One of the promises of magnetic resonance guided radiation therapy on hybrid MRI-linac (MRL) systems (Lagendijk et al. 2008 , Mutic and Dempsey 2014 , Fallone 2014 , Keall et al. 2014 ) is the ability to assess tumor response on a daily basis. The daily response is currently assessed using anatomical imaging, but could be replaced with precise quantitative imaging techniques (van der Heide and Thorwarth 2018 , Hall et al. 2019 , Kooreman et al. 2019 . Traditional quantitative imaging techniques based on steady-state methods, such as variable flip angle (T 1 -mapping) (Fram et al. 1987) or multi-echo spin echo (T 2 -mapping) (Meiboom and Gill 1958) , however, require long acquisition times. The long scan times pose a considerable practical challenge as the on table time is almost entirely filled with anatomical imaging (i.e., high-resolution 3D anatomical imaging for daily plan adaptation and fast real-time imaging for tumor tracking). Typical MRL treatment fractions have at most a couple of minutes of free imaging time available such that it does not interfere with the clinical workflow (Raaymakers et al. 2017) (Fig.1-A) . Therefore, the dual requirement of both fast and precise measurements mandates a sequence with a high precision per unit of time, i.e. quantification efficiency, for a practical implementation of online quantitative MRI-guided radiotherapy. Recently, transient-state-based quantitative imaging methods have been proposed to considerably improve this quantification efficiency. Magnetic resonance fingerprinting (MRF) (Ma et al. 2013 , Jiang et al. 2015 ) is such a transient-state method that enables rapid multiparametric imaging and therefore could be the ideal tool for therapy monitoring on the MRL.
Unlike steady-state methods, which aim to produce a constant MR signal over time, MRF deliberately creates a fluctuating signal (fingerprint) over the course of the acquisition, which is matched on a per voxel basis to a precomputed dictionary of signal responses during image reconstruction. The dictionary is populated with simulated responses for all possible tissue types, in terms of T 1 , T 2 and proton density, to the imposed transient-state MR sequence. Realistic simulations of these MR sequences are essential to accurately quantify the tissue properties , Assländer et al. 2017 . Therefore, the simulation of the MR sequences requires adequate control over system imperfections such as eddy currents and heterogeneous magnetic fields (B 0 and B + 1 ). These system imperfections are well characterised and controlled for diagnostic MR systems and MRF has been applied in multiple clinical studies , Rieger et al. 2018 , Liao et al. 2018 , Chen et al. 2016 , Chen et al. 2019 , Cavallo et al. 2019 . However, these system imperfections are not yet accurately mapped in MRL systems. The 1.5T MRL system used in our institution (Unity, Elekta, Crawley, UK) differs from diagnostic systems in the split gradient and split magnet coil design, the radiolucent 2x4 channel receive coil and a paramagnetic rotating gantry that holds all the beam generating components ( Fig.1-B) . These hardware modifications have an impact on the system imperfections, such as reduced signal-to- Schematic of a MRL radiotherapy treatment schedule. A) Example of a fractionation scheme where a patient is treated over multiple radiation fractions (F) distributed across multiple days. During each fraction, MR images are required for multiple purposes. During the first ≈ 5 minutes anatomical images are acquired for radiotherapy treatment planning. The treatment planning takes around 5 min (depending on plan complexity), which can be used for quantitative imaging. Finally the irradiation is started and requires continuous anatomical imaging for motion management. B) Impression of the MRL (Unity, Elekta) with the split gradient coil shown in yellow and the linear accelerator gun shown in red, as indicated with number 1 and 2 respectively. (Bruijnen et al. 2018) . The impact of these system imperfections on the accuracy and precision of MRF parameter quantification is unknown. Therefore, an experimental study on the precision and accuracy of MRF is crucial for the potential application of daily quantitative tumor response monitoring on a 1.5T MRL.
In this work we investigate the technical feasibility of 2D MRF in phantoms and in-vivo on a 1.5T MRL. We assess the accuracy, precision and temporal stability of the parameter quantification in a phantom. In addition, we showcase typical image quality of the parameter maps in comparison with clinically used qualitative scans in volunteers and patients.
A 2D gradient spoiled MRF pulse sequence was implemented on a 1.5T Unity MRlinac equiped with a 2x4 channel radiation translucent receive array. Imaging data were acquired using the MRF sequence described by Jiang et al. (Jiang et al. 2015) , which consists of an adiabatic inversion pulse and a sinusoidal flip angle train. One radial line was acquired per time-point (Cloos et al. 2016 ) and subsequent readouts were azimuthally incremented using the tiny golden angle to minimize eddy current effects (Wundrak et al. 2015 , Bruijnen et al. 2019 (Fig.2 ). K-space data and k-space trajectory were corrected using the zeroth and first order gradient impulse response functions (Vannesjo et al. 2013 , Bruijnen et al. 2018 . Tissue fingerprints were simulated with extended phase graphs (Weigel 2015) with T 1 ∈ [100 : 20 : 3000], T 2 ∈ [20 : 10 : 1000] and inclusion of the slice profile . All data were used to estimate the coil sensitivities using ESPIRiT (Ong et al. 2015) . MRF k-space data were reconstructed into singular value images with low rank inversion (Assländer et al. 2018 ) using the BART toolbox (Ong et al. 2015) . The singular value images were subsequently matched with the dictionary to reconstruct the parametric maps. The code to perform the image reconstruction code and one MRF dataset are available on https://github.com/tombruijnen/mrf-mrl . 
MRF data were acquired in a 2D transverse slice of 14 gadolinium-doped gel tubes (TO5, Eurospin II test system, Scotland). Relevant sequence parameters for all scans are shown in Table. 1. One fully sampled dataset was acquired, which consists of 276 repeated measurements of the MRF flip angle train, where for each measurement the azimuthal angle of the first spoke was rotated with the golden angle (111.2 • ). The measurements had a 10 second interval between repetitions to allow for full spin relaxation. Three and sixteen hours later MRF measurements were repeated with two minutes intervals for 30 minutes. Note that the fully sampled MRF scans were reconstructed with the maximum correlation method (Ma et al. 2013) . In total these scans provide 306 MRF measurements, which are used to estimate the precision, temporal stability and accuracy of the parameter quantification. The precision was quantified by calculating the standard deviation of parameter values within a tube. The temporal stability was quantified by calculating the standard deviation of the mean value within the tube over the repeated measurements. The accuracy was quantified by calculating the mean value within a tube and comparing it to reference measurements. The reference measurements were acquired using two separate inversion recovery (T 1 ) and spin-echo (T 2 ) scans. The reference data were acquired with single echo spin-echo measurements with: voxel size = 3x3x10 mm 3 scan time = 60 min, repetition time = 10 s and 10 inversion times ∈ [100:3000] ms or 10 echo times ∈ [20:500] ms.
This study was approved by the institutional review board of the UMC Utrecht (Medisch Ethische Toetsingscommissie Utrecht (METC), ID:17-010, "MRI protocol development for MR-linac") and informed consent was obtained from all the participants. MRF data were acquired in the brain and upper abdomen of a healthy volunteer. One patient with a recurrent colorectal liver metastasis, after hepatic surgery, was scanned using the described MRF sequence with the addition of an custom developed abdominal compression corset to reduce motion artefacts (Heerkens et al. 2017) . The complete MRI protocol consisted of multiple 2D MRF scans and qualitative T 1 and T 2 -w scans derived from the clinical protocol. The MRF scans in the upper abdomen were scanned in breathhold for the volunteer and in free-breathing for the patient. Regions of interest were manually selected on specific organs to compute the mean values, which were compared to literature values (de Bazelaire et al. 2004 , Deoni et al. 2005 . Relevant sequence parameters for all scans are shown in Table. 1. 
An exemplary time-point image of the fully sampled MRF scan along with the MRF proton density, T 1 and T 2 parameter maps are shown in Fig.3 . The bottom row shows the raw time domain signal (fingerprint) of voxels in tube 1 and 11 along with the match to the dictionary. For both these voxels the time domain signal shows close agreement with the dictionary match. The agreement holds for all the pixels within the tubes with a mean normalized root mean square error (NRMSE) = 0.06. Small differences between the MRF signal and the dictionary match are primarily observed during the first 50 snapshots directly after the inversion pulse and during the higher flip angles in time-points 500-600. The parameter quantification of the fully sampled (R=1) and undersampled (R=276) MRF reconstructions are compared against the spin-echo reconstructions in Fig.4 . Both the R=1 and R=276 MRF reconstructions showed good correlation in average values compared to the spin-echo measurements. The undersampled MRF has coefficients of determination R 2 T 1 = 0.999 and R 2 T 2 = 0.975 for T 1 and T 2 , respectively. Note that the accuracy of the T 1 -maps was slightly higher then the T 2 -maps. The precision over all the tubes for the undersampled MRF was σ T 1 = 8.6 ms and σ T 2 = 3.0 ms. The temporal stability of the parameter quantification (reproducibility) of the repeated measurements is shown in Fig.5 . The T 1 values were very stable, while the higher T 2 values show slightly higher deviation over time. The mean values within the tubes had an average standard deviation over time of σ T 1 = 6.4 ms and σ T 2 = 2.3 ms. Figure 5 . Repeated MRF measurement to assess the temporal stability of the parameter quantification. Top row shows the evolution of the mean T 1 values within the tubes and the bottom row shows the evolution of the T 2 values. Note that the tube numbers are added at the right side of the graph and they correspond with the numbers in Fig.3 . See the following link for video that shows the parameter maps over time: https://surfdrive.surf.nl/files/index.php/s/aOB3B2YlAxeT4mo
Brain volunteer data Two slices of the brain MRF scans in the volunteer are shown in Fig.6 . The T 1 and T 2 maps show clear boundaries between white and gray matter. The mean parameter values for gray and white matter are within the range of report literature values (Table. 2). Note that the T 2 values are on the low side, which is also reported in other MRF publications (Jiang et al. 2015) . The regions of interest that were used to compute the mean values are shown on the proton density image. Figure 6 . 2D brain MRF measurement in a healthy volunteer. Top row shows slice 1 of the MRF parameter maps and bottom row shows slice 2. Averaged T 1,2 values for white matter (green) and gray matter (blue) are shown in Table. 2. Volunteer abdomen data Two slices of the abdomen MRF scans in the volunteer are shown in Fig.7-8 . The boundaries between the medulla and cortex of the kidney are well defined on both the T 1 -map and the T 1 -w image, while the boundary is not visible on the T 2 -w image and T 2 -map. On the left side of the liver a small benign lesion is clearly visible on both the T 1 and T 2 map, which is characterised with a high T 1 and high T 2 . The T 2 values differ between the right and left kidney, which are 35 and 51 ms respectively. Region of interest analysis for multiple organs are shown in Table. 2. The kidney T 2 values also differ slightly between the two scans. However, the T 1 values were constant between the left and right kidney and between slice 1 and 2. The regions of interest that were used to compute the mean values are shown on the proton density image. Figure 7 . Breathhold 2D MRF measurement in a healthy volunteer. Top row shows the MRF parameter maps. Bottom row shows the qualitative images derived a clinical protocol. The T 1 -w scan is a spoiled gradient echo sequence, the T 2 /T 1 -w is a balanced gradient echo scan and FS = fat suppression. Note that the lesion that is visible in the liver is a benign cyst indicated by the white arrow. Mean T 1 and T 2 values were analyzed in regions of interest for liver (green), pancreas (orange), medulla (red) and cortex (blue) of the kidney. Patient abdomen data One slice of the abdomen MRF scan in the patient with a recurrent colorectal liver metastasis after hepatic resection is shown in Fig.9 . The metastasis is positioned in the anterior side of the liver and is clearly visible on the T 1 -map, T 1 -w image and on the diffusion-w image, while the lesion is less well defined on the T 2 -map and T 2 -w image.
The T 2 -map shows lower values in the liver and spleen compared to the volunteer scans, which could be due to patient motion. Figure 9 . Free-breathing 2D MRF measurement in a patient with a colorectal liver metastasis. Top row shows the MRF parameter maps. Bottom row shows the qualitative images from the clinically used protocol. The T 1 -w scan is a spoiled gradient echo sequence, the T 2 -w is a turbo spin echo sequence and the diffusion-w is a spin-echo sequence with EPI readout. The lesion is indicated with the red arrow on the diffusion-weighted image and is also clearly visible on the T 1 scans.
In this study we demonstrated technical feasibility of 2D MRF on a 1.5T MRL system. The phantom study indicated good agreement of parameter quantification (R 2 T 1 = 0.999 and R 2 T 2 = 0.975) with reference measurements, high precision (σ T 1 = 8.6ms and σ T 2 = 3.0ms) and temporally stable measurements during the day (σ T 1 = 6.4ms and σ T 2 = 2.3ms). The in vivo study showed high image quality of the fast MRF scans, where image features in the quantitative maps nicely corresponded with the qualitative scans. We believe these observations provide sufficient evidence that MRF is technically feasible on MRL systems and therefore could be further explored for online MR-guided radiotherapy applications on a 1.5T MRL. Besides MRF, these findings also apply for other transient-state parameter quantification methods (Sbrizzi et al. 2018) .
A possible use case for the quantitative maps could be patient-specific contrast optimization of the anatomical turbo spin-echo sequences, i.e. the reference MRI on which the treatment is planned. For example, liver metastasis are a heterogeneous group of lesions that show variable signal characteristics on both T 1 w and T 2 w imaging depending on the primary origin (Danet et al. 2003 , Namasivayam et al. 2007 . In this context, MRF could function as a contrast scout scan followed by an on-the-fly flip angle train optimization to maximize the contrast-to-noise ratio between the lesion and the liver. Contrast optimization techniques are well described in literature (Sbrizzi et al. 2017 ), but have never been applied in an on-the-fly setting for online contrast optimization on either diagnostic MR systems or MRL systems. Future work will focus on the implementation of these patient-specific contrast optimization techniques to investigate the potential improvement in image quality.
The rapid acquisition scheme of MRF (≈ 5 s per slice) could facilitate the integration of quantitative imaging to the clinical MRI-guided radiotherapy workflow without significantly lengthening of the treatment. The primary application of MRF would be for tumor response monitoring over multiple fractions during the treatment. The optimal timing to image changes in quantitative parameters post radiotherapy is an active topic of research (Fang et al. 2018 , van Schie et al. 2019 , Borggreve et al. 2019 ) and could be pushed forward with daily MRF on the MRL. The ability to pick up subtle changes in T 1 and T 2 values could be used to distinguish responders from non-responders. Ultimately, these potential changes in T 1 and T 2 could be used to intensify or reduce the (local) radiation during the radiotherapy treatment period based on the measured response.
Gradient spoiled 2D magnetic resonance fingerprinting is feasible on a 1.5T MRI-Linac with similar performance as on a diagnostic system. The precision and accuracy of the parametric maps are sufficient for further investigation of the clinical utility of magnetic resonance fingerprinting for online quantitatively MRI-guided radiotherapy.