Implementation of a triple Gaussian beam model with subdivision and redefinition against density heterogeneities in treatment planning for scanned carbon-ion radiotherapy

Abstract

Challenging issues in treatment planning for scanned carbon-ion (C-ion) therapy are (i) accurate calculation of dose distribution, including the contribution of large angle-scattered fragments, (ii) reduction in the memory space required to store the dose kernel of individual pencil beams and (iii) shortening of computation time for dose optimization and calculation. To calculate the dose contribution from fragments, we modeled the transverse dose profile of the scanned C-ion beam with the superposition of three Gaussian distributions. The development of pencil beams belonging to the first Gaussian component was calculated analytically based on the Fermi-Eyges theory, while those belonging to the second and third components were transported empirically using the measured beam widths in a water phantom. To reduce the memory space for the kernels, we stored doses only in the regions of interest considered in the dose optimization. For the final dose calculation within the patient's whole body, we applied a pencil beam redefinition algorithm. With these techniques, the triple Gaussian beam model can be applied not only to final dose calculation but also to dose optimization in treatment planning for scanned C-ion therapy. To verify the model, we made treatment plans for a homogeneous water phantom and a heterogeneous head phantom. The planned doses agreed with the measurements within ±2% of the target dose in both phantoms, except for the doses at the periphery of the target with a high dose gradient. To estimate the memory space and computation time reduction with these techniques, we made a treatment plan for a bone sarcoma case with a target volume of 1.94 l. The memory space for the kernel and the computation time for final dose calculation were reduced to 1/22 and 1/100 of those without the techniques, respectively. Computation with the triple Gaussian beam model using the proposed techniques is rapid, accurate and applicable to dose optimization and calculation in treatment planning for scanned C-ion therapy.

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.…”

“…The complex lateral spreading of a proton beam in the target is typically approximated with an ideal Gaussian shaped distribution [11], considering the direct superposition of several scattering contributions:…”

“…We could go on adding other Gaussians, but in this way we would include such a large number of parameters to result in a substantial increase in the computing time. This approach however gives good results when applied to C12 ion therapy [11].…”

Computational models and tools

“…The PD is generally obtained from measurements or from analytical calculations in water . The development of the primary core component in transverse directions is generally calculated by the Fermi–Eyges theory, while the nuclear‐halo component is transported empirically using the measured or simulated beam widths in water . The PBA is fast and applicable for dose calculation in homogeneous media.…”

“…To reduce the computation time with minor loss of accuracy, Inaniwa et al . applied a pencil beam redefinition algorithm (PBRA) for final patient‐dose calculation in scanned charged particle therapy treatment planning.…”