Comprehensive proton dose algorithm using pencil beam redefinition and recursive dynamic splitting

Abstract

We compute, from first principles, the absolute dose or fluence distribution per incident proton charge in a known heterogeneous terrain exposed to known proton beams. The algorithm is equally amenable to scattered or scanned beams. All objects in the terrain (including collimators) are sliced into slabs, of any convenient thickness, perpendicular to the nominal beam direction. Transport is by standard Fermi-Eyges theory. Transverse heterogeneities are handled by breaking up pencil beams (PBs) either by conventional redefinition or a new form of 2D recursive dynamic splitting: the mother PB is replaced, conserving emittance and charge, by seven daughters of equal transverse size. One has 1/4 the charge and travels in the mother's direction and six have 1/8 the charge, are arranged hexagonally and radiate from the mother's virtual point source. The longitudinal (energy-like) variable is pv (proton momentum times speed). Each material encountered is treated on its own merits, not referenced to water. Slowing down is handled by $R=a(pv)^b$ fitted to standard range-energy tables. Multiple Coulomb scattering is handled by a scattering power $T_\mathrm{dM}$ acting as a proxy for Moliere theory. We present examples from a proof-of-principle Fortran program and speculate about putting the algorithm into practice.