A method to study the characteristics of 3D dose distributions created by superposition of many intensity-modulated beams delivered via a slit aperture with multiple absorbing vanes

Highly conformal dose distributions can be created by the superposition of many radiation fields from different directions, each with its intensity spatially modulated by the method known as tomotherapy. At the planning stage, the intensity of radiation of each beam element (or bixel) is determined by working out the effect of superposing the radiation through all bixels with the elemental dose distribution specified as that from a single bixel with all its neighbours dosed (the 'independent-vane' (IV) model). However, at treatment-delivery stage, neighbouring bixels may not be closed. Instead the slit beam is delivered with parts of the beam closed for different periods of time to create the intensity modulation. As a result, the 3D dose distribution actually delivered will differ from that determined at the planning stage if the elemental beams do not obey the superposition principle. The purpose of this paper is to present a method to investigate and quantify the relation between planned and delivered 3D dose distributions. Two modes of inverse planning have been performed: (i) with a fit to the measured elemental dose distribution and (ii) with a 'stretched fit' obeying the superposition principle as in the PEACOCK 3D planning system. The actual delivery has been modelled as a series of component deliveries (CDs). The algorithm for determining the component intensities and the appropriate collimation conditions is specified. The elemental beam from the NOMOS MIMiC collimator is too narrow to obey the superposition principle although it can be 'stretched' and fitted to a superposition function. Hence there are differences between the IV plans made using modes (i) and (ii) and the raw and the stretched elemental beam, and also differences with CD delivery. This study shows that the differences between IV and CD dose distributions are smaller for mode (ii) inverse planning than for mode (i), somewhat justifying the way planning is done within PEACOCK. Using a stretched elemental beam is a useful adjustment to improve the accuracy of inverse planning but the 3D dose distribution actually delivered will display characteristics of the collimation.