References
- Parodi K, Mairani A, Sommerer F. Monte Carlo-based parametrization of the lateral dose spread for clinical treatment planning of scanned proton and carbon ion beams. J Radiat Res. 2013;54:91–96.
- Bellinzona EV, Ciocca M, Embriaco A, et al. A model for the accurate computation of the lateral scattering of protons in water. Phys Med Biol. 2016;61:N102–N117.
- Sawakuchi GO, Zhu XR, Poenisch F, et al. Experimental characterization of the low-dose envelope of spot scanning proton beams. Phys Med Biol. 2010;55:3467–3478.
- Schwaab J, Brons S, Fieres J, et al. Experimental characterization of lateral profiles of scanned proton and carbon ion pencil beams for improved beam models in ion therapy treatment planning. Phys Med Biol. 2011;56:7813–7827.
- Sawakuchi GO, Titt U, Mirkovic D, et al. Monte Carlo investigation of the low-dose envelope from scanned proton pencil beams. Phys Med Biol. 2010;55:711–721.
- Kusano Y, Kanai T, Yonai S, et al. Field-size dependence of doses of therapeutic carbon beams. Med Phys. 2007;34:4016–4022.
- Li Y, Zhu RX, Sahoo N, et al. Beyond Gaussians: a study of single-spot modeling for scanning proton dose calculation. Phys Med Biol. 2012;57:983–997.
- Zhang H, Dai Z, Liu X, et al. A novel pencil beam model for carbon-ion dose calculation derived from Monte Carlo simulations. Phys Medica. 2018;55:15–24.
- Hirayama S, Takayanagi T, Fujii Y, et al. Evaluation of the influence of double and triple Gaussian proton kernel models on accuracy of dose calculations for spot scanning technique. Med Phys. 2016;43:1437–1450.
- Tommasino F, Fellin F, Lorentini S, et al. Impact of dose engine algorithm in pencil beam scanning proton therapy for breast cancer. Phys Medica. 2018;50:7–12.
- Jan S, Santin G, Strul D, et al. GATE: a simulation toolkit for PET and SPECT. Phys Med Biol. 2004;49:4543.
- Yuanlin Y, Xingguo L, Tingyan F, et al. Monte Carlo simulation study on optimizing the active beam delivery system at HIRFL. Nucl Phys Rev. 2016;33:105–111.
- Lomax A. Intensity modulation methods for proton radiotherapy. Phys Med Biol. 1999;44:185–205.
- Bethe HA. Moliere’s theory of multiple scattering. Phys Rev. 1953;89:1256–1266.
- Highland VL. Some practical remarks on multiple scattering. Nucl Instruments Methods. 1975;129:497–499.