Skeletal Radiol (1994) 23:43-48

Skeletal Radiology

Clinical use of the simple 3D-calculation in J. Schmidt, F. Gassel

Klinik und Poliklinik ffir Orthop/idie der Universit~it zu K61n, Cologne, Germany

scoliosis

Abstract. In this paper we show the clinical application of a simple method for calculating three-dimensional shape in scoliosis by the use of two tables based on normal standard X-rays in the anteroposterior and lateral pro- jections. The three-dimensional alignment should be con- sidered in both conservative and operative correction. In 57 patients with 87 scoliotic curves we measured the well- known Cobb angle (e) and determined the vertebral rota- tion according to the method of Nash and Moe. We com- pared this information with the results of the calculated three-dimensional angles of scoliosis (angle/~ between the curvature plane and the sagittal plane, angle a as the true angle of scoliosis in this curvature plane). In 76 curves (87%) our method was practicable. The true angle o- is always higher than the projected angle e, especially in the clinically relevant range of 20o-40 ~ . Poor correlation is shown between the projected angle c~ and the true angle a (r=0.41 for thoracic curves and r=0 .57 for lumbar

Correspondence to: Dr. reed. Joachim Schmidt, Klinik und Poli- klinik ffir Orthop~idie der Universit~it zu K61n, Joseph-Stelzmann- Strasse 9, D-50924 K61n, Germany

curves) and almost no correlation between vertebral ro- tation and the true angle o- ( r=0.10 for thoracic curves and r--= 0.44 for lumbar curves) and the curvature plane ~) (r=0). The three-dimensional shape of scoliosis can- not be estimated by the well-established projected angles and indices and we recommend the use of our simple method for the radiological investigation of scoliotic pa- tients.

Key words: Scoliosis Three-dimensional investigation Standard X-rays - Diagnostic procedure

The importance of the three-dimensional alignment of scoliosis as the basis for determining the exact diagnosis and therapy has been stressed in the literature [2-6, 8-10, 12-15]. Great efforts have been made to obtain a very exact picture of the three-dimensional shape of scoliosis, but the techniques involved are very costly in time and effort and therefore not practicable for clinical purposes. The deformity of the spine is therefore usually measured

I plane

I plane

~ture plane

Fig. 1. Definition of the sagittal and curvature plane, the angles c~, s a. and /~ and the axis of scoliosis N1-N2. (By kind permission of Acta Orthopaedica Belgica)

�9 1994 International Skeletal Society

I~

~'~

~-~

0 ~'*

~ Z

~ ~r"

~.~

�9

~m

~

~ ~

' ~

~ ~

.~

~ ~.

~ ~

o~

0 ~

~' ~

~-*

~.,

~

,-

~

~

~

~

~

~

~

0

~ ~

~ ~

~ ~

~ ~

~'

~:r

~

~'

~ ~

~ ~

~ ~

~ ~

o ~

~ ~

. ~

~o

o

~ ~

~ ~

~.~0

_ ~"

~ ~

~ ~

~,.

o-

"

o m

~

~,.~

_..~

.,.,.~

~

~o

.~

~

~ ~

:r'~

. ,

Ur=

-~

~ ~

.~

~

&.

~ ~-~

-

�9

<~

~,

~ I~

~-

. ~ ~

~..~

~-

."

r ~

~-,

.

.~

~ [:

:Y'~

~

r _

,~,~

-~-~

l,O

0

~:~

~.

_,.,

~u

~ .

~

o =

.~

Z~

,~

~

~ ~

m.

o ~

~ ~ o o ~

~"

l::r

',.<

~

,-.,

�9

~ ~

~ ~

O~ "

~ ~

~-~

o o

~ o

"~

~

~ o.

, ~

.

~ ~

. ~-

--~

I~

~'~

I~

~

.

m

b..)

o" r 0 o o 9

tao

L/I

t,o

t-o

o,l

o o~

L~

o" E"

0 m o :tO

o 0 m

�9

o F

~o

~o

~"

0 o

J. Schmidt and F. Gassel: Simple 3D-calculation in scoliosis

Table 2. Table for the determination of the true angle of scoliosis cr in the range 0-90 ~ and l~ ~ in steps of 5 ~ and 2 ~

45

J, 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

5 45 27 19 14 12 10 9 8 7 7 6 6 6 5 5 5 5 10 64 45 34 27 23 19 17 15 14 13 12 12 11 11 10 10 10 15 72 57 46 38 32 28 25 23 21 19 18 17 16 16 16 15 15 20 77 64 55 47 41 36 32 30 27 25 24 23 22 21 21 20 20 25 79 70 61 54 48 43 39 36 33 31 30 28 27 26 26 25 25 30 81 73 66 59 54 49 45 42 39 37 35 34 32 32 31 30 30 35 83 76 70 64 59 54 51 47 45 42 41 39 38 37 36 35 35 40 84 78 73 68 63 59 56 53 50 48 46 44 43 42 41 40 40 45 85 80 75 71 67 63 60 57 55 53 51 49 48 47 46 45 45 50 86 82 78 74 70 67 64 62 59 57 55 54 53 52 51 50 50 55 87 83 80 77 74 71 68 66 64 62 60 59 58 57 56 55 55 60 87 84 82 79 76 74 72 70 68 66 65 63 62 62 61 60 60 65 88 85 83 81 79 77 75 73 72 70 69 68 67 66 66 65 65 70 88 86 85 83 81 80 78 77 76 74 73 73 72 71 71 70 70 75 89 87 86 85 84 82 81 80 79 78 78 77 76 76 75 75 75 80 89 88 87 87 86 85 84 84 83 82 82 81 81 81 80 80 80 85 90 89 89 88 88 87 87 87 86 86 86 86 85 85 85 85 85

~, 1 3 5 7 9 11 13 15 17 19 21 23 25

1 45 18 11 8 6 5 4 4 3 3 3 3 2 3 72 45 31 23 19 15 13 11 10 9 8 8 7 5 79 59 45 36 29 25 21 19 17 15 14 13 12 7 82 67 55 45 38 33 29 25 23 21 19 17 16 9 84 72 61 52 45 40 35 31 28 26 24 22 21

11 85 75 66 58 51 46 41 37 34 31 28 26 25 13 86 77 69 62 56 50 46 42 38 35 33 31 29 15 86 79 72 66 60 55 50 46 43 39 37 34 32 17 87 80 74 68 63 58 54 50 46 43 40 38 36 19 87 81 76 71 66 61 57 53 50 47 44 41 39 21 87 82 77 72 68 64 60 56 53 50 47 44 42 23 88 83 78 74 70 66 62 59 55 53 50 47 45 25 88 84 79 75 71 68 64 61 58 55 52 50 48

" Since the table is relevant for both measured angle cq and angle ez, read al and a2

example 28 ~ ) and the angle in the lateral projection (38 ~ ) are di- vided by a vertical line into the angles el (13~ ~2 (15~ and 61 (23~ In each of Tables 1 and 2 the upper one shows the whole spectrum of the angles. The lower one shows the relevant spectrum in steps of 2 ~ from 1 ~ to 25 ~ From Table 1 the angle /~ which indicates the position of the curvature plane can be read directly (29~ In Table 2 it is not possible to read the true angle of scoliosis directly. After measuring el (13 ~ it is read al (26~ with e2 it is read a2 (29~ The sum of al and a2 is the true angle a (55 ~ that is being sought. The reading is possible from the same table because the calculation is identical.

We examined the standard X-rays of the total spine in the anteroposterior and lateral projections of 57 patients with scoliosis who were treated conservatively at the Orthopaedic Clinic of the University of Cologne. Due to the presence of several double and triple curves, the number of curves rose to 87.

First of all we measured the projected Cobb angle and the vertebral rotation by Nash and Moe's method (index and approxi- mate degree of rotation) [11]. Then we calculated the true angles /~ and a using the above-mentioned method by dividing the pro- jected angles. Additionally we measured the axis of scoliosis, con- structed on the X-rays as a straight line through the centres of the end-vertebrae of the curves. Instead of the vertical line we

divided the measured projected angles on the X-rays also by a line parallel to this axis. Again we used our tables for a modified calculation of the true angles of scoliosis (Fig. 3).

Finally we compared the results of our calculations and mea- surements with diagrams, the Pearson correlation coefficient [7] and calculation of mean values.

Resu l t s

W i t h o u r p r e v i o u s l y d e s c r i b e d m e t h o d o f c a l c u l a t i o n , u s i n g a ve r t i ca l l ine, the c a l c u l a t i o n o f t he t rue ang les / / a n d o- was p r a c t i c a b l e o n l y in 67 cases ( 7 7 % ) , because it was n o t poss ib l e to d iv ide the p r o j e c t e d ang l e by this l ine in the r e m a i n i n g 20 curves .

T h e m e a s u r e m e n t o f the p o s i t i o n o f the axis o f sco l io- sis s h o w e d in the a n t e r o p o s t e r i o r v i e w a m e a n d e v i a t i o n to the ve r t i c a l l ine o f 3 . 7 o + 2 . 9 ~ ( r ange 0 ~ ~ ) a n d in the l a t e r a l v i e w o f 8.6~ 5.0 ~ ( r a n g e 0-2~~

D i v i d i n g the p r o j e c t e d ang les by a l ine pa ra l l e l to this axis we m e a s u r e d m o d i f i e d t rue ang les /~ a n d a.

46 J. Schmidt and F. Gassel: Simple 3D-calculation in scoliosis

Fig. 2A, B, Scoliotic spine: ~=28 ~ 6=38 ~ cq =13 ~ ~2=15 ~ 61 = 23 ~ From Tables 1 and 2 the interpolations f l=29 ~ and a = 5 5 ~ are derived

UB

Z:3

Fig. 3. Construction of the axis of scotiosis and the modified calcu- lation of the true angle of seoliosis

In this way the number of cases in which measurement was possible increased to 76 (87%).

The two methods, division of the projected angle by a vertical line and by a line parallel to the axis, show comparable results, especially in the range of the clini- cally relevant angles of scoliosis above 25 ~ (Fig. 4). The mean values (34.03 ~ vs 32.04 ~ modified) and the stan- dard deviation (12.49 ~ vs 14.51 ~ modified) are also simi- lar. Subsequent calculations are therefore obtained by

1~176 /

60

%

40 t 20

0 I I

0 10 20 30 40 50 60 70

Angle of scoliosis (o)

Fig. 4. Comparison of the two measurement techniques

the first-described method with the vertical line (67 curves).

Figure 5 shows the relation between the projected an- gle ~ and the true angle a of the scoliotic curves for the different types (thoracic, lumbar, C-shaped). Ob- viously the true angle o is higher than the projected angle e, which can also be read by the mean value (true 34.03~ ~ , projected 23.18~ ~ ) and by the number of curves above 40 ~ (true 26, projected 5).

The correlation between the Cobb angle c~ and the true angle a is, as expected, very low (thoracic r = 0.41), lumbar r = 0.57).

We found almost no correlation between the true an- gle of scoliosis o- and the rotation of the vertebrae in the measurement technique of Nash and Moe [11] (thor- acic r=0.10, lumbar r--0.44; Fig. 6), neither was there any correlation between the rotation of the vertebrae and the angle/~ (Fig. 7).

Discussion

Using our method for the three-dimensional calculation of scoliosis, the complex anatomical changes are reduced to clinically relevant angles, especially useful for the con- struction of braces, which are based on these angles. The direction and the position of the correction forces can be determined more exactly. The measurement may even be employed for operative procedures, although the intersegmental differences, which cannot be mea- sured, must be considered more precisely.

Using the two tables it was possible to calculate the true angles of scoliosis in 87% of our scoliotic curves. Normally simply a vertical line can be used for this calcu- lation. In some cases, however, this line does not divide the projected angles. In such cases it is possible to obtain the true angles by constructing the axis of scoliosis and divide the projected angles by a line parallel to this axis.

J. Schmidt and F. Gassel: Simple 3D-calculation in scoliosis 47

70:

60

50

b o 40

30

20

A

10

O

* 0 0 ~ ~ 0

oe ~ ~

o +** ~ ~{ 0 0 0 -~ 0

0 o 8

0 40 00~

% o 13

+~

Thoracic

o Lumbar

+ C-shaped

I I 1 I I I

10 20 30 40 50 60 70

Cobb angle

60

o_ 50

o 40

t~ 30

20 O

10

0 0

B

.,#

I I I I I

10 20 30 40 50 60

Cobb angle o~ thoracic

70

6O

50

40 0

30

20

10

i 0 i i i *

0 L 0 0 O -

13

0 10 20 30 40 50 60

C Cobb angle o~ lumbar

Fig. 5A-C. Relation between the projected angle c~ and the true angle ~ o f scoliosis. Correlations for A thoracic, lumbar, and C- s h a p e d curves, B thoracic curves alone and C lumbar curves alone

50

4O g--

r- 30 0

5 20 rr

10

X

x x x x

x x x x �9 x

x x x x x x �9 x x x x ~

x x ~ x �9 x x x x

xX x x x ~ t x x x x x x

x ~=~ x x x

, . . . . i : : t . - - . j

10 20 30 40 50

True angle o

0 x

0 60 70

Fig. 6. Correlation between the true angle a and the rotation of the vertebrae

The results of the two procedures are similar and there- fore comparable for clinical purposes. In the remaining curves, where a calculation was not possible, we found in the sagittal view either a C-shaped scoliosis (4 cases), with the upper end-vertebra in the thoracic kyphosis and the lower one in the lumbar lordosis, or a flat spine (7 cases).

The deviation of the axis of scoliosis from a vertical line is negligible in the anteroposterior view. In the later- al projection it can be taken into account, when it is necessary to form a parallel line to divide the angles in order to use the tables. In these cases, for the three- dimensional shape, we must consider that the length be- tween the sagittal and curvature plane (Fig. 1) is tilted by some degrees from the vertical.

For mathematical reasons, the true angle of scoliosis o- must be higher than the projected angle c~. The differ- ence is dependent on the position of the curvature plane, described by the angle/ / (Fig. 8). This figure also shows that the difference is greatest in the clinically relevant spectrum between a projected Cobb angle of 20 ~ and

50

40

c 30 O

% 20 rr"

10

X

X X

x x x x x

x x x x x x x

x x x x x z x x x ~x x

x x x x ~x x x x

x x x x x x x

x z x z x x x x

10 20 0

0 30 40 50 60 70 80 90

Angle [3

Fig. 7. Correlation between the angle /~ and the rotation of the vertebrae

9O

80- ~ . ~ - - -'~-: :

70-

60-

50-

40-

30-

20- [] 25 ~

o 45 ~ 10- �9 85 ~

01 I I 3 J 0 I I I t I

t 0 20 40 50 60 70 80 90

O :

Fig . 8. Relation between the projected angle c~ and the true angle cr of scoliosis depending on the position of the curvature plane (/~)

48 J. Schmidt and F. Gassel: Simple 3D-calculation in scoliosis

40 ~ . This should be considered especially in the indica- tion for bracing (normally > 20 ~ projected Cobb angle) and for operative treatment (> 40~

Vertebral rotation is measured in the projected an- tero-posterior view by an index or degrees [11]. This explains the poor correlation with the three-dimensional true angle of scoliosis, but the main problem is that the thoracic vertebrae are rotated in a direction opposite to the curvature plane (fl). Only in the lumbar spine are the rotation of the curvature plane and of the verte- brae in the same direction [15]. This is evident in the differing correlations (thoracic r= 0.1, lumbar r = 0.44) in our examination. Because of lack of correlation, the position of the curvature plane cannot be estimated by the rotation of the vertebrae.

Conclusion

The three-dimensional alignment of scoliosis should be considered in both conservative and operative treatment. This allows the direction for the necessary correction forces to be estimated more exactly. In control examina- tions additional information is obtainable by the three- dimensional investigation. In future it will probably prove useful for defining scoliosis more exactly.

Our results show that the calculation of three-dimen- sional deformity of scoliosis based on normal standard X-rays is practicable in the majority of scoliotic curves. The calculation can be performed in two ways, depend- ing on the position of the axis of scoliosis, using the same tables. The results of the two methods are nearly the same and they can therefore be regarded as equiva- lent for clinical purposes. Only techniques costly in time and effort with additional X-ray-investigations could in- crease the precision.

References

1. Cobb JR (1948) Outline for the study of scoliosis. Am Acad Orthop Surg Inst Course Lect 5:261

2. Deacon P, Flood BM, Dickson RA (1984) Idiopathic scoliosis in three dimensions. J Bone Joint Surg [Br] 66 : 509

3. De Smet AA, Tarlton MA, Cook LT, Fritz SL, Dwyer SJ (1980) A radiographic method for threedimensional analysis of spinal configuration. Radiology 137:343

4. Dickson RA (1987) Scoliosis: how big are you? Orthopedics 10:881

5. Du Peloux J, Fauchet R, Faucon B, Stagnara P (1965) Le plan d'~lection pour l'examen radiologique des cypho-scolioses. Rev Chir Orthop 51 : 517

6. Edholm P (1965) Anatomic angles determined from two projec- tions. Acta Radiol (Suppl) (Stockh) 259

7. Hengst M (1967) Einffihrung in die mathematische Statistik und ihre Anwendung. B. I. Hochschultaschenbficher Bd 42. Mannheim

8. Hindmarsh J, Larsson J, Mattsson O (1980) Analysis of changes in the scoliotic spine using a three-dimensional radio- graphic technique. J Biomech 13:279

9. Howell FR, Dickson RA (1989) The deformity of idiopathic scoliosis made visible by computer graphics. J Bone Joint Surg [Br] 71:399 Lindahl O, Movin A (1968) Measurement of the deformity in scoliosis. Acta Orthop Scand 39:291 Nash CL, Moe JH (1969) A study of vertebral rotation. J Bone Joint Surg [Am] 51:223 Pearcy M J, Whittle MW (1982) Movements of the lumbar spine measured by three-dimensional X-ray analysis. J Biomed Eng 4:107 Schmidt J, Gassel F, Naughton S (1992) Calculation of 3-D deformity in scoliosis by standard roentgenograms. Acta Orth- op Belg 58 : 60 Shufflebarger HL, King WF (1987) Composite measurement of scoliosis : a new method of analysis of the deformity. Spine 12:228 Stokes IAF, Bigalow LC, Moreland MS (1987) Three-dimen- sional spinal curvature in idiopathic scoliosis. J Orthop Res 5:102

10.

11.

12.

13.

14.

15.