Uncertainty in tissue equivalent proportional counter assessments of microdosimetry and RBE estimates in carbon radiotherapy
Shannon Hartzell, Fada Guan, Paige A. Taylor, Christine B. Peterson, P Taddei, Stephen F. Kry
Abstract
Abstract Microdosimetry is an important tool for assessing energy deposition distributions from ionizing radiation at cellular and cellular nucleus scales. It has served as an input parameter for multiple common mathematical models, including evaluation of relative biological effectiveness (RBE) of carbon ion therapy. The most common detector used for microdosimetry is the tissue-equivalent proportional counter (TEPC). Although it is widely applied, TEPC has various inherent uncertainties. Therefore, this work quantified the magnitude of TEPC measurement uncertainties and their impact on RBE estimates for therapeutic carbon beams. Microdosimetric spectra and frequency-, dose-, and saturation-corrected dose-mean lineal energy (****) were calculated using the Monte Carlo toolkit Geant4 for five monoenergetic and three spread-out Bragg peak carbon beams in water at every millimeter along the central beam axis. We simulated the following influences on these spectra from eight sources of uncertainty: wall effects, pulse pile-up, electronics, gas pressure, W-value, gain instability, low energy cut-off, and counting statistics. Statistic uncertainty was quantified as the standard deviation of perturbed values for each source. Bias was quantified as the difference between default lineal energy values and the mean of perturbed values for each systematic source. Uncertainties were propagated to RBE using the modified microdosimetric kinetic model (MKM). Variance introduced by statistic sources in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mi>y</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> </mml:msub> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mi>y</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> </mml:msub> </mml:math> averaged 3.8% and 3.4%, respectively, and 1.5% in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>y</mml:mi> </mml:mrow> <mml:mo>*</mml:mo> </mml:msup> </mml:math> across beam depths and energies. Bias averaged 6.2% and 7.3% in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mi>y</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> </mml:msub> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mi>y</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> </mml:math> and 4.8% in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>y</mml:mi> </mml:mrow> <mml:mo>*</mml:mo> </mml:msup> <mml:mo>.</mml:mo> </mml:math> These uncertainties corresponded to 1.2 ± 0.9% on average in RBE MKM . The largest contributors to variance and bias were pulse pile-up and wall effects. This study established an error budget for microdosimetric carbon measurements by quantifying uncertainty inherent to TEPC measurements. It is necessary to understand how robust the measurement of RBE model input parameters are against this uncertainty in order to verify clinical model implementation.