Dionne M. Aleman

Neighborhood search approaches to beam orientation optimization in intensity modulated radiation therapy treatment planning

The intensity modulated radiation therapy (IMRT) treatment planning problem consists of several subproblems which are typically solved sequentially. We seek to combine two of the subproblems: the beam orientation optimization (BOO) problem and the fluence map optimization (FMO) problem. The BOO problem is the problem of selecting the beam orientations to deliver radiation to the patient. The FMO problem is the problem of determining the amount of radiation intensity, or fluence, of each beamlet in each beam. The solution to the FMO problem measures the quality of a beam set, but the majority of previous BOO studies rely on heuristics and approximations to gauge the quality of the beam set. In contrast with these studies, we use an exact measure of the treatment plan quality attainable using a given beam set, which ensures convergence to a global optimum in the case of our simulated annealing algorithm and a local optimum in the case of our local search algorithm. We have also developed a new neighborhood structure that allows for faster convergence using our simulated annealing and local search algorithms, thus reducing the amount of time required to obtain a good solution. Finally, we show empirically that we can generate clinically acceptable treatment plans that require fewer beams than in current practice. This may reduce the length of treatment time, which is an important clinical consideration in IMRT.

A Response Surface Approach to Beam Orientation Optimization in Intensity-Modulated Radiation Therapy Treatment Planning

We view the beam orientation optimization (BOO) problem in intensity-modulated radiation therapy (IMRT) treatment planning as a global optimization problem with expensive objective function evaluations. We propose a response surface method that, in contrast with other approaches, allows for the generation of problem data only for promising beam orientations as the algorithm progresses. This enables the consideration of additional degrees of freedom in the treatment delivery, i.e., many more candidate beam orientations than is possible with existing approaches to BOO. This ability allows us to include noncoplanar beams and consider the question of whether or not noncoplanar beams can provide significant improvement in treatment plan quality. We also show empirically that using our approach, we can generate clinically acceptable treatment plans that require fewer beams than are used in current practice.

Comparative analysis of 60Co intensity-modulated radiation therapy

In this study, we perform a scientific comparative analysis of using (60)Co beams in intensity-modulated radiation therapy (IMRT). In particular, we evaluate the treatment plan quality obtained with (i) 6 MV, 18 MV and (60)Co IMRT; (ii) different numbers of static multileaf collimator (MLC) delivered (60)Co beams and (iii) a helical tomotherapy (60)Co beam geometry. We employ a convex fluence map optimization (FMO) model, which allows for the comparison of plan quality between different beam energies and configurations for a given case. A total of 25 clinical patient cases that each contain volumetric CT studies, primary and secondary delineated targets, and contoured structures were studied: 5 head-and-neck (H&N), 5 prostate, 5 central nervous system (CNS), 5 breast and 5 lung cases. The DICOM plan data were anonymized and exported to the University of Florida optimized radiation therapy (UFORT) treatment planning system. The FMO problem was solved for each case for 5-71 equidistant beams as well as a helical geometry for H&N, prostate, CNS and lung cases, and for 3-7 equidistant beams in the upper hemisphere for breast cases, all with 6 MV, 18 MV and (60)Co dose models. In all cases, 95% of the target volumes received at least the prescribed dose with clinical sparing criteria for critical organs being met for all structures that were not wholly or partially contained within the target volume. Improvements in critical organ sparing were found with an increasing number of equidistant (60)Co beams, yet were marginal above 9 beams for H&N, prostate, CNS and lung. Breast cases produced similar plans for 3-7 beams. A helical (60)Co beam geometry achieved similar plan quality as static plans with 11 equidistant (60)Co beams. Furthermore, 18 MV plans were initially found not to provide the same target coverage as 6 MV and (60)Co plans; however, adjusting the trade-offs in the optimization model allowed equivalent target coverage for 18 MV. For plans with comparable target coverage, critical structure sparing was best achieved with 6 MV beams followed closely by (60)Co beams, with 18 MV beams requiring significantly increased dose to critical structures. In this paper, we report in detail on a representative set of results from these experiments. The results of the investigation demonstrate the potential for IMRT radiotherapy employing commercially available (60)Co sources and a double-focused MLC. Increasing the number of equidistant beams beyond 9 was not observed to significantly improve target coverage or critical organ sparing and static plans were found to produce comparable plans to those obtained using a helical tomotherapy treatment delivery when optimized using the same well-tuned convex FMO model. While previous studies have shown that 18 MV plans are equivalent to 6 MV for prostate IMRT, we found that the 18 MV beams actually required more fluence to provide similar quality target coverage.

A derandomized approximation algorithm for the critical node detection problem

In this paper we propose an efficient approximation algorithm for determining solutions to the critical node detection problem (CNDP) on unweighted and undirected graphs. Given a user-defined number of vertices k>0, the problem is to determine which k nodes to remove such as to minimize pairwise connectivity in the induced subgraph. We present a simple, yet powerful, algorithm that is derived from a randomized rounding of the relaxed linear programming solution to the CNDP. We prove that the expected solution quality obtained by the linear-time algorithm is bounded by a constant. To highlight the algorithm quality four common complex network models are utilized, in addition to four real-world networks.

Evaluation of strategies to mitigate contagion spread using social network characteristics

Abstract Computer simulation is an effective tool for assessing mitigation strategies, with recent trends concentrating on agent-based techniques. These methods require high computational efforts in order to simulate enough scenarios for statistical significance. The population individuals and their contacts determined by agent-based simulations form a social network. For some network structures it is possible to gain high accuracy estimates of contagion spread based on the connection structure of the network, an idea that is utilized in this work. A representative social network constructed from the 2006 census of the Greater Toronto Area (Ontario, Canada) of 5 million individuals in 1.8 million households is used to demonstrate the efficacy of our approach. We examine the effects of six mitigation strategies with respect to their ability to contain disease spread as indicated by pre- and post-vaccination reproduction numbers, mean local clustering coefficients and degree distributions. One outcome of the analysis provides evidence supporting the design of mitigation strategies that aim to fragment the population into similarly sized components. While our analysis is framed in the context of pandemic disease spread, the approach is applicable to any contagion such as computer viruses, rumours, social trends, and so on.

Neighborhood search approaches to non-coplanar beam orientation optimization for total marrow irradiation using IMRT

We consider the beam orientation optimization (BOO) problem for total marrow irradiation (TMI) treatment planning using intensity modulated radiation therapy (IMRT). Currently, IMRT is not widely used in TMI treatment delivery; furthermore, the effect of using non-coplanar beam orientations is not known. We propose and implement several variations of a single neighborhood search algorithm that solves the BOO problem effectively when gantry angles and couch translations are considered. Our work shows that the BOO problem for TMI cases can be solved in a clinically acceptable amount of time and leads to treatment plans that are more effective than the conventional approach to TMI.

A Nonhomogeneous Agent-Based Simulation Approach to Modeling the Spread of Disease in a Pandemic Outbreak

To effectively prepare for a pandemic disease outbreak, knowledge of how the disease will spread is paramount. The global outbreak of severe acute respiratory syndrome (SARS) in 2002--2003 highlighted the need for such data. This need is also apparent in preparing for and responding to all disease outbreaks, from pandemic influenza to avian flu. Many previous studies of disease make simplistic assumptions about transmission and infection rates and assume that each member of the population is identical or homogeneous. We propose an agent-based simulation model that treats each individual as unique, with nonhomogeneous transmission and infection rates correlated to demographic information and behavior. The results of the model are output to geographic information system software to provide a map of the estimated disease spread area, which can be used as a policy-making tool for determining a suitable mitigation strategy. The Ontario Agency for Health Protection and Promotion (OAHPP) uses the model for pandemic planning for the Greater Toronto area in Ontario, Canada.

An Interior Point Constraint Generation Algorithm for Semi-Infinite Optimization with Health-Care Application

We propose an interior point constraint generation (IPCG) algorithm for semi-infinite linear optimization (SILO) and prove that the algorithm converges to an e-solution of SILO after a finite number of constraints is generated. We derive a complexity bound on the number of Newton steps needed to approach the updated μ-center after adding multiple violated constraints and a complexity bound on the total number of constraints that is required for the overall algorithm to converge. We implement our algorithm to solve the sector duration optimization problem arising in Leksell Gamma Knife® Perfexion™ (Elekta, Stockholm Sweden) treatment planning, a highly specialized treatment for brain tumors. Using real patient data provided by the Department of Radiation Oncology at Princess Margaret Hospital in Toronto, Ontario, Canada, we show that our algorithm can efficiently handle problems in real-life health-care applications by providing a quality treatment plan in a timely manner. Comparing our computational results with MOSEK, a commercial software package, we show that the IPCG algorithm outperforms the classical primal-dual interior point methods on sector duration optimization problem arising in Perfexion™ treatment planning. We also compare our results with that of a projected gradient method. In both cases we show that IPCG algorithm obtains a more accurate solution substantially faster.

Interior point algorithms: guaranteed optimality for fluence map optimization in IMRT

One of the most widely studied problems of the intensity-modulated radiation therapy (IMRT) treatment planning problem is the fluence map optimization (FMO) problem, the problem of determining the amount of radiation intensity, or fluence, of each beamlet in each beam. For a given set of beams, the fluences of the beamlets can drastically affect the quality of the treatment plan, and thus it is critical to obtain good fluence maps for radiation delivery. Although several approaches have been shown to yield good solutions to the FMO problem, these solutions are not guaranteed to be optimal. This shortcoming can be attributed to either optimization model complexity or properties of the algorithms used to solve the optimization model. We present a convex FMO formulation and an interior point algorithm that yields an optimal treatment plan in seconds, making it a viable option for clinical applications.

Network robustness versus multi-strategy sequential attack

We examine the robustness of networks under attack when the attacker sequentially selects from a number of different attack strategies, each of which removes one node from the network. Network robustness refers to the ability of a network to maintain functionality under attack, and the problem-dependent context implies a number of robustness measures exist. Thus, we analyze four measures: (1) entropy, (2) efficiency, (3) size of largest network component, and suggest to also utilize (4) pairwise connectivity. Six network centrality measures form the set of strategies at the disposal of the attacker. Our study examines the utility of greedy strategy selection versus random strategy selection for each attack, whereas previous studies focused on greedy selection but limited to only one attack strategy. Using a set of common complex network benchmark networks, in addition to real-world networks, we find that randomly selecting an attack strategy often performs well when the attack strategies are of high quality. We also examine defense against the attacks by adding k edges after each node attack and find that the greedy strategy is most useful in this context. We also observed that a betweenness-based attack often outperforms both random and greedy strategy selection, the latter often becoming trapped in local optima.