Column Generation-Based Techniques for Intensity-Modulated Radiation Therapy (IMRT) and Volumetric Modulated Arc Therapy (VMAT) Treatment Planning

RÉSUMÉ: Les statistiques ont estimé à environ 14,1 millions le nombre de cas de cancer en 2018 dans le monde, et qui devrait passer à 24 millions d’ici 2035. La radiothérapie est l’une des premières méthodes de traitement du cancer, qu’environ 50% des patients reçoivent au cours de leur maladie. Cette méthode endommage le matériel génétique des cellules cancéreuses, détruisant ainsi leur capacité de reproduction. Cependant, les cellules normales sont également affectées par le rayonnement ; par conséquent, le traitement doit être effectué de manière à maximiser la dose de rayonnement aux tumeurs, tout en minimisant les effets néfastes des radiations sur les tissus sains. Les techniques d’optimisation sont utilisées afin de déterminer la dose et la position du rayonnement à administrer au corps du patient. Ce projet aborde la radiothérapie externe à travers la radiothérapie par modulation d’intensité (IMRT), ainsi qu’une nouvelle forme appelée modulation d’intensité volumétrique par thérapie par arcs (VMAT). En IMRT, un nombre fini de directions sont déterminées pour le rayonnement du faisceau, tandis qu’en VMAT l’accélérateur linéaire tourne autour du corps du patient alors que le faisceau est allumé. Cette technologie permet de modifier dynamiquement la forme du faisceau et le débit de dose pendant le traitement. Le problème de planification du traitement consiste à choisir une séquence de distribution des formes de faisceaux, à optimiser le dé bit de dose du faisceau et à déterminer la vitesse de rotation du portique, si nécessaire. Cette recherche tire profit de la méthode de génération de colonnes, en tant que méthode d’optimisation efficace en particulier pour les problèmes à grande échelle. Cette technique permet d’améliorer le temps de traitement et les objectifs cliniques non linéaires et non convexes, dans la planification de traitement en VMAT. Un nouveau modèle multi-objectif de génération de colonnes pour l’IMRT est également développé. Dans le premier essai, nous développons un nouvel algorithme de génération de colonnes qui optimise le compromis entre le temps et la qualité du traitement délivré pour la planification de traitement en VMAT. Pour ce faire, une génération simultanée de colonnes et de rangées est développée, afin de relier les colonnes, contenant la configuration des ouvertures de faisceaux, aux rangées du modèle, représentant la restriction de temps de traitement. De plus, nous proposons une technique de regroupement par grappe modifiée, afin d’agréger des éléments de volume similaires du corps du patient, et de réduire efficacement le nombre de contraintes dans le modèle. Les résultats de calcul montrent qu’il est possible d’obtenir un traitement de haute qualité sur quatre processeurs en parallèle. Dans le deuxième essai, nous développons une approche de planification automatique intégrant les critères de l’histogramme dose-volume (DVH). Les DVH sont la représentation de dose la plus courante pour l’évaluation de la qualité de traitement en technologie VMAT. Nous profitons de la procédure itérative de génération de colonnes pour ajuster les paramètres du modèle lors de la génération d’ouverture, et répondre aux critères DVH non linéaires, sans tenir compte des contraintes dures dans le modèle. Les résultats sur les cas cliniques montrent que notre méthodologie a été significativement améliorée, pour obtenir des plans cliniquement acceptables sans intervention humaine par rapport à une simple optimisation VMAT. De plus, la comparaison avec un système de planification de traitement commercial existant montre que la qualité des plans obtenus à partir de la méthode proposée, en particulier pour les tissus sains, est largement meilleure alors que le temps de calcul est moindre. Dans le troisième essai, nous abordons la planification de traitement en IMRT, qui est formulée comme un problème d’optimisation convexe à grande échelle, avec un espace de faisabilité simplex. Nous intégrons d’abord une nouvelle approche de solution basée sur la méthode Frank-Wolfe, appelée Blended Conditional Gradients, dans la génération de colonnes, pour améliorer les performances de calcul de la méthode. Nous proposons ensuite une technique de génération de colonnes multi-objectif, pour obtenir directement des ouvertures qui se rapprochent d’un ensemble efficace de plans de traitement non dominés. A cette fin, nous trouvons les limites inférieure et supérieure du front de Pareto, et générons une colonne avec un vecteur de poids des objectifs pré-assigné ou nouveau, réduisant la distance maximale de deux bornes. Nous prouvons que cet algorithme converge vers le front de Pareto. Les résultats de recherche d’un bon compromis de traitement entre la destruction des volumes cibles et la protection des structures saines dans un espace objectif bidimensionnel, montrent l’efficacité de l’algorithme dans l’approche du front de Pareto, avec des plans de traitement livrables en 3 minutes environ, et évitant un grand nombre de colonnes. Cette méthode s’applique également à d’autres classes de problèmes d’optimisation convexe, faisant appel à la fois à une génération de colonnes et à une optimisation multi-objectifs.----------ABSTRACT: The statistics have estimated about 18.1 million cancer cases in 2018 around the world, which is expected to increase to 24 million by 2035. Radiation therapy is one of the most important cancer treatment methods, which about 50% of patients receive during their illness. This method works by damaging the genetic material within cancerous cells and destroying their ability to reproduce. However, normal cells are also affected by radiation; therefore, the treatment should be performed in such a way that it maximizes the dose of radiation to tumors, while simultaneously minimizing the adverse effects of radiations to healthy tissues. The optimization techniques are useful to determine where and how much radiation should be delivered to patient’s body. In this project, we address the intensity-modulated radiation therapy (IMRT) as a widelyused external radiotherapy method and also a novel form called volumetric modulated arc therapy (VMAT). In IMRT, a finite number of directions are determined for the beam radiation, while in VMAT, the linear accelerator rotates around the patient’s body while the beam is on. These technologies give us the ability of changing the beam shape and the dose rate dynamically during the treatment. The treatment planning problem consists of selecting a delivery sequence of beam shapes, optimizing the dose rate of the beam, and determining the rotation speed of the gantry, if required. In this research, we take advantages of the column generation technique, as a leading optimization method specifically for large-scale problems, to improve the treatment time and non-linear non-convex clinical objectives in VMAT treatment planning, and also develop a new multi-objective column generation framework for IMRT. In the first essay, we develop a novel column generation algorithm optimizing the trade-off between delivery time and treatment quality for VMAT treatment planning. To this end, simultaneous column-and-row generation is developed to relate the configuration of beam apertures in columns to the treatment time restriction in the rows of the model. Moreover, we propose a modified clustering technique to aggregate similar volume elements of the patient’s body and efficiently reduce the number of constraints in the model. The computational results show that a high-quality treatment is achievable using a four-thread CPU. In the second essay, we develop an automatic planning approach integrating dose-volume histogram (DVH) criteria, the most common method of treatment evaluation in practice, for VMAT treatment planning. We take advantage of the iterative procedure of column generation to adjust the model parameters during aperture generation and meet nonlinear DVH criteria without considering hard constraints in the model. The results on clinical cases show that our methodology had significant improvement to obtain clinically acceptable plans without human intervention in comparison to simple VMAT optimization. In addition, the comparison to an existing commercial treatment planning system shows the quality of the obtained plans from the proposed method, especially for the healthy tissues, is significantly better while the computational time is less. In the third essay, we address the IMRT treatment planning, which is formulated as a large scale convex optimization problem with simplex feasibility space. We first integrate a novel Frank-Wolfe-based solution approach, so-called Blended Conditional Gradients, into the column generation to improve the computational performance for the method. We then propose a multi-objective column generation technique to directly obtain apertures that approximate an efficient non-dominated set of treatment plans. To this end, we find lower and upper bounds for the Pareto front and generate a column with a pre-assigned or new weight-vector of the objectives, reducing the maximum distance of two bounds. We prove this algorithm converges to the Pareto front. The results in a two-dimensional objective space to find the trade-off plans between the treat of target volumes and sparing the healthy structures show the efficiency of the algorithm to approximate the Pareto front with deliverable treatment plans in about 3 minutes, avoiding a large number of columns. This method is also applicable for other classes of convex optimization problems requiring both column generation and multi-objective optimization

Application of constrained optimization methods in health services research: Report 2 of the ISPOR Optimization Methods Emerging Good Practices Task Force

Background Constrained optimization methods are already widely used in health care to solve problems that represent traditional applications of operations research methods, such as choosing the optimal location for new facilities or making the most efficient use of operating room capacity. Objectives In this paper we illustrate the potential utility of these methods for finding optimal solutions to problems in health care delivery and policy. To do so, we selected three award-winning papers in health care delivery or policy development, reflecting a range of optimization algorithms. Two of the three papers are reviewed using the ISPOR Constrained Optimization Good Practice Checklist, adapted from the framework presented in the initial Optimization Task Force Report. The first case study illustrates application of linear programming to determine the optimal mix of screening and vaccination strategies for the prevention of cervical cancer. The second case illustrates application of the Markov Decision Process to find the optimal strategy for treating type 2 diabetes patients for hypercholesterolemia using statins. The third paper (described in Appendix 1) is used as an educational tool. The goal is to describe the characteristics of a radiation therapy optimization problem and then invite the reader to formulate the mathematical model for solving it. This example is particularly interesting because it lends itself to a range of possible models, including linear, nonlinear, and mixed-integer programming formulations. From the case studies presented, we hope the reader will develop an appreciation for the wide range of problem types that can be addressed with constrained optimization methods, as well as the variety of methods available. Conclusions Constrained optimization methods are informative in providing insights to decision makers about optimal target solutions and the magnitude of the loss of benefit or increased costs associated with the ultimate clinical decision or policy choice. Failing to identify a mathematically superior or optimal solution represents a missed opportunity to improve economic efficiency in the delivery of care and clinical outcomes for patients. The ISPOR Optimization Methods Emerging Good Practices Task Force’s first report provided an introduction to constrained optimization methods to solve important clinical and health policy problems. This report also outlined the relationship of constrained optimization methods relative to traditional health economic modeling, graphically illustrated a simple formulation, and identified some of the major variants of constrained optimization models, such as linear programming, dynamic programming, integer programming, and stochastic programming. The second report illustrates the application of constrained optimization methods in health care decision making using three case studies. The studies focus on determining optimal screening and vaccination strategies for cervical cancer, optimal statin start times for diabetes, and an educational case to invite the reader to formulate radiation therapy optimization problems. These illustrate a wide range of problem types that can be addressed with constrained optimization methods

Planificación radioterápica de intensidad modulada basada en un modelo de simulación explícita del transporte de partículas mediante optimización por imágen médica

Falta resumen y palabras claveIntroducción: La planificación radioterápica más precisa es la basada en un cálculo del transporte explícito del haz de partículas, desde su generación en la cabeza del acelerador lineal, y en su interacción con los modificadores y colimadores, hasta la deposición de su energía en los tejidos del paciente con densidades heterogéneas. No obstante, este cálculo exige un tiempo de computación inviable para la práctica clínica diaria. En este trabajo se presenta un modelo de optimización de abertura directa que está exclusivamente basado en los datos de la imagen del paciente, y que se implementa en un sistema propio de planificación de tratamientos Monte Carlo (MCTPS), con objeto de resolver tratamientos de radioterapia complejos con resultados óptimos y en tiempos eficientes para ser adaptado a la práctica clínica. Método: El sistema de planificación es un sistema full Monte Carlo (fMC), controlado mediante una interfaz de Matlab®, que está basado en la generación de matrices, que conforman un mapa denominado biofísico, el cual es generado a partir de los datos de la imagen del paciente para conseguir un juego de segmentos realizable óptimo. En orden a reducir los tiempos de computación necesarios, el mapa de fluencia convencional ha sido sustituido por el conjunto de mapas biofísicos, el cual es secuenciado para proporcionar las aberturas que posteriormente serán pesadas mediante un algoritmo de optimización basado en un modelo de programación lineal, que permite optimizar la distribución de dosis al nivel del vóxel. Un algoritmo de ray-casting extrae del CT del paciente la información de las estructuras de interés, el espesor atravesado, así como los valores PET, si los hay. Los datos son guardados para generar los mapas biofísicos en cada incidencia. Estos mapas son los ficheros inputs de un secuenciador propio desarrollado para este fin. Se simularon espacios de fase para distintos aceleradores (Primus de Siemens y Axesse de Elekta) para varias energías (6, 9, 12, 15 MeVy 6 MV). Los espacios de fase fueron simulados con el código EGSnrc/BEAMnrc. El cálculo de dosis en el paciente fue simulado con el código BEAMDOSE. Este código es una versión modificada de EGSnrc/DOSXYZnrc capaz de calcular la dosis sobre cada vóxel debido a cada segmento, y así estar en disposición de combinarlos con diferentes pesos durante el proceso de optimización. Resultados: Se han estudiado casos complejos con distintas características, para chequear el algoritmo de planificación en situaciones en las que el cálculo MC ofrece un valor añadido: Un caso de cabeza y cuello (Caso I) con tres blancos delineados a partir de la imagen PET/CT y con un escalado de dosis exigente; un caso de mama parcial (Caso II) para ser resuelto con haces de electrones modulados (IMRT+MERT); y un caso de lecho prostático (Caso III) con una geometría cóncava acusada. En estos tres casos, las dosis de prescripción y límites en los órganos de riesgo fueron satisfactorias en un tiempo lo suficientemente corto como para permitir implementarlo en la rutina clínica. Estas soluciones teóricas fueron verificadas experimentalmente con éxito. Conclusiones: Se ha desarrollado un modelo de planificación de tratamiento Monte Carlo basado exclusivamente en mapas diseñados a partir de la imagen del paciente. La secuenciación de estos mapas permite obtener aberturas realizables las cuales son moduladas mediante una formulación de programación lineal, permitiendo una optimización de la dosis al nivel del vóxel. El modelo es capaz de resolver casos complejos de radioterapia con una gran precisión y empleando tiempos de computación asumibles para la aplicación clínica

A novel combination of Cased-Based Reasoning and Multi Criteria Decision Making approach to radiotherapy dose planning

In this thesis, a set of novel approaches has been developed by integration of Cased-Based Reasoning (CBR) and Multi-Criteria Decision Making (MCDM) techniques. Its purpose is to design a support system to assist oncologists with decision making about the dose planning for radiotherapy treatment with a focus on radiotherapy for prostate cancer. CBR, an artificial intelligence approach, is a general paradigm to reasoning from past experiences. It retrieves previous cases similar to a new case and exploits the successful past solutions to provide a suggested solution for the new case. The case pool used in this research is a dataset consisting of features and details related to successfully treated patients in Nottingham University Hospital. In a typical run of prostate cancer radiotherapy simple CBR, a new case is selected and thereafter based on the features available at our data set the most similar case to the new case is obtained and its solution is prescribed to the new case. However, there are a number of deficiencies associated with this approach. Firstly, in a real-life scenario, the medical team considers multiple factors rather than just the similarity between two cases and not always the most similar case provides with the most appropriate solution. Thus, in this thesis, the cases with high similarity to a new case have been evaluated with the application of the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). This approach takes into account multiple criteria besides similarity to prescribe a final solution. Moreover, the obtained dose plans were optimised through a Goal Programming mathematical model to improve the results. By incorporating oncologists’ experiences about violating the conventionally available dose limits a system was devised to manage the trade-off between treatment risk for sensitive organs and necessary actions to effectively eradicate cancer cells. Additionally, the success rate of the treatment, the 2-years cancer free possibility, has a vital role in the efficiency of the prescribed solutions. To consider the success rate, as well as uncertainty involved in human judgment about the values of different features of radiotherapy Data Envelopment Analysis (DEA) based on grey numbers, was used to assess the efficiency of different treatment plans on an input and output based approach. In order to deal with limitations involved in DEA regarding the number of inputs and outputs, we presented an approach for Factor Analysis based on Principal Components to utilize the grey numbers. Finally, to improve the CBR base of the system, we applied Grey Relational Analysis and Gaussian distant based CBR along with features weight selection through Genetic Algorithm to better handle the non-linearity exists within the problem features and the high number of features. Finally, the efficiency of each system has been validated through leave-one-out strategy and the real dataset. The results demonstrated the efficiency of the proposed approaches and capability of the system to assist the medical planning team. Furthermore, the integrated approaches developed within this thesis can be also applied to solve other real-life problems in various domains other than healthcare such as supply chain management, manufacturing, business success prediction and performance evaluation

A unified mixed-integer programming model for simultaneous fluence weight and aperture optimization in VMAT, Tomotherapy, and Cyberknife

In this paper, we propose and study a unified mixed-integer programming model that simultaneously optimizes fluence weights and multi-leaf collimator (MLC) apertures in the treatment planning optimization of VMAT, Tomotherapy, and CyberKnife. The contribution of our model is threefold: i. Our model optimizes the fluence and MLC apertures simultaneously for a given set of control points. ii. Our model can incorporate all volume limits or dose upper bounds for organs at risk (OAR) and dose lower bound limits for planning target volumes (PTV) as hard constraints, but it can also relax either of these constraint sets in a Lagrangian fashion and keep the other set as hard constraints. iii. For faster solutions, we propose several heuristic methods based on the MIP model, as well as a meta-heuristic approach. The meta-heuristic is very efficient in practice, being able to generate dose- and machinery-feasible solutions for problem instances of clinical scale, e.g., obtaining feasible treatment plans to cases with 180 control points, 6,750 sample voxels and 18,000 beamlets in 470 seconds, or cases with 72 control points, 8,000 sample voxels and 28,800 beamlets in 352 seconds. With discretization and down-sampling of voxels, our method is capable of tackling a treatment field of 8000cm3∼64000cm3, depending on the ratio of critical structure versus unspecified tissues