The main aim of our work was to determine axial rotation of the vertebra from AP projection with the assistance of graphical principles. The new radiographic method of quantifying axial vertebral rotation is based on geometric shape properties of the vertebrae and their mutual dimensional proportions ( (table 1–5, p. 29)). It is necessary to mention that the biomechanical terminology  is different to the terminology of the Scoliosis Research Society (SRS) according to Stokes . Both terminologies have different orientation of axis. Henceforth the SRS’s orientation will be used .Primarily a vertebral rotation device was made to compare particular readings of X-ray film with real known pre-defined values. The vertebral rotation device allows set rotation from zero to 45 degrees in 3 degree rotation increments, Figure 1.
The method was verified on 5 non-deformed human lumbar vertebrae of the same spine column and subsequently on non-deformed human thoracic and lumbar vertebrae of other individuals. The vertebrae were provided courtesy of both the Faculty of Science and the Faculty of Physical Education and Sport, Charles University in Prague.The method is based on the presumption that the diameter of measurable geometric rotation in the transversal plane is in a correlation with the height parameter of the vertebra. The basic idea of this method is illustrated on Figure 2.
The process of first axial vertebral rotation evaluation: The locations of pedicle shadows (inner or outer contour or middle of pedicles) were chosen as in the other previously mentioned methods [7, 8, 10, 11]. It would be advantageous to take the inner contours of pedicles. Two X-ray pictures of thoracic vertebra Th6 with rotation 21° and the lumbar one of vertebra L2 with rotation 21° were tested during the first stage. Perpendiculars were placed through the middle of the vertebral body and through the pedicle’s middle to the base of the vertebral body as shown in both pictures as the second step. The apex of the angle of 21° was placed towards the centre of the vertebral base so that one leg of the angle was adjacent to the perpendicular through the centre of the vertebral body and the second one crossed the perpendicular of the pedicle’s centre. The crossover was at almost the midpoint of vertebral body height of lumbar vertebra and close to ¾ of vertebral body height of thoracic vertebra. These principles were tested on all X-ray pictures with rotation from 0 to 45 degrees. The comparison was closely relevant. The idea was shown as applicable and following this it had to be verified, compared and demonstrated.
The variety of average dimensions of thoracic vertebrae , which are visible during AP projection of conventional films show that the average aspect ratio of vertebral widths to heights is less than 9%. The aspect ratio of radiuses (x = LED/2 + SCD/2); ) in the transversal plane to vertebral heights is less than 7%. It is possible to use the same algorithm for all thoracic vertebrae. There is a similar situation for lumbar vertebrae L1 to L4. They are very similar to each other. It seemed that vertebra L5, which is a little lower to the other lumbar vertebrae, would need its own algorithm too, but the experiment showed that thoracic succession could be likewise  applied to vertebra L5.
The non-rotated centre of the distance between the pedicles lies on the same sagittal plane as the centre of vertebral body width. If the vertebra is rotated the pedicle’s centre and vertebral body centre will recede. The distance between both centre points is named d. It represents the axial vertebral rotation on radius x. It is generally valid that d = x* tan α, for small angles tan α ~ α [m, rad] by goniometric functions (differences: 0.10° on angle 10°, 0.35° on angle 15°, 0.85° on angle 20°, 1.72° on angle 25° and 3.08° on angle 30°). It follows the accuracy of the radiographic method. It deteriorates with degree of rotation. The magnitude of error is very favourable up to 20° and acceptable to 30° for clinical practice.
Thoracic and lumbar vertebrae have different aspect ratio of radius x to height z (x/z(Th) = 1.21 and x/z
L 1−4 = 0.86; x = LED/2 + SCD/2; z = VBHp ). The verification of all tested vertebrae in all steps of rotation confirmed the criterions for thoracic spine and vertebra L5 x = 0.75*z [m] and for lumbar spine x = 0.5*z [m], Figure 3.The procedure which is applicable to lumbar vertebrae is illustrated in Figure 4. The procedure applicable to thoracic vertebrae is illustrated in Figure 5. The basic point was selected as the centre of the width of the projection of a vertebral body A. It is simply obtained by copying the outline 1 of the vertebral body or by drawing compromise rectangles or rhomboids over pictures of deformed vertebrae and marking their diagonals 2. The centre of the distance between the pedicles is determined by drawing perpendiculars 3 from the bottom edge of the vertebra at the point of the interior projection of pedicles (all perpendiculars are given as perpendiculars to the bottom edge of the vertebra). The points of the intersection of the perpendiculars and the straight line from the top and bottom edge of the vertebral projection constitute another quadrangle very similar to a rectangle. By drawing diagonals 4 of this rectangle, we obtain the required centre of the distance between pedicles B. Thus, we have determined the distance d. Another perpendicular 5 is drawn from the bottom edge of the vertebra through the centre of the projection of the vertebral body A. The point of intersection of this perpendicular with the bottom edge of the vertebra is shown as C. From this point, due to the proportions of the lumbar and thoracic vertebrae, we must adopt a different procedure for the thoracic and lumbar sections of the spine.In the case of lumbar vertebrae, the axial vertebral rotation angle is the angle between the perpendicular 5 leading through the centre of the vertebra A and the straight line 6 leading through points B and C. The whole procedure is described in stages in Figure 4.
In the case of thoracic vertebrae, it is necessary to find point D, obtained on the perpendicular from the bottom edge of the vertebra, leading through point B, by dividing in half the distance between point B and the top edge of the vertebra. This can be measured or just estimated without the risk of any significant error for determining the axial rotation angle.The identified point D corresponds to ¾ of the vertebral body height. The axial rotation of thoracic vertebrae and L5 vertebra is the angle between the straight line leading through point A – straight line 5 and the straight line leading through points C and D – straight line 7. The particular steps of the procedure are described in Figure 5. There is an important rule for observing the invisible pedicle shadow which is merged with the vertebral body contour in larger axial rotation - usually more than 30°. There is an important rule for observing the invisible pedicle shadow which is merged with the vertebral body contour in larger axial rotation. When the shadow of pedicle is not visible in the concave site, the contour of the vertebral body on the concave site instead of the pedicle contour will be visible. We suppose that the pedicle coincides with the vertebral body contour and the larger axial rotation - usually more than 30° - does not change its location.
Local axial vertebral rotation is different to global spine axis . The declination of vertebral body on a sagittal plane is displayed as an ovoid shadow on the frontal plane, but the width and height of the vertebra’s body is visible. The width of the vertebral body is decreased by the declination of the vertebra only slightly without observable influence to aspect ratio of vertebral width to heights.The vertebrae of severely affected scoliotic spines usually have local deformity and asymmetry. Severely affected structural scoliotic curves of the thoracic spine are shown as wedged vertebral bodies on X-ray pictures. The graphical centre of a wedged vertebral body drifts to the apex of the wedge according to standard geometrical principles, Figure 6a, and right substitute procedure on wedged vertebra, Figure 6b. It is supposable that the vertebral body basis is parallel to pedicle’s suture.As it is necessary to find both the centre of the vertebral body width on its base and the centre of the pedicle’s position, it is necessary to draw compromise rectangles or rhomboids relating to convex height over pictures of wedged vertebrae, Figure 6b. Preservation of habitual ratio height/width. The convex site isn’t deformed by compression. The base should be parallel to the pedicle’s suture. We presume that a small deviation in parallelism isn’t significant. Rectangles and rhomboids eliminate undesirable drift d’ into the radiographic method, Figure 6b. Examples in Figure 7 clearly explain possibilities how the approach could be applied to deformed vertebrae to find the centre of the vertebral body width.