^{1,a)}and Iwan Kawrakow

^{1}

### Abstract

**Purpose:**

Determine the effective point of measurement (EPOM) of 12 thimble ion chambers, including miniature chambers and three models widely used for clinical reference dosimetry. The EPOM is the point at which the measured dose would arise in the measurement medium in the absence of the probe: For cylindrical chambers, it is shifted upstream relative to the central axis of the chamber. Although current dosimetry protocols prescribe a blanket upstream EPOM shift of, with as the chamber cavity radius, it has been shown in recent years that the EPOM does, in fact, depend on every detail of the chamber design and on the beam characteristics. In the wake of this finding, the authors undertake a comprehensive study of the EPOM for a series of chambers in water.

**Methods:**

This work relies on EGSnrc Monte Carlo calculations for the central axis depth dose in a water phantom and in ion chambers. They use a full Elekta Precise linac treatment head simulation to generate realistic photon beams with nominal energies of 6 and and fields sizes of and . The correct EPOM shift for the 12 ion chambers, modeled in realistic detail, is taken as the one minimizing the deviation of the ratio between the dose to water and the dose to the gas of the chamber cavity, according to a method proposed and validated in previous work.

**Results:**

The analysis reveals that the actual EPOM shift is significantly smaller than the recommended value in current dosimetry protocols, by up to 25% for reference-class chambers and 80% for miniature chambers. The location of the EPOM also depends on the characteristics of the incident beam and varies in a well-defined way with the cavity length, the central electrode radius, and the thimble wall thickness.

**Conclusions:**

The authors confirm that an upstream EPOM shift of is too large for thimble ion chambers in high energy photon beams. Proper values for the EPOM shift could be tabulated per beam and per chamber, but they envisage that a single shift for all practical beams may prove sufficient. Moreover, the systematic dependence on chamber characteristics provides evidence that a universal parametrization in terms of a few design parameters is conceivable and has implication for the calculation of chamber correction factors.

The authors are grateful to Brian Hooten from Standard Imaging for providing the detailed technical specifications of the Exradin ion chambers and to Carl Ross as well as Malcolm McEwen from the NRC for comments on the manuscript.

I. INTRODUCTION

II. METHOD

II.A. Effective point of measurement

II.B. Determination of the effective point of measurement

II.C. Dose to water

II.D. Dose to ion chambercavity

III. RESULTS

III.A. Dose to water

III.B. Dose to ion chambercavity

III.C. Effective point of measurement

IV. DISCUSSION

IV.A. Comparison with the prescribed EPOM shift

IV.B. Dependence on beam energy and field size

IV.C. Dependence on dose buildup

IV.D. Dependence on chamber design parameters

IV.D.1. Cavity length

IV.D.2. Central electrode radius

IV.D.3. Cavity wall thickness

IV.E. Microchambers

IV.F. Chamber correction factors

V. CONCLUSION

### Key Topics

- Ionization chambers
- 32.0
- Dosimetry
- 25.0
- Electrodes
- 23.0
- Photons
- 21.0
- Field size
- 14.0

## Figures

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.)

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 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.

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 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 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 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 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 *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.

## Tables

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.

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 .

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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