From analytic inversion to contemporary IMRT optimization: Radiation therapy planning revisited from a mathematical perspective

Abstract

In this paper we look at the development of radiation therapy treatment planning from a mathematical point of view. Historically, planning for Intensity-Modulated Radiation Therapy (IMRT) has been considered as an inverse problem. We discuss first the two fundamental approaches that have been investigated to solve this inverse problem: Continuous analytic inversion techniques on one hand, and fully-discretized algebraic methods on the other hand. In the second part of the paper, we review another fundamental question which has been subject to debate from the beginning of IMRT until the present day: The rotation therapy approach versus fixed angle IMRT. This builds a bridge from historic work on IMRT planning to contemporary research in the context of Intensity-Modulated Arc Therapy (IMAT).

Patient Dose Computation

“…Establishing of standards for data structuring such as Digital Imaging and Communication in Medicine (DICOM) and managing the clinical information network by an oncology information system (OIS) have enabled development of integrated informationdriven workflows as discussed by Swerdloff (2007), , and . With the development of intensity-modulated radiation therapy (IMRT), the number of free parameters to be optimized during treatment planning exceeded what possibly could be handled by manual methods leading to extensive research of optimization methods (see, e.g., the reviews by Censor and Unkelbach (2012), Grégoire and Mackie (2011), and Ahnesjö et al (2006)). Initially, it was viewed as an inverse problem to determine the field parameters from a desired dose distribution, partly due to the existence of an analytic solution to a model problem in rotational therapy (Brahme et al, 1982), but in general, analytic inversion may not be the most suitable method (Censor and Unkelbach, 2012).…”

“…With the development of intensity-modulated radiation therapy (IMRT), the number of free parameters to be optimized during treatment planning exceeded what possibly could be handled by manual methods leading to extensive research of optimization methods (see, e.g., the reviews by Censor and Unkelbach (2012), Grégoire and Mackie (2011), and Ahnesjö et al (2006)). Initially, it was viewed as an inverse problem to determine the field parameters from a desired dose distribution, partly due to the existence of an analytic solution to a model problem in rotational therapy (Brahme et al, 1982), but in general, analytic inversion may not be the most suitable method (Censor and Unkelbach, 2012). However, the term 'inverse planning' is still used to describe the planning workflow where the user sets goals for the dose distribution that are then used by an optimizer routine to determine the irradiation parameters.…”

Operational research techniques applied throughout cancer care services: a review

“…We compare examples of IMRT treatment planning papers published since Censor and Unkelbach's (2012) paper that were identified from our search strategy. Some of these address the fluence map optimisation problem (Cabrera, Ehrgott, Mason, & Philpott, 2014;Chan, Mahmoudzadeh, & Purdie, 2014;Mahmoudzadeh, Purdie, & Chan, 2016;Van Haveren et al, 2017).…”

“…There is a large body of literature on designing IMRT plans and several review papers (Bortfeld, 2006;Censor & Unkelbach, 2012;Ehrgott, Güler, Hamacher, & Shao, 2010). Bortfeld (2006) discusses the mathematical, physical, and technological developments relating to IMRT.…”

“…Later Ehrgott et al (2010) reviewed optimisation approaches to three related problems: (1) fluence map optimisation, which consists of finding the best set of beamlet intensities, (2) beam angle optimisation, and (3) the segmentation problem, which is how to configure the multileaf collimators to achieve this. Censor and Unkelbach (2012) describe the two key approaches to solving the inverse problem: continuous analytic techniques and fully discretised algebraic methods. They explain the change in perspective to considering the problem as an optimisation where the damage to healthy tissue should be minimised.…”