- Email: [email protected]
Clinical applicability of using spherical fitting to find hip joint centers
Gait & Posture 22 (2005) 138–145 www.elsevier.com/locate/gaitpost
Clinical applicability of using spherical fitting to find hip joint centers Jennifer L. Hicks a,*, James G. Richards b b
a Bioengineering Department, Stanford University, Stanford, CA 94035-5444, USA Human Performance Laboratory, Department of Health, Nutrition and Exercise Science, University of Delaware, Newark, DE 19716, USA
Accepted 2 August 2004
Abstract The functional or sphere-fitting method has been proposed as an alternative to the traditional predictive approach to locating hip centers based on inter-ASIS breadth. In the functional approach, the movement of a marker on the thigh is fit to a sphere whose center coincides with the hip joint center. The first objective of this study was to determine the required parameters that allow an accurate application of a spherefitting method. The parameters examined in this study included: (1) the range of motion in flexion–extension and abduction–adduction, (2) the specific algorithm used to fit a sphere to the data, (3) the method of placing markers on the thigh, and (4) the type of motion used to generate points, either walking or a standing leg motion (SLM) trial. This objective was addressed with a computer simulation and clinical data. The second objective was to compare the accuracy of the functional method to the traditional predictive approach in a group of nine human subjects. The location of the hip center estimates from both methods were compared to an ultrasound-determined hip center standard, and linear errors and errors along each axis were compared. Results from the computer simulation indicated that an iterative algorithm is needed, with a method using the derivative yielding slightly more accurate results. Clinical results indicated that the functional method with a standing leg motion trial produced significantly smaller errors in hip joint center estimates (1.34 cm) versus the predictive method (2.16 cm). In addition, the range of error across hips was smaller for the functional method. If high joint center accuracy is needed or in populations characterized by obesity or pelvic asymmetries, the subject specificity and independence from anatomical landmarks characteristic of the functional method would likely provide more accurate results. # 2004 Elsevier B.V. All rights reserved. Keywords: Functional method; Sphere fitting; Hip center; Gait analysis
1. Introduction The accurate representation of kinematics and kinetics in the analysis of gait is predicated on several assumptions, including: (1) that clinicians responsible for placing markers on the patient can identify anatomical landmarks with a reasonable degree of accuracy, and (2) that algorithms used to define joint center locations based on surface marker positions are insensitive to a wide range of individual variations in anatomical structure. Errors in static determination of the knee and ankle joint centers are generally due to violations of the first assumption, but errors in the determination of the hip joint centers can often be attributed to problems with both assumptions. This is especially true when attempting to perform a gait analysis on obese patients * Corresponding author. Tel.: +1 650 725 4009; fax: +1 650 723 8544. E-mail address: [email protected] (J.L. Hicks). 0966-6362/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2004.08.004
or patients with pelvic deformities. Both of these patient populations possess anthropometric characteristics that complicate the accurate acquisition of gait analysis data. Ironically, gait analysis data frequently assumes greater importance in the surgical planning and assessment process for these populations. In the case of obese patients, finding the ASIS and Sacral marker locations presents a challenge to the most experienced clinicians. In patients with pelvic deformities, anatomical landmarks may be easily identified, but the traditional methods of calculating joint centers from these landmarks fail to account for aberrations in pelvic geometry. These problems ultimately serve to erode the confidence of the clinical planning team in utilizing data from the gait analysis for these special populations. The most common method of locating the hip center for gait analysis uses percentages of palpated bony landmarks, most commonly, the left and right ASIS. However, several studies using cadavers or a radiographic standard have
J.L. Hicks, J.G. Richards / Gait & Posture 22 (2005) 138–145
shown this method to be inaccurate even in a normal population [1–3]. Research has shown that a relatively small mislocation of the hip center can have a significant effect on the calculation of kinetics and kinematics at the hip and knee. The largest error resulted from displacement in the anterio–posterior direction, which affected the magnitude and timing of hip flexion–extension, especially at slower walking speeds [4,5]. This indicates that hip joint center mislocation may have a larger effect in special populations who tend to have slower self-selected walking speeds. Medial–lateral hip location error was also found to result in a change in magnitude of the peak hip abductor moment at all walking speeds [5]. The error associated with the traditional predictive approach has led to an increased interest in identifying hip joint centers using the functional method. The functional method is the name given to the process of fitting a sphere to a cluster of points. The cluster of points is formed by tracking a marker attached to the thigh while moving the thigh relative to the pelvis. In theory, the functional method overcomes the limitations associated with the use of constants or regression equations by identifying hip joint centers independent of pelvic geometry or pelvic marker placement. Consequently, it has the potential to provide more consistent estimates of hip center locations between anthropometrically diverse patient populations. Research focused on the functional method of hip center location has shown conflicting results, most likely as a result of varied sphere-fitting algorithms and marker movement used to fit the sphere. Two studies have compared the functional method to a radiographic standard. Bell et al. [6] found the total error of the functional method to be 3.79 cm, while Leardini et al. [7] found a mean error of 1.18 cm. Piazza et al. [8] tested the accuracy and robustness of the functional method by comparing several different simulated hip movement patterns using data generated by a mechanical apparatus, and found errors less than 1 cm. There are several possible sources for this varying accuracy. It can be reasonably argued that the amount of noise contained in each of the data sets is the most probable source of discrepancy. Data collected in a clinical environment is likely to contain more noise from soft tissue motion as well as lower measurement resolution (from larger volumes) when compared to data collected in a bench top test. The studies also used varying patterns and ranges of motion, although Piazza et al. [8] demonstrated that range of motion in the sagittal and frontal plane is more important than the pattern of motion. Additionally, it is unclear how conventional marker placement strategies such as cluster-based marker sets and minimized marker sets (i.e. the Helen Hayes marker set) interact with the spherical fit algorithms in clinic. Finally, the algorithm used to fit a sphere to the set of points was only reported in the study by Piazza et al. [8] although numerous algorithms of varying effectiveness are available. None of the previous clinical studies have reported information pertaining to the interaction between the
139
amount of surface represented by the cluster, the noise contained in the markers, and the characteristics of the spherical fit algorithm used in the investigations. This information is critical to understanding how the algorithms will function in a variety of clinical environments. The first objective of this study was to determine the required parameters that allow an accurate application of a sphere-fitting method. The parameters include: (1) the range of motion in flexion–extension and abduction–adduction, (2) the specific algorithm used to fit a sphere to the data, (3) the method of placing markers on the thigh, and (4) the type of motion used to generate points, either walking or a standing leg motion (SLM) trial. This objective was addressed with a computer simulation and clinical data from human subjects, using an ultrasound-determined hip joint center for comparison. The second objective was to compare the accuracy of the functional method to the traditional predictive approach. The linear and axial errors associated with the location of the hip center estimates from both methods were compared to an ultrasound-determined hip center standard.
2. Methods Computer simulated data was used to determine the type of sphere-fitting algorithm best suited to the ranges of motion seen in clinical data and the approximate range of flexion–extension and abduction–adduction needed for accurate results. The sphere-fitting algorithm with the best performance in the computer simulation was then compared to the standard predictive approach and an ultrasound ‘‘gold standard’’ using data from human subjects. This comparison was made with the algorithm applied to controlled leg movement in a standing position and leg movement measured from walking. 2.1. Computer modeling The first part of the study involved testing several spherefitting algorithms with computer simulated data. The basic goal for all of the algorithms was to minimize the distance between each point and the surface of the sphere. Three different algorithms for minimizing the total error of all points in the data set were tested in this study. The first was a non-iterative, least squares solution. The other two algorithms began with the least squares solution as an initial estimate then minimized the error in an iterative process. The two iterative algorithms tested were the Newton Method, which utilizes the derivative of the function, and the Nelder–Mead Downhill Simplex Method, which does not [9]. Each of these algorithms is described in the electronic addendum. To test each of the different sphere-fitting approaches used in the study, a software program simulated knee joint center motion relative to a fixed pelvis. The program
140
J.L. Hicks, J.G. Richards / Gait & Posture 22 (2005) 138–145
controlled the range of motion in two planes, generating a pattern similar to a standing leg motion trial, with an arc of flexion and a perpendicular arc of abduction. Since the points were computer generated, the exact location of the center of the sphere (i.e. the simulated hip joint center) was known. In order to simulate error in the markers, random noise was added to each of the points along the direction of the radius. Thus to each point, the distance between the center of the sphere was either increased or decreased by a random amount, determined by a function generating Gaussian white noise. The interactions between range of motion and noise were examined by systematically altering the magnitude of these parameters to create maps of the sphere center approximation error, which was defined as the distance between the true sphere center and the center derived by the sphere-fitting algorithm. Plots of sphere center error as a function of abduction and flexion range of motion were generated with noise ranging from 1 to 5% of the radius. For each of the plots, the percentage of sphere center error points having a magnitude less than one centimeter was used to compare the performance of the three algorithms. Although arbitrary, this 1 cm threshold represents a reasonable level of accuracy to expect of a method for locating hip joint centers. 2.2. Clinical assessment Laboratory testing was performed in a calibrated volume (6 m 3 m 2.5 m) with an 8-camera Motion Analysis digital camera system operating at 60 hz. Marker coordinate positions were filtered at 6 Hz. A total of nine subjects (five female, four male) ranging in age from 20 to 60 were tested, for a total of 18 hips. Subjects were of normal weight, in
order to allow for accurate ultrasound imaging. The pelvis was wrapped with a neoprene band and 7 mm reflective markers were placed on the band over the sacrum and right and left ASIS. The neoprene band prevented movement of the pelvic markers during activity. Three markers were also placed on the probe of a SonoSite 180 ultrasound unit (38 mm linear probe operating at 10 MHz) which enabled measurement of the probe’s position and vector orientation in the laboratory’s calibrated volume. As the subjects stood in a stationary standing position, the ultrasound probe was positioned to image the anterior surface of the femoral head while the video system recorded the position of markers on the subject and on the probe (Fig. 1). The recorded images of the anterior surface of the femoral head were analyzed using custom software that allowed a circle to be fit to four points manually positioned over the image of the femoral head (Fig. 2). The distance from the ultrasound probe to the center of the femoral head was determined by adding the distance between the end of the ultrasound probe and the surface of the femoral head to the radius of the fitted circle. Multiplying this distance by the unit vector representing the orientation of the probe during imaging enabled reconstruction of the hip joint centers in the pelvic coordinate system based on ultrasound imaging. The ultrasound hip joint center location was determined with the probe in both a horizontal and vertical orientation. The horizontal orientation is shown in Fig. 1, while the vertical orientation requires rotating the probe 908 to align the probe end vertically. The femoral head was centered in the ultrasound image with the probe in a horizontal orientation to obtain a slice in the coronal plane. The hip center location obtained from this orientation was used for the anterio–posterior and medial–lateral position. The
Fig. 1. Ultrasound probe positioned to image the femoral head. In this image, the probe is shown in a horizontal orientation.
J.L. Hicks, J.G. Richards / Gait & Posture 22 (2005) 138–145
141
Fig. 2. Ultrasound image of the femoral head in the frontal plane. A circle is fit to the contour formed by the femoral head to determine femoral head radius.
femoral head was then imaged with the probe in a vertical orientation to obtain a slice in the sagittal plane. The hip center location from this orientation was used to determine the hip center location along the inferior–superior axis. Since the ultrasound image shows a slice in the plane of the probe orientation, it was easy to center the femoral head in the given plane. However, it was difficult to be certain the given plane shown in the image reflected the widest arc of the femoral head, which corresponds to the center in the direction perpendicular to the plane. Thus, imaging the femoral head in two planes made the accuracy less dependent on finding the widest arc of the femur head. The final ultrasound-determined hip joint center obtained from these two readings provided a means of comparing measured hip joint centers with those determined using conventional predictive methods and the method of sphere fitting. After the ultrasound measures were obtained, the remaining markers required for a standard static trial were attached directly to the subjects’ skin using adhesive. These markers were placed in an orientation that enabled simultaneous calculation of joint centers using both Cleveland Clinic (CC) and Helen Hayes (HH) marker sets [10]. The subjects performed a standing leg motion trial that consisted of standing supported on one leg, and moving the free leg through an average of approximately 808 of hip flexion–extension and an orthogonal arc of 508 of hip abduction–adduction. Subjects were instructed to move through a comfortable range of motion in a slow and deliberate manner. This process was performed for both legs, and was used to (1) record the medial and lateral knee marker locations relative to the thigh coordinate system, and
(2) to track the path of the knee center for use in the spherical fit algorithm. Once the standing trials were completed, subjects performed three walking trials at a self-selected pace. Only the medial knee and ankle markers were removed, which allowed the walking trial data to be used with both a CC and HH marker set. The sphere-fitting algorithm utilized the reconstructed knee center localized to the pelvic coordinate system to determine hip center locations from walking trial data. Hip joint center locations were calculated using each of the four methods of estimation: prediction using inter-ASIS difference and constants, spherical fit from SLM trial data, spherical fit directly from walking trial data with a CC marker set and spherical fit from walking data with a HH marker set. Constants used for the prediction method were those supplied with Orthotrak gait analysis software. The constants represent percentages of the inter-ASIS distance, and were expressed relative to the midpoint between the two ASIS markers. Hip center locations calculated from ultrasound were subtracted from the hip center locations derived using each of the four methods. The resulting linear difference scores were analyzed using planned comparisons (t-tests) with a Bonferroni correction to hold the experiment-wise a level at 0.05. Comparisons of linear differences that yielded significant results were further analyzed to determine whether the hip center estimates were different along specific anatomical axes. The absolute distance along each axis was compared to determine the accuracy of each method in the three anatomical planes and the signed distance was averaged and compared to determine the general direction of the error.
142
J.L. Hicks, J.G. Richards / Gait & Posture 22 (2005) 138–145
Fig. 3. Percentage of area in surface plots with less than 1 cm error. The two iterative algorithms were significantly more accurate than the non-iterative algorithm. The Newton method was slightly more accurate than the Downhill Simplex method at the highest noise level.
Fig. 5. Centroid error map for the iterative, Downhill Simplex sphere-fitting algorithm with a noise level of 5% of the radius. Error is shown as a function of the angle of flexion–extension and abduction–adduction.
3. Results
3.2. Clinical assessment
3.1. Computer simulation
The four methods of finding hip joint centers were first compared by calculating the linear distance between the hip joint center derived by each method and the location of the hip joint center measured by the ultrasound. Comparing the linear difference scores indicated that the sphere fitting from the SLM trial, with a mean linear difference of 1.34 cm, was significantly more accurate than the three other methods (Table 1). The sphere fitting from the SLM trial was followed in accuracy by the traditional predictive method, with a mean of 2.16 cm, then the sphere fitting using walking data. The HH walking data, with a mean of 4.22 cm, was also significantly closer to the ultrasound than the CC walking data, with a mean of 10.29 cm. The components of the hip center error along the anatomical axes were calculated for each algorithm. In the inferior–superior direction, there was no significant difference between the SLM trial and the predictive methods. The predictive method tended to locate the hip joint center superior to the ultrasound, while the sphere fitting from the SLM trial located the hip center slightly inferior, and the two walking methods located the hip center significantly inferior to the ultrasound (Table 2). There was no significant difference in the absolute error in the anterio–posterior direction between the predictive, SLM or HH walking methods with a mean around 0.8 cm for all three methods. Sphere fitting using the CC walking data was significantly less accurate than all three other methods. The error for the predictive method was evenly dispersed along this axis, while the sphere fitting from the SLM trial tended to locate the hip center posterior to the ultrasound and the two walking methods located the hip center anterior to the ultrasound. In the medial–lateral direction, the SLM sphere-fitting method was evenly dispersed in both directions, while the predictive method tended to locate the hip center medial to the ultrasound in most subjects. Both sphere-fitting methods
When testing the three sphere-fitting algorithms under ideal conditions, with low levels of noise and a high range of motion, there was no significant difference between the algorithms. Restricting the range of motion and increasing the percentage of noise resulted in a drastic reduction in performance of the non-iterative algorithm when compared to the two iterative algorithms (Fig. 3). There was only a difference between the two iterative algorithms at a noise level of 5% (Figs. 4 and 5), where the Newton method slightly outperformed the Downhill Simplex method when comparing the percentage of area in the plots with less than 1 cm approximation error (Fig. 3). Thus for the clinical part of the study, the Newton method was used for sphere fitting.
Fig. 4. Centroid error map for the iterative, Newton sphere-fitting algorithm with a noise level of 5% of the radius. Error is shown as a function of the angle of flexion–extension and abduction–adduction. Data points are averaged for five random sets of data. Error was below 1 cm (blue and dark green) with flexion greater than 458 and abduction greater than 158.
J.L. Hicks, J.G. Richards / Gait & Posture 22 (2005) 138–145
143
Table 1 Mean (S.D.) distance scores (cm) for the four methods of locating the hip joint center (N = 18) Predictive Linear Inferior–superior Anterior–posterior Medial–lateral a
SLM sphere a
1.34 0.74 0.84 0.64
2.16 (0.53) 1.3 (0.62) 0.81 (0.44) 1.21 (0.57)a
CC walking sphere
a
(0.43) (0.46) (0.48) (0.31)a
10.29 4.56 1.59 5.26
HH walking sphere
a
4.22 (2.32)a 2.23 (1.82)a 0.8 (0.54) 2.98 (2.24)a
(4.61) (1.97)a (0.83)a (2.30)a
Significantly different from all other methods (P < 0.0083).
using walking data located the hip center lateral to the ultrasound, with the CC marker set significantly more lateral than the HH marker set.
4. Discussion The results of the computer simulation indicated that the two iterative methods of sphere fitting—the Newton and Downhill Simplex methods—were far more accurate than the non-iterative, least-squares approach with smaller ranges of motion and higher levels of noise. This is expected since the iterative methods, in theory, improve on the initial guess from the least squares approximation. The Newton method also seemed to perform slightly better than the Downhill Simplex method when the noise was greater than 4% of the radius of the sphere. There is a conceptual difference between these two algorithms–the Downhill Simplex method, an optimization algorithm which minimizes the sum of the squared error, finds some local minimum instead of the global minimum by ‘‘sliding downhill’’ along the error function [9]. In contrast, the Newton method is an attempt to find a sphere where the error associated with each individual point is zero. It is also possible that a more powerful type of optimization algorithm, like those using the derivative of the function to be minimized, might be more accurate [9]. The stopping tolerances used in the two algorithms might have also affected the accuracy. Still, the Newton method seemed to perform well, and using an optimization algorithm that utilizes the derivative would probably yield very similar results. Based on these findings, only the Newton method was applied to data collected from subjects. The error plots generated by the computer simulation also suggest requirements for joint ranges of motion necessary to produce accurate results when the noise is expressed as a specific percentage of the radius. With the noise level at 5% of the radius, the Newton method produced accurate results Table 2 Mean (S.D.) signed distance scores (cm) along the three anatomical axes (N = 18) Predictive Inferior Anterior Lateral
1.22 0.07 1.18
SLM sphere 0.18 0.70 0.17
CC walking sphere 4.51 1.57 4.77
HH walking sphere 1.80 0.50 0.74
with error less than 1 cm when the range of flexion– extension was greater than 458 and the range of abduction– adduction was greater than 108. These ranges should be feasible for the majority of the patient population to attain either actively or with the help of a clinician. In the clinical part of the analysis, physical assessments of hip joint centers were derived from images obtained using a targeted ultrasound probe. Results from the other methods were then compared to this data. The functional method, used with data generated from a standing leg motion trial, produced results significantly more accurate than the predictive method. The sphere-fitting method from an SLM trial had a lower mean error, as well as a lower maximum error when compared to the predictive approach. The error found in this study is consistent with the results of Leardini et al. [7] who compared the functional method to a radiographic standard. Although the predictive approach was very accurate for a small portion of subjects in the study, its use resulted in a higher error overall and also a potential for greater error in individual subjects (Table 3). It could be argued that using different constants for the predictive Table 3 Hip constants from ultrasound as % of ASIS breadth, with origin at midpoint of ASIS markers Subject
Inferior
Posterior
Lateral
1-R 1-L 2-R 2-L 3-R 3-L 4-R 4-L 5-R 5-L 6-R 6-L 7-R 7-L 8-R 8-L 9-R 9-L
32.09 32.31 37.21 36.70 39.81 37.39 30.35 34.46 41.09 41.07 36.64 37.43 41.77 42.39 44.91 39.68 40.01 38.66
17.82 16.96 23.71 23.91 25.10 26.89 23.12 25.24 21.10 18.01 17.48 16.48 22.35 23.76 24.01 26.40 18.75 22.24
35.97 36.29 38.67 38.20 33.89 38.87 32.36 38.53 34.51 37.75 36.27 30.40 33.53 36.64 43.06 41.63 38.35 40.26
Minimum Maximum
30.35 44.91
16.48 26.89
30.40 43.06
Average OrthoTrak Bell
38.00 34 30
21.85 22 19
36.95 32 36
144
J.L. Hicks, J.G. Richards / Gait & Posture 22 (2005) 138–145
approach would have yielded more accurate results. While the error for the predictive approach was not biased along the anterio–posterior axis, the predicted hip center estimates tended to be superior and medial to the ultrasounddetermined hip center, suggesting that the hip constants have some degree of specificity to the sample from which they were derived. In addition, a more individualized set of constants for the group could easily be derived from the ultrasound measures (Table 3). Using the averaged, ultrasound-based constants in this study would have decreased the error for the sample of the population tested; however, the traditional predictive approach still assumes that pelvic geometry is similar across all body types, and similar errors would be seen when applying the ultrasound constants from this study to another sample of the population. Previous studies investigating the effect of hip joint center mislocation on kinematics and kinetics found that displacement of the joint center in the anterio–posterior and medial–lateral directions had the greatest effect at the hip and knee [4,5]. While there was no difference between the predictive, SLM or HH walking methods in the anterio–posterior direction, the SLM sphere-fitting method was significantly more accurate in the medial–lateral direction. However, it is likely that error in the anterio– posterior direction would be greater in an obese population when the ASIS markers are covered with a thicker layer of soft tissue and palpation is difficult. This would have the effect of moving the origin of the pelvic coordinate system, and thus the hip joint centers, anterior to their true location. While the SLM sphere-fitting approach was more accurate than the predictive approach, it did not achieve the level of accuracy suggested by the computer simulation or previous research using a mechanical apparatus [8]. The most likely cause of this discrepancy is a difference in noise characteristics between the two types of data sets. In the computer simulation, the noise was random throughout the range of motion. Examining the data from the SLM and walking trials suggests that there is more systematic error as a function of both the limb movement speed and hip angle. For the SLM trials, this noise was minimized by instructing the subjects to move the leg slowly and deliberately throughout the range of motion. The effect of thigh velocity on the accuracy of sphere fitting was not quantified, but instructing the subjects to move their leg slowly and deliberately tended to improve the results. It was noted that when subjects moved their leg through the ranges of motion in a rapid, ballistic manner, the estimates from the spherefitting method were consistently inferior relative to the ultrasound measure, sometimes by several centimeters. This resulted from a change in the arc of the knee marker, presumably due to soft tissue motion associated with higher movement velocities. The error in using the walking data for sphere fitting partly resulted from a smaller range of motion in
abduction–adduction than in the SLM trials. A similar result was found in a recent study by Piazza et al. [11] that applied the sphere-fitting method to several functional activities. In addition, there was systematic error in the walking trial data sets that appeared to be a function of the angle of flexion and the phase in stride. Similar patterns of error were seen with both the HH and CC data sets, although in the CC walking trials, this error was magnified. The largest error was seen in the lateral and inferior directions. Examining the location of the reconstructed knee center shows that it was farther from the hip center during swing phase than during stance phase. Since the hip is more abducted during swing phase, this had the effect of moving the sphere and derived hip center laterally. With a greater distance between the knee and hip center during swing phase, and a smaller distance at toe-off and especially heel strike, the arc being fit to the sphere became deeper resulting in a sphere inferior to the true hip center. In addition, the distance between the knee and hip center increased as the angle of flexion increased. This had the effect of moving the sphere anterior. The trends in error seen in the data can best be explained by movement of the soft tissue as a result of acceleration of the leg at heel strike and during swing phase. The higher error found in the CC walking set suggests that there was greater soft tissue motion associated with the thigh markers than with the lateral knee marker used in the HH marker set. Since the reconstructed knee center was used to fit the sphere, this has implications for the accuracy of other aspects of gait analysis when using a CC instead of a HH marker set. The sphere-fitting approach from an SLM trial was found to be significantly more accurate than the predictive approach in this study. However, it is more labor intensive, requiring the recording and tracking of an 8–12 s static trial for each leg. In this study, the predictive approach was 2.16 cm away from the ultrasound-determined hip center on average, which is enough to result in noticeable changes in hip kinetics and kinematics if the error is in the AP or ML directions. If higher accuracy of hip joint kinematics and kinetics is desired, an SLM trial is justified. Another advantage of the sphere-fitting method is its independence from pelvic geometry, as it will not be affected by dimensional exaggerations or asymmetries in the pelvis. In addition, the functional method does not depend on accurately locating three specific anatomical landmarks on the pelvis. As long as three markers are fixed on the pelvis in an arrangement that allows for good estimates of pelvic orientation, the sphere-fitting method will work as intended. In some patients, the ASIS can be covered by soft tissue, and when walkers or crutches are used, traditional ASIS markers can be blocked from the cameras. In cases such as these, moving markers to more accessible locations on the pelvis (i.e. a triad over the sacrum) would facilitate the imaging process, and using the sphere-fitting method would provide a means to accurately determine the hip center locations.
J.L. Hicks, J.G. Richards / Gait & Posture 22 (2005) 138–145
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.gaipost. 2004.08.004.
References [1] Seidel GK, Marchinda DM, Dijkers M, Soutas-Little RW. Hip joint center location from palpable bony landmarks—a cadaver study. J Biomech 1995;28:995–8. [2] Marchinda D, Seidel G, Alderink G, Bothner K. A comparison study of hip joint center location models. In: Proceedings of the Fourth Annual Gait and Clinical Movement Analysis Meeting. Gait Post 1999;9:132–3. [3] Kirkwood RN, Culham EG, Costigan P. Radiographic and non-invasive determination of the hip joint center location: effect on hip joint moments. Clin Biomech 1999;14:227–35. [4] Stagni R, Leardini A, Capozzo A, Grazia Benedetti M, Capello A. Effects of hip joint center mislocation on gait analysis results. J Biomech 2000;33:1479–87.
145
[5] Holden JP, Stanhope SJ. The effect of uncertainty in hip center location estimates on hip joint moments during walking at different speeds. In: Proceedings of the Fifth Annual Gait and Clinical Movement Analysis Meeting. Gait Post 2000;11:119–20. [6] Bell AL, Pedersen DR, Brand RA. A comparison of the accuracy of several hip center location prediction methods. J Biomech 1990;23:617–21. [7] Leardini A, Cappozzo A, Catani F, Toksvig-Larsen S, Petitto A, Sforza V, Cassanelli G, Giannini S. Validation of a functional method for the estimation of hip joint center location. J Biomech 1999;32: 99–103. [8] Piazza SJ, Okita N, Cavanagh PR. Accuracy of the functional method of hip joint center location: effects of limited motion and varied implementation. J Biomech 2001;34:967–73. [9] Press WT, Flannery BP, Teukolsky SA, Vetterling WT. Numerical recipes: the art of scientific computing. Cambridge: Cambridge University Press, 1986. [10] OrthoTrak 4.2 Gait Analysis Software Reference Manual. Santa Rosa, CA: Motion Analysis Corporation; 2000. [11] Piazza SJ, Erdemir A, Okita N, Cavanagh PR. Assessment of the function method of hip joint center location subject to reduced range of motion. J Biomech 2004;37:349–56.
Clinical applicability of using spherical fitting to find hip joint centers Jennifer L. Hicks a,*, James G. Richards b b
a Bioengineering Department, Stanford University, Stanford, CA 94035-5444, USA Human Performance Laboratory, Department of Health, Nutrition and Exercise Science, University of Delaware, Newark, DE 19716, USA
Accepted 2 August 2004
Abstract The functional or sphere-fitting method has been proposed as an alternative to the traditional predictive approach to locating hip centers based on inter-ASIS breadth. In the functional approach, the movement of a marker on the thigh is fit to a sphere whose center coincides with the hip joint center. The first objective of this study was to determine the required parameters that allow an accurate application of a spherefitting method. The parameters examined in this study included: (1) the range of motion in flexion–extension and abduction–adduction, (2) the specific algorithm used to fit a sphere to the data, (3) the method of placing markers on the thigh, and (4) the type of motion used to generate points, either walking or a standing leg motion (SLM) trial. This objective was addressed with a computer simulation and clinical data. The second objective was to compare the accuracy of the functional method to the traditional predictive approach in a group of nine human subjects. The location of the hip center estimates from both methods were compared to an ultrasound-determined hip center standard, and linear errors and errors along each axis were compared. Results from the computer simulation indicated that an iterative algorithm is needed, with a method using the derivative yielding slightly more accurate results. Clinical results indicated that the functional method with a standing leg motion trial produced significantly smaller errors in hip joint center estimates (1.34 cm) versus the predictive method (2.16 cm). In addition, the range of error across hips was smaller for the functional method. If high joint center accuracy is needed or in populations characterized by obesity or pelvic asymmetries, the subject specificity and independence from anatomical landmarks characteristic of the functional method would likely provide more accurate results. # 2004 Elsevier B.V. All rights reserved. Keywords: Functional method; Sphere fitting; Hip center; Gait analysis
1. Introduction The accurate representation of kinematics and kinetics in the analysis of gait is predicated on several assumptions, including: (1) that clinicians responsible for placing markers on the patient can identify anatomical landmarks with a reasonable degree of accuracy, and (2) that algorithms used to define joint center locations based on surface marker positions are insensitive to a wide range of individual variations in anatomical structure. Errors in static determination of the knee and ankle joint centers are generally due to violations of the first assumption, but errors in the determination of the hip joint centers can often be attributed to problems with both assumptions. This is especially true when attempting to perform a gait analysis on obese patients * Corresponding author. Tel.: +1 650 725 4009; fax: +1 650 723 8544. E-mail address: [email protected] (J.L. Hicks). 0966-6362/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2004.08.004
or patients with pelvic deformities. Both of these patient populations possess anthropometric characteristics that complicate the accurate acquisition of gait analysis data. Ironically, gait analysis data frequently assumes greater importance in the surgical planning and assessment process for these populations. In the case of obese patients, finding the ASIS and Sacral marker locations presents a challenge to the most experienced clinicians. In patients with pelvic deformities, anatomical landmarks may be easily identified, but the traditional methods of calculating joint centers from these landmarks fail to account for aberrations in pelvic geometry. These problems ultimately serve to erode the confidence of the clinical planning team in utilizing data from the gait analysis for these special populations. The most common method of locating the hip center for gait analysis uses percentages of palpated bony landmarks, most commonly, the left and right ASIS. However, several studies using cadavers or a radiographic standard have
J.L. Hicks, J.G. Richards / Gait & Posture 22 (2005) 138–145
shown this method to be inaccurate even in a normal population [1–3]. Research has shown that a relatively small mislocation of the hip center can have a significant effect on the calculation of kinetics and kinematics at the hip and knee. The largest error resulted from displacement in the anterio–posterior direction, which affected the magnitude and timing of hip flexion–extension, especially at slower walking speeds [4,5]. This indicates that hip joint center mislocation may have a larger effect in special populations who tend to have slower self-selected walking speeds. Medial–lateral hip location error was also found to result in a change in magnitude of the peak hip abductor moment at all walking speeds [5]. The error associated with the traditional predictive approach has led to an increased interest in identifying hip joint centers using the functional method. The functional method is the name given to the process of fitting a sphere to a cluster of points. The cluster of points is formed by tracking a marker attached to the thigh while moving the thigh relative to the pelvis. In theory, the functional method overcomes the limitations associated with the use of constants or regression equations by identifying hip joint centers independent of pelvic geometry or pelvic marker placement. Consequently, it has the potential to provide more consistent estimates of hip center locations between anthropometrically diverse patient populations. Research focused on the functional method of hip center location has shown conflicting results, most likely as a result of varied sphere-fitting algorithms and marker movement used to fit the sphere. Two studies have compared the functional method to a radiographic standard. Bell et al. [6] found the total error of the functional method to be 3.79 cm, while Leardini et al. [7] found a mean error of 1.18 cm. Piazza et al. [8] tested the accuracy and robustness of the functional method by comparing several different simulated hip movement patterns using data generated by a mechanical apparatus, and found errors less than 1 cm. There are several possible sources for this varying accuracy. It can be reasonably argued that the amount of noise contained in each of the data sets is the most probable source of discrepancy. Data collected in a clinical environment is likely to contain more noise from soft tissue motion as well as lower measurement resolution (from larger volumes) when compared to data collected in a bench top test. The studies also used varying patterns and ranges of motion, although Piazza et al. [8] demonstrated that range of motion in the sagittal and frontal plane is more important than the pattern of motion. Additionally, it is unclear how conventional marker placement strategies such as cluster-based marker sets and minimized marker sets (i.e. the Helen Hayes marker set) interact with the spherical fit algorithms in clinic. Finally, the algorithm used to fit a sphere to the set of points was only reported in the study by Piazza et al. [8] although numerous algorithms of varying effectiveness are available. None of the previous clinical studies have reported information pertaining to the interaction between the
139
amount of surface represented by the cluster, the noise contained in the markers, and the characteristics of the spherical fit algorithm used in the investigations. This information is critical to understanding how the algorithms will function in a variety of clinical environments. The first objective of this study was to determine the required parameters that allow an accurate application of a sphere-fitting method. The parameters include: (1) the range of motion in flexion–extension and abduction–adduction, (2) the specific algorithm used to fit a sphere to the data, (3) the method of placing markers on the thigh, and (4) the type of motion used to generate points, either walking or a standing leg motion (SLM) trial. This objective was addressed with a computer simulation and clinical data from human subjects, using an ultrasound-determined hip joint center for comparison. The second objective was to compare the accuracy of the functional method to the traditional predictive approach. The linear and axial errors associated with the location of the hip center estimates from both methods were compared to an ultrasound-determined hip center standard.
2. Methods Computer simulated data was used to determine the type of sphere-fitting algorithm best suited to the ranges of motion seen in clinical data and the approximate range of flexion–extension and abduction–adduction needed for accurate results. The sphere-fitting algorithm with the best performance in the computer simulation was then compared to the standard predictive approach and an ultrasound ‘‘gold standard’’ using data from human subjects. This comparison was made with the algorithm applied to controlled leg movement in a standing position and leg movement measured from walking. 2.1. Computer modeling The first part of the study involved testing several spherefitting algorithms with computer simulated data. The basic goal for all of the algorithms was to minimize the distance between each point and the surface of the sphere. Three different algorithms for minimizing the total error of all points in the data set were tested in this study. The first was a non-iterative, least squares solution. The other two algorithms began with the least squares solution as an initial estimate then minimized the error in an iterative process. The two iterative algorithms tested were the Newton Method, which utilizes the derivative of the function, and the Nelder–Mead Downhill Simplex Method, which does not [9]. Each of these algorithms is described in the electronic addendum. To test each of the different sphere-fitting approaches used in the study, a software program simulated knee joint center motion relative to a fixed pelvis. The program
140
J.L. Hicks, J.G. Richards / Gait & Posture 22 (2005) 138–145
controlled the range of motion in two planes, generating a pattern similar to a standing leg motion trial, with an arc of flexion and a perpendicular arc of abduction. Since the points were computer generated, the exact location of the center of the sphere (i.e. the simulated hip joint center) was known. In order to simulate error in the markers, random noise was added to each of the points along the direction of the radius. Thus to each point, the distance between the center of the sphere was either increased or decreased by a random amount, determined by a function generating Gaussian white noise. The interactions between range of motion and noise were examined by systematically altering the magnitude of these parameters to create maps of the sphere center approximation error, which was defined as the distance between the true sphere center and the center derived by the sphere-fitting algorithm. Plots of sphere center error as a function of abduction and flexion range of motion were generated with noise ranging from 1 to 5% of the radius. For each of the plots, the percentage of sphere center error points having a magnitude less than one centimeter was used to compare the performance of the three algorithms. Although arbitrary, this 1 cm threshold represents a reasonable level of accuracy to expect of a method for locating hip joint centers. 2.2. Clinical assessment Laboratory testing was performed in a calibrated volume (6 m 3 m 2.5 m) with an 8-camera Motion Analysis digital camera system operating at 60 hz. Marker coordinate positions were filtered at 6 Hz. A total of nine subjects (five female, four male) ranging in age from 20 to 60 were tested, for a total of 18 hips. Subjects were of normal weight, in
order to allow for accurate ultrasound imaging. The pelvis was wrapped with a neoprene band and 7 mm reflective markers were placed on the band over the sacrum and right and left ASIS. The neoprene band prevented movement of the pelvic markers during activity. Three markers were also placed on the probe of a SonoSite 180 ultrasound unit (38 mm linear probe operating at 10 MHz) which enabled measurement of the probe’s position and vector orientation in the laboratory’s calibrated volume. As the subjects stood in a stationary standing position, the ultrasound probe was positioned to image the anterior surface of the femoral head while the video system recorded the position of markers on the subject and on the probe (Fig. 1). The recorded images of the anterior surface of the femoral head were analyzed using custom software that allowed a circle to be fit to four points manually positioned over the image of the femoral head (Fig. 2). The distance from the ultrasound probe to the center of the femoral head was determined by adding the distance between the end of the ultrasound probe and the surface of the femoral head to the radius of the fitted circle. Multiplying this distance by the unit vector representing the orientation of the probe during imaging enabled reconstruction of the hip joint centers in the pelvic coordinate system based on ultrasound imaging. The ultrasound hip joint center location was determined with the probe in both a horizontal and vertical orientation. The horizontal orientation is shown in Fig. 1, while the vertical orientation requires rotating the probe 908 to align the probe end vertically. The femoral head was centered in the ultrasound image with the probe in a horizontal orientation to obtain a slice in the coronal plane. The hip center location obtained from this orientation was used for the anterio–posterior and medial–lateral position. The
Fig. 1. Ultrasound probe positioned to image the femoral head. In this image, the probe is shown in a horizontal orientation.
J.L. Hicks, J.G. Richards / Gait & Posture 22 (2005) 138–145
141
Fig. 2. Ultrasound image of the femoral head in the frontal plane. A circle is fit to the contour formed by the femoral head to determine femoral head radius.
femoral head was then imaged with the probe in a vertical orientation to obtain a slice in the sagittal plane. The hip center location from this orientation was used to determine the hip center location along the inferior–superior axis. Since the ultrasound image shows a slice in the plane of the probe orientation, it was easy to center the femoral head in the given plane. However, it was difficult to be certain the given plane shown in the image reflected the widest arc of the femoral head, which corresponds to the center in the direction perpendicular to the plane. Thus, imaging the femoral head in two planes made the accuracy less dependent on finding the widest arc of the femur head. The final ultrasound-determined hip joint center obtained from these two readings provided a means of comparing measured hip joint centers with those determined using conventional predictive methods and the method of sphere fitting. After the ultrasound measures were obtained, the remaining markers required for a standard static trial were attached directly to the subjects’ skin using adhesive. These markers were placed in an orientation that enabled simultaneous calculation of joint centers using both Cleveland Clinic (CC) and Helen Hayes (HH) marker sets [10]. The subjects performed a standing leg motion trial that consisted of standing supported on one leg, and moving the free leg through an average of approximately 808 of hip flexion–extension and an orthogonal arc of 508 of hip abduction–adduction. Subjects were instructed to move through a comfortable range of motion in a slow and deliberate manner. This process was performed for both legs, and was used to (1) record the medial and lateral knee marker locations relative to the thigh coordinate system, and
(2) to track the path of the knee center for use in the spherical fit algorithm. Once the standing trials were completed, subjects performed three walking trials at a self-selected pace. Only the medial knee and ankle markers were removed, which allowed the walking trial data to be used with both a CC and HH marker set. The sphere-fitting algorithm utilized the reconstructed knee center localized to the pelvic coordinate system to determine hip center locations from walking trial data. Hip joint center locations were calculated using each of the four methods of estimation: prediction using inter-ASIS difference and constants, spherical fit from SLM trial data, spherical fit directly from walking trial data with a CC marker set and spherical fit from walking data with a HH marker set. Constants used for the prediction method were those supplied with Orthotrak gait analysis software. The constants represent percentages of the inter-ASIS distance, and were expressed relative to the midpoint between the two ASIS markers. Hip center locations calculated from ultrasound were subtracted from the hip center locations derived using each of the four methods. The resulting linear difference scores were analyzed using planned comparisons (t-tests) with a Bonferroni correction to hold the experiment-wise a level at 0.05. Comparisons of linear differences that yielded significant results were further analyzed to determine whether the hip center estimates were different along specific anatomical axes. The absolute distance along each axis was compared to determine the accuracy of each method in the three anatomical planes and the signed distance was averaged and compared to determine the general direction of the error.
142
J.L. Hicks, J.G. Richards / Gait & Posture 22 (2005) 138–145
Fig. 3. Percentage of area in surface plots with less than 1 cm error. The two iterative algorithms were significantly more accurate than the non-iterative algorithm. The Newton method was slightly more accurate than the Downhill Simplex method at the highest noise level.
Fig. 5. Centroid error map for the iterative, Downhill Simplex sphere-fitting algorithm with a noise level of 5% of the radius. Error is shown as a function of the angle of flexion–extension and abduction–adduction.
3. Results
3.2. Clinical assessment
3.1. Computer simulation
The four methods of finding hip joint centers were first compared by calculating the linear distance between the hip joint center derived by each method and the location of the hip joint center measured by the ultrasound. Comparing the linear difference scores indicated that the sphere fitting from the SLM trial, with a mean linear difference of 1.34 cm, was significantly more accurate than the three other methods (Table 1). The sphere fitting from the SLM trial was followed in accuracy by the traditional predictive method, with a mean of 2.16 cm, then the sphere fitting using walking data. The HH walking data, with a mean of 4.22 cm, was also significantly closer to the ultrasound than the CC walking data, with a mean of 10.29 cm. The components of the hip center error along the anatomical axes were calculated for each algorithm. In the inferior–superior direction, there was no significant difference between the SLM trial and the predictive methods. The predictive method tended to locate the hip joint center superior to the ultrasound, while the sphere fitting from the SLM trial located the hip center slightly inferior, and the two walking methods located the hip center significantly inferior to the ultrasound (Table 2). There was no significant difference in the absolute error in the anterio–posterior direction between the predictive, SLM or HH walking methods with a mean around 0.8 cm for all three methods. Sphere fitting using the CC walking data was significantly less accurate than all three other methods. The error for the predictive method was evenly dispersed along this axis, while the sphere fitting from the SLM trial tended to locate the hip center posterior to the ultrasound and the two walking methods located the hip center anterior to the ultrasound. In the medial–lateral direction, the SLM sphere-fitting method was evenly dispersed in both directions, while the predictive method tended to locate the hip center medial to the ultrasound in most subjects. Both sphere-fitting methods
When testing the three sphere-fitting algorithms under ideal conditions, with low levels of noise and a high range of motion, there was no significant difference between the algorithms. Restricting the range of motion and increasing the percentage of noise resulted in a drastic reduction in performance of the non-iterative algorithm when compared to the two iterative algorithms (Fig. 3). There was only a difference between the two iterative algorithms at a noise level of 5% (Figs. 4 and 5), where the Newton method slightly outperformed the Downhill Simplex method when comparing the percentage of area in the plots with less than 1 cm approximation error (Fig. 3). Thus for the clinical part of the study, the Newton method was used for sphere fitting.
Fig. 4. Centroid error map for the iterative, Newton sphere-fitting algorithm with a noise level of 5% of the radius. Error is shown as a function of the angle of flexion–extension and abduction–adduction. Data points are averaged for five random sets of data. Error was below 1 cm (blue and dark green) with flexion greater than 458 and abduction greater than 158.
J.L. Hicks, J.G. Richards / Gait & Posture 22 (2005) 138–145
143
Table 1 Mean (S.D.) distance scores (cm) for the four methods of locating the hip joint center (N = 18) Predictive Linear Inferior–superior Anterior–posterior Medial–lateral a
SLM sphere a
1.34 0.74 0.84 0.64
2.16 (0.53) 1.3 (0.62) 0.81 (0.44) 1.21 (0.57)a
CC walking sphere
a
(0.43) (0.46) (0.48) (0.31)a
10.29 4.56 1.59 5.26
HH walking sphere
a
4.22 (2.32)a 2.23 (1.82)a 0.8 (0.54) 2.98 (2.24)a
(4.61) (1.97)a (0.83)a (2.30)a
Significantly different from all other methods (P < 0.0083).
using walking data located the hip center lateral to the ultrasound, with the CC marker set significantly more lateral than the HH marker set.
4. Discussion The results of the computer simulation indicated that the two iterative methods of sphere fitting—the Newton and Downhill Simplex methods—were far more accurate than the non-iterative, least-squares approach with smaller ranges of motion and higher levels of noise. This is expected since the iterative methods, in theory, improve on the initial guess from the least squares approximation. The Newton method also seemed to perform slightly better than the Downhill Simplex method when the noise was greater than 4% of the radius of the sphere. There is a conceptual difference between these two algorithms–the Downhill Simplex method, an optimization algorithm which minimizes the sum of the squared error, finds some local minimum instead of the global minimum by ‘‘sliding downhill’’ along the error function [9]. In contrast, the Newton method is an attempt to find a sphere where the error associated with each individual point is zero. It is also possible that a more powerful type of optimization algorithm, like those using the derivative of the function to be minimized, might be more accurate [9]. The stopping tolerances used in the two algorithms might have also affected the accuracy. Still, the Newton method seemed to perform well, and using an optimization algorithm that utilizes the derivative would probably yield very similar results. Based on these findings, only the Newton method was applied to data collected from subjects. The error plots generated by the computer simulation also suggest requirements for joint ranges of motion necessary to produce accurate results when the noise is expressed as a specific percentage of the radius. With the noise level at 5% of the radius, the Newton method produced accurate results Table 2 Mean (S.D.) signed distance scores (cm) along the three anatomical axes (N = 18) Predictive Inferior Anterior Lateral
1.22 0.07 1.18
SLM sphere 0.18 0.70 0.17
CC walking sphere 4.51 1.57 4.77
HH walking sphere 1.80 0.50 0.74
with error less than 1 cm when the range of flexion– extension was greater than 458 and the range of abduction– adduction was greater than 108. These ranges should be feasible for the majority of the patient population to attain either actively or with the help of a clinician. In the clinical part of the analysis, physical assessments of hip joint centers were derived from images obtained using a targeted ultrasound probe. Results from the other methods were then compared to this data. The functional method, used with data generated from a standing leg motion trial, produced results significantly more accurate than the predictive method. The sphere-fitting method from an SLM trial had a lower mean error, as well as a lower maximum error when compared to the predictive approach. The error found in this study is consistent with the results of Leardini et al. [7] who compared the functional method to a radiographic standard. Although the predictive approach was very accurate for a small portion of subjects in the study, its use resulted in a higher error overall and also a potential for greater error in individual subjects (Table 3). It could be argued that using different constants for the predictive Table 3 Hip constants from ultrasound as % of ASIS breadth, with origin at midpoint of ASIS markers Subject
Inferior
Posterior
Lateral
1-R 1-L 2-R 2-L 3-R 3-L 4-R 4-L 5-R 5-L 6-R 6-L 7-R 7-L 8-R 8-L 9-R 9-L
32.09 32.31 37.21 36.70 39.81 37.39 30.35 34.46 41.09 41.07 36.64 37.43 41.77 42.39 44.91 39.68 40.01 38.66
17.82 16.96 23.71 23.91 25.10 26.89 23.12 25.24 21.10 18.01 17.48 16.48 22.35 23.76 24.01 26.40 18.75 22.24
35.97 36.29 38.67 38.20 33.89 38.87 32.36 38.53 34.51 37.75 36.27 30.40 33.53 36.64 43.06 41.63 38.35 40.26
Minimum Maximum
30.35 44.91
16.48 26.89
30.40 43.06
Average OrthoTrak Bell
38.00 34 30
21.85 22 19
36.95 32 36
144
J.L. Hicks, J.G. Richards / Gait & Posture 22 (2005) 138–145
approach would have yielded more accurate results. While the error for the predictive approach was not biased along the anterio–posterior axis, the predicted hip center estimates tended to be superior and medial to the ultrasounddetermined hip center, suggesting that the hip constants have some degree of specificity to the sample from which they were derived. In addition, a more individualized set of constants for the group could easily be derived from the ultrasound measures (Table 3). Using the averaged, ultrasound-based constants in this study would have decreased the error for the sample of the population tested; however, the traditional predictive approach still assumes that pelvic geometry is similar across all body types, and similar errors would be seen when applying the ultrasound constants from this study to another sample of the population. Previous studies investigating the effect of hip joint center mislocation on kinematics and kinetics found that displacement of the joint center in the anterio–posterior and medial–lateral directions had the greatest effect at the hip and knee [4,5]. While there was no difference between the predictive, SLM or HH walking methods in the anterio–posterior direction, the SLM sphere-fitting method was significantly more accurate in the medial–lateral direction. However, it is likely that error in the anterio– posterior direction would be greater in an obese population when the ASIS markers are covered with a thicker layer of soft tissue and palpation is difficult. This would have the effect of moving the origin of the pelvic coordinate system, and thus the hip joint centers, anterior to their true location. While the SLM sphere-fitting approach was more accurate than the predictive approach, it did not achieve the level of accuracy suggested by the computer simulation or previous research using a mechanical apparatus [8]. The most likely cause of this discrepancy is a difference in noise characteristics between the two types of data sets. In the computer simulation, the noise was random throughout the range of motion. Examining the data from the SLM and walking trials suggests that there is more systematic error as a function of both the limb movement speed and hip angle. For the SLM trials, this noise was minimized by instructing the subjects to move the leg slowly and deliberately throughout the range of motion. The effect of thigh velocity on the accuracy of sphere fitting was not quantified, but instructing the subjects to move their leg slowly and deliberately tended to improve the results. It was noted that when subjects moved their leg through the ranges of motion in a rapid, ballistic manner, the estimates from the spherefitting method were consistently inferior relative to the ultrasound measure, sometimes by several centimeters. This resulted from a change in the arc of the knee marker, presumably due to soft tissue motion associated with higher movement velocities. The error in using the walking data for sphere fitting partly resulted from a smaller range of motion in
abduction–adduction than in the SLM trials. A similar result was found in a recent study by Piazza et al. [11] that applied the sphere-fitting method to several functional activities. In addition, there was systematic error in the walking trial data sets that appeared to be a function of the angle of flexion and the phase in stride. Similar patterns of error were seen with both the HH and CC data sets, although in the CC walking trials, this error was magnified. The largest error was seen in the lateral and inferior directions. Examining the location of the reconstructed knee center shows that it was farther from the hip center during swing phase than during stance phase. Since the hip is more abducted during swing phase, this had the effect of moving the sphere and derived hip center laterally. With a greater distance between the knee and hip center during swing phase, and a smaller distance at toe-off and especially heel strike, the arc being fit to the sphere became deeper resulting in a sphere inferior to the true hip center. In addition, the distance between the knee and hip center increased as the angle of flexion increased. This had the effect of moving the sphere anterior. The trends in error seen in the data can best be explained by movement of the soft tissue as a result of acceleration of the leg at heel strike and during swing phase. The higher error found in the CC walking set suggests that there was greater soft tissue motion associated with the thigh markers than with the lateral knee marker used in the HH marker set. Since the reconstructed knee center was used to fit the sphere, this has implications for the accuracy of other aspects of gait analysis when using a CC instead of a HH marker set. The sphere-fitting approach from an SLM trial was found to be significantly more accurate than the predictive approach in this study. However, it is more labor intensive, requiring the recording and tracking of an 8–12 s static trial for each leg. In this study, the predictive approach was 2.16 cm away from the ultrasound-determined hip center on average, which is enough to result in noticeable changes in hip kinetics and kinematics if the error is in the AP or ML directions. If higher accuracy of hip joint kinematics and kinetics is desired, an SLM trial is justified. Another advantage of the sphere-fitting method is its independence from pelvic geometry, as it will not be affected by dimensional exaggerations or asymmetries in the pelvis. In addition, the functional method does not depend on accurately locating three specific anatomical landmarks on the pelvis. As long as three markers are fixed on the pelvis in an arrangement that allows for good estimates of pelvic orientation, the sphere-fitting method will work as intended. In some patients, the ASIS can be covered by soft tissue, and when walkers or crutches are used, traditional ASIS markers can be blocked from the cameras. In cases such as these, moving markers to more accessible locations on the pelvis (i.e. a triad over the sacrum) would facilitate the imaging process, and using the sphere-fitting method would provide a means to accurately determine the hip center locations.
J.L. Hicks, J.G. Richards / Gait & Posture 22 (2005) 138–145
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.gaipost. 2004.08.004.
References [1] Seidel GK, Marchinda DM, Dijkers M, Soutas-Little RW. Hip joint center location from palpable bony landmarks—a cadaver study. J Biomech 1995;28:995–8. [2] Marchinda D, Seidel G, Alderink G, Bothner K. A comparison study of hip joint center location models. In: Proceedings of the Fourth Annual Gait and Clinical Movement Analysis Meeting. Gait Post 1999;9:132–3. [3] Kirkwood RN, Culham EG, Costigan P. Radiographic and non-invasive determination of the hip joint center location: effect on hip joint moments. Clin Biomech 1999;14:227–35. [4] Stagni R, Leardini A, Capozzo A, Grazia Benedetti M, Capello A. Effects of hip joint center mislocation on gait analysis results. J Biomech 2000;33:1479–87.
145
[5] Holden JP, Stanhope SJ. The effect of uncertainty in hip center location estimates on hip joint moments during walking at different speeds. In: Proceedings of the Fifth Annual Gait and Clinical Movement Analysis Meeting. Gait Post 2000;11:119–20. [6] Bell AL, Pedersen DR, Brand RA. A comparison of the accuracy of several hip center location prediction methods. J Biomech 1990;23:617–21. [7] Leardini A, Cappozzo A, Catani F, Toksvig-Larsen S, Petitto A, Sforza V, Cassanelli G, Giannini S. Validation of a functional method for the estimation of hip joint center location. J Biomech 1999;32: 99–103. [8] Piazza SJ, Okita N, Cavanagh PR. Accuracy of the functional method of hip joint center location: effects of limited motion and varied implementation. J Biomech 2001;34:967–73. [9] Press WT, Flannery BP, Teukolsky SA, Vetterling WT. Numerical recipes: the art of scientific computing. Cambridge: Cambridge University Press, 1986. [10] OrthoTrak 4.2 Gait Analysis Software Reference Manual. Santa Rosa, CA: Motion Analysis Corporation; 2000. [11] Piazza SJ, Erdemir A, Okita N, Cavanagh PR. Assessment of the function method of hip joint center location subject to reduced range of motion. J Biomech 2004;37:349–56.