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Ulnar variance determination
Ulnar Variance Determination S. S. KRISTENSEN, E. THOMASSEN and F. CHRISTENSEN From Kolding Hospital, Denmark. Surgical procedures concerning the distal articular surfaces of the radius and ulna, demand an accurate method of measurement of ulnar variance. A new method, which is a modification of the method described by Palmer (1982), is introduced. 100 randomly selected healthy persons were submitted to X-ray of the wrist and the ulnar variance was determined independently by three observers using both methods. By “weighted kappa” statistics the results, expressed in intra- and interobserver agreement, showed a significantly higher reliability in favour of the Modified method. The accurate measurement of ulnar variance-the radiographic distance between contiguous articular surfaces of the distal radius and ulna-is crucial in various surgical procedures (Sundberg, 1984; Cooney, 1980; Ovesen, 1981). In 1982 Palmer introduced an accurate method of ulnar variance measurement. Studying Kienbock’s disease we intended to compare the ulnar variance in the patient group, with the ulnar variance in normal wrists. However, we found that the method described by Palmer was too inaccurate to obtain a reasonable high intra- and interobserver agreement and therefore we decided to modify Palmer’s method in order to obtain a more reliable procedure. Methods and materials Epner (1982) and Palmer (1982) showed that the relative length of the radius and ulna was dependent on the position of the antebrachium. In relation to the distal radius, pronation produced increased ulnar length, while supination produced decreased ulnar length. Relative smaller changes were produced by elbow position. To attain an accurate measurement of ulnar variance, Palmer suggested a standard posterior-anterior (PA) X-ray of the wrist, with the arm abducted to 90”, the elbow flexed to 90”, and the arm, forearm and hand placed on the X-ray table. A transparent template with concentric semi-circles at 1 mm intervals was used for accurate measurements. Palmer’s method was modified: The standard X-ray projection as described by Palmer is used. In this projection the radius and ulna are parallel. Two parallel lines (A and B) are outlined (Figure 1). A new line (C), parallel to A and B, which strikes the ulnar border of the distal subchorrdral sclerotic radiaI line (point D), is outlined. In PA X-ray of the wrist this ulnar border is a remarkably constant finding. A semi-circle, the radius being the distance between point D and the styloid process of the radius (point E), is drawn. The centre of the semi-circle lies on line C. This semi-circle approximates the distal subchondral sclerotic line of the Received for publication September, S. Skydt Kristensen, M.D., Engstien
VOL. 11-B No. 2 JUNE 1986
1985. 8 3 tv, 6000 Kolding,
Denmark.
Fig.
I
Shows ulnar method. For variance).
variance further
determination by the details see text. (U.V.
Modified = ulnar
radius. The ulnar variance is determined as the distance between the most distal part of the ulnar cortical rim and the semi-circle (Figure 1). In order to compare the two methods, 100 randomly selected persons were submitted to X-ray of the wrist. Criteria for selection:
1) Closed epiphysial plates. 2) No history nor radiological
evidence of previous injury or infection of the hand, forearm or elbow. 3) Cases of general affection of the skeleton were not accepted. 255
S. S. KRISTENSEN, E. THOMASSEN AND F. CHRISTENSEN
The ulnar variance of the 100 wrists was measured independently by three observers (the authors). To obtain the intra- as well as the interobserver agreement, the material was measured twice by each method. Consequently, each observer measured 100 wrists a.m. Palmer (Palmer I), 100 wrists by the Modified m_ethod (Mod. 11. 100 wrists. a:m: Palmer \-‘---- -,7 (Palmer II) and finally 100 wrists by the Modified method (Mod. II). The measurement
N being the sampling number. The difference between two independent tested for significance by the formula:
K, values is
accuracy was 0.5 mm. Where t is the value of “Student’s t-test”.
Statistical
method
The reliability of the two methods, expressed in intraobserver agreement and interobserver agreement in pairs, was calculated using “weighted kappa” statistics, as indicated by Cohen (1968). The advantage of this statistical method compared with the often used “chi square” method, is that “weighted kappa” takes the degree of disagreement into account.
Results
The distribution of the ulnar variance measurements are approximately normal using both methods, the mean value being slightly more negative using the Modified method (Figure 2).
N =
“Weighted kappa” values vary from - 1.0 (complete disagreement) through 0 (chance agreement) to + 1.O (complete agreement). The sampling distribution of “weighted kappa” values (IQ is approximately normal for large samples. Consequently, two independent K,,, values can be tested for statistical significance.
;; = - 0.60 SD = 1.38
The measurements were classified according to the rlparpp nf U~.~x‘ amrppmc=nt hptwppn nairc U’b’U’ “I ..‘._.“L “IC”I~~.. Y’u”U of nhw-rvltinnc VLJ0WI .ULIVI.LI (intra- and interobserver). Each class had previously been assigned a disagreement weight, w, (Table 1). Disagreement of varying gravity (eg. class D represents a more serious disagreement than class B) is weighted according to wX.
varianceinm
N
A B C D
in measurements (mm)
0.0 oro.5 1.0 or 1.5 2.0 or 2.5 more than 2.5
Disagreement
100
z = - 0.84
Classification of the agreement between pairs of observations based on an individual wrist. wx is disagreement weights for each class. Differences
= 2.0
..O
ulnx
TABLE 1
ClllS.7
loo
SD = 1.23
weights
(“J 0 1 2 3
“Weighted kappa” is calculated from the formula: 0
1.0
0.0
1n 2.0
ulnarvariarreinmn
Where POXis the observed, and PcXthe chance agreement in each class. Standard error of K, is: 256
Fig. 2
The
distribution
measured (below).
a.m.
of
Palmer
ulnar
variance
(above)
in 100 normal wrists and by the Modified method
THE JOURNAL OF HAND SURGERY
ULNAR
VARIANCE
lnvestigating the intraobserver agreement we found no statistical significant difference in K, values for observer A. The agreement for observer B and C was significantly greater in advantage of the Modified method (Table 2 and 3). TABLE 2 Jntraobserver agreement (K ) for observer A, B and C. (95 per cent cozfidence limits). Observer A K w
Observer B
Method
Kw
Kw
Palmer Modified
0.93 * 0.03 0.94 zk 0.03
0.73 k 0.05 0.82 k 0.07
0.70 + 0.06 0.92 5 0.04
Observer
C
TABLE 3 lntraobserver agreement. The difference in Kw.values by Palmer’s and the Modified method IS tested for significance. Observer A
Observer B
t = 0.43 (p = 0.66)
Observer
t =
Up to now, Palmer has introduced the only accurate method of ulnar variance measurements. Using the transparent template as indicated by Palmer we found it difficult to approach the distal subchondral sclerotic line of the radius, because this line seldom forms a perfect semi-circle. Consequently, with several measurements of an individual wrist, the centre of the chosen semi-circle will vary in ulnar or radial direction with disagreement in ulnar variance measurements as a result. This disagreement will even increase in diseased wrists, where the distal subchondral sclerotic line might be less well marked as osteoarthrosis supervenes. Parallel lines and fixed points are the basis of the Modified method, which offers a simple procedure of ulnar variance measurements. Using the width of the distal radius (point D to point E) as radius in the semicircle we found in each case a close approximation to the distal subchondral sclerotic line of the radius.
C
t =
1.97 (p
DETERMINATION
6.13 (p
t is the value of “Student’s t-**at”
The agreement between pairs of observers observer agreement) showed a significant higher of agreement in favour of the Modified method, in the second evaluation between observer A (Table 4 and 5).
(interdegree except and B
TABLE 4 Interobserver agreement between pairs of observers. (95 per cent confidence limits) Observers
Observers A/B Method
K&v
I
B/C
Acknowledgment
Observers A/C
K
Kw
W,
1
0.74 & 0.05 0.89 ? 0.05
0.53 i 0.07 0.85 & 0.05
0.73 & 0.05 0.88 * 0.05
Palmer 11 Modified II
0.82 * 0.05 0.80 f 0.08
0.51 i 0.06 0.78 & 0.09
0.63 ? 0.06 0.91 i 0.04
Palmer Modified
Interobsewer The
difference
Modified
TABLE 5 agreement between pairs.
in K,,values method
by Palmer’s
and the
IS tested for significance.
Observers A/B
Observers A/C
I
t = 3.95 (p
t = 4.14 (p
t = 8.89 (p
11
t = 0.41 (p = 0.68)
t = 7.69 (p
I = 4.91 (p
t is the
value of “Student’s
Observers
B/C
t-test”.
Discussion
Since Hulten (1928) introduced the term “ulnar variance”, several works have been published, concerning the distribution of this variance in normal and diseased wrists (Gelberman, 1975; Chan, 1971; Beckenbaugh, 1980). VOL. 11-B No. 2 JUNE
1986
Considering the K, values in intra- and interobserver agreement, we found both methods reliable, although it must be concluded that the reliability of the Modified method, is significantly better in accurate determination of the ulnar variance.
This study was kindly supported by funds from the Medical Foundation for Vejle County. References BECKENBAUGH, R. D., SHIVES, T. C., DOBYNS, J. H. and LINSCHEID, R. L. (1980). Kienbock’s Disease. The Natural History of Kienbbck’s Disease and Considerations of Lunate Fractures. Clinical Orthopaedics and Related Research 149: 98-106. CHAN, K. P. and HUANG, P. (1971). Anatomic Variations in Radial and Ulnar Length in the wrists of Chinese. Clinical Orthopaedics and Related Research 80: 17.20. COHEN, J. (1968). Nominal scale agreement with provision for scaled disagreement or partial credit. Psychological Bulletin 70: 213-220. COONEY, W. P., DOBYNS, J. H. and LINSCHEID, R. L. (1980). Complications of Colles Fractures. The Journal of Bone and Joint Surgery 62A: 4: 613-619. EPNER, R. A., BOWERS, W. H. and GUILFORD, W. B. (1982). Ulnar variance-The effect of wrist positioning and roentgen filming technique. The Journal of Hand Surgery 7: 3: 298-305. GELBERMAN, R. H., SALAMON, P. B., JURIST, J. M. and POSCH, J. L. (1975). Ulnar Variance in Kienbbck’s Disease. The Journal of Bone and Joint Surgery 57A: 674-676. HULBN, 0. (1928). ijber anatomische Variation der Hand Gelenkknochen. Ein Beitrag zur Kenntnis Oer Genese verschiedener zwer Mondbeinveranderungen Acta Radiologica 9: 155-169. OVESEN, J. (1981). Shortening of the Radius in the Treatment of Lunatommalacia. The Journal of Bone and Joint Surgery 63B: 231-232. PALMER, A. K., GLISSON, R. R. and WERNER, F. W. (1982). Ulnar Variance Determination. The Journal of Hand Surgery, 7: 4: 376-379. SUNDBERG, S. B. and LINSCHEID, R. L. (1984). Kienbdck’s Disease. Results of Treatment with Ulnar Lengthening, Clinical Orthopaedics and Related Research, 187: 43-51.
257
VOL. 11-B No. 2 JUNE 1986
1985. 8 3 tv, 6000 Kolding,
Denmark.
Fig.
I
Shows ulnar method. For variance).
variance further
determination by the details see text. (U.V.
Modified = ulnar
radius. The ulnar variance is determined as the distance between the most distal part of the ulnar cortical rim and the semi-circle (Figure 1). In order to compare the two methods, 100 randomly selected persons were submitted to X-ray of the wrist. Criteria for selection:
1) Closed epiphysial plates. 2) No history nor radiological
evidence of previous injury or infection of the hand, forearm or elbow. 3) Cases of general affection of the skeleton were not accepted. 255
S. S. KRISTENSEN, E. THOMASSEN AND F. CHRISTENSEN
The ulnar variance of the 100 wrists was measured independently by three observers (the authors). To obtain the intra- as well as the interobserver agreement, the material was measured twice by each method. Consequently, each observer measured 100 wrists a.m. Palmer (Palmer I), 100 wrists by the Modified m_ethod (Mod. 11. 100 wrists. a:m: Palmer \-‘---- -,7 (Palmer II) and finally 100 wrists by the Modified method (Mod. II). The measurement
N being the sampling number. The difference between two independent tested for significance by the formula:
K, values is
accuracy was 0.5 mm. Where t is the value of “Student’s t-test”.
Statistical
method
The reliability of the two methods, expressed in intraobserver agreement and interobserver agreement in pairs, was calculated using “weighted kappa” statistics, as indicated by Cohen (1968). The advantage of this statistical method compared with the often used “chi square” method, is that “weighted kappa” takes the degree of disagreement into account.
Results
The distribution of the ulnar variance measurements are approximately normal using both methods, the mean value being slightly more negative using the Modified method (Figure 2).
N =
“Weighted kappa” values vary from - 1.0 (complete disagreement) through 0 (chance agreement) to + 1.O (complete agreement). The sampling distribution of “weighted kappa” values (IQ is approximately normal for large samples. Consequently, two independent K,,, values can be tested for statistical significance.
;; = - 0.60 SD = 1.38
The measurements were classified according to the rlparpp nf U~.~x‘ amrppmc=nt hptwppn nairc U’b’U’ “I ..‘._.“L “IC”I~~.. Y’u”U of nhw-rvltinnc VLJ0WI .ULIVI.LI (intra- and interobserver). Each class had previously been assigned a disagreement weight, w, (Table 1). Disagreement of varying gravity (eg. class D represents a more serious disagreement than class B) is weighted according to wX.
varianceinm
N
A B C D
in measurements (mm)
0.0 oro.5 1.0 or 1.5 2.0 or 2.5 more than 2.5
Disagreement
100
z = - 0.84
Classification of the agreement between pairs of observations based on an individual wrist. wx is disagreement weights for each class. Differences
= 2.0
..O
ulnx
TABLE 1
ClllS.7
loo
SD = 1.23
weights
(“J 0 1 2 3
“Weighted kappa” is calculated from the formula: 0
1.0
0.0
1n 2.0
ulnarvariarreinmn
Where POXis the observed, and PcXthe chance agreement in each class. Standard error of K, is: 256
Fig. 2
The
distribution
measured (below).
a.m.
of
Palmer
ulnar
variance
(above)
in 100 normal wrists and by the Modified method
THE JOURNAL OF HAND SURGERY
ULNAR
VARIANCE
lnvestigating the intraobserver agreement we found no statistical significant difference in K, values for observer A. The agreement for observer B and C was significantly greater in advantage of the Modified method (Table 2 and 3). TABLE 2 Jntraobserver agreement (K ) for observer A, B and C. (95 per cent cozfidence limits). Observer A K w
Observer B
Method
Kw
Kw
Palmer Modified
0.93 * 0.03 0.94 zk 0.03
0.73 k 0.05 0.82 k 0.07
0.70 + 0.06 0.92 5 0.04
Observer
C
TABLE 3 lntraobserver agreement. The difference in Kw.values by Palmer’s and the Modified method IS tested for significance. Observer A
Observer B
t = 0.43 (p = 0.66)
Observer
t =
Up to now, Palmer has introduced the only accurate method of ulnar variance measurements. Using the transparent template as indicated by Palmer we found it difficult to approach the distal subchondral sclerotic line of the radius, because this line seldom forms a perfect semi-circle. Consequently, with several measurements of an individual wrist, the centre of the chosen semi-circle will vary in ulnar or radial direction with disagreement in ulnar variance measurements as a result. This disagreement will even increase in diseased wrists, where the distal subchondral sclerotic line might be less well marked as osteoarthrosis supervenes. Parallel lines and fixed points are the basis of the Modified method, which offers a simple procedure of ulnar variance measurements. Using the width of the distal radius (point D to point E) as radius in the semicircle we found in each case a close approximation to the distal subchondral sclerotic line of the radius.
C
t =
1.97 (p
DETERMINATION
6.13 (p
t is the value of “Student’s t-**at”
The agreement between pairs of observers observer agreement) showed a significant higher of agreement in favour of the Modified method, in the second evaluation between observer A (Table 4 and 5).
(interdegree except and B
TABLE 4 Interobserver agreement between pairs of observers. (95 per cent confidence limits) Observers
Observers A/B Method
K&v
I
B/C
Acknowledgment
Observers A/C
K
Kw
W,
1
0.74 & 0.05 0.89 ? 0.05
0.53 i 0.07 0.85 & 0.05
0.73 & 0.05 0.88 * 0.05
Palmer 11 Modified II
0.82 * 0.05 0.80 f 0.08
0.51 i 0.06 0.78 & 0.09
0.63 ? 0.06 0.91 i 0.04
Palmer Modified
Interobsewer The
difference
Modified
TABLE 5 agreement between pairs.
in K,,values method
by Palmer’s
and the
IS tested for significance.
Observers A/B
Observers A/C
I
t = 3.95 (p
t = 4.14 (p
t = 8.89 (p
11
t = 0.41 (p = 0.68)
t = 7.69 (p
I = 4.91 (p
t is the
value of “Student’s
Observers
B/C
t-test”.
Discussion
Since Hulten (1928) introduced the term “ulnar variance”, several works have been published, concerning the distribution of this variance in normal and diseased wrists (Gelberman, 1975; Chan, 1971; Beckenbaugh, 1980). VOL. 11-B No. 2 JUNE
1986
Considering the K, values in intra- and interobserver agreement, we found both methods reliable, although it must be concluded that the reliability of the Modified method, is significantly better in accurate determination of the ulnar variance.
This study was kindly supported by funds from the Medical Foundation for Vejle County. References BECKENBAUGH, R. D., SHIVES, T. C., DOBYNS, J. H. and LINSCHEID, R. L. (1980). Kienbock’s Disease. The Natural History of Kienbbck’s Disease and Considerations of Lunate Fractures. Clinical Orthopaedics and Related Research 149: 98-106. CHAN, K. P. and HUANG, P. (1971). Anatomic Variations in Radial and Ulnar Length in the wrists of Chinese. Clinical Orthopaedics and Related Research 80: 17.20. COHEN, J. (1968). Nominal scale agreement with provision for scaled disagreement or partial credit. Psychological Bulletin 70: 213-220. COONEY, W. P., DOBYNS, J. H. and LINSCHEID, R. L. (1980). Complications of Colles Fractures. The Journal of Bone and Joint Surgery 62A: 4: 613-619. EPNER, R. A., BOWERS, W. H. and GUILFORD, W. B. (1982). Ulnar variance-The effect of wrist positioning and roentgen filming technique. The Journal of Hand Surgery 7: 3: 298-305. GELBERMAN, R. H., SALAMON, P. B., JURIST, J. M. and POSCH, J. L. (1975). Ulnar Variance in Kienbbck’s Disease. The Journal of Bone and Joint Surgery 57A: 674-676. HULBN, 0. (1928). ijber anatomische Variation der Hand Gelenkknochen. Ein Beitrag zur Kenntnis Oer Genese verschiedener zwer Mondbeinveranderungen Acta Radiologica 9: 155-169. OVESEN, J. (1981). Shortening of the Radius in the Treatment of Lunatommalacia. The Journal of Bone and Joint Surgery 63B: 231-232. PALMER, A. K., GLISSON, R. R. and WERNER, F. W. (1982). Ulnar Variance Determination. The Journal of Hand Surgery, 7: 4: 376-379. SUNDBERG, S. B. and LINSCHEID, R. L. (1984). Kienbdck’s Disease. Results of Treatment with Ulnar Lengthening, Clinical Orthopaedics and Related Research, 187: 43-51.
257