A collision prevention software tool for complex ... - BIR Publications

The British Journal of Radiology, 73 (2000), 537±541

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2000 The British Institute of Radiology

Short communication

A collision prevention software tool for complex threedimensional isocentric set-ups I BEANGE, BSc and A NISBET, PhD Department of Medical Physics and Bioengineering, Raigmore Hospital, Inverness IV2 3UJ, UK

Abstract. During treatment planning it can be dif®cult to check whether a particular plan is workable, that is it avoids obstructing treatment beams with parts of the patient couch and it avoids collisions between the treatment machine head and the patient couch. To overcome this problem, the trigonometric relationships between the placement of treatment beams and the patient couch are examined. From these relationships a set of useful equations that can be generally applied is derived. The application of these equations practically as a simple (nongraphical) planning tool is described. The resulting tool enables the feasibility of a plan to be checked during treatment planning, and gives guidance as to how a patient could be repositioned to allow the use of a plan when potential beam obstructions are detected, prior to veri®cation of the treatment on a simulator.

A common problem in radiotherapy planning is to avoid obstructing treatment beams with parts of the patient couch. The use of carbon ®bre couch tops and interchangeable panels minimizes this problem, but problems still exist, for example owing to metal rails along the edges or under the centre of treatment couches. A further problem occurs in avoiding collisions between the treatment machine head and the patient couch. A variety of approaches can be used to prevent these problems being discovered only at the time of plan veri®cation or at the patient's ®rst treatment, e.g. tables or graphs of ``forbidden'' angles, or the use of a ``graphical simulator'' [1± 4]. There is also the possibility of using devices and models developed to check machine angles or visualize the beam alignment in a plan [5]. These approaches have a variety of strengths and weaknesses. Tables are inexpensive, quick, and simple to produce and use, but usually have greatly simplifying assumptions made during their production. Machine angle, beam alignment devices and models again usually only provide simpli®ed representations of the problem. While graphical simulators may not make simplifying assumptions, they are usually machine-dependent and more concerned with machine/machine and machine/patient collisions under automated set-up conditions. This work examines (under isocentric conditions) the trigonometric relationships between the placement of treatment beams and parts of the Received 1 June 1999 and in ®nal form 6 December 1999, accepted 20 January 2000. The British Journal of Radiology, May 2000

patient couch that could obstruct these beams. This provides a set of useful equations that can be generally applied for any model of treatment unit or simulator. These equations can be applied practically as a simple (non-graphical) planning tool that enables the feasibility of a plan to be checked prior to veri®cation or treatment.

Method When considering the relationship between beam placement and patient support structures it is necessary to look at a number of cases. The scales being modelled follow the convention described in BS5724 ``Speci®cation for medical electron accelerators in the range 1 MeV to 50 MeV'' section 2.1 [6].

Obstruction of treatment beams by couch edges By geometrical considerations we may show the following (see Appendix): Intersection with the outside edge of a couch obstruction (see Figure 1) x0 ~100 sin Az…100 cos Azh†= tan {A{‰arctan…f =200†z90Š}

…1†

Intersection with the inside edge of a couch obstruction (see Figure 2) x0 ~100 sin A{‰100 cos Az…hzT †Š| tan‰Azarctan…f =200†Š

…2† 537

I Beange and A Nisbet

Figure 1. Treatment beam intersecting with the outside edge of a couch obstruction.

The above analyses assume that the collimators are lying at a ``cardinal'' angle, such that the ®eld width and length are de®ned by collimator set dimensions, and that the couch is lying parallel to the gantry axis of rotation. The generality of Equations (1) and (2) can be improved by the following arguments.

Effect of collimator rotation (see Figure 3) Considering the effect of a collimator rotation a: here the ``effective ®eld width'' F is de®ned by a function of the set sizes B and C and the collimator rotation a. F ~C sin azB cos a

…3†

where F can be used to replace f in Equations (1) and (2) above. By the same argument, the ``effective ®eld length'' L is de®ned as: L~B sin azC cos a

…4†

Effect of ¯oor rotation (see Figure 4) To further the generality of these analyses, consider the similar case of a ¯oor rotation b. Here v is the ``effective'' blockage, or window of clearance, for comparison with the ®gures calculated using Equations (1) and (2) above, W is the couch width and L is the ``effective ®eld length'' as de®ned in Equation (4) above. u~…W =2†= cos b

…5†

The approach of the couch edge towards the treatment head off the central axis x s~…L=2† tan b

…6†

can be used to make further allowance for ¯oor rotation off the central axis.

Treatment head collisions (see Figure 5) Knowing the position of the couch edges and any shift applied to the patient position from the

Figure 2. Treatment beam intersecting with the inside edge of a couch obstruction.

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The British Journal of Radiology, May 2000

Short communication: Collision prevention for isocentric set-ups

centre of the couch allows an examination of the clearance between the couch and the treatment head. If hdwid and hdlen are the width and length of the treatment head respectively, D is the clearance between the isocentre and the front face of the treatment head, and A and a are as de®ned previously, by applying a similar argument to that applied in Equation (3), hw5hdlen (sin a)+hdwid (cos a): d~arctan‰…hw=2†=DŠ R~‰D2 z…hw=2†2 Š1=2 Q'~90{…A{d† and Q''~90{…Azd† X '~R cos Q' and X ''~R cos Q''

…7†

H'~R sin Q' and H''~R sin Q''

…8†

where X9, X0, H9 and H0 are the horizontal and vertical displacements of the treatment head edges from the isocentre; d is the angle of divergence between the central axis of the treatment head to the isocentre and the isocentre to the ``effective treatment head edge''; hw is the ``effective treatment head width''; R is the distance from the isocentre to the ``effective treatment head edge''; and Q9 and Q99 represent the angle from the horizontal to the upper and lower ``effective treatment head edge'', respectively. Knowing these positions and the height of the isocentre above the couch top, v+x can be assessed to determine whether the treatment head and couch are likely to collide.

Figure 3. Effect of collimator rotation. The British Journal of Radiology, May 2000

Figure 4. Effect of ¯oor rotation.

Development and results In this development it is assumed that the patient is positioned on the centre line of the treatment couch. The aim was to quantify whether, and by how much, the patient may require to be moved laterally to avoid the intersection of the treatment beam with couch obstructions, and hence provide an aid to deciding whether a treatment plan is viable and, if not, how to amend it. The equations described above have been implemented in a FORTRAN (Microsoft FORTRAN V5.1; Microsoft Corporation, Redmond, USA) program. The program progresses by obtaining information on the position of the planned isocentre (height above couch top and lateral displacement from the couch centre line) and details of the treatment beams (®eld size, and gantry, collimator and ¯oor rotation angles). It then simpli®es the plan set-up into two sides (e.g. gantry angles 359 Ê to 181 Ê are made 21 Ê to 2179 Ê) and uses Equations (1), (2) and (3) to calculate the points of intersection between the beam edges and the plane of the couch (Siemens ZIV couch; Siemens Medical Laboratories Inc., Walnut Creek, USA) for each beam whose lower edge lies below the horizontal in the treatment set-up. It then moves the set-up stepwise to the left and to the right (limited to the maximum couch movement) comparing the intersections with the couch 539

I Beange and A Nisbet

Figure 5. Treatment head intersection with patient couch.

clearances (calculated using Equation (5)) searching for null solutions that apply to all beams. This approach has proved successful in identifying the possible solutions, from the four physically feasible solutions (patient shifts to the left and right on both ``spine'' and ``tennis racquet'' ends), on our treatment couch. The program was tested with a set of simulated treatments and showed agreement generally to within 5 mm of expected results. This was considered acceptable, taking into account the purpose of this analysis and the variability of machine parameters and patient setup. Subsequently, Equations (7) and (8) were included and are used to calculate where the edges of the treatment head (Siemens M6700 Linear Accelerator: Siemens Medical Laboratories Inc., Walnut Creek, USA) lie with respect to the isocentre, allowing calculation of where the treatment head intersects the plane of the treatment couch. This is compared with the position of the treatment couch edges to determine whether the treatment head will collide with the couch when these shifts are applied. Consequently, any head± couch collisions are quanti®ed and avoiding corrections are fed back into further null searches for successful solutions. Finally Equations (4) and (6) were introduced to extend the analysis off the beam central axes by altering the ``effective'' blockage, or window of clearance, on the couch. This is subject to the simplying yet conservative assumption that the treatment beam has the dimensions L6F (from B6C with a collimator rotation of a). In use, the program has been designed to accept keyboard input of the isocentre position, height above couch top and displacement to the left or right with respect to the treatment couch centre line, and the proposed treatment beam details. This may be done as a stand-alone program or as an integrated part of our plan checking program. The identi®ed possible solutions are then displayed, providing the treatment planner with 540

information to decide whether to reject the treatment plan as impractical. A printed report is offered to accompany the treatment plan to the veri®cation session, and to treatment, to guide the radiographers in patient positioning.

Conclusion This model has been implemented and tested with a set of simulated treatments that have shown good agreement as to how a patient could be repositioned to allow use of a treatment plan when potential treatment beam obstructions are detected. The program has been extended to look for the possibility of the treatment head colliding with the couch, and for the effect of ¯oor rotation off the beam central axes. The FORTRAN program has been brought into clinical use as a routine planning tool. Although the existing program has been written for particular equipment, it can be easily adapted for other treatment machines. Use of a non-graphical interface allows the use of the planning tool on older PC compatible computers.

Acknowledgments We would like to acknowledge the assistance given by our colleagues Max Vollmar and Steve Colligan, in both testing and providing feedback on the practical operation of this software.

References 1. Kessler ML, McShan DL, Fraass BA. A computercontrolled conformal radiotherapy system. III: graphical simulation and monitoring of treatment delivery. Int J Radiat Oncol Biol Phys 1995;33: 1173±80. 2. Humm KL, Pizzuto D, Fleischman E, Mohan R. Collision detection and avoidance during treatment planning. Int J Radiat Oncol Biol Phys 1995;33: 1101±8. The British Journal of Radiology, May 2000

Short communication: Collision prevention for isocentric set-ups 3. Yorke ED. The geometry of avoiding beam intersections and blocking tray collisions. Med Phys 1989;16:288±91. 4. Muthuswamy MS, Lam KL. A method of beam± couch intersection detection. Med Phys 1999;26: 229±35. 5. Seaby AW, Thomas M, Craven C. A model simulator for radiotherapy treatment planning and checking. Br J Radiol 1999;72:293±5. 6. British Standards Institute. BS5724 12.1 Speci®cation for medical electron accelerators in the range 1 MeV to 50 MeV. British Standards Institute, 1989:7,23.

Appendix: detailed derivation of equations used Obstruction of treatment beams by couch edges Intersection with the outside edge of a couch obstruction (see Figure 1) Gantry angle A590+(a+t), where t is the angle between the divergent beam edge and the horizontal Field divergence a5arctan [(f/2)/100], where f is the ®eld dimension at the isocentre (100 cm) Height of isocentre above couch top h5H2(h9+T), where T is the thickness of the couch top, H is the vertical distance of the beam focus from the isocentre and h9 is the vertical distance of the beam focus from the couch base Horizontal distance of beam focus from isocentre X5x0+x9, where x0 is the horizontal distance of the beam intersection on the plane of the couch top from the isocentre and x9 is the horizontal distance of the beam intersection on the plane of the couch top from the beam focus cos (1802A)5H/100 sin (1802A)5X/100 tan t5(h9+T)/x9 Rearranging and substituting: H5100 cos (1802A)Rh9+T5100 cos (1802A)2h X5100 sin (1802A)Rx95100 sin (1802A)2x0

The British Journal of Radiology, May 2000

tan (A2a290)5[100 cos (1802A)2h]/ [100 sin (1802A)2x0] R[100 sin (1802A)2x0]5[100 cos (1802A)2h]/ tan [A2arctan (f/200)290] Rx05100 sinA2[100 cos (1802A)2h]/ tan {A2 [arctan (f/200)+90]} Which leads to: x0 ~100 sin Az…100 cos Azh†= tan {A{‰arctan…f =200†z90Š}

…1†

Intersection with the inside edge of a couch obstruction (see Figure 2) Similarly to the case above: Ganty angle A51802(a+t) Height of isocentre above couch top h5H2(h9+T) Field divergence a5arctan [(f/2)/100] Horizontal distance of beam focus from isocentre X5x0+x9 cos (1802A)5H/100 sin (1802A)5X/100 tan t5h9/x9 Rearranging and substituting; H5100 cos (1802A)Rh95100 cos (1802A) 2 (h+T) X5100 sin (1802A)Rx95100 sin (1802A)2x0 tan [1802(A+a)]5100 sin (1802A)2x0/ [100 cos (1802A)2(h+T)] R100 sin (1802A)2x05[100 cos (1802A)2(h+ T)] tan [1802(A+a)] Rx05100 sin A2[100 cos (1802A)2(h+T)]6 tan {1802[A+arctan (f/200)]} 5100 sin A+[100 cos (1802A)2(h+T)]6 tan [A+arctan (f/200)] Which leads to: x0 ~100 sin A{‰100 cos Az…hzT †Š| tan‰Azarctan…f =200†Š

…2†

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