Applications of mathematical network theory

This thesis is a collection of papers on a variety of optimization problems where network structure can be used to obtain efficient algorithms. The considered applications range from the optimization of radiation treatment plkans in cancer therapy to maintenance planning for maximizing the throughput in bulk good supply chains

PREDICTION OF RESPIRATORY MOTION

Radiation therapy is a cancer treatment method that employs high-energy radiation beams to destroy cancer cells by damaging the ability of these cells to reproduce. Thoracic and abdominal tumors may change their positions during respiration by as much as three centimeters during radiation treatment. The prediction of respiratory motion has become an important research area because respiratory motion severely affects precise radiation dose delivery. This study describes recent radiotherapy technologies including tools for measuring target position during radiotherapy and tracking-based delivery systems. In the first part of our study we review three prediction approaches of respiratory motion, i.e., model-based methods, model-free heuristic learning algorithms, and hybrid methods. In the second part of our work we propose respiratory motion estimation with hybrid implementation of extended Kalman filter. The proposed method uses the recurrent neural network as the role of the predictor and the extended Kalman filter as the role of the corrector. In the third part of our work we further extend our research work to present customized prediction of respiratory motion with clustering from multiple patient interactions. For the customized prediction we construct the clustering based on breathing patterns of multiple patients using the feature selection metrics that are composed of a variety of breathing features. In the fourth part of our work we retrospectively categorize breathing data into several classes and propose a new approach to detect irregular breathing patterns using neural networks. We have evaluated the proposed new algorithm by comparing the prediction overshoot and the tracking estimation value. The experimental results of 448 patients’ breathing patterns validated the proposed irregular breathing classifier

Accelerating Radiation Dose Calculation with High Performance Computing and Machine Learning for Large-scale Radiotherapy Treatment Planning

Radiation therapy is powered by modern techniques in precise planning and executionof radiation delivery, which are being rapidly improved to maximize its benefit to cancerpatients. In the last decade, radiotherapy experienced the introduction of advanced methodsfor automatic beam orientation optimization, real-time tumor tracking, daily planadaptation, and many others, which improve the radiation delivery precision, planning easeand reproducibility, and treatment efficacy. However, such advanced paradigms necessitatethe calculation of orders of magnitude more causal dose deposition data, increasing the timerequirement of all pre-planning dose calculation. Principles of high-performance computingand machine learning were applied to address the insufficient speeds of widely-used dosecalculation algorithms to facilitate translation of these advanced treatment paradigms intoclinical practice.To accelerate CT-guided X-ray therapies, Collapsed-Cone Convolution-Superposition(CCCS), a state-of-the-art analytical dose calculation algorithm, was accelerated through itsnovel implementation on highly parallelized GPUs. This context-based GPU-CCCS approachtakes advantage of X-ray dose deposition compactness to parallelize calculation acrosshundreds of beamlets, reducing hardware-specific overheads, and enabling acceleration bytwo to three orders of magnitude compared to existing GPU-based beamlet-by-beamletapproaches. Near-linear increases in acceleration are achieved with a distributed, multi-GPUimplementation of context-based GPU-CCCS.Dose calculation for MR-guided treatment is complicated by electron return effects(EREs), exhibited by ionizing electrons in the strong magnetic field of the MRI scanner. EREsnecessitate the use of much slower Monte Carlo (MC) dose calculation, limiting the clinicalapplication of advanced treatment paradigms due to time restrictions. An automaticallydistributed framework for very-large-scale MC dose calculation was developed, grantinglinear scaling of dose calculation speed with the number of utilized computational cores. Itwas then harnessed to efficiently generate a large dataset of paired high- and low-noise MCdoses in a 1.5 tesla magnetic field, which were used to train a novel deep convolutionalneural network (CNN), DeepMC, to predict low-noise dose from faster high-noise MC-simulation. DeepMC enables 38-fold acceleration of MR-guided X-ray beamlet dosecalculation, while remaining synergistic with existing MC acceleration techniques to achievemultiplicative speed improvements.This work redefines the expectation of X-ray dose calculation speed, making it possibleto apply new highly-beneficial treatment paradigms to standard clinical practice for the firsttime

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

Intensity modulated radiotherapy for inoperable, locally-advanced non-small cell lung cancer : development and clinical outcomes at a cancer centre in Eastern India

Background The submitted publications outline the sequential steps taken for clinical implementation of intensity modulated radiotherapy (IMRT) for lung cancer at a cancer centre in Eastern India. A literature review combined with a detailed risk assessment for IMRT in lung cancer guided the careful implementation for cases where three-dimensional conformal radiotherapy (3D-CRT) did not generate a safe radiotherapy (RT) plan with acceptable tumour coverage. With growing experience, IMRT was expanded to patients receiving concurrent chemoradiation (CCRT) and accelerated RT, including continuous hyperfractionated accelerated radiotherapy (CHART) as well as moderately hypofractionated accelerated radiotherapy. Survival outcomes from radical radiotherapy and chemoradiation (both sequential and concurrent) were audited and found to be comparable to contemporary published literature. In patients with large volume (>500ml) disease, IMRT resulted in non-inferior outcomes despite treating larger volumes and more advanced stage disease. A predictive model that estimates the probability that IMRT would be necessary to produce an acceptable and safe RT plan, was developed from the planning data of 202 patients. Methods An external prospective study was designed to validate this data-driven, decision aid in cohort of patients from multiple hospitals. Apart from assessing the accuracy of the developed predictive model, we are hoping to quantify the planning time saved by opting for IMRT without attempting a 3D-CRT plan. Updated systematic review of prospective studies was carried out to assess the efficacy and safety of IMRT for locally-advanced NSCLC. 9 Results and conclusion No direct impact of IMRT or volumetric modulated arc therapy (VMAT) was seen on local control and survival for these patients, on updated systematic review. IMRT and VMAT was shown to be feasible and safe in the treated patient population. IMRT makes curative treatment possible for large-volume or complex-shaped, locally-advanced NSCLC, resulting non-inferior survival outcomes

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 case-based reasoning system for radiotherapy treatment planning for brain cancer

In this thesis, a novel case-based reasoning (CBR) approach to radiotherapy treatment planning for brain cancer patients is presented. In radiotherapy, tumour cells are destroyed using ionizing radiation. For each patient, a treatment plan is generated that describes how the radiation should be applied in order to deliver a tumouricidal radiation dose while avoiding irradiation of healthy tissue and organs at risk in the vicinity of the tumour. The traditional, manual trial and error approach is a time-consuming process that depends on the experience and intuitive knowledge of medical physicists. CBR is an artificial intelligence methodology, which attempts to solve new problems based on the solutions of previously solved similar problems. In this research work, CBR is used to generate the parameters of a treatment plan by capturing the subjective and intuitive knowledge of expert medical physicists stored intrinsically in the treatment plans of similar patients treated in the past. This work focusses on the retrieval stage of the CBR system, in which given a new patient case, the most similar case in the archived case base is retrieved along with its treatment plan. A number of research issues that arise from using CBR for radiotherapy treatment planning for brain cancer are addressed. Different approaches to similarity calculation between cases are investigated and compared, in particular, the weighted nearest neighbour similarity measure and a novel non-linear, fuzzy similarity measure designed for our CBR system. A local case attribute weighting scheme has been developed that uses rules to assign attribute weights based on the values of the attributes in the new case and is compared to global attribute weighting, where the attribute weights remain constant for all target cases. A multi-phase case retrieval approach is introduced in which each phase considers one part of the solution. In addition, a framework developed for the imputation of missing values in the case base is described. The research was carried out in collaboration with medical physicists at the Nottingham University Hospitals NHS Trust, City Hospital Campus, UK. The performance of the developed methodologies was tested using brain cancer patient cases obtained from the City Hospital. The results obtained show that the success rate of the retrieval mechanism provides a good starting point for adaptation, the next phase in development for the CBR system. The developed automated CBR system will assist medical physicists in quickly generating treatment plans and can also serve as a teaching and training aid for junior, inexperienced medical physicists. In addition, the developed methods are generic in nature and can be adapted to be used in other CBR or intelligent decision support systems for other complex, real world, problem domains that highly depend on subjective and intuitive knowledge

A case-based reasoning system for radiotherapy treatment planning for brain cancer

In this thesis, a novel case-based reasoning (CBR) approach to radiotherapy treatment planning for brain cancer patients is presented. In radiotherapy, tumour cells are destroyed using ionizing radiation. For each patient, a treatment plan is generated that describes how the radiation should be applied in order to deliver a tumouricidal radiation dose while avoiding irradiation of healthy tissue and organs at risk in the vicinity of the tumour. The traditional, manual trial and error approach is a time-consuming process that depends on the experience and intuitive knowledge of medical physicists. CBR is an artificial intelligence methodology, which attempts to solve new problems based on the solutions of previously solved similar problems. In this research work, CBR is used to generate the parameters of a treatment plan by capturing the subjective and intuitive knowledge of expert medical physicists stored intrinsically in the treatment plans of similar patients treated in the past. This work focusses on the retrieval stage of the CBR system, in which given a new patient case, the most similar case in the archived case base is retrieved along with its treatment plan. A number of research issues that arise from using CBR for radiotherapy treatment planning for brain cancer are addressed. Different approaches to similarity calculation between cases are investigated and compared, in particular, the weighted nearest neighbour similarity measure and a novel non-linear, fuzzy similarity measure designed for our CBR system. A local case attribute weighting scheme has been developed that uses rules to assign attribute weights based on the values of the attributes in the new case and is compared to global attribute weighting, where the attribute weights remain constant for all target cases. A multi-phase case retrieval approach is introduced in which each phase considers one part of the solution. In addition, a framework developed for the imputation of missing values in the case base is described. The research was carried out in collaboration with medical physicists at the Nottingham University Hospitals NHS Trust, City Hospital Campus, UK. The performance of the developed methodologies was tested using brain cancer patient cases obtained from the City Hospital. The results obtained show that the success rate of the retrieval mechanism provides a good starting point for adaptation, the next phase in development for the CBR system. The developed automated CBR system will assist medical physicists in quickly generating treatment plans and can also serve as a teaching and training aid for junior, inexperienced medical physicists. In addition, the developed methods are generic in nature and can be adapted to be used in other CBR or intelligent decision support systems for other complex, real world, problem domains that highly depend on subjective and intuitive knowledge