The Study Of Mathematical Programming Problems In Intensity Modulated Radiation Therapy

Intensity-modulated radiation therapy technology has been considered as one of the main technical means in cancer treatment, because IMRT can guarantee killing cancer cells while protecting normal tissue from complications as much as possible. Inverse planning system is the core part of the whole IMRT software, which is mainly based on accurate mathematical modeling and fast solving methods. Where, fluence map optimization, map smoothing optimization, and two step integration optimization are research focuses currently. In solving these problems, we always adhere to create the mathematical models under the framework of convex programming, which avoids uncertainty and inaccuracy occurred in non-convex programming solving process and enables to integrate small-scale programming to large scale or enormous scale.We studied several key technical issues of the inverse planning system in intensity modulated radiation therapy, which included the following aspects.Firstly, fluence map optimization wants to inverse solve the ray intensity of each radiation field according to dose requirements from doctors. Fluence map optimization problems with dose-volume constraints as well as which based on equivalent uniform dose model are difficult to be solved. For the former, we pointed out the shortcomings of the traditional dose sorting technology, used the linear constrained quadratic programming model as a foundation, and gived the iterative solution strategy based on more scientific geometric distance sorting technique. For the latter, we changed the existing deficiencies of discrepancy in the traditional biological model and medical evaluation system, and gived the definition of equivalent uniform dose based on volume dose function as well as the corresponding mathematical model which can be transformed into a general dose-volume constraints fluence map optimization problem. The experiments of four opened clinical test cases showed that our method was able to obtain a higher degree of dose conformity while meeting the dose volume constraints.Secondly, ss the noise suppression could significantly reduce the total number of monitor units in intensity modulation, map smoothing optimization wants to reduce the map fluctuation. According to the five intractable issues from the traditional objective smoothing strategy, we proposed constrained smoothing strategy for the first time. The strategy could carry out intelligent smoothing and well linked the fluence map solving process and leaf sequence process. We created mathematical models for several typical unidirectional sweeping leaf sequencing patterns. Except for the partial synchronized/ strictly synchronized type, all other types have been successfully transformed into linear constrained quadratic programming models. The experimental results on two clinical testing cases showed that the new method can guarantee to use less total number of monitor units to achieve the radiotherapy under the same dose distribution.Thirdly, two step integration optimization hopes to reduce the gap between fluence map optimization and leaf sequencing optimization. For the reason that it was hard to solve the integration optimization model created by the traditional single-step style, we adopted the two-step integration strategy with feedback information to control the total number of monitor units and the total number of segments. With this idea, we have gived new integration optimization algorithms for two bidirectional sweeping leaf sequencing patterns. We tested the new algorithms and the total variation smoothing integration algorithms on two clinical testing cases respectively. The results showed that under the same condition of total number of monitor units and total number of segments, the new algorithm can produce better dose distribution.