Chapter 6 Commissioning of a Monte Carlo simulation of the iThemba
6.4 Validation of Material I-values
As discussed extensively in the literature [83, 15, 11], uncertainties in the I-values published in the literature are a major contributor to proton range uncertainty. The estimates of Paganetti [15] et al determined that on average, the uncertainty in published I-values contribute a range uncertainty of upto 1.5%. More recent work by has sought to reduce this uncertainty to between 0.3 and 0.5 % of the range of the beam [16] however the currently accepted
When the elements are combined into mixtures or compounds, their respec- tive I-values are determined either through experimental measurement or through use of the Bragg additivity rule. One such method, also used to determine the I- value of water, is to perform range measurements experimentally and compare them against Monte Carlo simulation, where the I-value of the material of interest can be defined by the user [84]. By minimising the range difference between the simulation and measurement, as a function of the I-value, the I-value of the material can be found.
In the following work, we want to run a Monte Carlo simulation of a proton dose distribution inside a phantom, using geometries acquired from x-ray CT and proton CT imaging. In order to compare these simulations to experiment, we need to validate range of the incoming proton beam. This is done by simulating the ex- periment with the real geometry and comparing the simulated beam against the film measurement. The phantom used was constructed using high-density polyethylene (HDPE). The quoted I-value of HDPE in the literature is 57.4±8 eV. This corre- sponds to an uncertainty in the relative stopping power of HDPE of about 3% for a 100 MeV proton beam. For a 15 mm sample, this corresponds to an uncertainty of over 0.4 mm in the range in water of the measurement, and in the following chapter would correspond to a range uncertainty of around 1.5 mm for a beam with an approximate range of 50 mm.
Using the energy and standard deviation that we calculated in the previous section, a new simulation was initiated. In the simulation, a cylindrical sample of polyethylene was inserted into 15 mm diameter aperture in the treatment collimator, so that the SuSi simulation replicated the experiment described in chapter 4. The polyethylene sample has a length of 14.88 mm and a mass density of 0.94 g/cm3, and these values were used in the simulation.
A new user option was defined in the simulation so that the I-value of the polyethylene insert could be defined. The simulation was performed using 17 dif- ferent I-value settings, from 49.4 eV to 64.4 eV in steps of 1 eV. Each simulation
was performed with 850 million primary protons, scoring the energy deposition in the whole water tank. A subset of the simulated depth-dose curves are shown in figure 6.7, alongside the experimental measurement. The range at 80% on the Bragg peak distal edge, R80 was used to determine the best fit to the data. The range
error, calculated by subtracting the simulatedR80 from R80 measured in the water
tank was then fitted as a function of the I-value of polyethylene by rearranging the Bethe-Bloch equation: ∆R=Aρe,rel× B−lnIpolyethylene B−lnIwater (6.4) where B = ln2mec2β2
β2 −β2 and is a coefficient accounting for the constants
in the Bethe-Bloch equation and the energy of the proton beam.
220 222 224 226 228 230
Depth (mm)
0 20 40 60 80 100Percentage Dose (%)
I = 49.4 eV I = 51.4 eV I = 53.4 eV I = 55.4 eV I = 57.4 eV I = 59.4 eV I = 61.4 eV I = 63.4 eV I = 65.4 eV Water Tank DataFigure 6.7: Simulated Bragg peaks incident on a sample of polyethylene. As the I-value reduces, the proton range increases. Error bars were too small to be visible on the water tank data.
The covariance of the fitted parameters was used to determine the 95% con- fidence limits, shown in figure 6.8. From the fit, we are able to determine the I-value of the HDPE sample used in this experiment as 50.8±1 eV. This value is in agreement with the accepted value of 57.4±8 eV however with significantly reduced uncertainties. It is noted that the uncertainties defined by the covariance matrix are lower than the random error in the data. We would expect to see a reduction in the random error by increasing the number of simulated protons however the process is already computationally demanding. We intend to apply this method to evaluate the I-values of tissue equivalent materials introduced in chapter 4. In future work,
45 50 55 60 65 I-value [eV] −0.2 0.0 0.2 0.4 0.6 Range Error [mm] R80,exp−R80,sim Fit 95% Confidence
Figure 6.8: Results from a Monte Carlo simulation showing the range difference at R80 between a water tank measurement and a simulation of a nominal 240 mm
range proton beam incident on a 15 mm sample of polyethylene. In the simulation, the I-value of the polyethylene sample was adjusted to tune the simulation in order to reduce the error and redefine the I-value of polyethylene.
it would be preferable to take water tank measurements using larger samples as this would increase the relative range error as a function of the I-value and thus reduce the need for such high-precision computation.
6.5
Conclusions
The performance of Monte Carlo simulation of the iThemba LABS proton beamline was validated against experimental measurement. The energy of the proton source in the simulation was tuned by performing a chi-square test and uncertainties on the input were defined. Following this work we used the simulation to calculate the I-value of polyethylene. This method provided a result with lower uncertainties than the current accepted value. We will use this simulation to calculate proton dose distributions on image data from proton and x-ray CT.