Investigation of contrast mechanisms for MRI phase signal‐based proton beam visualization in water phantoms

The low sensitivity and limitation to water phantoms of convection‐dependent MRI magnitude signal‐based proton beam visualization hinder its in vivo applicability in MR‐integrated proton beam therapy. The purpose of the present study was, therefore, to assess possible contrast mechanisms for MRI phase signal‐based proton beam visualization that can potentially be exploited to enhance the sensitivity of the method and extend its applicability to tissue materials.


INTRODUCTION
In contrast to photon beams used in conventional radiation therapy, proton beams have a tunable, finite range in matter and deposit most of their energy at the end of their range in the so-called "Bragg peak" region allowing dose sparing of healthy tissues, particularly distal to the tumor. Because the material composition in the beam path determines their range, proton therapy suffers from high sensitivity to patient-individual organ motion and deformation. 1 The current clinical practice lacks real-time imaging able to monitor anatomical changes or verify beam ranges. Instead, relatively large safety margins are applied around the tumor to account for range uncertainties, compromising the dose conformality and therefore, the potential benefit of proton therapy. In-beam MRI offers such real-time monitoring of anatomical changes at high soft-tissue contrast. It is, therefore, expected to improve the targeting accuracy and precision of proton therapy, especially for moving tumors. [2][3][4] In addition to that, MRI may enable the verification of dose delivery by means of direct, non-invasive proton beam visualization.
With the availability of a first research prototype in-beam MRI scanner, 5 the feasibility of visualizing proton beams and verifying beam ranges based on beam-induced MRI signal magnitude loss was demonstrated experimentally in liquid-filled phantoms. [6][7][8] The emergence of this signal loss was subsequently shown to be dependent on beam-induced convection, 9 which precludes this particular method's use in flow-restricting tissue. Moreover, its application to routine, water phantom-based clinical quality assurance (QA) is to date hampered by the high radiation doses required for beam visualization. Consequently, the current challenges in the development of MRI-based proton beam visualization lie in finding ways for sensitivity enhancement and beam detection in tissue.
To this day, only changes in the conventionally used magnitude, but not in the phase of the complex-valued MRI signal have been assessed in experimental studies of MRI-based proton beam visualization. Yet, the signal phase may contribute additional information on magnetic field changes and flow effects. 10 Because several proton beam-induced effects were hypothesized to locally influence the homogeneous static magnetic field around the imaging isocenter of the MRI scanner, these may potentially be detectable using phase imaging. First, the detection of a beam-induced magnetic field change by means of MRI 11 or optical magnetometry 12 was proposed. Second, the measurement of a susceptibility-related shift in resonance frequency induced by the radiochemical formation of paramagnetic radicals was suggested. 13 Closely related to this, photon beam-induced hypointense MRI signatures recently observed on an MR-Linac, a hybrid device combining MRI and a clinical electron linear accelerator to deliver photon beams, were ascribed to the radiochemical depletion of paramagnetic oxygen. 14 Moreover, the beam-induced bulk convection observed in a previous magnitude signal-based beam visualization study 9 could also be visualizable as phase contrast. 15 The purpose of the present study was, therefore, to assess the feasibility of MRI phase signal-based proton beam visualization and to test its ability to reflect energy-dependent changes in beam range. Furthermore, this study served to elucidate the irradiation-induced effect responsible for the emergence of the observed phase difference signatures, allowing the method's potential for sensitivity enhancement and clinical applicability to be assessed.

Experimental setup
The combined imaging and irradiation experiments were conducted using a permanent magnet-based prototype in-beam MRI scanner 5 (MrJ2200, ASG Superconductors S.p.A.) with a 0.22 T vertically upward oriented static magnetic field and a maximum gradient amplitude of 15 mT/m. This C-shaped open MRI scanner was enclosed by a copper-lined openable Faraday cage to shield it from external radiofrequency sources emanating from the proton therapy facility ( Figure 1A). Accounting for the deflection of the proton beam by the magnetic field of the scanner, it was placed in front of the horizontal research beamline driven by the isochronous cyclotron (C230, Ion Beam Applications SA) at the University Proton Therapy Dresden facility. The correct positioning of the MRI scanner relative to the proton beam was verified by irradiation of a sheet of radiochromic film (Gafchromic EBT3, Ashland) attached vertically to the proximal surface of a phantom located at the magnetic isocenter of the scanner. After entering the Faraday cage, the high energy proton beam first traversed a 20 cm thick polymethyl methacrylate (PMMA) range degrader to make the beam stop within the phantom volume ( Figure 1B).

Dosimetry
Beam currents of 0.1 to 64 nA were calibrated to the dose rate at 207 MeV beam energy using a cylindrical (2.5 mm radius), plane-parallel ionization chamber with 1 mm electrode distance and a sensitive volume of 0.02 cm 3 (Advanced Markus Chamber Type 34045, PTW Freiburg) attached to the proximal surface of the main phantom at the position marked in green (Figure 2A). For beam The proton beam entered the Faraday cage through a beam entry window consisting of 120 μm thick copper foil. Subsequently, it traversed a 20-cm thick polymethyl methacrylate range degrader to restrict its residual range to the phantom dimensions, thereby assuring that the protons were finally stopped within the water-filled phantom. The single-slice MR images acquired intersected the beam volume horizontally and were perpendicular to the direction of the static magnetic field B 0 .

F I G U R E 2
Phantoms and radiochromic film-based position verification. (A) The main phantom used in the majority of experiments was a tap water-filled cuboid plastic container. (B) A tap water-soaked foam-filled phantom was used for the mechanical restriction of convection. A foam sample and a metric ruler illustrate the pore sizes. (C) The air-insulated tap water-filled bottle served as a phantom for the thermal restriction of convection. (D) The EBT3 film attached to the proximal surface of the main phantom and irradiated with 207 MeV protons served to verify the correct relative positioning of the proton beam, the phantom and the ionization chamber used for dosimetry. The red dotted lines represent the crosshair marked on the phantom surface, which defined the position of the ionization chamber used for beam current to dose rate calibration. The chamber's active measurement area is indicated by the red circle. The white dashed square denotes the area considered in the 2D Gaussian fit for beam center determination. The identified beam center and the 1 σ beam width are marked by the solid white cross and circle, respectively. currents of up to 32 nA, the integral dose readings obtained were unaffected by recombination effects 16 and could, therefore, serve as estimates of the dose rate at the phantom surface after normalization to the irradiation durations ranging from 2 to 10 s for the maximum and minimum beam currents used, respectively. Radiochromic film was used for scanner and phantom positioning (batch number 04181701) and to measure depth-dose profiles (batch number 11192002). It was calibrated for clinical proton fields at a few gray dose levels using the red color channel. 16 The films were scanned with 24-bit color depth at a resolution of 300 dpi. In-house developed software was used for positional and dosimetric film evaluation. For the depth-dose measurement, a sheet of EBT3 film was placed between two parallel PMMA plates, which were angled by 1 • relative to the horizontal plane and irradiated in phantom position.

Phantoms
The main phantom used for the majority of experiments was a plastic container with nominal outer dimensions of 100 × 100 × 65 mm 3 filled with free-floating tap water at the ambient temperature of the scanner of 28 • C ± 1 • C ( Figure 2A). An identical container was filled with phenolic resin-based water-soaked wet floral foam (GLOREX AG) commonly used to keep floral arrangements moist, serving as a phantom for the mechanical restriction of convection ( Figure 2B). The water volume of this phantom relative to the main phantom was reduced by ∼ 3% by the foam insert. For the temperature-controlled restriction of convection, an air-insulated, cylindrical plastic bottle filled with cooled down, free-floating tap water was used ( Figure 2C). All phantoms were centrally positioned in a two-channel knee receiver coil held in place at the MRI isocenter by specifically designed holders. The correct positioning of all phantoms relative to the proton beam was confirmed by EBT3 film irradiation ( Figure 2D).

MRI pulse sequences, image processing and velocity encoding analysis
Two different 2D single gradient echo-based MRI pulse sequences were used to acquire single slice images intersecting the beam volume horizontally ( Figure 1B). For the majority of the experiments, a fast, flow-compensated time-of-flight (ToF) angiography pulse sequence with presaturation applied below the imaged slice was used (TE = 7 ms, TR = 19.2 ms, flip angle = 60 • , number of excitations = 1, slice thickness = 10 mm, in-plane resolution = 1.1 × 1.2 mm 2 , acquisition duration for container phantom = 3 s, acquisition duration for bottle phantom = 4 s). This sequence had previously proven capable of visualizing proton beam-induced MRI signal magnitude loss, 9 therefore, allowing a direct comparison of the characteristics and the convection dependence of the observed MRI magnitude and phase difference signatures. The phase encoding direction was selected perpendicular to the central axis of the beam. To verify the presence of buoyant flow and to test the feasibility of the MRI-based enhancement of convection-induced phase difference contrast, a velocity encoding (Venc) sequence (TE = 32 ms, TR = 160 ms, flip angle = 90 • , number of excitations = 1, slice thickness = 10 mm, in-plane resolution = 1.1 × 1.2 mm 2 , duration = 30 s) with adjustable sensitivity for cross-plane motion was developed (VENC parameter ranging from 5 to 44 mm/s). In contrast to conventional Venc imaging, 15 both images obtained successively for the subsequent phase difference calculation were acquired with motion sensitization, but motion only occurred during the second image acquisition, which was performed under simultaneous proton beam irradiation, whereas the first acquisition was performed without irradiation. Phase encoding was performed parallel to the central axis of the beam. Any deviations of the sequence settings from these default values are listed in the descriptions of the respective experiments. All images were processed from single-receiver-channel raw data using Python 3.8 scripts. To remove irradiation-independent background phase effects from the evaluated images, phase difference images were calculated from two complex image datasets, one acquired without and the other with simultaneous irradiation, using the complex conjugate method. 17 No additional phase difference unwrapping was applied. In the quantitative analysis of the Venc data, the phase difference image was first zeroed by subtraction of the mean phase difference determined in a background region of interest (ROI), Δϕ background . Subsequently, the mean phase difference within the Bragg peak ROI, Δϕ BP , representing the velocity dependent phase, was evaluated. The corresponding convection velocities v BP were calculated following the relation v BP = VENC ⋅ Δϕ BP ∕π. 15

Combined imaging and irradiation experiments
In all irradiation experiments, pairs of MR images without and with simultaneous irradiation were acquired for phase difference analysis. Reference phase difference images were calculated from two acquisitions without simultaneous irradiation. MR imaging and the proton beam irradiation were synchronized manually using a stopwatch. The beam energies and currents used ranged from 200 to 215 MeV and 1 to 64 nA, respectively. To allow for a dose build-up in the water phantom before image acquisition, the irradiation was started at 15, respectively, 10 s before image acquisition and was stopped after 20, respectively, 26 s in the ToF angiography and Venc experiments.

2.5.1
Comparison of the beam-induced MRI phase difference and magnitude signatures To directly compare the beam-induced MRI phase difference signatures to previously analyzed beam-induced ToF angiography signal magnitude signatures, 9 ToF angiography magnitude and phase difference images of the main phantom irradiated covering the full range of beam energies were acquired.

2.5.2
Assessment of beam-induced magnetic field perturbation phase difference contrast To assess whether a transient beam-induced magnetic field perturbation causes the observed phase difference shift within the beam volume, a ToF angiography image acquisition of the main phantom was started 3 s after stopping the irradiation.

2.5.3
Assessment of beam-induced altered magnetic susceptibility phase difference contrast A potential influence of locally altered magnetic susceptibility on the phase signal was tested by variation of TE from 7.0 to 14.0 ms at a fixed TR of 39.6 ms using the ToF angiography sequence. Phase encoding was applied along the beam's central axis. In consideration of the longer TR applied, the main phantom was irradiated for 24 s.

Assessment of beam-induced convection phase difference contrast
To test the hypothesis that convection causes the observed phase difference contrast, beam-induced convection was restricted either mechanically or by thermal control of water expansivity. Moreover, the presence of buoyant flow was confirmed by the beam current-mediated variation of the induced convection velocities, imaged at a fixed VENC parameter.

Restriction of beam-induced convection
The effect of the fine-meshed mechanical restriction of convection was tested by comparing ToF angiography images acquired during irradiation of the main and the foam-filled water phantoms. To assure correct slice positioning, the experiment was first conducted using the main phantom containing unrestricted water before it was repeated in the foam-filled phantom using identical geometry parameters. In a second experiment, the effect of the temperature-controlled restriction of convection was tested using the air-insulated bottle phantom filled with tap water cooled down to 3.5 • C ± 1 • C. Calibration, positioning, and two ToF angiography images, one without and one with simultaneous irradiation, were acquired within 15 min. To assess comparatively the influence of the lowered phantom temperature on the visibility of the beam-induced phase difference signature, the experiment was repeated after the phantom had assumed the ambient temperature of the scanner overnight. The water temperatures were measured in a similar, but unirradiated phantom at both irradiation time points. The uncertainty of the phantom temperature estimates during both irradiations, resulting from differences in phantom handling and measurement errors, was estimated to be 1 • C.

Confirmation of the presence of buoyant convection
To verify the presence of buoyant convection, Venc images with a VENC parameter of 5 mm/s were acquired during successive irradiations of the main phantom using a range of beam currents.

MRI-based enhancement of convection-induced phase difference contrast
To test the feasibility of the MRI-based enhancement of convection-induced phase difference contrast, Venc images with VENC parameter values ranging from 5 to 44 mm/s were acquired under simultaneous irradiation of the main phantom at fixed irradiation settings.

2.5.6
Model-based estimation of the convection velocities The dose D deposited in the Bragg peak during a Venc experiment can be calculated by multiplying the dose rateḊ with the irradiation duration t and a plateau-to-Bragg-peak dose ratio r. This ratio was determined from the proton depth-dose distribution measured by film dosimetry. Dose deposition results in a local increase in water temperature, 18 ΔT, which can be expressed per dose proton beam irradiation as ΔT∕D = c −1 w = 0.24 mK∕Gy, where c w = 4.183 kJ∕(kg K) is the specific heat capacity of water at 28 • C. 19 The concomitant local reduction in the initial density ρ 0 = 996.26 kg∕m 3 of water, 19 Δρ, can then be calculated as where T 0 and T 1 are the respective water temperatures before and during irradiation, and Γ = 2.87 ⋅ 10 −4 K −1 is the corresponding temperature-dependent volumetric thermal expansion coefficient. 19 Using Stokes' viscosimeter model and assuming this heated volume to be spherical and the flow laminar, the net upward force acting on the sphere is where V S = 4∕3πR 3 is the volume of the sphere with radius R, g = 9.81 m∕s 2 is the gravitational acceleration, μ 0 = 8.35 ⋅ 10 −4 Pa s is the dynamic viscosity of water at its initial temperature 19 and v i (t) is the instantaneous velocity. The reformulation and integration of Eq. (1) yields the time-and dose rate-dependent instantaneous velocity, which was calculated at 26 s, (i.e., at mid-image acquisition) using where Ei is the exponential integral function, and A = ΓḊr∕c are auxiliary variables.
The input parameters r, R, T 0 , andḊ were determined in the experiments. For the derivation of Eqs. (1) and (2) see Supporting Information.

Dosimetry
Sufficient beam coverage of the sensitive volume of the ionization chamber with submillimeter offsets of the centers of both the beam and the chamber was verified using EBT3 film ( Figure 2D). Dose rates between 6 and 3033 Gy/min were measured for beam current settings of 0.1-64 nA, respectively. For beam currents of 1, 2, 4, and 8 nA, relevant to the estimation of convection velocities in the Venc experiments, dose rates in the dose plateau region on the phantom surface of 58, 125, 258, and 524 Gy/min, respectively, were obtained by linear regression. Based on the proton beam dose distribution measured by film dosimetry, a plateau-to-Bragg-peak dose ratio of 1.5, and a FWHM beam diameter of 38 mm at the Bragg peak depth were estimated (Figure 3). The resulting Bragg peak doses applied over the 26 s irradiation interval were estimated to be 38 ± 4, 81 ± 8, 168 ± 17, and 340 ± 34 Gy for beam currents of 1, 2, 4, and 8 nA, respectively.

F I G U R E 3
Estimation of the plateau-to-Bragg-peak dose ratio and the beam radius at Bragg peak depth by analysis of the relative proton dose distribution measured by radiochromic film dosimetry. A plateau-to-Bragg-peak dose ratio of 1.5 was determined based on the dose regions roughly covering the central dose plateau where the 5 mm diameter ionization chamber was positioned and the region of interest used to evaluate the Bragg peak phase difference, respectively. The red-marked proton beam's FWHM at Bragg peak depth was estimated based on the 50% isodose. This analysis resulted in estimates of the beam diameter and radius of 38 and 19 mm, respectively.

3.1.1
Comparison of the beam-induced MRI phase difference and magnitude signatures A beam-induced MRI phase difference signature was clearly visible in the ToF angiography phase difference image obtained by subtraction of image acquisitions with and without simultaneous proton beam irradiation of the water-filled main phantom ( Figure 4A). This phase difference signature was similar in position and shape to the corresponding beam-induced hypointense signature observed in the ToF angiography magnitude image acquired under simultaneous irradiation ( Figure 4B). Moreover, the shape and position of both beam-induced signatures closely resembled a planar proton pencil beam dose distribution ( Figure 4C).
Under variation of the beam energies at a fixed beam current, the increase in residual proton beam range with increasing beam energy is clearly observed from the beam-induced phase difference and magnitude signatures in the ToF angiography images ( Figure 5). It can be seen from this figure that the ranges of the phase difference and magnitude signatures show a similar dependence on beam energy, as indicated by the red dotted lines. For further details on the quantitative assessment of the energy-range relationship from these images, reference is made to a previous publication on magnitude MRI-based beam visualization. 8

3.1.2
Assessment of beam-induced magnetic field perturbation phase difference contrast A spatially broadened beam-induced phase difference signature was still clearly visible in a ToF angiography phase difference image acquired 3 s after the beam had been turned off ( Figure 6B), demonstrating that the contrast-inducing effect persists after termination of the irradiation.

3.1.3
Assessment of beam-induced altered magnetic susceptibility phase difference contrast The variation of TE between 7 and 14 ms did not influence the beam-induced signatures observed in ToF angiography phase difference images acquired at fixed irradiation parameters (Figure 7). Therefore, the observed phase difference shifts cannot originate from any beam-induced effects acting throughout TE.

F I G U R E 4
Comparison of the beam-induced signatures in MR phase difference and magnitude images and the corresponding measured relative proton dose distribution. (A) A beam-induced phase difference shift is observed in a time-of-flight angiography phase difference image of acquisitions without and with simultaneous irradiation of the main phantom. (B) A beam-induced hypointense signature is observed in the corresponding magnitude image acquired during irradiation. (C) The relative absorbed planar proton pencil beam dose distribution was measured in the horizontal plane by radiochromic film dosimetry. The resulting dose distribution was scaled by the water equivalent path length of 1.1593 ± 0.007 (experimentally determined for clinical QA purposes at our facility) in longitudinal direction to correct for differences in the proton beam range in the measurement medium of polymethyl methacrylate relative to water. All irradiations were conducted at 32 nA beam current and 207 MeV beam energy with plateau doses at phantom entry of 700 Gy for imaging and 1.4 Gy for film dosimetry deposited within 16.5 s and 40 ms, respectively. The black and white rounded squares indicate the external contour of the water phantom.

F I G U R E 5
Comparable beam energy-dependent range shifts in time-of-flight angiography phase difference and magnitude signatures are clearly observed with increasing beam energies of (B,F) 200, (C,G) 207, and (D,H) 215 MeV at 32 nA current. The reference images (A,E) were acquired without simultaneous irradiation. The vertical red dotted lines were added to help the comparison of the position of the distal beam edges as observed in the phase difference and magnitude images acquired at the same beam energy.

F I G U R E 6
The beam-induced signature in the time-of-flight angiography phase difference image is still visible after irradiation has terminated. (B) The acquisition of the image with preceding irradiation started 3 s after the termination of a 20-s proton beam irradiation at 215 MeV beam energy and 64 nA current. The reference image (A) was acquired without preceding irradiation.

Restriction of beam-induced convection
Unlike in free-floating water at ambient temperature ( Figure 8B), no beam-induced ToF angiography phase difference signature was observed during 64 nA irradiation in the convection-restricted foam phantom ( Figure 8C). Similarly, unlike in free-floating water at an ambient temperature of 28 • C ± 1 • C ( Figure 8D), the 64 nA irradiation of water at 5 • C ± 1 • C ( Figure 8E), a temperature at which the onset of convection is largely suppressed, 20 resulted in the absence of a beam-induced ToF angiography phase difference signature.

F I G U R E 7
The beam-induced phase difference contrast in time-of-flight (ToF) angiography phase difference images is not enhanced by increasing the TE. The images were acquired with TEs of (A) 7.0, (B) 10.5, and (C) 14.0 ms at a fixed TR of 39.6 ms. Deviating from the default setting for ToF angiography acquisitions, phase encoding was applied along the central beam axis. The main phantom was irradiated at 207 MeV beam energy and 16 nA current.

F I G U R E 8
The

Confirmation of the presence of buoyant convection
Phase difference images acquired using the Venc sequence with a fixed VENC parameter of 5 mm/s showed a linearly increasing mean phase difference in the Bragg peak region with increasing beam current ( Figure 9A-C). The velocities estimated from these images were 0.5, 0.9, and 1.4 mm/s for beam currents of 1, 2, and 4 nA, respectively ( Figure 9D).

MRI-based enhancement of convection-induced phase difference contrast
At a fixed beam current of 8 nA, Venc phase difference images showed an increase in phase difference contrast with decreasing VENC parameter ( Figure 10A-I). After the linearization of the inversely proportional relation of phase difference and VENC parameter, the inverse of the mean phase difference in the Bragg peak region was found to decrease approximately linearly with decreasing VENC parameter ( Figure 10J). The corresponding velocity estimates ranged from 8.8 to 2.7 mm/s for VENC parameters between 28 and 5 mm/s, respectively.

3.1.6
Model-based estimation of the convection velocities Based on the 38 mm FWHM beam diameter estimate at Bragg peak depth, a beam radius of 19 mm was used as

F I G U R E 9
The beam-induced phase difference shifts in Venc phase difference images and the corresponding velocity estimates increase with increasing beam current. Successive irradiations were performed with a 207 MeV proton beam at currents of (A) 1, (B) 2 and (C) 4 nA. All phase difference images were cropped to within the phantom borders. (C) The red and blue rectangular ROIs were used for the determination of the mean phase difference in the Bragg peak and background phase difference correction, respectively. (D) The mean phase differences in the Bragg peak (red scale) and the corresponding mean velocity estimates in the Bragg peak (purple scale) show a linear dependence on beam current. The error bars represent the standard deviation of the phase difference values within the Bragg peak and the propagated error in the velocity estimates, respectively. the input parameter for the sphere radius in the Stokes' viscosimeter model. The initial water temperature T 0 was measured to be 28 • C ± 1 • C. The resulting instantaneous convection velocities after the 26 s irradiation interval, corresponding to the time point of the acquisition of the central lines of k-space, were estimated to be 0.3, 0.7, 1.5, and 3.0 mm/s for 1, 2, 4, and 8 nA beam current, respectively.

DISCUSSION
The exploitation of the full potential of particle therapy in delivering highly conformal external beam radiation dose distributions to the tumor volume is still hampered by several sources of treatment uncertainties, particularly by those related to the limited ability to localize the Bragg peak during dose delivery. 21 Beam range uncertainties are currently accounted for by the addition of safety margins of ∼3% of the nominal range plus 2 mm, 22 which impairs the dose conformality. Consequently, appropriate methods for monitoring the actual beam range or the dose distribution delivered during treatment are much needed. Existing non-invasive techniques to obtain such feedback on-line either detect heat-induced pressure waves 23,24 or secondary radiation. 25,26 Both methods, however, lack the capability of extracting the beam characteristics of interest from images concurrently showing the patient anatomy.
Off-line MRI has been used to assess the beam range in post-treatment anatomical images of irradiated tissue, 27,28 but in turn lacks on-line capability. Because in-beam MRI may have the capability to overcome the above limitations, the consequential next step in the assessment of methods for particle beam range monitoring is to test its capability for the on-line detection of beam-induced effects in anatomical images.
With the increasing clinical availability of MR-Linac devices, MRI has already demonstrated its capabilities for the on-line verification of volumetric photon beam dose distributions in polymer and Fricke-type gel phantoms. 29,30 Moreover, the photon beam of an MR-Linac has recently been visualized during the irradiation of oxygen-enhanced liquid water phantoms based on oxygen depletion. 14 All these MRI methods rely on chemical reactions with radicals formed as a consequence of the radiation hydrolysis of water, leading to detectable changes in the MR relaxation times. Although these achievements have been made in the field of MRI-based photon beam detection, they are indicative of the potential of in-beam MRI for visualization of proton and heavier particle beams, as substantial overlap in the underlying mechanisms can be expected.
After the first prototype in-beam MRI scanner at a proton beamline became operational, 5 the feasibility of MRI-based visualization of proton beams stopping in liquid phantoms was first demonstrated using a series of gradient echo-based MRI pulse sequences. [6][7][8][9] Furthermore, this magnitude signal-based method showed potential for proton beam range verification in water-filled phantoms readily available in the radiation oncology clinics. The main limitation precluding its application to routine geometric beam QA, however, remains the high dose levels required for gradient echo-based beam detection resulting in unacceptable levels of phantom radiation activation. Moreover, because the emergence of the observed beam-induced hypointense MRI magnitude signatures showed a clear dependence on convection, 9 this particular method is unlikely to be transferable to tightly compartmentalized tissue where flow effects are restricted. Consequently, exploiting the versatility of MRI, novel ways of MRI-based proton beam visualization require exploration to ultimately enable the detection of beam-induced effects at clinically acceptable

F I G U R E 10
The beam-induced phase difference shifts in Venc phase difference images increase with decreasing VENC parameter. (A-I) The Venc images were acquired during 207 MeV proton beam irradiation at 8 nA beam current with VENC parameter values decreasing from 44 to 5 mm/s. (A) The red and blue regions of interest (ROIs) enclose the voxels assessed for the determination of the mean phase difference in the Bragg peak and the background phase difference correction, respectively. All images were cropped to within the phantom dimensions. (J) The VENC parameter-dependent mean phase difference in the Bragg peak (red) and the corresponding mean velocity estimates in the Bragg peak (purple) were analyzed quantitatively, the mean phase difference values being inverted for linearization purposes. The red and purple error bars represent the errors in the inverted phase difference and the velocity values, respectively, propagated from the phase difference standard deviation determined in the Bragg peak ROI.
dose levels under the flow-restricted conditions found in vivo.
In this study, a new approach to MRI-based proton beam visualization was explored by investigating possible changes in the MRI phase signal during irradiation. Such changes had not been assessed in previous studies, which so far, focused exclusively on the MRI magnitude signal-based detection of both photon and proton beam irradiation effects. For the first time, clear beam-induced signatures in ToF angiography phase difference images acquired during proton beam irradiation of liquid water phantoms were observed. This convincingly demonstrates the feasibility of MRI phase signal-based proton beam visualization. The observed beam-induced signatures in the ToF angiography phase difference images were comparable in position and shape to the hypointense beam signatures observed in the ToF angiography magnitude images, both resembling the corresponding dose distribution of the proton pencil beam. Moreover, energy-dependent changes in the residual proton beam range detected in phase difference and magnitude images were found to be of similar magnitude. Therefore, despite potential differences in sensitivity, both methods can be expected to have similar geometric potential for applicability in proton range verification. 8 The beam-induced effect responsible for the emergence of the phase difference contrast in the ToF angiography images was subsequently unraveled in a series of experiments testing the time and flow dependence of these beam-induced signatures. In the first experiment, beam-induced phase difference signatures were found to be still visible several seconds after the irradiation terminated, which excludes a transient beam-induced magnetic field perturbation to cause the observed phase difference contrast. This is supported by a simulation study assessing the magnetic field induced by a cylindrical proton beam of 150 MeV, demonstrating that the temporal profile of such a perturbing magnetic field closely follows the shape of the irradiation pulse with a delay in the order of nanoseconds. 12 Moreover, there is no congruence between the experimentally observed MRI phase difference signatures acquired during or after irradiation and the shape of this calculated beam-induced magnetic field. Finally, the calculated beam-induced magnetic field strengths over relevant distances 12 were orders of magnitude below the detection threshold of low-field MRI, although the calculations were performed for beam currents three orders of magnitude higher than the ones used in our study. This further supports the absence of visible beam-induced magnetic field perturbation effects in our experiments. In the second experiment, no changes in phase difference contrast were observed under variation of TE. Consequently, because of the established proportionality of susceptibility-induced phase difference shifts to TE, 31 the emerging phase difference contrast cannot be explained by locally altered magnetic susceptibility secondary to radiochemical changes in radical 13 or oxygen concentrations. 14 Furthermore, this observation confirms that the previously excluded influence of a beam-induced perturbation of the magnetic field, which would also act throughout TE, does not cause the observed phase difference contrast. In the third experiment, on the contrary, the observed phase difference contrast was found to be sensitive to phantom changes that restricted beam-induced convection. Although a beam-induced signature of phase difference was clearly observed under irradiation of free-floating water at ambient temperature where convection was allowed to develop, no beam-induced phase difference shift occurred when the experiment was repeated in a foam-filled water phantom in which convection was mechanically restricted. 32 Similarly, exploiting the very small volumetric thermal expansion coefficient of 1.14 × 10 −5 K −1 at 5 • C water temperature relative to 2.87 × 10 −4 K −1 at 28 • C, 19 beam-induced phase difference contrast was well visible at 28 • C water temperature, whereas it remained undetectable at 5 • C where the onset of convection was inhibited. 20 These findings are a strong indication that the observed ToF angiography phase difference contrast is dependent on the onset of convection. However, the underlying MRI contrast mechanism remains unresolved because of several peculiarities of the technical implementation of the ToF angiography sequence applied in this study, such as its non-deselectable first-order flow compensation and its non-functional RF spoiling that complicate the qualitative and quantitative interpretation of phase difference effects induced by bulk flow (see Figures S2 and S3).
Based on the convection dependence of the beam-induced signatures observed in the ToF angiography phase difference images, it was then hypothesized that Venc MRI could be used to probe the presence of buoyant flow. Therefore, the influence of beam current variation on the observed Venc phase difference contrast at fixed motion sensitivity of the pulse sequence was tested. This experiment showed that the mean phase difference in the Bragg peak and the corresponding velocity estimates increased linearly with increasing beam current. This observation is consistent with the modified Stokes model used for the estimation of convection velocities predicting approximately linearly increasing velocities with increasing beam current. Inevitably, other dose-and dose rate -dependent quantities influencing the MRI phase difference, namely phantom temperature and magnetic susceptibility, have also changed during this experiment. However, no confounding influence was expected because the anticipated corresponding phase difference changes were at least one order of magnitude below the observed phase difference contrast (see Supporting Information).
An increase in the cross-plane motion sensitivity of the Venc sequence led to increased observed beam-induced phase difference shifts at fixed irradiation settings, demonstrating the feasibility of the Venc MRI-based enhancement of convection-induced phase difference contrast. The inversely proportional relationship between the phase difference and VENC parameter 15 was sufficiently reflected in the experiment, with small deviations because of phase difference inhomogeneities in the ROI used for background zeroing.
The cross-plane velocities of 0.5, 0.9, 1.4, and 2.7 mm/s estimated from the Venc images with a VENC parameter of 5 mm/s for beam currents of 1, 2, 4, and 8 nA, respectively, are in good agreement with those estimated using the modified Stokes model being 0.3, 0.7, 1.5, and 3.0 mm/s, respectively. Both results, however, can only be interpreted as an order of magnitude estimate. The Venc-based velocity estimates may have been affected by phase difference offsets as well as by higher order 33 and in-plane motion. 34 The uncertainty in the velocity estimates obtained by the modified Stokes model was likely dominated by the simplifications made rather than by the small uncertainties associated with the measurement of the input parameters. Yet, it remains an open question why the phase difference shifts observed at the higher VENC parameter values are considerably larger than those expected for the estimated velocities (see Table S2).
The identified convection origin of the proton beam-induced signatures in the ToF angiography phase difference images precludes the translation of this particular method to the flow-restricted situation in vivo, thereby limiting its applicability to geometric beam QA with liquid phantoms. However, the feasibility of the enhancement of convection-induced phase difference contrast by Venc imaging could be successfully demonstrated. In the formerly studied ToF angiography, magnitude signal-based visualization of effects of beam-induced convection, a detection threshold of 8 nA beam current and 270 Gy integral Bragg peak dose was reported. 8 In comparison, phase signal-based visualization of convection effects using the Venc sequence allowed the detection of beam signatures of similar quality already at 2 nA and 52 Gy. Although this fivefold gain in sensitivity is a substantial achievement, further sensitivity improvement would be desirable for the method to be routinely used for clinical QA purposes. This could be achieved through simple spin echo-based Venc sequences that can recover signal losses because of magnetic field inhomogeneities or through more advanced MRI phase contrast pulse sequences originally developed for measuring flow velocities on the order of mm/s and μm/s in porous media 35 or natural convection, 36 respectively. However, the achievable VENC parameter values will always be limited by the maximum gradient strengths available on the MRI system. These are currently confined by the limited capabilities of the bi-planar gradient coils used in low-field open MRI whole-body scanners, 37 which make good in-beam MRI scanners in particle beam therapy because they provide sufficient flexibility for beam access at low levels of beam deflection. 38 Moreover, although considered negligible for maximum gradient strengths of 40 mT/m typically implemented in clinical scanners, potential adverse effects on beam spread of gradient strengths exceeding these by an order of magnitude 35,36 would require reassessment. 39

CONCLUSIONS
This experimental study has demonstrated the feasibility of MRI phase signal-based proton beam visualization in liquid water phantoms. The beam-induced signatures observed in ToF angiography phase difference images of the stopping proton beam were identified to be evoked by beam-induced buoyant convection rather than by beam-induced magnetic field perturbations or by radiochemical changes in magnetic susceptibility. Consequently, this method will not be applicable in tightly compartmentalized tissue, as fluid flow effects are restricted therein. Nevertheless, Venc imaging has demonstrated to enhance the detection sensitivity for beam-induced convection, making it a promising candidate for the future development of MRI-based methods for water phantom-based geometric proton beam QA.

SUPPORTING INFORMATION
Additional supporting information may be found in the online version of the article at the publisher's website.
Appendix A: Estimation of buoyant convection velocities Appendix B: ToF angiography pulse sequence Appendix C: Venc pulse sequence Figure S1: Force diagram of a sphere immersed in water. Figure S2: Modified versions of the ToF angiography pulse sequence without (left), with first order (middle), and with second order (right) flow compensation in slice select direction were used to acquire images during 207 MeV beam energy and 8 nA current irradiation at a TE/TR of 9/29.4 ms. No flow compensation was applied in phase and frequency encode direction. Figure S3: ToF angiography phase difference images acquired during proton beam irradiation at 207 MeV beam energy and 16 nA current. At a TE of 7 ms, images were acquired at TRs of 19.2, 29.4, 49.8 and 60.0 ms (left to right). Table S1: Definition of variables and parameters.