Example radiobiology

Author

L Pandola, D Chiappara, GAP Cirrone, G Petringa, A Sciuto, S Fattori; - INFN LNS (Italy)
Radiobiology is an application realized for dosimetric and radiobiological applications of proton and ion beams. Specific tools were built to evaluate primaries and secondary energy spectra and a set of classes, dedicated to the computation of biological, as LET (Linear Energy Transfer), RBE (Relative Biological Effectiveness), Survival Fraction, and physical (as dose and fluence) quantities were implemented.

1- GEOMETRY DEFINITION

The physical and dosimetric quantities are calculated in the water tank by scoring every quantity in each of the slices, representing a customizable (in terms of dimensions and materials) volume that can be voxelized depending on the user's needs.

In the proposed example, the “default” water tank represents a phantom typically used in the clinical hadrontherapy practice, to reconstruct the dose profile distributions in water. The phantom has a standard dimension of 4 x 4 x 4 cm and was sectioned into 0.2 x 40 x 40 mm slices (See Figure 1). The voxel dimensions can be user defined and can vary from 1um to 1 mm The source is positioned on one of the faces of the box

The default macro uses the default geometry configuration mentioned above with a simple run of 100k protons with a Gaussian energy distribution with a mean of 62 MeV and a standard deviation of 0.65 MeV The visualize.mac just creates a teest geometry and opens visualization

2- PHYSICS LIST

In Radiobiology it is possible to activate three physics lists that are those already recommended for medical physics applications and that cover all the physics processes needed for a correct simulation in this field.

The electromagnetic interactions are modeled using the G4EmStandardPhysics_option4 constructor, which uses a condensed history algorithm based on the Beth-Bloch energy loss formula. This physics constructor was created for applications requiring high accuracy in electron, hadron, and ion tracking. It contains the most accurate standard and low-energy models and is recommended for simulations focused on medical physics applications. The hadronic interactions are simulated using models implemented in the QGSP BIC and QGSP BIC HP constructors, which employ Geant4 native preequilibrium and de-excitation models as low energy stages of the Binary Cascade model for protons, neutrons, and ions. The QGSP BIC HP constructor uses, in addition, the high precision neutron package (ParticleHP) to transport neutrons and light-charged particles with energies from 20 MeV down to thermal energy.

Production cuts for secondary generation are an important element in any MC simulation. It has a significant impact on energy deposition, particularly when small quantities are examined. The production cut in Geant4 is a distance (given in units of length), and secondary particles (electrons, positrons, gammas, and secondary protons) are only monitored if their expected range in that medium is greater than the imposed cut. Otherwise, secondary energy is not tracked and is deposited in the secondary production position. The cut for this example is achieved through the standard Geant4 implementation.

 /run/setCutForAGivenParticle e- 0.1 mm
 /run/setCutForAGivenParticle e+ 0.1 mm
 /run/setCutForAGivenParticle proton 0.1 mm

3- LET CALCULATION

Radiobiology simulates and calculates the averaged LET-dose and LET-track fully accounting for the contribution of secondary particles generated in the target fragmentation Dependencies as respect to the transport parameters adopted during the Monte Carlo simulations as the production cut of secondaries particles, voxel size and the maximum steps length are minimized in the LET calculation. At run time, data needed to calculate LET are collected. At the end of simulation, LET mean values are calculated and stored into a file.

The Let.out file will be produced at the end of a run, where you can find the dose and track average LET for each tracked particles (both primary and secondary ones) and the total mean LET.

The file is structured as follows:

• The first three columns contain the voxel indexes (first index "i" refers to the beam direction);
• The fourth and fifth columns contain respectively total mean dose LET (LDT) and total mean track LET (LTT)
• The rest of columns contain LET Dose and Track for each single ion (whose name is in the top row of the file).

4- RBE and Survival calculation

A method was developed to assess the biological damages produced by proton and ion beams in terms of survival fraction curves, i.e of the number of cells able to survive after the irradiation at different dose. The approach is based on the combined use of Monte Carlo Geant4 simulations (to calculate the doses deposited and the energy spectra of particles interacting with cells) and of the Survival analytical code (Manganaro L, Russo G, et al. Survival: a simulation toolkit introducing a modular approach for radiobiological evaluations in ion beam therapy. Phys. Med. Biol. 2018;63(8). 08–01). The Monte Carlo simulations permit the calculation of the Edep and Ekin distributions that, coupled with the radiobiological response model, allow the final and calculation of a survival curve. The kinetic energy and the LET value of any primary ion and of the secondaries generated in each slice of the simulated water phantom are retrieved at each simulation step. The corresponding values of αi and βi, for each specific ion i with a kinetic energy Ei and a released dose Di, are then calculated by direct linear interpolation of the Look-up-tables provided by the Survival analytical code. (G.Petringa et al., Physica Medica 58 (2019) 72–80)

The AlphaAndBeta.out and RBE.out files are produced at the end of the run. AlphaAndBeta.out contains the average alpha (first column) and beta (second column) parameters calculated for each slice (third column).

RBE.out contains the following quantities:

• Dose (Gy): the physical dose;
• ln(S): the natural log of the Survival Fraction;
• Survival Fraction;
• DoseB (Gy): the biological dose;
• RBE: relative biological effectiveness;
• depth (slice): n. of the slice;