Measurement of Ulnar Variance on Uncalibrated Digital Radiographic Images

Abstract

Uncalibrated digital radiographs used in multicenter trials hinder quantitative measures such as articular step and ulnar variance. This investigation tested the reliability of alternative measures of ulnar variance that are scaled to the length of the capitate. A sample of 30 sets of radiographs from patients enrolled in a prospective study of operative treatment of fractures of the distal radius were blinded and randomized. Five observers measured the ulnar variance (UV) and longitudinal length of the capitate (CH) on two separate occasions with greater than 2 weeks between measurements. During each measurement session, the observers made the measurements on both a calibrated and a noncalibrated workstation. The ratio of the ulnar variance to the length of capitate was calculated (UV/CH ratio). Paired t tests were used to compare two rounds of measurements for both methods. Intra- and interobserver reliability was assessed by the Pearson product-moment correlation coefficients. The ratios were compared using analysis of variance with a Bonferroni correction. The intraobserver reliability was excellent for each of the three variables (UV, CH, UV/CH ratio) for each workstation. The interobserver reliability of the UV/CH ratios obtained for each workstation was moderate to excellent as judged by the Pearson correlations between observers. The Bland–Altman method indicated a mean difference in UV/CH between calibrated and uncalibrated measurement techniques of 0.002 with limits of agreement of −0.11 to 0.11. Measurements of ulnar variance that are scaled to the length of the capitate may be useful measures of deformity in studies that utilize uncalibrated digital radiographs.

Introduction

Ulnar variance and articular step and gap are important quantitative measures of the alignment of the articular surface of the distal radius that are used to evaluate the results of fracture treatment [9, 11, 18]. Steyers and colleagues compared various methods for measuring ulnar variance including the project-a-line technique, the method of concentric circles, and the method of perpendiculars and found that the method of perpendiculars was most reliable for both intraobserver and interobserver comparisons [16].

Whereas angular measurements do not change with scale, measures of ulnar variance and articular incongruity in millimeters require knowledge of the scale or calibration of the radiographs. Given the increasing use of digital images, and the transfer of uncalibrated or unscaled versions of those images between centers for multicenter research, there is a need for measures of ulnar variance and articular incongruity that are expressed as ratios that can be used when the scale of the radiograph is not known. In this study, we evaluated calibrating ulnar variance by dividing it by the length of capitate. The hypothesis of our study was that the use of measurements scaled to the capitate length would be as accurate and reproducible as measurements on calibrated or actual-size images.

Materials and Methods

Thirty standard radiographs of the wrist obtained after manipulative reduction of a fracture of the distal radius were selected from an IRB approved clinical trial enrolling patients who elect open reduction and internal plate fixation. Inclusion criteria for this study were: (1) calibrated digital post-reduction posteroanterior and lateral radiographs including the base of the third metacarpal. Exclusion criteria included (1) complex multifragmentary intra-articular fracture (e.g., greater than three articular fragments); (2) fracture dislocations of the wrist; (3) intercarpal injuries; (4) dislocation at the distal radio-ulnar joint determined on a true lateral radiograph (reference).

According to the Comprehensive Classification for Fractures [13], there were one A2.2 fracture, two A3.2 fractures, one B2.1 fracture, one B2.2 fracture, one B2.3 fracture, one B3.1 fracture, one B3.3 fracture, four C1.1 fractures, six C1.2 fractures, one C1.3 fracture, four C2, four C3.1 fractures, two C3.2 fractures, and one C3.3 fracture. According to the Fernandez classification [6], there were three extra articular bending fractures, five shearing (type 2) fractures, and 22 compression fractures.

Calibrated Measurements

Using commercial software (IMPAX ES DS3000, Agfa-Gevaerts N.V., Mortsel, Belgium), we made direct, calibrated measurements of length of capitate and the ulnar variance in millimeters using a digital ruler tool.

Using the posteroanterior radiographs, the length of capitate was measured as the longest distance between the subchondral margin of the capitate at the capitate–third metacarpal junction to the proximal aspect of the capitate, as described by Natrass et al. [14] (Fig. 1). Ulnar variance was measured as the distance between a line perpendicular to the longitudinal axis through the distal ulnar aspect of the radius and the distal cortical rim of the ulna [3, 16]. In order to correct for angulation of the distal radius fragment, we had to adjust the perpendicular line through the distal ulnar aspect of the radius. First, a line was drawn from the tip of the radial styloid to the dorsal margin lunate facet of the distal radius at the sigmoid notch. A second line perpendicular to the first was placed at the volar margin of the lunate facet at the sigmoid notch. The point at which a third perpendicular line drawn midway between the volar and dorsal articular marginal lines intersects the ulnar margin of the distal radial articular surface was used as the point of reference for the radial articular surface (Fig. 1).

Figure 1.

Example of a radiograph for which correction was necessary to account for rotation/angulation of the distal fracture fragments. A Length of capitate. B The distal cortical rim of the ulna. C The tip of the radial styloid to the dorsal aspect of the sigmoid notch. D The tip of the radial styloid to the volar aspect of the sigmoid notch. E The perpendicular line corrected for angulation.

Uncalibrated Measurements

The 30 radiographs were introduced as jpeg images into an uncalibrated workstation. (eFilm software, Merge Healthcare, Milwaukee, WI, USA). Using the same guidelines, the measurements of the length of the capitate and the ulnar variance were quantified with a digital ruler tool and expressed in pixels instead of millimeters.

Study Design

Five observers not involved in the care of the patients measured all 30 radiographs blinded and in random order using the techniques described. The measurements were scheduled into two rounds; each round consisting of two sessions—one session on the calibrated and one on the uncalibrated workstation. The observers were trained by one of us using three sets of radiographs that were not used in the study.

In the first round, the five observers performed the measurements on the 30 radiographs using the calibrated workstation for a total of 150 observations (one observation includes length of capitate and ulnar variance). The images were then randomized and introduced into an uncalibrated workstation. After 7 days, the observers repeated all the measurements on an uncalibrated workstation for another total of 150 observations.

The second round was performed more than 2 weeks after completion of the first round. Again, all observers performed the measurements on the calibrated workstation (150 observations) followed by a final session on the uncalibrated workstation (150 observations).

Statistical Analysis

Intra- and interobserver reliability was assessed by the Pearson product-moment correlation coefficient (r). Paired t tests were used to compare measurements of ulnar variance (UV), capitate height (CH), and the UV/CH ratio between rounds 1 and 2 for the calibrated IMPAX and noncalibrated eFilm workstations. Repeated-measures mixed-model analysis of variance (ANOVA) with Bonferroni correction for multiple comparisons was used to compare the UV/CH ratios obtained by the five observers in each of two rounds based on IMPAX and eFilm systems [19]. In addition, the Bland–Altman method in which the average UV/CH is plotted against the difference with 95% limits of agreement was applied to evaluate differences in the ratio between the two workstations for all five observers pooled together based on a paired analysis of the same 30 X-rays and two rounds for each observer using IMPAX and eFilm (300 paired observations) [1].

One common application of the standard Bland–Altman method is to compare a new measurement technique with an established one. The primary objective of comparison studies is to determine whether the two methods agree closely enough to be used interchangeably. However, use of the Bland–Altman methodology, including the 95% limits of agreement, does not require that one method be a ‘gold standard.’ For example, two different assays can be compared, two different devices for measuring bone density, two different workstation systems for measuring ulnar variance. The analysis does not depend on either method being a gold standard, rather that the two methods measure the same variable on the same scale in the same patients (paired analysis) and that the difference between methods should be approximately normally distributed. This is unlike correlation analysis, which does not require that the two measurements be on the same scale or even that they represent the same characteristic or quantity. The Bland–Altman technique was applied in this context to graphically examine the agreement beween in UV, CH, and UV/CH between IMPAX and eFilm methods in order to determine the average difference (i.e., bias) and the limits of agreement (precision) between these methods. The Bland–Altman technique does not have p values associated with it but does allow comparison of two methods based on how closely the individual patients fall with respect to the 45° line of identity, in which the two methods perfectly agree (Y = X).

The mean difference (bias) between the two workstations and 95% CI for the difference (precision) indicate the level of agreement between the two methods of measurement. A linear regression model strategy was applied, using the general form y = mx + b, to derive the linear relationship between the UV/CH ratio based on the IMPAX and eFilm workstations. A power analysis indicated that 30 X-rays assessed twice by five different observers using each workstation (300 paired data points) for UV, CH, and UV/CH would provide sufficient number of observations to construct a 95% confidence interval around the difference in UV/CH ratio between the IMPAX and eFilm systems with a precision of 0.1 (version 7.0, nQuery Advisor, Statistical Solutions, Saugus, MA). Statistical analysis was performed using the Stata software package (version 9, Stata Corporation, College Station, Texas). Two-tailed values of p < 0.05 were considered statistically significant with a Bonferroni correction for multiple comparisons between observers.

Results

The intraobserver reliability was excellent for each of the three variables (UV, CH, UV/CH ratio) for each workstation as indicated by no significant differences between round 1 and round 2 for the five observers (all p > 0.20, paired t tests). The correlations are all excellent and highly significant in terms of measurements between the two rounds (Table 1). Interobserver reliability regarding the UV/CH ratios obtained for each workstation was moderate to excellent as judged by the average Pearson correlations between observers (Table 2). No differences were found between observers using the IMPAX system, whereas with the noncalibrated eFilm workstation, only observer 4 showed significantly different results as compared to other observers. The average correlation between the five observers was moderately high on both rounds 1 and 2 using the IMPAX workstation (r = 0.82 and r = 0.89, respectively, both p < 0.001), whereas with eFilm the interobserver correlations were similar for the two rounds, on the average (r = 0.86 and r = 0.82, respectively, both p < 0.001).

Table 1.

Intraobserver reliability for measurements based on each workstation.

	Round 1	Round 2	Mean difference	SD of difference	p valuea	Pearson r correlationb
IMPAX
UV (cm)	0.057	0.055	−0.002	0.091	0.84	0.932
CH (cm)	2.364	2.397	0.033	0.111	0.22	0.894
UV/CH	0.023	0.023	0.000	0.039	0.89	0.931
eFilm
UV (pixels)	8.1	8.7	0.6	14.4	0.57	0.884
CH (pixels)	281.6	281.0	−0.6	18.3	0.73	0.975
UV/CH	0.024	0.027	0.003	0.050	0.50	0.889

Data are based on mean values for all 5 observers pooled together

^aPaired t test.

^bCorrelations indicate excellent agreement between rounds for each variable (p < 0.001)

Table 2.

Intraobserver reliability for the ulnar variance/capitate height ratio based on each workstation.

	Round 1	Interobserver correlation (r)	Round 2	Interobserver correlation (r)
	Mean ± SD	Mean (range)a	Mean ± SD	Mean (range)a
IMPAX
Observer1	0.032 ± 0.112		0.019 ± 0.100
Observer 2	0.017 ± 0.106		0.012 ± 0.105
Observer 3	0.011 ± 0.102		0.017 ± 0.095
Observer 4	0.028 ± 0.092		0.037 ± 0.089
Observer 5	0.028 ± 0.124		0.030 ± 0.120
Total	0.023 ± 0.107	0.86 (0.77–0.94)	0.023 ± 0.102	0.89 (0.83–0.94)
eFilm
Observer1	0.011 ± 0.095		0.016 ± 0.087
Observer 2	0.019 ± 0.105		0.004 ± 0.113
Observer 3	0.026 ± 0.095		0.028 ± 0.096
Observer 4	0.049 ± 0.099a		0.056 ± 0.107a
Observer 5	0.013 ± 0.115		0.029 ± 0.128
Total	0.024 ± 0.102	0.86 (0.76–0.94)	0.027 ± 0.107	0.82 (0.72–0.98)

Repeated-measures analysis of variance was used to compare observers to account for the same 30 X-rays evaluated by each observer. No significant differences were detected between observers for the IMPAX workstation. For the eFilm workstation, the UV/CH ratio was greater for observer 4 compared to observers 1, 2, and 5 in round 1, and compared to observers 1 and 2 in round 2 (p < 0.05, ANOVA with Bonferroni correction).

^aHighly significant average correlations between observers, with ranges that indicate at least moderately high interobserver agreement).

The Bland–Altman method indicated a mean difference in UV/CH between calibrated and uncalibrated measurement techniques of 0.002 with limits of agreement of −0.11 to 0.11. Linear regression analysis indicated a strong positive relationship between IMPAX and eFilm UV/CH with a prediction equation, y = 0.86x + 0.005, where x is the ratio as obtained using the IMPAX workstation (r² = 0.73, p < 0.001). The scatter plot of the UV/CH measurements for the two systems shows a moderately strong positive linear relationship (Fig. 2). The histogram of the difference between the IMPAX and eFilm UV/CH ratios is centered very close to zero but clearly shows variation such that the ratio can be larger or smaller with either workstation (Fig. 3). In fact, the mean difference is constant across the range of possible values for UV/CH as demonstrated by a lack of a correlation (i.e., no significant slope) between the difference in UV/CH (IMPAX − eFilm) versus the average UV/CH based on both workstations (Pearson r = −0.01, p = 0.95, Fig. 2).

Figure 2.

A scatter plot of the calibrated (Impax) and uncalibrated (Efilm) UV/CH measurements shows a moderately strong positive linear relationship.

Figure 3.

The histogram of the difference between the calibrated (IMPAX) and uncalibrated (eFilm) UV/CH ratios is centered very close to zero but clearly shows variation such that the ratio can be larger or smaller with either workstation.

Discussion

We realize that there is not yet an accepted standard measurement of ulnar variance. The issues relate not only to the method of measurement [10, 15, 16] but also to methods of accounting for the position of the patient and the distal radial fracture fragment [8, 17, 20] as well as the position of the radiographic beam and the machine [2, 4, 7, 20]. We could not find a reference for our technique of using the radial styloid and the volar and dorsal margins of the lunate fossa to determine a reference point on the radius for determining ulnar variance and the technique may or may not be novel. On the other hand, for the purposes of this study, the exact technique is not as important as the reliability of the measurements made on calibrated and uncalibrated digital images.

We chose the capitate as a reference for standardizing measurements made on calibrated films because there is precedent for its use in this regard. One common use of the capitate is in the revised carpal height ratio. This was devised because wrist radiographs do not routinely include the entire third metacarpal as needed for the original carpal height ratio [12, 21]. The advantages of using the longitudinal length of the capitate include: consistent measurement in length [5]; the length measurement is not subject to ulnar or radial deviation of less than 18° [14], and injury to the capitate is uncommon. Furthermore, the capitate is consistently present on standard wrist radiographs.

Our results suggest that observers using the capitate to scale radiographic length measure of deformity of the distal radius make consistent measurements and agree with one another. Measurements of ulnar variance that are scaled to the length of the capitate may be useful alternative measures of deformity in studies that utilize uncalibrated digital radiographs. The ratio is best used for statistical comparisons within a single study and is less intuitive when comparing data from different studies.

Some aspects of our analysis may have affected the results. For instance, we rounded the ratios to two significant digits while recording the measurements. Although highly reliable in our hands, the findings should be confirmed in other settings using various accepted techniques and workstations for verification.