MRI magnitude signal-based proton beam visualisation in water phantoms reflects composite effects of beam-induced buoyant convection and radiation chemistry

Objective. Local magnetic resonance (MR) signal loss was previously observed during proton beam irradiation of free-floating water phantoms at ambient temperature using a research prototype in-beam magnetic resonance imaging (MRI) scanner. The emergence of this MR signal loss was hypothesised to be dependent on beam-induced convection. The aim of this study was therefore to unravel whether physical conditions allowing the development of convection must prevail for the beam-induced MRI signatures to emerge. Approach. The convection dependence of MRI magnitude signal-based proton beam visualisation was investigated in combined irradiation and imaging experiments using a gradient echo (GE)-based time-of-flight (ToF) angiography pulse sequence, which was first tested for its suitability for proton beam visualisation in free-floating water phantoms at ambient temperature. Subsequently, buoyant convection was selectively suppressed in water phantoms using either mechanical barriers or temperature control of water expansivity. The underlying contrast mechanism was further assessed using sagittal imaging and variation of T1 relaxation time-weighting. Main results. In the absence of convection-driven water flow, weak beam-induced MR signal changes occurred, whereas strong changes did occur when convection was not mechanically or thermally inhibited. Moreover, the degree of signal loss was found to change with the variation of T1-weighting. Consequently, beam-induced MR signal loss in free-floating water phantoms at ambient temperature does not exclusively originate from buoyant convection, but is caused by local composite effects of beam-induced motion and radiation chemistry resulting in a local change in the water T1 relaxation time. Significance. The identification of ToF angiography sequence-based proton beam visualisation in water phantoms to result from composite effects of beam-induced motion and radiation chemistry represents the starting point for the future elucidation of the currently unexplained motion-based MRI contrast mechanism and the identification of the proton beam-induced material change causing T1 relaxation time lengthening.


Introduction
The full technical integration of magnetic resonance imaging (MRI) with proton therapy (PT) is expected to improve the latter's targeting accuracy and precision, especially for moving tumours and non-stationary healthy tissues surrounding the tumour (Oborn et al 2017. Besides providing real-time anatomical images for improved target localisation, in-beam MRI was hypothesised to have the potential to visualise the therapeutic proton beam during dose delivery. Such direct, non-invasive feedback on the delivered proton beam range and dose distribution on images simultaneously showing the patient anatomy would be invaluable for treatment verification and adaptation. Therefore, the feasibility of MRI-based proton beam visualisation was experimentally assessed once the technical combination into a first research prototype in-beam MRI scanner was achieved (Schellhammer et al 2018).
Initial proof-of-principle studies demonstrated the feasibility of the MRI-based visualisation of a stopping proton beam in water (Schellhammer 2019, Schellhammer et al 2020. During simultaneous irradiation of a water-filled phantom at ambient temperature, spatial signatures of beam-induced local MR signal loss were reported for different gradient echo (GE) sequence-based coronal, i.e. horizontal, image acquisitions. The observation that high doses and fluid-filled phantoms were required for MRI-based proton beam visualisation to be feasible led to the hypothesis that the emergence of the local MR signal loss depends on beam-induced buoyant convection. More precisely, it was hypothesised that the dose deposition by the beam induces local heating and thermal expansion which results in a local decrease in water density, causing an upthrust (i.e. buoyancy) of water molecules. The induced coherent and incoherent motion in turn leads to the emergence of local MR signal loss within the beam volume.
Moreover, a first study on the successful MRI-based visualisation of photon beams in aqueous phantoms conducted on a 0.35 T hybrid MRI linear accelerator device (MR-Linac) has been published (Wancura et al 2023). The beam-induced MR signal loss observed in their images acquired using an inversion recovery-spin echo pulse sequence under 80 Gy photon irradiation of phantoms with enhanced initial oxygen concentration or enhanced coumarin-mediated oxygen consumption was attributed to radiochemical oxygen depletion and a concurrent local lengthening of the water T1 relaxation time. This first publication of an MRI contrast mechanism explaining the observed signal loss obviously poses the question whether there is overlap in the underlying contrast mechanisms of MRI-based x-ray and proton beam visualisation.
So far, the convection hypothesis as well as the potential influence of a proton beam-induced change in water T1 relaxation time lacked experimental assessment. Yet, the identification of the beam-induced effect required for the MRI signatures to emerge would represent the crucial first step in the elucidation of the actual MRI contrast mechanism responsible for the observed signal loss. The sound understanding of this contrast mechanism should allow the development of dedicated MRI pulse sequences for proton beam visualisation with enhanced sensitivity for the contrast-determining beam-induced effect, based on which a more comprehensive assessment of this method's potential should be made possible.
The aim of the present study was therefore to experimentally assess whether the emergence of local MR signal loss within the beam volume during proton beam irradiation of free-floating water phantoms at ambient temperature depends solely on convection or whether a local change in T1 relaxation time also contributes to the observed MR signal loss. For this purpose, convection was inhibited by either the introduction of different physical barriers into water-filled phantoms (Domen et al 1991) or by phantom temperature control, exploiting the temperature dependence of the thermal volumetric expansion coefficient of water (Schulz and Weinhous 1985). Moreover, sagittal imaging, i.e. the acquisition of vertical slices parallel to the central axis of the beam, was used to further characterise the beam-induced signatures and flip angle variation was used to vary the T1-weighting of the beam visualisation images. In order to enhance the negative beam contrast observed in the proof-of-principle study (Schellhammer 2019), a GE-based time-of-flight (ToF) angiography MRI pulse sequence based on the principle of flow saturation Ehman 1987, Ehman andFelmlee 1990) was selected for the present study. This sequence was first thoroughly tested for its ability to visualise beam currentand energy-dependent effects in a baseline experiment before it was used to test the contrast hypotheses.

Materials and methods
2.1. Experimental setup A C-shaped open MRI scanner (MrJ2200, ASG Superconductors S.p.A., Genoa, Italy) with a vertically upwards oriented static magnetic field B 0 of 0.22 T generated by a Nd 2 Fe 14 B permanent magnet was combined with a horizontal research beamline at the University Proton Therapy Dresden facility, that is based on an isochronous cyclotron (C230, Ion Beam Applications SA, Louvain-la-Neuve, Belgium). The scanner was enclosed by an openable Faraday cage made of plywood panels cladded with copper sheets (figure 1(a)) in order to shield it from external radiofrequency (RF) sources originating from the proton therapy facility. More detailed information on this prototype in-beam MRI scanner has been published by Schellhammer et al (2018). The scanner was first positioned at the horizontal research beamline under longitudinal alignment of the magnetic and beam isocentres, i.e. along the beam's central axis. Subsequently, it was displaced off-axis by 13 mm to the right in beam's eye view to assure that a deflected 200 MeV proton beam would centrally impinge on a phantom positioned centrally at the magnetic isocentre. A sheet of radiochromic EBT3 film (Gafchromic EBT3, Ashland, Wilmington, Delaware, USA) attached vertically to the phantom was used to visually confirm that the beam was impinging on the proximal phantom surface. The beam entered the Faraday cage through a window covered with a 120 μm thick copper foil and subsequently traversed a 20 cm long cylindrical polymethyl methacrylate (PMMA) range degrader before it was stopped within the phantom volume. The distal end of the PMMA cylinder was located 15 cm in front of the proximal phantom surface ( figure 1(b)). The use of this range degrader was mandatory to ensure that the residual ranges of the high-energy proton beams were limited to the dimensions imposed by the phantom sizes.

MRI phantoms
A first phantom consisting of a tap water-filled high-density polyethylene (HDPE) container with nominal outer dimensions of 100 × 100 × 65 mm 3 and a wall thickness of 1 mm was used for the baseline experiments testing the MRI pulse sequence's general ability to visualise the beam and for the sagittal imaging and T1 variation experiments (figure 2(a)). Identical containers were used to accommodate different inserts to serve as MRI phantoms for the mechanical inhibition of convection. In order to enable the selective mechanical inhibition of convection in selected parts of a second phantom, the first phantom was further compartmentalised using a 15 mm thick PMMA insert featuring a matrix of 7 × 7 − 1 vertical tubes each having a 10 mm diameter (figure 2(c)). A vertically centred, reproducible positioning of this insert was assured using a set of four small plastic legs in the lower corners of the container. The upper left tube was omitted to allow reproducible positioning of the flow restriction plates and to facilitate orientation in the images. For the selective inhibition of convection-induced flow in every second tube, two additional complementary chequerboard patterned 1 mm thick perforated plate inserts were used (figures 2(d)-(e)). These flow restriction plates could be interchangeably placed on top of the tube insert in the second phantom. Additional information on this second phantom has been published by Gantz (2022). To build the third phantom, another such container was filled with an insert of wet floral foam (GLOREX AG, Füllinsdorf, Switzerland) cropped to the inner dimensions of the phantom container for isotropic and fine-meshed restriction of macroscopic water mobility (figure 2(b)). The water volume within this third phantom was reduced by the foam insert by approximately 3%. For the temperaturecontrolled suppression of convection, a fourth phantom was developed comprising an air-insulated plastic bottle filled with free-floating water that provided sufficient thermal stability over the time span of the experiment, limiting phantom warming to 0.1 K min −1 . The nearly cylindrical plastic bottle with an upper and lower diameter of 9.5 and 9.0 cm, respectively, a length of 20.5 cm and a wall thickness of 1 mm was filled with tap water, cooled down and put into an air-filled, heat-insulating polypropylene container with 2 mm wall thickness (figure 2(f)). Small pieces of polystyrene were used to fixate the bottle inside the insulating shell The Faraday cage was opened for illustrative purposes (a). After entering the Faraday cage, the proton beam first traversed the 20 cm thick PMMA range degrader so that it was stopped inside the water-filled phantom. The coronal MRI slice acquired intersected the beam horizontally. The beam axis and the MRI slice were both perpendicular to the direction of the static magnetic field B 0 (b). Phase encoding was predominantly performed perpendicular to the beam axis for coronal images (c).
ensuring that the bottom surfaces facing the proton beam were aligned and that the contact surface of the bottle and the surrounding air-filled container was minimised. For all experiments, the phantoms were centrally positioned in the knee receiver coil placed at the MRI isocentre supported by specifically designed holders. EBT3 film was fixed vertically at the proximal end of the respective phantoms to visually confirm that the beam was impinging on the phantoms.
2.1.2. EBT3 film depth-dose measurement and film evaluation The depth-dose measurement in EBT3 film was performed using a PMMA phantom consisting of two filmenclosing parallel plates angled by 1°relative to the horizontal plane. The 40 ms irradiation at 207 MeV beam energy and 32 nA current was performed at the phantom position indicated in figure 1(b). The EBT3 films (batch number 04181701 and 11192002) were calibrated for clinical proton fields using the red colour channel (Beyreuther et al 2019) and scanned with a flat-bed document scanner (Expression 11000XL, Epson America, Long Beach, CA, USA) in landscape orientation, transmission mode, 24-bit colour mode at a resolution of 300 dpi. The film evaluation was performed using in-house developed software.

Dose rate calibration
To estimate the dose delivered to the phantom during the irradiation experiments, the beam current was calibrated to the dose rate measured at 207 MeV using a cylindrical plane-parallel ionisation chamber with 2.5 mm radius, 1 mm electrode distance and a sensitive volume of 0.02 cm 3 (Advanced Markus ® Chamber Type 34045, PTW Freiburg GmbH, Freiburg, Germany) attached to the proximal surface of the first phantom. The position of the chamber was marked in blue on the container surface ( figure 2(a)). The beam current setting was varied between 0.5 and 64 nA, with irradiation times ranging from 30 to 5 s, respectively. The integral dose readings were normalised to the irradiation time yielding an estimate of the dose rate at the phantom surface. Recombination effects were negligible (Beyreuther et al 2019).

MRI pulse sequence
The choice of the MRI pulse sequence was motivated by three different requirements. Firstly, the pulse sequence had to be sensitive enough to detect the beam-induced MRI signature. Secondly, a short overall sequence duration was desired in order to limit phantom activation by minimising the total irradiation times required at a fixed beam current. Thirdly, the sequence should ideally be able to intensify the visibility of convection effects in the resulting images. Consequently, a fast GE-based 2D ToF angiography sequence based on the principle of flow saturation Ehman 1987, Ehman andFelmlee 1990) was chosen that pre-saturates the magnetisation of the spins in a slab located below the imaging volume. With a convection-driven influx of presaturated signal into the imaging slice, the signal loss observed within the beam volume in the previous proof-of- Figure 2. MRI phantoms. For the baseline experiments, the first phantom (a) was used, filled with tap water and closed with a lid. The equally-sized but water-soaked foam-filled container (b) was used for the isotropic and fine-meshed restriction of convection of water. A foam sample and a metric ruler were placed in front of this third phantom to illustrate the pore sizes. To assemble the second phantom, the tube insert (c) was put into the phantom container (a) and the flow restriction plates in either (d) or (e) were used for the selective mechanical inhibition of convection-induced flow in every second tube. Temperature-controlled experiments were performed using phantom number four, the air-insulated water-filled flask shown in (f).
principle study (Schellhammer 2019) was expected to be further intensified. A short echo-time was preferred to minimise signal losses from phase dispersion. The main image plane was chosen perpendicular to the expected flow direction to achieve maximum flow saturation effects in the imaged slice.
For the majority of experiments, single slice images intersecting the beam volume horizontally in the central coronal plane were acquired using a flow-compensated ToF angiography sequence (TE = 7 ms, TR = 19.2 ms, flip angle = 60°, number of excitations = 1, slice thickness = 10 mm, FOV container = 180 × 180 mm 2 , FOV flask = 240 × 240 mm 2 , samples container = 152, samples flask = 224, encodings container = 164 or 167, encodings flask = 203, dummy scans = 3, total scan duration container = 3 s, total scan duration flask = 4 s). The 40 mm thick presaturation band was located below the imaging slice, separated by a 10 mm gap. Sagittal images centrally intersecting the irradiated volume were acquired using the same pulse sequence parameters. The DICOM data used for display had an in-plane resolution of 0.55 × 0.79 mm 2 and 0.59 × 0.71 mm 2 for the container and flask phantom acquisitions, respectively. Image analysis was performed using Python 3.8 scripts.

Baseline experiments
In order to examine whether the ToF angiography sequence is sensitive enough to detect the beam-induced MRI signature and can visualise beam current-and energy-dependent effects, a baseline experiment was performed in free-floating water at ambient temperature using the first phantom. In the irradiation protocol designed, irradiation and imaging were synchronised manually using a stopwatch. The proton beam irradiation was started 15 s prior to image acquisition and was set to a total irradiation duration of 20 s to allow for a dose buildup in the water phantom before imaging. Since the ToF angiography sequence had a total duration of 3-4 s, it terminated 2-1 s before the end of irradiation, respectively. The coronal MRI slice position was determined relative to the vertical extent of the phantom using the irradiated radiochromic film fixed to the proximal phantom surface as a reference for the vertical beam position. The baseline experiment was performed using proton beam energies of 200, 207 and 215 MeV and proton beam currents of 8, 16, 32 and 64 nA. Furthermore, images without simultaneous irradiation were acquired for reference purposes.

Prediction of the residual proton beam ranges
Previous investigations at our facility have shown that the nominal energies, E , N used for beam energy setting on the operator console of the horizontal proton research beamline cannot be directly converted to accurate residual ranges using one of the standard libraries such as PSTAR (Schellhammer 2019). Consequently, for the residual ranges in water, R , w representing the starting values for all subsequent calculations of the residual ranges in the MRI phantom, R , predict the results of preceding internal range calibration measurements were used (Wohlfahrt et al 2018, Schellhammer 2019. For the actual prediction of the residual proton ranges in the MRI container phantom, all materials in the beam path between the beam exit window and the water inside the phantom were taken into account. This included the 120 μm thick copper foil of the beam entry window of the Faraday cage, the 20 cm thick PMMA range degrader, about 80 cm of air and the 1 mm thick HDPE phantom wall. The resulting range-in-water losses in air, R , where S m /r ( ) is the mean mass stopping power of protons, m r the mass density and t m the thickness of the respective material, S w /r ( ) and w r being the respective water quantities. For both air and copper, the thin approximation of radiative transfer was applied (Zhang and Newhauser 2009). Hence, single values from PSTAR for the initial proton beam energy, E 200 MeV, 0 = were used instead of mean mass stopping powers. The corresponding mass stopping power values S/r were 3.976 and 3.042 (MeV cm 2 ) g −1 for air and copper, respectively, compared to a mass stopping power of liquid water of 4.492 (MeV cm 2 ) g −1 at 20°C. The mass densities were estimated as 1.19 g cm , r = for PMMA, air, copper and water, respectively. For the simplicity of calculation, the 1 mm HDPE phantom wall thickness was approximated by 1 mm of PMMA. The range loss in water for the resulting total material thickness of PMMA of 20.1 cm, R , PMMA D was estimated using a water equivalent path length (WEPL) of 1.1593 ± 0.007 that was experimentally determined for clinical quality assurance (QA) purposes at our facility. The residual ranges in water within the phantom were calculated as The overall uncertainty originating from setup uncertainties and approximations was estimated to be 2 mm. R predict D refers to predicted residual range differences between the distal beam edge positions of different beam energies. The uncertainty estimates for the residual range differences were obtained by doubling the respective residual range uncertainty values as a worst case estimate assuming fully random error.

Measurement of the residual proton beam ranges in the MR images
The MR image-based residual beam ranges, R , MR were measured by first calculating the mean central image intensity profile by averaging over 10 central line profiles in the MR images (figure 5(e)). In a next step, a grey value threshold of 600, representing the lower limit of the water signal intensity under reference conditions, was applied to the mean central profile (figure 5(f)). Subsequently, the shift of the position of this threshold transgression relative to that coincident with the proximal phantom boundary in a reference image acquired in absence of irradiation was calculated. The uncertainty for R MR was estimated to be 3 mm, accounting for image resolution and averaging of grey values. R MR D refers to the measured residual range differences for different beam energies. These range differences are considered more relevant for the comparison of predicted and measured results because the range difference analysis reduces the influence of systematic uncertainty components in calculation and measurement, which is especially relevant for the large systematic uncertainty inherent in the definition of the applied grey value threshold.

Estimation of the convection velocities
Dose deposition is known to lead to an increase in water temperature (Renaud et al 2020). This local increase in temperature, T, D induced per gray proton beam irradiation can be expressed as T D c 0.24 mK Gy , , r D which can be calculated as e 1 , ) where T 0 and T 1 are the water temperatures in the depth-dose plateau region before and during irradiation, respectively, and G is the corresponding temperature-dependent volumetric coefficient of thermal expansion. Consequently, the heated and expanded volume experiences a buoyancy force resulting in a local upthrust of the heated water molecules as described by Stokes' viscosimeter model. Under the assumption that this heated volume is spherical and the flow laminar, the net upward force F N acting on the sphere is given by is the volume of the sphere with radius R, g 9.81 m s 2 / = is the gravitational acceleration, )and the exponential integral function Ei. The input parameters D,  T 0 and R were determined in the experiment. A more detailed derivation of equations (1) and (2) can be found in the supplementary material provided.

Contrast experiments
In a first experiment, the influence of the choice of the pre-saturation slab position on the observed MR signal loss was assessed because the inflow of pre-saturated spins into the imaged slice could lead to signal loss. The hypothesis that the emergence of the local MR signal loss observed under simultaneous proton beam irradiation of free-floating water at ambient temperature depends on beam-induced convection was tested in independent experiments by suppression of convection using methods established in the field of water calorimetry. While the development of convection-induced flow was inhibited using mechanical barriers (Domen et al 1991) in the second and third experiments, the volumetric expansion of water under beam-induced energy deposition, representing the initial step in the development of thermal convection, was suppressed by phantom temperature control (Schulz and Weinhous 1985) in a fourth experiment. Furthermore, the appearance of the beam-induced MRI signatures was assessed in sagittal images. A potential contribution of a local change in T1 relaxation time to the observed MR signal loss was tested by flip angle variation. All experiments were performed using the same irradiation protocol as described in section 2.3. for the baseline experiments.
2.4.1. Assessment of the influence of the pre-saturation slab position In order to experimentally assess the influence of pre-saturation on the MR signal loss observed within the beam volume, the baseline experiment testing the beam current dependence of the beam-induced signature was repeated using a beam energy of 207 MeV and currents of 8, 16, 32 and 64 nA. In contrast to the initial baseline experiment, the 40 mm thick pre-saturation slab was now located above the imaging slice, separated by a 10 mm gap. Images at 64 nA beam current were acquired twice, with the pre-saturation slab located below and above the imaging slice to allow for a direct comparison.

Assessment of the influence of the spatially selective mechanical inhibition of convection
In the second experiment, firstly, a reference image of the tube phantom with all tubes opened was acquired without irradiation, before additional images were acquired under simultaneous proton beam irradiation using energies of 200, 207 and 215 MeV at a constant beam current of 64 nA. In order to investigate the effect of spatially-selective mechanically-inhibited convection on the beam-induced signature in the MR image, the full experiment was repeated twice, realising selective inhibition of flow in every second tube by putting either of the two flow restriction plates, A or B, on top of the tube insert. All data were acquired in water at ambient temperature. Contours of the lateral and distal edges of the beam were obtained by applying median filtering and canny edge detection to the images acquired under 32 nA irradiation at beam energies of 200, 207 and 215 MeV in the baseline experiments and were overlayed on the MR images for visual guidance to localise the beam. The occurrence of artefacts possibly arising from counterflow effects in the images acquired at 64 nA beam current precluded their use for automated beam contour determination.

Assessment of the influence of the isotropic mechanical inhibition of convection
To investigate the effect of isotropic, fine-meshed restriction of convection on MRI-based proton beam visualisation in liquid water at ambient temperature, this third experiment was performed twice, without (first phantom) and with (third phantom) the water-soaked floral foam insert in the tap water-filled container. A proton beam energy of 207 MeV and a current of 64 nA were used. Images were acquired before, during and immediately after irradiation. Following the exchange and accurate repositioning of the phantom container between both runs of the experiment, the geometry parameters for imaging were copied from the image acquired without foam insert in order to assure that the beam volume was still captured when the foam insert was in place. The correct slice positioning was verified using a 3 cm long cylindrical MRI fiducial marker (MR Spot ® 121, Beekley Medical, Bristol, Connecticut, USA) positioned horizontally at equal height relative to the bottom surface of both equally-sized phantom containers.

Assessment of the influence of the temperature-controlled inhibition of convection
The fourth experiment included temperature-controlled convection inhibition using an air-insulated tap waterfilled flask phantom (figure 2(f)). All temperature measurements were performed using a digital thermometer (GTH 175 PT, GHM Messtechnik GmbH, Regenstauf, Germany) after shaking the bottle thoroughly. Without its insulating shell, the phantom was put into the freezer to cool the water to below 3.5°C but preventing freezing. The phantom was taken out of the freezer after falling below the temperature threshold. When the phantom temperature reached 3.5°C, the phantom was enclosed by the insulating shell and immediately put into the MRI scanner. The total time required to obtain a scout image for calibration, ToF angiography images for positioning and two more ToF angiography images, one without and one with simultaneous irradiation at a proton beam energy of 207 MeV and a current of 64 nA, was 15 min. In order to enable the comparative assessment of the influence of the lowered phantom temperature on the visibility of the beam-induced signature, the combined imaging and irradiation experiment was repeated after the phantom had assumed the ambient temperature of the scanner overnight. Temperature measurements at both irradiation timepoints were obtained in a similar, but unirradiated phantom. The uncertainty of these phantom temperature estimates during both irradiations resulting from measurement errors and differences in the treatment of both, irradiated and unirradiated phantoms, were estimated to be 1°C.

Assessment of sagittal beam visualisation
To assess the appearance of the beam-induced MRI signatures in the sagittal plane, sagittal images were acquired during irradiation of the first phantom with 207 MeV protons at beam currents of 16, 32 and 64 nA. A reference image was also acquired. Phase encoding was performed parallel to the beam's axis.
2.4.6. Assessment of the influence of flip angle variation on MR signal loss To assess the effects of flip angle variation on the observed beam-induced MRI contrast, coronal images were acquired during 207 MeV beam energy and 16 nA current irradiation of the first phantom with flip angles ranging from 10 to 90°.

Dosimetry and convection velocity estimates
The positioning of the centre of the beam relative to the crosshair on the proximal phantom surface, indicating the position of the ionisation chamber, as well as the sufficient coverage of the sensitive volume of this chamber by the beam, were verified using an EBT3 film attached to the proximal phantom surface. The results of the absolute dose evaluation of this film as well as any positional information on the co-localisation of the beam centre and the ionisation chamber centred on the phantom are shown in figure 3. The offset between the beam centre determined by a 2D Gaussian fit and the centre of the ionisation chamber, indicated by the crosshair transferred from the centred phantom surface markings, amounted to 1.2 and 2.4 mm in horizontal and vertical direction, respectively. The beam diameter's full width at half maximum (FWHM) of 22 mm enclosed the 2.5 mm radius measuring sensitive volume of the plane-parallel ionisation chamber and translated into a beam radius R of 11 mm at phantom entry. The initial water temperature T 0 was measured to be 28°C. A summary of the measured dose rates D  within the depth-dose plateau area of the beam, the corresponding absorbed doses D applied within 16.5 s, the concomitant changes in the physical properties of water, the net upward force and the resulting instantaneous convection velocities is given in table 1.

Baseline experiments
A beam-induced hypointense signature was clearly visible in the coronal ToF angiography images acquired under simultaneous proton beam irradiation of the free-floating tap water-filled first phantom ( figure 4(a)). The shape of the beam-induced signature closely resembled a planar proton pencil beam dose distribution ( figure 4(b)). Figure 5 shows the beam-induced signatures in the MR images acquired with the ToF angiography pulse sequence during simultaneous proton beam irradiation using different beam energies at a fixed beam current of Figure 3. Absolute dose evaluation of the EBT3 film attached to the proximal end of the first phantom, irradiated with a 207 MeV proton beam. The grey dashed lines represent the crosshair as marked on the phantom surface. The blue dashed rectangle encloses the area used for the 2D Gaussian fit for the beam centre determination, the centre being marked by the black cross. The FWHM beam diameter is indicated by the solid black circle. The red circle denotes the active measurement area of the plane-parallel ionisation chamber used for the beam current to dose rate calibration measurements. Table 1. Dosimetry results and dose-dependent changes in the physical properties of water resulting in buoyant convection. The beam current-dependent dose rates were measured within the depth-dose plateau area of the beam at phantom entry. The corresponding values for absorbed dose, temperature and density change, net upward force and instantaneous velocity all apply to the timepoint of mid-image acquisition at 16.5 s after the start of irradiation.

Beam current dependence of the beam-induced signature
The influence of beam current variation from 8 to 64 nA on the beam-induced MRI signature is displayed in figure 6. For a beam current of 8 nA, an elliptical region of hypointense signal appeared at the end of the beam range which developed into a distinct beam profile for higher current setting. The increase of the hypointense signal area observed with increasing beam current was more pronounced in lateral than in longitudinal direction but still amounted to a maximum profile range difference of 7 mm for the two extreme cases studied at 8 and 64 nA. At a beam current of 64 nA, a decrease in signal intensity surrounding the proximal beam signature occurred.

Contrast experiments 3.3.1. Assessment of the influence of the pre-saturation slab position
The ToF angiography images acquired with the pre-saturation slab located above the imaging slice (figures 7(a)-(e)) show signal loss within the beam volume comparable to the images obtained with pre-saturation applied below the imaged slice ( figure 6). For beam currents of 32 and 64 nA, the application of pre-saturation above the imaged slice seems to increase signal loss in the area surrounding the beam volume, though. A direct comparison of the application of pre-saturation above and below the imaging slice at 64 nA beam current (figures 7(e)-(f)) also shows no difference in the observable signal loss within the beam volume, but a slightly increased signal loss surrounding the proximal beam signature when pre-saturation is applied above the imaged slice.

Assessment of the influence of the spatially selective mechanical inhibition of convection
In a reference acquisition without irradiation, the water-filled tubes of the second phantom showed normointense MRI signals, whereas areas of signal void occurred in the intermediate regions occupied by PMMA ( figure 8(a)). Imaging under simultaneous irradiation using a constant beam current of 64 nA and different beam energies yielded images exhibiting the same beam energy-dependent local MR signal loss in water as observed in the baseline experiment (figures 8(b)-(d)). Spatially selective inhibition of convection by either of the two flow restriction plates A or B resulted in the absence of MR signal loss within the beam volume in the motion-restricted tubes, whereas signal loss persisted in the motion-unrestricted tubes (figures 8(e)-(f)). No

Assessment of the influence of the isotropic mechanical inhibition of convection
The isotropic restriction of convection in the third phantom containing water-soaked, fine-meshed floral foam resulted in the absence of a beam-induced MRI signature during irradiation at 64 nA beam current ( figure 9(b)).
In the coronal image acquired immediately after irradiation, however, very weak MR signal loss was observed (figure 9(c)).

Assessment of the influence of the temperature-controlled inhibition of convection
The irradiation of free-floating water at 5 ± 1°C in the fourth phantom resulted in very weak local MR signal loss within the beam volume compared to irradiation at an ambient temperature of 28 ± 1°C (figure 10).

Assessment of sagittal beam visualisation
Sagittal images acquired during simultaneous irradiation show beam-induced hypointense MRI signatures which expand with increasing beam current ( figure 11). While the distal edge of the beam-induced signature is vertical for the lowest beam current of 16 nA, it presents increasingly tilted with increasing beam current. The MRI signal below the beam-induced signature is reduced, while no reduction in signal intensity is observed distally.
3.3.6. Assessment of the influence of flip angle variation on MR signal loss The beam-induced negative MRI contrast decreases with decreasing flip angle ( figure 12).

Discussion
To this day, several sources of treatment uncertainties, especially those related to the limitations to locate the position of the Bragg peak during dose delivery, hamper the exploitation of the full potential of particle therapy (Parodi and Polf 2018). Therefore, improved feedback on the actual dose distribution delivered, or at least the beam range, during treatment is mandatory. Existing techniques for the non-invasive monitoring of proton dose distributions are based on the detection of secondary radiation (Richter et al 2016, Hueso-González et al 2018 or heat-induced pressure waves (Hayakawa et al 1995, Lehrack et al 2017. Although these methods have shown promising results, they do not enable the determination of beam effects on images concurrently showing the patient anatomy. MR imaging has so far only been used for this purpose in an offline retrospective approach to verify the end-of-beam range in irradiated tissue after treatment (Yuan et al 2013). With the availability of a first in-beam MRI system, a logical step in the quest for online beam range monitoring is the direct application of MR imaging and its capability to visualise the beam during dose delivery. The work presented by our group is by no means the first attempt to use MRI for the visualisation and measurement of effects of ionising radiation beams in aqueous materials. On the contrary, a wide variety of evolved methods exploiting the reactivity of the free radicals formed during the radiation hydrolysis of water, leading to MRI-detectable changes in the water relaxation times, exists. These methods comprise Fricke-type dosimetry, which relies on the oxidation of ferrous (Fe 2+ ) to ferric (Fe 3+ ) ions in fluids or gels (Gore and Kang 1984), and polymer gel dosimetry, which is based on monomer copolimerisation (Lepage et al 2001) and was recently assessed for its capability for 4D radiation dosimetry on an MR-Linac (De Deene et al 2020). Although being mostly applied in photon dosimetry, these methods have also found application in the analysis of electron (Hammer et al 2011) and proton beams (Hillbrand et al 2019). The uniqueness of the proposed novel convection-based method assessed here lies in its potential independence from chemical reactions, being purely physics-based, which allows the use of free-floating water phantoms readily available in radiation oncology clinics.
The feasibility of the MRI-based visualisation of a stopping proton beam in water was demonstrated in the first proof-of-principle study, showing beam energy-and current-dependent spatial signatures of beaminduced local MR signal loss using an IR-GE pulse sequence (Schellhammer 2019, Schellhammer et al 2020. In the baseline experiments of the present study, the faster ToF angiography sequence chosen for the experimental assessment of the convection hypothesis has proven comparable capability to visualise the stopping proton beam in free-floating water at ambient temperature in coronal acquisitions. The beam-induced MRI signatures  observed were also characterised by hypointense MR signal resembling a proton pencil beam dose distribution and showed a clear energy and beam current dependence. In the quantitative analysis of the predicted and MR image-based residual beam ranges, the ranges and range differences obtained by both methods agreed within 4 and 1 mm, respectively. The discrepant accuracy of the MR image-based residual range and range difference measurements to reflect the respective predicted results can be explained by the uncalibrated determination of the grey value threshold defining the end-of-range in the MR images, which is influenced by MRI pulse sequence-specific characteristics of the beam-induced signature and by the choice of the applied doses and dose rates. Since systematic uncertainties inherent in range calculation and measurement, including the aforementioned pronounced uncertainty in grey value threshold definition, are reduced in the process of range difference evaluation, the smaller difference in predicted and measured residual range differences demonstrates the capability of the beam-induced signatures in ToF angiography images to reflect changes in beam energy. Comparably sized differences of 1 mm in predicted and measured residual range differences were previously reported for the IR-GE sequence (Schellhammer 2019).
The variation of the beam current had a pronounced influence on the visibility and the spatial extent of the beam-induced effect. At the lowest beam current setting of 8 nA, first signal changes emerged in the Bragg peak region where the dose deposition is expected to be maximal, whereas the plateau region only manifested itself in the images with a further increase in beam current. This supports the assumption of the existence of a dose and dose rate threshold of visibility, which had also been reported previously for the IR-GE sequence used in the first proof-of-principle experiments (Schellhammer 2019). In the present study using the ToF angiography pulse sequence, this threshold of depth-dose plateau region visibility was at a dose rate of 1300 Gy min −1 , corresponding to 16 nA beam current setting, and an integral dose of 360 ± 30 Gy. The strong beam current dependence of the spatial extent of the beam signature was a relevant influencing factor on the residual range measurements obtained in this study, even though it was less severe in longitudinal compared to lateral direction. The observed decrease in signal intensity surrounding the beam profile at the highest beam current of 64 nA can possibly be attributed to retrograde flow, reflected by the lid of the phantom.
The first milestone to be reached in the comprehensive, structured experimental assessment of MRI-based proton beam visualisation is the identification of the beam-induced effect required for the emergence of the MR signal loss observed under simultaneous proton beam irradiation of water phantoms. Based on the observation that beam-induced MRI signatures were only visible in liquid phantoms at high doses and dose rates in the initial proof-of-principle studies, the emergence of this MR signal loss was hypothesised to be dependent on beaminduced convection (Schellhammer 2019. Numerous studies from the field of water calorimetry (Schulz andWeinhous 1985, Domen et al 1991) and target technology for radionuclide production (Hong and Jung 2017) reporting the onset of convective flow due to the irradiation-induced thermal expansion of water support this hypothesis. Moreover, a reduction of MR signal amplitude has been reported for temporally or spatially varying blood flow occurring during MR imaging Felmlee 1990, Drangova andPelc 1996). Consequently, it can be hypothesised that beam-induced temporally or spatially varying convective flow similarly affects the MR signal.
The expected convection velocities in the depth-dose plateau area of the beam were estimated using an adapted version of the viscosimeter model based on Stokes' law and ranged from 1 to 8 mm s −1 for beam currents of 8 to 64 nA. Consequently, the resulting convection velocities lie in the range of capillary blood flow velocities (Le Bihan et al 1988). The obtained values, however, can only be interpreted as an order of magnitude estimate because of the large overall uncertainty associated, which is expected to be dominated by the use of a very simplified model assuming the heated water in the roughly cylindric beam volume to move like a solid sphere, rather than by the comparatively small uncertainties in the measured input parameters. In a similar study on MRI phase signal-based proton beam visualisation, however, the model output was found to compare well with the beam-induced convection velocity estimates obtained by velocity encoding MRI .
The convection hypothesis for the emergence of beam-induced MR signal loss was tested in three experiments in the present study. All reference images acquired at baseline without simulteous irradiation were free from MR signal loss potentially resulting from underlying spatial or temporal temperature gradients within the phantoms (Oglesby et al 2021). In the first experiment, horizontal mechanical barriers for the spatially selective inhibition of convection-induced flow were installed on top of the compartmentalising vertical tube insert in the second water phantom. MR signal loss within the beam volume was observed in opened tubes where convection-induced flow could develop, but not in closed tubes in which convection was suppressed. In the second experiment, convection of water was isotropically restricted by a phantom insert consisting of fine-pored floral foam. The prevailing severe restriction of water motion led to an absence of beam-induced effects in the coronal ToF angiography images acquired during simultaneous irradiation. This finding is in agreement with previous observations in which no MR signal loss could be observed within the beam volume in narrowly compartmentalised tissue-like phantoms or fluid materials other than water where convection was isotropically restricted by material viscosity (Schellhammer 2019). In the image acquired immediately after the termination of irradiation, however, slight MR signal loss can be observed, which is hypothesised to be caused by beam-induced oxygen depletion (Jansen et al2021) concurrent with a local increase in T1 relaxation time (Wancura et al 2023). A third independent irradiation experiment was conducted in free-floating water under temperature control, preventing changes in the mass density of water upon irradiation by exploitation of a very small volumetric thermal expansion coefficient of 1.14 × 10 −5 K −1 at 5°C water temperature compared to 2.87 × 10 −4 K −1 at 28°C (Dinçer and Zamfirescu 2016). While the concomitant temperature-dependent changes in the viscosity and the diffusion coefficient of water reinforced the inhibition of beam-induced convection at 5°C water temperature in this experiment, the associated changes in the mass density and oxygen concentration of water were found to lead to a uniform signal enhancement. This signal enhancement, however, was measured to be smaller than the beam-induced signal loss, and was therefore not expected to compromise the general visualisability of the beam-induced signatures. In the absence of the development of pronounced beam-induced local upthrust, very little MR signal loss was observed within the beam volume for irradiation at 5 ± 1°C compared to irradiation at an ambient temperature of 28 ± 1°C where developing upthrust led to severe signal loss. The slight reduction in MR signal at 5 ± 1°C can either result from the non-zero thermal expansion coefficient of water and therefore reflect a convection effect, or it may be indicative of T1 relaxation time lengthening. The sagittal images further support the convection hypothesis, showing different effects of buoyant convection. Firstly, the observed tilting of the signature's distal edge at higher beam currents in sagittal images is indicative of the deflection of the upwards moving volume at the phantom's lid. Secondly, the hypointensity observed below, but not distal to the beam volume may be explained by the circulation associated with buoyant convection. The fact that the beam-induced hypointense signatures are also visible in the sagittal plane, however, may hint at the involvement of a more localised contrast phenomenon, such as a local increase in incoherent motion or radiochemical changes in the irradiated material. From these findings it is plausible to conclude that the emergence of the local MR signal loss observed during proton beam irradiation of free-floating water phantoms at ambient temperature strongly, but not exclusively, depends on beam-induced buoyant convection.
Based on the slight MR signal reduction observed under motion-restricted conditions, it can be hypothesised that T1 relaxation time lengthening resulting from radiochemical oxygen depletion may furthermore contribute to the observed local MR signal hypointensities as an overlaying contrast mechanism already well-explained by Wancura et al 2023. The contribution of T1 contrast to the observed beam-induced MR signal hypointensities was finally confirmed in the last experiment, in which a reduction in T1-weighting of the images realised by a decrease in flip angle resulted in a reduction of beam-induced contrast.
The ToF angiography sequence used in the present study and the GE-based pulse sequences previously used by Schellhammer (2019) were all strongly T1-weighted and all showed a wide absence of beam-induced signatures in motion-restricted material. This supports the notion that the results of the present study can be expected to have general validity for other GE-based sequences as well. However, for different MRI pulse sequences, this might likely not hold true.
In contrast to the well-explained mechanism of photon irradiation-induced radiochemical oxygen depletion-evoked MR signal loss (Wancura et al 2023), which is hypothesised to also cause the proton beaminduced T1-dependent signal changes, the mechanism of MR signal loss based on beam-induced motion is hitherto unexplained. Therefore, this mechanism should be briefly discussed in light of the ToF angiographyspecific sequence characteristics, previous findings from the proof-of-principle experiments by Schellhammer et al (2020) using a wider range of MRI pulse sequences, and the literature related to MRI of flow effects. After all, the identified convection component of beam-induced MR signal loss in water using the ToF angiography and similar GE-based sequences does by no means imply that uniform convective upwards directed motion directly causes the observed contrast. On the contrary, uniform flow of excited spins orthogonal to the imaged slice cannot be expected to result in signal loss in GE-based imaging where non-selective refocusing pulses are used for echo generation (Axel 1984). Indeed, previous experimental findings by Schellhammer (2019) showed that spin echo imaging, which applies selective refocusing pulses and should therefore be sensitive to signal washout, i.e., the outflow of excited spins from the imaged slice before the slice-selective refocusing RF pulse creating the spin echo for acquisition is played, had a very low sensitivity for beam-induced irradiation effects in free-floating water. Moreover, based on the convection velocity estimates obtained in this study, the uniform upward motion of spins cannot be expected to result in relevant signal displacement or to have a significant influence on the effectiveness of signal excitation with maximum expected displacements for a 64 nA irradiation of 0.03 and 0.01 mm during TE/2 or the excitation pulse, respectively. Finally, the repeated beam current dependence experiment testing the possible influence of convection-driven inflow of pre-saturated signal into the imaging slice, an influencing factor specific to the ToF angiography sequence, showed that the signal loss observed within the beam volume was independent of the localisation of the pre-saturation slab below or above the imaged slice. Taking these findings together, the mechanism of the convection-induced MR signal loss observed under irradiation of free-floating water at ambient temperature remains unresolved and has to be explained by types of motion other than purely upward bulk flow of water molecules at a constant velocity, for example by higher terms of motion (Ehman and Felmlee 1990), turbulence (Urchuk and Plewes 1992), a local increase in diffusion (Bryant et al 1984) or pulse sequence-specific characteristics.
Consequently, future MRI methodology-based studies are required to further assess how beam-induced convection leads to MR signal loss. These experiments, that should investigate the effects of second order flow compensation and diffusion weighting on beam-induced MR signal loss, should be conducted in deoxygenated water to exclude signal loss secondary to beam-induced changes in the local oxygen concentration. In addition to that, another study is required to verify that the local T1 relaxation time lengthening observed in this study is indeed caused by proton beam-induced oxygen depletion. Here, quantitative T1 mapping could enable the spatially resolved comparison of the oxygen depletion-related expected and observed effects. To separate the effects of radiochemical oxygen depletion from those of beam-induced convection in these experiments, this study should be conducted in motion-restricted material such as fine-pored, water-soaked foam or gel. Lastly, potential synergies of both contrast mechanisms should be investigated in a quantitative study. The results of these studies may then enable the development of specialised, more sensitive pulse sequences for MRI-based proton beam visualisation. Once such specifically-tailored MRI sequences are available, the potential suitability of motion-and oxygen depletion-driven MRI-based proton beam visualisation for water phantom-based QA and in vivo applications can be evaluated.

Conclusion
This experimental study has identified beam-induced buoyant convection and a local change in water T1 relaxation time to induce local MR signal loss during proton beam irradiation of free-floating water phantoms at ambient temperature using a GE-based ToF angiography pulse sequence. Future MRI methodology-based studies are required for the elucidation of the motion-based MRI contrast mechanism. Moreover, the beaminduced effect underlying the observed T1 relaxation time change requires identification. Based on the results of these future studies, more sensitive, dedicated pulse sequences for MRI-based proton beam visualisation can be developed, for which the method's applicability to water phantom-based geometric QA of in-beam MRI systems currently under development or its eligibility for in vivo applications in the clinical routine can be evaluated.