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.
Materials and methods
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.
- 1. Spatial distribution of energy deposition by ionizing radiation source. Radiat Res. 1960; 2: 290–299.
- 2. Microdosimetry. Biophys Asp Radiat Qual IAEA, Tech Reports Ser;1966:58.
- 3, . The theory of dual radiation action. In: M Ebert, A Howard, eds. Current Topics in Radiation Research. Vol. VIII. Manchester, UK: American Elsevier Publishing Company; 1974: 85–156.
- 4, . Concepts of microdosimetry - II. Probability distributions of the microdosimetry variables. Radiat Environ Biophys. 1975; 12: 205–216.
- 5, . Concepts of microdosimetry - I. Quantities. Radiat Environ Biophys. 1975; 12: 61–69.
- 6, . Concepts of microdosimetry - III. Mean values of the microdosimetric distributions. Radiat Environ Biophys. 1975; 12: 321–335.
- 7, , , et al. RBE-LET relationships for cell inactivation and mutation induced by low energy protons in V79 cells: further results at the LNL facility. Int J Radiat Biol. 1998; 74: 501–509.
- 8. A microdosimetric-kinetic model for the effect of non-poisson distribution of lethal lesions on the variation of RBE with LET. Radiat Res. 2003; 160: 61–69.
- 9. The relationships between RBE and LET for different types of lethal damage in mammalian cells: biophysical and molecular mechanisms. Radiat Res. 1994; 139: 257–270.
- 10. Fundamentals of microdosimetry. In: KR Kase, BE Bjarngard, FH Attix, eds. The Dosimetry of Ionization Radiation, Vol. I. Cambridge: Academic Press Inc; 1985: 77–162.
- 11, . Microdosimetry and Its Applications. Berlin: Springer; 1996.
- 12. The microdosimetric one-hit detector model for calculating the response of solid state detectors. Radiat Meas. 2002; 35: 255–267.
- 13, , , , , . Dose-averaged LET calculation for proton track segments using microdosimetric Monte Carlo simulations. Med Phys. 2019; 46: 4184–4192.
- 14, , , . Segment-averaged LET concept and analytical calculation from microdosimetric quantities in proton radiation therapy. Med Phys. 2019; 46: 4204–4214.
- 15 ICRU. Report 36. Microdosimetry; 1983.
- 16. Analysis of patterns of energy deposition. In: HG Ebert, ed. Second Symposium on Microdosimetry. Stresa, Italy: Commission of the European Communities; 1970: 107–136.
- 17, , , et al. The Geant4-DNA project. Int J Model Simul Sci Comput. 2010; 1: 157–178.
- 18, , , et al. Comparison of GEANT4 very low energy cross section models with experimental data in water. Med Phys. 2010; 37: 4692–4708.
- 19, , , et al. Track structure modeling in liquid water: a review of the Geant4-DNA very low energy extension of the Geant4 Monte Carlo simulation toolkit. Phys Medica. 2015; 31: 861–874.
- 20, , , et al. Geant4-DNA example applications for track structure simulations in liquid water: a report from the Geant4-DNA Project. Med Phys. 2018; 45: e722–e739.
- 21, , , et al. A benchmarking method to evaluate the accuracy of a commercial proton monte carlo pencil beam scanning treatment planning system. J Appl Clin Med Phys. 2017; 18: 44–49.
- 22, , , et al. Dosimetric evaluation of a commercial proton spot scanning Monte-Carlo dose algorithm: comparisons against measurements and simulations. Phys Med Biol. 2017; 62: 7659–7681.
- 23, , , . A kernel-based algorithm for fluence and spectral fluence in clinical proton beams to calculate dose-averaged LET and other dosimetric quantities of interest. Med Phys [SUBMITTED]. 2019.
- 24, , , et al. Geant4—a simulation toolkit. Nucl Instruments Methods Phys Res Sect A. 2003; 506: 250–303.
- 25, , , et al. Geant4 developments and applications. IEEE Trans Nucl Sci. 2006; 53: 270–278.
- 26, , , et al. Recent developments in Geant4. Nucl Instruments Methods Phys Res Sect A. 2016; 835: 186–225.
- 27. Theoretical aspects of energy-range relations, stopping power and energy straggling of protons. Radiat Phys Chem. 2007; 76: 1089–1107.
- 28 Varian. Eclipse Proton Algorithms Reference Guide, v13.7. 2015.
- 29, , . Fast multipurpose Monte Carlo simulation for proton therapy using multi- and many-core CPU architectures. Med Phys. 2016; 43: 1700–1712.
- 30, , , et al. Experimental assessment of proton dose calculation accuracy in inhomogeneous media. Phys Medica. 2017; 38: 10–15.
- 31, , , et al. Validation and clinical implementation of an accurate Monte Carlo code for pencil beam scanning proton therapy. J Appl Clin Med Phys. 2018; 19: 558–572.
- 32, , , et al. On the parametrization of lateral dose profiles in proton radiation therapy. Phys Medica. 2015; 31: 484–492.
- 33, . Elevated LET components in clinical proton beams. Phys Med Biol. 2011; 56: 6677–6691.