324 - First Analytic Dose Calculation Algorithm for Proton Minibeam Radiotherapy

Purpose/Objective(s): Proton minibeam radiation therapy (pMBRT) offers superior normal tissue sparing compared to a conventional proton therapy due to its characteristic peak-and-valley dose distribution, achieved through a multislit collimator with submillimeter-sized slits. However, the complex lateral scattering and energy spectrum variability introduced by the collimator have hindered the development of analytic dose calculation algorithms, limiting the clinical translation of pMBRT. This study presents the first analytic algorithm for computing the dose influence matrix in pMBRT, facilitating its integration into inverse treatment planning.

Materials/Methods: The dose distribution was computed based on the Fermi-Eyges theory, which describes the phase-space evolution of monoenergetic protons as they propagate through a water phantom. By solving the transport equation with appropriate initial conditions and integrating over the angular spectrum, we obtained the relative dose distribution at various depths. The final dose deposition was determined by combining these results with Monte Carlo measured integral depth doses (IDDs). The initial conditions were categorized based on proton interactions with the collimator: (1) pristine protons, which traverse the slit without scattering, were modeled using truncated two-dimensional Gaussian functions; and (2) slit-scattered protons, which undergo energy loss and angular deviation due to interactions with the collimator, were characterized using Monte Carlo (MC) simulations and approximated by a combination of Gaussian and Lorentzian functions. The total dose was computed as a weighted sum of contributions from individual monoenergetic beam components.

Results: The proposed analytic algorithm was validated against MC simulation for a multislit collimator with 400-µm slit width and a 2.8-mm center-to-center (ctc) distance. Excellent agreement was observed across a broad energy range (56–142 MeV). The gamma passing rates for a 3%/0.4 mm gamma index exceeded 90% for all tested energies, demonstrating the algorithm’s accuracy as shown in the table.