Impact of scoring volume on Linear Energy Transfer (LET) scoring using Monte Carlo simulations

Introduction


The goal of this project is to measure the impact of the linear energy transfer (LET) volume scoring on LET values in a FLUKA simulation. To do this I use a single beam and measure the LET along the beam path, then vary the scoring volumes and finally compare the results to see what effect the size of the volume has on the scoring.

Theory

The linear energy transfer (LET) is an important parameter that measures the energy lost by a charged particle per unit distance, it is especially important in relation to medical physics. LETt is called the "track averaged linear energy transfer", it is the mean value of the fluence spectrum of LET, this is very close to the ICRU defined meaning of LET. For medical purposes one should use a factor that considers both dose and LET, this is the LETd quantity, this is the one that can best predict the biological effects of the radiation.

Method

The simulation program (FLUKA) can export files in a .dat format where the values and uncertainties are taken from the simulation. Since LETd and LETt are not values that FLUKA scores directly, I wrote a C++ that reads these files and calculates the dose averaged LET (LETd) and the track averaged LET (LETt). The program then exports them to a simple three column (x, y, uncertainty) .txt format for easy handling in ROOT. ROOT is used in this project to mainly plot the different values and uncertainties against each other, I chose to plot the uncertainties by themselves, since the values weren't very different for the different scoring.

I used 5 different scoring volumes in μm they are: 100, 250, 500, 750, 1000. I ran the simulation using 40 million primary particles with a proton beam energy of 102.809MeV. The phantom was a 20*20*20cm water phantom, the geometries and input files where gotten from Haukeland University Hospital.

The different codes can be found separately: LETd and LETt calculations and exporting in suitable format, root script for comparative plots, root script for comparative uncertainty plots:relative, absolute. Finally the .tar file with all the code files. The .dat files used in the project can be found here.

Results

The result I got was that the values stayed the same for all scoring volumes, but the uncertainty was significantly different between each. Following are some generated plots to demonstrate this effect, all values above 8.4 can be disregarded due to the low LET values leading to artifacts in the LETd calculations. The choice to plot the values without error bars becomes evident when one sees the result of plotting them with the error bars.

Figure 1: Calculated LETd in the water phantom, it's evident that the physical values don't vary with scoring volume.
Figure 2: Calculated LETt in the water phantom, same as for LETd, values don't vary with scoring volume.

The difference is therefore mainly in the uncertainties, this will be demonstrated by the following plots.

Figure 3: Uncertainties of the LETd in absolute values.
Figure 4: Uncertainties of the LETd in relative values, as we can see there seems to be a constant difference between the scoring volumes
Figure 5: Uncertainties of the LETt in absolute values, the same trend as for the LETd can be observed.
Figure 6: Uncertainties of the LETt in relative values, the same trend as for the LETd can be observed.
Table 1: Table comparing the numerical values and uncertainties of the different scoring volumes at some given depths (z).

As we can see the difference between the scoring volumes lies in the amount of uncertainty where a smaller scoring volume is correlated with a smaller uncertainty, as one would expect. When put into a table it's possible to see that the uncertainty in % follows linearly as the size increases.

In this formula the delta is a percentage, the S denotes the length of each side in the cubic scoring volume, this relation holds true until z~8.4cm.

Discussion

The size of the scoring volume seems to have a strong linear correlation to the uncertainty of the measurements. This is what one would expect, when comparing to a previous article written on the subject of volume scoring. One can see that the result is the same for the numerical values of LETd and LETt at volumes >100μm, 100μm was the smallest scoring volume I could achieve, and so I did not have the opportunity to see the same effect as they did for the part where 50μm > scoring volume.

References

Analysis of the track- and dose-averaged LET and LET spectra in proton therapy using the geant4 Monte Carlo code.