Exploring the sensitivity of Magnetic Resonance Fingerprinting to k-space trajectory uncertainties
Alessandro Palombit1,2, Alessandra Bertoldo1,2, Zidan Yu3,4,5, Riccardo Lattanzi3,4,5, and Martijn Anton Cloos3,4,5

1Information Engineering, University of Padova, Padova, Italy, 2Padova Neuroscience Center, Padova, Italy, 3Center for Advanced Imaging Innovation and Research (CAI2R), New York, NY, United States, 4Bernard and Irene Schwartz Center for Biomedical Imaging, New York, NY, United States, 5New York University School of Medicine, The Sackler Institute of Graduate Biomedical Sciences, New York, NY, United States


In this work, we experimentally explore the sensitivity of Magnetic Resonance Fingerprinting (MRF) to k-space trajectory uncertainties typically encountered in non-cartesian imaging. We demonstrate that T1 and T2* quantification can be affected by minor gradient delays observed in stack-of-stars 3D MRF implementations, particularly resulting in severely disrupted T2* measures. As a first approximation, we modeled these imperfections as constant readout sampling shifts of a few integer k-space steps along every trajectory direction. We show that by simply shifting back the nominal sampling locations before the reconstruction can restore reliable MRF parametric estimates.


Magnetic Resonance Fingerprinting (MRF)1 provides an attractive means for fast and robust relaxation mapping2. Its speed depends on incoherent k-space under-sampling, which could be achieved, for example, by using non-cartesian readouts (e.g. spiral1, or radial2). However, these readouts require high-fidelity gradient control. In this work, we explore the sensitivity of MRF-derived relaxation to the k-space trajectory uncertainties typically encountered using a radial sampling strategy. We also provide a simple correction strategy that largely restore the accuracy of parametric estimates.


Sequence design: Two MRF implementations were evaluated (Fig. 1), both based on a 3D stack-of-stars readout (2 spokes/star, golden angle increment3). The first (MRF3D), estimates T1, B1+ as described by Fujimoto et al4. The second (MRF3D-vTE), was derived from the first by varying the echo time in fixed incremental steps to simultaneously measure T2* (Fig. 1-B). The underlying pulse sequence consists in an adiabatic non-selective inversion followed by 750 spoiled excitations, with variable Flip-Angle (FA) pattern (Fig. 1-B).

MRF Reconstruction: MRF data was reconstructed in Matlab (MathWorks, MA, USA) using Fessler’s NUFFT5 toolkit as in Fujimoto et al4. The TE-independent phase-offset (i.e., the transmit/receive phase) was removed using a separate set of coil sensitivities for each TE-section6. An MRF dictionary was created using the Extended Phase Graph7 approach and matched to the experimental fingerprints by maximum inner product.

Trajectory correction: We assumed that, as a first order approximation, trajectory imperfections can be described as shifts along the sampling direction8. For simplicity, but without loss of generality, we have considered only integer steps (fixed readout bandwidth).

Experimental setting: The MRF3D-vTE implementation was first validated on phantom. Subsequently, both the MRF3D (M0,T1, B1+) and MRF3D-vTE (M0, T1, B1+, T2*) were used along with standard morphologic pulse sequences over two healthy volunteers. All experiments were performed on a MAGNETOM 7T (Siemens Healthineers, Erlangen, Germany) using a 1TX-32RX head coil (Nova Medical, Wilmington, MA, USA). The study was approved by our local institutional review board.

Results & Discussion

Figure 2 (top) shows the high level of agreement achieved between the T1 measured using the MRF-vTE and a gold standard reference scan (series of inversion-recovery spin-echo measurements). A similar agreement was observed when comparing the observed T2* to estimates derived from a multi-echo gradient-echo (ME-GRE) measurement (Fig. 2, bottom).

Figure 3 shows the MRF estimates together with a reference T1-w and T2* map (as from ME-GRE) in one volunteer. T1 estimates were geometrically consistent with the T1-w image (Fig. 3, top-left) across posterior brain areas, but were severely distorted frontally (Fig. 3, left column), with non-physiologic apparent T1 values with both MRF implementations. Quantitative T2* measures exhibited a relatively viable tissue contrast across middle/posterior brain areas (high B1+), but the same frontal distortion pattern of T1 maps (Fig. 3, middle column). Since these effects are observed in both MRF implementations, the T2* encoding is unlikely to be the cause of these artifacts. At the same time, they cannot be explained by the measured B1+ (Fig. 3, right column), which appears to be adequate for T1 quantification3,9.

Reconstructing the MRF3D with various k-space shifts (Fig. 4-A) resulted in the M0 maps of Fig. 4-B. Less or equal than zero shifts resulted in atypical M0 maps with visual artifacts. Positive shifts, on the other hand, progressively restored the expected M0 pattern (peaking at +2 px). Note that, under our prescribed settings, a +2 px shift corresponds to an 8.2 μs delay, less than the typical gradient raster time of the scanner (10 μs), suggesting that the observed artifacts cannot be attributed to extensive gradient mis-calibrations or eddy-currents, but rather to small synchronization imperfections between ADC and gradient events.

Figure 5 shows the effect of adding positive k-space shifts (+2 px) on the MRF parametric maps. Both MRF implementations resulted in large improvements over the frontal brain region, particularly evident in the T2* maps (Fig.5-B, middle column), where the k-space shifts recovered a consistent anatomical structure. Considering the impact of such first-order corrections, even higher robustness may be enabled with higher order schemes, for example accounting for readout uncertainties not necessarily fixed along the fingerprint (i.e., variable at single-shot level).


In this study, we investigated the sensitivity of MRF to 3D k-space trajectory uncertainties. We demonstrated that even a minor gradient delay can severely affect the T1 and T2* estimates in a high-resolution stack-of-stars based MRF sequence. Delaying the nominal radial trajectories by integer k-space steps along each spoke direction can provide a simple means to restore the accuracy of the parameter maps.


This work was supported in part by NIH R01 AR070297 and NIH R21 EB020096, and it was performed under the rubric of the Center for Advanced Imaging Innovation and Research (CAI2R, www.cai2r.net), a NIBIB Biomedical Technology Resource Center (NIH P41 EB017183).


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Figure 1. MRF sequence overview. A) Pulse sequence diagram and k-space readout scheme with golden angle increment between consecutive shots. B) TE pattern (green trace) used in MRF3D-vTE (MRF3D: fixed TE/TR = 3/8 ms, MRF3D-vTE used TE = 3/8/23 ms over three sectors) and FA pattern (blue trace). TR trace (omitted) mimics the TE one with an offset of 5 ms. Shared: FA schedule (blue trace); readout bandwidth (BWpp) of 500 Hz; k-space sample number of 240 (2 x oversampling); reconstructed voxel-size of 1x1x2 mm (in-vivo).

Figure 2. Phantom validation of MRF3D-vTE. The top-left plot represents the linear regression analysis between T1 measures obtained with MRF3D-vTE (also represented laterally) and standard inversion-recovery (TI ranged from 50 to 6000 ms) over regions delineated within the phantom test tubes (as shown laterally). A regression equation is reported above with associated parametric coefficient of variation within parenthesis. The bottom-left plot similarly represents the regression between T2* measures obtained with MRF3D-vTE and a standard gradient-echo repeated ranging TE from 5 - 60 ms and observing acceptable agreement under 30 ms. All measurements considered matched voxel-size (1x1x5 mm).

Figure 3. In-vivo MRF results at 7T. Anatomical structural image (MP2RAGE, top-left) and gradient-echo derived T2* (top-middle) are reported as reference scans. Quantitative T1 (left column), T2* (middle column) and B1+ (right column) obtained with the MRF3D (middle row) and MRF3D-vTE (bottom row) are reported across corresponding slice locations. The MRF spatial bias of T1 and T2* was particularly visible across frontal lobe areas with disruptive effects on T2*. The B1+ pattern was consistent among MRF implementations but under-estimated by as much as 17% by using MRF3D-vTE as compared to the MRF3D.

Figure 4. K-space shift effects. A) K-space samples along each spoke direction (i.e. a single readout) can be negatively (e.g. -1 px, pixel) or positively shifted (e.g. +1 px) by moving their nominal k-space locations of an integer number of k-space steps (i.e. the readout k-space step). B) M0 maps obtained by shifting the MRF3D data as specified in (A). All shift conditions except for +2 px, exhibited heavily non-physiological M0 amplitude modulations recalling artefact-like effects.

Figure 5. Delay-corrected MRF estimates. A) Quantitative T1 maps obtained using the MRF3D sequence while increasing the k-space shift from zero (uncorrected) to the optimum previously found (+2 px), from left to right. B) Quantitative T1, T2 and B1+ obtained with MRF3D-vTE without (top row) or with (bottom row) k-space shift (+2 px), highlighting a substantial recovery of anatomical accuracy and T2 contrast by accounting for even minor gradient delay effects.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)