Investigation of Freedom-Degrees impact on Modulation of Radiation

Introduction: Nowadays tendency to apply more degrees of freedom in high-tech radiotherapy systems, and consequent complex process to optimize dose calculation and delivery algorithms, is a challenge of radiation therapy optimization. Faster MLC speed, dose rate, Gantry angle variation, and other degrees, which have been utilized in IMRT, IMAT, VMAT, improved modulation of intensity radiation that resulted in better quality in treatment plans. In this study, we modeled a pair of multi leaf collimators(MLC) to investigate ideal dynamical features such as speed and acceleration of MLC mathematically. Then we estimate an equation of MLC's motion in dynamical sliding window algorithm to investigate impact of some factors such as initial position of MLC, speeding up MLC, delivery time and variable dose rate on optimizing dose delivery algorithms. Materials and Methods: Seven intensity maps extracted from a prostate RT plan. MATLAB environment (R2017a version) was selected to define and solve optimization problem. In one dimension a pair of MLC modeled to reach out a row of intensity matrix diagram. Because of nonconcave nature of problem, gradient descent algorithm utilized and many criteria such as different start and end point of movement of MLC, direction of MLC, time delivery and dose rate subjected to optimization process. Results: Intensity map, velocity, acceleration, and output errors were plotted. However, the increase in the time can lead to a decrease in the error value - from 91% to an optimum of 2%; the error value did not reduce by increasing over optimum time significantly. Also increasing the speed of MLCs results in a significant reduction in relative error, although the assumption of the ability to reach out the infinite velocity does not lead to a reduction in relative error rate, and the optimization process was stopped. Conclusion: Although unidirectional movement in sliding window algorithm demonstrates as a suboptimal method, in volumetric methods bidirectional movement could have been optimal. Although that seems to get better outcome by speeding up MLC, it’s not as a rule routinely and infinite speed have been result in stopping optimization prematurely. In higher speed, we don’t see the linear relationship mathematically and over speeding up may lead to more anarchy in MLC movements reality. Not only increasing time delivery dose after a certain limit did not cause to significant decrease in optimization error, but also it may lead to other errors, and trade of between time and quality should be recognized. Variable dose rate can save more photons which sacrificed in modulation with tungsten blocks.