Effective point of measurement of thimble ion chambers in megavoltage photon beams
A graphical illustration of the optimization procedure to determine the EPOM shift of an ion chamber. The main graph shows the dose ratio for different shifts: (thick line), (thin line), and the optimal value (solid dots). For the optimal case, we show the statistical uncertainties in the dose ratios as vertical bars and the value of the optimal constant dose ratio (dashed line). In the inset we plot the value of the per degree of freedom , as a function of ; the value of that minimizes is the optimal EPOM shift. (The data presented here are for the Exradin A12 chamber in a beam and a field size.)
Dose in water as a function of depth for the two photon beam energies of 6 and , as labeled on the graph, and two field sizes at each energy: Solid dots (●) stand for the small field, while open circles (○) stand for the wider field. For clarity, we only show 30 out of the 320 data points collected for each curve. Uncertainties are not visible here, as they are much smaller than the symbol size. The continuous curves show the smooth splines fitted to the full data set: These are the functions that we use as our water depth-dose curves in our analysis. The vertical dashed line is a reminder that our EPOM calculations only rely on depths less than . The dose is given per incident electron on the linac bremsstrahlung target.
Dose in the cavity of the Exradin A12 ion chamber at 45 different depths inside a water phantom for the two photon beam energies of 6 and , as labeled on the graph, and two field sizes at each energy: Solid dots (●) for the field and open circles (○) for the field. The solid curves are added to guide the eye. The statistical uncertainty in the data points ranges from 0.05% to 0.1%, so error bars are not visible here. The vertical dashed line is located at a depth equal to the overall radius of the Exradin A12 chamber; our analysis only considers data points to the right of this line, for which the chamber is completely immersed in water. The dose is given per incident electron on the linac bremsstrahlung target.
The upstream EPOM shift relative to the chamber cavity radius for 12 ion chambers in each of the four beams surveyed. For both the energy (circles) and the energy (triangles), solid symbols denote the field, while open symbols denote the larger field. Where visible, the error bars indicate the statistical uncertainty in the relative EPOM shift. Data points are missing for the , beam for the three chambers to the left of the dashed line because in these scenarios the EPOM analysis fails.
The relative upstream EPOM shift as a function of the minimum depth cutoff for three ion chambers in a energy beam: Solid dots (●) for the field and open circles (○) for the field. Points enclosed in square symbols correspond to the smallest value of for which the chamber is completely immersed in water (our choice of in the analysis).
The relative upstream EPOM shift as a function of length for bare cylindrical cavities with (open circles) and bare ion chamber models (solid dots), i.e., chambers with no wall nor central electrode, as labeled (the A1 and A1SL chambers are barely distinguishable here). The solid line is fitted to the bare cavity data.
The relative upstream EPOM shift as a function of the central electrode radius , expressed as , for chambers with no wall. Each symbol shape corresponds to a different chamber: The solid symbol in each data set corresponds to the electrode radius for the actual chamber, as labeled, while open symbols show how the EPOM changes with changes in the electrode radius. Straight lines are fitted to the data for each chamber; the dashed line distinguishes the A12 chamber.
The additional relative upstream EPOM shift as a function of chamber wall thickness: The zero on the vertical axis here thus corresponds to the solid symbols in Fig. 7, respectively, for each chamber. The solid dots correspond to the wall thickness of the real chambers, as labeled, and the open symbols correspond to 25 other scenarios with varying wall thickness. The label A1SLa draws attention to the case of a thick-walled A1SL chamber which exhibits no EPOM shift. The solid line is simply a linear function of slope and zero intercept. For most points, the error bar is not visible because it is smaller than the symbol size.
The main physical characteristics of the ion chambers studied in this paper. The shell and electrode material is Shonka air-equivalent plastic C552 unless otherwise noted. The dimensions quoted here are nominal ones gleaned from product documentation; in our simulations, we use more precise values provided by the manufacturer except for the NE2571 and the PTW30013. Exradin chamber images used with permission from Standard Imaging, Inc.
Detailed EPOM analysis results. For each case (chamber model, nominal energy, and field size) we list (a) the EPOM shift relative to the chamber cavity radius, (b) the actual EPOM shift in millimeters, (c) the difference in millimeters between the EPOM and the recommended value of , (d) the optimal value of the proportionality constant [see Eq. (1)], (e) the goodness-of-fit estimator , (f) the relative rms deviation of the dose ratio with respect to [see Eq. (4)], and (g) the same rms measure evaluated for a shift of . Numbers in parentheses give the statistical uncertainty in the EPOM values in terms of the last two digits of the reported value, i.e., means .
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