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Estimating patient specific uncertainty parameters for adaptive treatment re-planning in proton therapy using in vivo range measurements and Bayesian inference: application to setup and stopping power errors

In proton therapy, quantification of the proton range uncertainty is important to achieve dose distribution compliance. The promising accuracy of prompt gamma imaging (PGI) suggests the development of a mathematical framework using the range measurements to convert population based estimates of uncertainties into patient specific estimates with the purpose of plan adaptation. We present here such framework using Bayesian inference. The sources of uncertainty were modeled by three parameters: setup bias m, random setup precision r and water equivalent path length bias u. The evolution of the expectation values E(m), E(r) and E(u) during the treatment was simulated. The expectation values converged towards the true simulation parameters after 5 and 10 fractions, for E(m) and E(u), respectively. E(r) settle on a constant value slightly lower than the true value after 10 fractions. In conclusion, the simulation showed that there is enough information in the frequency distribution of the range errors measured by PGI to estimate the expectation values and the confidence interval of the model parameters by Bayesian inference. The updated model parameters were used to compute patient specific lateral and local distal margins for adaptive re-planning.