Deep Image Prior Cine Magnetic Resonance Fingerprinting with B₁⁺ Spin History Correction

Abstract

Purpose:

To develop a deep image prior reconstruction for B₁⁺-corrected 2D cine magnetic resonance fingerprinting (MRF).

Methods:

The proposed method combines low-rank modeling with a deep image prior to generate cardiac phase-resolved parameter maps without motion correction, employing self-supervised training to enforce consistency with undersampled spiral k-space data. Two implementations were tested—one approach (DIP) for cine T₁, T₂, and M₀ mapping, and a second approach (DIP-B1) that also generated an effective B₁⁺ map to correct for errors due to RF transmit inhomogeneities, through-plane motion, and blood flow. Cine MRF data were acquired in 14 healthy subjects and four reconstructions were compared: low-rank (LR), low-rank motion-corrected (LRMC), DIP, and DIP-B1. Results were compared to diastolic ECG-triggered MRF, MOLLI, and T₂-prep bSSFP. Additionally, bright-blood and dark-blood images calculated from cine MRF maps were used to quantify ventricular function and compared to reference cine measurements.

Results:

DIP and DIP-B1 outperformed other cine MRF reconstructions with improved noise suppression and delineation of high-resolution details. Within-segment variability in the myocardium (reported as the coefficient of variation for T₁/T₂) was lowest for DIP-B1 (2.3/8.3%) followed by DIP (2.7/8.7%), LRMC (3.5/10.5%), and LR (15.3/39.6%). Spatial homogeneity improved with DIP-B1 having the lowest intersegment variability (2.6/4.1%). The mean bias in ejection fraction was −1.1% compared to reference cine scans.

Conclusion:

A deep image prior reconstruction for 2D cine MRF enabled cardiac phase-resolved mapping of T₁, T₂, M₀, and the effective B₁⁺ with improved noise suppression and precision compared to low-rank and motion-corrected techniques.

Introduction

Cardiac magnetic resonance (CMR) imaging is a powerful diagnostic modality that can interrogate cardiac anatomy, function, and tissue properties. Cine MRI is the gold standard for quantifying cardiac function and can be used to assess wall motion abnormalities.¹ T₁ mapping can offer insights into focal and diffuse disease processes including infarct,^2,3 fibrosis,⁴ inflammation,⁵ amyloidosis,⁶ and fat infiltration.⁷ T₂ mapping can help evaluate edema,^8,9 acute inflammatory disease, and myocarditis,¹⁰ among other conditions. Traditionally, cine imaging and parametric mapping are performed in separate acquisitions, with cine scans requiring multiple breathholds to quantify function over the left ventricle (LV), and conventional mapping techniques having limitations including low scan efficiency, mis-registration between maps acquired in separate breathholds, and sensitivity to confounding factors, such as parameter interdependence.¹¹

Multiparametric techniques can potentially overcome these limitations by providing co-registered maps of multiple properties. Approaches for simultaneous cardiac T₁ and T₂ mapping include CAIBIRIA,¹² QALAS,¹³ saturation and T₂-prep based mapping,¹⁴ multiparametric SASHA,¹⁵ and magnetic resonance fingerprinting (MRF).^16,1716,17 In particular, MRF encodes T₁ and T₂ information in magnetization signal timecourses that are produced by variable excitations and timings, whereby highly undersampled images are matched to a dictionary to obtain quantitative maps. However, many of these techniques require prospective ECG triggering, which is inefficient as it limits data collection to one cardiac phase. Motion-resolved techniques have been proposed to improve scan efficiency by quantifying tissue properties over multiple cardiac phases, allowing for joint evaluation of cardiac function. Various methods have been developed for cine T₁ mapping, such as TOPAZ,¹⁸ model-based iterative reconstructions,¹⁹ SPARCS,²⁰ and multitasking.²¹ Joint cine T₁ and T₂ mapping has been proposed using multitasking,²² free-running inversion recovery and T₂-preparation with nonrigid motion correction,²³ and cine magnetic resonance fingerprinting (MRF).^24,25

Previous studies using cine MRF employed a continuous acquisition with retrospective ECG gating, followed by a low-rank image reconstruction with non-rigid cardiac motion correction to improve SNR. Cine MRF has been demonstrated at 1.5T using a radial bSSFP sequence during a 29-second breathhold with 8 cine phases,²⁵ and at 3T using a spiral fast imaging with steady-state precession (FISP) sequence during an 11-second breathhold with 24 cine phases.²⁴ However, accurately estimating the parameters for non-rigid cardiac motion correction remains challenging in MRF due to variable contrast weightings, residual aliasing artifacts, and low SNR. Additionally, motion-corrected methods may not capture potential changes in T₁ or T₂ throughout the cardiac cycle, as images from multiple phases are registered to a single phase before dictionary matching.

Free-running 2D acquisitions may also be sensitive to errors from B₁⁺ inhomogeneities, through-plane motion, and blood flow. Myocardial tissue may move in and out of the excited slice volume with each cardiac contraction by up to 10 mm for the left ventricle,²⁶ causing deviations between measured and simulated signal evolutions. Similar discrepancies occur for blood that flows into the slice, which will not have experienced the previous RF excitations. For cine T₁ mapping, a dual flip angle acquisition has been used to improve T₁ precision by correcting for the B₁⁺ spin history (or effective B₁⁺), which reflects spatial inhomogeneities in the RF transmit field and the time-cumulative RF excitations experienced by spins moving in and out of the slice volume throughout the scan, thus absorbing errors due to through-plane motion and flow.^27,28 However, similar methods have not yet been applied to cine MRF for T₁ and T₂ mapping.

This study extends a self-supervised deep learning reconstruction first introduced for diastolic (single cardiac phase) MRF T₁, T₂, and M₀ mapping.²⁹ Here, a deep image prior reconstruction is introduced for B₁⁺-corrected 2D cine MRF T₁, T₂, and M₀ mapping and synthetic bright-blood and dark-blood cine imaging during an 11-second breathhold, which enables improved image quality and precision compared to previous low-rank and motion-corrected techniques. The proposed method combines neural networks that do not require prior training with low-rank subspace modeling to generate cardiac phase-resolved maps without motion correction. In addition, a cine map of the effective B₁⁺ is estimated to reduce errors in T₁ and T₂ estimates due to RF transmit inhomogeneities, through-plane motion, and inflowing blood. Results are presented in simulations, phantoms, and in vivo scans of 14 healthy subjects at 1.5T comparing cine MRF using low-rank, low-rank motion-corrected, and deep image prior reconstructions with and without effective B₁⁺ correction. Cine MRF T₁ and T₂ maps are compared to diastolic ECG-triggered MRF and conventional mapping sequences, and ventricular volumes and ejection fraction are validated against reference cine scans.

Methods

Cine MRF Data Acquisition

Data were acquired using a FISP-based sequence during a 10.7s breathhold with 4–15$°$ flip angles, multiple inversions and T₂ preparations, and 1820 total excitations, as previously described for cine MRF (additional sequence details are provided in Supporting Figure S1).²⁴ The ECG signal was recorded to retrospectively sort the k-space data into 24 cardiac phases by dividing each RR interval into bins of equal width. Data were sampled using a variable density spiral with 24 interleaves to fully sample the central 25% of k-space and 48 interleaves to sample the entire k-space for a 192×192 matrix size and 300×300 mm² field of view (FOV).³⁰ A pseudo golden angle ordering was used, whereby the nominal rotation was incremented by the golden angle (111$°$) every TR, and one of the 48 interleaves (equally spaced over 360$°$) was selected that was closest to the nominal angle.

Dictionary Simulation

One goal of this study was to improve T₁ and T₂ mapping precision by correcting for the effective B₁⁺. Thus, two dictionaries were simulated with and without modeling B₁⁺. A Bloch equation simulation was performed to create a dictionary assuming ideal B₁⁺ with 20,375 entries for T₁ between 60 to 4000 ms and T₂ between 6 to 1000 ms, including corrections for slice profile and preparation pulse efficiency.^31,32 A second dictionary was generated with 590,875 combinations of T₁, T₂, and B₁⁺, including B₁⁺ from 0.1 to 1.5 with a step size of 0.05. B₁⁺ was modeled as a scaling factor applied to the flip angle pattern (but not the preparation pulses). The dictionaries were precomputed because the scan was not prospectively triggered, so the subject’s cardiac rhythm did not affect the sequence timings. The dictionaries were compressed along the time dimension using a singular value decomposition (SVD).³³ The compression threshold was calculated to retain 99.99% of the energy of the uncompressed dictionary, resulting in ranks of 17 and 8 for the dictionaries with and without B₁⁺, respectively. Let $D\in {\mathbb{C}}^{p\times t}$ represent a dictionary with $t$ time points and $p$ tissue property combinations. The compressed dictionary $D_k\in {\mathbb{C}}^{p\times k}$ with rank $k$ was obtained by multiplication with the truncated right singular matrix $V_k\in {\mathbb{C}}^{t\times k}$.

$$D_k=D{V}_k$$ [1]

Reconstruction of Cine MRF Maps

The deep image prior (DIP) reconstruction was compared to two reconstructions previously employed for motion-resolved MRF: a low-rank (LR) subspace approach²⁴ and a low-rank nonrigid motion-corrected (LRMC) method.³⁴ None of these methods employed view-sharing between cardiac phases.

Low-Rank Reconstruction (LR)

Let $x\in {\mathbb{C}}^{n\times t}$ denote the MRF time-series images having $n$ pixels and $t$ time points. These images were sorted into $q$ cardiac phases using the ECG signal, with $x_j\in {\mathbb{C}}^{n\times t_j}$ denoting the images binned into cardiac phase $j$, which had $t_j<t$ time points. The LR reconstruction solved for cardiac phase-resolved “subspace images”, or images that reside in the low-dimensional subspace derived from the SVD of the dictionary. The subspace images for the $j^{th}$ cardiac phase, $x_{k,j}\in {\mathbb{C}}^{n\times k}$, were calculated by multiplying the binned time-series images by $V_{k,j}$, a matrix obtained by extracting rows from $V_k$ corresponding to the time points binned into phase $j$.

$$x_{k,j}=x_j{V}_{k,j}$$ [2]

The subspace images for all cardiac phases are collectively denoted $x_k\in {\mathbb{C}}^{n\times k\times q}$. These were solved using the following expression.

$$\underset{x_k}{\min }\sum _{j=1}^q{‖y_j-FS\left(x_{k,j}{\left(V_{k,j}\right)}^H\right)‖}_2^2+{\lambda }_{\mathit{\text{spatial}}}T{V}_{\mathit{\text{spatial}}}\left(x_k\right)+{\lambda }_{\mathit{\text{cardiac}}}T{V}_{\mathit{\text{cardiac}}}\left(x_k\right)$$ [3]

$S$ is the coil sensitivities, $F$ is the non-uniform fast Fourier Transform (NUFFT),³⁵ and $y_j\in {\mathbb{C}}^{n_{\mathit{\text{coil}}}\times n_{\mathit{\text{read}}}\times t_j}$ is the acquired spiral k-space data sorted into cardiac phase $j$, with $n_{\mathit{\text{coil}}}$ coils and $n_{\mathit{\text{read}}}$ readout points. To regularize the reconstruction, an $l_1$ total variation penalty was applied along the spatial and cardiac motion dimensions with weights ${\lambda }_{spatial}=0.003$ and ${\lambda }_{\mathit{\text{cardiac}}}=0.02$ relative to the maximum intensity in the subspace images. The weights were empirically tuned to balance noise reduction and temporal fidelity using three in vivo datasets, similar to work by Feng, et al.³⁶ Eq. 3 was solved using nonlinear conjugate gradient descent with backtracking line search with 50 iterations. Dot product matching¹⁶ was performed between the subspace images for each cardiac phase and the SVD-compressed dictionary; this process was repeated for all phases to yield motion-resolved maps.

Generalized Low-Rank Motion-Corrected Reconstruction (LRMC)

The LRMC method included nonrigid cardiac motion correction in the iterative low-rank reconstruction as proposed by Cruz, et al.³⁴ First, an auxiliary LR reconstruction was performed, and the resulting images were used to calculate nonrigid transformations for warping images from a source cardiac phase $j$ to a target phase $i$, represented by the sparse matrix $M_{j\to i}$. This transformation was computed between all possible pairs of cardiac phases using subspace images corresponding to the 2^nd singular value, as these images had high contrast between blood and myocardium.²⁴ Next, the nonrigid transformations were included in an iterative low-rank reconstruction to solve for $x_{k,j}$, the motion-corrected subspace images for cardiac phase $j$.

$$\underset{x_{k,j}}{\min }\sum _{i=1}^q{‖y^{\left(i\right)}-FS{M}_{j\to i}\left(x_{k,j}{\left(V_{k,i}\right)}^H\right)‖}_2^2+{\lambda }_{\mathit{\text{spatial}}}T{V}_{\mathit{\text{spatial}}}\left(x_{k,j}\right)+\sum _b{\lambda }_{LLR}{‖R_b{x}_{k,j}‖}_{\mathrm{*}}$$ [4]

Spatial total variation and locally low-rank (LLR) patch-based regularization were used, where $R_b$ selected an image patch of size 8×8 around pixel $b$ and reshaped it to a local Casorati matrix, with empirically tuned parameters of ${\lambda }_{spatial}=0.003$ and ${\lambda }_{LLR}=0.02$. Eq. 4 was solved using the alternating direction method of multipliers (ADMM) with 25 iterations. After reconstruction, the subspace images $x_{k,j}$ were matched to the compressed dictionary to yield motion-corrected maps for a single cardiac phase $j$. Eq. 4 was repeatedly solved, each time choosing a different phase as the target for motion correction, to obtain motion-resolved maps.

Deep Image Prior (DIP)

An overview of the DIP reconstruction is shown in Figure 1. No additional MRF datasets were used for pre-training. After each acquisition, the networks were initialized with random values and trained de novo by enforcing consistency with undersampled k-space data from the current scan. The reconstruction used a system of three neural networks.

Figure 1:

The DIP reconstruction uses two untrained neural networks: the Image Reconstruction Network (IRN) and the Parameter Estimation Network (PEN). (A) The IRN is a u-net that generates images in a low-dimensional subspace derived from the MRF dictionary. This network takes a random noise tensor as input, with a different input tensor $z_j$ initialized for each cardiac phase $j$, and generates subspace images $x_{k,j}$ for the corresponding cardiac phase. During training, the MRF forward encoding model is simulated, and the mean squared error (MSE) loss is calculated with respect to the acquired spiral k-space data to update the IRN weights. (B) The PEN is a fully-connected network that generates quantitative maps of T₁, T₂, M₀ (real and imaginary parts), and the effective B₁⁺ from the subspace images. To update the PEN weights, the maps are used to calculate synthetic subspace images by replacing each voxel with simulated signal evolutions generated by a pre-trained fully-connected network called the Fingerprint Generator Network (FGN). The MSE loss is then computed between these synthetic images and the IRN-generated subspace images.

1. Image Reconstruction Network (IRN): a 2D convolutional u-net (without prior training) that generated cardiac phase-resolved subspace images.

2. Parameter Estimation Network (PEN): a fully-connected network (without prior training) that estimated quantitative maps from subspace images.

3. Fingerprint Generator Network (FGN): a fully-connected network (pre-trained using the MRF dictionary) that output simulated signal evolutions for input T₁, T₂, and B₁⁺ values.

For static imaging, the input to a deep image prior is typically a tensor of randomly initialized values that remains fixed throughout training.³⁷ In this work, a DIP reconstruction originally developed for diastolic (single-phase) MRF²⁹ was generalized to cine MRF by using a different input tensor for each cardiac phase. Let $z_j\in {\mathbb{R}}^{n_y\times n_x\times d}$ denote the input for phase $j$, where $n_y$ and $n_x$ are the matrix size, and $d$ is an adjustable parameter defining the number of feature maps in the input (this study used $d=32$). The inputs for the first ($z_1$) and last ($z_q$) cardiac phases were initialized with random values between −1 and 1, and the inputs for intermediate phases were calculated by linear interpolation, which imposed some regularization along the cardiac motion dimension. For a given cardiac phase $j$, the tensor $z_j$ was input to the IRN to generate subspace images $x_{k,j}$.

$$x_{k,j}=\mathbf{I}\mathbf{R}\mathbf{N}\left(z_j\right)$$ [5]

Self-supervised training was performed by computing the forward encoding model, which included coil sensitivities, a low-rank MRF signal approximation, and spiral k-space sampling. The mean squared error (MSE) loss was calculated at the sampled locations in k-space after multiplication by the density compensation function $W$. Only the IRN weights were updated during training, while the inputs $z_j$ remained fixed.

$$\underset{\mathbf{IRN}}{\min }{‖W{y}_j-WFS\left(x_{k,j}{\left(V_{k,j}\right)}^H\right)‖}_2^2$$ [6]

Next, the subspace images were input to the PEN, which performed voxelwise estimation of T₁, T₂, M₀ (modeled as a complex scaling factor), and the effective B₁⁺. This network was trained in a self-supervised manner by calculating synthetic subspace images using the T₁, T₂, M₀, and B₁⁺ maps, which were compared to the images generated by the IRN in the previous step using an MSE loss. One approach to calculate the synthetic images would be to project the maps onto the MRF dictionary, updating each pixel location with a signal from the dictionary based on its T₁, T₂, and B₁⁺ value. However, a more efficient strategy was used here since this step must be executed repeatedly during training. A neural network (the FGN) was used that takes T₁, T₂, and B₁⁺ values as inputs and generates signal evolutions (in the subspace), which avoided the need for dictionary searching. The FGN was trained using the SVD-compressed dictionary; it was the only pre-trained network in the DIP pipeline. The PEN training is represented by Eqs. 7 and 8, where T_1,j, T_2,j, M_0,j, and B_1,j⁺ denote the maps for cardiac phase j.

$$T_{1,j},T_{2,j},M_{0,j},B_{1,j}^{+}=\mathbf{P}\mathbf{E}\mathbf{N}\left(x_{k,j}\right)$$ [7]

$$\underset{\mathbf{PEN}}{\min }{‖{x_{k,j}-M}_{0,\mathrm{j}}\mathbf{F}\mathbf{G}\mathbf{N}\left(T_{1,j},T_{2,j},B_{1,j}^{+}\right)‖}_2^2$$ [8]

The DIP reconstruction was implemented using Tensorflow/Keras on one GPU on a high-performance computing cluster. A 10% dropout was incorporated after each convolutional layer in the IRN during training to mitigate overfitting, as in prior work for diastolic mapping.²⁹ The IRN and PEN were trained in parallel for 30,000 iterations with an Adam optimizer and a learning rate of 0.001. On each iteration, 10 TRs acquired during the same cardiac phase were used as a mini-batch. The final motion-resolved maps were obtained by applying an exponential average with a weight of 0.99 to the network output over the final 1,000 iterations to smooth out instabilities during training due to stochastic gradient descent, as described in the original DIP publication by Ulyanov, et al.³⁷ Additional details about the network architectures are provided in Supporting Figures S2, S3, and S4.

Calculation of Synthetic Multi-Contrast Cine Images

MRF maps were used to calculate synthetic cine images that approximated the contrast of traditional weighted images and were segmented to quantify ventricular volumes and ejection fraction (EF). Bright-blood images were obtained by using T₁, T₂, and M₀ maps to simulate a steady-state bSSFP sequence with flip angle $\alpha$=70$°$ and TE=2 ms.

$$S_{bSSFP}=M_0\sin \left(\alpha \right)\mathrm{ }\frac{\exp \left(-\frac{TE}{T_2}\right)}{1+\cos \left(\alpha \right)+\left(1-\cos \left(\alpha \right)\right)\left(\frac{T_1}{T_2}\right)}$$ [9]

To demonstrate that the image contrast can be adjusted retrospectively, dark-blood cine images were also simulated. Dark-blood images are conventionally acquired using double inversion recovery.³⁸ However, simulating this sequence is not straightforward since it relies on properties of flowing blood. A simpler approach was used to approximate a dark-blood contrast by taking the difference between two synthetic bSSFP images with flip angles of 120$°$ and 70$°$, inspired by a similar strategy for obtaining high-contrast difference images in SASHA.³⁹

Simulations

Simulations were performed to compare the accuracy of LR, LRMC, and DIP reconstructions using the XCAT phantom.⁴⁰ The phantom incorporated cardiac motion at 70 beats per minute (bpm), 8-channel coil sensitivity maps, and relaxation times relevant for 1.5T. The purpose of these experiments was to evaluate the deep learning reconstruction, so B₁⁺ inhomogeneities and through-plane motion were not simulated. Two phantom scenarios were created. The first scenario employed a constant myocardial T₁ of 1050 ms and T₂ of 50 ms. The second scenario had cyclical variations every heartbeat, with T₁ ranging from 1000 ms (diastole) to 1100 ms (systole) and T₂ ranging from 50 ms (diastole) to 40 ms (systole), to test the ability of each reconstruction to capture changes in relaxation times. These values were selected based on similar trends reported with multitasking, which found higher T₁ and lower T₂ in systole.²² Cine MRF data were simulated by performing Bloch equation signal generation, spiral k-space sampling, and retrospective ECG binning. Cardiac phase-resolved maps were reconstructed using LR, LRMC, and DIP methods. The normalized root mean square error (nRMSE) in the T₁ and T₂ maps was calculated for each method, reported as an average over all phases. Mean T₁ and T₂ values within the myocardium at each cardiac phase were compared to ground truth values. For the scenario with constant relaxation times, additional simulations were performed using (1) different numbers of feature maps $d$ in the input tensors, and (2) randomly initialized input tensors without linear interpolation along the cardiac phase dimension.

Phantom Experiments

The purpose of the phantom experiments was to evaluate the accuracy of different cine MRF reconstructions and assess the impact of B₁⁺ correction on T₁ and T₂ measurements. The ISMRM/NIST MRI system phantom⁴¹ was scanned at 1.5T (Sola, MAGNETOM Siemens, Erlangen, Germany). Cine MRF data were collected at a single slice planned through the T₂ layer of the phantom with the following imaging parameters: 192×192 matrix, 300×300 mm² FOV, 1.6×1.6×8.0 mm³ resolution, 10.7s scan duration. Although the phantom was stationary, data were binned into 24 phases using an ECG signal recorded from a separate healthy subject scan. Maps were reconstructed without B₁⁺ correction using LR and LR-MOCO methods. The deep image prior reconstruction was performed with and without effective B₁⁺ correction; these will be abbreviated DIP-B1 and DIP. For comparison, data were collected using a 15-heartbeat MRF scan with prospective ECG triggering and a 250 ms acquisition window, with a 60 bpm heart rate simulated at the scanner. T₁, T₂, and M₀ maps without B₁⁺ correction were reconstructed using a deep image prior method for single-phase (not cine) mapping.²⁹ A 5(3)3 MOLLI T₁ map⁴² and a T₂-prepared bSSFP map (T₂ prep times of 0, 25, and 55 ms)⁸ were also collected with matched imaging parameters. A reference B₁⁺ map was obtained using a presaturation-based sequence provided by the scanner vendor.⁴³ Mean T₁, T₂, and B₁⁺ measurements were compared to reference values using linear regression and Bland-Altman analyses.⁴⁴ T₂ values above 300 ms were excluded from analysis because the MRF sequences were not designed for that regime, considering that the longest T₂ prep time was 80 ms.

Healthy Volunteer Scans

Data Acquisition

Fourteen healthy subjects were scanned at 1.5T after obtaining written informed consent in this IRB-approved, HIPAA-compliant study. Cine MRF scans were collected at a mid-ventricular short-axis slice using the same imaging parameters as the phantom experiment and reconstructed using LR, LR-MOCO, DIP, and DIP-B1 methods. Synthetic bright-blood and dark-blood cine images were computed from the maps. For comparison, single-phase diastolic T₁, T₂, and M₀ maps were collected using MRF (15-heartbeat breathhold) with prospective ECG triggering, 5(3)3 MOLLI (11-heartbeat breathhold), and T₂-prep bSSFP (10-heartbeat breathhold). In 8 out of 14 subjects, a short-axis stack of cine MRF data were collected with full LV coverage to quantify end-diastolic volume (EDV), end-systolic volume (ESV), and ejection fraction (EF). Each cine MRF slice was imaged in a separate breathhold with a 25% slice gap and 9–12 total slices, depending on the heart size. Reference measurements were obtained from a Cartesian bSSFP cine scan with 24 phases, 6.2-second breathhold per slice, TR/TE 4.0/2.0 ms, GRAPPA R=2, flip angle 70$°$, and 1.6×1×6×8.0 mm³ resolution.

Image Analysis

Regions of interest (ROIs) were manually drawn in six myocardial segments on the T₁ and T₂ maps using the standardized American Heart Association (AHA) model.⁴⁵ Cine MRF maps were analyzed both at end-diastole and end-systole. Mean T₁ and T₂ values within each segment were computed for all subjects. Precision was evaluated in two ways. First, the within-segment coefficient of variation (CoV) for each subject was calculated by normalizing the standard deviation (SD) within each segment by the mean T₁ or T₂. Second, the intersegment CoV for each subject was found by computing the SD of the mean T₁ or T₂ values over all six AHA segments.

For reference and synthetic cine images, EDV and ESV were quantified by manually delineating the endocardial borders on image frames at end-diastole and end-systole. For cine MRF, this analysis was performed while viewing the co-registered bright-blood and dark-blood images simultaneously. EF was computed using the following expression.

$$EF=\frac{EDV-ESV}{EDV}\times 100\mathrm{\%}$$ [10]

Differences in myocardial T₁ and T₂ measurements among methods were assessed using a Kruskal-Wallis test with Bonferroni post-hoc correction. Differences between cine MRF T₁ and T₂ values measured in diastole versus systole were assessed using a paired t-test. The agreement between MRF and reference EDV, ESV, and EF measurements was evaluated using Bland-Altman tests. Statistical significance was defined as $p<0.05$.

Results

Simulations

For the scenario with constant relaxation times (Figure 2A), the average T₁/T₂ RMSE values over the whole image were 6.6/15.0% for LR, 3.0/9.0% for LRMC, and 0.9/1.6% for DIP. Peak errors in the estimated myocardial relaxation times (reported as T₁/T₂) over all cardiac phases were 8.6/37.0% for LR, 1.2/1.4% for LRMC, and 0.2/0.7% for DIP (Figures 2B–2C). DIP also yielded the lowest errors in the scenario with variable relaxation times (Figures 2D–2F). The LRMC reconstruction incorrectly estimated a constant T₁ of 1070 ms and T₂ of 43 ms, reflecting a weighted average of the true T₁ and T₂, which varied between 1000–1100 for T₁ and 40–50 ms for T₂ over the cardiac cycle. DIP was the only technique that accurately resolved the dynamic T₁ and T₂ values. As shown in Supporting Figure S5, the number of feature maps in the input tensors had negligible impact on the reconstruction error. Using random input tensors for each cardiac phase resulted in higher RMSE values (T₁ 1.2%, T₂ 2.9%) than inputs that were linearly interpolated along the cardiac phase dimension (T₁ 0.9%, T₂ 1.6%).

Figure 2:

XCAT simulation results for two scenarios with myocardial T₁ and T₂ values that either remain constant (top row) or vary cyclically (bottom row) within every heartbeat. For the scenario with constant relaxation times, (A) the RMSE for cine MRF T₁ and T₂ maps, averaged over all cine phases, is shown using low-rank (LR), low-rank motion-corrected (LRMC), and deep image prior (DIP) reconstructions. (B) Mean measured myocardial T₁ and (C) T₂ values using each reconstruction are plotted as a function of cardiac phase. Similar results for the simulation with varying myocardial T₁ and T₂ values are shown in (D-F).

Phantom Experiments

Linear regression plots from the phantom experiment are shown in Supporting Figure S6, along with linear regression statistics in Supporting Table S1 and Bland-Altman statistics in Supporting Table S2. All methods had excellent agreement with inversion recovery for T₁ with R² > 0.999. While T₂-prep bSSFP generally overestimated T₂ values (especially for short T₂ species), all MRF sequences had excellent agreement with spin echo measurements. The correlation between cine MRF and reference T₂ estimates improved when the effective B₁⁺ was estimated in the DIP-B1 reconstruction. R² values increased from 0.997 to 0.999, mean bias improved from −0.5 to 0.0 ms, and the Bland-Altman 95% limits of agreement narrowed from (−12.1, 11.1) to (−7.1, 7.1) ms. Effective B₁⁺ values using cine MRF were higher than reference values with a mean bias of 0.10 and 95% limits of agreement (0.06, 0.13). Plots demonstrating the temporal stability of T₁, T₂, and effective B₁⁺ measurements over cardiac phases are shown in Supporting Figure S7.

Healthy Volunteer Scans

Figure 3 shows representative maps from one subject, including diastolic maps using ECG-triggered sequences (MOLLI, T₂-prep bSSFP, and MRF), as well as cine MRF maps in diastolic and systolic phases using LR, LRMC, DIP, and DIP-B1 methods. The LR reconstruction showed severe noise enhancement. The LRMC reconstruction exhibited noise enhancement to a lesser degree; however, slight motion blurring and a loss of high-resolution details were observed (e.g., in the small vessels in the liver and trabeculations in the heart). The DIP reconstruction provided excellent noise suppression and better delineation of high-resolution details compared to LRMC. With the DIP-B1 reconstruction, the spatial homogeneity in the T₁ and T₂ maps improved both in myocardium and blood, as did the temporal homogeneity in myocardial T₁ and T₂ measured over the cardiac cycle. The improved spatial and temporal homogeneity can be appreciated in Supporting Videos S1–S4. Figure 4 shows synthetic bright-blood and dark-blood cine images for the same subject. The full FOV maps and synthetic images are shown in Supporting Figures S8–S11. Reference cine images for this subject are shown in Supporting Video S5.

Figure 3:

Representative maps from a healthy subject. (A) Diastolic T₁ and T₂ maps are displayed using conventional MOLLI and T₂-prep bSSFP sequences. (B) T₁, T₂, and M₀ maps are presented using MRF with prospective ECG triggering with a diastolic acquisition window reconstructed using a deep image prior (DIP). Cine MRF T₁, T₂, and M₀ maps are shown in diastolic and systolic phases using (C) low-rank, (D) low-rank motion-corrected (LRMC), and (E) DIP reconstructions. (F) Cine MRF maps using a DIP reconstruction with effective B₁⁺ estimation are presented in the rightmost column. Maps are cropped to a central 96 × 96 region over the heart. Full FOV maps are shown in Supporting Figure S3.

Figure 4:

Cine images for the same subject as shown in Figure 3. (A) Reference Cartesian cine bSSFP images are shown in diastolic and systolic phases. Synthetic bright-blood bSSFP (top row) and dark-blood (bottom row) images derived from the cine MRF tissue property maps are presented using various reconstructions methods including (B) low-rank, (C) low-rank motion-corrected, (D) deep image prior, and (E) deep image prior with effective B₁⁺ estimation. Images are cropped to a central 96 × 96 region over the heart. Full FOV images are shown in Supporting Figure S4.

Figure 5 shows cine MRF maps at multiple cardiac phases using each reconstruction, along with x-t profiles to visualize the temporal dynamics. Myocardial T₁ and T₂ values were constant throughout the cardiac cycle with LRMC; this was expected since the motion correction step combined time points from all cardiac phases before pattern matching, thus favoring a constant T₁ and T₂. Variations in T₁ and T₂ across phases were observed using the LR and DIP reconstructions without B₁⁺ correction. In this subject, for example, T₁ in myocardium and blood appeared lower, T₂ in myocardium appeared lower, and T₂ in blood appeared higher during systole (Phases 7–15) than diastole (Phases 1–6 and 16–24), as indicated by the arrows in panels A and C. These fluctuations in T₁ and T₂ were believed to be an artifact due to through-plane motion during cardiac contraction, as the DIP-B1 reconstruction led to improved temporal homogeneity with more consistent T₁ and T₂ values in myocardium and blood over the cardiac cycle. The improvement in temporal homogeneity is also seen in Supporting Figure S10, which compares diastolic and systolic relaxation times for all reconstructions. The relative change between diastolic and systolic T₁, reported as mean $\pm$ SD over all subjects (with positive indicating higher systolic measurements), was $-0.1\pm 21.3\%$ for LR, $1.0\pm 1.4\%$ for LRMC, $-3.8\pm 6.1\%$ for DIP, and $-0.1\pm 1.3\%$ for DIP-B1. The relative change in T₂ was $-10.6\pm 36.7\%$ for LR, $-0.6\pm 5.9\%$ for LRMC, $-3.1\pm 6.2\%$ for DIP, and $0.7\pm 4.3\%$ for DIP-B1. There were no significant differences in diastolic versus systolic relaxation times with any method.

Figure 5:

Cine MRF maps displayed over multiple cardiac phases using various reconstruction techniques, along with x-t profiles to visualize temporal dynamics. Cardiac phase-resolved T₁, T₂, and M₀ maps are shown using (A) low-rank, (B) low-rank motion-corrected, and (C) deep image prior reconstructions, along with (D) T₁, T₂, M₀, and effective B₁⁺ maps using a deep image prior with simultaneous B₁⁺ estimation. The arrows in (A) and (C) indicate an artifactual (non-physiological) decrease in myocardial and blood T₁, decrease in myocardial T₂, and increase in blood T₂ that were observed in systole for the DIP reconstruction in this subject, which were mitigated when B₁⁺ spin history effects were modeled in the reconstruction in (D). Maps were cropped to a central 96×96 region over the heart.

Figure 6 compares diastolic T₁ and T₂ values in the inferolateral septum using different techniques. T₁ values (mean $\pm$ SD over all subjects) were 1007$\pm$25 ms with MOLLI and 1020$\pm$38 ms with ECG-triggered MRF. Cine MRF T₁ values were 1024$\pm$144 ms with LR, 1069$\pm$41 ms with LRMC, 1077$\pm$34 ms with DIP, and 1039$\pm$32 ms with DIP-B1. LR had the highest intersubject variability, while DIP-B1 had the lowest. LRMC and DIP (but not DIP-B1) had significantly higher T₁ values than MOLLI and ECG-triggered MRF. Average T₂ values were 48.0$\pm$2.9 ms with T₂-prep bSSFP and 41.2$\pm$4.9 ms with ECG-triggered MRF. Cine MRF T₂ values were 56.0$\pm$14.6 ms with LR, 42.6$\pm$3.7 ms with LRMC, 39.5$\pm$3.7 ms with DIP, and 39.2$\pm$3.8 ms with DIP-B1. All MRF methods had significantly lower T₂ values than T₂-prep bSSFP.

Figure 6:

Mean diastolic (A) T₁ and (B) T₂ values measured in the left ventricular inferolateral septum using conventional MOLLI and T₂-prep bSSFP sequences, ECG-triggered MRF, and cine MRF with various reconstruction methods including low-rank (LR), low-rank motion-corrected (LRMC), deep image prior (DIP), and deep image prior with effective B₁⁺ estimation (DIP-B1). The mean $\pm$ standard deviation over all subjects is reported on the graphs.

Figure 7 compares the precision of various cine MRF reconstructions in the myocardium. The within-segment variability for cine MRF T₁ and T₂ was highest with LR and progressively lower with LRMC, DIP, and DIP-B1 in most segments. For the inferolateral septum (segment 9), the within-segment CV (reported as T₁/T₂) was 15.3/39.6% for LR, 3.5/10.5% for LRMC, 2.7/8.7% for DIP, and 2.3/8.3% for DIP-B1, 2.2/5.0% for ECG-triggered MRF, and 4.9/8.8% for conventional mapping (MOLLI and T₂-prep bSSFP). The intersegment variability for T₁/T₂ was 5.5/8.4% for LR, 5.6/6.5% for LRMC, 3.0/4.3% for DIP, 2.6/4.1% for DIP-B1, 3.2/5.2% for ECG-triggered MRF, and 2.2/3.4% for conventional mapping.

Figure 7:

Variability of T₁ and T₂ measurements for conventional mapping, ECG-triggered MRF, and cine MRF with various reconstruction techniques. (A,B) The within-segment coefficient of variation (CoV) within AHA segments 7–12 is shown for T₁ and T₂, along with (C,D) the intersegment CoV.

Figure 8 shows Bland-Altman plots comparing ESV, EDV, and EF from cine MRF with the DIP-B1 reconstruction to a reference cine scan. For LVEF, the mean bias was 0.8% with 95% limits of agreement (−3.9, 5.5)%. For EDV, the mean bias was −0.8 mL with 95% limits of agreement (−13.8, 12.2) mL. For ESV, the mean bias was −1.1 mL with 95% limits of agreement (−10.4, 8.1) mL.

Figure 8:

Bland-Altman plots comparing (A) left ventricular ejection fraction, (B) end-diastolic volume, and (C) end-systolic volume between cine MRF DIP-B1 and a reference Cartesian bSSFP cine scan. The solid line indicates the mean bias, and the two dotted lines indicate the 95% upper and lower limits of agreement.

Figure 9 displays a short-axis stack of cine MRF T₁, T₂, M₀, and effective B₁⁺ maps using the DIP-B1 reconstruction, along with synthetic bright-blood and dark-blood cine images. Six out of ten acquired slices are shown. All ten slices were collected in 3.2 minutes, accounting for the MRF scan (10.7s breathhold per slice) followed by a 10s pause to allow the subject to recover their breath. A movie showing the DIP-B1 short-axis cine maps is provided in Supporting Video S6.

Figure 9:

Cine MRF T₁, T₂, M₀, and effective B₁⁺ maps and synthetic bright-blood bSSFP and dark-blood images acquired from multiple short-axis slices, shown in (A) diastolic and (B) systolic cardiac phases.

Discussion

This study presented a deep image prior reconstruction for 2D cine MRF T₁, T₂, and M₀ mapping with effective B₁⁺ correction, which also provides synthetic bright-blood and dark-blood cine images. The deep image prior outperformed a low-rank (LR) subspace reconstruction and a low-rank reconstruction with non-rigid cardiac motion correction (LRMC), offering superior noise suppression and delineation of high-resolution features. The deep image prior improved T₁ and T₂ mapping precision, with lower within-segment and intersegment variability, which was further enhanced when correcting for the effective B₁⁺. Excellent agreement with reference measurements of ventricular volumes and ejection fraction was observed. Motion-resolved mapping at a single slice was performed with 24 cine phases at 1.6×1.6×8 mm³ at 1.5T during an 11-second breathhold. This work has potential clinical implications for streamlining CMR exams, as the average scan time to acquire 2D multislice cine MRF data with short-axis coverage (3.2 minutes) was comparable to the conventional cine stack (2.5 minutes), while enabling simultaneous assessment of cardiac tissue and function.

Zero-Shot Deep Learning

For each dataset, training was performed de novo with randomly initialized network weights and input tensors. This strategy avoids challenges with obtaining ground truth (e.g., fully-sampled) data for network training, which can be difficult to due long scan times and physiological motion. The cine MRF deep image prior is an extension of previous work for diastolic mapping²⁹ that used a 2D u-net to generate subspace images, taking a single tensor with randomly initialized values as input. For cine MRF, the same network architecture was used, but with multiple input tensors (one per cardiac phase). An alternative but more computationally intensive approach that was not explored here could be to use a 3D u-net, which takes a single input tensor and outputs subspace images for all cardiac phases simultaneously.

B₁⁺ Spin History Correction

This study explored the impact of effective B₁⁺ correction in cine MRF, inspired by related work using dual flip angle continuous inversion recovery T₁ mapping²⁷ and multitasking.²⁸ The term “effective B₁⁺” is used because it includes both the instantaneous B₁⁺ (spatial variations in the RF transmit field) and time-cumulative B₁⁺ (experienced by spins moving in and out of the excited slice volume) to mitigate through-plane motion and flow effects. These effects are important to consider for free-running 2D mapping sequences. Although the scan was breathheld, through-plane motion due to cardiac contraction may cause deviations from the expected signal behavior. In addition, blood entering the slice will not have experienced previous RF excitations, leading to a lower effective B₁⁺ in blood than myocardium. The mean effective B₁⁺ over all subjects using cine MRF was 0.66$\pm$0.08 in myocardium and 0.21$\pm$0.04 in LV blood (Supporting Figure S11). Correcting for effective B₁⁺ improved the spatial homogeneity in the T₁ and T₂ maps, as evidenced by the lower within-segment and intersegment variability, and improved temporal homogeneity in T₁ and T₂ across cardiac phases.

Diastolic and Systolic Mapping

Due to the thicker myocardium, systolic maps may have reduced partial volume artifacts that facilitate easier myocardial segmentation. There have been conflicting findings in the literature about potential differences in relaxation times during diastole and systole.^{18,19,46–48} Before correcting for the effective B₁⁺, inconsistent measurements were obtained with some subjects showing higher T₁ or T₂ in different parts of the cardiac cycle using reconstructions without motion correction (LR and DIP). After accounting for the effective B₁⁺, the DIP-B1 reconstruction showed less variability with no significant difference between diastolic and systolic measurements, which can be appreciated visually in Supporting Videos S3–S4.

Average T₁ measurements using cine MRF with DIP-B1 were 1039$\pm$32 ms, which were somewhat (but not significantly) higher than MOLLI (1007$\pm$25 ms) and similar to single-phase MRF with prospective triggering (1020$\pm$38 ms),³² although lower than literature values for SASHA.⁴⁹ MRF accounts for slice profile imperfections and inversion efficiency, which has been shown to increase T₁ slightly.³² Consistent with prior studies,^24,50 T₁ measurements from MRF were closer to MOLLI than literature values for SASHA. Because MRF and MOLLI rely on inversions to generate much of the T₁ encoding, MRF measurements are likely biased by magnetization transfer, which has been shown to cause an underestimation of myocardial T₁ using MOLLI.⁵¹ Average T₂ measurements using cine MRF with DIP-B1 were 39.2$\pm$3.8 ms, which were similar to ECG-triggered MRF (41.2$\pm$4.9 ms) and significantly lower than T₂-prep bSSFP (48.0$\pm$2.9 ms). Discrepancies between MRF and conventional T₂ mapping have been reported previously and may be caused by magnetization transfer,⁵² intravoxel dephasing,⁵³ and motion sensitivity along the unbalanced gradient direction.⁵⁴

Synthetic Cine Images

In clinical practice, cine images are collected using a bright-blood bSSFP sequence to quantify cardiac function, and dark-blood images are often acquired using a double inversion recovery sequence to visualize the chamber walls.³⁸ In this study, bright-blood and dark-blood cine images derived from MRF maps were viewed simultaneously to improve confidence in contouring the endocardium. However, functional measurements could also be obtained by directly segmenting the motion-resolved maps.

Motion Correction

Motion correction in cardiac MRF is a challenging problem due to the variable contrast weightings, high undersampling factors, and often low SNR in the time series images. In addition, motion-corrected approaches combine images collected at different time points in the cardiac cycle, registering them to the same cardiac phase before parameter quantification. While these maps depict cardiac motion, the myocardial T₁ and T₂ values are forced to be constant, which was observed in simulations and in vivo using the LRMC reconstruction. There are conflicting reports regarding the variation of relaxation times over the cardiac cycle and their clinical relevance.^{18,19,46–48} Nevertheless, the deep image prior reconstruction does not employ motion correction and was the only technique capable of resolving dynamic changes in T₁ and T₂ in simulations, although no differences between diastolic and systolic values were observed in vivo.

Limitations and Future Work

One limitation of this approach is the long reconstruction time of approximately 2 hours per slice since the network is re-trained for each scan. Future work will investigate using transfer learning to shorten the reconstruction time by initializing with pre-trained network weights, followed by fine-tuning on a specific dataset. Because the cardiac rhythm affects how time points in the MRF signal evolutions are binned, it is possible that some cardiac rhythms may result in poor T₁ and T₂ encoding for certain phases. The DIP-B1 reconstruction used smoothly varying network inputs to impose regularization across cardiac phases to counter this problem; however, the interaction between binning and parametric encoding for different cardiac rhythms requires further investigation. The cine MRF pulse sequence was empirically designed for T₁ and T₂ quantification. This sequence was not optimized numerically and was not designed to increase B₁⁺ sensitivity, as B₁⁺ was considered a confounding factor. Various MRF optimization schemes have been proposed, including methods based on Cramer Rao lower bounds^55,56 and methods that consider effects of k-space undersampling,^57,58 which could be applied to cine MRF. Additionally, MRF flip angle patterns designed to increase B₁⁺ sensitivity could be incorporated to improve the accuracy of B₁⁺ mapping.⁵⁹ The DIP-B1 reconstruction may enable reductions in the cine MRF breathhold duration, as demonstrated in Supporting Figure S12, which will be explored in future work. Another limitation is that validation was only performed in healthy subjects for native mapping. Future work will include validation for post-contrast cine mapping and in patients.

Conclusion

A deep image prior reconstruction was developed for cine MRF, which uses neural networks to generate cardiac phase-resolved T₁, T₂, M₀, and effective B₁⁺ maps without prior training, along with synthetic bright-blood and dark-blood cine images. The deep image prior outperformed low-rank and motion-corrected reconstructions, yielding improved noise suppression and improved T₁ and T₂ mapping precision. This work has clinical implications for streamlining CMR exams by allowing rapid assessment of myocardial tissue and cardiac function during one acquisition.

Supplementary Material

Video S3

Supporting Video S3: Cine MRF T₁, T₂, and M₀ maps and synthetic bright-blood and dark-blood images from a healthy subject obtained using the deep image prior (DIP) reconstruction

Video S2

Supporting Video S2: Cine MRF T₁, T₂, and M₀ maps and synthetic bright-blood and dark-blood images from a healthy subject obtained using the generalized low-rank non-rigid motion-corrected (LRMC) reconstruction.

Video S4

Supporting Video S4: Cine MRF T₁, T₂, and M₀ maps and synthetic bright-blood and dark-blood images from a healthy subject obtained using the deep image prior reconstruction with B₁⁺ spin history correction (DIP-B1).

Video S5

Supporting Video S5: Reference Cartesian cine images from the same healthy subject as in Supporting Videos S1-S4.

Video S6

Supporting Video S6: Six short-axis slices acquired using cine MRF in sequential breathholds (one breathhold per slice) and reconstructed using the deep image prior with B₁⁺ spin history correction (DIP-B1).

Video S1

Supporting Video S1: Cine MRF T₁, T₂, and M₀ maps and synthetic bright-blood and dark-blood images from a healthy subject obtained using the low-rank (LR) reconstruction.

Supinfo

Supporting Figure S1: The pattern of flip angles and preparation pulse employed in cine MRF. Data were collected using a FISP sequence with variable flip angles ranging from 4 to 15°. Inversion pulses (blue arrows) with a duration of 21 ms and T₂ preparation pulses (red arrows) with durations of 30, 50, and 80 ms were periodically applied during the scan. The TE (1.4 ms) and TR (5.4 ms) were held constant. A total of 1820 excitations were acquired during a breathhold of 10.7 seconds.

Supporting Figure S2: Architecture of the Image Reconstruction Network (IRN). A u-net architecture is used with five downsampling and upsampling layers with skip connections. The blue rectangles represent 2D convolutions; the number above each rectangle gives the number of convolutional filters. The network input is a tensor of uniform random numbers with size $n_y\times n_x\times d$, where the number of feature maps in the input is set to $d=32$ for this study. A different input is used for each cardiac phase; the input tensors are linearly interpolated along the cardiac phase dimension as described in the main text as a form of regularization. The network outputs the real and imaginary parts of the $k$ subspace images, which are combined to yield complex images, for a particular cardiac phase.

Supporting Figure S3: Architecture of the Parameter Estimation Network (PEN). The input to the network is the MRF subspace images for a particular cardiac phase. These images are reshaped (vectorized), and the real and imaginary parts are interleaved before being input to the network. The network has two fully-connected layers with 300 nodes each. The output consists of T₁, T₂, the effective B₁⁺, and the real and imaginary parts of M₀. Note that this network does not share information across different spatial locations (it operates on each pixel location independently).

Supporting Figure S4: Architecture of the Fingerprint Generator Network (FGN). The network takes a T₁ value, T₂ value, and effective B₁⁺ value as the input. The network has two fully-connected layers with 300 nodes per layer. The output consists of interleaved real and imaginary parts of the MRF signal in the low-dimensional (dictionary-derived) subspace. Unlike the IRN and PEN, which are re-trained specifically for each new MRF scan, the FGN was pre-trained using signal evolutions in the cine MRF dictionary. The dictionary consisted of 590,875 signals with T₁ 60–4000 ms, T₂ 6–1000 ms, and B₁⁺ 0.1–1.5. The dictionary was compressed along the time dimension using the SVD, truncated to a rank of $k$. The FGN training data consisted of pairs of (T₁, T₂, B₁⁺) values and their Bloch-simulated signal evolutions after SVD compression.

Supporting Figure S5: XCAT simulation results are shown investigating different inputs to the Image Reconstruction Network. First, the DIP reconstruction was performed using input tensors with sizes of $d=$ 1, 4, 8, 16, 32, 64, 128, and 256 for the feature map dimension (recall that the network input for cardiac phase $i$ is denoted $z_i$ and has size $n_y\times n_x\times d$, where $d$ is the number of feature maps). For this simulation, the input tensors were linearly interpolated along cardiac phases. RMSE values for (A) T₁ and (B) T₂ are shown for the DIP reconstruction with different values for $d$, along with errors using low-rank (LR) and low-rank motion-corrected (LRMC) reconstructions for comparison. Similar errors were obtained for all values of $d$. Next, simulations were performed with $d=32$ to compare: 1) randomly initializing input tensors for the first and last cardiac phases and using linear interpolation to calculate input tensors for intermediate cardiac phases, as described in the main text, and 2) randomly initializing input tensors for all cardiac phases without linear interpolation. As shown in (C), the linear interpolation strategy yielded lower errors for T₁ and T₂.

Supporting Figure S6: Validation in the ISMRM/NIST MRI system phantom. (A) T₁ and (B) T₂ estimates using MOLLI, single-phase MRF with prospective ECG triggering, and cine MRF with a deep image prior (DIP) reconstruction (both with and without B₁⁺ estimation) are plotted against reference inversion recovery and spin echo values. (C) B₁⁺ estimates using cine MRF with a DIP reconstruction (red) are shown along with reference measurements using a separate presaturation-based B₁⁺ mapping scan.

Supporting Figure S7: Temporal stability of DIP-B1 cine MRF T₁, T₂, and effective B₁⁺ measurements in the ISMRM/NIST MRI system phantom and in one healthy subject. Temporal stability was quantified using the coefficient of variation (CV), defined as the standard deviation over cardiac phases divided by the mean value, expressed as a percent. Phantom data were binned into different cardiac phases using an ECG signal from a separate scan in a healthy subject. (A) The mean T₁, T₂, and effective B₁⁺ over all cardiac phases were measured in one vial having a T₁ time similar to myocardium (mean MRF T₁ 947 ms and T₂ 129 ms). The shaded region indicates the standard deviation. MRF measurements were stable over cardiac phases, with CV values for (T₁, T₂, B₁⁺) of (0.2%, 0.5%, 0.2%). (B) Similar results were obtained in a vial having a T₂ time similar to myocardium (mean MRF T₁ 434 ms and T₂ 48 ms), with CV values of (0.7%, 0.8%, 0.3%). (C) Measurements were made in one healthy subject (slice #4 in Figure 9) in static muscle near the chest wall (mean T₁ 898 ms and T₂ 26 ms), which should not exhibit variations across the cardiac cycle. Stable T₁, T₂, and effective B₁⁺ measurements were observed with CV values of (0.3%, 0.8%, 1.1%). (D) In myocardium (mean T₁ 1041 ms and T₂ 34 ms), the CV values were (0.2%, 1.1%, 2.1%). Compared to static muscle, both T₂ and the effective B₁⁺ exhibited slightly larger variations over the cardiac cycle, as evidenced by their higher CV values. There was a slight increase in T₂ (33 to 35 ms) and decrease in effective B₁⁺ (0.59 to 0.54) during systole compared to diastole.

Supporting Figure S8: Full FOV maps for the same data presented in Figure 3. (A) Diastolic T₁ and T₂ maps are displayed using conventional MOLLI and T₂-prep bSSFP sequences. (B) T₁, T₂, and M₀ maps are presented using MRF with prospective ECG triggering with a diastolic acquisition window reconstructed using a deep image prior (DIP). Cine MRF T₁, T₂, and M₀ maps are shown in diastolic and systolic phases using (C) low-rank, (D) low-rank motion-corrected (LRMC), and (E) DIP reconstructions. (F) Cine MRF maps using a DIP reconstruction with effective B₁⁺ estimation are presented in the rightmost column.

Supporting Figure S9: Full FOV images for the same data presented in Figure 4. (A) Reference Cartesian cine bSSFP images are shown in diastolic and systolic phases. Synthetic bright-blood bSSFP (top row) and dark-blood (bottom row) images derived from the cine MRF tissue property maps are presented using various reconstructions methods including (B) low-rank, (C) low-rank motion-corrected, (D) deep image prior, and (E) deep image prior with effective B₁⁺ estimation.

Supporting Figure S10: Relative changes in systolic versus diastolic myocardial T₁ and T₂ measurements using various cine MRF reconstruction methods for all subjects. Negative values indicate lower measurements during systole. (A) The LR reconstruction exhibited a large spread in measurements, with some subjects having higher T₁ or T₂ values in diastole versus systole, and vice versa. The high variability can be attributed to noise enhancement and aliasing artifacts in the maps. (B) The LRMC reconstruction yielded better agreement between diastolic and systolic measurements. However, it is important to note that the LRMC method combines (registers) images across multiple cardiac phases before pattern matching. (C) The DIP reconstruction without B₁⁺ correction showed a larger spread in measurements, with some subjects having higher values in diastole versus systole, and vice versa. (D) The DIP reconstruction with effective B₁⁺ estimation reduced these discrepancies, resulting in better agreement between diastolic and systolic values. These results suggest that some of the differences in diastolic/systolic values may be attributed to cumulative B₁⁺ spin history effects—for example, due to through-plane motion during cardiac contraction—rather than true physiological variations in T₁ or T₂. Note the difference in y-scaling for (A) compared to (B-D).

Supporting Figure S11: Distribution of mean effective B₁⁺ values measured in myocardium and in LV blood using cine MRF with the DIP-B1 reconstruction over all subjects.

Supporting Figure S12: The DIP-B1 reconstruction may enable reductions in the cine MRF breathhold duration. To investigate this, cine MRF data collected in one healthy subject during a 10.7s breathhold with 1820 total TR were used to simulate shortened breathhold durations and reconstructed using the DIP-B1 technique. Time points were retrospectively discarded from the end of the scan to simulate shortened breathholds of 8.0s (1365 TRs), 5.4s (910 TRs), and 2.7s (455 TRs). These times were selected because an inversion pulse is applied in the sequence every 2.7s (every 455 TRs). Maps reconstructed with different breathhold durations are shown above, in diastolic (A) and systolic (B) cardiac phases. Visually, maps from the 10.7s and 8.0s scans appeared similar, while noise enhancement became more apparent for the 5.4s scan. The mean and standard deviation in (C) T₁ and (D) T₂ are also shown, using values measured in the left ventricular septum during diastole and systole. The mean tissue property values were generally in agreement for all breathhold durations. Mean T₂ values trended towards marginally higher values with shorter breathholds, with T₂ in the range of 33–36 ms for longer breathholds (8.0s and 10.7s), and T₂ in the range of 35–37 ms for shorter breathholds (2.7s and 5.4s). The standard deviations increased with shorter breathhold durations for both T₁ and especially T₂. For example, the standard deviation for T₂ approximately doubled when the breathhold was shortened from 10.7 to 5.4s. These results suggest that it may be possible to reduce the breathhold to 8.0 seconds and still obtain maps with a similar accuracy and precision.

Supporting Table S1: Linear regression results (R², slope, and y-intercept of the best-fit line) are reported for the phantom (A) T₁ and (B) T₂ measurements shown in Supporting Figure S2.

Supporting Table S2: Bland-Altman statistics for the phantom data presented in Supporting Figure S2 for (A) T₁ and (B) T₂. The tables report the mean bias (test method – reference method) and the 95% upper and lower limits of agreement (LoA).