Calculation of clinical dose distributions in proton therapy from microdosimetry

To introduce a new algorithm-MicroCalc-for dose calculation by modeling microdosimetric energy depositions and the spectral fluence at each point of a particle beam. Proton beams are considered as a particular case of the general methodology. By comparing the results obtained against Monte Carlo computations, we aim to validate the microdosimetric formalism presented here and in previous works.

In previous works, we developed a function on the energy for the average energy imparted to a microdosimetric site per event and a model to compute the energetic spectrum at each point of the patient image. The number of events in a voxel is estimated assuming a model in which the voxel is completely filled by microdosimetric sites. Then, dose at every voxel is computed by integrating the average energy imparted per event multiplied by the number of events per energy beam of the spectral distribution within the voxel. Our method is compared with the proton convolution superposition (PCS) algorithm implemented in Eclipse™ and the fast Monte Carlo code MCsquare, which is here considered the benchmark, for in-water calculations, using in both cases clinically validated beam data. Two clinical cases are considered: a brain and a prostate case.

For a SOBP beam in water, the mean difference at the central axis found for MicroCalc is of 0.86% against 1.03% for PCS. Three-dimensional gamma analyses in the PTVs compared with MCsquare for criterion (3%, 3 mm) provide gamma index of 95.07% with MicroCalc vs 94.50% with PCS for the brain case and 99.90% vs 100.00%, respectively, for the prostate case. For selected organs at risk in each case (brainstem and rectum), mean and maximum difference with respect to MCsquare dose are analyzed. In the brainstem, mean differences are 0.25 Gy (MicroCalc) vs 0.56 Gy (PCS), whereas for the rectum, these values are 0.05 Gy (MicroCalc) vs 0.07 Gy (PCS).

The accuracy of MicroCalc seems to be, at least, not inferior to PCS, showing similar or better agreement with MCsquare in the considered cases. Additionally, the algorithm enables simultaneous computation of other quantities of interest. These results seem to validate the microdosimetric methodology in which the algorithm is based on.