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

Abstract

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 the present 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.

Commissioning dose computation models for spot scanning proton beams in water for a commercially available treatment planning system

“…In fact, we have recently demonstrated that a modified Cauchy-Lorentz distribution function is a better choice for modeling the low-dose envelopes in the water phantom. 25 Between March 2010 and June 2012, we treated more than 500 patients with scanning proton beams using the DG fluence model, including approximately more than 150 patients with central nerve system, head and neck, and other cancers. We used SFUD, single field integrated boost, and IMPT for these treatments.…”

On the parametrization of lateral dose profiles in proton radiation therapy

“…Considering these results, in addition to the well known double Gaussian and to the more recently proposed and accurate parametrizations (triple Gaussian [11] and double Gaussian CauchyeLorentz [13]), the GausseRutherford function is a good compromise to evaluate the lateral energy deposition of real beam shapes: indeed, with only 4 free parameters, it ensures a good accuracy, but also a fast calculation time. Moreover, this parametrization is firmly justified by a physical explanation because the tails of the distribution are also due to the single scattering events at big angles, as shown by Rutherford.…”

“…Among these it is worth mentioning the approach of Soukup et al [12] that parametrizes the nuclear halo tails with a modified CauchyeLorentz function, the work of Li et al [13] and the recent review by Gottschalk [14] that proposes a very detailed model with 25 parameters.…”

“…Finally we also analyzed a recent parametrization proposed by Soukup et al [12] and by Li et al [13] where a second Gaussian function with a large standard deviation and a modified CauchyeLorentz distribution function are added to the Gaussian profile of the core:…”

Effect of Scanning Beam for Superficial Dose in Proton Therapy

“…The beam spread is described by the parameter sigma 1 (σ), the Gaussian approximation of the main part of the dose distribution in a single spot (20). The results are presented below in terms of σ.…”