How should we model and evaluate breathing interplay effects in IMPT?

Breathing interplay effects in Intensity Modulated Proton Therapy (IMPT) arise from the interaction between target motion and the scanning beam. Assessing the detrimental effect of interplay and the clinical robustness of several mitigation techniques requires statistical evaluation procedures that take into account the variability of breathing during dose delivery. In this study, we present such a statistical method to model intra-fraction respiratory motion based on breathing signals and assess clinical relevant aspects related to the practical evaluation of interplay in IMPT such as how to model irregular breathing, how small breathing changes affect the final dose distribution, and what is the statistical power (number of different scenarios) required for trustworthy quantification of interplay effects. First, two data-driven methodologies to generate artificial patient-specific breathing signals are compared: a simple sinusoidal model, and a precise probabilistic deep learning model generating very realistic samples of patient breathing. Second, we investigate the highly fluctuating relationship between interplay doses and breathing parameters, showing that small changes in breathing period result in large local variations in the dose. Our results indicate that using a limited number of samples to calculate interplay statistics introduces a bigger error than using simple sinusoidal models based on patient parameters or disregarding breathing hysteresis during the evaluation. We illustrate the power of the presented statistical method by analyzing interplay robustness of 4DCT and Internal Target Volume (ITV) treatment plans for a 8 lung cancer patients, showing that, unlike 4DCT plans, even 33 fraction ITV plans systematically fail to fulfill robustness requirements.