Monte Carlo simulation of single-plane magnetically focused narrow proton beams

We present Monte Carlo simulations of magnetically focused proton beams shaped by a single quadrapole magnet. Such beams are narrowly focused in one longitudinal plane but fan out in the perpendicular plane producing elongated elliptical beam spots (a 'screwdriver' shape). The focused beams were compared to passively collimated beams (the current standard of delivery for small radiosurgery beams). Beam energies considered were relevant to functional radiosurgery and standard radiosurgery clinical applications. Three monoenergetic beams (100, 125, and 150 MeV) and a modulated beam were simulated. Monoenergetic magnetically focused beams demonstrated 28 to 32% lower entrance doses, 31 to 47% larger central peak to entrance depth dose ratios, 26 to 35% smaller integral dose, 25 to 32% smaller estimated therapeutic ratios, 19 to 37% smaller penumbra volumes, and 38 to 65% smaller vertical profile lateral penumbras at Bragg depth, compared to the collimated beams. Focused modulated beams showed 31% larger central peak to entrance dose ratio, and 62 to 65% smaller vertical lateral penumbras over the plateau of the spread out Bragg peak. These advantages can be attributed to the directional acceleration of protons in the transverse plane due to the magnetic field. Such beams can be produced using commercially available assemblies of permanent rare earth magnets that do not require electric power or cryrogenic cooling. Our simulations suggest that these magnets can be inexpensively incorporated into the beam line to deliver reduced dose to normal tissue, and enhanced dose to elongated elliptical targets with major and minor axes on the order of a few centimeters and millimeters, respectively. Such beams may find application in novel proton functional and standard radiosurgery treatments in and around critical structures.