Prediction and compensation of magnetic beam deflection in MR-integrated proton therapy: a method optimized regarding accuracy, versatility and speed

Abstract

The integration of magnetic resonance imaging (MRI) and proton therapy for on-line image-guidance is expected to reduce dose delivery uncertainties during treatment. Yet, the proton beam experiences a Lorentz force induced deflection inside the magnetic field of the MRI scanner, and several methods have been proposed to quantify this effect. We analyze their structural differences and compare results of both analytical and Monte Carlo models. We find that existing analytical models are limited in accuracy and applicability due to critical approximations, especially including the assumption of a uniform magnetic field. As Monte Carlo simulations are too time-consuming for routine treatment planning and on-line plan adaption, we introduce a new method to quantify and correct for the beam deflection, which is optimized regarding accuracy, versatility and speed. We use it to predict the trajectory of a mono-energetic proton beam of energy E traversing a water phantom behind an air gap within an omnipresent uniform transverse magnetic flux density B. The magnetic field induced dislocation of the Bragg peak is calculated as function of E and B and compared to results obtained with existing analytical and Monte Carlo methods. The deviation from the Bragg peak position predicted by Monte Carlo simulations is smaller for the new model than for the analytical models by up to 2 cm. The model is faster than Monte Carlo methods, less assumptive than the analytical models and applicable to realistic magnetic fields. To compensate for the predicted Bragg peak dislocation, a numerical optimization strategy is introduced and evaluated. It includes an adjustment of both the proton beam entrance angle and energy of up to 25° and 5 MeV, depending on E and B. This strategy is shown to effectively reposition the Bragg peak to its intended location in the presence of a magnetic field.

Technical Note: Experimental verification of magnetic field‐induced beam deflection and Bragg peak displacement for MR‐integrated proton therapy

“…The obtained range in Bragg peak displacement of 1–10 mm corresponds well with previous theoretical studies in a homogeneous magnetic field in water . As opposed to a previous study for photons, no systematic differences in absolute dose were found between the film measurements with and without magnetic field, which may be caused by the fact that film dosimeters were oriented perpendicular to the magnetic field in this study.…”

“…As expected, the deflected beam trajectories [see Fig. (a)] did not coincide for different energies, but fanned out energy dependently, as the radius of beam path increases with increasing proton energy . No magnetic field‐induced change in the absolute measured dose was observed.…”

“…For inhomogeneous media, a magnetic field‐induced dose enhancement at medium‐air material boundaries in the order of 2% has been predicted for 250 MeV and 3 T caused by electrons returning to the material boundary after being deflected by Lorentz force in air . For media other than PMMA, changes in stopping power affect the range and the local beam curvature, and thus, the displacement of the Bragg peak . Therefore, future measurements in inhomogeneous media are desirable.…”

“…A number of simulation studies have been performed using Monte Carlo methods or (semi‐)analytical approaches to investigate deflected beam trajectories of monoenergetic beams in a water phantom or patient placed in a uniform magnetic field, and considerable distortions of the dose distribution in the patient have been predicted. Particularly, the Bragg peak is expected to be displaced by a few millimeters up to several centimeters, depending on the beam energy and magnetic flux density distribution …”

“…However, there is no clear consensus on the exact amount of magnetic field‐induced Bragg peak displacement to be expected in tissue‐like materials, and experimental benchmark data do not exist. We, therefore, perform a first measurement thereof and compare it against Monte Carlo‐based predictions.…”