This paper considers the problem of radiation therapy treatment planning for cancer patients. During radiation therapy, beams of radiation pass through a patient. This radiation kills both cancerous and normal cells, so the radiation therapy must be carefully planned to deliver a clinically prescribed dose to certain targets while sparing nearby organs and tissues. Currently, a technique called intensity modulated radiation therapy (IMRT) is considered to be the most effective radiation therapy for many forms of cancer. In IMRT, the patient is irradiated from several different directions. From each direction, one or more irregularly shaped radiation beams of uniform intensity are used to deliver the treatment. This paper deals with the problem of designing a treatment plan for IMRT that determines an optimal set of such shapes (called apertures) and their corresponding intensities. This is in contrast with established two-stage approaches where, in the first phase, each radiation beam is viewed as consisting of a set of individual beamlets, each with its own intensity. A second phase is then needed to approximate and decompose the optimal intensity profile into a set of apertures with corresponding intensities. The problem is formulated as a large-scale convex programming problem, and a column generation approach to deal with its dimensionality is developed. The associated pricing problem determines, in each iteration, one or more apertures to be added to our problem. Several variants of this pricing problem are discussed, each corresponding to a particular set of constraints that the apertures must satisfy in one or more of the currently available types of commercial IMRT equipment. Polynomial-time algorithms are presented for solving each of these variants of the pricing problem to optimality. Finally, the effectiveness of our approach is demonstrated on clinical data.
We present a novel linear programming (LP) based approach for efficiently solving the intensity modulated radiation therapy (IMRT) fluence-map optimization (FMO) problem to global optimality. Our model overcomes the apparent limitations of a linear-programming approach by approximating any convex objective function by a piecewise linear convex function. This approach allows us to retain the flexibility offered by general convex objective functions, while allowing us to formulate the FMO problem as a LP problem. In addition, a novel type of partial-volume constraint that bounds the tail averages of the differential dose-volume histograms of structures is imposed while retaining linearity as an alternative approach to improve dose homogeneity in the target volumes, and to attempt to spare as many critical structures as possible. The goal of this work is to develop a very rapid global optimization approach that finds high quality dose distributions. Implementation of this model has demonstrated excellent results. We found globally optimal solutions for eight 7-beam head-and-neck cases in less than 3 min of computational time on a single processor personal computer without the use of partial-volume constraints. Adding such constraints increased the running times by a factor of 2-3, but improved the sparing of critical structures. All cases demonstrated excellent target coverage (> 95%), target homogeneity (< 10% overdosing and < 7% underdosing) and organ sparing using at least one of the two models.
We consider the problem of radiation therapy treatment planning for cancer patients. During radiation therapy, beams of radiation pass through a patient, killing both cancerous and normal cells. Thus, the radiation therapy must be carefully planned so that a clinically prescribed dose is delivered to targets containing cancerous cells, while nearby organs and tissues are spared. Currently, a technique called intensity-modulated radiation therapy (IMRT) is considered to be the most effective radiation therapy for many forms of cancer. In IMRT, the patient is irradiated from several beams, each of which is decomposed into hundreds of small beamlets, the intensities of which can be controlled individually. In this paper, we consider the problem of designing a treatment plan for IMRT when the orientations of the beams are given. We propose a new model that has the potential to achieve most of the goals with respect to the quality of a treatment plan that have been considered to date. However, in contrast with established mixed-integer and nonlinear programming formulations, we do so while retaining linearity of the optimization problem, which substantially improves the tractability of the optimization problem. Furthermore, we discuss how several additional quality and practical aspects of the problem that have been ignored to date can be incorporated into our linear model. We demonstrate the effectiveness of our approach on clinical data.
The Weapon Target Assignment (WTA) problem is a fundamental problem arising in defense-related applications of operations research. This problem consists of optimally assigning n weapons to m targets so that the total expected survival value of the targets after all the engagements is minimum. The WTA problem can be formulated as a nonlinear integer programming problem and is known to be NP-complete. There do not exist any exact methods for the WTA problem which can solve even small size problems (for example, with 20 weapons and 20 targets). Though several heuristic methods have been proposed to solve the WTA problem, due to the absence of exact methods, no estimates are available on the quality of solutions produced by such heuristics. In this paper, we suggest linear programming, integer programming, and network flow based lower bounding methods using which we obtain several branch and bound algorithms for the WTA problem. We also propose a network flow based construction heuristic and a very large-scale neighborhood (VLSN) search algorithm. We present computational results of our algorithms which indicate that we can solve moderately large size instances (up to 80 weapons and 80 targets) of the WTA problem optimally and obtain almost optimal solutions of fairly large instances (up to 200 weapons and 200 targets) within a few seconds.
Environmental and genetic causes are implicated in the etiopathogenesis of Parkinson's disease (PD), a neurodegenerative movement disorder. DJ-1, a putative gene recessively linked to early onset PD, functions as an antioxidant, transcriptional co-activator, and molecular chaperone. We examined DJ-1 status following global perturbation of protein thiol homeostasis by depleting cellular antioxidant glutathione or downregulating glutaredoxin 1, a thiol disulfide oxidoreductase, wherein both paradigms generate oxidative stress. While these perturbations did not affect expression of DJ-1 mRNA, downregulation of glutaredoxin 1 but not glutathione depletion caused loss of DJ-1 protein, translocation of Daxx (a death-associated protein) from nucleus, and cell death. Overexpression of wild-type DJ-1, but not the cysteine mutants, prevented Daxx translocation and cytotoxicity. Protease inhibitors prevented constitutive DJ-1 loss. Residual DJ-1 was present in reduced state, indicating that DJ-1 when oxidized was degraded through proteolysis. Thus, loss of DJ-1 occurring through its oxidative modification and subsequent proteolysis mediated through dysregulation of thiol disulfide oxidoreductase may contribute to pathogenesis of sporadic PD, thus providing a link between environmental challenges and constitutive levels of this vital protein.
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