Synopsis

Keywords: MR Fingerprinting/Synthetic MR, MR Fingerprinting

Traditional MR fingerprinting involves matching the acquired signal evolutions against a dictionary of expected tissue fingerprints to obtain the corresponding tissue parameters. Since this dictionary is essentially a discrete representation of a physical model and the matching process amounts to brute-force search in a discretized parameter space, there arises a tradeoff between discretization error and parameter estimation time. In this work, we investigate this tradeoff and show via numerical simulation how a neural net-based approach solves it. We additionally conduct a phantom study using 1.5T and 3T data to demonstrate the consistency of neural net-based estimation with dictionary matching.

Introduction

Magnetic Resonance Fingerprinting (MRF) ¹ is a quantitative MRI technique combining fast data acquisition with robust parameter mapping. One of its key enablers is dictionary-based parameter estimation. An MRF dictionary is a discrete representation of a physical model constructed by grid-sampling the parameter space. Naturally, there comes a tradeoff between grid density and matching speed. In neural network (NN)-based MRF parameter estimation ^2-4, a trained NN model represents a continuous functional approximation of the inverse physical model and can, in theory, overcome the fundamental limitation of traditional matching. We show via numerical simulation that the NN-based approach is consistent with full dictionary matching (FDM) and that fast matching at the speed of the NN performed with a reduced dictionary (RDM) produces a predictable worst-case discretization error. Further, to strengthen the former result, we evaluate the agreement between NN and FDM on phantom data acquired using two field strengths.

Methods

We used a sequence of 625 time points, TR=12 ms, TE=3 ms, and an optimized FA pattern ⁵. A dictionary of 308922 fingerprints was computed using Bloch simulation for a T₁/T₂ grid with T₁ range 9-5056 ms, T₂ range 5-2018 ms, and 2% grid spacing relative to T₁/T₂ values. The dictionary was compressed in time domain to 6 coefficients using SVD. A 6-layer complex-valued NN ³ was defined that accepts compressed fingerprints and outputs T₁ and T₂ parameters. To simulate realistic signal corruption for training, fingerprints were scaled by a random complex scaling factor with magnitude 0.4-2.4 and phase 0-2π. Complex Gaussian noise of σ=0.01 was added resulting in SNR_max range 40-240, where SNR_max is defined as the noise level relative to the MR signal from a fully relaxed spin system (with M₀=1) excited by a 90° pulse ⁶. The fingerprints were normalized to have unit L₂ norm. The dictionary was randomly split 90%-10% for training and validation. The NN model was trained using Cramér-Rao bound-weighted MSE loss ⁴ and Adam optimizer (0.001 learning rate, 512 batch-size, 500 epochs). For numerical simulation, first, the estimation time was defined as the time required to compute T₁/T₂ maps given a single-slice image series of size 224x224 and 6 coefficients. On Intel Xeon W-2235 CPU, FDM and NN inference required 23.4 s and 0.5 s, respectively. Then, a coarse dictionary was created with a 36x subsampled T₁/T₂ grid - 6x along each axis - which matched within the same time budget as our NN. We conducted in-dictionary and out-of-dictionary bias-variance analyses where 12 T₁/T₂ combinations were chosen from the reduced dictionary's grid and 12 from halfway between its grid points. In each case, 250 noisy realizations of fingerprints per T₁/T₂ combination were produced at 4 noise levels - SNR_max={50,100,150,200}. Estimation bias and variance of FDM, RDM, and our NN were calculated. For the phantom study, four scans of the T₂-plane of an HPD System Phantom Model 130 ⁷ were acquired using Philips Ingenia 1.5T/3T scanners with 15-channel head coil. All scans were in coronal orientation with 224 mm x 224 mm FOV, 1 mm x 1 mm in-plane resolution, and 4 mm slice thickness. A multi-slice spiral acquisition trajectory (5.9 ms window, 36 interleaves) was used to obtain k-space data for 15 slices. Coefficient images were reconstructed from the non-Cartesian k-space data using a non-iterative low-rank inversion method. For each series, T₁/T₂ maps were estimated for the central slice using FDM and our NN, and their probe-wise distributions were compared.

Results and Discussion

In the in-dictionary simulation scenario (Figure 1), RDM was comparable to FDM at SNR_max=50. With increasing SNR, RDM's variance became slightly lower. This can be attributed to the greater noise contribution than the discretization's contribution (which is zero) to the variance. At SNR_max≥100, RDM's coarse T₁/T₂ grid offered greater isolation between signal noise and estimate variance resulting in more robust matching. In the out-of-dictionary case (Figure 2), while all three methods were comparable at SNR_max=50, RDM approached a fixed 6% standard deviation in higher T₁ and mid-range T₂ values at SNR_max≥100. This was expected considering the 6x reduction factor along the T₁ and T₂ grid axes of the reduced dictionary and because the out-of-dictionary T₁/T₂ values represented the worst-case off-grid points for RDM which maximized the contribution of discretization in the estimation variance. Thus, the drawback of RDM in the out-of-dictionary scenario outweighed its advantage in the in-dictionary case. In contrast, our NN was consistent with FDM in each case in terms of variance. In the phantom results (Figures 3, 4, and 5), a high agreement between our NN and FDM was observed for T1 and T2 at both 1.5T and 3T field strengths.

Conclusion

T₁/T₂ estimation using an NN was not only comparable in precision to matching with a dense dictionary but also was 46x faster. To achieve fast matching, the dictionary had to be heavily subsampled by a factor of 36 thereby trading away its precision and demonstrating a fundamental limitation of dictionary matching. Estimation using a simulation-trained NN can replace FDM without significant change in estimation quality for scans of a standardized phantom at multiple field strengths. Future work will investigate the effect of discretization on in vivo data where the T₁/T₂ distribution is more heterogeneous.

Acknowledgements

We would like to thank Kay Nehrke and Yoo Jin Lee for their support with data acquisition and pre-processing and Thomas Amthor for his support with the software implementation of the MRF physical model and dictionary matching.