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Inverse planning problems applied to radiation therapy treatments are of interest for both the academic and applied points of view. From the development and improvement of mathematical models to the design of innovative resolution algorithms capable of dealing with large scale mathematical problems, this area of research is an almost inexhaustible source of scientific challenges. From the applied point of view, inverse planning methodologies can help the daily work of radiation therapy treatment planners, increasing the quality of treatment delivered to patients. The increased capabilities of the present physical devices allow the delivery of treatments that are more effective and that have fewer side effects. Nevertheless, their increased complexity makes the planning task harder, and the trial and error procedures do not guarantee the best possible treatment. These problems are interdisciplinary by nature and require the collaboration of computer science and operations research specialists with medical physicists.
In this project we intend to focus our attention in the resolution of the BAO problem. This problem is important due to two main reasons. First, the choice of adequate directions may be decisive for the quality of the treatment. Second, changing beam directions during treatment is time consuming, and short treatments are desirable because the probability of the patient altering his position on the couch increases with the duration of the treatment. It is a challenging global non-convex optimization problem with many local minima yet to be solved satisfactorily. Not only good quality solutions have to be found, but also they have to be found within a reasonable time window (due to clinical practice requirements).
Our objective is to introduce new approaches for the resolution of the BAO problem, using direct search methods and evolutionary algorithms. We also intend to investigate the use of non-coplanar beam directions and to determine the minimum number of incidence directions to be used.
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The formulation of the BAO problem as a continuous non-convex optimization instead of the traditional combinatorial optimization problem is a natural formulation since BAO problem is in fact continuous. The common choice of using a combinatorial optimization formulation problem is mainly caused by the non-use of appropriate methods to address the non-convex nonlinear formulation, namely methods that require few function evaluations, and that are suited to address problems with many local minima. Among direct search methods we intend to develop strategies based on pattern search methods tailored for the BAO problem. Pattern search methods are a suitable approach due to their structure, organized around two phases at each and every iteration, one where convergence to a local minima is assured (poll), and other (search), where flexibility is given to the method since any strategy can be applied as long as only a finite number of points is tested. This allows the insertion of previously used and tested strategies/heuristics that successfully address the BAO problem and enhance a global search by influencing the quality of the local minimizer or stationary point found by the method. Pattern search methods have the ability to avoid being trapped by the closest local minima of the starting iterate, and find a local minimum in a lowest region. Preliminary tests were conducted on the basis of retrospective treated cases of head and neck tumors. We have shown that, for head and neck cases, a beam angle set can be locally improved in a continuous manner using pattern search methods. Moreover, it was shown that high-quality coplanar beam directions can be obtained and compete with equispaced beam directions within a clinically acceptable time frame. We have to highlight, as well, the low number of function evaluations required to obtain locally optimal solutions. The number of times the function value has to be computed is of the utmost importance, particularly when the BAO problem is modeled using the optimal values of the FMO problem. The results obtained are very encouraging and reinforce our belief that pursuing this line of research can produce effective improvements on the quality of this type of oncologic treatments.
Optimization problems involving a huge search space are good candidates to be solved by an Evolutionary Algorithm. Even if we know, since the No Free Lunch (NFL) theorem, that there is no best algorithmic problem solver, that does not mean that we cannot have a good solution for a particular class of problems. In the case of the BAO problem we will need to develop and test an EA tuned for that problem. To that end, we will use a representation that takes into account that we have to deal with a continuous domain. Second, special variations operators will be tested that will incorporate knowledge about the problem. Both the representation and the operators will foster evolvability. This is important because, due to time constraints, we will need to reduce the number of generations that the EA will use to evolve a good solution. Third, the variation operators must be such as to maintain a high diversity in the population, to avoid premature convergence. Fourth, we will introduce a memory mechanism, so the algorithm can react quickly every time a similar situation to one already solved in the past appears. It is also worth mentioning that relying on an individual representation with variable length, we can also test the ability of our algorithm to come up with a solution that minimizes the number of beams.
The far most important objective of this research is to provide means for the quality improvement of treatments delivered to patients.Summarizing, we can say that our main objective is to develop computer-aided algorithms that will improve/complement the existing commercial inverse planning software and are able to help medical physicists to build better treatment plans, with an improvement in the quality of treatments delivered to patients.
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