According to the American Academy of Orthopaedic Surgeons (AAOS), more than 172,221 total hip arthroplasties (THAs) are performed annually in the United States.1 Excellent outcomes require technically accurate surgery including proper prosthesis positioning and soft tissue management. The term positioning includes location and orientation. Orientation implies two parameters: abduction and anteversion.
Abduction can be measured easily using an ordinary protractor on an anteroposterior (AP) radiograph. Abduction is the angle between the long axis of the ellipse formed by the cup and the horizontal line of the pelvis. However, true (anatomic) and planar (radiographic) ante- version are more difficult to measure. Numerous methods for measurement have been reported.2-6,8-12 The method of Olivecrona et al requires a computed tomography (CT) scan and special software.9 The other methods require high-quality AP radiographs with good patient positioning and radiographic conditioning. The methods of Lewinnek et al5 and Pradhan10 are trigonometric methods, which require a numerical table or a calculator. Long and short axes of the ellipse need to be drawn in the method of Lewinnek et al5 and another perpendicular axis located ⅕ of the distance along the long axis needs to be drawn in the method of Pradhan.10 The methods of Fabeck et al4 and that of Widmer12 do not require a calculator. The method of Fabeck et al4 takes a longer time to determine the center of the circle. Widmer's12 method is better, but it is not very precise in determining abduction.
We introduce a simple new protractor used to measure anteversion and abduction using an AP radiograph of the pelvis.
MATERIALS AND METHODS
According to Murray's definition,8 if the acetabulum axis (or normal vector of the acetabulum plane) (Fig 1A) is defined, then the true (anatomic) anteversion can be measured by projecting the acetabulum axis onto the transverse plane (Fig 1B). Planar (radiographic) anteversion is measured by projecting the acetabulum axis to the plane perpendicular to the coronal plane and the acetabulum plane (Fig 1C). Flexion (operative anteversion) is measured by projecting the same vector onto the sagittal plane (Fig 1D). Abduction (inclination) is measured by projecting that vector onto the coronal plane (Fig 1E).8 These angles are not independent, because when one angle is changed, so are the others, unless the vector lies in one of the four planes.
An accepted method of measuring the opening angle αP (planar version) is based on the respective lengths of the short (sP) and long (lP) axes of the elliptical outline of the shell in the AP radiograph (Fig 2A).5 Using these quantities, the planar version αP may be calculated using the formula:
The l is Line AB where the s is Line CD (Fig 2A). When considering the true version, the principle is the same, but the equation must be modified to Equation 1.1.11 The st becomes the distance between the center of the ellipse and the intersection of the horizontal line passing through the center of the ellipse, as shown by Line EF (Fig 2B). The lt becomes ½ the length of the long axis, as shown by Line DE (Fig 2B).11
This method requires a table or calculator with an inverse sine (sin−1) function and is not convenient. We designed a new pro- tractor to replace the cumbersome calculations.
The method for measuring planar version is as follows: (1) Draw a line across the maximal diameter of the ellipse in the AP radiograph, such as Line AB (Fig 2A);
(2) Determine point C midway on the ellipse (Fig 2A), which is the intersection of ellipse and the line perpendicular and going through the midpoint of AB. (3) Draw another line from the apex A to point C (Fig 2A); and (4) Use an ordinary protractor to measure the angle βP (Fig 2A), which is formed by Lines AC and AB.
To measure true version: (1) Draw a line from point E (the top-most point of the semicircle) to point F (the center of the ellipse) (Fig 2B); (2) Determine point G (Fig 2B) by the intersection of the horizontal line passing through point F; (3) Draw a line from point E to point G (Fig 2B); and (4) Use an ordinary protractor to measure the angle βt (Fig 2A), which is formed by lines EG and EF.
This is deduced from simple trigonometry. In Situation 1, we measured planar version; sP was the length of short axis and lP was the length of long axis (Fig 2A). In Situation 2, we measured true version; st was the length of line FG and lt was the length of Line EF (Fig 2B).
Using traditional procedures, one would measure angles βp and βt with an ordinary protractor, then use equations 3 and 3.1 to calculate the true and planar versions. By equation 4, we make the first part of our protractor by marking αp (the version) with βp (the real angle). This special protractor can be used to measure αp directly, with no need for calculations (Fig 3). For the second part, we used an ordinary protractor to measure abduction. We explained how to measure αp directly, and a similar way to measure αt.
To use the protractor, we aligned the base line of the protractor with the long axis of the ellipse to read the planar version angle defined by point C (Fig 4A-B). To measure the true version angle, we aligned the base line of the protractor with Line EF, and then read the true version angle defined by point G (Fig 4C-D).
When measuring the planar version, part 2 of our protractor (an ordinary protractor) can be used simultaneously to measure the abduction angle. We can read this angle by the protractor of a horizontal line, which is parallel to the line passing through both teardrop landmarks, as indicated by the arrow labeled H (Fig 4A-B).
We determined the accuracy of our method by comparing it with the trigonometric method.5,6 We used software simulating 45 radiographs of THAs with 15 different anteversions ranging from 15°-29° (Fig 5A). We also collected 45 actual radiographs of THAs. These simulated and real radiographs were printed on paper. One of the authors (C.K.L.) measured the planar version of the 45 simulated and 45 real radiographs using the method described by Lewinnek et al5 (Fig 5B) and 1 week later with our method (Fig 5C). We randomly ordered the simulated radio- graphs on each measurement.
The two errors were compared with a two-sample Student's t test. Significance was set at the p < 0.05 level.
The median errors were within 1° with our method and 1.23° with the method of Lewinnek et al. Maximal errors were 3° with our method and 2.61° with the method of Lewinnek et al, and the mean errors were 0.96° and 1.2°, respectively. The standard deviation was 0.74° with our method and 0.57° with the method of Lewinnek et al. (Fig 6) There was no statistical difference between the two methods. For the real radiographs, the mean of absolute difference between the two methods was 1.34°, and the standard deviation was 1.13°.
Current methods of measuring the version angle require good quality radiographs, which means a nearly perfect AP projection without rotation on the transverse and longitudinal axes, and centered at the hip. If the projection is not perfect, there will be measurement errors. If there is a 5° rotation on the transverse axis, then it will cause a 5° error in the flexion angle. A change in one angle causes the other three angles to change. The changes in the other three angles (true version, planar version, and abduction) will be smaller than the flexion angle. Similarly, for the longitudinal axis, a 5° rotation will cause a 5° error in the true version. The error of the other three angles will be smaller. The detailed mathematical formulas were described by Murray.8
No solution exists for perfect patient positioning using the plain radiograph method. However, CT can solve this problem. With a virtual plane as described by McKibben (including the anterior superior iliac spines and the pubic tubercles), the software can measure the angle between the cup and plane.9 The method described by Olivecrona et al9 is excellent but unpractical because of the high cost of CT and the risk of radiation exposure. The relationship between position and version were discussed by Moritz et al.7
The greatest error in our method was finding point C (for planar version) and point F (for true version). In most patients, the femoral head obscured these points. Pradhan's solution was to measure the ellipse by the length of the perpendicular axis located ⅕ of the distance along the long axis from the apex to avoid the obscured region.10 The point is on middle part of the ellipse. It follows the rules of an ellipse which makes it easier to estimate. The mean error and standard deviation of error from Pradhan's data were 0.88 and 0.65, respectively.10
Bias in anteversion measurements using radiographs is inevitable because of measuring a three-dimensional object using a two-dimensional image projection. Some methods require using a ruler to measure two or more distances which then are used to make various calculations.5,10 For example, The method of Lewinnek et al needs measurement of the long and short axes of the ellipse.5 However, with every measurement, operational errors are inevitable. Therefore, we think our method is superior to that of Lewinnek et al. However, this could be the effect of operational error. Both methods have similar errors; possibly because the femoral head obscured measurement points in our method caused a similar error to the operational error in the method by Lewinnek et al. The method of Fabeck et al does not require ruler measurements, as it is determined by lines drawn on a radiograph.4 Our method requires only one measurement, which reduces the operational error. Widmer's method calculates the measurement using only one step, but there are errors with different abduction angles.12 Our method can measure without influencing abduction.
Our method is a simplified version of the method of Lewinnek et al.5 However, we only compared its ability to measure planar version. Measuring simulated and real radiographs shows little difference between the two methods. We can extend the result to the true version. When measuring a true version, we need to draw a horizontal line on the radiograph. However, it is still convenient when compared with other measurement methods. Our new pro- tractor allows measurement of true version, planar version, and abduction. Additional studies are needed to provide a gold standard for measurement.
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© 2006 Lippincott Williams & Wilkins, Inc.
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