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Recent theoretical research on spatiobiologically integrated radiotherapy has focused on optimization models that adapt fluence-maps to the evolution of tumor state, for example, cell densities, as observed in quantitative functional images acquired over the treatment course. We propose an optimization model that adapts the length of the treatment course as well as the fluence-maps to such imaged tumor state. Specifically, after observing the tumor cell densities at the beginning of a session, the treatment planner solves a group of convex optimization problems to determine an optimal number of remaining treatment sessions, and a corresponding optimal fluence-map for each of these sessions. The objective is to minimize the total number of tumor cells remaining (TNTCR) at the end of this proposed treatment course, subject to upper limits on the biologically effective dose delivered to the organs-at-risk. This fluence-map is administered in future sessions until the next image is available, and then the number of sessions and the fluence-map are re-optimized based on the latest cell density information. We demonstrate via computer simulations on five head-and-neck test cases that such adaptive treatment-length and fluence-map planning reduces the TNTCR and increases the biological effect on the tumor while employing shorter treatment courses, as compared to only adapting fluence-maps and using a pre-determined treatment course length based on one-size-fits-all guidelines.

Hypoxia, that is, insufficient oxygen partial pressure, is a known cause of reduced radiosensitivity in solid tumors, and especially in head-and-neck tumors. It is thus believed to adversely affect the outcome of fractionated radiotherapy. Oxygen partial pressure varies spatially and temporally over the treatment course and exhibits inter-patient and intra-tumor variation. Emerging advances in non-invasive functional imaging offer the future possibility of adapting radiotherapy plans to this uncertain spatiotemporal evolution of hypoxia over the treatment course. We study the potential benefits of such adaptive planning via a theoretical stochastic control framework using computer-simulated evolution of hypoxia on computer-generated test cases in head-and-neck cancer. The exact solution of the resulting control problem is computationally intractable. We develop an approximation algorithm, called certainty equivalent control, that calls for the solution of a sequence of convex programs over the treatment course; dose-volume constraints are handled using a simple constraint generation method. These convex programs are solved using an interior point algorithm with a logarithmic barrier via Newton's method and backtracking line search. Convexity of various formulations in this paper is guaranteed by a sufficient condition on radiobiological tumor-response parameters. This condition is expected to hold for head-and-neck tumors and for other similarly responding tumors where the linear dose-response parameter is larger than the quadratic dose-response parameter. We perform numerical experiments on four test cases by using a first-order vector autoregressive process with exponential and rational-quadratic covariance functions from the spatiotemporal statistics literature to simulate the evolution of hypoxia. Our results suggest that dynamic planning could lead to a considerable improvement in the number of tumor cells remaining at the end of the treatment course. Through these simulations, we also gain insights into when and why dynamic planning is likely to yield the largest benefits.

Purpose: To evaluate how a more flexible and thorough multiobjective search of feasible IMRT plans affects performance in IMRT optimization., Methods: A multiobjective evolutionary algorithm (MOEA) was used as a tool to investigate how expanding the search space to include a wider range of penalty functions affects the quality of the set of IMRT plans produced. The MOEA uses a population of IMRT plans to generate new IMRT plans through deterministic minimization of recombined penalty functions that are weighted sums of multiple, tissue-specific objective functions. The quality of the generated plans are judged by an independent set of nonconvex, clinically relevant decision criteria, and all dominated plans are eliminated. As this process repeats itself, better plans are produced so that the population of IMRT plans will approach the Pareto front. Three different approaches were used to explore the effects of expanding the search space. First, the evolutionary algorithm used genetic optimization principles to search by simultaneously optimizing both the weights and tissue-specific dose parameters in penalty functions. Second, penalty function parameters were individually optimized for each voxel in all organs at risk (OARs) in the MOEA. Finally, a heuristic voxel-specific improvement (VSI) algorithm that can be used on any IMRT plan was developed that incrementally improves voxel-specific penalty function parameters for all structures (OARs and targets). Different approaches were compared using the concept of domination comparison applied to the sets of plans obtained by multiobjective optimization., Results: MOEA optimizations that simultaneously searched both importance weights and dose parameters generated sets of IMRT plans that were superior to sets of plans produced when either type of parameter was fixed for four example prostate plans. The amount of improvement increased with greater overlap between OARs and targets. Allowing the MOEA to search for voxel-specific penalty functions improved results for simple cases with three structures but did not improve results for a more complex case with seven structures. For this modification, the amount of improvement increased with less overlap between OARs and targets. The voxel-specific improvement algorithm improved results for all cases, and its clinical relevance was demonstrated in a complex prostate and a very complex head and neck case., Conclusions: Using an evolutionary algorithm as a tool, it was found that allowing more flexibility in the search space enhanced performance. The two strategies of (a) varying the weights and reference doses in the objective function and (b) removing the constraint of equal penalties for all voxels in a structure both generated sets of plans that dominated sets of plans considered to be "Pareto optimal" within the conventional, more limited search space. When considering voxel-specific objectives, the very large search space can lead to convergence problems in the MOEA for complex cases, but this is not an issue for the VSI algorithm.

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.

Fluence map optimization for intensity-modulated radiation therapy planning can be formulated as a large-scale inverse problem with competing objectives and constraints associated with the tumors and organs at risk. Unfortunately, clinically relevant dose–volume constraints are nonconvex, so standard algorithms for convex problems cannot be directly applied. Although prior work focuses on convex approximations for these constraints, we propose a novel relaxation approach to handle nonconvex dose–volume constraints. We develop efficient, provably convergent algorithms based on partial minimization, and show how to adapt them to handle maximum-dose constraints and infeasible problems. We demonstrate our approach using the CORT data set and show that it is easily adaptable to radiation treatment planning with dose–volume constraints for multiple tumors and organs at risk. Summary of Contribution: This paper proposes a novel approach to deal with dose–volume constraints in radiation treatment planning optimization, which is inherently nonconvex, mixed-integer programming. The authors tackle this NP-hard problem using auxiliary variables and continuous optimization while preserving the problem's nonconvexity. Algorithms to efficiently solve the nonconvex optimization problem presented in this paper yield computation speeds suitable for a busy clinical setting. [ABSTRACT FROM AUTHOR]

Purpose: To build a new treatment planning approach that extends beyond radiation transport and IMRT optimization by modeling the radiation therapy process and prognostic indicators for more outcome-focused decision making.Methods: An in-house treatment planning system was modified to include multiobjective inverse planning, a probabilistic outcome model, and a multi-attribute decision aid. A genetic algorithm generated a set of plans embodying trade-offs between the separate objectives. An influence diagram network modeled the radiation therapy process of prostate cancer using expert opinion, results of clinical trials, and published research. A Markov model calculated a quality adjusted life expectancy (QALE), which was the endpoint for ranking plans.Results: The Multiobjective Evolutionary Algorithm (MOEA) was designed to produce an approximation of the Pareto Front representing optimal tradeoffs for IMRT plans. Prognostic information from the dosimetrics of the plans, and from patient-specific clinical variables were combined by the influence diagram. QALEs were calculated for each plan for each set of patient characteristics. Sensitivity analyses were conducted to explore changes in outcomes for variations in patient characteristics and dosimetric variables. The model calculated life expectancies that were in agreement with an independent clinical study.Conclusions: The radiation therapy model proposed has integrated a number of different physical, biological and clinical models into a more comprehensive model. It illustrates a number of the critical aspects of treatment planning that can be improved and represents a more detailed description of the therapy process. A Markov model was implemented to provide a stronger connection between dosimetric variables and clinical outcomes and could provide a practical, quantitative method for making difficult clinical decisions. [ABSTRACT FROM AUTHOR]

Purpose: To investigate how using different sets of decision criteria impacts the quality of intensity modulated radiation therapy (IMRT) plans obtained by multiobjective optimization. Methods: A multiobjective optimization evolutionary algorithm (MOEA) was used to produce sets of IMRT plans. The MOEA consisted of two interacting algorithms: (i) a deterministic inverse planning optimization of beamlet intensities that minimizes a weighted sum of quadratic penalty objectives to generate IMRT plans and (ii) an evolutionary algorithm that selects the superior IMRT plans using decision criteria and uses those plans to determine the new weights and penalty objectives of each new plan. Plans resulting from the deterministic algorithm were evaluated by the evolutionary algorithm using a set of decision criteria for both targets and organs at risk (OARs). Decision criteria used included variation in the target dose distribution, mean dose, maximum dose, generalized equivalent uniform dose (gEUD), an equivalent uniform dose (EUDα,β) formula derived from the linear-quadratic survival model, and points on dose volume histograms (DVHs). In order to quantatively compare results from trials using different decision criteria, a neutral set of comparison metrics was used. For each set of decision criteria investigated, IMRT plans were calculated for four different cases: two simple prostate cases, one complex prostate Case, and one complex head and neck Case. Results: When smaller numbers of decision criteria, more descriptive decision criteria, or less anticorrelated decision criteria were used to characterize plan quality during multiobjective optimization, dose to OARs and target dose variation were reduced in the final population of plans. Mean OAR dose and gEUD (a = 4) decision criteria were comparable. Using maximum dose decision criteria for OARs near targets resulted in inferior populations that focused solely on low target variance at the expense of high OAR dose. Target dose range, (Dmax-Dmin), decision criteria were found to be most effective for keeping targets uniform. Using target gEUD decision criteria resulted in much lower OAR doses but much higher target dose variation. EUDα,β based decision criteria focused on a region of plan space that was a compromise between target and OAR objectives. None of these target decision criteria dominated plans using other criteria, but only focused on approaching a different area of the Pareto front. Conclusions: The choice of decision criteria implemented in the MOEA had a significant impact on the region explored and the rate of convergence toward the Pareto front. When more decision criteria, anticorrelated decision criteria, or decision criteria with insufficient information were implemented, inferior populations are resulted. When more informative decision criteria were used, such as gEUD, EUDα,β, target dose range, and mean dose, MOEA optimizations focused on approaching different regions of the Pareto front, but did not dominate each other. Using simple OAR decision criteria and target EUDα,β decision criteria demonstrated the potential to generate IMRT plans that significantly reduce dose to OARs while achieving the same or better tumor control when clinical requirements on target dose variance can be met or relaxed. [ABSTRACT FROM AUTHOR]