JBJS | Quantification of the Radial Torsion Angle with Computerized Tomography in Cadaver Specimens*

The Journal of Bone & Joint Surgery, Volume 79, Issue 6

Articles | June 01, 1997

Quantification of the Radial Torsion Angle with Computerized Tomography in Cadaver Specimens*

RANDIP R. BINDRA, M.D.†; R. JEFFREY COLE, M.D.‡; KEN YAMAGUCHI, M.D.†; BRADLEY A. EVANOFF, M.D., M.P.H.†; THOMAS K. PILGRAM, PH.D.§; LOUIS A. GILULA, M.D.§; RICHARD H. GELBERMAN, M.D.†, ST. LOUIS, MISSOURI

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Investigation performed at the Department of Orthopaedic Surgery, Washington University School of Medicine, St. Louis

The Journal of Bone & Joint Surgery. 1997; 79:833-7

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Abstract

Torsion of a long bone is the twist along its longitudinal axis; torsion of the radius is defined by the angle between the proximal and distal metaphyses in the transverse plane. Measurement of the radial torsion angle provides a means of detection and quantification of malrotation after a fracture. The purpose of the current study was to develop and standardize a technique for the measurement of torsion of the radius. Axial computerized tomographic images of thirty-nine pairs of dry cadaver specimens of normal radii, and an additional four pairs of radii with a unilateral deformity of the distal metaphysis that was consistent with a previous fracture, were studied and a measurement protocol was established. The radial torsion angle was measured by three independent observers on two separate occasions. Reproducibility of the technique was determined with use of the intraclass correlation coefficient to express both interobserver and intraobserver reliability. Consistency of measurements between observers and by the same observer was high, with intraclass correlation coefficients ranging from 0.87 to 0.94.The mean torsion angle for the eighty-two normal radii in the study was 32.6 degrees (95 per cent confidence interval of the mean, 30.3 to 34.9 degrees; range, 1.4 to 58.8 degrees). There were small variations in torsion angle between the two radii of each normal pair (mean side-to-side difference, 4.9 degrees; 95 per cent confidence interval of the mean, 3.5 to 6.3 degrees). The mean torsion angle of the four radii with a malunited fracture was 10.4 degrees (95 per cent confidence interval of the mean, 5.7 to 15.1 degrees), and the mean side-to-side difference in the pairs containing these radii was 24.1 degrees (95 per cent confidence interval of the mean, 8.5 to 39.6 degrees; p < 0.0001 compared with the normal radii).CLINICAL RELEVANCE: Measurements of torsion may be useful for the planning of corrective osteotomies of the radius. Conventional computerized tomographic scanning provides a simple, reproducible technique for the measurement of radial torsion that can be accurately applied. Images of both forearms allow the direction of rotation of the radius to be identified, with a decrease in the torsion angle indicating supination of the distal fragment and an increase indicating pronation. Because of the wide range of radial torsion angles in normal individuals, values should be interpreted with reference to the contralateral side.

Figures in this Article

Introduction

Introduction | Materials and Methods | Results | Discussion | References

Malrotation of the radius after a fracture of the distal metaphysis has been recognized as a cause of persistent pain, limited motion, and instability of the distal radio-ulnar articulation^13,25. While descriptions of corrective osteotomy of the distal aspect of the radius have focused on the correction of angular deformities in the sagittal and coronal planes in symptomatic patients, less attention has been devoted to correction of malrotation of the distal fragment^5-7,10,12,23. A major cause of the failure to assess rotation on a routine basis may be the difficulty associated with calculating rotational deformity with use of plain radiographs of the wrist and the forearm. Torsion of the radius is the angle between the proximal and distal metaphyses in the transverse plane, and an accurate means for measuring such torsion may provide a way to calculate the degree of malrotation after a fracture. We know of no reports in which such a method for measuring radial torsion has been shown to be highly accurate and reproducible.

Computerized tomography has been used to measure tibial^17,18,26 and femoral^16,22 torsion by calculating the angle between defined axes of the proximal and distal metaphyses of those bones. Because accurate values have been obtained with use of low doses of radiation^16,26, computerized tomographic scanning has been routinely employed in the evaluation of rotational abnormalities of the lower limbs^20,24. To our knowledge, this technique has not been previously applied for the measurement of torsion of the radius.

We hypothesized that, for the evaluation of rotational deformity after fracture, the radial torsion angle could be measured on axial computerized tomographic images made through the proximal and distal aspects of the radius. The purpose of the current study was to develop and standardize a technique, on the basis of serial computerized tomographic images of paired radii from cadavera, for the determination of the radial torsion angle. The interobserver and intraobserver reliability of this technique was determined by statistical analysis of the measurements made by three independent observers on two separate occasions.

*No benefits in any form have been received or will be received from a commercial party related directly or indirectly to the subject of this article. No funds were received in support of this study.

†Department of Orthopaedic Surgery (R. R. B., K. Y., and R. H. G.) and Division of General Medical Sciences, Department of Medicine (B. A. E.), Washington University School of Medicine, One Barnes Hospital Plaza, St. Louis, Missouri 63110.

‡The Orthopaedic Clinic, 1068 Cresthaven Road, Suite 400, Memphis, Tennessee 38119.

§Mallinckrodt Institute of Radiology, One Barnes Hospital Plaza, St. Louis, Missouri 63110.

*No benefits in any form have been received or will be received from a commercial party related directly or indirectly to the subject of this article. No funds were received in support of this study.

‡The Orthopaedic Clinic, 1068 Cresthaven Road, Suite 400, Memphis, Tennessee 38119.

§Mallinckrodt Institute of Radiology, One Barnes Hospital Plaza, St. Louis, Missouri 63110.

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Fig. 1 Axial computerized tomographic images made through the proximal and distal aspects of the radius. Line A is projected tangential to the cortical surface of the bicipital tuberosity. Line B is the bisector of the lines joining the dorsal and palmar corners of the axial image of the distal aspect of the radius at a subchondral level. The torsion angle is the acute angle between lines A and B.

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Fig. 2 Graph demonstrating the mean (circles), the 95 per cent confidence interval of the mean (I-bars), and the distribution of the torsion angles for the normal and fractured specimens of the radius.

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Fig. 3 Graph demonstrating the mean (circles), the 95 per cent confidence interval of the mean (I-bars), and the distribution of side-to-side differences in the torsion angle for the normal pairs and the pairs containing normal and fractured specimens of the radius.

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Fig. 4 Scatterplot showing the relationship between the mean torsion angle of each pair of normal radii and the absolute side-to-side difference in the pair. s.d. = standard deviation.

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TABLE I MEASUREMENTS OF THE RADIAL TORSION ANGLE (IN DEGREES) FOR THE FOUR PAIRS OF SPECIMENS WITH A PREVIOUS UNILATERAL FRACTURE

Specimen	Normal Radius	Fractured Radius	Side-to-Side Difference
1	46.5	12.1	34.4
2	27.5	11.7	15.8
3	21.7	6.0	15.7
4	42.3	11.9	30.4

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TABLE I MEASUREMENTS OF THE RADIAL TORSION ANGLE (IN DEGREES) FOR THE FOUR PAIRS OF SPECIMENS WITH A PREVIOUS UNILATERAL FRACTURE

Specimen	Normal Radius	Fractured Radius	Side-to-Side Difference
1	46.5	12.1	34.4
2	27.5	11.7	15.8
3	21.7	6.0	15.7
4	42.3	11.9	30.4

Materials and Methods

Introduction | Materials and Methods | Results | Discussion | References

Selection of the Specimens

Forty-three pairs of dry cadaver specimens of the radius were studied. The mean age of the donors at the time of death was eighty-two years (range, sixty-seven to ninety-two years). Before computerized tomographic scanning, all specimens were examined visually for structural abnormalities. Four pairs demonstrated a unilateral deformity of the distal metaphysis that was consistent with a previous fracture. Additional evaluation with plain radiography confirmed the presence of a malunited extra-articular fracture of the distal aspect of the radius in these four specimens.

Scanning Technique

The paired specimens were assigned random numbers and were mounted in a standardized manner on a molded template with use of nylon straps. Four pairs of specimens were placed on each template with the longitudinal axes parallel and the dorsal surfaces superior to simulate a fully pronated position of the forearm in a computerized tomographic scanner. The template was aligned with the long axis of the table of a Somatom-Plus scanner (Siemens Medical Systems, Iselin, New Jersey), and serial, contiguous, ultra-high-resolution (bone algorithm), two-millimeter-thick magnified sections were made in the axial plane. Full-length scans were made of the first eight pairs of specimens in order to study the cross-sectional morphology of the radius and to identify landmarks for measurement. Subsequent specimens were scanned through the distal two centimeters and proximally through the entire length of the bicipital tuberosity.

Determination of Reference Axes

After review of the initial full-length scans, we agreed on the selection of proximal and distal reference axes. The head and neck of the radius appeared circular on axial images and did not allow the projection of a reproducible transverse axis. The bicipital tuberosity provided the most distinct and consistent landmark in the proximal aspect of the radius. The eccentric protuberance from the proximal aspect of the shaft was identifiable on scout radiographs and on axial images. At its maximum prominence, the bicipital tuberosity projected medially from the radial shaft, with a flattened cortical surface inclined to the horizontal at an acute angle. This appearance of the bicipital tuberosity on axial images was consistent for all specimens that were studied.

A tangent was constructed to the cortical surfaces of the anterior and posterior edges of the bicipital tuberosity to represent the proximal reference axis (Fig. 1, line A). The distal aspect of the radius appeared quadrilateral on axial images, with four well defined corners in all sections, from the radiocarpal articular surface to the proximal edge of the sigmoid notch. The axial image through the subchondral bone of the articular surface of the distal aspect of the radius was used for measurement. This image was just proximal to the section demonstrating the articular cartilage of the lunate fossa. Two vertical lines were constructed through the palmar and dorsal corners of the distal aspect of the radius along the radial and ulnar borders. A transverse line bisecting the two vertical lines was selected as the distal reference axis (Fig. 1, line B). The angle of torsion was defined as the angle between the proximal and distal reference axes. With use of this technique, a supination deformity of the distal fragment would result in a decrease in the torsion angle and a pronation deformity of the distal fragment would result in an increase in the angle.

Measurement Technique

To facilitate the measurement of the radial torsion angle in multiple sections, the images were relayed to a computer (MacIntosh Powermac; Apple Computer, Cupertino, California) and measurements were made with use of the public-domain National Institutes of Health Image program (United States National Institutes of Health, National Technical Information Service, Springfield, Virginia). This software allows the importation of radiographic images and provides tools for the projection of lines and the measurement of angles. Each observer, working independently, manually projected the reference axes on the images with use of the landmarks described, allowing automated calculation of the torsion angle. The measurements then were exported to a spreadsheet for statistical analysis. For each measurement, the observer constructed the proximal and distal reference lines and calculated the angle. Measurements were made by three independent observers and were repeated by each observer two weeks later.

Data Analysis

All numerical analyses were performed with JMP software (SAS Institute, Cary, North Carolina). The reliability (reproducibility) of the measurement technique was examined with the intraclass correlation coefficient to express both interobserver reliability (measurements made by different observers) and intraobserver reliability (measurements repeated at different points in time by the same observer) for repeat measurements. Like the kappa statistic, the intraclass correlation coefficient is a measure of agreement between two sets of observations^3,8,9. The intraclass correlation coefficient can be used for continuous as well as categorical data. The measurements—in this case, the differences in the radial torsion angle—are the dependent variable, and the groups—in this case, two different measurements or three different observers—are the independent variables.

The variance components derived from the analysis are used to calculate the proportion of variability that is due to variation between individuals as opposed to variation in measurements made by the same individual. This value, known as the intraclass correlation coefficient, can range from 0 to 1. Large values indicate that a relatively small proportion of the total variability is due to intraobserver or interobserver variability; that is, values close to 1 indicate high reliability of the measurements.

For calculation of the radial torsion angle, the mean of the first measurements that were made by the three observers was used. In order to detect a difference in the radial torsion angle between normal bones and fractured bones, the mean for the thirty-nine pairs of normal radii and the mean for the four radii that had a malunited fracture of the distal metaphysis were compared statistically with use of the t test.

For analysis of the side-to-side variability of the radial torsion angle, the thirty-nine pairs of normal specimens and the four pairs of specimens with a unilateral fracture were separated into two different groups. The absolute side-to-side differences in the radial torsion angle of the paired specimens were examined statistically. Differences between the normal and fractured radii were examined by calculating the means for the two groups. The pattern was tested for significance with a difference-of-means t test. This test is used to compare the difference of means with the variability of the two samples, thus determining whether the difference is greater than that expected by chance. In addition, to investigate any association between the magnitude of the angle and the difference between sides, a scatterplot of the mean value of the torsion angle of the normal specimens and the absolute side-to-side (right-left) difference was examined visually⁴ and through simple linear regression analysis.

Results

Introduction | Materials and Methods | Results | Discussion | References

Reliability of Measurements

The measurement technique was very reliable, with high intraclass correlation coefficients for the measurements between different observers and for different measurements by the same observer. The intraclass correlation coefficient for the three observers was 0.94, indicating excellent interobserver reliability. Very high reliability of the repeat measurements of the individual readers also was seen. The intraclass correlation coefficients for intraobserver reliability ranged from 0.87 to 0.89.

Radial Torsion Angles

The mean torsion angle for the normal radii was 32.6 degrees (95 per cent confidence interval of the mean, 30.3 to 34.9 degrees; range, 1.4 to 58.8 degrees). The mean torsion angle for the four specimens with a previous fracture of the distal aspect of the radius was 10.4 degrees (95 per cent confidence interval of the mean, 5.7 to 15.1 degrees; range, 6.0 to 12.1 degrees; Table I). The reduction in the torsion angle for the previously fractured specimens was significant (p < 0.0001; Fig. 2) and reflected relative supination of the distal fragment in relation to the radial shaft.

Side-to-Side Variability

The mean side-to-side difference in torsion angle for the paired normal radii was different from that for the pairs containing a normal and a previously fractured specimen (Fig. 3). For the paired normal specimens, the mean difference was 4.9 degrees (95 per cent confidence interval of the mean, 3.5 to 6.3 degrees; 95th percentile, 13.9 degrees; range, 0.01 to 18.1 degrees). The mean side-to-side difference for the four pairs with a unilateral malunited fracture was 24.1 degrees (95 per cent confidence interval of the mean, 8.5 to 39.6 degrees; range, 15.7 to 34.4 degrees). This difference between the two groups was highly significant (p < 0.0001). The scatterplot did not reveal any association between the mean torsion angle of each normal pair and the difference between the two radii of the pair (Fig. 4).

Discussion

Introduction | Materials and Methods | Results | Discussion | References

Previous investigators have described different radiographic techniques for the identification of rotational deformity of the radius after fracture. Some authors have advocated making comparative radiographs of the tuberosity of both forearms to identify malrotation with reference to a calibration chart of the normal appearance of the bicipital tuberosity at various degrees of rotation of the forearm¹¹. Others have made radiographs of the entire forearm to identify torsional changes after fracture²¹. The use of axial computerized tomographic scans at the mid-level of the forearm to identify and subjectively assess malrotation of the radius was described recently for a series of seven patients²⁵. However, none of the techniques that have been described provide a quantitative measure of radial torsion, and none have been evaluated for reliability and reproducibility. We describe a technique for reliable, reproducible measurement of radial torsion on axial computerized tomographic scans.

Despite a wide variation in the torsion angle among specimens from different cadavera, we found that the angle varied little between the two normal radii of the same individual (mean side-to-side difference, 4.9 degrees). The mean difference in the torsion angle between the radii with a previous fracture and the contralateral, normal radii was 24.1 degrees; this difference was significant (p < 0.0001). On the basis of these data demonstrating a wide range of values in the population but little variation in the radii of individuals, it appears that the radial torsion angle may be interpreted most reliably with reference to the contralateral side. These findings and conclusions are similar to those reported in studies of torsion of the tibia^18,26.

Measurements of torsion may be useful in the planning of corrective osteotomies of the radius. Because reports of symptomatic instability of the distal radio-ulnar articulation secondary to malrotation of the radius have been substantiated by studies of cadavera^1,13,25, several authors have recommended that corrective osteotomy include correction of the rotation of the radius along with correction of angular deformities in the coronal and sagittal planes^2,13,19,25. Angular deformities and shortening of the radius are calculated preoperatively from radiographs of the wrist to allow precise operative correction^{2,5,10,12,13,19,25}. Correction of rotation of the distal aspect of the radius has been largely subjective, with estimated values based on intraoperative visual assessment of the alignment of the dorsal radial cortex^2,19 or on alignment achieved by application of a buttress plate¹³. Because of formation of callus and remodeling at the site of the fracture, visual alignment of cortical surfaces may be difficult and inaccurate. Computerized tomographic scanning of both forearms allows the direction of rotation of the radius to be identified, with a decrease in the torsion angle indicating supination of the distal fragment and an increase indicating pronation of the distal fragment.

Values for radial torsion provide additional radiographic parameters for long-term outcome studies of fractures of the distal aspect of the radius. Currently, the evaluation of these fractures is based on correlation of clinical findings with radiographic criteria of radial inclination, radial length, and palmar tilt^14,15. While metaphyseal rotation has been recognized to occur, measurement of malrotation has not been included in radiographic evaluations after fracture. Measurements of radial torsion may help to provide data on the magnitude of rotation of the distal fragment that occurs with fracture, the correction that is achieved with closed manipulation, and the threshold beyond which malrotation causes symptoms.

Measurement of radial torsion with use of the described technique has limitations. The technique cannot be used reliably for fractures with severe comminution of the distal aspect of the radius because of the loss of anatomical landmarks. Also, when the fracture is bilateral there are no references for comparison. The cadavera used in the current study were skeletally mature, with well defined osseous landmarks. The minimum age for the application of this technique, the range of normal torsion angles in children, and changes in the torsion angle with growth are not known.

The computerized tomographic technique that we have described for the measurement of radial torsion can be applied clinically. With the patient lying prone in the scanner, both arms are positioned overhead; the elbows are extended and the forearms are pronated so that the palms and the elbows are placed flat on the table. Axial images through the maximum prominence of the bicipital tuberosity and the distal two centimeters of both radii are made simultaneously with use of a routine computerized tomographic imaging protocol. The reference axes are projected, and the radial torsion angle can be measured manually on the hard copy or directly at the terminal of the computerized tomography scanner. The technique is simple and reliable, with good reproducibility among observers. The measurements are interpreted with reference to the contralateral side because of the wide variation in values in normal individuals.

NOTE: The authors acknowledge the assistance of Dan Margiotta, R.T.(R), Mallinckrodt Institute of Radiology, and Gayle King, Department of Anatomy, Washington University School of Medicine, St. Louis, Missouri.

References

Introduction | Materials and Methods | Results | Discussion | References

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Fig. 4 Scatterplot showing the relationship between the mean torsion angle of each pair of normal radii and the absolute side-to-side difference in the pair. s.d. = standard deviation.

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TABLE I MEASUREMENTS OF THE RADIAL TORSION ANGLE (IN DEGREES) FOR THE FOUR PAIRS OF SPECIMENS WITH A PREVIOUS UNILATERAL FRACTURE

Specimen	Normal Radius	Fractured Radius	Side-to-Side Difference
1	46.5	12.1	34.4
2	27.5	11.7	15.8
3	21.7	6.0	15.7
4	42.3	11.9	30.4

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TABLE I MEASUREMENTS OF THE RADIAL TORSION ANGLE (IN DEGREES) FOR THE FOUR PAIRS OF SPECIMENS WITH A PREVIOUS UNILATERAL FRACTURE

Specimen	Normal Radius	Fractured Radius	Side-to-Side Difference
1	46.5	12.1	34.4
2	27.5	11.7	15.8
3	21.7	6.0	15.7
4	42.3	11.9	30.4