Optimization Problems in Radiation Therapy Treatment Planning.

Radiation therapy is one of the most common methods used to treat many types of cancer. External beam radiation therapy and the models associated with developing a treatment plan for a patient are studied. External beams of radiation are used to deliver a highly complex so-called dose distribution to a patient that is designed to kill the cancer cells while sparing healthy organs and normal tissue. Treatment planning models and optimization are used to determine the delivery machine instructions necessary to produce a desirable dose distribution. These instructions make up a treatment plan. This thesis studies four problems in radiation therapy treatment plan optimization. First, treatment planners generate a plan with a number of competing treatment plan criteria. The relationship between criteria is not known a priori. A methodology is developed for physicians and treatment planners to efficiently navigate a clinically relevant region of the Pareto frontier generated by trading off these different criteria in an informed way. Second, the machine instructions for intensity modulated radiation therapy, a common treatment modality, consist of the locations of the external beams and the non-uniform intensity profiles delivered from each of these locations. These decisions are traditionally made with separate, sequential models. These decisions are integrated into a single model and propose a heuristic solution methodology. Third, volumetric modulated arc therapy (VMAT), a treatment modality where the beam travels in a coplanar arc around the patient while continuously delivering radiation, is a popular topic among optimizers studying treatment planning due to the difficult nature of the problem and the lack of a universally accepted treatment planning method. While current solution methodologies assume a predetermined coplanar path around the patient, that assumption is relaxed and the generation of a non-coplanar path is integrated into a VMAT planning algorithm. Fourth, not all patient information is available when developing a treatment plan pre-treatment. Some information, like a patient's sensitivity to radiation, can be realized during treatment through physiological tests. Methodologies of pre-treatment planning considering adaptation to new information are studied.PhDIndustrial and Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113366/1/troylong_1.pd

AGENT-BASED DISCRETE EVENT SIMULATION MODELING AND EVOLUTIONARY REAL-TIME DECISION MAKING FOR LARGE-SCALE SYSTEMS

Computer simulations are routines programmed to imitate detailed system operations. They are utilized to evaluate system performance and/or predict future behaviors under certain settings. In complex cases where system operations cannot be formulated explicitly by analytical models, simulations become the dominant mode of analysis as they can model systems without relying on unrealistic or limiting assumptions and represent actual systems more faithfully. Two main streams exist in current simulation research and practice: discrete event simulation and agent-based simulation. This dissertation facilitates the marriage of the two. By integrating the agent-based modeling concepts into the discrete event simulation framework, we can take advantage of and eliminate the disadvantages of both methods.Although simulation can represent complex systems realistically, it is a descriptive tool without the capability of making decisions. However, it can be complemented by incorporating optimization routines. The most challenging problem is that large-scale simulation models normally take a considerable amount of computer time to execute so that the number of solution evaluations needed by most optimization algorithms is not feasible within a reasonable time frame. This research develops a highly efficient evolutionary simulation-based decision making procedure which can be applied in real-time management situations. It basically divides the entire process time horizon into a series of small time intervals and operates simulation optimization algorithms for those small intervals separately and iteratively. This method improves computational tractability by decomposing long simulation runs; it also enhances system dynamics by incorporating changing information/data as the event unfolds. With respect to simulation optimization, this procedure solves efficient analytical models which can approximate the simulation and guide the search procedure to approach near optimality quickly.The methods of agent-based discrete event simulation modeling and evolutionary simulation-based decision making developed in this dissertation are implemented to solve a set of disaster response planning problems. This research also investigates a unique approach to validating low-probability, high-impact simulation systems based on a concrete example problem. The experimental results demonstrate the feasibility and effectiveness of our model compared to other existing systems

Multi-objective optimization techniques in electricity generation planning

The objective of this research is to develop a framework of multi-objective optimization (MOO) models that are better capable of providing decision support on future long-term electricity generation planning (EGP), in the context of insufficient electricity capacity and to apply it to the electricity system for a developing country. The problem that motivated this study was a lack of EGP models in developing countries to keep pace with the countries' socio-economic and demographic dynamics. This research focused on two approaches: mathematical programming (MP) and system dynamics (SD). Detailed model descriptions, formulations, and implementation results are presented in the thesis along with the observations and insights obtained during the course of this research

Advancing multiple model-based control of complex biological systems: Applications in T cell biology

Activated CD4+ T cells are important regulators of the adaptive immune response against invading pathogens and cancerous host cells. The process of activation is mediated by the T cell receptor and a vast network of intracellular signal transduction pathways, which recognize and interpret antigenic signals to determine the cell\u27s response. The critical role of these early signaling events in normal cell function and the pathogenesis of disease ultimately make them attractive therapeutic targets for numerous autoimmune diseases and cancers. Scientists increasingly rely on predictive mathematical models and control-theoretic tools to design effective strategies to manipulate cellular processes for the advancement of knowledge or therapeutic gain. However, the application of modern control theory to intracellular signal transduction is complicated by a unique set of intrinsic properties and technical limitations. These include complexities in the signaling network such as crosstalk, feedback and nonlinearity, and a dearth of rapid quantitative measurement techniques and specific and orthogonal modulators, the major consequences of which are uncertainty in the model representation and the prevention of real-time measurement feedback. Integrating such uncertainties and limitations into a control-theoretic approach under practical constraints represents an open challenge in controller design. The work presented in this dissertation addresses these challenges through the development of a computational methodology to aid in the design of experimental strategies to predictably manipulate intracellular signaling during the process of CD4+ T cell activation. This work achieves two main objectives: (1) the development of a generalized control-theoretic tool to effectively control uncertain nonlinear systems in the absence of real-time measurement feedback, and (2) the development and calibration of a predictive mathematical model (or collection of models) of CD4+ T cell activation to help derive experimental inputs to robustly force the system dynamics along prescribed trajectories. The crux of this strategy is the use of multiple data-supported models to inform the controller design. These models may represent alternative hypotheses for signaling mechanisms and give rise to distinct network topologies or kinetic rate scenarios and yet remain consistent with available data. Here, a novel adaptive weighting algorithm predicts variations in the models\u27 predictive accuracy over the admissible input space to produce a more reliable compromise solution from multiple competing objectives, a result corroborated by several experimental studies. This dissertation provides a practical means to effectively utilize the collective predictive capacity of multiple prediction models to predictably and robustly direct CD4 + T cells to exhibit regulatory, helper and anergic T cell-like signaling profiles through pharmacological manipulations in the absence of measurement feedback. The framework and procedures developed herein are expected to widely applicable to a more general class of continuous dynamical systems for which real-time feedback is not readily available. Furthermore, the ability to predictably and precisely control biological systems could greatly advance how we study and interrogate such systems and aid in the development of novel therapeutic designs for the treatment of disease

Optimising water quality outcomes for complex water resource systems and water grids

As the world progresses, water resources are likely to be subjected to much greater pressures than in the past. Even though the principal water problem revolves around inadequate and uncertain water supplies, water quality management plays an equally important role. Availability of good quality water is paramount to sustainability of human population as well as the environment. Achieving water quality and quantity objectives can be conflicting and becomes more complicated with challenges like, climate change, growing populations and changed land uses. Managing adequate water quality in a reservoir gets complicated by multiple inflows with different water quality levels often resulting in poor water quality. Hence, it is fundamental to approach this issue in a more systematic, comprehensive, and coordinated fashion. Most previous studies related to water resources management focused on water quantity and considered water quality separately. However, this research study focused on considering water quantity and quality objectives simultaneously in a single model to explore and understand the relationship between them in a reservoir system. A case study area was identified in Western Victoria, Australia with water quantity and quality challenges. Taylors Lake of Grampians System in Victoria, Australia receives water from multiple sources of differing quality and quantity and has the abovesaid problems. A combined simulation and optimisation approach was adopted to carry out the analysis. A multi-objective optimisation approach was applied to achieve optimal water availability and quality in the storage. The multi-objective optimisation model included three objective functions which were: water volume and two water quality parameters: salinity and turbidity. Results showed competing nature of water quantity and quality objectives and established the trade-offs. It further showed that it was possible to generate a range of optimal solutions to effectively manage those trade-offs. The trade-off analysis explored and informed that selective harvesting of inflows is effective to improve water quality in storage. However, with strict water quality restriction there is a considerable loss in water volume. The robustness of the optimisation approach used in this study was confirmed through sensitivity and uncertainty analysis. The research work also incorporated various spatio-temporal scenario analyses to systematically articulate long-term and short-term operational planning strategies. Operational decisions around possible harvesting regimes while achieving optimal water quantity and quality and meeting all water demands were established. The climate change analysis revealed that optimal management of water quantity and quality in storage became extremely challenging under future climate projections. The high reduction in storage volume in the future will lead to several challenges such as water supply shortfall and inability to undertake selective harvesting due to reduced water quality levels. In this context, selective harvesting of inflows based on water quality will no longer be an option to manage water quantity and quality optimally in storage. Some significant conclusions of this research work included the establishment of trade-offs between water quality and quantity objectives particular to this configuration of water supply system. The work demonstrated that selective harvesting of inflows will improve the stored water quality, and this finding along with the approach used is a significant contribution to decision makers working within the water sector. The simulation-optimisation approach is very effective in providing a range of optimal solutions, which can be used to make more informed decisions around achieving optimal water quality and quantity in storage. It was further demonstrated that there are range of planning periods, both long-term (>10 years) and short-term (<1 year), all of which offer distinct advantages and provides useful insights, making this an additional key contribution of the work. Importantly, climate change was also considered where it was found that diminishing water resources, particularly to this geographic location, makes it increasingly difficult to optimise both quality and quantity in storage providing further useful insights from this work.Doctor of Philosoph

Quality Representation in Multiobjective Programming

In recent years, emphasis has been placed on generating quality representations of the nondominated set of multiobjective programming problems. This manuscript presents two methods for generating discrete representations with equidistant points for multiobjective programs with solution sets determined by convex cones. The Bilevel Controlled Spacing (BCS) method has a bilevel structure with the lower-level generating the nondominated points and the upper-level controlling the spacing. The Constraint Controlled Spacing (CCS) method is based on the epsilon-constraint method with an additional constraint to control the spacing of generated points. Both methods (under certain assumptions) are proven to produce (weakly) nondominated points. Along the way, several interesting results about obtuse, simplicial cones are also proved. Both the BCS and CCS methods are tested and show promise on a variety of problems: linear, convex, nonconvex (CCS only), two-dimensional, and three-dimensional. Sample Matlab code for two of these examples can be found in the appendices as well as tables containing the generated solution points. The manuscript closes with conclusions and ideas for further research in this field