Multicriteria optimization in intensity-modulated radiation therapy treatment planning for locally advanced cancer of the pancreatic head. Int J Radiat Oncol Biol Phys. 2008;72:1208-1214. [PMID: 18954714 DOI: 10.1016/j.ijrobp.2008.07.015]

A hierarchical evolutionary algorithm for multiobjective optimization in IMRT

PURPOSE

The current inverse planning methods for intensity modulated radiation therapy (IMRT) are limited because they are not designed to explore the trade-offs between the competing objectives of tumor and normal tissues. The goal was to develop an efficient multiobjective optimization algorithm that was flexible enough to handle any form of objective function and that resulted in a set of Pareto optimal plans.

METHODS

A hierarchical evolutionary multiobjective algorithm designed to quickly generate a small diverse Pareto optimal set of IMRT plans that meet all clinical constraints and reflect the optimal trade-offs in any radiation therapy plan was developed. The top level of the hierarchical algorithm is a multiobjective evolutionary algorithm (MOEA). The genes of the individuals generated in the MOEA are the parameters that define the penalty function minimized during an accelerated deterministic IMRT optimization that represents the bottom level of the hierarchy. The MOEA incorporates clinical criteria to restrict the search space through protocol objectives and then uses Pareto optimality among the fitness objectives to select individuals. The population size is not fixed, but a specialized niche effect, domination advantage, is used to control the population and plan diversity. The number of fitness objectives is kept to a minimum for greater selective pressure, but the number of genes is expanded for flexibility that allows a better approximation of the Pareto front.

RESULTS

The MOEA improvements were evaluated for two example prostate cases with one target and two organs at risk (OARs). The population of plans generated by the modified MOEA was closer to the Pareto front than populations of plans generated using a standard genetic algorithm package. Statistical significance of the method was established by compiling the results of 25 multiobjective optimizations using each method. From these sets of 12-15 plans, any random plan selected from a MOEA population had a 11.3% +/- 0.7% chance of dominating any random plan selected by a standard genetic package with 0.04% +/- 0.02% chance of domination in reverse. By implementing domination advantage and protocol objectives, small and diverse populations of clinically acceptable plans that approximated the Pareto front could be generated in a fraction of 1 h. Acceleration techniques implemented on both levels of the hierarchical algorithm resulted in short, practical runtimes for multiobjective optimizations.

CONCLUSIONS

The MOEA produces a diverse Pareto optimal set of plans that meet all dosimetric protocol criteria in a feasible amount of time. The final goal is to improve practical aspects of the algorithm and integrate it with a decision analysis tool or human interface for selection of the IMRT plan with the best possible balance of successful treatment of the target with low OAR dose and low risk of complication for any specific patient situation.

An approach to multiobjective optimization of rotational therapy. II. Pareto optimal surfaces and linear combinations of modulated blocked arcs for a prostate geometry

PURPOSE

The purpose of this work is twofold: To further develop an approach to multiobjective optimization of rotational therapy treatments recently introduced by the authors [J. Pardo-Montero and J. D. Fenwick, "An approach to multiobjective optimization of rotational therapy," Med. Phys. 36, 3292-3303 (2009)], especially regarding its application to realistic geometries, and to study the quality (Pareto optimality) of plans obtained using such an approach by comparing them with Pareto optimal plans obtained through inverse planning.

METHODS

In the previous work of the authors, a methodology is proposed for constructing a large number of plans, with different compromises between the objectives involved, from a small number of geometrically based arcs, each arc prioritizing different objectives. Here, this method has been further developed and studied. Two different techniques for constructing these arcs are investigated, one based on image-reconstruction algorithms and the other based on more common gradient-descent algorithms. The difficulty of dealing with organs abutting the target, briefly reported in previous work of the authors, has been investigated using partial OAR unblocking. Optimality of the solutions has been investigated by comparison with a Pareto front obtained from inverse planning. A relative Euclidean distance has been used to measure the distance of these plans to the Pareto front, and dose volume histogram comparisons have been used to gauge the clinical impact of these distances. A prostate geometry has been used for the study.

RESULTS

For geometries where a blocked OAR abuts the target, moderate OAR unblocking can substantially improve target dose distribution and minimize hot spots while not overly compromising dose sparing of the organ. Image-reconstruction type and gradient-descent blocked-arc computations generate similar results. The Pareto front for the prostate geometry, reconstructed using a large number of inverse plans, presents a hockey-stick shape comprising two regions: One where the dose to the target is close to prescription and trade-offs can be made between doses to the organs at risk and (small) changes in target dose, and one where very substantial rectal sparing is achieved at the cost of large target underdosage. Plans computed following the approach using a conformal arc and four blocked arcs generally lie close to the Pareto front, although distances of some plans from high gradient regions of the Pareto front can be greater. Only around 12% of plans lie a relative Euclidean distance of 0.15 or greater from the Pareto front. Using the alternative distance measure of Craft ["Calculating and controlling the error of discrete representations of Pareto surfaces in convex multi-criteria optimization," Phys. Medica (to be published)], around 2/5 of plans lie more than 0.05 from the front. Computation of blocked arcs is quite fast, the algorithms requiring 35%-80% of the running time per iteration needed for conventional inverse plan computation.

CONCLUSIONS

The geometry-based arc approach to multicriteria optimization of rotational therapy allows solutions to be obtained that lie close to the Pareto front. Both the image-reconstruction type and gradient-descent algorithms produce similar modulated arcs, the latter one perhaps being preferred because it is more easily implementable in standard treatment planning systems. Moderate unblocking provides a good way of dealing with OARs which abut the PTV. Optimization of geometry-based arcs is faster than usual inverse optimization of treatment plans, making this approach more rapid than an inverse-based Pareto front reconstruction.

Volumetric modulated arc therapy (VMAT) vs. serial tomotherapy, step-and-shoot IMRT and 3D-conformal RT for treatment of prostate cancer

INTRODUCTION

Volumetric modulated arc therapy (VMAT), a complex treatment strategy for intensity-modulated radiation therapy, may increase treatment efficiency and has recently been established clinically. This analysis compares VMAT against established IMRT and 3D-conformal radiation therapy (3D-CRT) delivery techniques.

METHODS

Based on CT datasets of 9 patients treated for prostate cancer step-and-shoot IMRT, serial tomotherapy (MIMiC), 3D-CRT and VMAT were compared with regard to plan quality and treatment efficiency. Two VMAT approaches (one rotation (VMAT1x) and one rotation plus a second 200 degrees rotation (VMAT2x)) were calculated for the plan comparison. Plan quality was assessed by calculating homogeneity and conformity index (HI and CI), dose to normal tissue (non-target) and D(95%) (dose encompassing 95% of the target volume). For plan efficiency evaluation, treatment time and number of monitor units (MU) were considered.

RESULTS

For MIMiC/IMRT(MLC)/VMAT2x/VMAT1x/3D-CRT, mean CI was 1.5/1.23/1.45/1.51/1.46 and HI was 1.19/1.1/1.09/1.11/1.04. For a prescribed dose of 76 Gy, mean doses to organs-at-risk (OAR) were 50.69 Gy/53.99 Gy/60.29 Gy/61.59 Gy/66.33 Gy for the anterior half of the rectum and 31.85 Gy/34.89 Gy/38.75 Gy/38.57 Gy/55.43 Gy for the posterior rectum. Volumes of non-target normal tissue receiving > or =70% of prescribed dose (53 Gy) were 337 ml/284 ml/482 ml/505 ml/414 ml, for > or =50% (38 Gy) 869 ml/933 ml/1155 ml/1231 ml/1993 ml and for > or =30% (23 Gy) 2819 ml/3414 ml/3340 ml/3438 ml /3061 ml. D(95%) was 69.79 Gy/70.51 Gy/71,7 Gy/71.59 Gy/73.42 Gy. Mean treatment time was 12 min/6 min/3.7 min/1.8 min/2.5 min.

CONCLUSION

All approaches yield treatment plans of improved quality when compared to 3D-conformal treatments, with serial tomotherapy providing best OAR sparing and VMAT being the most efficient treatment option in our comparison. Plans which were calculated with 3D-CRT provided good target coverage but resulted in higher dose to the rectum.