Optimization of a novel large field of view distortion phantom for MR‐only treatment planning

Abstract Purpose MR‐only treatment planning requires images of high geometric fidelity, particularly for large fields of view (FOV). However, the availability of large FOV distortion phantoms with analysis software is currently limited. This work sought to optimize a modular distortion phantom to accommodate multiple bore configurations and implement distortion characterization in a widely implementable solution. Method and Materials To determine candidate materials, 1.0 T MR and CT images were acquired of twelve urethane foam samples of various densities and strengths. Samples were precision‐machined to accommodate 6 mm diameter paintballs used as landmarks. Final material candidates were selected by balancing strength, machinability, weight, and cost. Bore sizes and minimum aperture width resulting from couch position were tabulated from the literature (14 systems, 5 vendors). Bore geometry and couch position were simulated using MATLAB to generate machine‐specific models to optimize the phantom build. Previously developed software for distortion characterization was modified for several magnet geometries (1.0 T, 1.5 T, 3.0 T), compared against previously published 1.0 T results, and integrated into the 3D Slicer application platform. Results All foam samples provided sufficient MR image contrast with paintball landmarks. Urethane foam (compressive strength ∼1000 psi, density ~20 lb/ft3) was selected for its accurate machinability and weight characteristics. For smaller bores, a phantom version with the following parameters was used: 15 foam plates, 55 × 55 × 37.5 cm3 (L×W×H), 5,082 landmarks, and weight ~30 kg. To accommodate > 70 cm wide bores, an extended build used 20 plates spanning 55 × 55 × 50 cm3 with 7,497 landmarks and weight ~44 kg. Distortion characterization software was implemented as an external module into 3D Slicer's plugin framework and results agreed with the literature. Conclusion The design and implementation of a modular, extendable distortion phantom was optimized for several bore configurations. The phantom and analysis software will be available for multi‐institutional collaborations and cross‐validation trials to support MR‐only planning.


| INTRODUCTION
Due to the superior soft tissue contrast provided by magnetic resonance imaging (MRI), its use can provide increased delineation accuracy over computed tomography (CT) for radiation treatment planning 1,2 . However, implementation of MRI into treatment planning may be limited by both system-level and patient-induced geometric distortions 3,4 . The magnitude of patient-induced distortions arise from susceptibility differences within the patient and chemical shift effects, while system-level distortion is a result of B 0 field inhomogeneity and gradient nonlinearity (GNL). While patient-specific distortion is dependent on field strength and acquisition parameters and thus must be minimized on a per-scan basis, GNL-induced distortions have been shown to be independent of acquisition sequence 5 . As one of the dominant sources of image distortion 6 , GNL distortion is further exacerbated by modern systems with fast slew rates 7 or by systems with an 'open'-bore design. 8 These system-specific distortions have been shown to increase with increased distance from isocenter, making accurate measurement and correction over large fields of view (FOVs) important for radiation treatment planning involving anatomy positioned away from isocenter. 8 To characterize large FOV GNL distortion, several investigators Both of these phantoms required a fluid filling to serve as contrast from the markers. More recently, Huang et al. devised a hybrid design comprised of regularly spaced spherical cavities connected by channels in a grid-like pattern 11 . This design also utilized liquid contrast filling, but unlike the others, directed the contrast into the hollow landmarks themselves, creating the potential for air bubbles.
Also, while large in the axial plane (46.5 9 35 cm 2 ), they did not provide full S-I FOV characterization, spanning a distance of only 16.8 cm in that dimension. Walker et al. developed a full FOV distortion phantom, utilizing an array of vitamin E capsules over a diameter of 500 mm and length of 513 mm and used this phantom to characterize the entire FOV for a 3T Siemens system 12 .
While many in-house 3D distortion phantoms have been developed, some of the current designs are limited by a single geometric configuration to accommodate the institution's particular MRI system. While Walker et al.'s phantom configuration was modular, this was not explored in their recent publication 12 . Furthermore, although various phantoms have been created, the availability of comprehensive distortion analysis software is currently limited. Thus, the goal of this work was to evaluate the phantom design needs of the MR-SIM community based on currently available platforms and bore sizes and to develop a modular large FOV phantom using easily obtainable materials that can be optimized for many MR systems.
Lastly, in-house distortion characterization software was optimized for several MR platforms and integrated into a widely available medical imaging application platform. Importantly, the modular phantom design and availability of standardized analysis can be used in the future to facilitate collaboration and perform benchmarking for multi-institutional trials of MR-only treatment planning.

2.A | Phantom materials
The phantom design utilized in this work was adapted from a previously described study 13 that used a stack of low-density polyurethane foam plates (6 lbs/ft 3 , 2.5 cm thick) with 6 mm paintball inserts (polyethylene base) as signal generators (available at: www. MCSUS.com, UPC: 844596050069). While the original phantom design was lightweight, the low-density foam was found to be pliable and easily damaged, making long-term stability of the phantom's geometric integrity a potential concern. To build a more robust phantom with a material that could withstand transport to multiple Radiation Oncology centers for benchmarking, twelve urethane foam-based materials of various density and strength characteristics (4-40 lbs/ft 3 and 8-72 Shore D hardness, where Shore D is a hardness scale commonly used for plastics and elastomers 14 ) were identified. Test slabs were custom machined by Non-Magnetic Specialties for each candidate material (25 AE 0.25 mm center-to-center spacing, 6.5 mm deep using a~6.4 mm ball nosed endmill) and 6 mm paintballs were inserted into the foam. MR and CT images were acquired to assess the paintball signal intensity relative to each background material. Because CT will serve as the "ground truth" image for distortion calculations, intensity-based automatic segmentation of the paintballs from the background material was an important consideration. Final material selection was performed based on a balance of strength, weight, machinability, and cost.
Eight high-strength fiberglass threaded rods (McMaster-Carr, Part #91315A231) with corresponding nuts were used to affix the phantom plates together (four placed in the corners of the largest plates and an additional four that affixed the smaller plates to the largest ones) and add stability to the phantom construction as shown in Fig. 1F. The dimensions of the rod holes were machined with a tolerance of AE0.125 mm. Once the plates were aligned in the stack, the nuts were tightened to add additional stability to the phantom assembly.
2.B | Bore/phantom model Bore sizes and minimum aperture widths (smallest diameter of clearance within the bore once the couch is positioned inside) were tabulated for fourteen MR systems and one MR-IGRT system across five vendors as shown in Table 1. An in-house MATLAB â (Mathworks, Natick, MA, USA) script was used to generate shape models of each bore geometry, with input constraints including (1) the physical bore sizes and (2) the minimum aperture widths (smallest diameter of clearance within the bore once the couch is positioned inside) for each MRI make/model, assuming a flat table top was used. Optimized phantom configurations for each bore model were then generated by iteratively varying the phantom slab widths and total number of slabs until an optimized geometrical phantom configuration was found using the largest FOV physically possible. In order to simplify the model, the script assumes a circular cross-sectioned bore for all MR systems other than the Philips Panorama High Field Open (HFO) and a flat couch-top. Nonetheless, it was useful for visualization and planning of the final phantom construction.

2.C | Phantom setup reproducibility
To evaluate phantom setup reproducibility, 5 repeat CTs with independent setup and alignments to the CT external lasers were performed. DICOM CT data of Trials 2-5 were rigidly registered to Trial 1 using the previously validated FMRIB's Linear Image Registration Tool (FLIRT) module in the FMRIB Software Library (FSL) 15,16 . Six parameter (translation and rotation) and three parameter (translation only) rigid registrations were performed using the spline function for interpolation and mutual information as the cost function.

2.D | Software design
In-house image processing software was developed in C++ to automatically generate geometric distortion maps from phantom DICOM MRI data using similar techniques described in detail in our previous work 8 assuming the reverse gradient methodology is used (described in detail in Section 2.E). The useful marker signal was extracted from the image using a connectivity algorithm combined with masking and thresholding. Finally, x, y, and z control point positions were determined by finding the centroid of each marker as described in a previous publication 8   To make our work widely available to the community, we integrated our distortion characterization software into the 3D Slicer application platform 18 . 3D Slicer is an extensive medical image processing toolset, widely available open-source code, and modular design that is designed as a plugin framework. This then allowed for our distortion software to be written as a loadable C++ module that can utilize any of the robust C++ libraries already integrated into the 3D Slicer core. Specifically, our module uses existing DICOM import plugins, as well as existing VTK 19 visualization mechanisms, Qt 20 for user-interface construction, and both ITK 21 and VTK for image processing. C++ also offers the advantage of faster run-times as compared to MATLAB and other computing software.

2.E | Software evaluation
To evaluate the 3D Slicer software performance, GNL was evaluated for the 1.0 T HFO MR-SIM and compared against our previously published results using MATLAB and a different large FOV distortion phantom as described by Huang et al. 11 . Our previous work illustrated that the GNL for this magnet was stable compared to baseline measurements over more than 6 months of operation, thus suggesting that benchmarking with this magnet was appropriate. Distortion maps were compared directly via difference maps within the FOV covered by both phantoms. Global distortion statistics (including the percent of voxels distorted over 1, 2, 3, 4, and 5 mm and maximum distortions) were also compared between approaches, and comparisons in polynomial data fits were evaluated based on the mean absolute error. Finally, distortion maps were plotted as a function of radial distance from isocenter to compare the overall distribution of new distortions maps with those that we were previously validated.
It is important to note that exact agreement cannot be expected between the previously measured data using a different phantom and software and our new modular phantom. While the model fitting (singular value decomposition to fit the data to a sixth-degree polynomial, magnet measured, and acquisition sequences) were identical between trials, major differences between the approaches include:   from GNL are present in all directions, and are independent of acquisition sequence. Also, when the polarity of the read gradient is reversed, the polarity of any B 0 distortions will also be reversed while GNL distortion remains constant, and thus, the GNL distortion can be isolated by taking the average distortion between the two scans.
All scans were acquired with vendor supplied 3D geometry corrections enabled. Thus, it is important to note that all data shown are after vendor corrections were applied and thus represent the residual distortion in the datasets. The corresponding MR and CT scans for three phantom configurations were then uploaded into 3D Slicer for GNL and distortion analysis. Also, as each MR system produced images of different contrast, resolution, and signal to noise, the parameters utilized for thresholding and object identification were changed for each magnet to yield optimal results. Figure 1 shows the setup and corresponding MR images for the initial signal test as well as CT images of the polyurethane foam plates used in the CT contrast analysis. All urethane foam materials did not provide measurable MR signal and were thus considered adequate for our purposes. Materials with densities less than 20 lbs/ft 3 were found to be too brittle for precise machining; the materials were prone to crumbling and did not hold their precision-machined shapes. Thus, signal analysis was performed on the five foam samples that met the ≥20 lbs/ft 3 criteria. CT signal was found to be À547, À396, À382, À680, and À505 HU for the materials shown in   Philips Panorama, the middle shows the 60 cm cylindrical bore con-

3.A | Final phantom design and construction
figurations, and the right shows a 70 cm bore configuration. The The right panel of Fig. 2 is illustrates this extended build in a 70 cm bore.
Additional holes were drilled and fit with fiberglass tubing inserts to allow the plates to be stacked, with the plates held together using 3/8 inch diameter and 16 threads per inch fiberglass rods and hardware to secure the stack together once the paintballs were loaded.
One advantage of using this modular design was that each successive plate in the stack locks the paintballs into the plate below it.

3.D | Software validation
To evaluate the software performance, GNL was evaluated for our     | 57 than 10-15 cm. All systems had less than 1 mm of distortion for radii less than 100 mm from the magnet isocenter, and started to deviate at distances above this for both the LR and SI directions.

3.E | Multiple magnet distortion characterization
However, for the AP axis, both cylindrical bore systems nearly maintained less than 1 mm of distortion for the entire FOV.
While the 1.0 T Panorama yielded more than 1 mm of distortion in the L-R direction for over 45% of voxels, the 1.5 T Ingenia yielded this magnitude of distortion for about 21% of voxels, and the 3.0 T for roughly 39% of voxels. Both cylindrical bore magnets performed better in the A-P direction, with 1.4% and 12.6% of voxels respectively for the 1. cylindrical bore magnets has also reported in a recent study by Torfeh et al. 30 . Here, except near isocenter, the authors found that the through-plane (S-I) distortion was consistently higher than the in-plane distortion for both 2D and 3D sequences. Possible causes include the gradient design for this axis or shimming in the S-I dimension. It is also worth noting that the data shown in Fig. 6 31 . Notable validation steps were performed including using the CTest test system to perform nightly tests using reference input data and automatically comparing these results to a baseline solution. Future work will also include developing and implementing modules for synCT generation and patient-specific distortion into the same 3D Slicer toolkit to support an MR-only treatment planning workflow.

| CONCLUSION
We optimized the design and implementation of a modular, extendable distortion phantom to support an MR-only workflow and MR-IGRT. A modular phantom design was deemed necessary for large FOV distortion characterization to accommodate a wide range of bore sizes and configurations. Utility was shown for three different bore designs. The phantom blueprints and accompanying analysis software will be widely available through online libraries, which will help to facilitate collaboration and multi-institutional trials for MRonly treatment planning.

ACKNOWLEDG MENTS
Research reported in this publication was supported by the