Approximated multileaf collimator field segmentation

In intensity-modulated radiation therapy the aim is to realize given intensity distributions as a superposition of differently shaped fields. Multileaf collimators are used for field shaping. This segmentation task leads to discrete optimization problems, that are considered in this dissertation. A variety of algorithms for exact and approximated segmentation, for different objective functions and various technical as well as dosimetric constraints are developed

A shortest path-based approach to the multileaf collimator sequencing problem

AbstractThe multileaf collimator sequencing problem is an important component in effective cancer treatment delivery. The problem can be formulated as finding a decomposition of an integer matrix into a weighted sequence of binary matrices whose rows satisfy a consecutive ones property. Minimising the cardinality of the decomposition is an important objective and has been shown to be strongly NP-hard, even for a matrix restricted to a single column or row. We show that in this latter case it can be solved efficiently as a shortest path problem, giving a simple proof that the one-row problem is fixed-parameter tractable in the maximum intensity. We develop new linear and constraint programming models exploiting this result. Our approaches significantly improve the best known for the problem, bringing real-world sized problem instances within reach of exact algorithms

On the minimum cardinality problem in intensity modulated radiotherapy

The thesis examines an optimisation problem that appears in the treatment planning of intensity modulated radiotherapy. An approach is presented which solved the optimisation problem in question while also extending the approach to execute in a massively parallel environment. The performance of the approach presented is among the fastest available

Analytical Models for Probabilistic Inverse Treatment Planning in Intensity-modulated Proton Therapy

The sensitivity of intensity-modulated proton therapy to uncertainties requires case-specific uncertainty assessment and mitigation. As an alternative to scenario-based methods, this thesis describes the implementation, application and conceptual extension of the Analytical Probabilistic Modeling (APM) framework introduced by Bangert, Hennig, and Oelfke (2013). APM represents moments of the probability distribution over dose in closed-form, providing a probabilistic analog to nominal pencil-beam dose calculation subject to range and setup uncertainties that further enables probabilistic optimization. First, APM was implemented in MITKrad, a treatment planning plugin for MITK built completely from scratch. APM’s computations were validated against sample statistics, showing nearly perfect agreement. Run-times within minutes could be realized for uncertainty assessment and probabilistic optimization on patient data. Reformulation of APM enabled linear separation of the computations into random and systematic uncertainty components. Uncertainty over the full fractionation spectrum could then be modeled and optimized with a single pre-computation. It could be shown that fractionation is exploited in optimization with APM for additional organ at risk sparing. APM was then extended to propagation of uncertainties from dose to clinically relevant plan quality metrics. Expectation and variance could be modeled accurately for organ mean dose and dose-volume histograms. However, approximations for equivalent uniform dose and minimum and maximum dose values did not provide reliable results. Finally, the closed-form plan metrics were used to conceptualize constrained probabilistic optimization. Besides novel probabilistic objectives, confidence constraints could be established. Due to increased computational complexity of the new models, the proof-of-concept was provided through evaluations on a one-dimensional prototype anatomy. In conclusion, the herein extended APM framework is able to provide probabilistic analogs to established nominal concepts of dose calculation, plan quality metrics, and constrained optimization. If computational hurdles can be overcome in the future, clinical application would be within reach

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

Proceedings of the XIII Global Optimization Workshop: GOW'16

[Excerpt] Preface: Past Global Optimization Workshop shave been held in Sopron (1985 and 1990), Szeged (WGO, 1995), Florence (GO’99, 1999), Hanmer Springs (Let’s GO, 2001), Santorini (Frontiers in GO, 2003), San José (Go’05, 2005), Mykonos (AGO’07, 2007), Skukuza (SAGO’08, 2008), Toulouse (TOGO’10, 2010), Natal (NAGO’12, 2012) and Málaga (MAGO’14, 2014) with the aim of stimulating discussion between senior and junior researchers on the topic of Global Optimization. In 2016, the XIII Global Optimization Workshop (GOW’16) takes place in Braga and is organized by three researchers from the University of Minho. Two of them belong to the Systems Engineering and Operational Research Group from the Algoritmi Research Centre and the other to the Statistics, Applied Probability and Operational Research Group from the Centre of Mathematics. The event received more than 50 submissions from 15 countries from Europe, South America and North America. We want to express our gratitude to the invited speaker Panos Pardalos for accepting the invitation and sharing his expertise, helping us to meet the workshop objectives. GOW’16 would not have been possible without the valuable contribution from the authors and the International Scientific Committee members. We thank you all. This proceedings book intends to present an overview of the topics that will be addressed in the workshop with the goal of contributing to interesting and fruitful discussions between the authors and participants. After the event, high quality papers can be submitted to a special issue of the Journal of Global Optimization dedicated to the workshop. [...

Tree tensor networks for high-dimensional quantum systems and beyond

This thesis presents the development of a numerical simulation technique, the Tree Tensor Network, aiming to overcome current limitations in the simulation of two- and higher-dimensional quantum many-body systems. The development and application of methods based on Tensor Networks (TNs) for such systems are one of the most relevant challenges of the current decade with the potential to promote research and technologies in a broad range of fields ranging from condensed matter physics, high-energy physics, and quantum chemistry to quantum computation and quantum simulation. The particular challenge for TNs is the combination of accuracy and scalability which to date are only met for one-dimensional systems by other established TN techniques. This thesis first describes the interdisciplinary field of TN by combining mathematical modelling, computational science, and quantum information before it illustrates the limitations of standard TN techniques in higher-dimensional cases. Following a description of the newly developed Tree Tensor Network (TTN), the thesis then presents its application to study a lattice gauge theory approximating the low-energy behaviour of quantum electrodynamics, demonstrating the successful applicability of TTNs for high-dimensional gauge theories. Subsequently, a novel TN is introduced augmenting the TTN for efficient simulations of high-dimensional systems. Along the way, the TTN is applied to problems from various fields ranging from low-energy to high-energy up to medical physics.In dieser Arbeit wird die Entwicklung einer numerischen Simulationstechnik, dem Tree Tensor Network (TTN), vorgestellt, die darauf abzielt, die derzeitigen Limitationen bei der Simulation von zwei- und höherdimensionalen Quanten-Vielteilchensystemen zu überwinden. Die Weiterentwicklung von auf Tensor-Netzwerken (TN) basierenden Methoden für solche Systeme ist eine der aktuellsten und relevantesten Herausforderungen. Sie birgt das Potential, Forschung und Technologien in einem breiten Spektrum zu fördern, welches sich von der Physik der kondensierten Materie, der Hochenergiephysik und der Quantenchemie bis hin zur Quantenberechnung und Quantensimulation erstreckt. Die besondere Herausforderung für TN ist die Kombination von Genauigkeit und Skalierbarkeit, die bisher nur für eindimensionale Systeme erfüllt wird. Diese Arbeit beschreibt zunächst das interdisziplinäre Gebiet der TN als eine Kombination von mathematischer Modellierung, Computational Science und Quanteninformation, um dann die Grenzen der Standard-TN-Techniken in höherdimensionalen Fällen aufzuzeigen. Nach einer Beschreibung des neu entwickelten TTN stellt die Arbeit dessen Anwendung zur Untersuchung einer Gittereichtheorie vor, die das Niederenergieverhalten der Quantenelektrodynamik approximiert und somit die erfolgreiche Anwendbarkeit von TTNs für hochdimensionale Eichtheorien demonstriert. Anschließend wird ein neuartiges TN eingeführt, welches das TTN für effiziente Simulationen hochdimensionaler Systeme erweitert. Zusätzlich wird das TTN auf diverse Probleme angewandt, die von Niederenergie- über Hochenergie- bis hin zur medizinischen Physik reichen