On the role of modeling parameters in IMRT plan optimization

A hyperparameter-tuning approach to automated inverse planning

BACKGROUND

In current practice, radiotherapy inverse planning often requires treatment planners to modify multiple parameters in the treatment planning system's objective function to produce clinically acceptable plans. Due to the manual steps in this process, plan quality can vary depending on the planning time available and the planner's skills.

PURPOSE

This study investigates the feasibility of two hyperparameter-tuning methods for automated inverse planning. Because this framework does not train a model on previously-optimized plans, it can be readily adapted to practice pattern changes, and the resulting plan quality is not limited by that of a training cohort.

METHODS

We retrospectively selected 10 patients who received lung stereotactic body radiation therapy using manually-generated clinical plans. We implemented random sampling and Bayesian optimization to automatically tune objective function parameters using linear-quadratic utility functions based on 11 clinical goals. Normalizing all plans to deliver a minimum dose of 48 Gy to 95% of the planning target volume, we compared plan quality for the automatically-generated plans to the manually-generated plans. We also investigated the impact of iteration count on the automatically-generated plans, comparing planning time and plan utility for randomized and Bayesian plans with and without stopping criteria.

RESULTS

Without stopping criteria, the median planning time was 1.9 and 2.3 hours for randomized and Bayesian plans, respectively. The organ-at-risk doses in the randomized and Bayesian plans had a median percent difference (MPD) of 48.7% and 60.4% below clinical dose limits and an MPD of 2.8% and 3.3% below clinical plan doses. With stopping criteria, the utility decreased by an MPD of 5.3% and 3.9% for randomized and Bayesian plans, but the median planning time was reduced to 0.5 and 0.7 hours, and the organ-at-risk doses still had an MPD of 42.9% and 49.7% below clinical dose limits and an MPD of 0.3% and 1.8% below clinical plan doses.

CONCLUSIONS

This study demonstrates that hyperparameter-tuning approaches to automated inverse planning can reduce the treatment planner's active planning time with plan quality that is similar to or better than manually-generated plans. This article is protected by copyright. All rights reserved.

Differences in predictions of ODE models of tumor growth: a cautionary example

BACKGROUND

While mathematical models are often used to predict progression of cancer and treatment outcomes, there is still uncertainty over how to best model tumor growth. Seven ordinary differential equation (ODE) models of tumor growth (exponential, Mendelsohn, logistic, linear, surface, Gompertz, and Bertalanffy) have been proposed, but there is no clear guidance on how to choose the most appropriate model for a particular cancer.

METHODS

We examined all seven of the previously proposed ODE models in the presence and absence of chemotherapy. We derived equations for the maximum tumor size, doubling time, and the minimum amount of chemotherapy needed to suppress the tumor and used a sample data set to compare how these quantities differ based on choice of growth model.

RESULTS

We find that there is a 12-fold difference in predicting doubling times and a 6-fold difference in the predicted amount of chemotherapy needed for suppression depending on which growth model was used.

CONCLUSION

Our results highlight the need for careful consideration of model assumptions when developing mathematical models for use in cancer treatment planning.

Analyzing the quality robustness of chemotherapy plans with respect to model uncertainties

Mathematical models of chemotherapy planning problems contain various biomedical parameters, whose values are difficult to quantify and thus subject to some uncertainty. This uncertainty propagates into the therapy plans computed on these models, which poses the question of robustness to the expected therapy quality. This work introduces a combined approach for analyzing the quality robustness of plans in terms of dosing levels with respect to model uncertainties in chemotherapy planning. It uses concepts from multi-criteria decision making for studying parameters related to the balancing between the different therapy goals, and concepts from sensitivity analysis for the examination of parameters describing the underlying biomedical processes and their interplay. This approach allows for a profound assessment of a therapy plan, how stable its quality is with respect to parametric changes in the used mathematical model.

The use of a multiobjective evolutionary algorithm to increase flexibility in the search for better IMRT plans

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.