01.12.2017 | Research | Ausgabe 1/2017 Open Access

# Using field size factors to characterize the in-air fluence of a proton machine with a range shifter

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- Radiation Oncology > Ausgabe 1/2017

## Introduction

## Methods and Materials

### Double-Gaussian model for proton fluence

_{ j },y

_{ j }) and has energy E

_{ k }, \( {D}_{E_k}^{Kernel}\left( x-{x}_j, y-{y}_j, d(z)\right) \) is the dose kernel, d is the depth in medium, and z is the distance from isocenter along the beam direction. For the double-Gaussian fluence model, the distribution of protons is described as:

_{2}(E

_{ k }) is the weight of the second Gaussian function, and σ

_{1}(E

_{ k }, z) and σ

_{2}(E

_{ k }, z) are the standard deviations of the first and second Gaussian, respectively. Properly configuring the model is therefore a matter of finding the optimal values of σ

_{1}(E

_{ k }, z), σ

_{2}(E

_{ k }, z) and w

_{2}(E

_{ k }).

### Field size factor measurements

^{3}, radius 2.5 mm and a 1.06 mm WET entrance window. To keep the chamber in place, it was inserted into a cutout within a 30 cm × 30 cm × 3 cm acrylic plate machined to hold the chamber. The chamber surface and the effective measurement point (1 mm below the surface) were aligned with the laser, and the couch was moved vertically to bring the chamber to the five measurement positions. At each new couch position, beam with the smallest field size (2 cm) was delivered five times at the center and at offsets by ±1 mm in the x and y directions from the center, which ensures that the chamber was properly centered before beginning the FSF measurements. The smallest field size (2 cm) was delivered five times and charges were collected with beam offsets from the current center by ±1 mm in the x and y directions, respectively. The reproducibility of the FSF measurements was checked by repeating them multiple times on multiple days.

### Characterizing the parameters for proton fluence

_{ x }and VSAD

_{ y }are the virtual SAD in the x and y directions, respectively. SS

_{ x }

^{'}and SS

_{ y }

^{'}are the projected spot spacing in the non-isocentric plane in the x and y directions, respectively. After the proton fluence was calculated for each square field, the FS were obtained by normalizing to the field size of 10 cm: \( F S F=\frac{PF(FS)}{PF\left( FS=10\right)} \).

_{1}(E

_{ k }, z), σ

_{2}(E

_{ k }, z), and w

_{2}(E

_{ k })) were used to calculate FSFs for each energy at all five positions. The many calculated FSFs were then compared with the measured FSFs, and the optimal fit parameters were chosen to be those that led to the minimum differences between the measured and calculated FSFs.

_{1}, σ

_{2}, and w

_{2}) for nominal energy E = 130.9 MeV. Each fit parameter was then adjusted separately and new FSFs were calculated. The red, green and blue circles in Fig. 3 show the new FSFs found by changing the fit parameters σ

_{1}, σ

_{2}, and w

_{2}by ±10, ±20, and ±20%, respectively. The greater the change in the calculated FSF, the more sensitive the FSF is to that particular fit parameter. Figure 3a, for example, shows that the FSFs for FS = 2 cm are very sensitive to the primary Gaussian (σ

_{1}). A 10% primary Gaussian change causes >5% change in the FSFs for this smallest field size. However, the FSFs for this same FS = 2 cm are not sensitive to the secondary Gaussian at all: there was virtually no change in the calculated FSF when σ

_{2}was changed by ±20%. Conversely, Fig. 3b shows that the FSFs for FS = 20 cm are not sensitive to the primary Gaussian but rather to the secondary Gaussian. The FSFs for both FS = 2 cm and 20 cm are mildly affected by the variation in the parameter w

_{2}. The data in Fig. 3 shows that with a set of FSFs from 2 cm to 20 cm, the double-Gaussian fluence parameters for a RS may be fitted with high accuracy because of these high sensitivities to the appropriate parameters in the respective field size ranges.

### Validation of the model

## Results

### Field size factors from best fit parameters

### Model validation results

## Discussion

_{1}of the primary Gaussian for the 2 cm field size. For spot sizes less than 5 mm, it is quite possible that any direct spot profile measurements would bring sub-mm measurement uncertainties. However, Fig. 3a shows that even a 0.5 mm deviation may cause an error in FSFs greater than 5%, which is certainly not negligible. Therefore, the FSF measurements for the RS are more accurate and robust in characterizing the proton fluence.

^{−4}of the central axis dose, is necessary to avoid dose inaccuracies [7]. Therefore, achieving an accurate dose calculation for an IMPT plan relies on the accurate modelling of every spot including 1

^{st}and 2

^{nd}Gaussian as well as their relative weights.