Spatial Frequency-Based Objective Function for Optimization of Dose Heterogeneity in Grid Therapy
Abstract: In this project we introduced a spatial frequency-based objective function for optimization of dose distributions used in spatially fractionated radiotherapy (also known as grid therapy). Several studies indicate that tissues can tolerate larger mean doses of radiation if the dose is delivered heterogeneously or to a partial volume of the organ. The objective function rewards heterogeneous dose distributions in the collaterally irradiated healthy tissues and is based on the concept of a maximum stem-cell migration distance. The stem-cell depletion hypothesis stipulates that damaged tissues can be repopulated by nearby surviving stem-cells within a critical volume outlined by the maximum migration distance. Proton grid therapy dose distributions were calculated to study the viability of our spatial frequency-based objective function. These were computed analytically with a proton pencil beam dose kernel. A multi-slit collimator placed flush against the surface of a water phantom defined the entrance fluence. The collimator geometry was described by two free parameters: the slit width and the number of slits within a specified field width. Organs at risk (OARs) and a planning target volume (PTV) were defined. Two dose constraints were set on the PTV and objective function values were computed for the OARs. The objective function measures the high-frequency content of a masked dose distribution, where the distinction between low- and high frequencies was made based on a characteristic distance. Out of the feasible solutions, the irradiation geometry that produced the maximum objective function value was selected as the optimal solution. With the spatial frequency-based objective function we were able to find, by brute-force search, unique optimal solutions to the constrained optimization problem. The optimal solutions were found on the boundary of the solution space. The objective function can be applied directly to arbitrarily shaped regions of interest and to dose distributions produced by multiple field angles. The next step is to implement the objective function in an optimization environment of a commercial treatment planning system (TPS).
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