Exact/Approximated Geometrical Determinations of IMRT Photon Pencil-Beam Path Through Alloy Static Wedges in Radiotherapy Using the Anisothropic Analytic Algorithm (AAA)

Abstract

Static wedge filters are commonly used in Radiation Therapy, Forward and/or Inverse Planning, to obtain a conformal optimized dose distribution, both in the tumor target and organs at risk zones (OARs); in other words, the Treatment Planning Optimization (TPO) zone and annexes. We have calculated the exact 2D/3D geometrical pathway of the Photon-Beam through the usual alloy static wedges, in order to get a better dose determination related to the Beam Intensity Attenuation Factor(s), after the beam has passed through the alloy wedge. The Radiotherapy model used to develop this mathematical task is the classical Superposition-Convolution Algorithm, so-called AAA (Anisothropic Analytical Algorithm). In addition, we present some optimal geometrical approximations to make the computational calculations quicker in IMRT, and reduce the planning-system routine time. The practical objective is to provide a general formulation into the AAA Model Coordinates System (depending on Collimator and Wedge Angles) that also can be applied with simple changes of coordinates to other models, if necessary. These transformations are also explained for the convenience of the TPO selected for a particular model. As a result, it is possible to determine the best individual treatment dose distribution for each patient, and conform the tumor volume and shape accurately in the technical planning process related to the selected wedges. Geometrical and Computational techniques are detailed and developed for a clear reading. Finally, we show basic simulations and numerical examples for Standard Manufacturing wedge filters of straight sloping surface, to check the accuracy and errors of the approximated calculations. Simulations results give low RMS and Relative Error values for standard wedge filters of 15°, 30°, 45°, and 60°.