A noise correction of the γ-index method for Monte Carlo dose distribution comparison

Due to the increasing complexity of IMRT/IMPT treatments, quality assurance (QA) is essential to verify the quality of the dose distribution actually delivered. In this context, Monte Carlo (MC) simulations are more and more often used to verify the accuracy of the treatment planning system (TPS). The most common method of dose comparison is the γ-test, which combines dose difference and distance-to-agreement (DTA) criteria. However, this method is known to be dependent on the noise level in dose distributions. We propose here a method to correct the bias of the γ passing rate (GPR) induced by MC noise.

The GPR amplitude was studied as a function of the MC noise level. A model of this noise effect was mathematically derived. This model was then used to predict the time-consuming low-noise GPR by fitting multiple fast MC dose calculations. MC dose maps with a noise level between 2% and 20% were computed, and the GPR was predicted at a noise level of 0.3%. Due to the asymmetry of the γ-test, two different cases were considered: the MC dose was first set as reference dose, then as evaluated dose in the γ-test. Our method was applied on six proton therapy plans including analytical doses from the TPS or patient-specific QA measurements.

An average absolute error of 4.31% was observed on the GPR computed for MC doses with 2% statistical noise. Our method was able to improve the accuracy of the gamma passing rate by up to 13%. The method was found especially efficient to correct the noise bias when the DTA criterion is low.

We propose a method to enhance the γ-evaluation of a treatment plan when there is noise in one of the compared distributions. The method allows, in a tractable time, to detect the cases for which a correction is necessary and can improve the accuracy of the resulting passing rates.