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A non-invasive protocol to determine the personalized moment arms of knee and ankle muscles
ARTICLE IN PRESS
Journal of Biomechanics 40 (2007) 1776–1785 www.elsevier.com/locate/jbiomech www.JBiomech.com
A non-invasive protocol to determine the personalized moment arms of knee and ankle muscles A. Bonnefoya,b,, N. Doriota, M. Senka, B. Dohina,c, D. Pradond, L. Che`zea a
Laboratoire de Biome´canique et Mode´lisation Humaine, LRE_T32, Universite´ Lyon 1 (Claude Bernard), Baˆt. Ome´ga, Bd du 11 Novembre 1918, 69622 Villeurbanne, France b Me´dimex, 56 avenue du 11 novembre 1918, 69160 Tassin la demi lune, France c Service de chirurgie orthope´dique pe´diatrique, Pavillon Tbis, Hoˆpital Edouard Herriot, Place d’Arsonval 69437 Lyon, France d Laboratoire d’Analyse du Mouvement, Pavillon : Netter1, Hoˆpital Raymond POINCARE, 104, boulevard Raymond Poincare´ 92380 Garches, France Accepted 29 July 2006
Abstract One difficulty that comes with predicting muscular forces is the accuracy of experimental data, particularly the assessment of muscle moment arms with respect to each joint rotation axis. This paper presents a non-invasive experimental protocol to obtain the personalized muscle moment arms with respect to the ankle and knee joints. A specific pointer is used by a specialist of lower limb anatomy in order to define the local portion of the line of action of the different muscles closed to the joint on the standing subject’s lower limb. With this pointer, the three-dimensional coordinates of several points representing the line of action of 12 ankle and knee muscles are collected by a Motion Analysis system. The collection is done five times by the same operator and one time by two different operators. From this data, the intra and inter operator repeatabilities are tested. Relative (ICC) and absolute (SEM) reliabilities are determined in order to evaluate the intra operator repeatability of this non-invasive protocol. The ICC values obtained are higher than 0.91 for 10 among 12 muscles. The intra operator repeatability is thus confirmed. From the records realized by the two operators, the differences are negligible. Thus, the inter operator repeatability is also confirmed. The moments arms obtained using this non-invasive experimental protocol are compared with those calculated from origin and insertion points reported in the literature, according to the work of Whites, Pierrynowskis and Kepples, respectively. The estimations obtained using the non-invasive experimental protocol are found, for some muscles, more realistic than those calculated using the literature data and are always coherent with the role of the muscles described in anatomical books. r 2006 Published by Elsevier Ltd. Keywords: Gait analysis; Muscle moment arm; Muscle path
1. Introduction An accurate representation of the lower limb musculoskeletal system is required for the prediction of the locomotor muscle-tendon forces during gait. The prediction of the muscle tendon forces is currently an important research axis in the field of biomechanics (Pandy, 2001). A large number of the lower limb muscles involved in locomotion are biarticular. This is why models defining the Corresponding author. Tel.: +33 04 78 34 32 48; fax: +33 04 78 34 69 25. E-mail address: [email protected] (A. Bonnefoy).
0021-9290/$ - see front matter r 2006 Published by Elsevier Ltd. doi:10.1016/j.jbiomech.2006.07.028
line of action of muscles crossing the three lower limb joints, are necessary. Seireg and Arvikar (1973), and Ro¨hrle et al. (1984) have published schematic representations of the line of action of the whole lower limb muscles. At the same time, Frigo and Pedotti (1978) presented a two-dimensional (2D) model of 11 locomotor muscles, which includes five biarticular muscles. Pierrynowski and Morrison (1985a, b) estimated the origin and insertion points of the 47 muscles of the lower limb. However, in these publications, the 3D coordinates were not extensively presented. In 1990, Yamaguchi et al. synthesized, in the Appendix A1 of the Winter and Woos’ book (Winter and Woo,
ARTICLE IN PRESS A. Bonnefoy et al. / Journal of Biomechanics 40 (2007) 1776–1785
1990), all the 3D upper and lower limb muscle origin and insertion coordinates available in the literature. Nowadays, the four models extensively used in the musculoskeletal models are: Brand et al. (1982), White et al. (1989), Pierrynowski, 1995 and Kepple et al. (1998). In the study of Brand et al., all the muscles were dissected on three fresh cadaver specimens of varying heights and sexes (1.63 m female, 1.72 m male, and 1.83 m male). In the study of White et al., the insertion and origin points of all muscles crossing the hip, knee and ankle joints were located on six disarticulated dry bone pelvis, nine dry bone femurs, tibia and fibula, one reconstructed skeletal foot and one dissected cadaver foot. In the Kepple’s study, all the muscles were collected on 52 dry human skeletal specimens chosen from the Terry Collection (Smithsonian Institution, Washington, DC). In the Pierrynowski’s study, the insertion and the origin points of all muscles crossing the hip, knee and ankle joints came from different articles. The most recent musculoskeletal models take into account muscle deviation by bone pieces (An et al., 1979; Pedersen et al., 1997; Delp et al., 1990; Pierrynowski, 1995; Kepple et al., 1998) and these authors suggest the use of a subject fitted model. Indeed, these models are still sensitive to changes in musculoskeletal geometry (Brand et al., 1986; Hoy et al., 1990; Winters and Stark, 1987; Kepple et al., 1998). Moreover, differences between the above mentioned models are not negligible. For that, the determination of the line of action of the muscles personalized to subject morphology is one of the major steps in the development of reliable musculoskeletal models. A recent study from Bonajic and Pandy (Gfo¨hler et al., 2006), presents a method in order to define the lower limb musculoskeletal model of a child based on MRI. This technique could be applied to adult subject. By this method, we can obtain the ‘‘real’’ volume, PCSA, length, and insertion—origin points of the lower limb muscles and will be the more realistic definition of the musculoskeletal model. However, MRI yield time and cost considerations. Besides, two different methods are commonly used to model the paths of the muscle in the body: the straight line and the centroı¨ d line methods. In the straight line method, the path of a muscle is represented by a straight line joining only the two the centroı¨ ds of the muscles attachment sites (Seireg and Arvikar, 1989; Pierrynowski, 1995). This method is easy to implement but when a muscle wraps around a bone or another muscle, the results would be meaningless. In the second method, centroı¨ d line, the muscle path is represented as a line passing through the locus of all the cross sectional centroı¨ ds of the muscle. This method is more accurate in the representation of the muscle line of action but can be difficult to apply. Indeed, even if a muscle’s centroı¨ d path is known for one position of the body, it is practically impossible to determine how the muscle paths change as body position changes. To overcome the problem, the introduction of effective attachment sites or via points at
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specific location along the line of action could be a good solution. However, the determination of these via points, personalized to subject morphology has not been previously studied. The goal of this paper is to present a non-invasive experimental protocol established to collect the coordinate of relevant points that define the local portion of the line of action of each muscle. The local portions of the line of action have been directly measured by means of manual pointing. In this study, the main muscle moment arms calculated are those of the knee and ankle joint. Five records with a pointer have been done with the same operators and two records have been done by two different operators. The hip muscles are not evaluated during this work because they are deep and large so manual pointing does not allow a reliable determination of the insertion and origin points. 2. Materials and methods 2.1. The musculoskeletal model The major muscles were selected from the literature (Doriot, 2001; Kapandji, 1980; Calais-Germain, 1989; Bouisset and Maton, 1995; Hansen, 2004) and the selection was completed following advices from specialists of lower limb anatomy (Table 1). To better define the insertions, origins and via points, a table is added in Appendix A1 that defines the anatomic names of the points presented in the Table 1.
2.2. Protocol In order to measure directly the via points of the muscles, a pointer has been designed. This pointer is a metal rod equipped with two markers (see Fig. 2). The two markers define the direction of the rod in 3D space, as well as the 3D coordinates of the end point, which distance is known with respect to both markers. For the quadriceps muscle, the deviating effect of the patella was introduced in order to calculate a more accurate moment arm (Brand et al., 1982; White et al., 1989; Delp, 1990, Pierrynowski, 1995). In this case, the local portion of the line of action of the muscle has been defined as the path between the head of the tibialis anterior and the kneecap as indicated on the Fig. 1. The musculoskeletal model was identified on one healthy subject (29-years old, 1.74 m and 76 kg). The first part of the protocol corresponds to the collection, by a unique operator, of the specific points of muscular portion line of action (Fig. 2) at five different instants in the day. The local portion of the action lines of muscles is determined in a static standing position. For this, an opto-electronic Motion Analysis system (Santa Rosa, CA) consisting of five digital cameras is used. The subject is equipped with passive reflective markers used to define segment reference frames (Wu et al., 2002). With the subject in static position, via points (I and O) were also collected using the pointer. Between each record, five stances phase of the gait have been recorded. No particular recommendation is given to the subject; it is a ‘‘free gait’’ according to Viel (2000). After the gait trials collection, the subject performs a circumduction movement of the leg. This will be used to determine the hip joint centre (Gutierrez, 1996). The 3D trajectories of the cutaneous markers are computed and then corrected by a low-pass filter (Butterworth, fourth-order, with a cut-off frequency of 5 Hz) followed by a solidification of each body segment (Che`ze et al., 1995). The via points coordinates were obtained in the laboratory reference frame and then computed, with the homogenous matrix
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Table 1 Specific points (O and I) chosen to define each muscle action line on the knee and the ankle Insertions (I) Origins (O)
Muscles
Joints
02
1 = Tibialis anterior (O1 and I1)
2 = Extensor Digitorum (O2 and
1
4
I2)
3 = Peroneus longus (O3 and I3)
Ankle Knee
3 2
4 =Triceps surae: Gas trocnemius (O4 and I4)
sup
sup
12
sup
ant
med
lat
13 sup sup
1
1 = Tibialis posterior (O1 and I1) post
ant
01
02
lot
Ankle
2 = Flexor hallucis longus (O2 and I2)
l1
02 2 1 = Quadriceps femoris : Rectus femoris (O1 and I1)
04 4
03
2 = Sartorius (O2 and I2)
3 6
3 = Gracilis (O3 and I3)
5
1
4 = Tensor fasciae latae (O4 and I4)
Knee
5 = Biceps Femoris (O5 and I5)
16 15 6 = Semitendinosus (O6 and I6)
14
12=13 sup
sup med
algebra (Doriot, 2001; Legnani et al., 1996), in the corresponding segment reference frames. From this, the trajectories of the via points could be derived during the stance phase of the gait.
lat
The second part of this protocol corresponds to the record of via points with the pointer on the subject, in static position, by two different operators. From this, the differences in the moment arm estimation between the operators have been evaluated.
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2.3. Statistical analysis
o o
In this study, a repeated measure ANOVA study was chosen in order to evaluate the repeatability of personalized moment arms. The norm of the moment arm vectors has been calculated from the pointer data recorded during the five repeated trials (at different instants in the same day). Data were examined for normality and homogeneity of variance to ensure they fulfilled the criteria for parametric tests. ICC is the ratio between-subjects variance divided by the total variance (Denegar and Ball, 1993). Using one-way analysis of variance (one-way ANOVA), ICC(1,1) was determined as estimator of reproducibility.
Sup Ant
o′
Ok
MA′
Ok
l
ICC ¼
MA′
o′
l′ l
(a)
l′
(b) >
>
(MA' u) = Ok I ′
I ′O ′ I ′O ′ u
Fig. 1. Picture representing, in the sagittal plane, the two specific points O0 and I0 measured to define the quadriceps muscle moment arm. Ok is the knee centre and MA0 represents the Moment Arm of the quadriceps muscle. MA0 is calculated with the formula indicated, in the reference frame segment. The case a, corresponding at the beginning of the stance phase. The case b, corresponding at the end of the stance phase. O and I are the points available in the literature in order to define the line of action of the quadriceps muscle.
BMS WMS , BMS þ ððk=k0 Þ 1ÞWMS
where BMS is between-subjects mean square representing true variance, WMS is within-subject mean square representing the error variance, k is the number of measurements administered and k0 is the number of repeated measures which reliability is estimated. The ICC algorithm generally returns a value between 0 and 1, where 0 stands for no reproducibility and 1 for the perfect reproducibility. There is no really universal method for categorizing ICC levels, given that errors in determining reliability may occur even with high ICC levels. The following general guidelines (Hager, 2003) were used: 0–0.39 poor, .40–0.59 fair, 0.60–0.79 good, 0.8–1.0 excellent. Another commonly used reliability index is the standard error of measurement (SEM), which is an absolute measurement of repeatability. SEM is defined as pffiffiffiffiffiffiffiffiffiffiffi SEM ¼ s 1 r, where s is the standard deviation of the measurements and r is the ICC.
2.4. Comparison with the literature’s data After the records of the via points on subject, we compared the moment arms calculated from the pointer data to those obtained from mapping White’s, Kepple’s and Pierrynowski’s data with the morphology of our subject. For each literature data, the skeletal segment frames have been defined from the anatomic points available in the literature tables (Wu et al., 2002). Then, the transformation matrices have been calculated in order to map the literature data in the local reference frame of the subject. Thus, the literature data have been derived during the stance phase of the gait.
3. Results The mean and the standard deviation of Euclidian norm ! of the moment arm vectors, generally noted:MA0 (see Fig. 1 for the definition of this vector) obtained from five trials with the pointer are presented in Table 2. The ICC and the SEM are also presented in the Table 2. The differences between operators in the moment arm estimation are directly displayed in Table 3. Table 4 presents, for our protocol and for the Whites’, Kepples’ and Pierrynowskis’ mapped data, the mean coordinates X, Y, Z of the moment arm vectors MA0 in the segment frame and their standard deviations, the mean ! norm (distance) and standard deviation of MA0 . Fig. 2. Picture from motion analysis recording for the semitendinosus muscle. It represents the biceps thigh points collected for the origin using the pointer equipped with passive reflective markers.
In Table 4, we can observe that the sign of the main component of the moment arm vector is systematically in agreement with the known role of each muscle (described
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Table 2 Measures of the average and the standard deviation (in cm) of muscle moment arm norms from five trial pointer. Measures of absolute and relative repeatability Muscles
Mean distance
STD
ICC
SEM
Tibialis anterior Triceps surae Peroneus Tibialis posterior (TP) Extensor digitorum Flexor hallucis longus Quadriceps femoris Biceps femoris Semitendinosus–Semimembranosus Sartorius Tensor fasciae latae Gracilis
2.8 4.6 3.4 2.4 2.9 2.6 3.8 6.0 6.4 5.7 6.0 5.8
0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.1 0.1 0.1 0.1 0.1
0.99 0.94 0.99 0.99 0.99 0.99 0.99 0.95 0.91 0.75 0.91 0.25
0.003 0.013 0.000 0.001 0.001 0.000 0.001 0.022 0.021 0.030 0.040 0.100
The subject is in a relaxed static standing position during the record of the data.
in anatomical books). We note that the signs of the components are not always the same. In term of distance, in the case of the Tensor fascia latae, the mean distance obtained with White’s and Kepple’s data are, respectively, 12 and 12.8 cm as for the pointer and Pierrynowski’s data the distance are, respectively, 6.4 and 4.5 cm. Table 5 presents the differences between mean moment arm distances obtained with our method and the others. In order to verify the influence of the four configurations on the quadriceps moment arms, the average evolution during the stance phase is presented with the different sets of literature and via point data. The results presented in the Table 5 allow to have an idea on the numerical difference in term of distance between the pointer and the three others bibliographic data. We can note that the numerical differences between the pointer and White’s method are more important than with the two others bibliographic data. Compared with the Kepple and Pierrynowski data, the moment arm distances obtained with the pointer are, generally, of the same order. Fig. 3 presents, in the sagittal plane, the comparison between quadriceps moment arms calculated using the pointer and the three other bibliographic data on the same subject. We can observe this on the comparison between the quadriceps moment arms in the sagittal plane obtained from pointers’ data and with Whites’, Kepples’ and Pierrynowskis’data (Fig. 3). Indeed, at the end of the stance phase the White’s and Kepple’s moment arms are negative while the pointer and Pierrynowski’s moment arms are positive.
4. Discussion The computation of muscular actions requires the evaluation, with a good accuracy, of muscle moment arms with respect to each joint rotation axis at any given time during the stance phase of gait. Indeed, a reasonable
Table 3 Comparison of the muscle moment arms distance obtained with pointer used by two different investigators on the same subject Muscles
Difference of the distance between two different investigator (cm)
Tibialis anterior Triceps surae Peroneus Tibialis posterior (TP) Extensor digitorum Flexor hallucis longus Quadriceps femoris Biceps femoris Semitendinosus–Semimembranosus Sartorius Tensor fasciae latae Gracilis ¼ DI
0.470.0 0.370.1 0.470.1 0.0 0.770.0 0.370.0 0.170.0 0.470.1 0.170.0 0.0 0.0 0.970.0
The subject is in a relaxed static standing position during the record of the data.
estimate of muscle locations relative to joints is critical to mathematically calculate muscle force. Thus, this study presents a non-invasive protocol to model the local portion of the lines of action of the lower limb muscles crossing ankle and knee joints, measured directly by directing the end of a pointer on each specific points on the surface on the skin of the subject in standing position. One limitation of this technique arises from the use of a pointer to access to some muscles. Indeed, deep and large muscles crossing the hip are difficult to locate by the pointer and thus the moment arm variations are not representative (Delp, 1990). A second limitation is that the validity of the results depends on the accuracy of the data recorded during the motion analysis experiment. The errors introduced by the techniques based on movement analysis data collect must to be taken into account. In the Gorton’s study (Gorton et al., 2001); it appears that the main source of variation in the kinematic results of a gait analysis of a same subject in
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Table 4 Mean components, standard deviations (in cm) of the muscle moment arms during the stance phase obtained with the pointer, White’s data, Kepple’s data and Pierrynowski’s data Muscles’ moment arms
Mean (7SD) component X
Tibialis Anterior Pointer White Kepple Pierrynowski Triceps surae Pointer White Kepple Pierrynowski Peroneus Pointer White Kepple Pierrynowski Tibialis posterior (TP) Pointer White Kepple Pierrynowski Extensor digitorum Pointer White Kepple Pierrynowski Flexor hallucis longus Pointer White Kepple Pierrynowski Quadriceps femoris Pointer White Kepple Pierrynowski Biceps Femoris Pointer White Kepple Pierrynowski Semitendinosus–Semimembranosus Pointer White Kepple Pierrynowski Sartorius Pointer White Kepple Pierrynowski Tensor fasciae latae Pointer White Kepple Pierrynowski
Y 0.470.3
Joints and action of the muscle
Distance
Z
0.0
3.070.3
Ankle
2.770.2
0.970.7 1.970.3 2.370.1
0.0 0.0 0.870.0
7.070.6 3.570.6 0.870.5
Dorsal flexor (+Z)
7.070.7 3.970.3 2.470.1
0.870.3
0.0
5.070.6
Ankle
5.070.6
0.770.3 1.170.3 4.470.3
0.0 0.870.1 0.570.1
5.570.6 5.870.6 4.970.4
Extensor (Z)
5.570.6 5.970.6 6.770.4
0.970.5
2.070.2
2.070.2
Ankle
2.970.1
3.070.7 3.070.2 0.270.3
0.870.1 0.670.1 1.670.1
5.870.1 2.070.4 0.870.1
Pronator (X)
6.570.8 3.670.4 1.870.1
0.870.2
2.070.2
1.070.1
Ankle inversion
2.470.1
0.670.5 1.170.3 1.770.0
0.0 0.0 0.470.3
3.670.6 1.670.6 0.670.6
Supinator (+X)
3.670.7 1.970.2 1.870.1
0.570.3
0.570.0
3.070.3
Ankle
3.070.3
4.070.7 0.570.3 0.170.1
0.870.1 0.470.1 0.370.1
5.270.1 2.870.3 4.270.3
Dorsal flexor (+Z)
6.670.8 2.870.3 4.270.3
1.370.2
2.070.2
1.070.1
Ankle
2.570.1
3.070.7 1.070.2 3.170.3
0.270.1 0.770.1 1.670.1
4.870.8 3.370.3 1.570.9
Plantar flexor (+Z)
5.770.9 3.570.3 3.970.0
0.570.1
0.570.1
4.070.3
Knee
4.070.3
2.070.0 2.270.2 1.270.1
0.170.2 0.370.3 0.670.4
1.470.8 1.671.3 4.570.3
Extensor (+Z)
2.470.3 3.170.3 4.770.4
4.670.3
0.970.1
4.470.7
Knee
6.470.7
2.370.3 3.370.3 5.670.3
0.570.1 0.770.1 0.370.7
1.970.8 2.970.6 3.170.9
Flexor (Z)
2.870.7 4.270.7 6.670.5
4.070.2
0.470.2
5.070.5
Knee
6.470.2
2.070.3 2.370.3 2.170.4
0.170.2 0.270.3 1.570.7
3.270.2 2.371.0 3.571.1
Flexor (Z)
3.771.5 4.071.3 4.471.1
3.070.3
0.570.0
570.7
Knee
5.870.5
7.570.3 4.570.3 2.070.3
0.870.2 1.070.1 1.370.7
6.071.0 9.071.0 2.871.4
Flexor (Z)
6.070.1
0.970.1
3.071.0
Knee lateral rotator
10.970.2 10.670.2 2.470.2
1.070.1 0.870.2 0.0
6.670.9 5.771.0 2.672.7
Flexor (Z)
9.670.8 10.271.0 3.771.3 6.770.7 12.870.4 12.070.4 4.570.8
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1782 Table 4 (continued ) Muscles’ moment arms
Mean (7SD) component X
Gracilis Pointer White Kepple Pierrynowski
Joints and action of the muscle
Distance
Y
Z
4.070.3
1.070.2
5.070.5
Knee
5.970.3
2.070.3 3.070.8 2.170.2
0.0 0.670.4 0.570.6
0.571.3 0.671.7 1.671.8
Flexor (Z)
2.770.3 3.670.8 3.071.5
These components are computed in the segment reference frame, with X roughly in antero-posterior direction, Y in vertical direction and Z in lateral direction. The distance (and standard deviation) of moment arms are calculated for each method (cm). The subject is in a relaxed static standing position during the record of the data.
Table 5 Comparison of the muscle moment arms distance obtained with each method: pointer (dPT), White (dW), Kepple (dK) and Pierrynowski (dP) Muscles
Difference of the moment arm distances between each method
Tibialis anterior Triceps surae Peroneus Tibialis posterior (TP) Extensor digitorum Flexor hallucis longus Quadriceps femoris Biceps femoris Semitendinosus–Semimembranosus Sartorius Tensor fasciae latae Gracilis
dPT-dW
dPT-dK
dPT-dP
4.170.6 0.270.0 3.270.8 1.470.5 3.970.6 3.170.9 1.270.4 3.370.1 2.770.7 4.170.7 6.470.7 3.370.3
1.370.2 0.770.1 0.570.2 0.270.1 0.370.1 1.070.4 0.770.3 1.970.1 3.070.9 4.570.9 5.670.8 2.470.6
1.170.1 1.470.3 1.470.3 0.470.2 1.670.0 1.470.1 170.1 0.270.1 2.070.6 2.070.6 2.170.3 3.170.8
The subject is in a relaxed static standing position during the record of the data.
Evolution of the Quadriceps moment arms (cm)
6 5 4 3 2 1 0
1
11
21
31
41
51
61
71
81
91
-1 -2 -3 -4 Stance phase (Time 10-2s)
Fig. 3. Evolution of Quadriceps moment arm during the stance phase. The black bold line represents the mean evolution of the Quadriceps moment arm obtained from five records of the pointer data. The black solid line represents the moment arm obtained with the Pierrynowski data. The black dotted line represents the moment arm obtained from the White data. The dashed dotted black line represents the moment arm obtained with the Kepple data.
12 labs equipped with a movement analysis system is due to the localization of markers representing body segments by different clinicians. Therefore, in order to limit the main source of variation, the placement of the passive reflective markers on the subject and the use of the pointers have been carried out by the same clinician and the trials were always recorded during the same day in the same environment. Despite these limitations, the non-invasive protocol presents an original and different approach over previous works. In most reported investigations of muscle forces during gait, the anatomical insertion and origin points of the muscles were based on textbook drawing and/or markings on dry bone specimens (Crowninshield and Brand, 1981; Hardt and Mann, 1979; Seireg and Arvikar, 1989; White et al., 1989) and also measured directly on cadavers (Kepple et al., 1994). Usually, the researchers are then forced to extrapolate and to map such measurements from a statistically small sample in order to adapt to the geometry of the subject (Sommer et al., 1982). The direct measurements on the subject avoid the mapping from the different database published. Besides, via points belonging to the action lines of muscles are collected instead of origin and insertion points, to better define the moment arms of the muscles with respect to each joint. In order to establish the location of the via points a mechanical point of view has to be introduced in the anatomical description of the muscle action. Contrary to many studies reported in the literature which assume that the muscle tendons insert at single points of the bones (Crowninshield and Brand, 1981; Davy and Audu, 1987; Hoy et al., 1990), the musculoskeletal model established here aims to define the moment arm and direction of traction of each muscle with respect to each crossed joint by direct measurements on the tested subject. So, though the muscle origin and insertion coordinates are available in the literature (Brand et al., 1982; White et al., 1989; Yamaguchi et al., 1990; Pierrynowski, 1995, Kepple et al., 1998), we preferred to measure
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via points concentring on mechanical action of the muscles. Concerning the repeatability, as a ‘‘gold standard’’ is not available to compare with our results. Thus, a test has been chosen in order to test if our protocol is reliable or not. There are several methods to assess reliability. It appears that the Intraclass Correlation Coefficient: ICC (Bennell et al., 1998; Larsson et al., 2003; Hager, 2003; Henriksen et al., 2004) is more appropriate to the consistency in the repetition of a measurement process (Table 2). However, it seems that ICC take into account the between subject variance and has been criticized for the fact that great variance between subjects gives high repeatability. On the other hand, it is obviously more difficult to detect small difference between subjects. Thus, researchers suggest that ICC and SEM be reported together (Larsson et al., 2003; Hager, 2003). This seems logical, since ICC is a ‘‘relative’’ repeatability index, while SEM is an ‘‘absolute’’ repeatability index. The results presented in the Table 2 are generally reliable. Indeed, if we compare to the following general guidelines: the ICC values obtained were excellent (higher than 0.91 for 10 among 12 muscles). The low values of the SEM index confirm this interpretation. We can remark that for only two muscles the results on the repeatability are not so good: the Sartorius and the Gracilis. The ICC of the Sartorius moment arm distance is 0.75 thus the repeatability is qualified as good. Besides the SEM of the Sartorius is 0.03 thus the Sartorius moment arm distance is reliable. In the case of the Gracilis moment arm distance, the ICC is 0.25, the repeatability is poor and the SEM is 0.1. This can be explained by the fact that the origin point (Table 1) of the Gracilis muscle (i.e. the pubis) is difficult to assess using the pointer. The conclusion of this statistical study is that the moment arms obtained with our non-invasive protocol are consistent in the repetition of a measurement process. Moreover, in order to test this influence of the investigator in the moment arm estimation, two investigators (specialists of the lower limb anatomy) have pointed all the necessary points on the same subject. The differences between the moment arm norms (Table 3) showed that the influence of the results is negligible. Thus, the inter and intra influence of the operator has been tested during this study and allow to prove that the protocol is repeatable. Concerning the comparison of our non-invasive protocol with the literature data (Table 4), in the case of the quadriceps muscle, the definition of the insertion and origin points has a major influence on the moment arms of the muscle. The quadriceps is an extensor of the knee all along the stance phase thus, the line of action in the sagittal plane should always be positive, like it does for the pointer and Pierrynowski’s line of action. This difference of sign observed on the Fig. 3 could be stem from the position of the lines of action in regard to the crossing joints. It is interesting to note that in the case of Pierrynowski’s data,
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via points are used to define the line of action of the quadriceps, like for the pointer contrary to the anatomical insertion and origin points used for White’s and Kepple’s. This points out the importance of the definition of the lines of action of muscles in accordance to the action of the muscle on the joint during the movement. Moreover, a recent study from Carman and Milburn (e.g. Carman, 2005) proposed a new mathematical approach to determinate the dynamic coordinate data for describing muscle-tendon paths. This study is the only one to present the evolution of the Rectus Femoris moment arm, in the sagittal plane, for various angles of the knee. In comparison with our results, between 101 and 701 (knee angle variation during the stance phase), the moment arm ranged between in 6 and 4 cm. The shape of the curve is similar to that we obtain (Fig. 3). Thus, methods based on the use of the local muscle-tendon path, offer a significant improvement on previous studies based on the fixed deflection points (Carman and Milburn, 2005). Concerning the distance, the estimations obtained using this non-invasive protocol are always coherent with the role of the muscles described in anatomical books, and for some muscles more realistic that those calculated using bibliographic data. The significant difference observed can be explained by: methods taking into account only insertion and origin points (White and Kepple) and methods using via points (Pierrynowski and the pointer). These differences in term of sign and distance can deal with significant changes in the muscular forces further calculated. Thus, the non-invasive protocol that we propose allows to record, using a pointer, the local portion of the lines of action of some muscles in accordance with the movement and the joint studied. This method is designed for superficial muscles only. So it can be used for example for the elbow and wrist joints. For the other joints crossed by deep and large muscles, a ‘‘mixed’’ method (using both manually pointed and bibliographic data) could be considered. The experimental data used in our model is simple and allows specific to each subject’s morphology. This non-invasive protocol is not more relevant than the work previously published, but it allows a better control of the experimental errors introduced in the model. Acknowledgement The authors would like to thank Dr. Raphael Dumas for insightful, rigorous critiques and helpful comments on the manuscript. Appendix A1 Table A1
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Table A1 Anatomic names of the insertion-origin points (measured with the pointer) defining the local portion of the line of action of the different muscles closed to the joint on the standing subject’s lower limb Muscles
Origins (O)
Insertions (I)
Joints
Tibialis anterior Extensor digitorum Peroneus longus Triceps surae: Gastrocnemius Tibialis posterior Flexor hallucis longus Quadriceps femoris: Rectus femoris Sartorius Gracilis Tensor fasciae latae Biceps femoris Semitendinosus
Tuberosity Tibiae Head of Fibula Behind lateral malleolus Hollow the knee Behind medial malleolus Behind medial malleolus Patellar Ilium–Iliac Spine (anterior superior) Pubis–inferior ramus Greater Trochanter Ishium–ishial Tuberosity Ishium–ishial Tuberosity
Tarsal–medial cuneiform Tarsal–lateral cuneiform Lateral projection of the first cuneiform Calcaneous–achilles tendon Medial projection of the tubercle of navicular Distal projection of the third cuneiform Tuberosity Tibiae Tibia–Medial condyle (anterior) Tibia–mediale condyle Head of Fibula Tibia–lateral condyle Tibia–medial condyle
Ankle Ankle Ankle Ankle and knee Ankle Ankle Knee Knee Knee Knee Knee Knee
References An, et al., 1979. Normative model of human hand for biomechanical analysis. Journal of Biomechanics 12, 775–788. Bennell, K., et al., 1998. Intra-rater inter-rater reliability of weight bearing lunge measure of ankle dorsiflexion. Australian Journal of Physiotherapy 44, 175–180. Bouisset, S., Maton, B. (Eds.), 1995. Muscles, posture et mouvement. Hermann. Brand, R.A., Crowninshield, R.D., Wittstock, C.E., Pedersen, D.R., Clark, C.R., 1982. A model of lower extremity. Muscular anatomy. Journal of Biomechanics 104, 304–310. Brand, R.A., Pedersen, D.R., Friederich, J.A., 1986. The sensitivity of muscle prediction to charges in physiologic cross-sectional area. Journal of Biomechanics 19, 589–596. Calais-Germain B. (Ed.), 1989. Anatomie pour le mouvement. Des Iris. Carman, A.B., Milburn, P.D., 2005. Dynamic coordinate data for describing muscle-tendon paths: a mathematical approach. Journal of Biomechanics 38, 943–951. Che`ze, L., Fregly, B.J., Dimnet, J., 1995. A solidification procedure to facilitate kinematic analysis based on video system data. Journal of Biomechanics 28, 879–884. Crowninshield, R.D., Brand, R.A., 1981. A physiologically based criterion of muscle force prediction in locomotion. Journal of Biomechanics 14, 793–801. Davy, D.T., Audu, M.L., 1987. A dynamic optimisation technique for predicting muscle forces in the swing phase of gait. Journal of Biomechanics 20, 187–201. Delp, S.L., 1990. Surgery simulation: a computer graphics system to analyze and design musculoskeletal reconstructions of the lower limb. Ph.D. Thesis, Standford University Press, Standford. Delp, S.L., Loan, J.P., Hoy, M., Zajac, F., Topp, E., Rosen, J., 1990. An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures. IEEE, Transaction on Biomedical Engineering 37, 757–765. Denegar, C., Ball, D., 1993. Assessing reliability and precision of measurement: an introduction to intraclass correlation and standard error of measurement. Journal of Sport and Rehabilitation 2, 35–42. Doriot, N., 2001. Mode´lisation dynamique du membre infe´rieur pour l’estimation des forces articulaires et musculaires mises en jeu pendant la phase d’appui de la marche. The`se de Doctorat/Universite´ Lyon1. Frigo, C., Pedotti, A., 1978. Determination of muscle length during locomotion. In: Asmussen, E., Jorgensen, K. (Eds.), Proceeding of the Sixth international Congress of Biomechanics, Copenhagen, Denmark–Biomechanics VI , vol. VI-A, University Park Press, Baltimore, MD, pp. 355–360.
Gfo¨hler, M., Pandy, M.G, Granfinger M., Kronnerwetter C., 2006. MRBased lower-limb musculoskeletal model of a child. In: Proceedings of the Seventh International Symposium on Computer in Biomechanics and Biomedical Engineering. Antibes, France. Gorton, G., Herbert, D., Goode, B., 2001. Assessment of the kinematic variability between twelve shiners motion analysis laboratories. In: VIth Annual Gait and Clinical Movement Analysis Meeting, Sacramento, California. Gutierrez, C., 1996. Etude des fonctionnalite´s du membre supe´rieur en mouvement par l’exploitation de trajectoires de marqueurs externes. Ph.D. Thesis, Lyon 1 University. Hager, K.M.R., 2003. Reliability of fatigue measures in an overhead work task: a study of shoulder muscle electromyography and perceived discomfort. Master Thesis. Faculty of the Virginia polytechnic institute. Hansen, J.T. (Ed.), 2004. Me´mofiches Anatomie, Membres, Masson, p. 135. Hardt, D.E., Mann, R.W., 1979. A five-body three-dimensional dynamic analysis of walking. Journal of Biomechanics 13, 455–457. Henriksen, M., et al., 2004. Test-retest reliability of trunk accelerometric gait analysis. Gait and Posture 19, 288–297. Hoy, M.G., Zajac, F.E., Gordon, M.E., 1990. A musculoskeletal model of the human lower extremity: the effect of muscle, tendon, and moment arm on the moment-angle relationship of musculo-tendon actuators at the hip, knee, and ankle. Journal of Biomechanics 23, 157–169. Kapandji, A. (Ed.), 1980. Physiologie articulaire—Membre infe´rieur. Tome III. Maloine. Kepple, T.M., Arnold, A.S., Stanhope, S.J., Lohmann Siegel, K., 1994. Assessment of a method to estimate muscle attachments from surface landmarks: a 3D computer graphics approach. Journal of Biomechanics 27, 365–371. Kepple, T.M., Sommer III, H.J., Lohmann Siegel, K., Stanhope, S.J., 1998. A three-dimensional musculoskeletal database for the lower extremities. Journal of Biomechanics 31, 77–80 http://pdb.cc.nih.gov/ resources/files/terry/terry.htm. Larsson, B., Karlsson, S., Eriksson, M., Gerdle, B., 2003. Test-retest reliability of EMG and peak torque during repetitive maximum concentric knee extensions. Journal of Electromyography and Kinesiology 13, 281–287. Legnani, G., Casolo, F., Righettini, P., Zappa, B., 1996. A homogeneous matrix approach to 3D kinematics and dynamics. Mechanisms and Machine Theory (IFToMM) 31, 573–587, 589–605. Pandy, M.G., 2001. Computer modelling and simulation of human movement. Annual Review of Biomedical Engineering 3, 245–273.
ARTICLE IN PRESS A. Bonnefoy et al. / Journal of Biomechanics 40 (2007) 1776–1785 Pedersen, D.R., Brand, R.A., Davy, D.T., 1997. Pelvic muscle and acetabular contact forces during gait. Journal of Biomechanics 30, 959–965. Pierrynowski, M.R., Morrison, J.B., 1985a. Estimating the muscle forces generated in human lower extremity when walking, a physiological solution. Mathematical Bioscience 75, 43–68. Pierrynowski, M.R., Morrison, J.B., 1985b. A physiological model for the evaluation of muscular forces in human locomotion. Theoretical aspects. Mathematical Bioscience 75, 69–101. Pierrynowski, M.R., 1995. Analytic representation of muscle line of action and geometry. In: Allard, P., Stokes, I.A.F., Blanchi, J.P. (Eds.), Human Kinetics. Champaign, IL, pp. 214–256. Ro¨hrle, H., Sholten, R., Sigolotto, C., Sollbach, W., Kellner, H., 1984. Joint forces in the human pelvis-leg skeleton during the walking. Journal of Biomechanics 17, 409–424. Seireg, A., Arvikar, R., 1973. A mathematical model for evaluation of forces in lower extremeties of the musculoskeletal system. Journal of Biomechanics 6, 313–322. Seireg, A., Arvikar, R., 1989. Biomechanical Analysis of the Musculoskeletal Structure for Medicine and Sports. Hemisphere Publishing Corporation, New York.
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Sommer, H.J., Miller, N.R., Pijanowski, G.J., 1982. Three dimensional osteometric scaling and normative modelling of skeletal segments. Journal of Biomechanics 15, 171–180. Viel, E. (Ed.), 2000. La marche humaine, la course et le saut. Biome´canique, exploration, normes et dysfonctionnements. Masson, Paris. White, S.C., Yack, H.J., Winter, D.A., 1989. A three dimensional musculoskeletal model for gait analysis. Anatomical variability estimates. Journal of Biomechanics 22, 885–893. Winters, J., Stark, L., 1987. Muscle models: what is gained and what is lost by varying modem complexity. Biological Cybernetics 55, 403–420. Winter, J.M., Woo, S.L.-Y. (Eds.), 1990. Multiple muscle systems: Biomechanics and movement organization. Springer, New York, pp. 717–773. Wu, G., et al., 2002. ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human motion—part I: ankle, hip, and spine. Journal of Biomechanics 35, 543–548. Yamaguchi, G.T., et al., 1990. A survey of human musculotendon actuator parameters. In: Winters, J.M., Woo, S.L-Y. (Eds.), Multiple Muscle System: Biomechanics and Movement Organisation. Springer, Berlin Appendix.
Journal of Biomechanics 40 (2007) 1776–1785 www.elsevier.com/locate/jbiomech www.JBiomech.com
A non-invasive protocol to determine the personalized moment arms of knee and ankle muscles A. Bonnefoya,b,, N. Doriota, M. Senka, B. Dohina,c, D. Pradond, L. Che`zea a
Laboratoire de Biome´canique et Mode´lisation Humaine, LRE_T32, Universite´ Lyon 1 (Claude Bernard), Baˆt. Ome´ga, Bd du 11 Novembre 1918, 69622 Villeurbanne, France b Me´dimex, 56 avenue du 11 novembre 1918, 69160 Tassin la demi lune, France c Service de chirurgie orthope´dique pe´diatrique, Pavillon Tbis, Hoˆpital Edouard Herriot, Place d’Arsonval 69437 Lyon, France d Laboratoire d’Analyse du Mouvement, Pavillon : Netter1, Hoˆpital Raymond POINCARE, 104, boulevard Raymond Poincare´ 92380 Garches, France Accepted 29 July 2006
Abstract One difficulty that comes with predicting muscular forces is the accuracy of experimental data, particularly the assessment of muscle moment arms with respect to each joint rotation axis. This paper presents a non-invasive experimental protocol to obtain the personalized muscle moment arms with respect to the ankle and knee joints. A specific pointer is used by a specialist of lower limb anatomy in order to define the local portion of the line of action of the different muscles closed to the joint on the standing subject’s lower limb. With this pointer, the three-dimensional coordinates of several points representing the line of action of 12 ankle and knee muscles are collected by a Motion Analysis system. The collection is done five times by the same operator and one time by two different operators. From this data, the intra and inter operator repeatabilities are tested. Relative (ICC) and absolute (SEM) reliabilities are determined in order to evaluate the intra operator repeatability of this non-invasive protocol. The ICC values obtained are higher than 0.91 for 10 among 12 muscles. The intra operator repeatability is thus confirmed. From the records realized by the two operators, the differences are negligible. Thus, the inter operator repeatability is also confirmed. The moments arms obtained using this non-invasive experimental protocol are compared with those calculated from origin and insertion points reported in the literature, according to the work of Whites, Pierrynowskis and Kepples, respectively. The estimations obtained using the non-invasive experimental protocol are found, for some muscles, more realistic than those calculated using the literature data and are always coherent with the role of the muscles described in anatomical books. r 2006 Published by Elsevier Ltd. Keywords: Gait analysis; Muscle moment arm; Muscle path
1. Introduction An accurate representation of the lower limb musculoskeletal system is required for the prediction of the locomotor muscle-tendon forces during gait. The prediction of the muscle tendon forces is currently an important research axis in the field of biomechanics (Pandy, 2001). A large number of the lower limb muscles involved in locomotion are biarticular. This is why models defining the Corresponding author. Tel.: +33 04 78 34 32 48; fax: +33 04 78 34 69 25. E-mail address: [email protected] (A. Bonnefoy).
0021-9290/$ - see front matter r 2006 Published by Elsevier Ltd. doi:10.1016/j.jbiomech.2006.07.028
line of action of muscles crossing the three lower limb joints, are necessary. Seireg and Arvikar (1973), and Ro¨hrle et al. (1984) have published schematic representations of the line of action of the whole lower limb muscles. At the same time, Frigo and Pedotti (1978) presented a two-dimensional (2D) model of 11 locomotor muscles, which includes five biarticular muscles. Pierrynowski and Morrison (1985a, b) estimated the origin and insertion points of the 47 muscles of the lower limb. However, in these publications, the 3D coordinates were not extensively presented. In 1990, Yamaguchi et al. synthesized, in the Appendix A1 of the Winter and Woos’ book (Winter and Woo,
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1990), all the 3D upper and lower limb muscle origin and insertion coordinates available in the literature. Nowadays, the four models extensively used in the musculoskeletal models are: Brand et al. (1982), White et al. (1989), Pierrynowski, 1995 and Kepple et al. (1998). In the study of Brand et al., all the muscles were dissected on three fresh cadaver specimens of varying heights and sexes (1.63 m female, 1.72 m male, and 1.83 m male). In the study of White et al., the insertion and origin points of all muscles crossing the hip, knee and ankle joints were located on six disarticulated dry bone pelvis, nine dry bone femurs, tibia and fibula, one reconstructed skeletal foot and one dissected cadaver foot. In the Kepple’s study, all the muscles were collected on 52 dry human skeletal specimens chosen from the Terry Collection (Smithsonian Institution, Washington, DC). In the Pierrynowski’s study, the insertion and the origin points of all muscles crossing the hip, knee and ankle joints came from different articles. The most recent musculoskeletal models take into account muscle deviation by bone pieces (An et al., 1979; Pedersen et al., 1997; Delp et al., 1990; Pierrynowski, 1995; Kepple et al., 1998) and these authors suggest the use of a subject fitted model. Indeed, these models are still sensitive to changes in musculoskeletal geometry (Brand et al., 1986; Hoy et al., 1990; Winters and Stark, 1987; Kepple et al., 1998). Moreover, differences between the above mentioned models are not negligible. For that, the determination of the line of action of the muscles personalized to subject morphology is one of the major steps in the development of reliable musculoskeletal models. A recent study from Bonajic and Pandy (Gfo¨hler et al., 2006), presents a method in order to define the lower limb musculoskeletal model of a child based on MRI. This technique could be applied to adult subject. By this method, we can obtain the ‘‘real’’ volume, PCSA, length, and insertion—origin points of the lower limb muscles and will be the more realistic definition of the musculoskeletal model. However, MRI yield time and cost considerations. Besides, two different methods are commonly used to model the paths of the muscle in the body: the straight line and the centroı¨ d line methods. In the straight line method, the path of a muscle is represented by a straight line joining only the two the centroı¨ ds of the muscles attachment sites (Seireg and Arvikar, 1989; Pierrynowski, 1995). This method is easy to implement but when a muscle wraps around a bone or another muscle, the results would be meaningless. In the second method, centroı¨ d line, the muscle path is represented as a line passing through the locus of all the cross sectional centroı¨ ds of the muscle. This method is more accurate in the representation of the muscle line of action but can be difficult to apply. Indeed, even if a muscle’s centroı¨ d path is known for one position of the body, it is practically impossible to determine how the muscle paths change as body position changes. To overcome the problem, the introduction of effective attachment sites or via points at
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specific location along the line of action could be a good solution. However, the determination of these via points, personalized to subject morphology has not been previously studied. The goal of this paper is to present a non-invasive experimental protocol established to collect the coordinate of relevant points that define the local portion of the line of action of each muscle. The local portions of the line of action have been directly measured by means of manual pointing. In this study, the main muscle moment arms calculated are those of the knee and ankle joint. Five records with a pointer have been done with the same operators and two records have been done by two different operators. The hip muscles are not evaluated during this work because they are deep and large so manual pointing does not allow a reliable determination of the insertion and origin points. 2. Materials and methods 2.1. The musculoskeletal model The major muscles were selected from the literature (Doriot, 2001; Kapandji, 1980; Calais-Germain, 1989; Bouisset and Maton, 1995; Hansen, 2004) and the selection was completed following advices from specialists of lower limb anatomy (Table 1). To better define the insertions, origins and via points, a table is added in Appendix A1 that defines the anatomic names of the points presented in the Table 1.
2.2. Protocol In order to measure directly the via points of the muscles, a pointer has been designed. This pointer is a metal rod equipped with two markers (see Fig. 2). The two markers define the direction of the rod in 3D space, as well as the 3D coordinates of the end point, which distance is known with respect to both markers. For the quadriceps muscle, the deviating effect of the patella was introduced in order to calculate a more accurate moment arm (Brand et al., 1982; White et al., 1989; Delp, 1990, Pierrynowski, 1995). In this case, the local portion of the line of action of the muscle has been defined as the path between the head of the tibialis anterior and the kneecap as indicated on the Fig. 1. The musculoskeletal model was identified on one healthy subject (29-years old, 1.74 m and 76 kg). The first part of the protocol corresponds to the collection, by a unique operator, of the specific points of muscular portion line of action (Fig. 2) at five different instants in the day. The local portion of the action lines of muscles is determined in a static standing position. For this, an opto-electronic Motion Analysis system (Santa Rosa, CA) consisting of five digital cameras is used. The subject is equipped with passive reflective markers used to define segment reference frames (Wu et al., 2002). With the subject in static position, via points (I and O) were also collected using the pointer. Between each record, five stances phase of the gait have been recorded. No particular recommendation is given to the subject; it is a ‘‘free gait’’ according to Viel (2000). After the gait trials collection, the subject performs a circumduction movement of the leg. This will be used to determine the hip joint centre (Gutierrez, 1996). The 3D trajectories of the cutaneous markers are computed and then corrected by a low-pass filter (Butterworth, fourth-order, with a cut-off frequency of 5 Hz) followed by a solidification of each body segment (Che`ze et al., 1995). The via points coordinates were obtained in the laboratory reference frame and then computed, with the homogenous matrix
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Table 1 Specific points (O and I) chosen to define each muscle action line on the knee and the ankle Insertions (I) Origins (O)
Muscles
Joints
02
1 = Tibialis anterior (O1 and I1)
2 = Extensor Digitorum (O2 and
1
4
I2)
3 = Peroneus longus (O3 and I3)
Ankle Knee
3 2
4 =Triceps surae: Gas trocnemius (O4 and I4)
sup
sup
12
sup
ant
med
lat
13 sup sup
1
1 = Tibialis posterior (O1 and I1) post
ant
01
02
lot
Ankle
2 = Flexor hallucis longus (O2 and I2)
l1
02 2 1 = Quadriceps femoris : Rectus femoris (O1 and I1)
04 4
03
2 = Sartorius (O2 and I2)
3 6
3 = Gracilis (O3 and I3)
5
1
4 = Tensor fasciae latae (O4 and I4)
Knee
5 = Biceps Femoris (O5 and I5)
16 15 6 = Semitendinosus (O6 and I6)
14
12=13 sup
sup med
algebra (Doriot, 2001; Legnani et al., 1996), in the corresponding segment reference frames. From this, the trajectories of the via points could be derived during the stance phase of the gait.
lat
The second part of this protocol corresponds to the record of via points with the pointer on the subject, in static position, by two different operators. From this, the differences in the moment arm estimation between the operators have been evaluated.
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2.3. Statistical analysis
o o
In this study, a repeated measure ANOVA study was chosen in order to evaluate the repeatability of personalized moment arms. The norm of the moment arm vectors has been calculated from the pointer data recorded during the five repeated trials (at different instants in the same day). Data were examined for normality and homogeneity of variance to ensure they fulfilled the criteria for parametric tests. ICC is the ratio between-subjects variance divided by the total variance (Denegar and Ball, 1993). Using one-way analysis of variance (one-way ANOVA), ICC(1,1) was determined as estimator of reproducibility.
Sup Ant
o′
Ok
MA′
Ok
l
ICC ¼
MA′
o′
l′ l
(a)
l′
(b) >
>
(MA' u) = Ok I ′
I ′O ′ I ′O ′ u
Fig. 1. Picture representing, in the sagittal plane, the two specific points O0 and I0 measured to define the quadriceps muscle moment arm. Ok is the knee centre and MA0 represents the Moment Arm of the quadriceps muscle. MA0 is calculated with the formula indicated, in the reference frame segment. The case a, corresponding at the beginning of the stance phase. The case b, corresponding at the end of the stance phase. O and I are the points available in the literature in order to define the line of action of the quadriceps muscle.
BMS WMS , BMS þ ððk=k0 Þ 1ÞWMS
where BMS is between-subjects mean square representing true variance, WMS is within-subject mean square representing the error variance, k is the number of measurements administered and k0 is the number of repeated measures which reliability is estimated. The ICC algorithm generally returns a value between 0 and 1, where 0 stands for no reproducibility and 1 for the perfect reproducibility. There is no really universal method for categorizing ICC levels, given that errors in determining reliability may occur even with high ICC levels. The following general guidelines (Hager, 2003) were used: 0–0.39 poor, .40–0.59 fair, 0.60–0.79 good, 0.8–1.0 excellent. Another commonly used reliability index is the standard error of measurement (SEM), which is an absolute measurement of repeatability. SEM is defined as pffiffiffiffiffiffiffiffiffiffiffi SEM ¼ s 1 r, where s is the standard deviation of the measurements and r is the ICC.
2.4. Comparison with the literature’s data After the records of the via points on subject, we compared the moment arms calculated from the pointer data to those obtained from mapping White’s, Kepple’s and Pierrynowski’s data with the morphology of our subject. For each literature data, the skeletal segment frames have been defined from the anatomic points available in the literature tables (Wu et al., 2002). Then, the transformation matrices have been calculated in order to map the literature data in the local reference frame of the subject. Thus, the literature data have been derived during the stance phase of the gait.
3. Results The mean and the standard deviation of Euclidian norm ! of the moment arm vectors, generally noted:MA0 (see Fig. 1 for the definition of this vector) obtained from five trials with the pointer are presented in Table 2. The ICC and the SEM are also presented in the Table 2. The differences between operators in the moment arm estimation are directly displayed in Table 3. Table 4 presents, for our protocol and for the Whites’, Kepples’ and Pierrynowskis’ mapped data, the mean coordinates X, Y, Z of the moment arm vectors MA0 in the segment frame and their standard deviations, the mean ! norm (distance) and standard deviation of MA0 . Fig. 2. Picture from motion analysis recording for the semitendinosus muscle. It represents the biceps thigh points collected for the origin using the pointer equipped with passive reflective markers.
In Table 4, we can observe that the sign of the main component of the moment arm vector is systematically in agreement with the known role of each muscle (described
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Table 2 Measures of the average and the standard deviation (in cm) of muscle moment arm norms from five trial pointer. Measures of absolute and relative repeatability Muscles
Mean distance
STD
ICC
SEM
Tibialis anterior Triceps surae Peroneus Tibialis posterior (TP) Extensor digitorum Flexor hallucis longus Quadriceps femoris Biceps femoris Semitendinosus–Semimembranosus Sartorius Tensor fasciae latae Gracilis
2.8 4.6 3.4 2.4 2.9 2.6 3.8 6.0 6.4 5.7 6.0 5.8
0.0 0.1 0.0 0.0 0.1 0.0 0.0 0.1 0.1 0.1 0.1 0.1
0.99 0.94 0.99 0.99 0.99 0.99 0.99 0.95 0.91 0.75 0.91 0.25
0.003 0.013 0.000 0.001 0.001 0.000 0.001 0.022 0.021 0.030 0.040 0.100
The subject is in a relaxed static standing position during the record of the data.
in anatomical books). We note that the signs of the components are not always the same. In term of distance, in the case of the Tensor fascia latae, the mean distance obtained with White’s and Kepple’s data are, respectively, 12 and 12.8 cm as for the pointer and Pierrynowski’s data the distance are, respectively, 6.4 and 4.5 cm. Table 5 presents the differences between mean moment arm distances obtained with our method and the others. In order to verify the influence of the four configurations on the quadriceps moment arms, the average evolution during the stance phase is presented with the different sets of literature and via point data. The results presented in the Table 5 allow to have an idea on the numerical difference in term of distance between the pointer and the three others bibliographic data. We can note that the numerical differences between the pointer and White’s method are more important than with the two others bibliographic data. Compared with the Kepple and Pierrynowski data, the moment arm distances obtained with the pointer are, generally, of the same order. Fig. 3 presents, in the sagittal plane, the comparison between quadriceps moment arms calculated using the pointer and the three other bibliographic data on the same subject. We can observe this on the comparison between the quadriceps moment arms in the sagittal plane obtained from pointers’ data and with Whites’, Kepples’ and Pierrynowskis’data (Fig. 3). Indeed, at the end of the stance phase the White’s and Kepple’s moment arms are negative while the pointer and Pierrynowski’s moment arms are positive.
4. Discussion The computation of muscular actions requires the evaluation, with a good accuracy, of muscle moment arms with respect to each joint rotation axis at any given time during the stance phase of gait. Indeed, a reasonable
Table 3 Comparison of the muscle moment arms distance obtained with pointer used by two different investigators on the same subject Muscles
Difference of the distance between two different investigator (cm)
Tibialis anterior Triceps surae Peroneus Tibialis posterior (TP) Extensor digitorum Flexor hallucis longus Quadriceps femoris Biceps femoris Semitendinosus–Semimembranosus Sartorius Tensor fasciae latae Gracilis ¼ DI
0.470.0 0.370.1 0.470.1 0.0 0.770.0 0.370.0 0.170.0 0.470.1 0.170.0 0.0 0.0 0.970.0
The subject is in a relaxed static standing position during the record of the data.
estimate of muscle locations relative to joints is critical to mathematically calculate muscle force. Thus, this study presents a non-invasive protocol to model the local portion of the lines of action of the lower limb muscles crossing ankle and knee joints, measured directly by directing the end of a pointer on each specific points on the surface on the skin of the subject in standing position. One limitation of this technique arises from the use of a pointer to access to some muscles. Indeed, deep and large muscles crossing the hip are difficult to locate by the pointer and thus the moment arm variations are not representative (Delp, 1990). A second limitation is that the validity of the results depends on the accuracy of the data recorded during the motion analysis experiment. The errors introduced by the techniques based on movement analysis data collect must to be taken into account. In the Gorton’s study (Gorton et al., 2001); it appears that the main source of variation in the kinematic results of a gait analysis of a same subject in
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Table 4 Mean components, standard deviations (in cm) of the muscle moment arms during the stance phase obtained with the pointer, White’s data, Kepple’s data and Pierrynowski’s data Muscles’ moment arms
Mean (7SD) component X
Tibialis Anterior Pointer White Kepple Pierrynowski Triceps surae Pointer White Kepple Pierrynowski Peroneus Pointer White Kepple Pierrynowski Tibialis posterior (TP) Pointer White Kepple Pierrynowski Extensor digitorum Pointer White Kepple Pierrynowski Flexor hallucis longus Pointer White Kepple Pierrynowski Quadriceps femoris Pointer White Kepple Pierrynowski Biceps Femoris Pointer White Kepple Pierrynowski Semitendinosus–Semimembranosus Pointer White Kepple Pierrynowski Sartorius Pointer White Kepple Pierrynowski Tensor fasciae latae Pointer White Kepple Pierrynowski
Y 0.470.3
Joints and action of the muscle
Distance
Z
0.0
3.070.3
Ankle
2.770.2
0.970.7 1.970.3 2.370.1
0.0 0.0 0.870.0
7.070.6 3.570.6 0.870.5
Dorsal flexor (+Z)
7.070.7 3.970.3 2.470.1
0.870.3
0.0
5.070.6
Ankle
5.070.6
0.770.3 1.170.3 4.470.3
0.0 0.870.1 0.570.1
5.570.6 5.870.6 4.970.4
Extensor (Z)
5.570.6 5.970.6 6.770.4
0.970.5
2.070.2
2.070.2
Ankle
2.970.1
3.070.7 3.070.2 0.270.3
0.870.1 0.670.1 1.670.1
5.870.1 2.070.4 0.870.1
Pronator (X)
6.570.8 3.670.4 1.870.1
0.870.2
2.070.2
1.070.1
Ankle inversion
2.470.1
0.670.5 1.170.3 1.770.0
0.0 0.0 0.470.3
3.670.6 1.670.6 0.670.6
Supinator (+X)
3.670.7 1.970.2 1.870.1
0.570.3
0.570.0
3.070.3
Ankle
3.070.3
4.070.7 0.570.3 0.170.1
0.870.1 0.470.1 0.370.1
5.270.1 2.870.3 4.270.3
Dorsal flexor (+Z)
6.670.8 2.870.3 4.270.3
1.370.2
2.070.2
1.070.1
Ankle
2.570.1
3.070.7 1.070.2 3.170.3
0.270.1 0.770.1 1.670.1
4.870.8 3.370.3 1.570.9
Plantar flexor (+Z)
5.770.9 3.570.3 3.970.0
0.570.1
0.570.1
4.070.3
Knee
4.070.3
2.070.0 2.270.2 1.270.1
0.170.2 0.370.3 0.670.4
1.470.8 1.671.3 4.570.3
Extensor (+Z)
2.470.3 3.170.3 4.770.4
4.670.3
0.970.1
4.470.7
Knee
6.470.7
2.370.3 3.370.3 5.670.3
0.570.1 0.770.1 0.370.7
1.970.8 2.970.6 3.170.9
Flexor (Z)
2.870.7 4.270.7 6.670.5
4.070.2
0.470.2
5.070.5
Knee
6.470.2
2.070.3 2.370.3 2.170.4
0.170.2 0.270.3 1.570.7
3.270.2 2.371.0 3.571.1
Flexor (Z)
3.771.5 4.071.3 4.471.1
3.070.3
0.570.0
570.7
Knee
5.870.5
7.570.3 4.570.3 2.070.3
0.870.2 1.070.1 1.370.7
6.071.0 9.071.0 2.871.4
Flexor (Z)
6.070.1
0.970.1
3.071.0
Knee lateral rotator
10.970.2 10.670.2 2.470.2
1.070.1 0.870.2 0.0
6.670.9 5.771.0 2.672.7
Flexor (Z)
9.670.8 10.271.0 3.771.3 6.770.7 12.870.4 12.070.4 4.570.8
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1782 Table 4 (continued ) Muscles’ moment arms
Mean (7SD) component X
Gracilis Pointer White Kepple Pierrynowski
Joints and action of the muscle
Distance
Y
Z
4.070.3
1.070.2
5.070.5
Knee
5.970.3
2.070.3 3.070.8 2.170.2
0.0 0.670.4 0.570.6
0.571.3 0.671.7 1.671.8
Flexor (Z)
2.770.3 3.670.8 3.071.5
These components are computed in the segment reference frame, with X roughly in antero-posterior direction, Y in vertical direction and Z in lateral direction. The distance (and standard deviation) of moment arms are calculated for each method (cm). The subject is in a relaxed static standing position during the record of the data.
Table 5 Comparison of the muscle moment arms distance obtained with each method: pointer (dPT), White (dW), Kepple (dK) and Pierrynowski (dP) Muscles
Difference of the moment arm distances between each method
Tibialis anterior Triceps surae Peroneus Tibialis posterior (TP) Extensor digitorum Flexor hallucis longus Quadriceps femoris Biceps femoris Semitendinosus–Semimembranosus Sartorius Tensor fasciae latae Gracilis
dPT-dW
dPT-dK
dPT-dP
4.170.6 0.270.0 3.270.8 1.470.5 3.970.6 3.170.9 1.270.4 3.370.1 2.770.7 4.170.7 6.470.7 3.370.3
1.370.2 0.770.1 0.570.2 0.270.1 0.370.1 1.070.4 0.770.3 1.970.1 3.070.9 4.570.9 5.670.8 2.470.6
1.170.1 1.470.3 1.470.3 0.470.2 1.670.0 1.470.1 170.1 0.270.1 2.070.6 2.070.6 2.170.3 3.170.8
The subject is in a relaxed static standing position during the record of the data.
Evolution of the Quadriceps moment arms (cm)
6 5 4 3 2 1 0
1
11
21
31
41
51
61
71
81
91
-1 -2 -3 -4 Stance phase (Time 10-2s)
Fig. 3. Evolution of Quadriceps moment arm during the stance phase. The black bold line represents the mean evolution of the Quadriceps moment arm obtained from five records of the pointer data. The black solid line represents the moment arm obtained with the Pierrynowski data. The black dotted line represents the moment arm obtained from the White data. The dashed dotted black line represents the moment arm obtained with the Kepple data.
12 labs equipped with a movement analysis system is due to the localization of markers representing body segments by different clinicians. Therefore, in order to limit the main source of variation, the placement of the passive reflective markers on the subject and the use of the pointers have been carried out by the same clinician and the trials were always recorded during the same day in the same environment. Despite these limitations, the non-invasive protocol presents an original and different approach over previous works. In most reported investigations of muscle forces during gait, the anatomical insertion and origin points of the muscles were based on textbook drawing and/or markings on dry bone specimens (Crowninshield and Brand, 1981; Hardt and Mann, 1979; Seireg and Arvikar, 1989; White et al., 1989) and also measured directly on cadavers (Kepple et al., 1994). Usually, the researchers are then forced to extrapolate and to map such measurements from a statistically small sample in order to adapt to the geometry of the subject (Sommer et al., 1982). The direct measurements on the subject avoid the mapping from the different database published. Besides, via points belonging to the action lines of muscles are collected instead of origin and insertion points, to better define the moment arms of the muscles with respect to each joint. In order to establish the location of the via points a mechanical point of view has to be introduced in the anatomical description of the muscle action. Contrary to many studies reported in the literature which assume that the muscle tendons insert at single points of the bones (Crowninshield and Brand, 1981; Davy and Audu, 1987; Hoy et al., 1990), the musculoskeletal model established here aims to define the moment arm and direction of traction of each muscle with respect to each crossed joint by direct measurements on the tested subject. So, though the muscle origin and insertion coordinates are available in the literature (Brand et al., 1982; White et al., 1989; Yamaguchi et al., 1990; Pierrynowski, 1995, Kepple et al., 1998), we preferred to measure
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via points concentring on mechanical action of the muscles. Concerning the repeatability, as a ‘‘gold standard’’ is not available to compare with our results. Thus, a test has been chosen in order to test if our protocol is reliable or not. There are several methods to assess reliability. It appears that the Intraclass Correlation Coefficient: ICC (Bennell et al., 1998; Larsson et al., 2003; Hager, 2003; Henriksen et al., 2004) is more appropriate to the consistency in the repetition of a measurement process (Table 2). However, it seems that ICC take into account the between subject variance and has been criticized for the fact that great variance between subjects gives high repeatability. On the other hand, it is obviously more difficult to detect small difference between subjects. Thus, researchers suggest that ICC and SEM be reported together (Larsson et al., 2003; Hager, 2003). This seems logical, since ICC is a ‘‘relative’’ repeatability index, while SEM is an ‘‘absolute’’ repeatability index. The results presented in the Table 2 are generally reliable. Indeed, if we compare to the following general guidelines: the ICC values obtained were excellent (higher than 0.91 for 10 among 12 muscles). The low values of the SEM index confirm this interpretation. We can remark that for only two muscles the results on the repeatability are not so good: the Sartorius and the Gracilis. The ICC of the Sartorius moment arm distance is 0.75 thus the repeatability is qualified as good. Besides the SEM of the Sartorius is 0.03 thus the Sartorius moment arm distance is reliable. In the case of the Gracilis moment arm distance, the ICC is 0.25, the repeatability is poor and the SEM is 0.1. This can be explained by the fact that the origin point (Table 1) of the Gracilis muscle (i.e. the pubis) is difficult to assess using the pointer. The conclusion of this statistical study is that the moment arms obtained with our non-invasive protocol are consistent in the repetition of a measurement process. Moreover, in order to test this influence of the investigator in the moment arm estimation, two investigators (specialists of the lower limb anatomy) have pointed all the necessary points on the same subject. The differences between the moment arm norms (Table 3) showed that the influence of the results is negligible. Thus, the inter and intra influence of the operator has been tested during this study and allow to prove that the protocol is repeatable. Concerning the comparison of our non-invasive protocol with the literature data (Table 4), in the case of the quadriceps muscle, the definition of the insertion and origin points has a major influence on the moment arms of the muscle. The quadriceps is an extensor of the knee all along the stance phase thus, the line of action in the sagittal plane should always be positive, like it does for the pointer and Pierrynowski’s line of action. This difference of sign observed on the Fig. 3 could be stem from the position of the lines of action in regard to the crossing joints. It is interesting to note that in the case of Pierrynowski’s data,
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via points are used to define the line of action of the quadriceps, like for the pointer contrary to the anatomical insertion and origin points used for White’s and Kepple’s. This points out the importance of the definition of the lines of action of muscles in accordance to the action of the muscle on the joint during the movement. Moreover, a recent study from Carman and Milburn (e.g. Carman, 2005) proposed a new mathematical approach to determinate the dynamic coordinate data for describing muscle-tendon paths. This study is the only one to present the evolution of the Rectus Femoris moment arm, in the sagittal plane, for various angles of the knee. In comparison with our results, between 101 and 701 (knee angle variation during the stance phase), the moment arm ranged between in 6 and 4 cm. The shape of the curve is similar to that we obtain (Fig. 3). Thus, methods based on the use of the local muscle-tendon path, offer a significant improvement on previous studies based on the fixed deflection points (Carman and Milburn, 2005). Concerning the distance, the estimations obtained using this non-invasive protocol are always coherent with the role of the muscles described in anatomical books, and for some muscles more realistic that those calculated using bibliographic data. The significant difference observed can be explained by: methods taking into account only insertion and origin points (White and Kepple) and methods using via points (Pierrynowski and the pointer). These differences in term of sign and distance can deal with significant changes in the muscular forces further calculated. Thus, the non-invasive protocol that we propose allows to record, using a pointer, the local portion of the lines of action of some muscles in accordance with the movement and the joint studied. This method is designed for superficial muscles only. So it can be used for example for the elbow and wrist joints. For the other joints crossed by deep and large muscles, a ‘‘mixed’’ method (using both manually pointed and bibliographic data) could be considered. The experimental data used in our model is simple and allows specific to each subject’s morphology. This non-invasive protocol is not more relevant than the work previously published, but it allows a better control of the experimental errors introduced in the model. Acknowledgement The authors would like to thank Dr. Raphael Dumas for insightful, rigorous critiques and helpful comments on the manuscript. Appendix A1 Table A1
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Table A1 Anatomic names of the insertion-origin points (measured with the pointer) defining the local portion of the line of action of the different muscles closed to the joint on the standing subject’s lower limb Muscles
Origins (O)
Insertions (I)
Joints
Tibialis anterior Extensor digitorum Peroneus longus Triceps surae: Gastrocnemius Tibialis posterior Flexor hallucis longus Quadriceps femoris: Rectus femoris Sartorius Gracilis Tensor fasciae latae Biceps femoris Semitendinosus
Tuberosity Tibiae Head of Fibula Behind lateral malleolus Hollow the knee Behind medial malleolus Behind medial malleolus Patellar Ilium–Iliac Spine (anterior superior) Pubis–inferior ramus Greater Trochanter Ishium–ishial Tuberosity Ishium–ishial Tuberosity
Tarsal–medial cuneiform Tarsal–lateral cuneiform Lateral projection of the first cuneiform Calcaneous–achilles tendon Medial projection of the tubercle of navicular Distal projection of the third cuneiform Tuberosity Tibiae Tibia–Medial condyle (anterior) Tibia–mediale condyle Head of Fibula Tibia–lateral condyle Tibia–medial condyle
Ankle Ankle Ankle Ankle and knee Ankle Ankle Knee Knee Knee Knee Knee Knee
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