Bare spherical gel dosimeter with optical computed tomography scanning

Radiochromic polyvinyl alcohol-iodide (PVA-I) hydrogel dosimeter with crosslinking by glutaraldehyde (GTA) has been reported. Because of the transparent gel’s mechanical strength, a study to cast samples in spherical shapes was initiated. The bare sample, 47 mm in diameter was mounted on a funnel and held by suction in a custom, 96 mm diameter, cylindrical vessel for 3D optical CT scanning. A solution of the same formulation without GTA provided refractive index matching inside the vessel for optic scanning and eliminated concentration gradients. The gel sphere remained in the vessel after draining the solution for the ‘in-air’ irradiation. A 20 Gy, maximum dose to the gel sphere was delivered by a single, 6 MV, x-ray beam. Comparison of central axis depth doses for the gel reconstruction and Monte Carlo calculation revealed similar results, indicating accurate 3D dosimetry within 1 mm of the gel surface will be possible. The gel recorded slightly greater dose in build-up region and slightly lower dose in the exit hemisphere relative to the calculation.


Introduction
Recently a formulation of a radiochromic polyvinyl alcohol-iodide (PVA-I) hydrogel dosimeter with crosslinking by glutaraldehyde (GTA) was introduced by Hayashi et al [1].The dosimeter has several advantages for optical computed tomography (CT) readout.These include; high transparency, very low diffusion, no dose rate effect, high melting point and reusability following thermal annealing.Crosslinking results in a relatively strong and elastic hydrogel.While investigating formulations with lower concentrations of potassium iodide for 3D dosimetry at orthovoltage energies, we decided to revisit 3D gel dosimetry for gels outside of protective vessels.In principle, if the vessel can be eliminated, 3D optical CT scanning is improved since refractive index matching between gel and liquid can be achieved.The plastic vessels typically have refractive indices (n) near 1.5 while for gel formulations n ~ 1.35.This refractive index mismatch leads to missing data near the vessel walls at higher incident angles.An initial investigation with FX-5% gelatin dosimeters determined they were mechanically too weak to handle without the support of the vessel.It was also realized that a vessel wall was needed to provide a barrier to oxygen (O2) diffusion since the gel was consuming O2 through autooxidation.Without the vessel barrier, a 3D O2 gradient would form causing spatial artifacts in dosimeter response.The O2 dependence of the PVA-I gels has not been reported.Several years later, a genipin crosslinked gelatin dosimeter without a vessel was evaluated, but at the degree of crosslinking appropriate for optical transmission, this formulation was again too mechanically fragile [2].The performance of transparent latex balloons as thin-walled vessels for optically scanning radiochromic gels was also examined [3,4].The thin walls allowed accurate dosimetry to within 2 mm of the gel perimeter.Also, the balloon acted as a skin so that non-crosslinked gelatin gels could deform without tearing.Other groups have made bare dosimeters for optical CT scanning.For example, silicone gel dosimeters have been cast into a cylindrical shape for deformable dosimetry and plastic Presage dosimeters have been cast in the shape of a mouse [5,6].
In this study, we investigate casting PVA-I hydrogels in a spherical shape and irradiating the sphere in-air to provide a simple experiment for comparison with Monte Carlo calculations.The spherical shape was chosen based on symmetry and availability of hollow plastic spheres to serve as moulds.

Methods
The PVA-I gel formulation included: 8% PVA (Mowiol 18-88, Sigma-Aldrich #81365) [7], 20 mM potassium iodide, 200 mM gluconic acid lactone, 100 mM fructose and 5 mM GTA.This solution was poured into clear polymethyl methacrylate (PMMA) hollow spheres purchased from Amazon (item description, clear fillable plastic balls), OD=50 mm, ID=47 mm.The inner surfaces of the PMMA spheres were coated with alpine ski wax and polished to a smooth finish to act as a mould release agent.Samples were stored for 3 days at 20 ℃ in the dark for the crosslinking reaction to complete.Attempts at crosslinking at higher temperatures such as 45 ℃ sometimes resulted in bubble formation.Samples prepared with 4% PVA were more flexible and deformed in air due to gravity and were excluded for this project.
Following the removal of gel spheres from their respective moulds, they were stored in a solution of this same formulation minus the GTA providing no net diffusion of mobile solutes.This solution also provided refractive index matching for the optical CT scans.Gel spheres were held by suction to a funnel mount in the custom 9.6 cm diameter, cylindrical vessel for optical CT scanning, see Fig. 1.This liquid was drained for 'in-air' irradiation, leaving the gel sphere secured to the funnel.The liquid was returned to the vessel for post irradiation scans.This approach avoided trying to remount the gel sphere in the same orientation on the funnel for post irradiation scans.The gel sphere had been irradiated with an 8 Gy uniform dose and this same single beam irradiation, optically scanned and then thermally annealed 3 days prior to this experiment.The scanner was a Vista16 (ModusQA) modified with a custom 1.5 cm, ~530 nm source [8].Outside of the custom vessel the aquarium was filled with ~22% propylene glycol -water solution, to maximize field of view.The iterative CT algorithm, OSC-TV with 0.25x0.25x0.25 mm voxels was used to reconstruct the 1000 projection data set.The Monte Carlo calculation was performed with DoseXYZnrc for a 47 mm diameter sphere of water with mass density of 1.027 g-cm -3 , irradiated in-air at 100 cm SAD with jaw-defined 8x8 cm, 6 MV, Varian TrueBeam x-ray beam.Voxel size was 1x1x1 mm with estimated calculation error of 1% for the maximum dose voxel.The centre of the gel sphere was placed at linac isocentre and irradiated to 2000 monitor units (MU, ~20 Gy) at 600 MU/minute with a horizontal beam.The sample was again scanned after a 60 minute radiochromic development time.Note this sample had been previously irradiated to a similar dose and then annealed at 47 C for 3 hours.

Results
Handling the gel sphere in the solution was challenging since it was nearly invisible in the solution and had similar density.For this data set, the equator of the gel sphere was tilted from the horizontal plane and the data in Fig. 2 represents a horizontal plane ~1 mm above the highest position of equator.The equator is the line where the two halves of the spherical mould connect.In Fig. 2, the upper panels are central slices from the 3D arrays of reconstructed gel attenuation coefficient and Monte Carlo calculated dose normalized to maximum dose.Note the gel image is the average of 4 adjacent 0.25 mm slices to match the slice thickness of calculation for comparison purposes.The 6 MV x-ray beam was incident from the left and the gel centre was located at the TrueBeam machine isocentre.From the optical CT reconstruction, the gel diameter was 46.5 mm while the plastic mould had an inner diameter of 47 mm.Possibly the sphere relaxed in size when extracted from the mould.In the central axis depth dose plot the voxels of 1x1x0.25 mm were obtained by averaging voxels from the 0.25x0.25x0.25 mm reconstruction in order to compare with the calculation.In Fig. 2, the lower right panel is a dose difference plane containing the beam central axis, calculation-gel.Both MC calculation and gel measurements were normalized at maximum dose and attenuation coefficient, respectively.In this case the gel was reconstructed with 1 mm isotropic voxel size, (not shown) which enhanced the apparent differences in the high gradient surface voxels.The planar dose difference shows the same gel under-response in the exiting hemisphere as seen for the central axis depth dose graph.

Discussion
This study has demonstrated that PVA-I hydrogels can be cast in a 3D, clear, colourless shape such as a sphere.The mechanical strength of this 8% PVA formulation allowed the spherical shape to be maintained in air while being held by a suction, funnel mount.Accurate positioning of the sphere was a problem and we are currently investigating casting the sphere with an indexed mounting post embedded within the gel.The agreement between calculation and measurement suggests that accurate dosimetry to within 1 mm of the surface will be achievable.Since, the edge of the gel sphere is observed in Figure 1, transmission image refractive index matching could be improved.This would reduce reconstruction artefacts at gel surface.A better agreement between the incident surface and central axis maximum dose would be obtained by shifting the gel depth ~1 mm.However, additional experiments are required to determine if this difference is real or an artefact.One confounding factor is that the gel was irradiated while still in the empty vessel.The 0.5 mm thick PFA Teflon wall may have had a measurable effect that was not included in the calculation.Also note the lower response of the gel in the exit hemisphere.Possibly, the previous dose history and annealing contributed to the differences observed.A more thorough evaluation will involve, irradiating the sample with a uniform dose to verify isotropic response and ensuring linear dose response before the in-air irradiation.If the uniform dose response shows nearsurface artefacts, oxygen gradient and evaporation effects will require assessment.When handling the bare gel sample, it is anticipated that temporarily covering the gel with a thin plastic film will provide protection.Other data in larger vessels indicate a threshold dose of ~5 Gy before linear response is achieved.This gel formulation is elastic due to the crosslinking and quantitative deformable 3D dosimetry should be possible.
In conclusion, 3D dosimetry of a PVA-I, 47 mm, gel sphere with optical CT readout has been demonstrated and the initial results are similar to a Monte Carlo calculation after normalizing the 3D data sets.

Disclosure
K. Jordan has a licensing agreement with ModusQA related to dosimetry applications of optical computed tomography.
on 3D and Advanced Dosimetry Journal of Physics: Conference Series 2630 (2023) 012024