Mathematical optimization of high dose-rate brachytherapy—derivation of a linear penalty model from a dose-volume model

Abstract

High dose-rate brachytherapy is a method for cancer treatment where the radiation source is placed within the body, inside or close to a tumour. For dose planning, mathematical optimization techniques are being used in practice and the most common approach is to use a linear model which penalizes deviations from specified dose limits for the tumour and for nearby organs. This linear penalty model is easy to solve, but its weakness lies in the poor correlation of its objective value and the dose-volume objectives that are used clinically to evaluate dose distributions. Furthermore, the model contains parameters that have no clear clinical interpretation. Another approach for dose planning is to solve mixed-integer optimization models with explicit dose-volume constraints which include parameters that directly correspond to dose-volume objectives, and which are therefore tangible. The two mentioned models take the overall goals for dose planning into account in fundamentally different ways. We show that there is, however, a mathematical relationship between them by deriving a linear penalty model from a dose-volume model. This relationship has not been established before and improves the understanding of the linear penalty model. In particular, the parameters of the linear penalty model can be interpreted as dual variables in the dose-volume model.

Investigating the role of constrained CVT and CVT in HIPO inverse planning for HDR brachytherapy of prostate cancer

“…11 Several algorithms and commercial software are available for performing the optimization of dwell times at given dwell positions using a stepping source within preplanned or implanted catheters considering the 3D dose distribution in the planning target volume (PTV) and organs at risk (OARs). [17][18][19][20][21][22] Currently there is only one commercial system -Oncentra Prostate â (OcP)where the Hybrid-Inverse-Planning-Optimization (HIPO) algorithm 17,19,23,24 provides a real inverse planning solution for automatic optimization of the placement of a given number of catheters with simultaneous adjustment of dwell positions and dwell times of a stepping source. HIPO constitutes an integrated process utilizing dedicated dose-volume objective functions for PTV, boost volumes (GTVs), and OARs when a discretized set of feasible catheter pathways is considered, which is the case in PCA HDRBT with transperineal catheter implantation through template holes.…”

“…Several algorithms and commercial software are available for performing the optimization of dwell times at given dwell positions using a stepping source within preplanned or implanted catheters considering the 3D dose distribution in the planning target volume (PTV) and organs at risk (OARs) . Currently there is only one commercial system — Oncentra Prostate ® (OcP) — where the Hybrid‐Inverse‐Planning‐Optimization (HIPO) algorithm provides a real inverse planning solution for automatic optimization of the placement of a given number of catheters with simultaneous adjustment of dwell positions and dwell times of a stepping source.…”

Optimization in treatment planning of high dose‐rate brachytherapy — Review and analysis of mathematical models

“…54 Such models for HDR BT were further developed and studied. 41,[55][56][57][58] The DI is related to concepts in other fields of research; the counterpart in finance is called value-at-risk (VaR), 59 and concepts similar to DIs also appear in the field of chance constraints. 60…”

Robust Optimization to Reduce Dose Delivery Uncertainty by Potential Applicator Displacements for a Cervix Brachytherapy

“…Therefore, the genetic algorithm (GA) is well suited to solve multi-objective optimization problems due to the population-based searching approach. Given the above, a preferred efficient GA that can search global minimum points as a multi-objective optimizer engine was selected to overcome the complexity of global searches [34][35][36][37].…”