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Convex reformulation of biologically-based multi-criteria intensity-modulated radiation therapy optimization including fractionation effects.

Abstract：

:Finding fluence maps for intensity-modulated radiation therapy (IMRT) can be formulated as a multi-criteria optimization problem for which Pareto optimal treatment plans exist. To account for the dose-per-fraction effect of fractionated IMRT, it is desirable to exploit radiobiological treatment plan evaluation criteria based on the linear-quadratic (LQ) cell survival model as a means to balance the radiation benefits and risks in terms of biologic response. Unfortunately, the LQ-model-based radiobiological criteria are nonconvex functions, which make the optimization problem hard to solve. We apply the framework proposed by Romeijn et al (2004 Phys. Med. Biol. 49 1991-2013) to find transformations of LQ-model-based radiobiological functions and establish conditions under which transformed functions result in equivalent convex criteria that do not change the set of Pareto optimal treatment plans. The functions analysed are: the LQ-Poisson-based model for tumour control probability (TCP) with and without inter-patient heterogeneity in radiation sensitivity, the LQ-Poisson-based relative seriality s-model for normal tissue complication probability (NTCP), the equivalent uniform dose (EUD) under the LQ-Poisson model and the fractionation-corrected Probit-based model for NTCP according to Lyman, Kutcher and Burman. These functions differ from those analysed before in that they cannot be decomposed into elementary EUD or generalized-EUD functions. In addition, we show that applying increasing and concave transformations to the convexified functions is beneficial for the piecewise approximation of the Pareto efficient frontier.

journal_name

Phys Med Biol

journal_title

Physics in medicine and biology

authors

Hoffmann AL,den Hertog D,Siem AY,Kaanders JH,Huizenga H

doi

10.1088/0031-9155/53/22/006

subject

Has Abstract

pub_date

2008-11-21 00:00:00

pages

6345-62

issue

22

eissn

0031-9155

issn

1361-6560

pii

S0031-9155(08)78385-4

journal_volume

53

pub_type

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