Dose-Volume Based Ranking of Incident Beams and its Utility in Facilitating IMRT Beam Placement Jenny Hai, PhD. Department of Radiation Oncology Stanford University School of Medicine

Purpose Beam orientation optimization in IMRT is computationally intensive and various single beam ranking techniques have been proposed to reduce the search space. Up to this point, none of the existing ranking techniques considers the clinically important dose-volume effects of the involved structures, which may lead to clinically irrelevant angular ranking. The purpose of this work is to develop a clinically sensible angular ranking model with incorporation of dose-volume effects and to show its utility for IMRT beam placement. 1

Difficulty The general consideration in constructing an angular ranking function is that a beamlet/beam is more preferable if it can deliver a higher dose to the target without exceeding the tolerance of the sensitive structures located on the path of the beamlet/beam. In the previously proposed dose-based approach, the beamlets are treated independently and, to compute the maximally deliverable dose to the target volume, the intensity of each beamlet is pushed to its maximum intensity without considering the values of other beamlets. When volumetric structures are involved, a complication arises from the fact that there are numerous dose distributions corresponding to the same dose-volume tolerance. In this situation, the beamlets are no longer independent and an optimization algorithm is required to find the intensity profile that delivers the maximum target dose while satisfying the volumetric constraint(s). 2

Method In this study, the behavior of a volumetric organ was modeled by using the equivalent uniform dose (EUD). A constrained sequential quadratic programming algorithm (CFSQP) was used to find the beam profile that delivers the maximum dose to the target volume without violating the EUD constraint(s). To access the utility of the proposed technique, we planned a head and neck and thoracic case with and without the guidance of the angular ranking information. The qualities of the two types of IMRT plans were compared quantitatively. 3

Ranking function The figure of merit of a beam direction is generally measured by how much dose can be delivered to the target and is calculated using the a priori dosimetric and geometric information of the given patient. A beam direction is divided into a grid of beamlets. After a forward dose calculation using the maximum beam intensity profile, the score of the given beam direction (indexed by i) is obtained according to dose delivered to the voxel by the beam from the direction indexed by i number of voxels in the target target prescription 4

Constraints For each OAR we define the optimization constraint such that the EUD value derived for the given dose distribution during the optimization process should not exceed a user- defined limit: 5

Optimization algorithm Variables to be optimized included the intensities of the beamlets passing through the PTV.We use CFSQP, having the advantage of being capable of dealing with nonlinear inequality constraints. The calculation starts with an initial intensity profile, in which each beamlet is assigned with a small but random value, and then iteratively maximize the angular ranking function while satisfying the constraints. 6

Comparison previous scores Dependence of EUD score on the a parameter is presented in figure 3a. As a increases, the angular score curve approaches to the curve (denoted by the open circles) computed using the method proposed by Pugachev This calculation provides a useful check of the new algorithm. It is interesting to note that the change in the peak positions of the angular function can be as large as 20 o when the sensitive structures are changed from serial (corresponding to a high a value) to parallel (corresponding to a low a value). The change in amplitude is also striking (from ~0.2 to ~0.7 at 80º and 280º). 7

Clinical utility We compare conventional, equispaced, plans with “ optimized ” plan having beams directions selected at peaks of the score function. After beam selection for both types of plans, beamlets are optimized using a published multi- objective approach. The DVHs for both cases show improvements in all objectives. 8

CFSQP convergence Convergence behavior of the CFSQP algorithm is demonstrated by plotting the angular score as a function of iteration step (figure 2a) for the 225 o direction. The EUDs of the sensitive structures at each iteration step are shown in figure 2b. With the chosen initial beamlet intensities (small but random values), the angular score is progressively increased while constraints are progressively saturated, limited by the tolerances of the sensitive structures. Constraints of the sensitive structures that are not on the path of the beam remain to be constant through the iterative calculation. 9

Head case: DVHs of the optimized and conventional plans

Thoracic case: DVHs of the optimized and conventional plans

Head case: Angular score obtained with published EUD model parameters superimposed on the patient’s geometry. Angles selected for IMRT planning are shown by arrows.

Thoracic case: Angular score obtained with published EUD model parameters superimposed on the patient’s geometry. Angles selected for IMRT planning are shown by arrows.

FIGURE 2a Convergence behavior of the CFSQP algorithm for the 255º beam direction. Presented are evolutions of the angular ranking function

FIGURE 2b Convergence behavior of the CFSQP algorithm for the 255º beam direction.Presented are the sensitive structure constraints. Only the right kidney and the liver influence algorithm’s convergence since other structures are not on the path of the beam.

Head case: Angular ranking function of coplanar beam for a series of EUD a parameter values. The selected five beam directions for IMRT planning are labeled by arrows. The curve depicted by the open circles represents the result obtained using the approach described by Pugachev.

Thoracic case: Angular ranking function of coplanar beam for a series of EUD a parameter values. The selected five beam directions for IMRT planning are labeled by arrows. The curve depicted by the open circles represents the result obtained using the approach described by Pugachev.

Conclusion The EUD-based function is a general approach for angular ranking and allows us to identify the potentially good and bad angles for clinically complicated cases. The ranging can be used either as a guidance to facilitate the manual beam placement or as prior information to speed up the computer search for the optimal beam configuration. Given its simplicity and robustness, the proposed technique should have positive clinical impact in facilitating the IMRT planning process 10