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Variability of knee moment arms in the frontal and sagittal planes during normal gait
Clin. Biomech.
1993; 8: 59-65
Papers
Variability of knee moment arms in the frontal and sagittal planes during normal gait 0 K Svensson
MD PhDl,
L Weidenhielm
’Kinesiology Research Group, Department Department of Anatomy, Karolinska Institute, St Gijrans Hospital, Stockholm, Sweden
MD~ of Physical Medicine and Rehabilitation, and *Department of Orthopaedic Surgery,
Summary A new measure, the length of the moment arm at the knee joint in the frontal and sagittal planes during normal gait, was assessed, and the variability tested. Simultaneously the external moments about the hip, knee and ankle were analysed. A gait analysis system with a force platform and two video cameras was used. Two recordings in each plane with a few minutes’ interval were collected in 10 healthy normal subjects walking at free cadence in their own shoes. For one subject, two recordings in each plane were obtained for 5 consecutive days. The mean moment arm length in the frontal plane at mid-stance, when trials were done minutes apart, was 48 mm, with a coefficient of variation of 7.9%. The mean moment arm length for the peak knee moment was 63 mm with a coefficient of variation of 7.9%. For the moment arm lengths at the peak moments in the sagittal plane, the variability was very high. The variability of the trials done minutes apart was in most cases less than of those done days apart. In the frontal plane, the smallest variability in trials done minutes apart was in the external hip peak and mid-stance moments and the external knee peak and mid-stance moments. In the sagittal plane, the smallest variability was in the external peak dorsiflexing moments and mid-stance dorsiflexing moments about the ankle. All ankle moments in the frontal plane and the peak moments about the hip and knee in the sagittal plane showed a high variability. Thus, care should be taken when these moments are evaluated with similar methods.
Relevance In surgical treatment of varus or valgus deformity knee moment arm in the moment arm in healthy evaluated. In addition it
osteoarthrosis of the knee, restoration of leg alignment from a has been considered important. This involves a change of the frontal plane. Thus, it is important to know the length of the knee subjects, especially in the frontal plane, when patient data are is important to know the variability of the analysis method.
Key words: Ankle, biomechanics,
gait, hip, knee
Introduction
In surgical treatment of osteoarthrosis of the knee, restoration of leg alignment from a varus or valgus deformity has been considered important’. In a tibia1 osteotomy for a varus deformity, the idea is to decrease the load on the medial knee compartment*. This is accomplished by reducing the moment brm in the frontal plane between the ground reaction force and the knee”. Received: 3 July 1991 Accepted: 14 March 1992 Correspondence and reprint requests to: Ola K Svensson, MD PhD. Department of Physical Medicine and Rehabilitation, Karolinska Institute, Norrbacka ltr, PO Box 60500, S-10401 Stockholm, Sweden 0 1993 Butterworth-Heinemann 0268-0033/93/020059-07
Ltd
Previously the reduced moment arm during gait after surgery has been analysed indirectly by assessment of the knee moment, i.e. the product of the ground reaction force and the moment armzW4. A higher body-weight and walking speed increase the magnitude of the ground reaction forces3”. Increased walking speed after knee surgery produces an increased ground reaction force6, and consequently a higher moment about the knee even if the moment arm is shortened due to surgery. Therefore, to decrease the effect of walking speed, it has been considered of value to use the moment arm by itself as a parameter to evaluate surgical procedures of the knee3. The purpose of the present study was (1) to introduce the knee moment arm length as a measure to evaluate knee load pre- and postoperatively; (2) to determine the variability in trials done minutes apart and trials
60
Clin. Biomech. 1993; 8: No 2
done days apart; (3) to present some normative data for healthy subjects for use as reference values in assessment of patients with knee deformities; and (4) to determine the variability in the hip, knee and ankle moments in the frontal and sagittal planes, in trials done minutes apart and days apart.
Methods Subjects
Ten healthy volunteers with no symptoms from joints in the lower extremities, five men and five women, mean age 26 years (range 19-34) participated in the study. The mean body weight was 67.1 kg (SD 8.4), the mean distance from spina iliaca anterior superior to the medial malleolus was 0.89 m (SD 0.06), the mean distance from spina iliaca anterior superior to the medial knee joint line was 0.52 m (SD 0.03). The subjects’ mean walking speed was 1.43 m/s (SD 0.21), the mean step length 0.74 m (SD 0.08), and the mean step frequency 1.92 steps/s (SD 0.11). Experimental set-up
The subjects walked in the shoes that they normally used, at free cadence, on a 13-m long and 1.4-m wide walkway consisting of a thin rubber mat. A force platform (Kistler 9281B, Kistler Instrumente AG, Winterthur, Switzerland) was hidden in the middle of the walkway under the mat. The subjects were instructed to look at a cross at eye-height on the wall in front of them while they walked, and their starting position was adjusted until they stepped on the force platform with the appropriate foot. Floor reaction forces were obtained at the stance phase of the middle stride. After amplification (Kistler type 5001 and 5006) and A/D conversion, the force platform recordings were collected in a personal computer (ABC 800, Luxor) at a frequency of 250 Hz. The subjects were filmed with two video cameras (Hitachi FP-10) in the frontal and sagittal planes at 25 Hz. In the frontal plane, a skin marker was placed to mark the hip joint 25 mm distal to the midpoint of a line from the anterior superior iliac spine to the pubic tubercle’. For the knee, the marker was placed at the tuberositas tibiae, and for the ankle joint at the midpoint of a line from the tip of the medial malleolus to the tip of the lateral malleolus’. In the sagittal plane, skin markers were placed at the centre of the greater trochanter, at the centre of the lateral femoral epicondyle, and at the most lateral point on the lateral malleolus of the fibula’. For synchronization of the video frames with the force platform recordings, an LED display panel indicating time down to one-thousandth of a second was visible on the video frames. The display was connected to the computer. After the data collection, the coordinates for the hip, knee, and ankle joint were manually digitized into the computer using a crosshair (VPA-1000, Panasonic).
Figure 1. The calibration set-up. To the left the calibration frame with the two plumb-lines hanging just above two of the four transducers. Plumb-line A is at the back end of the force plate and plumb-line B at the front. To the right, the frontal-plane camera, 6 m in front of the short side of the platform. The other camera was placed facing the long side of the platform.
Calibration procedure
The calibration set-up for the video-recording system is shown in Figure 1. A metal frame containing two plumb-lines with length indication was placed on the force platform. Viewed from the camera in front of the short side of the platform, one plumb-line hung just above the left transducer at the front edge of the platform (B in Figure 1). The other plumb-line hung above the transducer to the right, at the back edge of the platform (A in Figure 1). The distance between the camera lens and the middle of the force platform was 6 m, and the centre of the lens was 0.65 m above the floor. Viewed from the side, the calibration procedure can be simplified as in Figure 2, where A and B are the distances indicated on the plumb-lines, and a and b the
A
.
L
Figure 2. Schematized description of the calibration set-up viewed from the side. A is the distance indicated on the plumb-line at the back end of the force platform and B is the distance on the plumb-line at the front end. a is the image of A on the projection plane or the video frame, and b is the image of B. Zis the vertical distance to be calculated and z is this distance projected on the video frame. L is the distance from the lens position of the camera to A, and /is the distance to the projection plane. dp is the distance between A and Band x is the distance from A to the point of application of the ground reaction force.
Svensson
images of A and B on the projection plane. 2 is the vertical distance to be calculated, and z is this distance on the projection plane. L is the distance from the camera lens to A, and I the distance to the projection plane. dp is the distance between A and B and x is the distance from A to the point of application of the ground reaction force. The coordinates for the point of to the calculated according application were manufacturer’s instruction’. From this, the following equation system can be set up: AIL
= all
BI(L
- dp) = bll
Zl(L
- x) = z/l
This gives: Z = (1 - (x(1 - k)ldp))Azla;
k = aBIAb
A = B gives k = alb
Experimental
design
To test the variability of the moment values measured, four trials were recorded within a few minutes interval and collected for 10 subjects; two in the frontal plane and two in the sagittal. Additionally, for one of the subjects chosen by lottery, four trials were recorded each day, during 5 consecutive days. The subjects wore T-shirts, tight shorts and sports-shoes without socks. Subjects’ body-weight was obtained with clothes and shoes on. Calculation procedure
The computer program was designed by our group, based on a free-body diagram described by Bresler and Frankeli’. It calculated the external moments in the frontal and sagittal planes about the hip, knee and ankle during the stance phase. The calculations consisted of the ground reaction and gravitational forces, but the inertial components were omitted. The effect of inertia on the knee moments is small throughout most of the stance phase”,“. Weights for each body segment in relation to body mass, and the location of the centres of mass relative to segment length, were obtained from Dempster’s anthropometric data’. To attenuate the high-frequency noise a filtering window of three points was used. The filter works like a low-pass filter and can be described by the following formula: Vt = V(n - 1)/4 + Vn/2 + V(n + 1)/4
where Vn is the nth sampled value. The window was then moved one sample forward successively along the whole force curve. The bandwidth, equivalent to the spectral density of the filter, was 22.0246. The following parameters were analysed: 1. The peak, moment.
i.e. the recorded
maximum
external
and Weidenhielm:
Knee moment
arms in normal
gait
61
2. The mid stance moments, i.e. the recorded external moment at 50% of stance phase about the hip, knee, and ankle joint in the frontal and sagittal planes. 3. Moment arms about the knee in the frontal and sagittal planes. The moment arm was defined as the perpendicular distance between the ground reaction force vector and tuberositas tibiae in the frontal plane, and as the perpendicular distance between the ground reaction force vector and the centre of the lateral femoral epicondyle in the sagittal plane. 4. The vertical, mediolateral, and fore-and-aft components of the ground reaction force during the stance phase. The distance from the surface of the platform down to the transducers where the shear forces were actually measured was 54 mm. If this is ignored, errors will occur. Therefore, in the computer program, the centre of pressure was projected up to the top surface of the platform along the line of action of the resultant force vector, as described by Shimba’* and Lamoreux13. Statistical analysis
The variability when trials were done minutes apart was calculated using the formula
where d is the difference between the two measurments on each subject and n is the number of subjects. The variability when trials were done days apart was calculated with an analysis of variance (ANOVA). The coefficients of variation (CV) were calculated and expressed as a percentage. The coefficients of correlation (r) between the two steps, for the intra-day measurements of the 10 subjects, were calculated. Results
The variability for the investigated variables for the frontal plane are presented in Table 1, and for the sagittal plane in Table 2. The three columns to the left show the results from the trials done minutes apart on 10 subjects, and the two columns to the right show the results from trials done days apart during 5 consecutive days on one subject. Concerning the frontal plane, the variability (s) of the trials done minutes apart was always less than that of trials done days apart. In the sagittal plane this was the case for 10 of the 15 parameters. In the frontal plane, the external moment about the hip and knee was adducting, except for a short period at the beginning and end of the stance phase. For the ankle, the pattern varied for different subjects. Except for the moment arm of the mid-stance knee moment, the variability was higher for the moments and moment arms in the sagittal plane than for those in the frontal plane when trials were done minutes apart (Tables 1 and 2). Table 3 shows the obtained mean
62
Clin. Biomech.
1993; 8: No 2
Table 1. Variability of the forces, the external moments and knee moment arms for the two trials done minutes apart on ICI subjects. Variability for the trials done days apart on one subject on five consecutive days. Coefficients of correlation (r), variability (s), and coefficients of variation (CV%) in the frontal plane for the peak vertical and medially directed components of the ground reaction force (N), the external peak and mid-stance moments (N m), and moment arm length (mm) for the peak and mid-stance moments at the knee Variability of trials Frontalplane
minutes apart (10 subjects)
days apart (1 subject)
r
S
Vertical force Medial force
0.97 0.92
17.6 6.1
2.1 13.5
28.1 7.9
3.7 16.5
Hip Peak moment Mid-stance moment
0.93 0.92
4.9 2.9
4.8 5.3
11.3 6.9
15.3 19.0
0.93 0.83
4.1 6.2
6.9 7.9
13.3 16.0
29.2 26.9
0.91 0.88
2.6 4.8
8.7 7.9
6.8 14.7
37.1 38.5
0.80 0.87 0.44
2.4 2.1 2.3
24.3 18.4 91.0
8.0 7.9 6.6
76.2 65.2 94.6
Knee Peak Moment Moment arm Mid-stance Moment Moment arm Ankle Peak add. moment Peak abd. moment Mid-stance moment
CV%
S
CV%
Table 2. Variability of the forces, the external moments and knee moment arms for the two trials done minutes apart on IO subjects. Variability for the trials done days apart on one subject on five consecutive days. Coefficients of correlation (r), variability (s), and coefficients of variation (CV%) in the sagittal plane for the peak vertical, anteriorly and posteriorly directed components of the ground reaction force (N), the peak external flexing and extending moments (N m), the external mid-stance moments (N m), and the corresponding length (mm) of the knee moment arms Variability of trials Sagittalplane
minutes apart (10 subjects) r
Vertical force Anterior force Posterior force Hip Peakflexing moment Peak extending moment Mid-stance flexing moment Knee Peak flexing Moment Moment arm Peak extending Moment Moment arm Mid-stance extending Moment Moment arm Ankle Peak plantarflexing moment Peak dorsiflexing moment Mid-stance dorsiflexing moment
0.96 0.95 0.72
S
days apart (7 subject) CV%
S
CV%
32.6 5.5 13.4
3.6 2.9 7.6
28.1 14.2 12.8
3.7 9.6 7.7
-0.15 0.24 0.89
21.8 201 .o 3.6
34.6 72.5 27.8
22.9 118.8 4.8
58.2 141.6 33.9
0.21 -0.05
32.1 96.1
49.3 71 .o
39.3 14.8
63.1 21.2
0.70 0.26
9.2 114.1
23.9 95.0
13.7 17.6
39.3 37.4
3.1 4.0
64 90.5
6.2 13.1
37.6 40.5
49.5 4.9 3.3
71.3 3.6 6.8
65.3 11.8 5.4
181.7 10.7 10.3
0.92 0.91 -0.26 0.99 0.95
Svensson and Weidenhielm:
Table 3. Mean values and standard deviations
(SD)
for the investigated
Knee moment
arms in normal gait
63
variables
Frontal plane
All (n = 10) (20 trials) SD Mean
Men (n = 5) (10 trials) SD Mean
Women In = 5) (70 trials) Mean SD
Vertical force Medial force
750.7 39.3
87.9 15.3
778.0 46.6
117.1 16.2
723.3 32.1
30.6 10.7
80.0 42.2
16.2 9.8
87.9 46.7
17.0 7.5
72.1 37.7
11.3 10.1
45.8 63.2
14.0 14.6
55.6 72.9
13.0 13.2
36.1 53.5
5.8 8.2
21.5 47.7
7.2 12.2
25.4 52.6
6.1 13.5
17.5 42.8
6.1 8.9
8.8 6.6 2.9
5.4 4.8 4.0
10.8 9.1 3.5
5.6 5.1 4.5
6.7 4.2 2.3
4.7 3.1 3.6
Hip Peak moment Mid-stance moment Knee Peak Moment Moment arm Mid-stance Moment Moment arm Ankle Peak add. moment Peak abd. moment Mid-stance moment
Sagittalplane
All (n = 10) (20 trials) Mean SD
Men (n = 5) (10 trials) Mean SD
Women (n = 5) (10 trials) Mean SD
Vertical force Anterior force Posterior force
751.3 152.2 137.5
94.5 21.3 24.8
781.3 146.0 141.4
112.1 27.4 24.8
721.2 158.4 133.6
65.5 10.9 25.5
Hip Peakflexing moment Peak extending moment Mid-stance flexing moment
47.9 149.4 10.4
20.4 234.3 10.4
49.2 150.6 16.0
24.6 219.0 8.9
46.6 148.3 4.9
16.4 260.6 8.9
53.3 89.8
34.6 93.5
56.6 89.0
49.6 116.9
50.0 90.6
6.9 69.2
26.9 77.0
12.7 109.4
34.2 105.4
13.0 144.9
19.5 48.7
7.1 49.8
4.2 6.2
10.5 20.8
5.3 8.5
14.2 27.4
3.2 4.0
5.2 12.1
29.6 105.8 41.0
47.3 25.8 12.9
44.9 119.0 43.1
64.6 30.2 10.2
14.4 92.7 38.9
6.3 10.7 15.5
Knee Peak flexing Moment Moment arm Peak extending Moment Moment arm Mid-stance extending Moment Moment arm Ankle Peak plantarflexing moment Peak dorsiflexing moment Mid-stance dorsiflexing moment
values for the frontal and sagittal planes. For men and women combined, when trials were done minutes apart, the mean knee moment arm length in the frontal plane at mid-stance was 48 mm and at the peak moment 63 mm. When analysed separately, the men had a 5-mm longer moment arm and the women a 5mm shorter moment arm than the mean moment arm at mid-stance. At the peak moment the corresponding figure was 10 mm.
Validity
The results of the present study were compared to those presented by Winter in 19876. To do this, the ground reaction forces and moments were divided by body-weight for each individual. Figure 3 shows the
vertical component of the ground reaction force. Figure 4 shows the moments about the knee in the sagittal plane. A high conformity was observed between the present study and Winter’s data. No similar data for moments in the frontal plane or moment arms have been found in the literature.
Discussion Like others, we found the vertical component of the ground reaction force to be remarkably constant for each subject. It is known to vary with body mass and walking speed6. Similarly, we found a rather small variability of the anteroposterior and mediolateral components of the ground reaction force. The results concerning the vertical and the fore-and-aft forces and
64
Clin. Biomech.
1993; 8: No 2
the knee moments in the present study are very similar to Winter’s for the sagittal plane6. To our knowledge no data for the frontal plane that allow comparison with our results have been published. The data presented in the literature are usually normalized to body-weight, height, or leg-length. In some studies walking speed has been predetermined2. We chose to perform our tests at self-selected free walking speed, because we believe that if the subjects are instructed to walk at a specific predetermined walking speed, they might change their normal gait pattern, which might affect the magnitude of the moments about the joints. The variability of the moments will, of course, increase if walking speed is not predetermined. As expected, the variability was greater when trials were done days apart than minutes apart. One explanation of this is that the subjects actually walked differently on different days. Another is that the skin markers could have been applied slightly differently on the various days. There are other sources of error. One is that the crosshair could have been placed inaccurately when the video frames were digitized. An error of more than kO.5 mm when positioning the crosshair on the video screen is not likely. Since the scale used was 1:4.7, the maximum error concerning the moment and moment arm would then be about 3%) which for a recorded mid-stance moment of 21 N m would be 0.6 N m and for a recorded mid-stance moment arm of 48 mm would be 1.4 mm. Yet another source of error is that with this two-dimensional system it has to be assumed that the distance from the centre of the camera lens to the hip, knee and ankle was the same as the distance to the point of application of the ground reaction force vector. This is not exactly true, but since the distance from the camera lens to the centre of the platform is 6 m, the error is very small. For all subjects during mid-stance and for nine out of ten at the peak moment, the distance between the knee and the point of application was less than 60 mm. This results in an error of 0.5 mm, which is about 1% of the mean moment in the frontal plane at mid-stance. An additional source of error is that during the
ZZ -0.060-0.080
t -O.lOOl
0
I
10
1
20
I
30
I
40
,
50
I
60
I
70
I
80
1
90
J
100
Percent of stance phase
Figure 4 Graphic presentation of the sagittal plane knee moments during stance phase. This study, 0, and Winter’s’, 0.
procedure a perspective correction was done for the vertical coordinate but not for the horizontal coordinate. The result is that if the subject steps on the centre of the platform, the calculated moment arm will be 1.7% shorter than it actually is, which for a moment arm of 48 mm is 0.8 mm. This is a systematic error and could be corrected for in the computer program, but since it is so small it has no practical significance. It has been shown that the recorded point of application of the ground reaction force vector may be inaccurate by 30 mm14. This might explain why the variability is much higher for the ankle than for the hip and knee in the frontal plane, since the ankle has a shorter moment arm. In the sagittal plane the variability was generally higher for the hip and knee than for the frontal plane. One reason for this is the motion blur due to the relatively high walking speed. This problem can be solved by using a high-speed shutter and reducing the exposure time. In surgical treatment of osteoarthrosis of the knee the importance of correcting leg alignment in the frontal plane has been emphasized in many clinical studies’. This involves a change of the knee moment arm in the frontal plane. Thus it is important to know the length of the knee moment arm in healthy normal subjects when patient data are evaluated. Based on the results concerning the variability of the forces and moments, we have found our method to be suitable for studying such changes in the hip and knee moments, and the knee moment arms in the frontal plane. Care should be taken when changes in the moments about the hip and knee in the sagittal plane and the ankle in the frontal plane are evaluated because of the great variability found by us in these moments in healthy normal subjects.
calibration
Acknowledgements
0
10
20
30
40
50
60
70
80
90
04 100
Percent of stance phase
Figure 3. Graphic presentation of the vertical component ofthe ground reaction force during stance phase. Results from this study, a, and Winter’s’, 0, are presented.
This project has been supported by the Karolinska Institute. We wish to extend our thanks to Peter Ekberg MSc for computer programming, and to Jan Gyllenstein RPT, Per Skarrie RPT and Par Westblad RPT for their help during the experiments. We wish to thank Staffan Ekblom for statistical advice.
Svensson and Weidenhielm:
References Tjomstrand B. Prediction of long-term outcome of tibia1 osteotomy for medial gonarthrosis. Arch Orthop Trauma Surg 1985; 103: 369-401
Prodromos CC, Andriacchi TP, Galante JO. A relationship between gait and clinical changes following high tibia1 osteotomy. J Bone Joint Surg 1985; 67-A: 1188-93 Lanshammar H, Lindroth T. Assessment of tibia1 osteotomy using gait analysis. Part 1, methods and genuine three-dimensional results presentation. In: Jonssoin B (ed.). Biomechanics XA. Illinois: Human Kinetic Publishers Campaign, 1987; 95- 101 Jefferson RJ, Whittle MW. Biomechanical assessment of unicompartmental knee arthroplasty, total condylar arthroplasty and tibia1 osteotomy. Clin Biomech 1989; 4: 232-41
Nilsson J, Torstensson A. Ground reaction forces at different speeds of human gait and running. Acta Physiol Stand 1989; 136: 217-27
Winter DA. Kinetics. In: The Biomechanics and Motor Control of Human Gait. Ontario, Canada: University of Waterloo Press, Dana Porter Library, 1987; 29-43
We offer a reprints
service
Knee moment
arms in normal gait
65
7 Lundberg A, Svensson OK, Nemeth G, Selvik G. The axis of rotation of the ankle joint. J Bone Joint Surg 1989; 71-B: 94-9 8 Winter DA. Biomechanics of Human Movement. New
York: John Wiley and Sons, 1979 9 Kistler. Multicomponent Measuring Platform for Biomechanics and Industry. Type 9281B. Winterthur, Switzerland: Kistler Instrumente AG, 1984 10 Bresler B, Frankel JP. The forces and moments in the leg during level walking. Trans ASME 1950; 72: 27-36 11 Lanshammar H. Vifor - a system of force line visualisation. In: de Groot, Hollander, Huyjing, van Ingen Schenau (eds). Biomechanics XI-B. Amsterdam, The Netherlands: Free University Press, 1988: 984-88 12 Shimba I. An estimation of center of gravity from force platform data. J Biomech 1984; 17: 53-60 13 Lamoreux L. Measurements and analysis of ground reaction forces. In: Lanshammar H (ed.). Gait Analysis Theory and Practice. Uppsala; Dept of Technology, Uppsala Univ., 1985; 47-69 14 Bobbert MF, Schamhardt HC. Accuracy of determining the point of force application with piezoelectrical force plates. J Biomech 1990; 23: 705-10
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1993; 8: 59-65
Papers
Variability of knee moment arms in the frontal and sagittal planes during normal gait 0 K Svensson
MD PhDl,
L Weidenhielm
’Kinesiology Research Group, Department Department of Anatomy, Karolinska Institute, St Gijrans Hospital, Stockholm, Sweden
MD~ of Physical Medicine and Rehabilitation, and *Department of Orthopaedic Surgery,
Summary A new measure, the length of the moment arm at the knee joint in the frontal and sagittal planes during normal gait, was assessed, and the variability tested. Simultaneously the external moments about the hip, knee and ankle were analysed. A gait analysis system with a force platform and two video cameras was used. Two recordings in each plane with a few minutes’ interval were collected in 10 healthy normal subjects walking at free cadence in their own shoes. For one subject, two recordings in each plane were obtained for 5 consecutive days. The mean moment arm length in the frontal plane at mid-stance, when trials were done minutes apart, was 48 mm, with a coefficient of variation of 7.9%. The mean moment arm length for the peak knee moment was 63 mm with a coefficient of variation of 7.9%. For the moment arm lengths at the peak moments in the sagittal plane, the variability was very high. The variability of the trials done minutes apart was in most cases less than of those done days apart. In the frontal plane, the smallest variability in trials done minutes apart was in the external hip peak and mid-stance moments and the external knee peak and mid-stance moments. In the sagittal plane, the smallest variability was in the external peak dorsiflexing moments and mid-stance dorsiflexing moments about the ankle. All ankle moments in the frontal plane and the peak moments about the hip and knee in the sagittal plane showed a high variability. Thus, care should be taken when these moments are evaluated with similar methods.
Relevance In surgical treatment of varus or valgus deformity knee moment arm in the moment arm in healthy evaluated. In addition it
osteoarthrosis of the knee, restoration of leg alignment from a has been considered important. This involves a change of the frontal plane. Thus, it is important to know the length of the knee subjects, especially in the frontal plane, when patient data are is important to know the variability of the analysis method.
Key words: Ankle, biomechanics,
gait, hip, knee
Introduction
In surgical treatment of osteoarthrosis of the knee, restoration of leg alignment from a varus or valgus deformity has been considered important’. In a tibia1 osteotomy for a varus deformity, the idea is to decrease the load on the medial knee compartment*. This is accomplished by reducing the moment brm in the frontal plane between the ground reaction force and the knee”. Received: 3 July 1991 Accepted: 14 March 1992 Correspondence and reprint requests to: Ola K Svensson, MD PhD. Department of Physical Medicine and Rehabilitation, Karolinska Institute, Norrbacka ltr, PO Box 60500, S-10401 Stockholm, Sweden 0 1993 Butterworth-Heinemann 0268-0033/93/020059-07
Ltd
Previously the reduced moment arm during gait after surgery has been analysed indirectly by assessment of the knee moment, i.e. the product of the ground reaction force and the moment armzW4. A higher body-weight and walking speed increase the magnitude of the ground reaction forces3”. Increased walking speed after knee surgery produces an increased ground reaction force6, and consequently a higher moment about the knee even if the moment arm is shortened due to surgery. Therefore, to decrease the effect of walking speed, it has been considered of value to use the moment arm by itself as a parameter to evaluate surgical procedures of the knee3. The purpose of the present study was (1) to introduce the knee moment arm length as a measure to evaluate knee load pre- and postoperatively; (2) to determine the variability in trials done minutes apart and trials
60
Clin. Biomech. 1993; 8: No 2
done days apart; (3) to present some normative data for healthy subjects for use as reference values in assessment of patients with knee deformities; and (4) to determine the variability in the hip, knee and ankle moments in the frontal and sagittal planes, in trials done minutes apart and days apart.
Methods Subjects
Ten healthy volunteers with no symptoms from joints in the lower extremities, five men and five women, mean age 26 years (range 19-34) participated in the study. The mean body weight was 67.1 kg (SD 8.4), the mean distance from spina iliaca anterior superior to the medial malleolus was 0.89 m (SD 0.06), the mean distance from spina iliaca anterior superior to the medial knee joint line was 0.52 m (SD 0.03). The subjects’ mean walking speed was 1.43 m/s (SD 0.21), the mean step length 0.74 m (SD 0.08), and the mean step frequency 1.92 steps/s (SD 0.11). Experimental set-up
The subjects walked in the shoes that they normally used, at free cadence, on a 13-m long and 1.4-m wide walkway consisting of a thin rubber mat. A force platform (Kistler 9281B, Kistler Instrumente AG, Winterthur, Switzerland) was hidden in the middle of the walkway under the mat. The subjects were instructed to look at a cross at eye-height on the wall in front of them while they walked, and their starting position was adjusted until they stepped on the force platform with the appropriate foot. Floor reaction forces were obtained at the stance phase of the middle stride. After amplification (Kistler type 5001 and 5006) and A/D conversion, the force platform recordings were collected in a personal computer (ABC 800, Luxor) at a frequency of 250 Hz. The subjects were filmed with two video cameras (Hitachi FP-10) in the frontal and sagittal planes at 25 Hz. In the frontal plane, a skin marker was placed to mark the hip joint 25 mm distal to the midpoint of a line from the anterior superior iliac spine to the pubic tubercle’. For the knee, the marker was placed at the tuberositas tibiae, and for the ankle joint at the midpoint of a line from the tip of the medial malleolus to the tip of the lateral malleolus’. In the sagittal plane, skin markers were placed at the centre of the greater trochanter, at the centre of the lateral femoral epicondyle, and at the most lateral point on the lateral malleolus of the fibula’. For synchronization of the video frames with the force platform recordings, an LED display panel indicating time down to one-thousandth of a second was visible on the video frames. The display was connected to the computer. After the data collection, the coordinates for the hip, knee, and ankle joint were manually digitized into the computer using a crosshair (VPA-1000, Panasonic).
Figure 1. The calibration set-up. To the left the calibration frame with the two plumb-lines hanging just above two of the four transducers. Plumb-line A is at the back end of the force plate and plumb-line B at the front. To the right, the frontal-plane camera, 6 m in front of the short side of the platform. The other camera was placed facing the long side of the platform.
Calibration procedure
The calibration set-up for the video-recording system is shown in Figure 1. A metal frame containing two plumb-lines with length indication was placed on the force platform. Viewed from the camera in front of the short side of the platform, one plumb-line hung just above the left transducer at the front edge of the platform (B in Figure 1). The other plumb-line hung above the transducer to the right, at the back edge of the platform (A in Figure 1). The distance between the camera lens and the middle of the force platform was 6 m, and the centre of the lens was 0.65 m above the floor. Viewed from the side, the calibration procedure can be simplified as in Figure 2, where A and B are the distances indicated on the plumb-lines, and a and b the
A
.
L
Figure 2. Schematized description of the calibration set-up viewed from the side. A is the distance indicated on the plumb-line at the back end of the force platform and B is the distance on the plumb-line at the front end. a is the image of A on the projection plane or the video frame, and b is the image of B. Zis the vertical distance to be calculated and z is this distance projected on the video frame. L is the distance from the lens position of the camera to A, and /is the distance to the projection plane. dp is the distance between A and Band x is the distance from A to the point of application of the ground reaction force.
Svensson
images of A and B on the projection plane. 2 is the vertical distance to be calculated, and z is this distance on the projection plane. L is the distance from the camera lens to A, and I the distance to the projection plane. dp is the distance between A and B and x is the distance from A to the point of application of the ground reaction force. The coordinates for the point of to the calculated according application were manufacturer’s instruction’. From this, the following equation system can be set up: AIL
= all
BI(L
- dp) = bll
Zl(L
- x) = z/l
This gives: Z = (1 - (x(1 - k)ldp))Azla;
k = aBIAb
A = B gives k = alb
Experimental
design
To test the variability of the moment values measured, four trials were recorded within a few minutes interval and collected for 10 subjects; two in the frontal plane and two in the sagittal. Additionally, for one of the subjects chosen by lottery, four trials were recorded each day, during 5 consecutive days. The subjects wore T-shirts, tight shorts and sports-shoes without socks. Subjects’ body-weight was obtained with clothes and shoes on. Calculation procedure
The computer program was designed by our group, based on a free-body diagram described by Bresler and Frankeli’. It calculated the external moments in the frontal and sagittal planes about the hip, knee and ankle during the stance phase. The calculations consisted of the ground reaction and gravitational forces, but the inertial components were omitted. The effect of inertia on the knee moments is small throughout most of the stance phase”,“. Weights for each body segment in relation to body mass, and the location of the centres of mass relative to segment length, were obtained from Dempster’s anthropometric data’. To attenuate the high-frequency noise a filtering window of three points was used. The filter works like a low-pass filter and can be described by the following formula: Vt = V(n - 1)/4 + Vn/2 + V(n + 1)/4
where Vn is the nth sampled value. The window was then moved one sample forward successively along the whole force curve. The bandwidth, equivalent to the spectral density of the filter, was 22.0246. The following parameters were analysed: 1. The peak, moment.
i.e. the recorded
maximum
external
and Weidenhielm:
Knee moment
arms in normal
gait
61
2. The mid stance moments, i.e. the recorded external moment at 50% of stance phase about the hip, knee, and ankle joint in the frontal and sagittal planes. 3. Moment arms about the knee in the frontal and sagittal planes. The moment arm was defined as the perpendicular distance between the ground reaction force vector and tuberositas tibiae in the frontal plane, and as the perpendicular distance between the ground reaction force vector and the centre of the lateral femoral epicondyle in the sagittal plane. 4. The vertical, mediolateral, and fore-and-aft components of the ground reaction force during the stance phase. The distance from the surface of the platform down to the transducers where the shear forces were actually measured was 54 mm. If this is ignored, errors will occur. Therefore, in the computer program, the centre of pressure was projected up to the top surface of the platform along the line of action of the resultant force vector, as described by Shimba’* and Lamoreux13. Statistical analysis
The variability when trials were done minutes apart was calculated using the formula
where d is the difference between the two measurments on each subject and n is the number of subjects. The variability when trials were done days apart was calculated with an analysis of variance (ANOVA). The coefficients of variation (CV) were calculated and expressed as a percentage. The coefficients of correlation (r) between the two steps, for the intra-day measurements of the 10 subjects, were calculated. Results
The variability for the investigated variables for the frontal plane are presented in Table 1, and for the sagittal plane in Table 2. The three columns to the left show the results from the trials done minutes apart on 10 subjects, and the two columns to the right show the results from trials done days apart during 5 consecutive days on one subject. Concerning the frontal plane, the variability (s) of the trials done minutes apart was always less than that of trials done days apart. In the sagittal plane this was the case for 10 of the 15 parameters. In the frontal plane, the external moment about the hip and knee was adducting, except for a short period at the beginning and end of the stance phase. For the ankle, the pattern varied for different subjects. Except for the moment arm of the mid-stance knee moment, the variability was higher for the moments and moment arms in the sagittal plane than for those in the frontal plane when trials were done minutes apart (Tables 1 and 2). Table 3 shows the obtained mean
62
Clin. Biomech.
1993; 8: No 2
Table 1. Variability of the forces, the external moments and knee moment arms for the two trials done minutes apart on ICI subjects. Variability for the trials done days apart on one subject on five consecutive days. Coefficients of correlation (r), variability (s), and coefficients of variation (CV%) in the frontal plane for the peak vertical and medially directed components of the ground reaction force (N), the external peak and mid-stance moments (N m), and moment arm length (mm) for the peak and mid-stance moments at the knee Variability of trials Frontalplane
minutes apart (10 subjects)
days apart (1 subject)
r
S
Vertical force Medial force
0.97 0.92
17.6 6.1
2.1 13.5
28.1 7.9
3.7 16.5
Hip Peak moment Mid-stance moment
0.93 0.92
4.9 2.9
4.8 5.3
11.3 6.9
15.3 19.0
0.93 0.83
4.1 6.2
6.9 7.9
13.3 16.0
29.2 26.9
0.91 0.88
2.6 4.8
8.7 7.9
6.8 14.7
37.1 38.5
0.80 0.87 0.44
2.4 2.1 2.3
24.3 18.4 91.0
8.0 7.9 6.6
76.2 65.2 94.6
Knee Peak Moment Moment arm Mid-stance Moment Moment arm Ankle Peak add. moment Peak abd. moment Mid-stance moment
CV%
S
CV%
Table 2. Variability of the forces, the external moments and knee moment arms for the two trials done minutes apart on IO subjects. Variability for the trials done days apart on one subject on five consecutive days. Coefficients of correlation (r), variability (s), and coefficients of variation (CV%) in the sagittal plane for the peak vertical, anteriorly and posteriorly directed components of the ground reaction force (N), the peak external flexing and extending moments (N m), the external mid-stance moments (N m), and the corresponding length (mm) of the knee moment arms Variability of trials Sagittalplane
minutes apart (10 subjects) r
Vertical force Anterior force Posterior force Hip Peakflexing moment Peak extending moment Mid-stance flexing moment Knee Peak flexing Moment Moment arm Peak extending Moment Moment arm Mid-stance extending Moment Moment arm Ankle Peak plantarflexing moment Peak dorsiflexing moment Mid-stance dorsiflexing moment
0.96 0.95 0.72
S
days apart (7 subject) CV%
S
CV%
32.6 5.5 13.4
3.6 2.9 7.6
28.1 14.2 12.8
3.7 9.6 7.7
-0.15 0.24 0.89
21.8 201 .o 3.6
34.6 72.5 27.8
22.9 118.8 4.8
58.2 141.6 33.9
0.21 -0.05
32.1 96.1
49.3 71 .o
39.3 14.8
63.1 21.2
0.70 0.26
9.2 114.1
23.9 95.0
13.7 17.6
39.3 37.4
3.1 4.0
64 90.5
6.2 13.1
37.6 40.5
49.5 4.9 3.3
71.3 3.6 6.8
65.3 11.8 5.4
181.7 10.7 10.3
0.92 0.91 -0.26 0.99 0.95
Svensson and Weidenhielm:
Table 3. Mean values and standard deviations
(SD)
for the investigated
Knee moment
arms in normal gait
63
variables
Frontal plane
All (n = 10) (20 trials) SD Mean
Men (n = 5) (10 trials) SD Mean
Women In = 5) (70 trials) Mean SD
Vertical force Medial force
750.7 39.3
87.9 15.3
778.0 46.6
117.1 16.2
723.3 32.1
30.6 10.7
80.0 42.2
16.2 9.8
87.9 46.7
17.0 7.5
72.1 37.7
11.3 10.1
45.8 63.2
14.0 14.6
55.6 72.9
13.0 13.2
36.1 53.5
5.8 8.2
21.5 47.7
7.2 12.2
25.4 52.6
6.1 13.5
17.5 42.8
6.1 8.9
8.8 6.6 2.9
5.4 4.8 4.0
10.8 9.1 3.5
5.6 5.1 4.5
6.7 4.2 2.3
4.7 3.1 3.6
Hip Peak moment Mid-stance moment Knee Peak Moment Moment arm Mid-stance Moment Moment arm Ankle Peak add. moment Peak abd. moment Mid-stance moment
Sagittalplane
All (n = 10) (20 trials) Mean SD
Men (n = 5) (10 trials) Mean SD
Women (n = 5) (10 trials) Mean SD
Vertical force Anterior force Posterior force
751.3 152.2 137.5
94.5 21.3 24.8
781.3 146.0 141.4
112.1 27.4 24.8
721.2 158.4 133.6
65.5 10.9 25.5
Hip Peakflexing moment Peak extending moment Mid-stance flexing moment
47.9 149.4 10.4
20.4 234.3 10.4
49.2 150.6 16.0
24.6 219.0 8.9
46.6 148.3 4.9
16.4 260.6 8.9
53.3 89.8
34.6 93.5
56.6 89.0
49.6 116.9
50.0 90.6
6.9 69.2
26.9 77.0
12.7 109.4
34.2 105.4
13.0 144.9
19.5 48.7
7.1 49.8
4.2 6.2
10.5 20.8
5.3 8.5
14.2 27.4
3.2 4.0
5.2 12.1
29.6 105.8 41.0
47.3 25.8 12.9
44.9 119.0 43.1
64.6 30.2 10.2
14.4 92.7 38.9
6.3 10.7 15.5
Knee Peak flexing Moment Moment arm Peak extending Moment Moment arm Mid-stance extending Moment Moment arm Ankle Peak plantarflexing moment Peak dorsiflexing moment Mid-stance dorsiflexing moment
values for the frontal and sagittal planes. For men and women combined, when trials were done minutes apart, the mean knee moment arm length in the frontal plane at mid-stance was 48 mm and at the peak moment 63 mm. When analysed separately, the men had a 5-mm longer moment arm and the women a 5mm shorter moment arm than the mean moment arm at mid-stance. At the peak moment the corresponding figure was 10 mm.
Validity
The results of the present study were compared to those presented by Winter in 19876. To do this, the ground reaction forces and moments were divided by body-weight for each individual. Figure 3 shows the
vertical component of the ground reaction force. Figure 4 shows the moments about the knee in the sagittal plane. A high conformity was observed between the present study and Winter’s data. No similar data for moments in the frontal plane or moment arms have been found in the literature.
Discussion Like others, we found the vertical component of the ground reaction force to be remarkably constant for each subject. It is known to vary with body mass and walking speed6. Similarly, we found a rather small variability of the anteroposterior and mediolateral components of the ground reaction force. The results concerning the vertical and the fore-and-aft forces and
64
Clin. Biomech.
1993; 8: No 2
the knee moments in the present study are very similar to Winter’s for the sagittal plane6. To our knowledge no data for the frontal plane that allow comparison with our results have been published. The data presented in the literature are usually normalized to body-weight, height, or leg-length. In some studies walking speed has been predetermined2. We chose to perform our tests at self-selected free walking speed, because we believe that if the subjects are instructed to walk at a specific predetermined walking speed, they might change their normal gait pattern, which might affect the magnitude of the moments about the joints. The variability of the moments will, of course, increase if walking speed is not predetermined. As expected, the variability was greater when trials were done days apart than minutes apart. One explanation of this is that the subjects actually walked differently on different days. Another is that the skin markers could have been applied slightly differently on the various days. There are other sources of error. One is that the crosshair could have been placed inaccurately when the video frames were digitized. An error of more than kO.5 mm when positioning the crosshair on the video screen is not likely. Since the scale used was 1:4.7, the maximum error concerning the moment and moment arm would then be about 3%) which for a recorded mid-stance moment of 21 N m would be 0.6 N m and for a recorded mid-stance moment arm of 48 mm would be 1.4 mm. Yet another source of error is that with this two-dimensional system it has to be assumed that the distance from the centre of the camera lens to the hip, knee and ankle was the same as the distance to the point of application of the ground reaction force vector. This is not exactly true, but since the distance from the camera lens to the centre of the platform is 6 m, the error is very small. For all subjects during mid-stance and for nine out of ten at the peak moment, the distance between the knee and the point of application was less than 60 mm. This results in an error of 0.5 mm, which is about 1% of the mean moment in the frontal plane at mid-stance. An additional source of error is that during the
ZZ -0.060-0.080
t -O.lOOl
0
I
10
1
20
I
30
I
40
,
50
I
60
I
70
I
80
1
90
J
100
Percent of stance phase
Figure 4 Graphic presentation of the sagittal plane knee moments during stance phase. This study, 0, and Winter’s’, 0.
procedure a perspective correction was done for the vertical coordinate but not for the horizontal coordinate. The result is that if the subject steps on the centre of the platform, the calculated moment arm will be 1.7% shorter than it actually is, which for a moment arm of 48 mm is 0.8 mm. This is a systematic error and could be corrected for in the computer program, but since it is so small it has no practical significance. It has been shown that the recorded point of application of the ground reaction force vector may be inaccurate by 30 mm14. This might explain why the variability is much higher for the ankle than for the hip and knee in the frontal plane, since the ankle has a shorter moment arm. In the sagittal plane the variability was generally higher for the hip and knee than for the frontal plane. One reason for this is the motion blur due to the relatively high walking speed. This problem can be solved by using a high-speed shutter and reducing the exposure time. In surgical treatment of osteoarthrosis of the knee the importance of correcting leg alignment in the frontal plane has been emphasized in many clinical studies’. This involves a change of the knee moment arm in the frontal plane. Thus it is important to know the length of the knee moment arm in healthy normal subjects when patient data are evaluated. Based on the results concerning the variability of the forces and moments, we have found our method to be suitable for studying such changes in the hip and knee moments, and the knee moment arms in the frontal plane. Care should be taken when changes in the moments about the hip and knee in the sagittal plane and the ankle in the frontal plane are evaluated because of the great variability found by us in these moments in healthy normal subjects.
calibration
Acknowledgements
0
10
20
30
40
50
60
70
80
90
04 100
Percent of stance phase
Figure 3. Graphic presentation of the vertical component ofthe ground reaction force during stance phase. Results from this study, a, and Winter’s’, 0, are presented.
This project has been supported by the Karolinska Institute. We wish to extend our thanks to Peter Ekberg MSc for computer programming, and to Jan Gyllenstein RPT, Per Skarrie RPT and Par Westblad RPT for their help during the experiments. We wish to thank Staffan Ekblom for statistical advice.
Svensson and Weidenhielm:
References Tjomstrand B. Prediction of long-term outcome of tibia1 osteotomy for medial gonarthrosis. Arch Orthop Trauma Surg 1985; 103: 369-401
Prodromos CC, Andriacchi TP, Galante JO. A relationship between gait and clinical changes following high tibia1 osteotomy. J Bone Joint Surg 1985; 67-A: 1188-93 Lanshammar H, Lindroth T. Assessment of tibia1 osteotomy using gait analysis. Part 1, methods and genuine three-dimensional results presentation. In: Jonssoin B (ed.). Biomechanics XA. Illinois: Human Kinetic Publishers Campaign, 1987; 95- 101 Jefferson RJ, Whittle MW. Biomechanical assessment of unicompartmental knee arthroplasty, total condylar arthroplasty and tibia1 osteotomy. Clin Biomech 1989; 4: 232-41
Nilsson J, Torstensson A. Ground reaction forces at different speeds of human gait and running. Acta Physiol Stand 1989; 136: 217-27
Winter DA. Kinetics. In: The Biomechanics and Motor Control of Human Gait. Ontario, Canada: University of Waterloo Press, Dana Porter Library, 1987; 29-43
We offer a reprints
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Knee moment
arms in normal gait
65
7 Lundberg A, Svensson OK, Nemeth G, Selvik G. The axis of rotation of the ankle joint. J Bone Joint Surg 1989; 71-B: 94-9 8 Winter DA. Biomechanics of Human Movement. New
York: John Wiley and Sons, 1979 9 Kistler. Multicomponent Measuring Platform for Biomechanics and Industry. Type 9281B. Winterthur, Switzerland: Kistler Instrumente AG, 1984 10 Bresler B, Frankel JP. The forces and moments in the leg during level walking. Trans ASME 1950; 72: 27-36 11 Lanshammar H. Vifor - a system of force line visualisation. In: de Groot, Hollander, Huyjing, van Ingen Schenau (eds). Biomechanics XI-B. Amsterdam, The Netherlands: Free University Press, 1988: 984-88 12 Shimba I. An estimation of center of gravity from force platform data. J Biomech 1984; 17: 53-60 13 Lamoreux L. Measurements and analysis of ground reaction forces. In: Lanshammar H (ed.). Gait Analysis Theory and Practice. Uppsala; Dept of Technology, Uppsala Univ., 1985; 47-69 14 Bobbert MF, Schamhardt HC. Accuracy of determining the point of force application with piezoelectrical force plates. J Biomech 1990; 23: 705-10
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