Toward Magnetic Resonance Fingerprinting for Low-Field MR-Guided Radiation Therapy

Abstract

Purpose:

The acquisition of multi-parametric quantitative magnetic resonance imaging (qMRI) is becoming increasingly important for functional characterization of cancer prior to- and throughout the course of radiation therapy. The feasibility of a qMRI method known as magnetic resonance fingerprinting (MRF) for rapid T₁ and T₂ mapping was assessed on a low-field MR-linac system.

Methods:

A three-dimensional MRF sequence was implemented on a 0.35T MR-guided radiotherapy system. MRF-derived measurements of T₁ and T₂ were compared to those obtained with gold standard single spin echo methods, and the impacts of the radiofrequency field homogeneity and scan times ranging between six and 48 minutes were analyzed by acquiring between one and eight spokes per time point in a standard quantitative system phantom. The short-term repeatability of MRF was assessed over three measurements taken over a 10-hour period. To evaluate transferability, MRF measurements were acquired on two additional MR-guided radiotherapy systems. Preliminary human volunteer studies were performed.

Results:

The phantom benchmarking studies showed MRF is capable of mapping T₁ and T₂ values within 8% and 10% of gold standard measures, respectively, at 0.35T. The coefficient of variation of T₁ and T₂ estimates over three repeated scans was < 5% over a broad range of relaxation times. The T₁ and T₂ times derived using a single-spoke MRF acquisition across 3 scanners were near unity and mean percent errors in T₁ and T₂ estimates using the same phantom were <3%. The mean percent differences in T₁ and T₂ as a result of truncating the scan time to 6 minutes over the large range of relaxation times in the system phantom were 0.65% and 4.05%, respectively.

Conclusions:

The technical feasibility and accuracy of MRF on a low-field MR-guided radiation therapy device has been demonstrated. MRF can be used to measure accurate T₁ and T₂ maps in three dimensions from a brief six-minute scan, offering strong potential for efficient and reproducible qMRI for future clinical trials in functional plan adaptation and tumor/normal tissue response assessment.

Introduction

Using multi-parametric quantitative magnetic resonance imaging (qMRI) to adapt radiation therapy (RT) plans is a highly sought after frontier in personalized cancer treatment¹. Efforts are ongoing to acquire quantitative imaging data throughout the course of RT^2–5 and determine the best way to accommodate observed changes in tumor biology in the adaptive RT plan. However, acquiring qMRI data is currently limited by the prohibitively long scan times required to acquire data with sufficient accuracy and spatial resolution. This is especially the case for time-consuming relaxometry (i.e., mapping of the longitudinal and transverse relaxation times T₁ and T₂), which has been shown to correlate with RT treatment response in prostate and brain malignancies^3,6–8.

To improve the likelihood of patient compliance, innovative methods to minimize qMRI scan time are being developed⁹. One such emerging technique is magnetic resonance fingerprinting (MRF)¹⁰. MRF has emerged as an exciting new method for efficient multi-parametric qMRI. Contrary to conventional techniques, MRF acquires data in the transient state by continuously varying pulse sequence parameters like flip angle and repetition time, thereby efficiently encoding differences between qMRI tissue properties into the measured signal at many hundreds to thousands of independent contrast time points. In this manner, each tissue has its own unique MR “fingerprint” that can be matched to a “dictionary” of simulated fingerprints from known tissues. Quantitative parameter maps are then generated through a look-up procedure with the best-matching fingerprint from the dictionary. MRF-derived quantitative measurements of T₁ and T₂ have shown promising clinical use in detecting cancer in the brain¹¹, prostate^12–14, and liver¹⁵ with total scan times near five minutes on 3T MRI scanners. Despite the promise of MRF in diagnostic radiology, however, its use in radiation oncology applications has not been thoroughly investigated.

For radiation oncology applications, preliminary characterizations of MRF have been performed on a dedicated MR-simulator¹⁶ and a high-field (1.5T) MR-linear accelerator (MR-linac)¹⁷. To-date, however, no studies have been carried out to investigate the feasibility MRF on low-field (0.35T) MR-linacs, and the feasibility of MRF below 0.55T¹⁸ has not yet been demonstrated. Since T₁ and T₂ times vary with field strength and the signal-to-noise ratio is dramatically lower at low-field¹⁹, a thorough investigation of the technical feasibility of MRF at 0.35T is required prior to performing large scale clinical imaging studies. MR-linacs present a unique opportunity to perform longitudinal imaging of cancer patients imaged in the treatment position and open up new potential for acquiring MRF throughout the course of radiation therapy.

This study establishes several important technical characteristics of MRF to enable quantitative T₁ and T₂ mapping on a low-field MR-linac system. First, the accuracy of MRF-derived values of T₁ and T₂ were compared to gold standard methods in a quantitative standardized phantom. The accuracy of MRF as a function of scan time was then studied followed through investigations into the repeatability of MRF and the effects of the transmitting radiofrequency (RF) field homogeneity, including examination of the reproducibility of MRF across three unique MR-linac platforms. Finally, preliminary in vivo MRF experiments were performed on the 0.35T MR-linac. When taken in concert, multi-parametric quantitative MRI provides enormous potential to provide actionable information for radiation therapy plan adaptation. The validation of MRF at 0.35T is a step toward enabling efficient qMRI-guided radiation therapy on low-field MR-linac systems.

Materials and Methods

MRF Implementation

A three-dimensional (3D) gradient spoiled magnetic resonance fingerprinting pulse sequence was implemented on a low-field 0.35 T MR-linac (MRIdian Linac, ViewRay, Mountain View, CA). The MRF sequence employed radial k-space coverage in-plane and phase encoded Cartesian coverage along the slice dimension. Radial k-space coverage was chosen over the conventional variable density spiral coverage owing to the 0.35T systems being equipped gradient systems capable of producing gradient strengths of only 18 mT/m, which are not strong enough to traverse k-space with spiral coverage within the 12 ms repetition time employed in this work. Slab-selective RF pulses with a time-bandwidth product of 10.8 were used for excitation. Between successive RF excitations, the radial spoke rotated by a golden angle of 23.628°.²⁰ Each repetition of the MRF sequence consisted of non-selective adiabatic inversion preparation followed by a train of N_RF = 512 gradient echo segments. The flip angle for each of these RF pulses is shown in Figure 1. This pattern was optimized to minimize the theoretical variance in the estimation of T₁ and T₂ using well-established methods²¹. The repetition time (TR) for each of the gradient echo readouts was held constant throughout this study at 12 ms. A delay time of three seconds between MRF repetitions was used to allow for T₁ recovery prior to subsequent inversion pulses.

Figure 1.

Flip angle modulation pattern with 512 radiofrequency (RF) pulse indices used for all magnetic resonance fingerprinting experiments performed in this work.

MRF Reconstruction

As in Jiang et. al.,²² a dictionary was calculated for this MRF sequence using the extended phase graph formalism²³ with 163 T₁ values between 25 ms and 3000 ms in steps of 3%, 204 T₂ values between 5 ms and 2000 ms in steps of 2%, and 60 $B_1^{+}$ scaling factors evenly spaced between 0.3 and 1.2. Tissues with the unlikely combination of T₂ > T₁ were omitted^10,22. A total of 1,324,620 entries were included in the dictionary. To be conservative, the dictionary used here contains approximately 15 times more entries than the $B_1^{+}$-corrected approach of Chen et. al.,¹⁵ which employs a coarser sampling of T₁, T₂, and $B_1^{+}$.

All image reconstructions were performed with a combination of custom Matlab (R2020b, The MathWorks, Natick, MA) and Python code on a laptop with 4-core 2.3GHz processer and 32 GB RAM. To allow for high acceleration factors, the signal evolution throughout the MRF train of excitation pulses was constrained to span a low-dimensional subspace²⁴. The K most dominant basis functions as determined from principal component analysis (PCA) of the dictionary were used to obtain the subspace $\mathbf{\Phi }\in {ℂ}^{N_{RF}\times K}$.²⁵ In this study, K = 8 was heuristically chosen for all reconstructions as this is the threshold at which 90% of the energy of the MRF dictionary is contained. The reconstruction problem posed in Equation 1 was solved for each slice individually with 15 iterations of a linear conjugate gradient algorithm.

$${\min }_{\alpha }{\Vert \mathit{F}\mathbf{\Phi }\mathit{S}\mathit{\alpha }-y\Vert }_2^2$$ (1)

Here, $\alpha \in {ℂ}^{N\times N\times K}$ is the K -dimensional 2D image to be reconstructed, F is the 2D non-uniform fast Fourier transform operator²⁶, S is the RF coil sensitivity map operator, and y is the measured k-space data. The coil sensitivity maps were estimated using the ESPIRiT method²⁷. Following reconstruction, a dictionary matching procedure as described in Ma et. al. was used to map T₁, T₂, and B₁ in each imaging voxel¹⁰. Proton density (M₀) was also estimated in arbitrary units (a.u.) as the ratio of the ℓ₂-norm of the measured signal evolution in a voxel to that of the matching dictionary entry. The total processing time for each 3D MRF dataset was approximately 30 minutes.

MRF Benchmarking Data Acquisition

Benchmarking coronal MRF data were acquired in Scanner A in the NIST/ISMRM System Standard Model 130 Phantom (S/N 130–0130, QalibreMD, Boulder, CO) at a spatial resolution of 1.64 × 1.64 × 5 mm³ and a matrix size of 128 × 128 × 32. To investigate the impact of undersampling k-space, a large dataset consisting of 8 unique radial spokes per point in the MRF pattern were acquired. The angle of each of these spokes were defined by the golden angle increment of θ = 111.246° · n where n ∈ [1, 2, … 8].²⁸ This resulted in a total MRF scan time of about 48 minutes. To investigate the impact of reducing MRF scan time on the estimated values of T₁ and T₂, MRF reconstructions were performed using all available data and for retrospectively undersampled datasets with 1, 2, 3, and 5 spokes per frame, which corresponded to scan times of 6, 12, 18, and 30 minutes respectively. The number of spokes in each of these retrospectively undersampled MRF datasets was chosen to be a Fibonacci number to ensure approximately uniform azimuthal k-space coverage using the golden angle increment²⁸. An actual flip angle imaging (AFI) sequence²⁹ was acquired to externally map $B_1^{+}$ at a resolution of 4.92 × 4.92 × 5 mm³ with a flip angle of 45°, TR₁ of 20 ms, TR₂ of 100 ms, and total scan time of 4 minutes. Gold standard (GS) T₁ and T₂ maps were acquired in the NIST/ISMRM phantom³⁰ with approximately 10 hours of scan time using the parameters of a 2D spin echo pulse sequence shown in Table 1. The field-of-view and spatial resolution matched that of the MRF scans. Temperature was monitored within the phantom to ensure reliability and the difference was less than 0.3°C over the entire experiment.

Table 1.

Scan parameters of a 2D spin echo pulse sequence for gold standard (GS) T₁ and T₂ mapping.

	Inversion Time [ms]	Echo Time [ms]	TR [ms]
GS T1 Mapping	23, 100, 200, 400, 800, 1600, 3200	12	10,000
GS T2 Mapping	N/A	12, 22, 42, 62, 102, 152, 202	10,000

Analysis 1: Comparison of MRF and Gold Standard T₁ and T₂ Times

Within circular regions of interest (ROIs) with radii of 4 pixels (6.56 mm), the mean T₁ and T₂ times within the spheres in the T₁ and T₂ plates of the NIST/ISMRM phantom were calculated for the GS and full (i.e., 8 spokes per frame) MRF measurements. The ROIs were small enough to be fully contained within the cross section of the phantom spheres to mitigate any potential partial volume effects. This was done for three $B_1^{+}$ compensation approaches: 1) fitting for T₁ and T₂ using an externally calibrated $B_1^{+}$ map¹⁵ from the AFI scan, 2) fitting for T₁, T₂, and $B_1^{+}$ simultaneously using the MRF dictionary³¹, and 3) ignoring $B_1^{+}$ variations²². These 3 approaches were used to determine if the externally mapped $B_1^{+}$ compensation and the dictionary-compensated $B_1^{+}$ approaches yielded similar T₁ and T₂ times, thus making the separate AFI acquisition unnecessary, which has implications for throughput and efficiency. Regression analyses were performed to characterize the performance of MRF relative to GS methods for each of the $B_1^{+}$ compensation approaches. Following Kolmogorov-Smirnov (KS) tests for normality, paired t-tests were used to compare the T₁ and T₂ times from each MRF dataset to those estimated using the gold standard methods.

Analysis 2: Comparison of Full MRF and Accelerated MRF T₁ and T₂ Times

The retrospectively undersampled phantom MRF datasets were used to assess the impact of MRF scan duration on calculated T₁ and T₂ times. Within the spheres in the T₁ and T₂ plates of the NIST/ISMRM phantom, the mean T₁ and T₂ times were calculated for reconstructions from 1, 2, 3, 5, and 8 radial k-space spokes per frame. Regression and Bland-Altman analyses were performed using Matlab for quantitative comparison between relaxation times derived from varying MRF scan durations. Mean percent differences were calculated for the accelerated T₁ and T₂ measurements compared to the fully sampled measurements. Once normality was confirmed via KS testing, paired t-tests were also used to test for significant differences between the accelerated and 8-spoke MRF T₁ and T₂ times in Matlab.

Analysis 3: Short-Term Repeatability of MRF

The repeatability of T₁ and T₂ times derived using MRF was assessed in three single-spoke-per-frame datasets. The first two datasets were acquired within twelve minutes of each other while the third dataset was acquired after completion of the 10 hours of gold standard data acquisition. The coefficient of variation, calculated as the ratio of the standard deviation to the mean, over these three measurements was calculated as a function of mean T₁ and T₂ time. The repeatability coefficient (RC), as described by Barnhart et. al.³², was calculated for T₁ and T₂ over the three measurements. The interpretation of the repeatability coefficient here is that the difference in T₁ or T₂ between any two of the serial measurements in the same phantom vial is expected to be within −RC to +RC for 95% of all of the vials.

Analysis 4: Inter-Scanner Reproducibility of MRF

Using identical scan protocols for the phantom experiment as those shown above, a NIST/ISMRM system phantom with Serial Number 0088 was scanned three times on two additional 0.35T MR-Linac systems (Scanners B and C). The mean percent difference in T₁ and T₂ times calculated between Scanners B and C were calculated where the same phantom was used on both systems. Using the R language³³, the intraclass correlation coefficient (ICC) was used to assess the consistency of the three repeated measures of T₁ and T₂ measurements made between all three scanners^34,35. Separately for T₁ and T₂, a Kruskal-Wallis one-way analysis of variance was also used to test if the differences between the relaxation time measurements from the three scanners were statistically significant^36,37. Mean relaxation times were estimated within fixed ROI sizes between scanners.

Analysis 5: In Vivo MRF

MRF data in the pelvis, thigh, brain, and head/neck were acquired as part of an institutional review board approved healthy volunteer study. Common parameters for all in vivo scans include a matrix size of 256 × 256 × 32, readout bandwidth of 200 Hz/pixel, slice thickness of 3 mm, and 25% slice oversampling. Based on results of the phantom experiments shown below, the in vivo MRF datasets were acquired with a single spoke per contrast point in 6 minutes of scan time. The in-plane fields-of-view for the pelvis, thigh, brain, and head/neck acquisitions were 360, 300, 300, and 350 mm, respectively. Qualitative evaluation was conducted of the presence and severity of artifacts in the MRF data. In the brain MRF dataset, the mean and standard deviation of T₁ and T₂ times from an 8×8 pixel region in frontal white matter were calculated for comparison with published values at 0.35T.

Results

Analysis 1 Results: MRF vs Gold Standard

For qualitative comparison, the T₁, T₂, proton density (M₀), and $B_1^{+}$ maps from the 8-spoke MRF reconstruction in the system phantom can be seen in Figure 2 for the dictionary $B_1^{+}$-compensated approach. The difference maps shown in Figure 2 highlight that while the differences in T₁ maps between the $B_1^{+}$ compensation approaches are minimal, larger deviations can be observed in T₂ maps in spheres with longer T₂ times, particularly when ignoring $B_1^{+}$ variations as evidenced by the larger differences in T₂ (Figure 2 (bottom)).

Figure 2.

(Top Row) T₁, T₂, and proton density (M₀) maps shown in their respective slices of the NIST/ISMRM system phantom using the 8-spokes per frame magnetic resonance fingerprinting (MRF) dataset on a 0.35T MR-linac. The top row was generated using a dictionary matching procedure that included the mapping of $B_1^{+}$ (top right). Differences between each quantitative map for the actual flip angle imaging (AFI) compensated reconstruction and ignoring $B_1^{+}$ variations can be seen in the middle and bottom rows, respectively. The $B_1^{+}$ maps are shown in the same plate as the T₂ maps.

Figure 3 better quantifies the impact of the MRF approaches on T₁ and T₂ values as compared with gold standard methods. The linear equations of best fit of MRF-derived values of T₁ and T₂ compared with those derived with gold standard methods can be seen in the Figures 3a and 3b, respectively. The R² values from the linear fits were greater than or equal to 0.998 in each case. Bland-Altman plots in Figures 3c and 3d show the difference between MRF and gold standard T₁ and T₂ values as a function of mean gold standard value. The differences between all mean MRF and gold standard T₁ and T₂ values were found to lie on a normal distribution from the KS test for normality (p>0.05). With all approaches, MRF underestimates T₁ (6.3% for AFI-mapped $B_1^{+}$ (p=0.002), 8.2% for dictionary-mapped $B_1^{+}$ (p=0.001), and 9.7% for ignored $B_1^{+}$ (p=0.002)) and T₂ (18.6% for AFI-mapped $B_1^{+}$ (p=0.005), 10.0% for dictionary-mapped $B_1^{+}$ (p=0.003), and 9.22% for ignored $B_1^{+}$ (p=0.006)). Mapping $B_1^{+}$ with the dictionary matching procedure improved the mean percent error in the estimation of T₂ by 8.6% compared with the AFI-mapped $B_1^{+}$ compensation.

Figure 3.

Mean MRF-derived T₁ and T₂ values versus mean gold standard T₁ and T₂ times derived using inversion recovery spin echo and multi-echo spin echo imaging, respectively, in the NIST/ISMRM phantom. These MRF values were obtained using the full 48-minute (8 spoke) dataset. The R² values from the linear fits were greater than or equal to 0.998 in each case. The Bland-Altman plots below show the bias and 95% confidence interval for the difference between the gold standard and MRF measurements.

Analysis 2 Results: Scan Time Comparison

The quantitative impact of retrospectively undersampling the 8-spoke MRF dataset to 1, 2, 3, and 5 spokes can be seen in Figure 4. The equations of best fit of the mean T₁ and T₂ times of the accelerated MRF datasets to those of the full 8-spoke dataset are shown in Figures 4a and 4b. The R² values from the linear fits were greater than or equal to 0.997 in each case. For both T₁ and T₂, small errors were observed (mean percent errors of 0.65% and 4.05%, respectively) between the single-spoke and full datasets. For very short T₁ times less than 250 ms, the error due to using a shorter scan time was less than 10 ms. The error for T₁ times greater than 250 ms increases with increasing T₁ time, with the largest deviations observed for the two-spoke MRF dataset. The one- and five-spoke reconstructions performed similarly well in terms of T₁ accuracy. The T₂ values from all undersampled MRF datasets were close to those from the full 8-spoke dataset as seen with the slopes of the lines of best fit near 1.0 and small differences across the full 700 ms range in the Bland-Altman plot in Figure 4d. The differences between the T₁ and T₂ times estimated from the accelerated MRF datasets and those from the full 8-spoke datasets were found to lie on a normal distribution (KS test p-value >0.05) and were not significantly different (t-test p-value >0.05 in all cases).

Figure 4.

Comparison of MRF-derived measures of T₁ and T₂ for truncated MRF datasets with 1, 2, 3, and 5 spokes per frame compared with the full 8-spokes per frame. Plots (a) and (b) show the agreement between the accelerated and full MRF scans while (c) and (d) show the relaxation time-dependent differences. The R² values from the linear fits were greater than or equal to 0.997 in each case. The Bland-Altman plots below show the bias and 95% confidence interval for the difference between the 48-minute and accelerated MRF measurements.

Analysis 3 Results: Repeatability

The mean values of T₁ and T₂ within the NIST/ISMRM system phantom over three separate single-spoke MRF measurements (sequential and then 10 hours after) can be seen in Figure 5a and 5b, respectively. The coefficient of variation for T₁ and T₂ times for each sphere in the phantom are shown in Figures 5c and 5d. Except for T₁ times smaller than 35 ms, which are unlikely to be encountered in vivo, the coefficient of variation in T₁ times was less than 4%. The coefficients of variation in T₂ estimates made over the three MRF measurements were larger than those for T₁, but still were near or under 5% for T₂ times greater than 30 ms. The RC values for T₁ and T₂ were calculated to be 21.6 ms and 51.5 ms, respectively.

Figure 5.

Short-term repeatability results for MRF-derived values of T₁ and T₂ at 0.35T. Measurements 1 and 2 were acquired within a twelve-minute period while Measurement 3 was acquired approximately 10 hours later. In (a) and (b), the mean T₁ and T₂ times are plotted across the three measurements with each line belonging to one sphere of the system phantom. The coefficients of variation (Coeff. Var.) across the three timepoints for T₁ and T₂ are shown in (c) and (d), respectively. The color of each line in (a) and (b) corresponds to the mean T₁ and T₂ times in (c) and (d).

Analysis 4 Results: Reproducibility

The results of the reproducibility experiments can be seen in Figure 6. Scanner A served as a reference for measurements made from scanners B and C as it was used for all benchmarking experiments shown above. The mean percent error between T₁ and T₂ estimates made between Scanners B and C was 2.92% and 2.71%, respectively. For both T₁ and T₂, the ICC was found to be equal to 1, with the 95% confidence interval for the ICC being [1,1]. No significant differences were observed in the Kruskal-Wallis tests between scanners (A, B, and C, with 2 different ISMRM/NIST phantoms) for both T₁ and T₂ (p=0.99 and p=0.98, respectively). When the same phantom was used for Scanners B and C, no statistically significant differences were found for both T₁ and T₂ (p=0.89 and p=0.93, respectively).

Figure 6.

Reproducibility of MRF at 0.35T. (A) and (B) demonstrate the strong agreement between T₁ and T₂ values acquired at two different institutions while (C) and (D) highlight the agreement using the same phantom on two different MR-linacs at the same institution.

Analysis 5 Results: In Vivo MRF

Quantitative in vivo T₁ and T₂ maps derived from MRF data acquired in 6 minutes for the pelvis and thigh MRF datasets are shown in Figure 7. As expected within the prostate in the pelvic MRF datasets³⁸, longer mean T₁ and T₂ times in the peripheral zone (2024.9 ms and 576.3 ms, respectively) were observed relative to those from the central gland (790.2 ms and 150.2 ms, respectively). The T₂ maps in both the pelvic and thigh datasets appear noisier than the T₁ maps, which is consistent with other MRF implementations³⁹. The quantitative parameter maps, however, do not contain radial streaking artifacts even though only a single radial k-space spoke was acquired at each point in the MRF flip angle pattern. The $B_1^{+}$ scaling factors are near unity (0.99 ± 0.19 a.u.) over the entire pelvic field-of-view, which is expected given the reduced dielectric effect at 0.35T compared to high field diagnostic systems¹⁹.

Figure 7.

In vivo MR fingerprinting results at 0.35T in the pelvis (top row) and thigh (bottom row) of a healthy male volunteer. Quantitative T₁ and T₂ maps are shown along with the quantitative $B_1^{+}$ scaling factor and semi-quantitative proton density (M₀).

MRF-derived measures of T₁, T₂, and proton density in the brain and head/neck are shown in Figure 8. Two axial slices of the brain data are shown, and the natively acquired axial images are shown for the head/neck dataset along with a reformatted sagittal view. The sagittal view demonstrates the ability of MRF to generate T₁ and T₂ maps throughout the entire prescribed 3D volume. In the brain, the mean and standard deviations of frontal white matter T₁ and T₂ times were observed to be 433.1 ± 15.2 ms and 55.5 ± 5.3 ms, respectively. In the axial plane, the T₁ and T₂ maps from the head and neck dataset do not contain radial streaking artifacts and exhibit similar image quality to the other anatomical sites. The sagittal reformat of the head and neck T₁ and T₂ maps demonstrates the capability of MRF to map relaxation times with high quality throughout all measured slices.

Figure 8.

MR Fingerprinting maps of T₁, T₂, and proton density (M₀) in the brain and head/neck volunteer studies on a 0.35T MR-guided radiation therapy system. Two axial slices are shown in the brain (top), while a single axial slice and a sagittal reformatted image are shown in the head/neck dataset (bottom).

Discussion

To our knowledge, this work is the first to report the potential utility of MRF at a low field strength (0.35T) with the overarching goal of supporting using MRF for multiparametric quantitative imaging biomarker studies in MR-guided radiotherapy. It was shown that the 3D MRF implementation made at 0.35T produced T₁ and T₂ values from a six-minute scan that were highly correlated with those derived using gold standard spin echo methods. Similar to the work of Assländer et. al.,⁴⁰ this rapid scan time was achieved by acquiring a single radial k-space spoke per point in the MRF pattern for each phase encoded 3D partition. A minor underestimation of T₁ and T₂ values was observed, though this is consistent with other MRF validation studies^10,22,41. In Figure 3, the Bland-Altman plots appear to show a dependence of the difference in MRF- and GS-derived T₁ and T₂ estimates on mean T₁ and T₂ times. At small T1 and T2 times, MRF underestimates relaxation times, and the differences vary slowly as relaxation times increase. A similar result can be seen in Jiang et. al.⁴² Further, with the coefficients of variation over several measurements near or below 5%, it was demonstrated that MRF-derived T₁ and T₂ values are repeatable over a wide range of relaxation times. The in vivo MRF-derived T₁ and T₂ maps produced measurements were devoid of streaking artifacts despite the extreme undersampling of k-space performed herein.

It was expected that measuring $B_1^{+}$ using the well-established AFI method and incorporating this information into the MRF reconstruction would improve the accuracy of both T₁ and T₂ estimates. However, with respect to gold standard methods, MRF-based T₁ mapping was most accurate when incorporating the $B_1^{+}$ map calculated with AFI, but the accuracy in T₂ was worst when incorporating the externally measured $B_1^{+}$ map. Confounding effects that may have contributed to errors in the AFI $B_1^{+}$ maps could include insufficient gradient spoiling⁴³ and lack of an optimized selection of the flip angle and repetition times⁴⁴. Nevertheless, the use of the dictionary-based mapping of T₁, T₂, and $B_1^{+}$ provided T₁ and T₂ estimates that were near 8% and 10% of gold standard measurements, respectively, and we were still able to confirm our hypothesis that a separate AFI scan is not required to obtain accurate quantitative T₁ and T₂ maps using MRF at 0.35T.

Overall, excellent reproducibility of MRF at 0.35T was observed via phantom experiments conducted on three low-field MR-linac systems. The MRF-derived measurements of T₁ and T₂ made between three scanners from two institutions were found to be highly reproducible, as determined by very strong ICC values. Further no statistically significant differences were observed between the distribution of the T₁ and T₂ measurements between scanners, regardless of whether the same phantom was used. Using the same phantom for Scanners B and C allowed a direct mean percent error comparison of T₁ and T₂ times in the phantom that were calculated to be < 3%. This supports the implementation of MRF at 0.35T to yield reproducible estimates of T₁ and T₂, suggesting promise for future multi-institutional quantitative imaging biomarker studies using MR-linacs. Recent work has also highlighted the high degree of repeatability and reproducibility of MRF based measurements of T₁ and T₂ at field strengths of 1.5T and 3T between three international centers⁴¹.

In vivo, the observed T₁ and T₂ values from the MRF dataset in frontal white matter of 433.1 ms and 55.5 ms, respectively, were comparable to the T₁ (390–414 ms) and T₂ (54.3 ms) times available in the literature at 0.35T^3,45. The elongated T₁ and T₂ times in the peripheral zone of the prostate relative to those within the central gland as observed by MRF here at 0.35T are not directly comparable to those observed at high field, but they exhibit a similar magnitude of difference between these areas of the prostate as those measured at 3T¹² (i.e., approximately 2–3 times longer T₁ values and 3–4 times longer T₂ values). While published T₁ and T₂ times are not readily available for direct comparison within the other body sites evaluated (i.e., thigh for soft tissue sarcoma and head and neck), the overall quality of the in vivo MRF datasets was comparable to previously published methods at higher field strengths, despite being performed at the low field strength of 0.35T.

There are a few limitations of this implementation of MRF at 0.35T. First, a relatively low readout bandwidth between 150 and 200 Hz/pixel was used to compensate for the poor signal-to-noise ratio at the low magnetic field strength. This could result in blurring of the quantitative maps if areas of severe magnetic field homogeneity are encountered⁴⁶. Further, water and fat partial volume effects could have led to a bias in the in vivo relaxation maps⁴⁷. A water-fat separated MRF implementation could minimize these biases⁴⁸. Other confounding effects such as diffusion and magnetization transfer were also not considered here but can be explored in future work.

Compared with previously published MRF studies^31,49, this approach employed a relatively large dictionary to eliminate the possibility of a coarse dictionary resolution biasing the results. Future studies will seek an optimal balance between dictionary resolution, quantitative parameter accuracy, and computation time in the context of low-field MR-guided radiation therapy. An approach like Roeloffs et. al. in which small dictionaries are used in conjunction with an interpolation of the Bloch-response manifold to map tissue parameters with arbitrary resolution may be explored⁵⁰.

Future work may explore the use of more advanced MRF reconstruction algorithms employing data-driven regularization and dictionary-free parameter mapping to allow the boundaries of scan time acceleration to be pushed in support of rapid acquisition during MR-guided radiation therapy treatments. Finally, with further motion robustness strategies, extensions toward other body sites such as abdomen will be pursued in future work.

Conclusions

This feasibility study on MR fingerprinting at 0.35T demonstrated the promising potential for the rapid acquisition of T₁ and T₂ maps on low-field MR-guided radiation therapy systems. Like the work of Bruijnen et. al. demonstrating the feasibility of MRF on a high-field MR-Linac¹⁷, this work at low-field opens the door for future investigations into the characterization of tumors for outcome prediction, response assessment, and the exploratory use of MRF for qMRI-based dose plan adaptation with efficiently acquired multi-parametric quantitative imaging.

Supplementary Material

Supplementary Figure S1

Supplementary Material Figure S1. Subspace coefficient images for K=8 MRF reconstructions from one slice of the brain dataset. Note that each image is scaled individually, and the actual intensity of the images decreases dramatically as a function of k.

Data Availability Statement

The data supporting the results of this study are available upon reasonable request to the corresponding author.