Advancing proton minibeam radiation therapy: magnetically focussed proton minibeams at a clinical centre

Proton minibeam radiation therapy (pMBRT) is a novel therapeutic strategy that has proven to significantly increase dose tolerances and sparing of normal tissue. It uses very narrow proton beams (diameter ≤1 mm), roughly one order of magnitude smaller than state-of-the-art pencil beams. The current implementation of pMBRT with mechanical collimators is suboptimal as it is inflexible, decreases efficiency and produces additional secondary neutrons. As a potential solution, we explore in this article minibeam generation through magnetic focussing and investigate possibilities for the integration of such a technique at existing clinical centres. For this, a model of the pencil beam scanning (PBS) nozzle and beam at the Orsay Proton Therapy Centre was established and Monte Carlo simulations were performed to determine its focussing capabilities. Moreover, various modifications of the nozzle geometry were considered. It was found that the PBS nozzle in its current state is not suitable for magnetic minibeam generation. Instead, a new, optimised nozzle design has been proposed and conditions necessary for minibeam generation were benchmarked. In addition, dose simulations in a water phantom were performed which showed improved dose distributions compared to those obtained with mechanical collimators.


Definition of the beam source for the model of the PBS nozzle at ICPO
lists the parameters of the final beam source model for various beam energies between 100 and 220 MeV. The values for σ x and σ y were obtained through measurements with the ionisation chamber at the nozzle entrance (IC1). The remaining parameters were estimated via a best-fit approach by simulating many different beam sources with varying values for x , y and r xx , r yy .
In order to determine how well a source parametrisation fits the beam at ICPO, the simulated beam size was compared to measurements at five different positions around the isocentre (-40 cm, -20 cm, 0 cm = isocentre, +20 cm and +40 cm) and the mean squared error of the five values was computed. The resulting errors are shown in Figure 2. A red colour represents a smaller error (better fit) and the circles indicate the best fitting parameters for each beam energy. Horizontal and vertical beam parameters, (σ x , x , r xx ) and (σ y , y , r yy ), were considered separately because the two transversal planes are not correlated. The final beam model listed in Table 1 was defined as a smooth interpolation between the best-fit parameters (circles in Figure 2).

Example of the beam size minimisation procedure
The minimisation of the beam size was done in an iterative process simulating the same initial beam with many different configurations of the pair of quadrupole magnets. These configurations differed in the field strength and orientation of the focussing plane of the quadrupoles. Concretely, the field at the pole tips was varied in steps of 0.04 T between 0 and 2 T (4 T for some cases, see main text) and two orientations where the beam is focussed horizontally and vertically, respectively, were considered for each quadrupole. A single quadrupole always focusses in only one direction while defocussing in the orthogonal direction. Nonetheless, a pair of quadrupoles can focus simultaneously in all directions if the focussing plane of the first quadrupole is orthogonal to that of the second one. This implies that a total of 51 × 51 × 2 configurations could be simulated for each beam minimisation. The optimisation procedure had to involve complete Monte Carlo simulations in order to properly account for beam scattering and its contribution to the final beam size.
As stated in the main text, the minimum beam size was found by minimising Ω = hFWHM 2 +vFWHM 2 over all 51 ×51 ×2 quadrupole configurations. Figure 3 shows the values of the hFWHM, vFWHM and Ω at the isocentre for the current geometry of the PBS nozzle as functions of the field at the pole tips of the quadrupoles Q1 and Q2 (labelled as B 1 and B 2 , respectively). The figure displays the case where Q1 focusses horizontally and Q2 focusses vertically. Lighter colours signify smaller values and circles mark the configurations yielding the minima of either quantity.
It becomes apparent that a small value of Ω is obtained only for a few combinations of rather low field strengths (0.3 T ≤ B 1 , B 2 ≤ 0.7 T). On the other hand, a small hFWHM can be obtained for any B 2 and a small vFWHM is possible for any B 1 . For this particular case, the minimum hFWHM is reached for very small fields (B 1 , B 2 ≤ 0.12 T) while the minimum vFWHM requires comparatively high field strengths (B 1 = 1.28 T, B 2 = 1.88 T). In practice, these values depend on the exact geometry of the quadrupoles which is why they were omitted in the main text.   Mean square errors for σ y Figure 2. Fitting the beam source parameters x , y , r xx and r yy : The coloured squares correspond to the logarithm of the mean squared error of the beam sizes at five positions around the isocentre. A red colour indicates a low error and good fit and the best fitting parameters are marked by circles.