A finite element method for the determination of the relative response of ionization chambers in MR-linacs: simulation and experimental validation up to 1.5 T

In magnetic resonance (MR) guided radiotherapy, the magnetic field-dependent change in the dose response of ionization chambers is typically included by means of a correction factor k((B) over right arrow ,M,Q). This factor can be determined experimentally or calculated by means of Monte Carlo (MC) simulations. To date, a small number of experimental values for k((B) over right arrow ,M,Q) at magnetic flux densities above 1.2 T have been available to benchmark these simulations. Furthermore, MC simulations of the dose response of ionization chambers in magnetic fields (where such simulations are based on manufacturer blueprints) have been shown to converge with results that deviate considerably from experimental values for orientations where the magnetic field is perpendicular to the axis of the ionization chamber and the influence of the magnetic field is largest. In this work, k((B) over right arrow ,M,Q) was simulated for a PTW 30013 Farmer ionization chamber using an approach based on finite element simulations. First, the electrical field inside the ionization chamber was simulated using finite element methods. The collecting volume of the ionization was not defined in terms of the physical dimensions of the detector but in terms of the simulated electrical field lines inside the chamber. Then, an MC simulation of the dose response of a Farmer type chamber (PTW 30013) was performed using EGSnrc with a dedicated package to consider the effect of the magnetic field. In the second part, k((B) over right arrow ,M,Q) was determined experimentally for two different PTW 30013 ionization chambers for a range of magnetic flux densities between B = 0 and 1.5 T, covering the range of commercially available MR-linacs. In the perpendicular orientation, the maximum difference between the simulated values for k((B) over right arrow ,M,Q) and the experimental values for k((B) over right arrow ,M,Q) was 0.31(30)% and the minimum difference was 0.02(24)%. For the PTW 30013 ionization chambers, the experimental values for k((B) over right arrow ,M,Q) were 0.9679(1) and 0.9681(1) for a magnetic flux density of 1.5 T. The value resulting from the simulation was 0.967(3). The comparison of the correction factors simulated using this new approach with the experimental values determined in this study shows excellent agreement for all magnetic flux densities up to 1.5 T. Integrating the explicit simulation of the collection volume inside the ionization chambers into the MC simulation model significantly improves simulations of the chamber response in magnetic fields. The results presented suggest that intra- type variations for k((B) over right arrow ,M,Q) may be neglectable for ionization chambers of the PTW 30013 type.