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2D T1, T2, T2* and PDFF mapping in the kidney with rosette MRF using Hermitian low-rank and dictionary-patch based regularization

Gastao Cruz¹, Evan Cummings^1,2, Tom Griesler^1,2, Jesse Hamilton^1,2, Vikas Gulani¹, Matthew Davenport¹, and Nicole Seiberlich^1,2
¹Radiology, University of Michigan, Ann Arbor, MI, United States, ²Biomedical Engineering, University of Michigan, Ann Arbor, MI, United States

Synopsis

Keywords: MR Fingerprinting, Kidney, MRF; low-rank;

Motivation: Subjective qualitative T2-weighted, T1-weighted (with and without contrast) and fat suppressed images are currently used to characterize renal masses. Characterization could be improved and standardized by using objective, generalizable, quantiative criteria.

Goal(s): In this work, 2D single-breathhold, high-resolution T1/T2/T2*/PDFF mapping rosette MRF is deployed for kidney tissue characterization.

Approach: A novel MRF reconstruction is introduced to enable reduced MRF data collection time, incorporating separate low-rank models along the TE and TR domains, Hermitian symmetry via virtual coils, and a dictionary-patch based regularization.

Results: In vivo results in healthy subjects demonstrate 2D 1x1x5 mm³ T1/T2/T2*/PDFF MRF kidney mapping in a single breath-hold.

Impact: Simultaneous mapping of T1/T2/T2*/PDFF in the kidney in a single high-resolution breath-hold scan via the proposed MRF approach is feasible. This technique could bolster traditional pre-/post- contrast renal mass protocols with objective characterization methods.

INTRODUCTION:

MR Fingerprinting (MRF)¹ employs highly undersampled acquisitions to sample transient state signals and provide high-quality tissue property maps. Advanced MRF reconstructions can minimize residual aliasing and noise amplification. Global low-rank (LR) models^2,3,4 and regularization approaches based on compressed sensing⁹, dictionary-based^4,11, locally low-rank¹⁰ and patch-based methods^12,13 have been demonstrated for this purpose, improving map quality. Hermitian symmetry⁵ has been proposed for steady-state imaging via PFPP⁶, LORAKS⁷ and Virtual Coil Concept (VCC).⁸ Here, we propose to enable high resolution T1/T2/T2*/Proton Density Fat (PDFF) kidney mapping within a breath-hold by incorporating Hermitian symmetry via VCC, and combining a global low-rank model along the TR domain, with a pixel-wise low-rank model along the TE domain. Furthermore, we develop a novel regularizer that combines patch-based locally low-rank with prior knowledge of the MR signal model, named LR^H-DP. These improvements enable 2D T1/T2/T2*/PDFF mapping in the kidneys with a resolution of 1x1x5 mm³ and improved apparent precision relative to conventional mapping methods.

METHODS:

The proposed approach combines low-rank Hermitian symmetry (LR^H) in the forward model with a dictionary-patch (DP) based regularizer. The proposed LR^H-DP reconstruction (Fig.1) is solved by the following optimization problem:
$$\widehat{y}=argmin_{y}\left\|SU_{TR}F\binom{P}{P^{*}}\binom{C}{C^{*}}U_{TE}y\binom{s}{s'}\right\|_{2}^{2}+\sum_b\lambda_b\left\|Q_bADD^HWy\right\|_{*} $$
where S is the sampling trajectory, U_TR is a global low-rank basis along the TR domain, F is the Fourier transform, P is the image phase of the MRF series, C are coil sensitivities, U_TE is a pixel-wise low-rank basis along the TE domain, y are the so-called singular images, s are the acquired data, $$$s'(k)=s^*(-k)$$$ (where k denotes k-space coordinate), $$$\lambda_b$$$ is the regularization strength for a given pixel b, Q_b identifies patches similar to the patch around b and sorts them in a Casorati matrix, A creates replicas of y mirrored and rotated about the center, D is the MRF dictionary capturing the dynamics along the TR, and W synthesizes images according to the water/fat/T2* model¹⁴ that captures dynamics along the TE. The operation DD^H synthesizes an MRF series with the signal evolution along the TR (i.e. changes in T1/T2 primarily due to inversion and T2prep pulse), according to the best dictionary match. The operation within W performs water/fat separation and T2* mapping following a standard signal model and synthesizes an MRF series with the signal evolution along the TE (i.e. changes along water/fat precession and T2* due to the multi-echo Rosette readout) based on the estimated water, fat, B0, and T2* values. The operators in the proposed forward model are estimated via preliminary processes: U_TR comes from the dictionary, P comes from a low-rank reconstruction and U_TE comes from a virtual-coil low-rank reconstruction (Fig.2). Following this initial estimation, LR^H-DP is performed, the reconstructed images undergo water/fat separation and T2* mapping via a graph-cut algorithm,¹⁴ and the water signal is matched to the dictionary for T1/T2 mapping.

EXPERIMENTS:

The proposed approach was evaluated in five healthy subjects (age 38.4±14.6 years, F:M 3:2) at 1.5T (Magnetom Sola, Siemens Healthineers, Erlangen, Germany). Imaging settings include: field of view (FOV)=300 mm²; 5 mm slice thickness; resolution=1.0×1.0 mm²; TE/ΔTE/TR=0.84/1.3/21.4 ms; flip angle=25º; FISP readout; 13-echo rosette trajectory; 20 second breath-hold. MRF data were reconstructed with both the originally proposed low-rank reconstruction4 and the proposed LR^H-DP. Conventional mapping was performed with MOLLI (T1), T2prep-bSSFP (T2) and 12-echo GRE (T2*/PDFF). Mean and standard deviation (precision surrogate) was measured with manual ROIs in the kidney cortex and medulla.

RESULTS:

The original low-rank MRF suffered from residual aliasing and noise amplification in the maps, in addition to loss of details around water/fat boundaries. The proposed LR^H-DP shows improved map quality with better detailed structures. Conventional maps exhibited noise amplification due to the relatively high resolution (Figs. 3 and 4). T1 and T2 values measured with MRF agree with literature values^15,16 and are lower than the conventional measurements acquired here, possibly due to magnetization transfer¹⁷ effects. Differences in T2* were also observed; however, both conventional and MRF sequences are less sensitive to high (>30ms) T2* values. Good agreement was observed for PDFF. The proposed LR^H-DP had the lowest standard deviation for all measurements (Fig. 5).

CONCLUSION:

A novel MRF reconstruction (LR^H-DP) combining low-rank models, Hermitian symmetry, and dictionary-patch based regularization was deployed to enable 2D T1/T2/T2*/PDFF kidney mapping in a single breath-hold with a resolution of 1x1x5 mm³. LR^H-DP demonstrated superior performance to conventional methods and may facilitate renal mass characterization via the analysis of these four co-registered tissue properties.

Acknowledgements

This work was supported in part by the NIH (R01 HL153034, R01HL163991, R01HL163030) and Siemens Healthineers.

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Figures

Fig.1: Diagram of the proposed LR^H-DP. The forward model (top) incorporates phase information to exploit the Hermitian symmetry of k-space. Low-rank subspaces, U_TR and U_TE, are employed to exploit redundant temporal information along the TR and TE dimensions, respectively. The proposed regularizer incorporates priors from the water/fat/T2* model (capturing signal dynamics along the TE) and from the MRF dictionary D (capturing signal dynamics along the TR), followed by patch self-similarity. Each set of similar blocks are jointly denoised via SVD.

Fig.2: Proposed MRF framework for kidney T1/T2/T2*/PDFF. 1.1 Data is acquired with a free-running 13-echo rosette, interrupted by inversion and T2prep pulses. 1.2 U_TRis derived from the dictionary. 1.3 Phase is estimated from a preliminary low-rank reconstruction. 1.4 U_TE is derived from a VCC-LR reconstruction. 2.1 The estimated U_TR, P and U_TE are incorporated into the proposed LR^H-DP (Fig.1). 2.2 The reconstructed MRF series is water/fat separated separation and T2* fitting, yielding T2* and PDFF. 2.3 The water images are used for MRF dictionary matching, yielding T1 and T2.

Fig.3: T1, T2, T2* and PDFF maps for a representative subject A, reconstructed with low rank (LR), the proposed LR^H-DP and corresponding conventional mapping sequences (MOLLI, T2prep bSSFP and 12-echo GRE). Improved map quality and water/fat boundaries are observed with the proposed approach relative to LR MRF and the conventional methods, which present residual aliasing and/or noise amplification.

Fig.4: T1, T2, T2* and PDFF maps for a representative subject B, reconstructed with low rank (LR), the proposed LR^H-DP and corresponding conventional mapping sequences (MOLLI, T2prep bSSFP and 12-echo GRE). Improved map quality and water/fat boundaries are observed with the proposed approach relative to LR MRF and the conventional methods, which present residual aliasing and/or noise amplification.

Fig.5: Table with measured T1/T2/T2*/PDFF in the kidney cortex and medulla with low rank MRF, the proposed LR^H-DP MRF and corresponding conventional sequences (MOLLI, T2prep bSSFP and 12-echo GRE). MRF presented lower values for T1 and T2, higher values for T2* and similar values for PDFF, relative to corresponding conventional methods. The proposed LR^H-DP consistently achieved the lowest standard deviation in the measurements.

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)

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DOI: https://doi.org/10.58530/2024/0578