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Prediction of hip joint centre location from external landmarks
Human Movement North-Holland
Science 8 (1989) 3-16
PREDICTION OF HIP JOINT CENTRE LOCATION FROM EXTERNAL LANDMARKS * Alexander L. BELL, Richard The University
A. BRAND
and Douglas
R. PEDERSEN
of Iowa Hospitals, Iowa City, USA
Bell, A.L., R.A. Brand and D.R. Pedersen, 1989. Prediction of hip joint centre location from external landmarks. Human Movement Science 8, 3-16.
The approaches to predicting the hip joint centre (HJC) location of Tylkowski’s group and Andriacchi’s group were evaluated for accuracy and validity in children and adults of both sexes. Using Tylkowski’s approach, we found that the three-dimensional (3-D) HJC location in adults (expressed as a percentage of the distance between the anterior superior iliac spines (ASK)) was 30% distal, 14% medial, and 22% posterior to the ASIS, and predicted the HJC location to within 3.3 cm of the true location with 95% certainty. Using Andriacchi’s approach. we found that the HJC was located in the frontal plane distal and lateral to the midpoint of a line between the ASIS and pubic symphysis, and varied from 2.2 cm distal and 0.78 cm lateral in girls to 4.6 cm distal and 1.7 cm lateral in men. A more accurate method of estimating the 3-D HJC location combined a modification of Andriacchi’s approach (estimating frontal plane location of HJC) with a modification of Tylkowski’s approach (estimating HJC location posterior to a frontal plane). and could predict the HJC location in adults to within 2.6 cm of the true location with 95% certainty.
Introduction Locating the hip joint centre (HJC) from external landmarks is important for many types of gait analysis studies. The HJC location is required to estimate pelvi-femoral motion and to calculate moment arms about the hip in inverse dynamics studies of hip joint forces (e.g., Cappozzo et al. 1975; Cappozzo and Gazzani 1986; Crowninshield et * The authors wish to thank Rose Britton for help in preparing the manuscript and the University of Iowa Department of Anthropology for making the pelves available. This work was supported in part by NIH grants AM35510 and AM07075-13, and a gift from the Tektronix Corporation. Requests for reprints should be sent to R.A. Brand. Dept. of Orthopaedic Surgery, The University of Iowa Hospitals, Iowa City, IA 52242, USA.
0167-9457/89/$3.50
0 1989, Elsevier Science Publishers
B.V. (North-Holland)
4
A.L. Bell et al. / Locating the HJC from external landmarks
al. 1978; Eberhart and Inman 1951; Ellis et al. 1979; Harrington 1976; Johnston et al. 1979; Paul 1965; Paul and Poulson 1974; Pedotti 1977; Seedhom and Teroyama 1976). However, the HJC’s location deep beneath the soft tissues of the hip precludes its exact determination in vivo without the aid of x-rays. Investigators have attempted to estimate the HJC’s location in the living subject by a variety of methods. The most common approach has been to estimate its location using the experimenter’s general knowledge of externally identifiable landmarks (Eberhart and Inman 1951; Harrington 1976; Paul 1965; Pedotti 1977). Some have used radiographs to precisely locate the HJC (Crowninshield et al. 1978; Ellis et al. 1979; Johnston et al. 1979). Others made no mention of how they found the location used in their calculations (Cappozzo et al. 1975; Cappozzo and Gazzani 1986; Paul and Poulson 1974; Seedhom and Teroyama 1976). No method is entirely satisfactory. While orthogonal x-rays will precisely locate the HJC, there are considerable logistical difficulties in taking, developing, and interpreting radiographs. Additionally, many individuals (children and adults of child-bearing age) should not be exposed to unnecessary ionizing radiation. La&in (1984) has shown that external estimation of HJC location is frequently inaccurate. During each of 25 consecutive total knee arthroplasties, surgeons estimated and localized with a radiopaque marker the location of the HJC. The true location was then determined by an AP radiograph, and the two were compared. Twenty percent of the time the true location of the femoral head center (hip joint centre was over 4 cm away from the surgeon’s estimate and in only 12% of the cases was the surgeon’s estimate within 2 cm of the actual femoral head centre. Obviously, then, estimation is inaccurate (88% of the time a greater than 2 cm error). To improve upon external estimates, several investigators developed approaches to estimate HJC location from palpable landmarks. Tylkowski et al. (1982) expressed HJC location as a constant percentage of the distance between the anterior superior iliac spines (ASIS). Specifically, they predicted that the joint centre was located 11% of the inter-ASIS distance (ASIS-ASIS) medial, 12% distal, and 21% posterior (along a line perpendicular to the plane created by the two ASIS’s and the public symphysis) to the ASIS. They developed this relationship from examining a number of children’s x-rays but pro-
A.L. Bell et al. / Locating the HJC from external landmarks
5
vided few details. Andriacchi et al. (1980; 1982; Andriacchi and Strickland 1983) predicted that the HJC would be found 1.5 cm or 1.5 to 2 cm distal to the midpoint of a line between the ASIS and the pubic symphysis in the frontal plane and an unspecified distance medial to the greater trochanter, but did not report how they devised these formulas. Neither group addressed whether the formulas were valid for children and adults of both sexes or just for certain population groups. The purposes of our study were to (1) determine the validity and accuracy of the approaches of Tylkowski and Andriacchi in children and adults of either sex, (2) develop a new method, should their approaches fail to predict the HJC location reasonably accurately, and (3) quantitate the confidence with which the various approaches can be applied in the experimental or clinical settings.
Materials and Methods We obtained the AP pelvic radiographs of 39 children (15 males, 24 females) and 31 adults (15 males, 16 females). The children were all between the ages of four and ten when the x-rays were taken, and the adults were 21 or older. All x-rays were read as having a normal bony framework by a staff radiologist. The x-rays were placed on a Graf/Pen Sonic Digitizer and six symmetrical points about the bony pelvis and hip were digitized: bilateral anterior superior iliac spines (ASIS), femoral head centers (FHC), and pubic tubercles (PT). The HJC was established as the centre of a series of concentric circles matched to the size of the particular femoral head shadow. The other two points (ASIS and PT) were easily palpable but not radiographically distinctive landmarks, and it was necessary to estimate their locations on an AP x-ray. We took a series of AP and right lateral x-rays of 20 skeletal pelves with radiopaque markers on these palpable landmarks and noted their usual locations in the AP view in relation to several radiographic landmarks (fig. la and b). These pelves were from adult males and females, but the sex of individual specimens was not known. The ASIS markers were approximately 1 cm directly superior to the point where the inferior iliac wing shadow turns from being predominantly horizontally-oriented to a more vertical orientation. There was almost always a vertical line visible on the radiograph that defined the medial border of that prominence. The pubic tubercles
I
A.L. Bell et al. / Locating the HJC from external landmarks Table 1 Actual hipjoint centre location from the ASIS as a percentage of ASK-ASIS Medial
Distal
Boys Girls Men Women Children (Average) Adults (Average) Boys (Average Girls (Average) Men (Average) Women (Average) Overall (Average)
distance.
Posterior
Right
Left
Right
Left
30% 28% 31% 29%
29% 28% 31% 29%
15% 15% 14% 14%
16% 16% 15% 15%
_ _ _ _
_
29%
0 = 3.3
16%
0=1.9
30%
0 = 3.5
14%
(T= 2.4
30%
D = 3.6
15%
a=2.3
_
28%
Q = 3.1
16%
(r =1.6
_
31%
0=3.6
14%
(T= 2.4
_
29%
0 = 3.4
15%
0=3.1
_
29%
0 = 3.4
15%
0=2.1
_
22%
0 = 3.0
were found to be directly superior to the most medial extension of the obturator foramen and approximately 1 cm below the superior pubic border shadow. The AP and right lateral x-rays of the 20 skeletal pelves were taken with the pelves within a wire cage x-ray surveying device that established a fixed reference frame and permitted 3-D coordinate estimation of the points of interest from the biplanar x-rays. This method is similar to that used by Brown et al. (1976) and Brand et al. (1982). The HJC’s were taken to be the centre of a solid plastic half-sphere matched to the size of the acetabulum and attached by clay. The x-rays were placed on the Graf-Pen Sonic Digitizer and the ASIS’s, HJC’s, and PT’s digitized in both the AP and lateral views.
Fig. 1. AP (A) and lateral (B) x-rays of skeletal pelvis showing location of palpable landmarks: anterior superior iliac spines and pubic tubercles. The lateral border of anterior superior iliac spines were edged with wire for better definition, and round markers were glued anterior to the landmarks in locations simulating markers used in gait studies (but without overlying soft tissues).
8
A. L. Bell et al. / Locating the HJC
fromexternal
Table 2 Actual hip joint centre location from the ASIS as a percentage adults (N = 31) vs. adult dry pelves (N = 20).
landmarks
of ASIS-ASIS
Distal
distance
for living
Medial
Adult x-rays
30b
0=3.5
14%
c = 2.4
Adult dry pelvis x-rays
31%
0 = 5.5
14%
0 = 3.3
After being stored in a VAX/VMS computer file, the digitized two-dimensional (2-D) coordinates from the 70 AP radiographs of the living subjects were separated into four groups: boys, girls, men, and women. In order to examine Tylkowski’s approach, we calculated the distance between the ASIS’s for each individual and described the actual positions of the HJC’s (left and right) as a percentage of that distance from the respective ASIS. This is expressed in its components of horizontal (medial) and vertical (distal) distance from the ASIS (table 1).
Table 3 Actual hip joint centre location pubic symphysis.
in centimeters
from the midpoint
Distal
Boys Girls Men Women Children (Average) Adults (Average) Boys (Average) Girls (Average) Men (Average) Women (Average)
of a line between
Lateral
Right
Left
Right
Left
2.6 2.3 4.6 3.7
2.5 2.2 4.6 3.7
1.0 0.9 1.9 1.6
0.7 0.7 1.5 1.3
2.3
c = 0.38
0.82
o = 0.41
4.1
0 = 0.77
1.6
c = 0.64
2.5
0 = 0.40
0.87
D = 0.46
2.2
0 = 0.34
0.78
c = 0.38
4.6
o = 0.69
1.7
r~= 0.64
3.7
Q = 0.55
1.5
0 = 0.64
the ASIS and
A.L. Bell et al. / Locating the HJC from external landmarks
Fig. 2. Three-dimensional 95% confidence interval (+ 1.96 u) around hip joint center (proportion of box to actual femoral head size is approximately correct).
In order to find the distance from the ASIS to the HJC in the AP direction, we calculated the 3-D coordinates of the digitized landmarks from the series of 20 adult skeletal pelvis AP and lateral x-rays. The ASIS’s and the PT’s defined the frontal plane and, using the lateral x-rays, we measured the distance posterior from that plane to the HJC and expressed it as a percentage of ASIS-ASIS separation. We also calculated the percentages for the distal and medial directions from the AP x-rays and compared them to those we obtained for the living adults in the first part of our study (table 2). To examine the approach of Andriacchi’s group, we found the midpoint of the line between the PT’s and assumed this to be the pubic symphysis. The midpoints of lines drawn between this point and the ASIS’s were found and the distances to the respective HJC’s were calculated in cm. Once again, they are expressed in their component horizontal (lateral) and vertical (distal) distances (table 3). We calculated 95% confidence intervals around the actual HJC for each approach using the respective standard deviations (a) in each dimension. This yielded a rectangle, when examining their predictions in the 2-D frontal plane, or a box, when examining their 3-D predictions, with sides of length 3.92 u( + / - 1.96 a). The length of the diagonal, i.e., the furthest the predicted HJC location could be from the true HJC location, was found by using the Pythagorean Theorem (fig. 2).
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A.L. Bell et al. / Locaiing the HJC from external landmarks
Results
Using Tylkowski’s approach of distance expressed as a percentage of ASIS-ASIS separation, we found that the actual 3-D HJC location averaged 30% distal, 14% medial, and 22% posterior to the ASIS in adults (table 1). The percentages were within 3% of each other in the distal direction and within 2% of each other in the medial direction for all four population groups, and there is excellent agreement between the percentages obtained from the AP x-rays of the living adults and the adult skeletal pelves (table 2). In two dimensions, we could predict the location of the HJC with 95% certainty to within 1.5 cm in children and within 2.7 cm in adults, of the true HJC location (table 4). In three dimensions, we could predict the location of the HJC in adults with 95% certainty to within 3.3 cm of the true location (table 4). Using Andriacchi’s approach of describing the HJC location from the midpoint of the line between the ASIS and pubic symphysis, we found that it was distal and lateral to that point in all four population groups (table 3). The exact distances varied from a low of 2.2 cm distal and 0.78 cm lateral in girls to a high of 4.6 cm distal and 1.7 cm lateral in men. In two dimensions, we could predict the HJC location with 95% certainty to within 1.1 cm in children, within 1.6 cm in women, and within 1.8 cm in men, of the true location (table 4). A hybrid method combining the frontal plane approach of Andriacchi with our distance (Tylkowski’s approach) posterior percentage of ASIS-ASIS
Table 4 A comparison of the accuracy dimensions using 95% confidence
of the HJC intervals.
location
prediction
methods
in two
Three dimensions
Two dimensions (frontal plane) (cm) Children
Adults
Adults
Tylkowski’s approach
1.5
2.7
3.3
Andriacchi’s approach
1.1
1.6 (women) 1.8 (men)
_
Combined approach
_
_
2.6
(cm)
and
three
A. L. Bell et al. / Locating the HJC from external landmarks
11
predicts the HJC location with 95% certainty to within 2.6 cm of the true location in adults (table 4). Discussion There are significant differences between actual HJC location and the locations estimated by the methods of Tylkowski’s group and Andriacchi’s group. There are also some significant differences between the population groups in our study, particularly when using Andriacchi’s method. Each method will be separately reviewed, its applicability to the general population and population subgroups examined, and its accuracy quantitated. Tylkowski’s group determined their relationship by examining the AP and lateral pelvic x-rays of 200 patients followed at the Children’s Hospital Medical Center (Boston) Growth Study Clinic and used five skeletal pelves to calculate the distance from the ASIS to the hip center, but gave no details of either procedure. The percentages they reported (12% distal, 11% medial, and 21% posterior to the ASIS) are considerably different from the ones we obtained (30% distal, 14% medial, and 22% posterior). Since no details are given as to their experimental method, it is difficult to analyze possible reasons for the discrepancy. The x-rays they examined were not those of normal children but children followed at a growth study clinic who carried a variety of diagnoses (cerebral palsy, spina bifida, acetabular dysplasia, etc.) causing a leg length discrepancy. Perhaps bony pelvic growth and/or acetabular location were also abnormal. They state that the actual percentages were derived from five skeletal pelves but make no mention of the pelves’ origin, sex, or age. A third factor may well be a consequence of the inherent magnification of x-rays. The ASIS’s, being anterior to the femoral head and thereby farther from the film in an AP radiograph, would be shifted more laterally and superiorly than the HJC by a radiation source aimed at the center of the pelvis. On the x-ray, it would appear as though the HJC was more inferior and medial to the ASIS than is actually the case in a living person or skeletal pelvis. This would result in an apparently greater absolute distance between the ASIS and HJC which would be expressed as larger percentages of the ASIS-ASIS separation. On the other hand, the ASIS-ASIS distance would also be greater and this would tend to reduce the percentages.
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A. L. Bell et al. / Locating the HJC from externul landmarks
Though the percentages were different from those reported by Tylkowski’s group, we obtained excellent consistency throughout all the population groups in our study. There is a 3% (28% vs. 31%) difference between the percentages of the lowest subgroup (girls) and the highest subgroup (men) in the distal direction (table 1). Correspondingly, there is a 2% (16% vs. 14%) difference in the percentages of the same two groups in the medial direction. Both differences are within one standard deviation of the respective means, and a Student’s t-test determined that neither difference was statistically significant. The data for the third (posterior) direction was derived from x-rays of adult skeletal pelves of unknown sex and cannot be grouped according to sex, although the percentages for the distal and medial directions derived from these x-rays showed excellent agreement with the percentages derived from the x-rays of living adults used in the first part of the study (table 2). Another important difference between our data and Tylkowski’s is the size of the standard deviations. They reported a standard deviation of 1% in all three dimensions. Our overall standard deviations were just over 3% (3.1%-3.6%) in the distal direction, about 2% (1.6%-2.6%) in the medial direction, and 3% in the posterior direction (table 1). Once again, it is difficult to pinpoint the probable causes of these two- and three-fold differences. There are the inherent difficulties in insuring standard x-ray techniques. Also, it is very difficult to precisely locate the ASIS in an AP radiograph. The most significant factor may well be the difference in sample size (5 in their study vs. 70 in ours) which, alone, could account for the discrepancies. The standard deviations affect the confidence with which the estimated HJC location can be used in the force prediction models mentioned in the Introduction. Using our mean ASIS-ASIS distance of 19.23 cm in children and 30.99 cm in adults, the standard deviations become 0.64 cm (children) and 1.1 cm (adults) in the distal direction, 0.36 cm (children) and 0.75 cm (adults) in the medial direction, and 0.93 cm (adults) in the posterior direction. The reader will recall that the dry pelves used to calculate the percentage in the third (AP) dimension were all from adults and we have no data on the antero-posterior location of the HJC in children. Calculating confidence intervals (+ 1.96 a) about the HJC shows that 95% of the time the actual HJC location will be within 1.5 cm in children and within 2.7 cm in adults of our predicted 2-D (distal and medial) location, and
A.L. Bell et al. / Locating the HJC
fromexternal landmarks
13
within 3.3 cm in adults of our predicted 3-D location (table 4). This is a significant improvement over the external estimation figures of Laskin, which showed surgeons to be able to estimate the position of the HJC in the 2-D frontal plane to within 2 cm or less of the actual HJC location only 12% of the time. We were unable to find any data on the accuracy of 3-D estimation. Although Andriacchi’s group did not describe the basis of their model, they predicted the HJC would lie 1.5 or 1.5 to 2 cm directly below the midpoint of a line between the ASIS and the pubic symphysis in the frontal plane. We obtained a consistent lateral component in all groups (table 3). This was approximately twice as large in adults as it was in children (1.6 cm vs. 0.82 cm), and the difference was significant (p < 0.05). The differences between the boys’ and girls’ values, as well as between the men’s and women’s values, were not significant, however. In no case was 0.0 cm, or no lateral component, within a 95% confidence interval ( f 1.96 a) of our means, indicating there is almost no chance that the differences between our figures and Andriacchi’s are due to random error. We also obtained somewhat different results as well as considerable intergroup variation in terms of the distal component. The best agreement of our figures with those of Andriacchi’s group came in children, where our mean of 2.3 cm (u = 0.38) was within one standard deviation of the upper end of their interval of 1.5 to 2.0 cm. Within this group, there was not a significant difference between the boys (2.5 cm, (J = 0.40) and girls (2.2 cm, u = 0.34) mean values. Less agreement was present in women (3.7 cm, (J = 0.55) and men (4.6 cm, u = 0.69). Student’s t-tests verified significant differences between the men’s and women’s values as well as between either group and the children’s values. Since the basis for this method of estimation is not reported, it is difficult to identify the possible sources of the differences between the data. Although we were unable to find documentation of the basis of Andriacchi’s approach in the literature, they did report an estimate of the error involved in predicting the HJC location by their method (Andriacchi and Strickland 1983). They examined the AP pelvic x-rays of 20 patients free of hip pathology and measured the distance between the point 1.5 cm directly below the midpoint of the ASIS-pubic symphysis line and the actual HJC. After correcting for magnification, they found that the average error was 0.79 cm. We found that the
14
A. L. Bell et al. / Locating the HJC from external landmarks
distance between that point and the actual HJC on x-rays varied from a low of 1.0 cm for girls to a high of 3.5 cm for men (using our distal value less 1.5 cm and our lateral value in the Pythagorean Theorem). Assuming 20% x-ray magnification, these figures become 0.83 cm for girls and 2.9 cm for men. The reasons for the discrepancy in the figures are unclear. Andriacchi does not report the age or sex of the 20 patients whose pelvic x-rays were used in the error analysis, but all our groups had a larger error than their figure of 0.79 cm and the size of the error in our adults (men and women) was approximately three to four times as large. Both sets of data were corrected for x-ray magnification, and 15-20% is generally accepted as the amount of magnification in a standard x-ray. We conclude that Andriacchi’s estimate of 0.79 cm of error between the predicted and actual HJC locations is relatively accurate only in children and that the error in adults is several times larger than that figure. Using our data and Andriacchi’s approach, 95% of the time the true 2-D (distal and lateral) HJC location will be within 1.1 cm in children, 1.6 cm in women, and 1.8 cm in men of the predicted location (table 4). This is much more accurate than external estimation (only 12% of the time within 2 cm, according to Laskin) and somewhat more accurate than our percentage modifications of Tylkowski’s approach. However, its relative usefulness may be hampered by the fact that separate formulas are needed for children, women, and men, whereas Tylkowski’s approach allows one to use the same formula for all groups. Andriacchi estimated the position of the HJC in the third (AP) dimension relative to the greater trochanter, but did not report the distance they used nor the errors of that procedure. As the respective femora of the skeletal pelves we used to find the antero-posterior location of the HJC were not available, we cannot describe the position of the HJC relative to the greater trochanter and, therefore, cannot predict the 3-D location of the HJC using Andriacchi’s approach. A more accurate method of predicting the 3-D HJC location with our data combined the two approaches. Andriacchi’s approach is the more accurate method of predicting the HJC location in the frontal plane. At least in adults, Tylkowski’s approach and our figure of 22% (a = 3.0) of the ASIS-ASJS distance can predict the HJC’s antero-posterior location in relation to the frontal plane. Combining these components and constructing a 3-D 95% confidence interval predicts the 3-D location of the HJC to within 2.6 cm of the true
A. L. Bell et al. / Locating the HJC from external landmarks
15
location with 95% certainty (table 4). This compares favorably with the figure of 3.3 cm we calculated using Tylkowski’s approach and our data. It appears that Andriacchi’s approach to locating the HJC in the frontal plane combined with Tylkowski’s approach to predicting its distance posterior to the frontal plane is a more accurate method of predicting the 3-D location of the hip joint center than either approach alone. Our evaluation of these methods has one limitation which should be mentioned. The measurements were taken from the radiographic bony landmarks and did not involve prior placement of skin markers over the palpable landmarks in living subjects as La&in did and as would take place in actual in vivo gait analysis studies. Thus, the possible contributions of the soft tissue over the ASIS’s and pubic symphysis to HJC estimation error were not quantitated. As these landmarks are very superficial, we would expect relatively little contribution from this factor in the average person, but this may not be true in a person with more adipose tissue. In that case, our error estimates would likely be too small. In summary, Tylkowski’s approach of predicting the 3-D HJC location as a percentage of ASIS-ASIS separation yields consistent results in all groups, but we obtained significantly different percentages than the ones they reported. The standard deviations are significant and, while the approach is considerably more accurate than the frequently used method of external estimation, it is yet to be determined whether the standard deviations are too large for the modified formula to be useful in hip joint force studies. Andricchi’s approach of predicting the HJC location from the midpoint of the line between the ASIS and pubic symphysis yielded more accurate predictions in the frontal plane but required addition of a lateral component in all groups and separate formulas for children, women, and men. A more accurate method of predicting the 3-D location of the HJC combines a modification of Andriacchi’s approach to estimation in the frontal plane with a posterior percentage modification of Tylkowski’s approach, and can predict the HJC location to within an inch of the true location in all adults. All methods appear more accurate than external estimation and safer and more efficient than x-rays.
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References Andriacchi, T.P. and A.B. Strickland, 1983. Gait analysis as a tool to assess joint kinetics. Proceedings of NATO Advanced Study Institute Biomechanics of Normal and Pathological Articulating Joints, pp. 833102. Andriacchi, T.P., J.O. Galante and R.W. Fermier, 1982. The influence of total knee-replacement design on walking and stair-climbing. Journal of Bone and Joint Surgery 64-A, 1328-1335. Andriacchi, T.P.. G.B.J. Andersson, R.W. Fermier, D. Stern and J.O. Galante, 1980. A study of lower-limb mechanics during stair-climbing. Journal of Bone and Joint Surgery 62-A, 749-757. Brand, R.A., R.D. Crowninshield, C.E. Wittstock. D.R. Pedersen, C.R. Clark and F.M. van Krieken, 1982. A model of lower extremity muscular anatomy. Journal of Biomechanical Engineering 104, 304-310. Brown, R.H., A.H. Burstein, CL. Nash and C. Schlock, 1976. Spinal analysis using a three-dimensional radiographic technique. Journal of Biomechanics 9, 355-365. Cappouo, A. and F. Gazzani, 1986. Joint functional assessment during physical exercise: Methodological considerations. Proceedings of the 5th Meeting of the European Society of Biomechanics, p. 87. Capozzo, A., T. Leo and A. Pedotti, 1975. A general computing method for the analysis of human locomotion. Journal of Biomechanics 8, 307-320. Crowninshield, R.D., R.C. Johnston, J.G. Andrews and R.A. Brand, 1978. A biomechanical investigation of the human hip. Journal of Biomechanics 11, 75-85. Eberhart, H.D. and V.T. Inman, 1951. An evaluation of experimental procedures used in a fundamental study of human locomotion. Annals of the New York Academy of Science 15, 1213-1228. Ellis, MI., B.B. Seedhom, A.A. Amis, D. Dowson and V. Wright, 1979. Forces in the knee Joint whilst rising from normal and motorized chairs. Engineering in Medicine 8, 33-40. Harrington, I.J., 1976. A bioengineering analysis of force actions at the knee in normal and pathological gait. Biomedical Engineering 11, 167-172. Johnston, R.C., R.A. Brand and R.D. Crowninshield, 1979. Reconstruction of the hip. Journal of Bone and Joint Surgery 61-A, 639-652. Laskin, RX, 1984. Alignment of total knee components. Orthopedics 7, 62-72. Paul, J.P., 1965. ‘Bio-engineering studies of the forces transmitted by joints; (III) Engineering analysis’. In: R.M. Kenedi (ed.), Biomechanics and related bioengineering topics. Oxford: Pergamon Press. pp. 3699380. Paul, J.P. and J. Poulson, 1974. The analysis of forces transmitted by joints in the human body. Proceedings of the 5th International Conference on Experimental Stress Analysis, pp. 34-42. Pedotti, A., 1977. A study of motor coordination and neuromuscular activities in human locomotion. Biol. Cybem. 26, 53-62. Seedhom, B.B. and K. Teroyama, 1976. Knee forces during the activity of getting out of a chair with and without the aid of arms. Biomedical Engineering 11, 278282. Tylkowski, CM., S.R. Simon and J.M. Mansour, 1982. ‘Internal rotation gait in spastic cerebral palsy’. In: J.P. Nelson (ed.), The hip, Proceedings of the 10th Open Scientific Meeting of the Hip Society. St. Louis: C.V. Mosby. pp. 89-125.
Science 8 (1989) 3-16
PREDICTION OF HIP JOINT CENTRE LOCATION FROM EXTERNAL LANDMARKS * Alexander L. BELL, Richard The University
A. BRAND
and Douglas
R. PEDERSEN
of Iowa Hospitals, Iowa City, USA
Bell, A.L., R.A. Brand and D.R. Pedersen, 1989. Prediction of hip joint centre location from external landmarks. Human Movement Science 8, 3-16.
The approaches to predicting the hip joint centre (HJC) location of Tylkowski’s group and Andriacchi’s group were evaluated for accuracy and validity in children and adults of both sexes. Using Tylkowski’s approach, we found that the three-dimensional (3-D) HJC location in adults (expressed as a percentage of the distance between the anterior superior iliac spines (ASK)) was 30% distal, 14% medial, and 22% posterior to the ASIS, and predicted the HJC location to within 3.3 cm of the true location with 95% certainty. Using Andriacchi’s approach. we found that the HJC was located in the frontal plane distal and lateral to the midpoint of a line between the ASIS and pubic symphysis, and varied from 2.2 cm distal and 0.78 cm lateral in girls to 4.6 cm distal and 1.7 cm lateral in men. A more accurate method of estimating the 3-D HJC location combined a modification of Andriacchi’s approach (estimating frontal plane location of HJC) with a modification of Tylkowski’s approach (estimating HJC location posterior to a frontal plane). and could predict the HJC location in adults to within 2.6 cm of the true location with 95% certainty.
Introduction Locating the hip joint centre (HJC) from external landmarks is important for many types of gait analysis studies. The HJC location is required to estimate pelvi-femoral motion and to calculate moment arms about the hip in inverse dynamics studies of hip joint forces (e.g., Cappozzo et al. 1975; Cappozzo and Gazzani 1986; Crowninshield et * The authors wish to thank Rose Britton for help in preparing the manuscript and the University of Iowa Department of Anthropology for making the pelves available. This work was supported in part by NIH grants AM35510 and AM07075-13, and a gift from the Tektronix Corporation. Requests for reprints should be sent to R.A. Brand. Dept. of Orthopaedic Surgery, The University of Iowa Hospitals, Iowa City, IA 52242, USA.
0167-9457/89/$3.50
0 1989, Elsevier Science Publishers
B.V. (North-Holland)
4
A.L. Bell et al. / Locating the HJC from external landmarks
al. 1978; Eberhart and Inman 1951; Ellis et al. 1979; Harrington 1976; Johnston et al. 1979; Paul 1965; Paul and Poulson 1974; Pedotti 1977; Seedhom and Teroyama 1976). However, the HJC’s location deep beneath the soft tissues of the hip precludes its exact determination in vivo without the aid of x-rays. Investigators have attempted to estimate the HJC’s location in the living subject by a variety of methods. The most common approach has been to estimate its location using the experimenter’s general knowledge of externally identifiable landmarks (Eberhart and Inman 1951; Harrington 1976; Paul 1965; Pedotti 1977). Some have used radiographs to precisely locate the HJC (Crowninshield et al. 1978; Ellis et al. 1979; Johnston et al. 1979). Others made no mention of how they found the location used in their calculations (Cappozzo et al. 1975; Cappozzo and Gazzani 1986; Paul and Poulson 1974; Seedhom and Teroyama 1976). No method is entirely satisfactory. While orthogonal x-rays will precisely locate the HJC, there are considerable logistical difficulties in taking, developing, and interpreting radiographs. Additionally, many individuals (children and adults of child-bearing age) should not be exposed to unnecessary ionizing radiation. La&in (1984) has shown that external estimation of HJC location is frequently inaccurate. During each of 25 consecutive total knee arthroplasties, surgeons estimated and localized with a radiopaque marker the location of the HJC. The true location was then determined by an AP radiograph, and the two were compared. Twenty percent of the time the true location of the femoral head center (hip joint centre was over 4 cm away from the surgeon’s estimate and in only 12% of the cases was the surgeon’s estimate within 2 cm of the actual femoral head centre. Obviously, then, estimation is inaccurate (88% of the time a greater than 2 cm error). To improve upon external estimates, several investigators developed approaches to estimate HJC location from palpable landmarks. Tylkowski et al. (1982) expressed HJC location as a constant percentage of the distance between the anterior superior iliac spines (ASIS). Specifically, they predicted that the joint centre was located 11% of the inter-ASIS distance (ASIS-ASIS) medial, 12% distal, and 21% posterior (along a line perpendicular to the plane created by the two ASIS’s and the public symphysis) to the ASIS. They developed this relationship from examining a number of children’s x-rays but pro-
A.L. Bell et al. / Locating the HJC from external landmarks
5
vided few details. Andriacchi et al. (1980; 1982; Andriacchi and Strickland 1983) predicted that the HJC would be found 1.5 cm or 1.5 to 2 cm distal to the midpoint of a line between the ASIS and the pubic symphysis in the frontal plane and an unspecified distance medial to the greater trochanter, but did not report how they devised these formulas. Neither group addressed whether the formulas were valid for children and adults of both sexes or just for certain population groups. The purposes of our study were to (1) determine the validity and accuracy of the approaches of Tylkowski and Andriacchi in children and adults of either sex, (2) develop a new method, should their approaches fail to predict the HJC location reasonably accurately, and (3) quantitate the confidence with which the various approaches can be applied in the experimental or clinical settings.
Materials and Methods We obtained the AP pelvic radiographs of 39 children (15 males, 24 females) and 31 adults (15 males, 16 females). The children were all between the ages of four and ten when the x-rays were taken, and the adults were 21 or older. All x-rays were read as having a normal bony framework by a staff radiologist. The x-rays were placed on a Graf/Pen Sonic Digitizer and six symmetrical points about the bony pelvis and hip were digitized: bilateral anterior superior iliac spines (ASIS), femoral head centers (FHC), and pubic tubercles (PT). The HJC was established as the centre of a series of concentric circles matched to the size of the particular femoral head shadow. The other two points (ASIS and PT) were easily palpable but not radiographically distinctive landmarks, and it was necessary to estimate their locations on an AP x-ray. We took a series of AP and right lateral x-rays of 20 skeletal pelves with radiopaque markers on these palpable landmarks and noted their usual locations in the AP view in relation to several radiographic landmarks (fig. la and b). These pelves were from adult males and females, but the sex of individual specimens was not known. The ASIS markers were approximately 1 cm directly superior to the point where the inferior iliac wing shadow turns from being predominantly horizontally-oriented to a more vertical orientation. There was almost always a vertical line visible on the radiograph that defined the medial border of that prominence. The pubic tubercles
I
A.L. Bell et al. / Locating the HJC from external landmarks Table 1 Actual hipjoint centre location from the ASIS as a percentage of ASK-ASIS Medial
Distal
Boys Girls Men Women Children (Average) Adults (Average) Boys (Average Girls (Average) Men (Average) Women (Average) Overall (Average)
distance.
Posterior
Right
Left
Right
Left
30% 28% 31% 29%
29% 28% 31% 29%
15% 15% 14% 14%
16% 16% 15% 15%
_ _ _ _
_
29%
0 = 3.3
16%
0=1.9
30%
0 = 3.5
14%
(T= 2.4
30%
D = 3.6
15%
a=2.3
_
28%
Q = 3.1
16%
(r =1.6
_
31%
0=3.6
14%
(T= 2.4
_
29%
0 = 3.4
15%
0=3.1
_
29%
0 = 3.4
15%
0=2.1
_
22%
0 = 3.0
were found to be directly superior to the most medial extension of the obturator foramen and approximately 1 cm below the superior pubic border shadow. The AP and right lateral x-rays of the 20 skeletal pelves were taken with the pelves within a wire cage x-ray surveying device that established a fixed reference frame and permitted 3-D coordinate estimation of the points of interest from the biplanar x-rays. This method is similar to that used by Brown et al. (1976) and Brand et al. (1982). The HJC’s were taken to be the centre of a solid plastic half-sphere matched to the size of the acetabulum and attached by clay. The x-rays were placed on the Graf-Pen Sonic Digitizer and the ASIS’s, HJC’s, and PT’s digitized in both the AP and lateral views.
Fig. 1. AP (A) and lateral (B) x-rays of skeletal pelvis showing location of palpable landmarks: anterior superior iliac spines and pubic tubercles. The lateral border of anterior superior iliac spines were edged with wire for better definition, and round markers were glued anterior to the landmarks in locations simulating markers used in gait studies (but without overlying soft tissues).
8
A. L. Bell et al. / Locating the HJC
fromexternal
Table 2 Actual hip joint centre location from the ASIS as a percentage adults (N = 31) vs. adult dry pelves (N = 20).
landmarks
of ASIS-ASIS
Distal
distance
for living
Medial
Adult x-rays
30b
0=3.5
14%
c = 2.4
Adult dry pelvis x-rays
31%
0 = 5.5
14%
0 = 3.3
After being stored in a VAX/VMS computer file, the digitized two-dimensional (2-D) coordinates from the 70 AP radiographs of the living subjects were separated into four groups: boys, girls, men, and women. In order to examine Tylkowski’s approach, we calculated the distance between the ASIS’s for each individual and described the actual positions of the HJC’s (left and right) as a percentage of that distance from the respective ASIS. This is expressed in its components of horizontal (medial) and vertical (distal) distance from the ASIS (table 1).
Table 3 Actual hip joint centre location pubic symphysis.
in centimeters
from the midpoint
Distal
Boys Girls Men Women Children (Average) Adults (Average) Boys (Average) Girls (Average) Men (Average) Women (Average)
of a line between
Lateral
Right
Left
Right
Left
2.6 2.3 4.6 3.7
2.5 2.2 4.6 3.7
1.0 0.9 1.9 1.6
0.7 0.7 1.5 1.3
2.3
c = 0.38
0.82
o = 0.41
4.1
0 = 0.77
1.6
c = 0.64
2.5
0 = 0.40
0.87
D = 0.46
2.2
0 = 0.34
0.78
c = 0.38
4.6
o = 0.69
1.7
r~= 0.64
3.7
Q = 0.55
1.5
0 = 0.64
the ASIS and
A.L. Bell et al. / Locating the HJC from external landmarks
Fig. 2. Three-dimensional 95% confidence interval (+ 1.96 u) around hip joint center (proportion of box to actual femoral head size is approximately correct).
In order to find the distance from the ASIS to the HJC in the AP direction, we calculated the 3-D coordinates of the digitized landmarks from the series of 20 adult skeletal pelvis AP and lateral x-rays. The ASIS’s and the PT’s defined the frontal plane and, using the lateral x-rays, we measured the distance posterior from that plane to the HJC and expressed it as a percentage of ASIS-ASIS separation. We also calculated the percentages for the distal and medial directions from the AP x-rays and compared them to those we obtained for the living adults in the first part of our study (table 2). To examine the approach of Andriacchi’s group, we found the midpoint of the line between the PT’s and assumed this to be the pubic symphysis. The midpoints of lines drawn between this point and the ASIS’s were found and the distances to the respective HJC’s were calculated in cm. Once again, they are expressed in their component horizontal (lateral) and vertical (distal) distances (table 3). We calculated 95% confidence intervals around the actual HJC for each approach using the respective standard deviations (a) in each dimension. This yielded a rectangle, when examining their predictions in the 2-D frontal plane, or a box, when examining their 3-D predictions, with sides of length 3.92 u( + / - 1.96 a). The length of the diagonal, i.e., the furthest the predicted HJC location could be from the true HJC location, was found by using the Pythagorean Theorem (fig. 2).
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A.L. Bell et al. / Locaiing the HJC from external landmarks
Results
Using Tylkowski’s approach of distance expressed as a percentage of ASIS-ASIS separation, we found that the actual 3-D HJC location averaged 30% distal, 14% medial, and 22% posterior to the ASIS in adults (table 1). The percentages were within 3% of each other in the distal direction and within 2% of each other in the medial direction for all four population groups, and there is excellent agreement between the percentages obtained from the AP x-rays of the living adults and the adult skeletal pelves (table 2). In two dimensions, we could predict the location of the HJC with 95% certainty to within 1.5 cm in children and within 2.7 cm in adults, of the true HJC location (table 4). In three dimensions, we could predict the location of the HJC in adults with 95% certainty to within 3.3 cm of the true location (table 4). Using Andriacchi’s approach of describing the HJC location from the midpoint of the line between the ASIS and pubic symphysis, we found that it was distal and lateral to that point in all four population groups (table 3). The exact distances varied from a low of 2.2 cm distal and 0.78 cm lateral in girls to a high of 4.6 cm distal and 1.7 cm lateral in men. In two dimensions, we could predict the HJC location with 95% certainty to within 1.1 cm in children, within 1.6 cm in women, and within 1.8 cm in men, of the true location (table 4). A hybrid method combining the frontal plane approach of Andriacchi with our distance (Tylkowski’s approach) posterior percentage of ASIS-ASIS
Table 4 A comparison of the accuracy dimensions using 95% confidence
of the HJC intervals.
location
prediction
methods
in two
Three dimensions
Two dimensions (frontal plane) (cm) Children
Adults
Adults
Tylkowski’s approach
1.5
2.7
3.3
Andriacchi’s approach
1.1
1.6 (women) 1.8 (men)
_
Combined approach
_
_
2.6
(cm)
and
three
A. L. Bell et al. / Locating the HJC from external landmarks
11
predicts the HJC location with 95% certainty to within 2.6 cm of the true location in adults (table 4). Discussion There are significant differences between actual HJC location and the locations estimated by the methods of Tylkowski’s group and Andriacchi’s group. There are also some significant differences between the population groups in our study, particularly when using Andriacchi’s method. Each method will be separately reviewed, its applicability to the general population and population subgroups examined, and its accuracy quantitated. Tylkowski’s group determined their relationship by examining the AP and lateral pelvic x-rays of 200 patients followed at the Children’s Hospital Medical Center (Boston) Growth Study Clinic and used five skeletal pelves to calculate the distance from the ASIS to the hip center, but gave no details of either procedure. The percentages they reported (12% distal, 11% medial, and 21% posterior to the ASIS) are considerably different from the ones we obtained (30% distal, 14% medial, and 22% posterior). Since no details are given as to their experimental method, it is difficult to analyze possible reasons for the discrepancy. The x-rays they examined were not those of normal children but children followed at a growth study clinic who carried a variety of diagnoses (cerebral palsy, spina bifida, acetabular dysplasia, etc.) causing a leg length discrepancy. Perhaps bony pelvic growth and/or acetabular location were also abnormal. They state that the actual percentages were derived from five skeletal pelves but make no mention of the pelves’ origin, sex, or age. A third factor may well be a consequence of the inherent magnification of x-rays. The ASIS’s, being anterior to the femoral head and thereby farther from the film in an AP radiograph, would be shifted more laterally and superiorly than the HJC by a radiation source aimed at the center of the pelvis. On the x-ray, it would appear as though the HJC was more inferior and medial to the ASIS than is actually the case in a living person or skeletal pelvis. This would result in an apparently greater absolute distance between the ASIS and HJC which would be expressed as larger percentages of the ASIS-ASIS separation. On the other hand, the ASIS-ASIS distance would also be greater and this would tend to reduce the percentages.
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A. L. Bell et al. / Locating the HJC from externul landmarks
Though the percentages were different from those reported by Tylkowski’s group, we obtained excellent consistency throughout all the population groups in our study. There is a 3% (28% vs. 31%) difference between the percentages of the lowest subgroup (girls) and the highest subgroup (men) in the distal direction (table 1). Correspondingly, there is a 2% (16% vs. 14%) difference in the percentages of the same two groups in the medial direction. Both differences are within one standard deviation of the respective means, and a Student’s t-test determined that neither difference was statistically significant. The data for the third (posterior) direction was derived from x-rays of adult skeletal pelves of unknown sex and cannot be grouped according to sex, although the percentages for the distal and medial directions derived from these x-rays showed excellent agreement with the percentages derived from the x-rays of living adults used in the first part of the study (table 2). Another important difference between our data and Tylkowski’s is the size of the standard deviations. They reported a standard deviation of 1% in all three dimensions. Our overall standard deviations were just over 3% (3.1%-3.6%) in the distal direction, about 2% (1.6%-2.6%) in the medial direction, and 3% in the posterior direction (table 1). Once again, it is difficult to pinpoint the probable causes of these two- and three-fold differences. There are the inherent difficulties in insuring standard x-ray techniques. Also, it is very difficult to precisely locate the ASIS in an AP radiograph. The most significant factor may well be the difference in sample size (5 in their study vs. 70 in ours) which, alone, could account for the discrepancies. The standard deviations affect the confidence with which the estimated HJC location can be used in the force prediction models mentioned in the Introduction. Using our mean ASIS-ASIS distance of 19.23 cm in children and 30.99 cm in adults, the standard deviations become 0.64 cm (children) and 1.1 cm (adults) in the distal direction, 0.36 cm (children) and 0.75 cm (adults) in the medial direction, and 0.93 cm (adults) in the posterior direction. The reader will recall that the dry pelves used to calculate the percentage in the third (AP) dimension were all from adults and we have no data on the antero-posterior location of the HJC in children. Calculating confidence intervals (+ 1.96 a) about the HJC shows that 95% of the time the actual HJC location will be within 1.5 cm in children and within 2.7 cm in adults of our predicted 2-D (distal and medial) location, and
A.L. Bell et al. / Locating the HJC
fromexternal landmarks
13
within 3.3 cm in adults of our predicted 3-D location (table 4). This is a significant improvement over the external estimation figures of Laskin, which showed surgeons to be able to estimate the position of the HJC in the 2-D frontal plane to within 2 cm or less of the actual HJC location only 12% of the time. We were unable to find any data on the accuracy of 3-D estimation. Although Andriacchi’s group did not describe the basis of their model, they predicted the HJC would lie 1.5 or 1.5 to 2 cm directly below the midpoint of a line between the ASIS and the pubic symphysis in the frontal plane. We obtained a consistent lateral component in all groups (table 3). This was approximately twice as large in adults as it was in children (1.6 cm vs. 0.82 cm), and the difference was significant (p < 0.05). The differences between the boys’ and girls’ values, as well as between the men’s and women’s values, were not significant, however. In no case was 0.0 cm, or no lateral component, within a 95% confidence interval ( f 1.96 a) of our means, indicating there is almost no chance that the differences between our figures and Andriacchi’s are due to random error. We also obtained somewhat different results as well as considerable intergroup variation in terms of the distal component. The best agreement of our figures with those of Andriacchi’s group came in children, where our mean of 2.3 cm (u = 0.38) was within one standard deviation of the upper end of their interval of 1.5 to 2.0 cm. Within this group, there was not a significant difference between the boys (2.5 cm, (J = 0.40) and girls (2.2 cm, u = 0.34) mean values. Less agreement was present in women (3.7 cm, (J = 0.55) and men (4.6 cm, u = 0.69). Student’s t-tests verified significant differences between the men’s and women’s values as well as between either group and the children’s values. Since the basis for this method of estimation is not reported, it is difficult to identify the possible sources of the differences between the data. Although we were unable to find documentation of the basis of Andriacchi’s approach in the literature, they did report an estimate of the error involved in predicting the HJC location by their method (Andriacchi and Strickland 1983). They examined the AP pelvic x-rays of 20 patients free of hip pathology and measured the distance between the point 1.5 cm directly below the midpoint of the ASIS-pubic symphysis line and the actual HJC. After correcting for magnification, they found that the average error was 0.79 cm. We found that the
14
A. L. Bell et al. / Locating the HJC from external landmarks
distance between that point and the actual HJC on x-rays varied from a low of 1.0 cm for girls to a high of 3.5 cm for men (using our distal value less 1.5 cm and our lateral value in the Pythagorean Theorem). Assuming 20% x-ray magnification, these figures become 0.83 cm for girls and 2.9 cm for men. The reasons for the discrepancy in the figures are unclear. Andriacchi does not report the age or sex of the 20 patients whose pelvic x-rays were used in the error analysis, but all our groups had a larger error than their figure of 0.79 cm and the size of the error in our adults (men and women) was approximately three to four times as large. Both sets of data were corrected for x-ray magnification, and 15-20% is generally accepted as the amount of magnification in a standard x-ray. We conclude that Andriacchi’s estimate of 0.79 cm of error between the predicted and actual HJC locations is relatively accurate only in children and that the error in adults is several times larger than that figure. Using our data and Andriacchi’s approach, 95% of the time the true 2-D (distal and lateral) HJC location will be within 1.1 cm in children, 1.6 cm in women, and 1.8 cm in men of the predicted location (table 4). This is much more accurate than external estimation (only 12% of the time within 2 cm, according to Laskin) and somewhat more accurate than our percentage modifications of Tylkowski’s approach. However, its relative usefulness may be hampered by the fact that separate formulas are needed for children, women, and men, whereas Tylkowski’s approach allows one to use the same formula for all groups. Andriacchi estimated the position of the HJC in the third (AP) dimension relative to the greater trochanter, but did not report the distance they used nor the errors of that procedure. As the respective femora of the skeletal pelves we used to find the antero-posterior location of the HJC were not available, we cannot describe the position of the HJC relative to the greater trochanter and, therefore, cannot predict the 3-D location of the HJC using Andriacchi’s approach. A more accurate method of predicting the 3-D HJC location with our data combined the two approaches. Andriacchi’s approach is the more accurate method of predicting the HJC location in the frontal plane. At least in adults, Tylkowski’s approach and our figure of 22% (a = 3.0) of the ASIS-ASJS distance can predict the HJC’s antero-posterior location in relation to the frontal plane. Combining these components and constructing a 3-D 95% confidence interval predicts the 3-D location of the HJC to within 2.6 cm of the true
A. L. Bell et al. / Locating the HJC from external landmarks
15
location with 95% certainty (table 4). This compares favorably with the figure of 3.3 cm we calculated using Tylkowski’s approach and our data. It appears that Andriacchi’s approach to locating the HJC in the frontal plane combined with Tylkowski’s approach to predicting its distance posterior to the frontal plane is a more accurate method of predicting the 3-D location of the hip joint center than either approach alone. Our evaluation of these methods has one limitation which should be mentioned. The measurements were taken from the radiographic bony landmarks and did not involve prior placement of skin markers over the palpable landmarks in living subjects as La&in did and as would take place in actual in vivo gait analysis studies. Thus, the possible contributions of the soft tissue over the ASIS’s and pubic symphysis to HJC estimation error were not quantitated. As these landmarks are very superficial, we would expect relatively little contribution from this factor in the average person, but this may not be true in a person with more adipose tissue. In that case, our error estimates would likely be too small. In summary, Tylkowski’s approach of predicting the 3-D HJC location as a percentage of ASIS-ASIS separation yields consistent results in all groups, but we obtained significantly different percentages than the ones they reported. The standard deviations are significant and, while the approach is considerably more accurate than the frequently used method of external estimation, it is yet to be determined whether the standard deviations are too large for the modified formula to be useful in hip joint force studies. Andricchi’s approach of predicting the HJC location from the midpoint of the line between the ASIS and pubic symphysis yielded more accurate predictions in the frontal plane but required addition of a lateral component in all groups and separate formulas for children, women, and men. A more accurate method of predicting the 3-D location of the HJC combines a modification of Andriacchi’s approach to estimation in the frontal plane with a posterior percentage modification of Tylkowski’s approach, and can predict the HJC location to within an inch of the true location in all adults. All methods appear more accurate than external estimation and safer and more efficient than x-rays.
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