  Single minibeams of protons, $^{4}$He, $^{12}$C and $^{16}$O in water were
modeled with Geant4, and their dose distributions were parameterized with
double-Gauss-Rutherford (DGR) functions. Dose distributions from arrays of 16
parallel minibeams centered on a rectangular or hexagonal grid were constructed
from the parameterized minibeam profiles to simulate the lateral convergence of
the minibeams resulting in a homogeneous dose field in the target tumor volume.
Peak-to-valley dose ratios (PVDR) and dose-volume histograms (DVH) were
calculated for the parameterized dose distributions and compared with those
obtained directly from Geant4 modeling of minibeam arrays. The similarity of
the results obtained by these two methods suggests that the fast calculation of
dose profiles of minibeam arrays based on the DGR parameterizations proposed
for the first time in this work can replace the time-consuming MC modeling in
future preclinical studies and also in the development of treatment planning
systems for minibeam therapy.
