0.3 +0.7
-0.4rfo.s _ 1.7kO.7 -0.1 +0.8 0.8 kO.5 0.8 f0.5 0.3 + 0.3 0 * 0.2 -0.2 f 0.2
1.9 + 1.2 - 2.0 + 0.5 - 1.6 t 0.5 0.1 * 0.4 0.4 * 0.2 0.4 c 0.3 0.3 + 0.3 0. I _t0.1
- 2.3 f 2.9 1.5 + 3.7 2.6 f 1.9 3.3 + 1.4 1.8 + 1.2 0.9 +0.8 0.4 f 0.7
12.4 f I.7 4.4 f 1.2 -0.6+0.6 -1.5kO.5 - 1.1 +0.4 -0.6kO.3 - 0.4 f 0.2
OkO.6 -0.5kO.3 -0.3*0.3 -0.2kO.3 -0.1 kO.3 -0.1 +0.3 -02+02
78.1 f 2.9
- 22.6 + 3.7
women). The new results nearly paralleled our original tindings in that age difference seems to cause deviation in ground reaction force patterns in women, and it appears to affect knee joint motion only in men,
particularly between the groups separated at 55 yr. In general, sex variation was found more significant than the age effects. Therefore, in grouping normative data it appears more appropriate to divide it according to
E. Y.
230
P D
60.
5 ‘G
40.
CHAO,
R. K.
LAUGHMAN, E. SCHNEIDERand R. N. STACFFER
_meanof7lparfern m one sublecf
--+-
mean ol 65 normals
mean+lsd.
5 2
20.
.s 2
0.
2 201
’ 0
I. 20
GOgait
Fycle
80
100
%
-
-20+
‘I %
of gait
80
100
<3
I
2ot
Fig. 9. Knee joint rotation patterns. (a) The mean and 1 standard deviation envelope of the ‘typical’ patterr. ofone normal subject based on 11 individual patterns. (b) The mean and 1 standard deviation envelope of the ‘general’ pattern in 65 normals (a subset of group I).
Table 8. The essential Fourier coefficients used to produce the ‘general‘ pattern of knee joint motion during gait. Fourier coefficient (degrees) A0 A, A, A3 A, A,
Flexion/extension
Subset of group II (n = 37) Abduction/adduction Inr-ext. rotation
A7 A,
24.69 k 3.74 - 8.73 k 3.01 - 12.71 f 2.63 0.49 * 1.13 -0.97+1.12 0.78 + 0.84 0.48 f 0.49 0.50 f. 0.39 0.26 + 0.25
- 2.93 + 2.09 - 0.36 + 0.95 1.50 * 1.19 0.80 & 0.61 0.10 + 0.42 -0.07 f 0.32 0.21 kO.23 0.06kO.16 0.13 kO.15
B, B, B3 B, B, B, B, &
- 20.10 + 2.72 10.96 + 2.57 4.21 * 1.10 1.83f1.11 1.22 * 0.57 0.45 * 0.48 0.38 + 0.46 -0.06 _+0.33
0.78 + 1.93 0.23 + 0.92 - 0.66 + 0.64 - 0.33 * 0.49 0.17 +0.28 0.09 * 0.20 -0.01 kO.18 0.12kO.16
A6
sex. When age variation is to be considered, a separation at 55-60 yr seems to be adequate. The temporal4istance parameters involved in freespeed walking have shown surprising consistent!
-
-
I .24 k 3.60 1.56 It: 1.79 0.96 k I.63 0.50 f. 0.92 _ 0.09 k 0.61 * 0.35 f 0.69 0.11 kO.49 0.29 f 0.46 0.20 + 0.41
-0.55 & 1.95 -0.86 f 1.30 - 0.05 + 0.85 0.63 + 0.90 0.22 f 0.50 0.76 + 0.56 0.50 + 0.44 0.3 1 * 0.28
among the two groups (I and II) analyzed. .Although walking speed varied among the individuals. the range of variation was too small to study its effect on other gait parameters. Linear extrapolation of the current
Normative data of knee joint motion ddta IO the extreme ranges of walking would not be reasonable. Speed of walking was found to be an important parameter. as identified from the correlation study. The normalization of distance related factors with respect to the lower extremity length (l_EI_) appears to reduce intersubject variation (Table 3). Single and double stance periods are closely related to weight acceptance in each leg. These parameters are expected to have a significant contribution in studying pathological gait, since the normal load acceptance capability of the lower extremity joints will be predisposed by the specific disease involved. The joint motion and ground reaction force parameters are important in the assessment of the quality and characteristics of human gait. However, not all of them need to be identified due to their inherent relationship. When a specific class of abnormal gait is to be investigated. R’ analysis (multiple correlation) must be conduc’ted in order to identify the key parameters which can help to differentiate the joint functional changes caused by the underlying pathological conditions. The relative importance of these parameters must also be established through the USC’of discriminate analysis. so that they can be properly weighted to improve the sensitivity of data separation. Not all of the motion and force parameters can be identified easily and repeatedly, especially when abnormal patterns are involved. When these values are read directly from the raw data tracings, the entire process can be extremely tedious and human error due to subjective judgment becomes inevitable. These drawbacks can be prevented by augmenting an automated search program using a computer. However, in the event of data pattern changes, this program may become very complex. Fourier analysis may alleviate this problem, since most of the parameters defined previously can be determined accurately by the Fourier series expression. Nova. variables capable of detecting pattern variation in gait data can also be investigated. The use of Fourier analysis has other advantages. Raw data on the joint motion and ground reaction force patterns can be stored efficiently in the computer using a finite number of Fourier coeficients instead of the digitized discrete data points. Typical and general patterns can be easily reconstructed in their graphical form for display or phasic analysis. The averaging process involving numerous patternscan be performed and presented conveniently. TO handle large normal and patient populations. this method of data handling ‘tnd analysis is extremely helpful. The ‘individual’ joint motion and ground reaction force patterns for each normal subject exhibited certain variations among the gait cycles tested. These iartations may be due to the natural responses, en\,ironmental effects and/or experimental errors. It is important that these patterns be averaged so that a representative ‘typical’ pattern can be produced for a specific subject. When the normal population is studied as a whole, the ‘typical’ patterns for all the subjects vary mainly in magnitude, but not in their
231
general wave form,due to baseline shift. Consequently. the ‘general’ pattern is a good representation for the entire group studied. However, such an averaging process tends to obscure subtle features occurring in a short period of time. If gait analysis is performed with the intention ofcharacterizing these minute events. the averaging process should be avoided to allow the individual patterns to be dealt with separately by using a maximum number of Fourier coefficients for their description. The present results, both in their parametric form and their characteristic wave patterns, have compared favorably with most of the available data in the literature. Although the definitions used for various gait parameters may vary from one institution to another, as long as the general patterns of the variables can be reproduced, such as in the present case. objective comparison should still be possible. To establish a useful reference data base for normal subjects requires an enormous amount of time and cost. If our data can be matched with other available sources, a combination of similar data series will provide a data bank of large sample size available to all investigators for clinical and research applications. It is important to recognize that the triaxial goniometer technique may not be the best method for joint motion measurement. The cross talk effect due to possible misplacement ofthe instrument can introduce artifacts. Soft tissue involvement may also cause error. although this drawback is difficult to avoid, regardless of the instrument system used. Despite their large variation, baseline measurements of abduction-adduction and rotational motion at the knee during stance phase can be useful in the study of pathological gait. If these motion components become large in abnormal gait, they may reflect possible pathological conditions. Due to the general lack of such data in a sizeable sample. the present results in three-dimensional knee motion can certainly be used as a common reference for comparison. In the advent of modern technology with fast-paced development of sophisticated electronics and computerized video instruments. it is expected that a completely automated method of conducting gait evaluation will emerge. However. the adoption of new instrumentation must be balanced with effective data reduction and analysis smce human gait is a highly variable biological phenomenon, and its problems cannot all be dealt with by sophisticated equipment alone. It is advisable that more effort be devoted to data analysis and the present paper only represents one such attempt.
Acknowledgemenrs-The work reported in this paper was supported in its entirety by NIH Grant No. Am 18029. Many people havedevoted their timeand etforts to the development ofthe instrumentation and data analysis methodology used in this study. We wish to specifically acknowledge the contributions made by Fred Axmear. Ross Hoffman. Mitsuo Tanaka and Joanie Bechtold.
232
E. Y. CHAO,
R. K. LAUGHMAN, E. SCHNEIDER
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