Full length article| Volume 100, P90-98, August 01, 2022

# Time-course assessment of 3D-image distortion on the 1.5 T Marlin/Elekta Unity MR-LINAC

Published:June 28, 2022

## Highlights

• We assessed the temporal stability of image distortion on a 1.5 T MR-LINAC.
• Distortion was evaluated over 200 – 500 mm DSVs via 76 weekly measurements.
• Time-average absolute (‘total’) distortion dr ≤ 1 mm for DSVs ≤ 300 mm.
• dr ≤ 1.5 mm for DSV 400 mm and ≤ 2.5 mm for DSV 500 mm.
• Total distortion on the MR-LINAC was stable across the 18-month evaluation period.
• Image distortion may change following gradient servicing and should be monitored.

## Abstract

### Purpose

The efficacy of MR-guided radiotherapy on a MR-LINAC (MR-L) is dependent on the geometric accuracy of its MR images over clinically relevant Fields-of-View (FOVs). Our objectives were to: evaluate gradient non-linearity (GNL) on the Elekta Unity MR-L across time via 76 weekly measurements of 3D-distortion over concentrically larger diameter spherical volumes (DSVs); quantify distortion measurement error; and assess the temporal stability of spatial distortion using statistical process control (SPC).

### Methods

MR-image distortion was assessed using a large-FOV 3D-phantom containing 1932 markers embedded in seven parallel plates, spaced 25 mm × 25 mm in- and 55 mm through-plane. Automatically analyzed T1 images yielded distortions in 200, 300, 400 and 500 mm concentric DSVs. Distortion measurement error was evaluated using median absolute difference analysis of imaging repeatability tests.

### Results

Over the measurement period absolute time-averaged distortion varied between: dr = 0.30 – 0.49 mm, 0.53 – 0.80 mm, 1.0 – 1.4 mm and 2.28 – 2.37 mm, for DSVs 200, 300, 400 and 500 mm at the 98th percentile level. Repeatability tests showed that imaging/repositioning introduces negligible error: mean ≤ 0.02 mm (max ≤ 0.3 mm). SPC analysis showed image distortion was stable across all DSVs; however, noticeable changes in GNL were observed following servicing at the one-year mark.

### Conclusions

Image distortion on the MR-L is in the sub-millimeter range for DSVs ≤ 300 mm and stable across time, with SPC analysis indicating all measurements remain within control for each DSV.

## Keywords

#### Abbreviations:

MRI (Magnetic Resonance Imaging), LINAC (Linear Accelerator), MR-LINAC (MRI/LINAC, Combined MRI/Linear Accelerator), MR-L (MR-LINAC), RT (Radiation Therapy), OAR (Organ at Risk), BW (Bandwidth), MV (Megavolt), DSV (Diameter Spherical Volume), 3D (Three Dimensional), SPC (Statistical Process Control), FOV (Field-of-View), GNL (Gradient Non-Linearity), OD (Outer Diameter)

## Introduction

MR-imaging constitutes a high-spatial-resolution imaging modality with excellent soft-tissue contrast, multi-planar acquisition capabilities, a large array of image acquisition-parameters to optimize contrast between tissue types, and the capacity to distinguish tumor borders from normal tissue [
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With the recent commercial introduction of a linear accelerator (LINAC) and magnetic resonance imaging (MRI) unit integrated into one MR-LINAC (MR-L), the way has been opened for soft-tissue based online adaptive radiation therapy (RT) [

Hehakaya C, Van der Voort van Zyp J R, Lagendijk JJW, Grobbee DE, Verkooijen HM and Moors EHM. Problems and promises of introducing the magnetic resonance imaging linear accelerator into routine care: the case of prostate cancer. Front. Oncol. 2020; 10.3389/fonc.2020.01741.

]. However, the efficacy of MR-guided radiotherapy on a MR-L is critically dependent on the precision and accuracy of its MR image-guided targeting, as defined by target and normal structures visualization and the geometric accuracy of the images themselves [
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Unlike CT, the geometric accuracy of MR images acquired over larger fields of view continue to be problematic. This has major implications for MR-image guided RT in that geometrical image distortion has the potential to introduce significant localization errors and impact dose calculation accuracy for targets and organs at risk (OARs) [
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The origins of MR image distortion, though multifactorial, are primarily due to gradient nonlinearity (GNL), static field inhomogeneity and patient-induced susceptibility artifacts. These distortions are highly dependent on imaging parameters, including but not limited to the choice of pulse sequence, acquisition orientation, field of view (FOV), bandwidth (BW) and magnetic field strength [
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MRI geometric accuracy is usually assessed by means of periodic quality control (QC) tests designed to quantify the spatial extent of image distortion through the routine imaging of objects with well-defined geometrical features [
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]. Although a variety of test devices are available, most are 2D-phantoms; more recently, a number of 3D-distortion phantom designs have become commercially available, capable of quantifying both in- and through-plane image distortion simultaneously [
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Numerous techniques have been introduced to mitigate GNL effects through the use of distortion correction algorithms applied during image reconstruction [

Glover GH, Pelc NJ. Method for correcting image distortion due to gradient nonuniformity. US Patent # 4,591,789, May 27, 1986. http://mriquestions.com/uploads/3/4/5/7/34572113/gradwarpus4591789.pdf [accessed February 25 2022].

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]. Although 2D-algorithms, correcting only in-plane distortions are still often the default, 3D-distortion correction, using 3D-models of gradient fields [
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,

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] is now the current standard of practice for MR-images used in radiation treatment planning [

Paulson ES, Crijns SPM, et al, Consensus opinion on MRI simulation for external beam radiation treatment planning, Radiotherapy and Oncology 2016; 121;187-192; 10.1016/j.radonc.2016.09.018.

]. However, the efficacy of these algorithms – and indeed overall MR-imaging performance – is only as good as the quality control tolerance levels to which the MRI systems are maintained. Moreover, overall MRI system-induced spatial distortions may change over time [

Doty FD. MRI gradient coil optimization. In: Blumler P, Blumich B, Botto R, Fukushima E. Spatially Resolved Magnetic Resonance. Wiley; 1998, p 647-674http://mri-q.com/uploads/3/4/5/7/34572113/1998_smr_doty_grad_opt.pdf [accessed February 25 2022].

], degrading the targeting and dosimetric accuracy of treatment delivery on MR-guided systems.
With the implementation of a combined MRI/LINAC [

Tijssen R H N, Philippens M E P et al, MRI commissioning of 1.5T MR-linac systems – a multi-institutional study. Radiotherapy and Oncology 2019;132;114; 10.1016/j.radonc.2018.12.011.

] – and the consequent sole reliance on MR-imaging for target and OAR localization – understanding, parameterizing and monitoring the stability of MR-image distortion over large FOVs becomes critical to the precision and accuracy of MR image-guided radiation therapy and is consistent with the recommendations of the AAPM TG-284 report: Magnetic resonance imaging simulation in radiotherapy: considerations for clinical implementation, optimization and quality assurance [

Glide-Hurst C K, Paulson E S et al, Task group 284 report: magnetic resonance imaging simulation in radiotherapy: considerations for clinical implementation, optimization and quality assurance. Med Phys 2021;48 10.1002/mp.14695.

] and the Canadian Partnership for Quality Radiotherapy (CPQR) Technical Quality Control Guidelines for Magnetic Resonance Imaging for Radiation Treatment Planning [

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].
In an effort to characterize MR-L image-based targeting accuracy, we present here the results of a time-course evaluation of overall MRI system-induced spatial distortions on the Elekta Unity MR-LINAC obtained through seventy-six weekly measurements of 3D-geometric image distortion over 200 – 500 mm diameter concentric spherical volumes. We also assess phantom imaging/repositioning error through an evaluation of distortion measurement repeatability. Finally, statistical process control (SPC) is used to evaluate the consistency and temporal stability of image distortion, in order to identify potential distortion tolerances for each DSV.

## Materials and Methods

### MR-LINAC

All MR-images used in this study were acquired on the Philips 1.5 T MRI subsystem (Philips Healthcare, Best, Netherlands, Model No: 7814–74) of the Elekta Unity MR-LINAC (Elekta AB, Stockholm, Sweden). The Unity consists of a 1.5 T MRI combined with a ring-based gantry-mounted 7 megavolt (MV) standing-wave linear accelerator. The MR is based on the Philips Marlin system, consisting of an actively shielded 1.5 T superconducting magnet, with a bore diameter of 70 cm and 130 cm length.

### 3D-Phantom

MR image distortion measurements were made using the large FOV 3D-geometric distortion phantom and automated analysis software (Philips). This same phantom and software were also used by the vendor to validate geometric distortion during the on-site acceptance testing of the MR-L.
The 3D-phantom comprises 1932, 1-cm outer-diameter oil-filled markers (‘vertices’) embedded in seven flat, parallel plastic plates, with a marker spacing of 25 mm × 25 mm in-plane and 55 mm through-plane. The plates are rigidly inter-connected via plastic rods such that the structural integrity and geometric precision of all image/reference components is maintained. Overall, the phantom encompasses an approximately cylindrical volume of diameter 500 mm and length 330 mm.
Since this is a 3D-phantom with markers rigidly positioned in a 3D-grid array of vertices, geometric distortion along the x, y and z directions is measured simultaneously, without the need to adjust or reposition the phantom to assess distortion in the through-plane direction, as would be the case with 2D-phantoms.
The phantom design allows 200, 300, 400 and 500 mm diameter concentric spherical volumes to be defined around the MR-isocenter, each DSV encompassing 123, 404, 918 and 1514 markers respectively; image distortion is explicitly calculated for each DSV in terms of the vector magnitude (Elekta uses the term ‘total’) distortion, dr and orthogonal component distortions, dx (L/R), dy (A/P) and dz (F/H). Given the 330 mm phantom length, DSVs 400 and 500 are calculated over a spherical frustum i.e. without inferior and superior (F/H direction) spherical end-caps.

### Phantom positioning and referencing

Phantom positioning is achieved by means of five clamps for indexing and rigid attachment to the tabletop of the MR-L couch; the clamps allow an accurate fit to the corresponding slots in the tabletop only when the phantom is correctly centered/positioned (source: Marlin 1.5 T for Elekta Unity User Manual).
Positional referencing is achieved through the use of a series of numerical indicators and index marks, scribed along both sides of the tabletop. When correctly positioned, the middle plate of the phantom is centered between two such reference indices, corresponding to the marked index number ‘22'; this value is set as isocenter in the LINAC computer. The phantom is then automatically transported into the bore such that this index position – and by extension the center of the phantom – is located precisely at the magnet/LINAC isocenter.
The accuracy of this positioning is checked daily via the MR-to-MV test, conducted using a purpose-built Elekta phantom, containing seven MR- and MV-visible markers mounted in a cylindrical housing. The phantom is first carefully aligned to correspond to the appropriate index-slot on the MR-couch, and then moved automatically to the MR/LINAC isocenter. The test acquires axial MR- and MV-images, following which the markers are identified in both by automated analysis software. The results are visually checked for accuracy and a transformation to bring the markers into coincidence is calculated. The accuracy of the coincidence-transformation is again visually checked and the calculated translational shifts compared against baseline values, typically < 0.2 mm in xy and z.

### MR imaging

All distortion measurements were done with the LINAC gantry set to the ‘home’ position of zero degrees. The contribution of B0 field inhomogeneity to geometric distortion was monitored over the course of the study using the Full-Width-Half-Maximum (water peak) method, measured over a 27 cm outer-diameter (OD) spherical, doped-water filled phantom.
MR-images were acquired using the magnet transmit/receive body coil and the Philips Axial Fast-Field-Echo 3D T1-weighted sequence with parameters: TR/TE: 6.7/3.4 ms; flip angle: 15 degrees; acquisition matrix: 372 × 374 × 200; reconstruction matrix: 512 × 512 × 400; image resolution: 1.09 × 1.09 × 1 mm; 560 × 560 × 400 mm reconstructed image volume; pixel BW: 431 Hz/pixel; averages: 1; phase-encode direction: R – L; total acquisition time: 523 sec. All MR-images were 3D-distortion corrected during image reconstruction.

### Geometric distortion analysis

3D-geometric image distortion was calculated in terms of the deviations dx, dy, dz and dr of the apparent/image coordinates of markers (i, j, k) from their true/reference values (corrected for possible phantom offset and rotation), as:
$dxijk=xijk′-xijk$
(1)

$dyijk=yijk′-yijk$
(2)

$dzijk=zijk′-zijk$
(3)

and
$drijk=dxijk2+dyijk2+dzijk2$
(4)

where −250 ≤ i, j ≤ 250, (in-plane, R/L and A/P respectively, both in 25 mm increments) and −165 ≤ k ≤ 165 (through-plane, F/H, in 55 mm increments); x'ijk, y'ijk, z'ijk and xijk, yijk, zijk are the image-based and reference coordinates of vertices (i, j, k) respectively.
Automated image distortion analysis was carried out using the Philips geometrical distortion software. The algorithm identifies the centroid of each marker in a given plane and reports the measured and reference coordinates for each of the 1932 markers in the phantom in terms of R/L (dx), A/P (dy), F/H (dz) and vector magnitude dr, distortion values. The validity of a given marker measurement is determined by calculating the standard deviations of the distances of the image pixel locations from the observed marker centroid, together with an effective radius equal to that of a sphere having the same volume as there are voxels in the observed marker.
Analysis results are summarized as the vector magnitude distortion, dr and absolute values of the orthogonal components dx, dy and dz [mm] over the 200, 300, 400 and 500 mm DSVs, reported in terms of the maximum and 98th percentile values in each volume. The number of markers (123, 404, 918 and 1514 for DSVs 200, 300, 400 and 500 mm, respectively) vs the number actually detected inside each volume, are also indicated.
The 98th percentile results represent the maximum value of distortion metrics dr, dx, dy and dz measured within a given DSV, with the largest or least-reliable 2% of measurements excluded. Markers having the largest distortion deviation values, but otherwise reliably detected, are included in the evaluation of the maximum distortion for each DSV; marker exclusion was observed only in the evaluation of DSV 500 mm distortion (76-week median value: 8 excluded markers (∼0.5%) per test) done to avoid biasing the results due to poorly or only partially visible markers at the edges of the image FOV.

### Assessment of 3D-MR image distortion repeatability

MR-image distortion measurement repeatability was assessed via ten back-to-back scans of the 3D-phantom, first without repositioning, followed by a second set of ten scans, with the phantom removed/repositioned between successive scans. Variations in repeatability determined from both series were used to evaluate measurement error consequent to repeat MR-imaging, as well as the degree of variability introduced by the combination of phantom set-up and imaging.
Repeatability was quantified by calculating the differences in deviations dx, dy, dz and dr for each marker across each set of ten scans using the Median Absolute Deviation [

Dodge Y, The Concise Encyclopedia of Statistics, New York, NY: Springer-Verlag; 2008 10.1007/978-0-387-32833-1_261.

(5)

The MAD is a robust measure of the variability of quantitative data, particularly appropriate to the assessment of repeatability as it is less sensitive to data outliers than the standard deviation. The MAD for each deviation parameter dx, dy, dz and dr was calculated over all 1932 markers and the mean and maximum frequency of discrete difference-values determined.

### Time-course assessment of 3D-MR image distortion

The long-term stability of gradient linearity on our Philips 1.5 T Marlin/Elekta Unity MR-LINAC was evaluated via weekly distortion measurements over the course of eighteen months. Measured weekly values of dx, dy, dz and total distortion dr at the 98th percentile and maximum levels were compiled in Excel (2016) for each DSV. Statistical process control was then used to evaluate statistical fluctuations in image distortion values for each DSV and provide estimates for test tolerances [

Wheeler DJ, Chambers DS. Understanding Statistical Process Control. 2nd ed. Knoxville, TN: SPC Press; 1992; isbn: 9780945320135 0945320132.

]. Control limits were determined as three times the standard deviations of the first 20 measurements acquired pre- and post-gradient service at the one-year mark.

## Results

Fig. 1 (a) shows the large FOV 3D-MR image distortion phantom with its regular grid array of markers embedded in seven parallel plates, rigidly spaced and inter-connected by rods, together with several of its six positioning clamps. MR-images of the center-slice of the phantom through isocenter (cross-hair lines) in the axial plane and reconstructed into the corresponding coronal and sagittal planes are shown in Fig. 1 (b) – (d) respectively.
B0 field inhomogeneity, measured across the 27 cm outer-diameter spherical phantom, (FWHM water-peak method) was observed to be 16 ± 6 Hz over the course of the study.

### 3D-MR image distortion repeatability

The results of 3D-MR image distortion repeatability measurements via ten back-to-back scans, without phantom re-positioning between scans and then re-done with the phantom removed and re-positioned prior to each subsequent scan, is shown in Table 1. Fig. 2 summarizes the MAD repeatability results with the 3D-phantom removed/re-positioned between subsequent scans as frequency histograms for deviations dx, dy, dz and dr.
Table 1Distortion measurement error introduced through repeated phantom imaging (left) or imaging/re-positioning following each of ten scans (right). The mean and maximum values of the median absolute difference (MAD) across repeated distortion measurements acquired over all markers is shown for deviations dx, dy, dz and dr.
Imaging onlyImaging & Repositioning
dx0.01 (0.19)0.02 (0.29)
dy0.01 (0.19)0.02 (0.26)
dz0.01 (0.17)0.02 (0.28)
dr0.01 (0.14)0.02 (0.29)

### Time-course assessment of the Unity MR-L geometric image distortion

Fig. 3, Fig. 4 show the 76-week time-course of total distortion dr at the 98th percentile and maximum levels for the 1.5 T MRI of the Elekta Unity. They indicate that image distortion is stable across time and within manufacturer’s specifications, shown in Table 2.
Table 2MR-L specifications for total image distortion vs DSV (mm) (source: Elekta Unity Product Data).
DSV (mm)200 (guaranteed)340 (guaranteed)420 (typically)
MR-L Specification (mm)≤ 1.0≤ 2.0≤ 2.0
Progressively larger distortion values observed across larger DSVs reflect increased GNL as radial distance from isocenter increases. This characteristic feature is maintained in the time-evolutions shown in Fig. 5a, b and c, corresponding to distortions along the x, y and z directions for each DSV. Furthermore, whereas component distortions are observed to be comparable in magnitude along the x (R/L) and z (F/H) directions for all DSVs, they are larger along the y (A/P) axis, reflecting increased distortion along the frequency-encode direction.
It is worth noting that total, maximum and component distortion measurements across the first fifty weeks remained in the sub-millimeter range for DSVs ≤ 300 mm and hovered in the ∼ 1 mm range for DSV 400 mm.
Statistical process control analysis underscored gradient stability across the first year of weekly measurements, with total distortion values falling within the control limits of the time-average distortion ± 3 SDs, i.e. 0.30 ± 0.04 mm, 0.53 ± 0.03 mm, 1.0 ± 0.07 mm and 2.28 ± 0.12 mm for DSVs 200, 300, 400 and 500 mm, respectively.
SPC analysis immediately detected the abrupt increase in total and component distortion values across all DSVs following scheduled maintenance gradient servicing at the one-year mark, increasing between 0.08 mm and 0.3 mm for DSVs ≤ 300 mm and 0.2 – 0.5 mm for 400 and 500 mm DSVs, representing increases in total image distortion of Δdr = 63%, 49%, 40% and 4%, for DSVs 200, 300, 400 and 500 mm, respectively.
Nevertheless, despite the ‘jump’, weekly distortion measurements following gradient-servicing were observed to remain stable; consequently, ‘new’ control limits and time-average means over the subsequent twenty measurements post-servicing were determined for each DSV (Fig. 3), indicating that total distortion remained in control across all DSVs both pre- and post-servicing, albeit with different time-average means. Pre- and post-service time-course distortion results for total and component distortions along the R/L, A/P and F/H directions at the 98th percentile- and maximum-levels for 200, 300, 400 and 500 mm DSVs are summarized in Table 3.
Table 3Pre- and post-service time-average and standard deviation results (mm) for total (vector magnitude) dr and component distortions dx, dy and dz at the 98th percentile- and maximum-levels for 200, 300, 400 and 500 mm DSVs.

## Discussion

MR-guided radiation therapy has revolutionized RT by providing a high spatial-resolution imaging modality with excellent soft-tissue contrast, multi-planar acquisition capabilities, a large array of MR-parameters to optimize contrast between tissue types and the capacity to distinguish tumor borders from normal tissue. The combination of a linear accelerator and MRI scanner into one hybrid unit furthers this evolution by enabling the visualization of both inter- and intra-fraction target motion [
• Kleijnen J.J.E.
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• et al.
] during the course of radiotherapy, information that can be used as the soft-tissue imaging input for adaptive RT.
Adaptive radiotherapy incorporates changes in anatomy and/or deviations in planned delivered dose due to patient setup variations or machine delivery deviations to estimate the actual delivered dose to a patient as the treatment progresses. [

Dietrich S, Ford E, Pavord D and Zeng J, Chapter 14 – Treatment Planning and Quality Metrics, Editor(s): Dietrich S, Ford E, Pavord D, Zeng J in Practical Radiation Oncology Physics, Elsevier, 2016, pp 189 – 206, ISBN 9780323262095https://www.sciencedirect.com/topics/medicine-and-dentistry/adaptive-radiotherapy10.1016/B978-0-323-26209-5.00014-6.

].
Inter-fraction MR-imaging can be used for soft-tissue targeting verification, assessment of treatment response [
• van der Heide U.A.
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,
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] or for re-planning to account for changes in tumor and/or normal tissue anatomy; intra-fraction MRI during beam delivery could be used to evaluate dose accumulation during treatment [
• Stemkens B.
• Glitzner M.
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Effect of intra-fraction motion on the accumulated dose for free-breathing MR-guided stereotactic body radiation therapy of renal-cell carcinoma.
] or potentially for real-time re-planning [
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,
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].
The MR-LINAC concept holds the promise of truly adaptive radiotherapy by enabling the visualization of soft-tissue anatomical changes during the course of RT, thus allowing treatment plan adaptation to optimize target conformality and reduce dose to normal structures. The targeting accuracy of a MR-LINAC is, however, dependent on the characterization of gradient linearity and image distortion across time for clinically relevant FOVs.
In this work we have evaluated the magnitude and temporal stability of MR-image distortion on the Elekta Unity MR-L for 200 – 500 mm diameter spherical volumes, using 3D-phantom imaging and automated distortion analysis. Our findings demonstrate very stable gradient system performance, with consistent values for total distortion across each DSV, though pushing against the boundaries of standard clinical image distortion limits at larger DSVs.
Clinically acceptable levels for geometric distortion of MR images used in RT planning are still being defined, though a number of recommendations have been proposed. Paulson et al suggest a tolerance ≤ 1 mm for stereotactic brain and ≤ 2 mm for non-SRS brain, head-and-neck, and the central region of cervix and prostate images used in radiotherapy MR-simulation imaging [

Paulson ES, Crijns SPM, et al, Consensus opinion on MRI simulation for external beam radiation treatment planning, Radiotherapy and Oncology 2016; 121;187-192; 10.1016/j.radonc.2016.09.018.

]. TG 284 proposes a total distortion ≤ 1 mm and ≤ 2 mm for 200 mm and 400 mm DSVs about isocenter respectively [

Glide-Hurst C K, Paulson E S et al, Task group 284 report: magnetic resonance imaging simulation in radiotherapy: considerations for clinical implementation, optimization and quality assurance. Med Phys 2021;48 10.1002/mp.14695.

] while the CPQR recommendations quote a tolerance ≤ 1 mm [

Canadian Partnership for Quality Radiotherapy (CPQR) Technical Quality Control Guidelines for Magnetic Resonance Imaging for Radiation Treatment Planning http://www.cpqr.ca/wp-content/uploads/2020/09/MRI-2020-05-01.pdf [accessed February 25 2022].

]. Still others suggest a maximum tolerance of 2 mm over a 200 mm DSV for MRI-CT co-registered images, but a mean tolerance of 1 and 2 mm over 200 and 400 mm DSVs respectively, for MRI-only based RT planning [

Kavaluus H, Nousiainen K et al, Determination of acceptance criteria for geometric accuracy of magnetic resonance imaging scanners used in radiotherapy planning. Physics and Imaging in Radiation Oncology 2021; 17 10.1016/j.phro.2021.01.003.

].
It is against this background that the MR-only ‘see-and-treat’ Elekta Unity MR-L makes its appearance in image-guided RT. Although Elekta’s specifications for total distortion of ≤ 1 mm and ≤ 2 mm for 200 mm and 340 mm DSVs are consistent with the above mentioned recommendations for MR-simulation, clinical tolerance levels for image distortion on the Unity have as yet to be defined. By way of comparison, CPQR guidelines recommend a 1 mm tolerance and 2 mm action level; however, our results show that this is fully achieved only for DSVs < 300 mm on the MR-L, with total distortion for larger FOVs straddling or exceeding these values, as seen in the 1–1.4 mm and 2.3–2.4 mm pre-/post-service results for 400 and 500 mm DSVs respectively.
It is with this in mind that the characterization of image distortion across progressively larger concentric DSVs on the Unity MR-L may be useful in helping identify clinically appropriate imaging FOVs for different target structures based on the measured distortions across the corresponding DSVs. So, for example, our results show that a 1 mm total distortion tolerance would translate to an approximate upper bound of ≤ 300 mm for the corresponding imaging FOV.

### MR-L geometric image distortion measurement repeatability

In order to assess the contribution to distortion measurement uncertainty introduced by imaging and/or a combination of imaging and phantom re-positioning, repeatability tests were carried out and evaluated using the MAD metric to assess the degree of point-wise distortion variability for all markers in the phantom across repeated imaging acquisitions. The MAD analysis yields the median difference between measurements at each vertex point, irrespective of the actual numerical value of the measurement. This is particularly useful in evaluating image-distortion repeatability with a 3D-grid phantom, in that the magnitude of the individual deviations measured at each vertex varies across the phantom – reflecting the volumetric distribution of geometric distortions – but the median deviation differences at each vertex between scans remain consistently small.
MR imaging-only tests (Table 1) show that ten repeated phantom scans/analyses (one imaging session) yield mean and maximum MADs of only 0.01 mm and ≤ 0.2 mm, respectively, for all distortion metrics.
Similarly, repeatability tests (Table 1, Fig. 2) with the phantom removed/repositioned following each of ten successive scans (same imaging session), show only marginally greater differences in mean and maximum MADs ≤ 0.02 mm and ≤ 0.3 mm respectively, demonstrating very good repeatability despite slight variations in positioning due to phantom set-up error. These results suggest that scanning and/or phantom-repositioning introduces minimal variability to distortion measurements on the MR-L.

### Time-course assessment of MR-L geometric image distortion

The first result of our study is the characterization of the magnitude of image distortion on the Unity MR-L for progressively larger diameter spherical volumes. Total distortion (98th percentile) for a 200 mm DSV is seen to be in the 0.30 – 0.5 mm range, increasing to 0.5 – 0.8 mm, 1.0 – 1.4 mm and ≤ 2.5 mm for 300, 400 and 500 mm DSVs, respectively.
MRI spatial distortion may, however, change over time; consequently, the evaluation of geometric image distortion is an important component of MR-imaging QC tests for radiation treatment planning. The American College of Radiology specifies weekly and annual MR-imaging QC tests, however, decisions concerning the frequency of image-distortion testing are generally determined by assessing gradient stability across time.
With this proviso in mind, the second notable feature of our 76-week study (Fig. 3, Fig. 4, Fig. 5) is the stability of MR-L image distortion across time, shown by the consistency in measured values over the first year of weekly testing (pre-service results, Table 3) for all DSVs.
The temporal stability of image distortion is further highlighted by the time-averaged mean across the first 50 measurements for total distortion (98th percentile) of 0.3, 0.5, 1 and 2.3 mm for 200, 300, 400 and 500 mm DSVs, respectively. Even the initial 12-month time-averaged maximum total distortion for DSVs ≤ 400 mm is seen to be 0.33, 0.6 and 1.25 mm, below the vendor’s specified tolerances of 1 and 2 mm for DSV 200 mm and DSVs 340/420 mm, respectively. This consistency is maintained in the subsequent set of 26 post-servicing measurements (Fig. 3, Fig. 4, Fig. 5, Table 3) – albeit with different time-average means.

### Statistical process control analysis

Fig. 3, Fig. 4, Fig. 5 are also indicative of the Unity MR-L system performance with respect to gradient linearity compliance, since statistical control limits can be used to establish the boundaries wherein subsequent measurements may be assessed as being within tolerance or not.
In order to characterize the temporal stability of gradient linearity on the Elekta Unity, we used Statistical Process Control to evaluate statistical fluctuations of distortion measurements and provide tolerance estimates for each DSV. Control limits were calculated as three standard deviations of the mean over the first 20 measurements acquired pre- and post-gradient service.
SPC analysis underscores the stability of gradient linearity across the first year of weekly measurements, with total distortion values falling well within the ± 3 SDs control limits of the time-average distortions for all DSVs. Closer inspection reveals that virtually all values of total distortion fall within ± 2 SDs of the pre- or post-service means, with outliers ≥ 2 SD making up only 2 – 4% of all results; no measurements exceeded ± 3 SDs.
QC testing is contingent on knowing the tolerance at which the system is to be maintained. The results of our SPC analysis could be used to provide test tolerances for MR-L distortion QC measurements, set to lie within control limits defined by our pre-/post-service 99% confidence intervals; however, depending on the characteristics of each system, this might risk false ‘failures’ being triggered by outliers that may be of little consequence yet difficult to resolve [

Schilling ED, Neubauer DV. Acceptance sampling in quality control. Chapter 11, 2nd ed. Boca Raton: Taylor & Francis Group; 2009; 10.1201/9781584889533.

]. Alternately, tolerances could be defined more loosely based on manufacturers’ specifications or on clinical precedent, informed by TG284 or CPQR guidelines. In either case, the discontinuity in the time-series observed following scheduled service certainly indicates baseline values may have to be reset following system maintenance, upgrades, or other changes.
It is this latter requirement to test following system upgrades/calibrations that led to the observation of the discontinuity in distortion values across all DSVs following gradient servicing. Although the cause of this shift is unclear, it is remarkable that distortion measurements have been as consistently maintained at the ‘new’ level for the subsequent six months (post-service results) as they were initially, with data points again falling within ± 3 SDs of the time-averaged mean (Fig. 3). It is worth noting that even the maximum increase in distortion values following servicing is still ≤ 0.5 mm for all DSVs.

## Conclusion

In this study we have evaluated gradient non-linearity on a 1.5 T Philips Marlin/Elekta Unity MR-LINAC over the course of eighteen months to assess the magnitude and temporal stability of image distortion over four concentric, progressively larger-diameter spherical volumes.
Our results indicate that total image distortion on the Unity is in the sub-millimeter range for DSVs ≤ 300 mm and < 1.5 mm and < 2.5 mm for DSVs ≤ 400 and 500 mm, respectively, in compliance with manufacturer’s specifications of dr ≤ 1 mm for DSV 200 mm and ≤ 2 mm for DSVs ≤ 340/420 mm. They also show that distortion is stable across an extended time-span, with SPC analysis demonstrating that total distortion remains within three standard deviations of the time-average means for each DSV. However, the jump in post-servicing values also illustrates the need for geometric distortion QC following system maintenance. Our findings substantiate the quantitative evaluation of MR-image distortion required to achieve confidence in the geometric accuracy of MR-L images used for RT treatment planning.

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

The authors wish to thank the Physics Associates at Princess Margaret Cancer Center, who were responsible for the acquisition of the image distortion measurements presented herein.

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