Quantitative ionization chamber alignment to a water surface: Theory and simulation

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Abstract

Purpose

To examine the response properties of cylindrical cavity ionization chambers (ICs) in the depth-ionization buildup region so as to obtain a robust chamber-signal — based method for definitive water surface identification, hence absolute ionization chamber depth localization.

Method & materials

An analytical model with simplistic physics and geometry is developed to explore the theoretical aspects of ionization chamber response near a phantom water surface. Monte Carlo simulations with full physics and ionization chamber geometry are utilized to extend the model's findings to realistic ion chambers in realistic beams and to study the effects of IC design parameters on the entrance dose response. Design parameters studied include full and simplified IC designs with varying central electrode thickness, wall thickness, and outer chamber radius. Piecewise continuous fits to the depth-ionization signal gradient are used to quantify potential deviation of the gradient discontinuity from the chamber outer radius. Exponential, power, and hyperbolic sine functional forms are used to model the gradient for chamber depths of zero to the depth of the gradient discontinuity.

Results

The depth-ionization gradient as a function of depth is maximized and discontinuous when a submerged IC's outer radius coincides with the water surface. We term this depth the gradient chamber alignment point (gCAP). The maximum deviation between the gCAP location and the chamber outer radius is 0.13 mm for a hypothetical 4 mm thick wall, 6.45 mm outer radius chamber using the power function fit, however, the chamber outer radius is within the 95% confidence interval of the gCAP determined by this fit. gCAP dependence on the chamber wall thickness is possible, but not at a clinically relevant level.

Conclusions

The depth-ionization gradient has a discontinuity and is maximized when the outer-radius of a submerged IC coincides with the water surface. This feature can be used to auto-align ICs to the water surface at the time of scanning and/or be applied retrospectively to scan data to quantify absolute IC depth. Utilization of the gCAP should yield accurate and reproducible depth calibration for clinical depth-ionization measurements between setups and between users.

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