Multi-dimensional Uncertainty Analysis for Proton FLASH Radiotherapy

Abstract

With FLASH proton radiotherapy, healthy tissue is spared more compared to conventional proton therapy. The FLASH effect is present at high fractional doses of more than 8 Gy, at ultra-high mean dose rates of more than 40 Gy per second and at dose delivery times of less than 200 milliseconds. However, particle accelerator intrinsic uncertainties can influence the FLASH effect negatively. FLASH proton therapy is affected by pencil beam positioning errors and by proton beam current fluctuations. In this work, these two types of uncertainties were added to a Gaussian two-dimensional analytical dose model. The impact of pencil beam placement errors was evaluated on dose deposition and related to clinically used metrics. These are the V95, V107, D2 and D98. The constraint on the V95 was violated for 5\% of patients first. For all evaluated FLASH dose fields, the allowed Gaussian pencil beam placement error is less than 1.0-mm in standard deviation. A trade-off between target coverage and the level of FLASH effect was found. Proton beam current fluctuations were coupled to the pencil beam scanning dose rate (PBSDR98), the minimum dose rate for 98\% of the target volume. For all evaluated FLASH fields the permitted beam current fluctuation was 6.8\%. This is considered more achievable than the limit on pencil beam placement errors. Proton FLASH radiotherapy is feasible, but proton beam characterisation is required to quantify for which patients this is the case.

The PBSDR is sensitive to added uncertainties and contradicts our current understanding of the FLASH effect. In this thesis, a more robust metric is developed which depends on the radiolytic oxygen depletion hypothesis for the FLASH effect. This metric is called the FER_eff. The oxygen concentration over time in a cell is modelled with an ordinary differential equation (ODE) involving an oxygen depletion and re-oxygenation term. The FER_eff can be calculated with the oxygen concentration over time for a treatment plan. Currently, The onset of the FLASH effect lies between a prescribed dose of 8 Gy and 16 Gy. This is in line with the FLASH dose threshold. The shortcomings of the PBSDR are dealt with.

A three-dimensional uncertainty analysis can be done with a semi-analytical dose engine from the TUD. With this engine, changes in dose deposition are coupled to Hounsfield unit (HU) perturbations without the necessity of a full dose re-computation. To study the machine uncertainties, an EMC FLASH treatment plan formed with iCycle was recreated with the TUD dose engine. The iCycle optimisation results contain all the required information for a dose calculation. The gamma pass rates between the iCycle dose and engine dose were satisfactory for the target but not good enough for an organ-at-risk (OAR) yet. Similarity can be improved by adjusting the dose recreation procedure. When the iCycle dose and engine dose are comparable, a trustworthy clinical uncertainty analysis can be done. The idea is to simulate field and individual pencil beam placement errors by shifting the original patient CT to a virtual CT. First, it should be studied if the computed dose response is valid for a combination of CT shifts and HU perturbations. In a later stage, pencil beam placement errors should be coupled to the clinically used ICRU metrics and constraints. The impact of beam current fluctuations can also be studied in the future.