Radiography (2008) 14, 170e174

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Selecting the correct x-ray tube tiltangle and roof pillar rotation for bedsideradiography with combined cranio-caudaland lateral cassette tilt

Djordje Kovacevic a,*, Arne Skretting b

a Department of Radiology, Rikshospitalet-Radiumhospitalet Medical Center,Ullernchausseen 70, 0310 Oslo, Norwayb Department of Medical Physics, Rikshospitalet-Radiumhospitalet Medical Center, Oslo, Norway

Received 6 May 2006; accepted 10 November 2006Available online 4 January 2007

KEYWORDSPerpendicularincidence;Bedside radiography;Cassette tilt

* Corresponding author. Tel.: þ47 2E-mail address: djordje.kovacev

Kovacevic).

1078-8174/$ - see front matter ª 200doi:10.1016/j.radi.2006.11.004

Abstract In bedside radiography it is sometimes necessary to use a combined cranio-caudaland lateral tilt. Setting up the unit so that the central ray of the beam enters perpendicular tothe surface of the image receptor is a non-trivial task as well as time consuming. The twographs presented here constitute a convenient means to select correct setup of the x-ray tubein cases where the cassette has a combined caudo-cranial and lateral tilt.ª 2006 The College of Radiographers. Published by Elsevier Ltd. All rights reserved.

Aim

To ensure perpendicular incidence on an imagereceptor (cassette) that has combined cranio-caudal andlateral tilt.

2430033.ic@radiumhospitalet.no (D.

6 The College of Radiographers.

Introduction

In bedside radiography it is sometimes necessary to usea combined cranio-caudal and lateral tilt. The x-ray unit athand in our hospital can rotate around a roof-mountedvertical pillar and tilt relative to a horizontal axis throughthis pillar (Fig. 1). Setting up the unit so that the central rayof the beam enters perpendicular to the surface of theimage receptor is a non-trivial task and may be timeconsuming.

Published by Elsevier Ltd. All rights reserved.

Figure 2 (a) Three-dimensional view of the position of the cassesubsequently an angle a around the y-axis. The unit vector z0 is pethe central axis of the x-ray beam must have. The two angles a anThe line AeA represents the direction of the projection of z0 intohead tilt angle. (c) A view of the line AeA in the xy-plane, showinto the xy-plane (the table) along the edges of the cassette.

Figure 1 The actual x-ray head can rotate around a verticalpillar and tilt around an axis perpendicular to the pillar, as il-lustrated schematically in this figure. The x0 and y0 axis runalong the edges of the cassette.

Bedside radiography with combined cranio-caudal and lateral cassette tilt 171

Methods

The geometry may be described using vector algebra asshown in Fig. 2.

Consider a fixed coordinate system with x, y, z axesassociated with the table. Assuming we start with thecassette flat on the table with its edges parallel to thoseof the table, then the orientation of its edges can bedescribed by the unit vectors x, and y. The normal to thecassette can be represented by the unit vector z. Oncethe cassette is rotated through an angle g about the x-axis and subsequently an angle a about the y-axis thenew position of its edges and normal would be repre-sented by the unit vectors x0, y0, z0 which are the vectorsobtained by rotating the unit vectors x, y, z through anangle g about the x-axis and subsequently an anglea about the y-axis. The vectors x0, y0, z0 can be obtainedfrom x, y, z using standard matrix methods. The z0 unitvector corresponds to the cassette and corresponds tothe direction that the central beam must have to obtainperpendicular incidence onto the cassette. We now de-termine the rotation and tilt angles qrot and 4tilt of thecentral beam.

From Fig. 2b one uses the scalar product to give

z$z0Zjzj$jz0jcosð4tiltÞ

The component of z0 in the xy-plane runs along the line AeA(Fig. 2a). The rotation angle relative to the y-axis (withouttube rotation, the tube will tilt in the yz-plane) of the

tte after rotating it through an angle g around the x-axis andrpendicular to the cassette and represents the direction thatd b are assumed to be known from protractor measurements.the xy-plane. (b) A section through AeA and z0 showing the

g the head rotation angle. (d) and (e) sections perpendicular

Figure 3 (a) Head rotation angle as a function x-axis protrac-tor reading for different y-axis protractor readings. As an ex-ample it is shown how an x-axis protractor angle of 22degrees and y-axis protractor angle of 12 degrees results ina head rotation equal to 58 degrees. (b) Head tilt as a functionof x-axis protractor reading for different y-axis protractorreadings. As an example it is shown how an x-axis protractorangle of 22 degrees and y-axis protractor angle of 12 degreesresults in a head tilt equal to 26 degrees.

172 D. Kovacevic, A. Skretting

original coordinate system may then be determined fromthe formula

y$z0xyZjyj$jz0xy jcosðqrotÞ

In the laboratory, the angles a and b may be measuredrelative to the horizontal xy-plane (the table) by usinga protractor.

The angle g may be determined from the fact that the zcomponent of y0 may be expressed in two different ways to

give the same result (refer to Fig. 2a). Putting these twoexpressions equal gives

Sin bZsin g cos a

from which sin g and cos g may be determined once a andb are known. The rotation and tilt angles are then calcu-lated as outlined above.

From the above formulas one may build a table that liststhe angles qrot and 4tilt as functions of a and b. However, itis also possible to present the correct head rotation angle(Fig. 3a) and head tilt angle (Fig. 3b) as two sets of graphswith the x-axis protractor angle (a) along the abscissa andone curve for each of a set of fixed values of the y-axis pro-tractor reading b. One has to read both figures to find thecorrect pair of angles. These graphs enable the user to in-terpolate between curves. Fig. 3a and b also illustrate theprocedure for an x-axis protractor angle of 22 degreesand a y-axis protractor reading of 12 degrees. For thiscombination the head rotation and tilt must be 58 and 26degrees, respectively.

Fig. 4 shows the step-by-step procedure to obtain thecorrect setup.

Experimental verification of the formulas andgraphs

In order to check that the use of the diagrams of Fig. 3a andb provided correct setup of the tube, we performed a testwith a collimator test tool from RMI phantom, Middletown,WI. The phantom has a 15.6 cm high PMA (perspex) cylindermounted perpendicularly to a base plate. On the axis of thecylinder there are two steel balls, one at the base plate andone at the top. If the central ray of the x-ray beam entersperpendicular to the cassette surface, the projections ofthe two balls will coinside. A thin dark circle inside the cyl-inder (the cylinder is represented by the white ring) marksa deviation of 2.4 degrees.

We obtained four images using filmefocusedistance(FFD) 100 cm, 75 kVp and 2 mA. The cassette was deliber-ately tilted in different ways, and its x- and y-axes angleswere measured with the protractor. The combinationsturned out to give 0/0, 4/10, 12/10 and 8/21 degrees forthe lateral and cranio-caudal tilt angles, respectively. Thetube was then tilted and rotated as read from the two dia-grams (Fig. 3a and b). By horizontal translation of the pa-tient bed the central beam of the x-ray field (as indicatedby the light field) was made to hit the upper lead beadand an image was produced. As is demonstrated in Fig. 5,the setup was correct to within 2.4 degrees in all cases.

Discussion and conclusion

The two graphs presented here constitute a convenientmeans to select correct setup of the x-ray tube in caseswhere the cassette has a combined caudo-cranial andlateral tilt, and the method is in daily use in our institution.It would of course also be possible to implement theformulas on a PC attached to the equipment, and havethe two angles computed immediately after manuallyentering the protractor readings or fetching them

Figure 4 Step-by-step illustration of the method. (a) Put the protractor along the lateral (x0) direction of the cassette (or imagereceptor) and measure the x-axis protractor angle (a). (b) Repeat with the protractor along the second edge (y0 axis) of the cassetteand measure y-axis protractor angle (b). (c) Read the rotation angle from Fig. 3a and rotate the tube using an angular scale of theequipment as illustrated in (d) (the photo is taken from the roof). (e) Read the tilt angle from Fig. 3b and the tilt. (f) Move the x-raytube horizontally until the central ray hits the centre of the cassette and adjust the collimator to the size of the cassette.

Bedside radiography with combined cranio-caudal and lateral cassette tilt 173

Figure 5 Experimental verifications of the method. The cassette was deliberately setup to give protractor readings of the lateraland cranio-caudal edge tilts, and an RMI phantom containing two small steel balls at different distances along an axis perpendicularto the detector, was used to verify that the projections of the two beads nearly coincide. The inner dark circles in the images marka deviation of 2.4 degrees.

174 D. Kovacevic, A. Skretting

automatically from an electronic device that could measurethe cassette tilt angles.

It is important for correct use of the method that the x-axis (the laterally running edge of the cassette) is tilted insuch a way that it remains in a plane that is perpendicularto the long axis of the table (the y-axis).

The slight deviations seen in Fig. 5 probably stem frominaccurate protractor readings as well as from practical

problems in setting up accurately the required tube tiltand rotation angles (the scales are too coarse).

For an x-ray tube that can rotate around a vertical pillarand tilt relative to an axis perpendicular to that pillar, themathematical framework presented here together with thegraphs of Fig. 3a and b provide an accurate and easy way toderive the correct head rotation and head tilt needed toobtain perpendicular incidence on the cassette.