- Email: [email protected]
Estimation of hamstring length at initial contact based on kinematic gait data
Gait and Posture 20 (2004) 61–66
Estimation of hamstring length at initial contact based on kinematic gait data Caroline Stewart a,∗ , Ilse Jonkers b , Andrew Roberts a a
ORLAU, Robert Jones and Agnes Hunt Orthopaedic and District Hospital, Oswestry, Shropshire SY10 7AG, UK b Laboratory of Ergonomics, Kinesiology Department, Faculteit Lichamelijke Opvoeding en Kinesitherapie, Katholieke Universiteit Leuven, Tervuursevest 101, 3001 Leuven, Belgium Received 13 April 2003; received in revised form 26 June 2003; accepted 11 July 2003
Abstract This study proposes a simple estimate of hamstring length at initial contact (LEST ) for use when musculoskeletal modelling is not available. The estimate is calculated by using the kinematic curves to measure the excessive flexion (above normal) at the hip and knee at initial contact. The excessive hip flexion is then multiplied by a scaling factor (k) and the excessive knee flexion subtracted from the result. Validation of this estimate was carried out using kinematic gait data from 25 children with cerebral palsy (50 limbs) by comparing the results of the estimate with an equivalent measure derived from musculoskeletal modelling (LTRUE ). Very high agreement was found when LTRUE and LEST were compared for the three biarticular hamstring muscles, demonstrated by correlation coefficients of over 0.9. Different k values were tested with a value of 3 giving the best results overall. The estimate is acceptable as a simple ‘rule of thumb’ for use in clinical practice. It can provide useful additional information to complement the clinical examination and gait assessment results. © 2003 Elsevier B.V. All rights reserved. Keywords: Musculoskeletal modelling; Hamstrings; Cerebral palsy; Gait analysis
1. Introduction Gait analysis is frequently used to screen children with cerebral palsy before multilevel surgery. A three-dimensional (3D) assessment produces a range of data, generally presented in graphical form. This includes 3D joint angles and moments, and the mechanical power generated or absorbed at the joint. This information is then combined with the results of clinical examination to assist in deciding an appropriate treatment plan for an individual patient. The plan might include a lengthening of one or more of the hamstring muscles. The justification for hamstring lengthening is based on the assumption that the musculotendinous unit is dynamically too short and the muscle is unable to lengthen adequately to allow normal gait. A review of hamstring lengthening was given by Bleck [1]. Indications for lengthening are generally perceived to be a high popliteal angle measurement on clinical examination in combination with excessive knee flexion ∗ Corresponding author. Tel.: +44-1691-404236; fax: +44-1691-404058. E-mail address: [email protected] (C. Stewart).
0966-6362/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0966-6362(03)00096-1
and prolonged activity during gait. Traditionally, the role of the hamstring muscles in determining hip posture has been underestimated. Unfortunately, it can be difficult to estimate the lengths of the muscles from inspection of the kinematic graphs alone. The level of difficulty varies between muscles according to the number of joints crossed and the ranges of motion possible at each joint. The length changes in the short head of biceps femoris, for example, are highly predictable as they mirror the flexion and extension of the knee. The situation for the long head is much more complex as it crosses both hip and knee joints, as do the remaining hamstrings. Recent developments in musculoskeletal modelling have made it possible to calculate muscle lengths on a more routine basis [2]. Detailed information is needed concerning the morphology of the bones, the path of the muscles and tendons and the kinematics of the joints to construct a model. Once these have been defined the model can be animated using joint kinematic data and a range of new parameters measured. These include the dynamic length changes of the muscles during gait. It is important to define what is meant by ‘muscle length’ in this context and it is the total distance along the muscle path from origin to insertion, including
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C. Stewart et al. / Gait and Posture 20 (2004) 61–66
both muscle and tendon. No attempt is made to describe the morphology of the muscle, for example the tendon length, muscle fibre length or pennation angle. The dynamic lengths of the hamstring muscles have been calculated using musculoskeletal modelling techniques. Results reported in the literature have changed common assumptions concerning the role of the muscles in the development of crouch gait. Delp et al. [3] reported that ‘most (80%) of the subjects with crouch gait had hamstrings of normal length or longer, despite persistent knee flexion during stance’. In this, they were able to confirm the earlier findings of Hoffinger et al. [4] and also highlighted the weaknesses of the popliteal angle test and dynamic knee flexion as indicators of abnormally short hamstring muscles during gait. The findings of Hoffinger et al. [4] and Delp et al. [3] can be explained by considering the hip and knee joints together. Crouch gait is characterised by excessive flexion at both joints. Flexion at the knee is associated with a shortening of the hamstring muscles. Flexion at the hip, however, has the opposite effect. The overall length of the muscle during gait depends on which effect dominates, allowing for the additional effects of hip adduction and rotation. As a joint rotates, the magnitude of the muscle length change depends on two factors, the size of the rotation and the instantaneous moment arm of the muscle. A variety of different methods has been used to measure the moment arms of the hamstring muscles. Some studies used cadaveric material [5], others imaging techniques [6,7]) and some computer models [8]. The results reported vary considerably between studies. This is not surprising given the different sample populations, measurement techniques and conventions represented. These factors make it difficult to make direct comparisons between studies. Overall, however, it is clear that the hamstring muscle extension moment arms at the hip are greater than the flexion moment arms at the knee. Dynamic muscle length information is available when motion analysis data (joint angles) are combined with musculoskeletal modelling (moment arms). Many centres performing gait analysis do not, however, have ready access to modelling software and validated models. This paper presents a potential estimate for the length of the hamstring muscles at initial contact based on kinematic gait analysis data alone.
2. Method 2.1. The definition of the estimate LEST = kΘh − Θk where Θh is the excessive hip flexion at initial contact (above normal), Θk the excessive knee flexion at initial contact (above normal), k the ratio of the extension moment arm at the hip to the flexion moment arm at the knee, and LEST is the estimated difference in length (in units of degrees).
For the estimate to be a valid measure of muscle length LEST must be strongly related to the true length difference with respect to normal for each muscle. The true length difference (LTRUE ) was calculated using a musculoskeletal model. 2.2. Definition of the model The musculoskeletal model was constructed using the SIMM software package, MusculoGraphics Inc. [2]. Physical bones were scanned to produce surface meshes. Joints were defined between the bones such that the axis systems and joint kinematics matched those used in the gait analysis software (VCM, Vicon Motion Systems), allowing flexion, abduction and rotation at the hip, flexion at the knee and plantarflexion at the ankle. The model could then be animated using kinematic data obtained from the gait analysis laboratory. An additional joint was incorporated into the intertrochanteric region of the femur that allowed the femoral anteversion of the model to be matched to that of the child. The semimembranosus, semitendinosus and both heads of biceps femoris were attached to this bony framework. An initial estimate of the muscle path was obtained by allowing the muscles to run in a straight line from origin to insertion. The path was then optimised by comparing muscle moment arm data with that from published studies [5–12]. The optimisation made use of wrapping points to contour the path of the muscles around the hip and knee joints. At the hip this prevented the muscle paths cutting through the ischial tuberosities at higher values of hip flexion. Wrapping at the knee was used to control the moment arms throughout the joint range. 2.3. Validation of the estimate Gait data from 25 children were selected to validate the estimate. All children had a diagnosis of spastic cerebral palsy, with both lower limbs affected. They had an average age of 11 years (7–17) and a mean popliteal angle measurement of 55◦ (40–80◦ ). Validation included a sample of children from across the range of gait patterns seen in the population. No attempt was made to select children with a particular walking pattern, for example crouch gait. None of the children had had previous surgery affecting the hamstring muscles. All had had full three-dimensional (3D) gait assessments and had given consent for resulting data to be used. The gait analysis was performed using a Vicon 370 motion analysis system in combination with a Kistler force platform. A standard lower limb marker set was used (VCM, Vicon Motion Systems). Each set of gait data was used to animate the musculoskeletal model. The length of each of the biarticular hamstring muscles was then calculated at initial contact for each of the 50 limbs. The lengths were normalised by expressing them as a percentage of the resting muscle length. This made the length measurement independent of the size of
C. Stewart et al. / Gait and Posture 20 (2004) 61–66
63
Moment Arm Ratio 4
Ratio
3 Biceps Femoris Semitendinosus Semimembranosus Average
2
1
0 0
20
40 60 % Gait Cycle
80
100
Fig. 1. The ratio of the moment arms at the hip and knee across the gait cycle.
the subject. In each case the normal length at initial contact was then subtracted to give the true length difference (LTRUE ). The value of the estimate (LEST ) was then calculated for each limb. To do this, a value was required for the constant k, the ratio of the moment arms at the hip and knee. The musculoskeletal model was used to calculate the value of k through the normal gait cycle. The results are shown in Fig. 1. Three different values of the constant k were tested in the validation, the true muscle specific ratio at initial contact in normal gait (3.01 for biceps femoris, 2.12 for semitendinosus and 2.71 for semimembranosus), the most representative integer value across the normal gait cycle (2) and the integer value above (3). LEST and LTRUE were then compared to assess agreement in sign and magnitude. The latter was examined using correlation coefficients.
3. Results Fig. 2 shows the LTRUE value calculated from the musculoskeletal model plotted against estimate LEST for all the biarticular hamstring muscles. The three individual plots show the three different values of k tested. A summary of the results for all three hamstring muscles is given in Table 1. Standard deviation values are quoted to give an impression of the magnitude of LEST in each case. As anticipated from the scatter plots in Fig. 2, the correlation coefficients are very high (0.935–0.959). Most of the false positives and false negatives occurred at very small values of LEST and LTRUE , with no extreme outliers. The different values for the constant k have a negligible effect on the correlation coefficients but do show differences in the numbers and distribution of false positives and negatives.
4. Discussion Surgical lengthening of the hamstring muscles was developed to treat dynamic muscle shortness. Musculoskeletal modelling techniques have been used to demonstrate that the muscles are very often of normal length or longer during crouch gait. This is because flexion at the hip, where the moment arm is greater, causes more than enough muscle lengthening to compensate for the shortening at the flexed knee. Lengthening muscles, which are already of normal length or longer, is likely to lead to a deterioration in the hip posture, with increased hip flexion and anterior pelvic tilt. Muscle length information is potentially very important in clinical decision-making but, unfortunately, it is not easily appreciated from an inspection of gait kinematics alone. This paper has presented a potential estimate for hamstring length at initial contact, for use when musculoskeletal modelling techniques are not available. Overall, the estimate has a very strong relationship with the results from musculoskeletal modelling. With a k value of 3 an average of 91% of the estimates (LEST ) agree with the model (LTRUE ). The agreement simply means the results are in the same quadrant, i.e. the same classification of ‘long’ or ‘short’. The very high correlation coefficients show that the estimate is not just predicting the sign correctly, but also the magnitude. False positives and negatives occur, as would be expected, close to the origin. To use the estimate it is necessary to select an appropriate value for k. The results (Table 1) show that all values of k give very high correlation coefficients. The choice of a value therefore depends on two other factors. The first is simplicity. The estimate has been designed as a ‘rule of thumb’, so there is a strong argument for using an integer value for k. The variability of moment arm values quoted in the literature also does not support the use of a very precise figure. Secondly, false positives and negatives must
C. Stewart et al. / Gait and Posture 20 (2004) 61–66 (a) Biceps Femoris
10.00
LTRUE
64
LEST -80
80
k = 2.00 k = 3.00 k = 3.01
-10.00
10.00 LTRUE
(b) Semitendinosus
LEST -80
80
k = 2.00 k = 3.00 k = 2.12
(c) Semimembranosus
10.00
LTRUE
-10.00
LEST -80
80
k = 2.00 k = 3.00 k = 2.71
-10.00
Fig. 2. Scatter plots of LTRUE (%) against LEST (◦ ) for all three biarticular hamstring muscles. Table 1 Comparison of LTRUE and LEST for different values of k
Biceps femoris Semitendinosus Semimembranosus Biceps femoris Semitendinosus Semimembranosus Biceps femoris Semitendinosus Semimembranosus
Value of constant, k
Correlation coefficients (Pearson)
False positive (%)
False negative (%)
Standard deviation of LEST (◦ ) (N = 50)
2 2 2 3 3 3 3.01 2.12 2.71
0.935 0.954 0.952 0.948 0.958 0.932 0.948 0.953 0.959
36 18 36 4 2 4 4 16 10
0 2 0 0 18 0 0 4 0
18.05 18.05 18.05 26.51 26.51 26.51 26.60 19.03 24.00
A false positive value is defined as one where the true length is longer than normal but the estimate predicts it to be short. A false negative value is defined as one where the true length is shorter than normal but the estimate predicts it to be long.
C. Stewart et al. / Gait and Posture 20 (2004) 61–66
also be considered. These cannot be eliminated completely but there will be increasing numbers if the trend line of the scatter plot does not pass through the origin (see biceps femoris with a k value of 2). Under some circumstances false positives may be preferred over false negatives or vice versa as a way of introducing a safety factor. In surgical screening it may be more important to avoid lengthening a muscle inappropriately than to miss the occasional muscle that is slightly short. For a physiotherapy stretching programme the reverse may be true. It is probably better to ensure all children with dynamic shortness are selected, even if that means some who do not also receive therapy. A k value of 3 gives the best overall results in this study. There is room for future refinement of the k value as more muscle moment arm data become available. The quality of estimate used in this study depends upon its underlying assumptions. The very good comparison with the results of musculoskeletal modelling gives considerable reassurance that the assumptions are appropriate. Further consideration, however, may help in indicating when the estimate’s results should be treated with caution. The estimate assumes that internal/external rotation and abduction/adduction movements at the hip and knee can be ignored. The magnitude of the error introduced here depends on two factors, the range of joint movement and the magnitude of the moment arm. At the knee these movements are very small for normal and most pathological gait patterns. The same is not true at the hip, but even so they are usually considerably smaller than the flexion/extension excursion. Data for internal/external rotation and abduction/adduction moment arms are limited. Dostal et al. [9] found average moment arm magnitudes for internal/external rotation of approximately 10% of those for flexion/extension. Abduction/adduction moment arm magnitudes were larger, at approximately 20%. The relative magnitudes for the model used in this study were closer to 5% (internal/external rotation) and 45% (abduction/adduction). From the moment arm data, it can be deduced that the greatest potential source of error in LEST would arise from large abduction/adduction movements at the hip. Caution should therefore be exercised when applying the estimate to gait patterns with significant scissoring or hip abduction. A survey of children assessed in the gait laboratory revealed that most children’s hip adduction at initial contact was within about 10◦ of normal. This is unlikely to compromise the estimate. Deviations in the region of 15–20◦ or above should be treated with more caution. In an adducted position at initial contact the hamstrings may be shorter than is suggested by LEST . In an abducted position they will tend to be longer. The estimate also assumes that the moment arm at the hip is a constant fixed ratio of that at the knee. In reality the ratio changes as the hip and knee joints flex and extend. This can be seen in Fig. 1 across the normal gait cycle. There is still considerable uncertainty concerning the actual moment arms at the hip and knee, with no strong consensus
65
in the literature. This is increasingly true as the limb posture moves away from the anatomical position. Published studies consider movements in isolation rather than in the combinations seen in cerebral palsy. It also becomes more difficult for the musculoskeletal model to control the muscle path using wrapping points. For this reason using the estimate for extreme joint ranges should be done with caution, for example in cases of severe crouch gait (knee flexion at initial contact greater than 60◦ ). Likewise, using the same estimation technique in swing phase would give less reliable results than for stance. In this study, the estimate only has been validated for initial contact. Basing the estimate on a single point in the gait cycle makes it much easier to apply as a ‘rule of thumb’ in clinical practice. In theory the same approach could be applied to any point in the gait cycle. Initial contact was chosen for two reasons. Firstly, making contact with a flexed knee is often thought to be associated with hamstring tightness. Secondly, at initial contact the muscle is at, or very close to, its maximum length in both normal and diplegic gait. Any restrictive shortening in muscle length is most likely to be observed when the muscle is at maximum stretch. Some diplegic children do, however, display their maximum muscle length in swing phase and the muscles are already shortening by initial contact. The estimate has been validated by comparison with musculoskeletal modelling. There are significant assumptions related to the modelling process that mean that the length described as LTRUE is not entirely accurate. The musculoskeletal model is based on adult non-pathological morphology. The only adaptation made is the introduction of femoral anteversion. There are also considerable uncertainties concerning the true paths of the muscles. Validation will be strongly influenced by the how the modelling technique deals with this and, in particular how wrapping points are used. Errors will also be carried through from the joint kinematic data collected during gait analysis. At present, however, musculoskeletal modelling provides the most practical method for assessing dynamic muscle length. The estimate described here provides a simpler method for obtaining that information. Throughout the design of the estimate, there has been an attempt to keep it as simple as possible. When reviewing clinicial data it should be possible to read off the two angles and multiply and combine them without the need for additional computation. An illustration of this is given in Fig. 3. The estimate is an indirect measurement of muscle length in degrees, rather than millimetres. This has the advantage of being more readily appreciated but the value should be placed in context. In normal gait the hamstring muscles change length, going through a range from approximately 96–109% of resting length. For an average adult male this would correspond to an excursion in length of about 57 mm. In theory, Fig. 2 could be used to translate between LEST in degrees and LTRUE in percent, and by deduction millimetres. The approximate nature of the
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muscle length information can be integrated into the development of an overall therapeutic plan. The hamstring muscles cannot be considered in isolation. If the hip flexors are to be lengthened, for example, the threshold for addressing the hamstring muscles would be reduced. Overall the calculation of the muscle length can provide useful information to assist in both clinical decision-making and the assessment of the eventual outcome.
Hip Flexion 70 60
Difference in Hip Flexion
50
Θh = 55.6 - 34.7 Θh = 20.9
40 30 20 10 0 -10 0
20
40
60
80
-20
100 Normal Patient
% Gait Cycle
Knee Flexion 80 70 60 50 40 30 20 10 0
Difference in Knee Flexion Θk = 44.0 - 7.4 Θk = 36.6
5. Conclusion Length information can give new insights into the behaviour of muscles, as demonstrated by previous work on the hamstring muscles. The estimate developed in this study (LEST ) has been successfully validated against musculoskeletal modelling and can therefore be used to assess hamstring muscle length at initial contact. It is important to use the data in conjunction with clinical examination and gait analysis results and to bear in mind the assumptions and uncertainties which underlie the calculations.
References 0
20
40
60
% Gait Cycle
80
100 Normal Patient
LEST = k Θh – Θk For k = 3 LEST = k Θh – Θk = 3 × 20.9 – 36.6 = 26.1º Fig. 3. An illustration of the calculation of LEST .
estimate, however, makes it more appropriate for use as an indication of length (in degrees) than as an absolute measure. The estimate should be used in addition to other information, including clinical examination data, gait analysis curves and electromyography (EMG). This other information may assist in deciding why a muscle is long or short. EMG, for example, can help to differentiate between a muscle that is abnormally short because it is unable to stretch any further and one that is actively contracting. Additional data on the muscle’s morphology will also aid understanding, allowing the individual contributions of the contractile tissue and tendon to be assessed. Many therapies, including surgery, aim to lengthen the musculotendinous unit. It is important to understand what a potential therapy is likely to achieve by knowing as much as possible about the pre-treatment status of a muscle. Dynamic
[1] Bleck EE. Orthopaedic management in cerebral palsy. Oxford: MacKeith Press; 1987. [2] Delp SL, Loan JP, Hoy MG, Zajac FE, Topp EL, Rosen JM. An interactive, graphics-based model of the lower extremity to study orthopaedic surgical procedures. IEEE Trans Biomed Eng 1990;37:757–67. [3] Delp SL, Arnold AS, Speers RA, Moore CA. Hamstrings and psoas lengths during normal and crouch gait: Implications for muscle-tendon surgery. J Orthop Res 1996;14:144–51. [4] Hoffinger SA, Rab GT, Abou-Ghaida H. Hamstrings in cerebral palsy crouch gait. J Pediatr Orthop 1993;13:722–6. [5] Herzog W, Read LJ. Lines of action and moment arms of the major force-carrying structures crossing the human knee joint. J Anat 1993;182:213–30. [6] Nemeth G, Ohlsen H. In vivo moment arm lengths for hip extensor muscles at different angles of hip flexion. J Biomech 1985;18:129– 40. [7] Wretenberg P, Nemeth G, Lamontagne M, Lundin B. Passive knee muscle moment arms measured in vivo with MRI. Clin Biomech 1996;11:439–46. [8] Lengsfeld M, Pressel T, Stammberger U. Lengths and lever arms of hip joint muscles: geometrical analyses using a human multibody model. Gait Posture 1997;6:18–26. [9] Dostal WF, Soderberg GL, Andrews JG. Actions of hip muscles. Phys Ther 1986;66:351–61. [10] Duda GN, Brand D, Freitag S, Lierse W, Schneider E. Variability of femoral muscle attachments (Technical Note). J Biomech 1996;29:1185–90. [11] Smidt GL. Biomechanical analysis of knee flexion and extension. J Biomech 1973;6:79–92. [12] Visser JJ, Hoogkamer JE, Bobbert MF, Huijing PA. Length and moment arm of human leg muscles as a function of knee and hip-joint angles. Eur J Appl Physiol 1990;61:453–60.
Estimation of hamstring length at initial contact based on kinematic gait data Caroline Stewart a,∗ , Ilse Jonkers b , Andrew Roberts a a
ORLAU, Robert Jones and Agnes Hunt Orthopaedic and District Hospital, Oswestry, Shropshire SY10 7AG, UK b Laboratory of Ergonomics, Kinesiology Department, Faculteit Lichamelijke Opvoeding en Kinesitherapie, Katholieke Universiteit Leuven, Tervuursevest 101, 3001 Leuven, Belgium Received 13 April 2003; received in revised form 26 June 2003; accepted 11 July 2003
Abstract This study proposes a simple estimate of hamstring length at initial contact (LEST ) for use when musculoskeletal modelling is not available. The estimate is calculated by using the kinematic curves to measure the excessive flexion (above normal) at the hip and knee at initial contact. The excessive hip flexion is then multiplied by a scaling factor (k) and the excessive knee flexion subtracted from the result. Validation of this estimate was carried out using kinematic gait data from 25 children with cerebral palsy (50 limbs) by comparing the results of the estimate with an equivalent measure derived from musculoskeletal modelling (LTRUE ). Very high agreement was found when LTRUE and LEST were compared for the three biarticular hamstring muscles, demonstrated by correlation coefficients of over 0.9. Different k values were tested with a value of 3 giving the best results overall. The estimate is acceptable as a simple ‘rule of thumb’ for use in clinical practice. It can provide useful additional information to complement the clinical examination and gait assessment results. © 2003 Elsevier B.V. All rights reserved. Keywords: Musculoskeletal modelling; Hamstrings; Cerebral palsy; Gait analysis
1. Introduction Gait analysis is frequently used to screen children with cerebral palsy before multilevel surgery. A three-dimensional (3D) assessment produces a range of data, generally presented in graphical form. This includes 3D joint angles and moments, and the mechanical power generated or absorbed at the joint. This information is then combined with the results of clinical examination to assist in deciding an appropriate treatment plan for an individual patient. The plan might include a lengthening of one or more of the hamstring muscles. The justification for hamstring lengthening is based on the assumption that the musculotendinous unit is dynamically too short and the muscle is unable to lengthen adequately to allow normal gait. A review of hamstring lengthening was given by Bleck [1]. Indications for lengthening are generally perceived to be a high popliteal angle measurement on clinical examination in combination with excessive knee flexion ∗ Corresponding author. Tel.: +44-1691-404236; fax: +44-1691-404058. E-mail address: [email protected] (C. Stewart).
0966-6362/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0966-6362(03)00096-1
and prolonged activity during gait. Traditionally, the role of the hamstring muscles in determining hip posture has been underestimated. Unfortunately, it can be difficult to estimate the lengths of the muscles from inspection of the kinematic graphs alone. The level of difficulty varies between muscles according to the number of joints crossed and the ranges of motion possible at each joint. The length changes in the short head of biceps femoris, for example, are highly predictable as they mirror the flexion and extension of the knee. The situation for the long head is much more complex as it crosses both hip and knee joints, as do the remaining hamstrings. Recent developments in musculoskeletal modelling have made it possible to calculate muscle lengths on a more routine basis [2]. Detailed information is needed concerning the morphology of the bones, the path of the muscles and tendons and the kinematics of the joints to construct a model. Once these have been defined the model can be animated using joint kinematic data and a range of new parameters measured. These include the dynamic length changes of the muscles during gait. It is important to define what is meant by ‘muscle length’ in this context and it is the total distance along the muscle path from origin to insertion, including
62
C. Stewart et al. / Gait and Posture 20 (2004) 61–66
both muscle and tendon. No attempt is made to describe the morphology of the muscle, for example the tendon length, muscle fibre length or pennation angle. The dynamic lengths of the hamstring muscles have been calculated using musculoskeletal modelling techniques. Results reported in the literature have changed common assumptions concerning the role of the muscles in the development of crouch gait. Delp et al. [3] reported that ‘most (80%) of the subjects with crouch gait had hamstrings of normal length or longer, despite persistent knee flexion during stance’. In this, they were able to confirm the earlier findings of Hoffinger et al. [4] and also highlighted the weaknesses of the popliteal angle test and dynamic knee flexion as indicators of abnormally short hamstring muscles during gait. The findings of Hoffinger et al. [4] and Delp et al. [3] can be explained by considering the hip and knee joints together. Crouch gait is characterised by excessive flexion at both joints. Flexion at the knee is associated with a shortening of the hamstring muscles. Flexion at the hip, however, has the opposite effect. The overall length of the muscle during gait depends on which effect dominates, allowing for the additional effects of hip adduction and rotation. As a joint rotates, the magnitude of the muscle length change depends on two factors, the size of the rotation and the instantaneous moment arm of the muscle. A variety of different methods has been used to measure the moment arms of the hamstring muscles. Some studies used cadaveric material [5], others imaging techniques [6,7]) and some computer models [8]. The results reported vary considerably between studies. This is not surprising given the different sample populations, measurement techniques and conventions represented. These factors make it difficult to make direct comparisons between studies. Overall, however, it is clear that the hamstring muscle extension moment arms at the hip are greater than the flexion moment arms at the knee. Dynamic muscle length information is available when motion analysis data (joint angles) are combined with musculoskeletal modelling (moment arms). Many centres performing gait analysis do not, however, have ready access to modelling software and validated models. This paper presents a potential estimate for the length of the hamstring muscles at initial contact based on kinematic gait analysis data alone.
2. Method 2.1. The definition of the estimate LEST = kΘh − Θk where Θh is the excessive hip flexion at initial contact (above normal), Θk the excessive knee flexion at initial contact (above normal), k the ratio of the extension moment arm at the hip to the flexion moment arm at the knee, and LEST is the estimated difference in length (in units of degrees).
For the estimate to be a valid measure of muscle length LEST must be strongly related to the true length difference with respect to normal for each muscle. The true length difference (LTRUE ) was calculated using a musculoskeletal model. 2.2. Definition of the model The musculoskeletal model was constructed using the SIMM software package, MusculoGraphics Inc. [2]. Physical bones were scanned to produce surface meshes. Joints were defined between the bones such that the axis systems and joint kinematics matched those used in the gait analysis software (VCM, Vicon Motion Systems), allowing flexion, abduction and rotation at the hip, flexion at the knee and plantarflexion at the ankle. The model could then be animated using kinematic data obtained from the gait analysis laboratory. An additional joint was incorporated into the intertrochanteric region of the femur that allowed the femoral anteversion of the model to be matched to that of the child. The semimembranosus, semitendinosus and both heads of biceps femoris were attached to this bony framework. An initial estimate of the muscle path was obtained by allowing the muscles to run in a straight line from origin to insertion. The path was then optimised by comparing muscle moment arm data with that from published studies [5–12]. The optimisation made use of wrapping points to contour the path of the muscles around the hip and knee joints. At the hip this prevented the muscle paths cutting through the ischial tuberosities at higher values of hip flexion. Wrapping at the knee was used to control the moment arms throughout the joint range. 2.3. Validation of the estimate Gait data from 25 children were selected to validate the estimate. All children had a diagnosis of spastic cerebral palsy, with both lower limbs affected. They had an average age of 11 years (7–17) and a mean popliteal angle measurement of 55◦ (40–80◦ ). Validation included a sample of children from across the range of gait patterns seen in the population. No attempt was made to select children with a particular walking pattern, for example crouch gait. None of the children had had previous surgery affecting the hamstring muscles. All had had full three-dimensional (3D) gait assessments and had given consent for resulting data to be used. The gait analysis was performed using a Vicon 370 motion analysis system in combination with a Kistler force platform. A standard lower limb marker set was used (VCM, Vicon Motion Systems). Each set of gait data was used to animate the musculoskeletal model. The length of each of the biarticular hamstring muscles was then calculated at initial contact for each of the 50 limbs. The lengths were normalised by expressing them as a percentage of the resting muscle length. This made the length measurement independent of the size of
C. Stewart et al. / Gait and Posture 20 (2004) 61–66
63
Moment Arm Ratio 4
Ratio
3 Biceps Femoris Semitendinosus Semimembranosus Average
2
1
0 0
20
40 60 % Gait Cycle
80
100
Fig. 1. The ratio of the moment arms at the hip and knee across the gait cycle.
the subject. In each case the normal length at initial contact was then subtracted to give the true length difference (LTRUE ). The value of the estimate (LEST ) was then calculated for each limb. To do this, a value was required for the constant k, the ratio of the moment arms at the hip and knee. The musculoskeletal model was used to calculate the value of k through the normal gait cycle. The results are shown in Fig. 1. Three different values of the constant k were tested in the validation, the true muscle specific ratio at initial contact in normal gait (3.01 for biceps femoris, 2.12 for semitendinosus and 2.71 for semimembranosus), the most representative integer value across the normal gait cycle (2) and the integer value above (3). LEST and LTRUE were then compared to assess agreement in sign and magnitude. The latter was examined using correlation coefficients.
3. Results Fig. 2 shows the LTRUE value calculated from the musculoskeletal model plotted against estimate LEST for all the biarticular hamstring muscles. The three individual plots show the three different values of k tested. A summary of the results for all three hamstring muscles is given in Table 1. Standard deviation values are quoted to give an impression of the magnitude of LEST in each case. As anticipated from the scatter plots in Fig. 2, the correlation coefficients are very high (0.935–0.959). Most of the false positives and false negatives occurred at very small values of LEST and LTRUE , with no extreme outliers. The different values for the constant k have a negligible effect on the correlation coefficients but do show differences in the numbers and distribution of false positives and negatives.
4. Discussion Surgical lengthening of the hamstring muscles was developed to treat dynamic muscle shortness. Musculoskeletal modelling techniques have been used to demonstrate that the muscles are very often of normal length or longer during crouch gait. This is because flexion at the hip, where the moment arm is greater, causes more than enough muscle lengthening to compensate for the shortening at the flexed knee. Lengthening muscles, which are already of normal length or longer, is likely to lead to a deterioration in the hip posture, with increased hip flexion and anterior pelvic tilt. Muscle length information is potentially very important in clinical decision-making but, unfortunately, it is not easily appreciated from an inspection of gait kinematics alone. This paper has presented a potential estimate for hamstring length at initial contact, for use when musculoskeletal modelling techniques are not available. Overall, the estimate has a very strong relationship with the results from musculoskeletal modelling. With a k value of 3 an average of 91% of the estimates (LEST ) agree with the model (LTRUE ). The agreement simply means the results are in the same quadrant, i.e. the same classification of ‘long’ or ‘short’. The very high correlation coefficients show that the estimate is not just predicting the sign correctly, but also the magnitude. False positives and negatives occur, as would be expected, close to the origin. To use the estimate it is necessary to select an appropriate value for k. The results (Table 1) show that all values of k give very high correlation coefficients. The choice of a value therefore depends on two other factors. The first is simplicity. The estimate has been designed as a ‘rule of thumb’, so there is a strong argument for using an integer value for k. The variability of moment arm values quoted in the literature also does not support the use of a very precise figure. Secondly, false positives and negatives must
C. Stewart et al. / Gait and Posture 20 (2004) 61–66 (a) Biceps Femoris
10.00
LTRUE
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LEST -80
80
k = 2.00 k = 3.00 k = 3.01
-10.00
10.00 LTRUE
(b) Semitendinosus
LEST -80
80
k = 2.00 k = 3.00 k = 2.12
(c) Semimembranosus
10.00
LTRUE
-10.00
LEST -80
80
k = 2.00 k = 3.00 k = 2.71
-10.00
Fig. 2. Scatter plots of LTRUE (%) against LEST (◦ ) for all three biarticular hamstring muscles. Table 1 Comparison of LTRUE and LEST for different values of k
Biceps femoris Semitendinosus Semimembranosus Biceps femoris Semitendinosus Semimembranosus Biceps femoris Semitendinosus Semimembranosus
Value of constant, k
Correlation coefficients (Pearson)
False positive (%)
False negative (%)
Standard deviation of LEST (◦ ) (N = 50)
2 2 2 3 3 3 3.01 2.12 2.71
0.935 0.954 0.952 0.948 0.958 0.932 0.948 0.953 0.959
36 18 36 4 2 4 4 16 10
0 2 0 0 18 0 0 4 0
18.05 18.05 18.05 26.51 26.51 26.51 26.60 19.03 24.00
A false positive value is defined as one where the true length is longer than normal but the estimate predicts it to be short. A false negative value is defined as one where the true length is shorter than normal but the estimate predicts it to be long.
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also be considered. These cannot be eliminated completely but there will be increasing numbers if the trend line of the scatter plot does not pass through the origin (see biceps femoris with a k value of 2). Under some circumstances false positives may be preferred over false negatives or vice versa as a way of introducing a safety factor. In surgical screening it may be more important to avoid lengthening a muscle inappropriately than to miss the occasional muscle that is slightly short. For a physiotherapy stretching programme the reverse may be true. It is probably better to ensure all children with dynamic shortness are selected, even if that means some who do not also receive therapy. A k value of 3 gives the best overall results in this study. There is room for future refinement of the k value as more muscle moment arm data become available. The quality of estimate used in this study depends upon its underlying assumptions. The very good comparison with the results of musculoskeletal modelling gives considerable reassurance that the assumptions are appropriate. Further consideration, however, may help in indicating when the estimate’s results should be treated with caution. The estimate assumes that internal/external rotation and abduction/adduction movements at the hip and knee can be ignored. The magnitude of the error introduced here depends on two factors, the range of joint movement and the magnitude of the moment arm. At the knee these movements are very small for normal and most pathological gait patterns. The same is not true at the hip, but even so they are usually considerably smaller than the flexion/extension excursion. Data for internal/external rotation and abduction/adduction moment arms are limited. Dostal et al. [9] found average moment arm magnitudes for internal/external rotation of approximately 10% of those for flexion/extension. Abduction/adduction moment arm magnitudes were larger, at approximately 20%. The relative magnitudes for the model used in this study were closer to 5% (internal/external rotation) and 45% (abduction/adduction). From the moment arm data, it can be deduced that the greatest potential source of error in LEST would arise from large abduction/adduction movements at the hip. Caution should therefore be exercised when applying the estimate to gait patterns with significant scissoring or hip abduction. A survey of children assessed in the gait laboratory revealed that most children’s hip adduction at initial contact was within about 10◦ of normal. This is unlikely to compromise the estimate. Deviations in the region of 15–20◦ or above should be treated with more caution. In an adducted position at initial contact the hamstrings may be shorter than is suggested by LEST . In an abducted position they will tend to be longer. The estimate also assumes that the moment arm at the hip is a constant fixed ratio of that at the knee. In reality the ratio changes as the hip and knee joints flex and extend. This can be seen in Fig. 1 across the normal gait cycle. There is still considerable uncertainty concerning the actual moment arms at the hip and knee, with no strong consensus
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in the literature. This is increasingly true as the limb posture moves away from the anatomical position. Published studies consider movements in isolation rather than in the combinations seen in cerebral palsy. It also becomes more difficult for the musculoskeletal model to control the muscle path using wrapping points. For this reason using the estimate for extreme joint ranges should be done with caution, for example in cases of severe crouch gait (knee flexion at initial contact greater than 60◦ ). Likewise, using the same estimation technique in swing phase would give less reliable results than for stance. In this study, the estimate only has been validated for initial contact. Basing the estimate on a single point in the gait cycle makes it much easier to apply as a ‘rule of thumb’ in clinical practice. In theory the same approach could be applied to any point in the gait cycle. Initial contact was chosen for two reasons. Firstly, making contact with a flexed knee is often thought to be associated with hamstring tightness. Secondly, at initial contact the muscle is at, or very close to, its maximum length in both normal and diplegic gait. Any restrictive shortening in muscle length is most likely to be observed when the muscle is at maximum stretch. Some diplegic children do, however, display their maximum muscle length in swing phase and the muscles are already shortening by initial contact. The estimate has been validated by comparison with musculoskeletal modelling. There are significant assumptions related to the modelling process that mean that the length described as LTRUE is not entirely accurate. The musculoskeletal model is based on adult non-pathological morphology. The only adaptation made is the introduction of femoral anteversion. There are also considerable uncertainties concerning the true paths of the muscles. Validation will be strongly influenced by the how the modelling technique deals with this and, in particular how wrapping points are used. Errors will also be carried through from the joint kinematic data collected during gait analysis. At present, however, musculoskeletal modelling provides the most practical method for assessing dynamic muscle length. The estimate described here provides a simpler method for obtaining that information. Throughout the design of the estimate, there has been an attempt to keep it as simple as possible. When reviewing clinicial data it should be possible to read off the two angles and multiply and combine them without the need for additional computation. An illustration of this is given in Fig. 3. The estimate is an indirect measurement of muscle length in degrees, rather than millimetres. This has the advantage of being more readily appreciated but the value should be placed in context. In normal gait the hamstring muscles change length, going through a range from approximately 96–109% of resting length. For an average adult male this would correspond to an excursion in length of about 57 mm. In theory, Fig. 2 could be used to translate between LEST in degrees and LTRUE in percent, and by deduction millimetres. The approximate nature of the
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muscle length information can be integrated into the development of an overall therapeutic plan. The hamstring muscles cannot be considered in isolation. If the hip flexors are to be lengthened, for example, the threshold for addressing the hamstring muscles would be reduced. Overall the calculation of the muscle length can provide useful information to assist in both clinical decision-making and the assessment of the eventual outcome.
Hip Flexion 70 60
Difference in Hip Flexion
50
Θh = 55.6 - 34.7 Θh = 20.9
40 30 20 10 0 -10 0
20
40
60
80
-20
100 Normal Patient
% Gait Cycle
Knee Flexion 80 70 60 50 40 30 20 10 0
Difference in Knee Flexion Θk = 44.0 - 7.4 Θk = 36.6
5. Conclusion Length information can give new insights into the behaviour of muscles, as demonstrated by previous work on the hamstring muscles. The estimate developed in this study (LEST ) has been successfully validated against musculoskeletal modelling and can therefore be used to assess hamstring muscle length at initial contact. It is important to use the data in conjunction with clinical examination and gait analysis results and to bear in mind the assumptions and uncertainties which underlie the calculations.
References 0
20
40
60
% Gait Cycle
80
100 Normal Patient
LEST = k Θh – Θk For k = 3 LEST = k Θh – Θk = 3 × 20.9 – 36.6 = 26.1º Fig. 3. An illustration of the calculation of LEST .
estimate, however, makes it more appropriate for use as an indication of length (in degrees) than as an absolute measure. The estimate should be used in addition to other information, including clinical examination data, gait analysis curves and electromyography (EMG). This other information may assist in deciding why a muscle is long or short. EMG, for example, can help to differentiate between a muscle that is abnormally short because it is unable to stretch any further and one that is actively contracting. Additional data on the muscle’s morphology will also aid understanding, allowing the individual contributions of the contractile tissue and tendon to be assessed. Many therapies, including surgery, aim to lengthen the musculotendinous unit. It is important to understand what a potential therapy is likely to achieve by knowing as much as possible about the pre-treatment status of a muscle. Dynamic
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