  This work addresses computing techniques for dose calculations in treatment
planning with proton and ion beams, based on an efficient kernel-convolution
method referred to as grid-dose spreading (GDS) and accurate
heterogeneity-correction method referred to as Gaussian beam splitting. The
original GDS algorithm suffered from distortion of dose distribution for beams
tilted with respect to the dose-grid axes. Use of intermediate grids normal to
the beam field has solved the beam-tilting distortion. Interplay of arrangement
between beams and grids was found as another intrinsic source of artifact.
Inclusion of rectangular-kernel convolution in beam transport, to share the
beam contribution among the nearest grids in a regulatory manner, has solved
the interplay problem. This algorithmic framework was applied to a tilted
proton pencil beam and a broad carbon-ion beam. In these cases, while the
elementary pencil beams individually split into several tens, the calculation
time increased only by several times with the GDS algorithm. The GDS and
beam-splitting methods will complementarily enable accurate and efficient dose
calculations for radiotherapy with protons and ions.
