Optimal solution for a cancer radiotherapy problem

Abstract

We address the problem of finding the optimal radiotherapy fractionation scheme, representing the response to radiation of tumour and normal tissues by the LQ model including exponential repopulation and sublethal damage due to incomplete repair. We formulate the nonlinear programming problem of maximizing the overall tumour damage, while keeping the damages to the late and early responding normal tissues within a given admissible level. The optimum is searched over a single week of treatment and its possible structures are identified. In the two simpler but important cases of absence of the incomplete repair term or of prevalent late constraint, we prove the uniqueness of the optimal solution and we characterize it in terms of model parameters. The optimal solution is found to be not necessarily uniform over the week. The theoretical results are confirmed by numerical tests and comparisons with literature fractionation schemes are presented.

Optimization of radiation dosing schedules for proneural glioblastoma

“…Previous reports have independently modeled the effect of either fixed or dynamic fractionation schemes (Brenner et al 1998;Lu et al 2008), the effect of incomplete DNA damage repair (Bertuzzi et al 2013), the impact of the 4R's and tumor proliferation (Yang and Xing 2005), and the impact of hyper-or hypo-fractionated schedules (Unkelbach et al 2013;Mizuta et al 2012). Dionysiou et al (2004) further examined hyper-fractionating using a novel fourdimensional simulation model of GBM and observed an increased tumor reduction when compared to standard fractionation.…”

The emergence of nonuniform spatiotemporal fractionation schemes within the standard BED model

“…Other authors have considered extensions to incorporate effects from repopulation, the overall treatment time, and incomplete repair. [6][7][8] The projected benefit of delivering different dose distributions in different fractions has been studied for a stylized proof-of-concept model in Ref. 9, and the idea was conceptually introduced in Refs.…”

Simultaneous optimization of dose distributions and fractionation schemes in particle radiotherapy

“…It has previously been demonstrated that time dependencies in tumor growth and radiation response, such as accelerated repopulation and incomplete repair, may give rise to nonuniform fractionation schemes. 8,9 In this paper, we consider the standard BED model. It is therefore interesting to note that the simultaneous optimization of fractionation schemes leads to nonuniform fractionation schemes that deliver distinct dose distributions in different fractions-even in the absence of any time dependencies in the BED model.…”

“…Other authors have considered extensions of the BED model to incorporate effects from repopulation, the overall treatment time, and incomplete repair. 8,9 In this paper, we consider the extension of BED-based fractionation to the fluence map optimization context. In other words, we consider the simultaneous optimization of the fluence map and the fractionation scheme.…”