Beyond Gaussians: a study of single-spot modeling for scanning proton dose calculation

Active spot scanning proton therapy is becoming increasingly adopted by proton therapy centers worldwide. Unlike passive-scattering proton therapy, active spot scanning proton therapy, especially intensity-modulated proton therapy, requires proper modeling of each scanning spot to ensure accurate computation of the total dose distribution contributed from a large number of spots. During commissioning of the spot scanning gantry at the Proton Therapy Center in Houston, it was observed that the long-range scattering protons in a medium may have been inadequately modeled for high-energy beams by a commercial treatment planning system, which could lead to incorrect prediction of field size effects on dose output. In this study, we developed a pencil beam algorithm for scanning proton dose calculation by focusing on properly modeling individual scanning spots. All modeling parameters required by the pencil beam algorithm can be generated based solely on a few sets of measured data. We demonstrated that low-dose halos in single-spot profiles in the medium could be adequately modeled with the addition of a modified Cauchy-Lorentz distribution function to a double-Gaussian function. The field size effects were accurately computed at all depths and field sizes for all energies, and good dose accuracy was also achieved for patient dose verification. The implementation of the proposed pencil beam algorithm also enabled us to study the importance of different modeling components and parameters at various beam energies. The results of this study may be helpful in improving dose calculation accuracy and simplifying beam commissioning and treatment planning processes for spot scanning proton therapy.