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).

Purpose: To develop a Ray Cast/Dose Superposition (RC/DS) algorithm for proton grid therapy. Its functionality needed to include automatic positioning of small proton pencil beams in a grid-pattern and superimposing thin beam Monte Carlo (MC) dose distribution data on a Computer Tomography (CT) density volume. The purpose was to calculate and store un-weighted volumetric dose distributions of individual proton energies for subsequent optimization. Materials & Methods: Using the programming language Python 3.6, CT and Volume Of Interest (VOI) data of various patients and phantoms were imported. The target VOI was projected to either two or four planes, corresponding to the number of used gantry positions. Rays were then traced through the CT voxels, which were converted from Hounseld Units to density using a look up table, to calculate Water Equivalent Distance and proton energy needed to reach the proximal and distal edge of the target volume. With automated grid-pattern beam positioning, thin beam MC calculated depth dose distribution files were interpolated, scaled and superimposed on the CT volume for all beamlet positions. The algorithm reliability was tested on several CT image sets, the proton range estimation compared to a commercial TPS and the depth dose interpolation analyzed using MC simulations. Results: The RC/DS algorithm computation time was on average around 6 hours and 30 minutes for each CT set. The dose distribution output visually conformed to target locations and maintained a grid pattern for all tested CT sets. It gave unwanted dose artifacts in situations when rays outside the beamlet center passed a significant length of low/high density regions compared to the center, which yielded dose distributions of unlikely shape. Interpolating MC dose distribution values showed comparability to true MC references of same energy, yielding results with 0.5% difference in relative range and dose. Conclusions: The developed algorithm provides unweighted dose distributions specific for small beam proton grid therapy and has been shown to work for various setups and CT data. Un-optimized code caused longer computation times then intended but was presumed faster than MC simulations of the same setup. Efficiency and accuracy improvements are planed for in future work. / Proton grid therapy group