Magnetic Resonance Fingerprinting Optimization With Variance Based Spiral Arm Ordering
Rasim Boyacioglu1, Debra McGivney1, Dan Ma1, Yun Jiang1, and Mark Griswold1

1Radiology, Case Western Reserve University, Cleveland, OH, United States


Magnetic Resonance Fingerprinting (MRF) maps various tissue properties and system parameters simultaneously. MRF time series, which are matched to a precalculated dictionary, are often obtained with fast acquisition of low resolution images with undersampled spiral trajectories using a regular sampling pattern. In this work, we propose to order a set of spiral trajectories based on dictionary variance instead of the standard sequential or golden-angle ordering. Phantom and in vivo results show that the variance based optimized order converges faster to expected true values. The optimized order does not limit other MRF optimization approaches and can be applied to any MRF sequence.


Magnetic Resonance Fingerprinting (MRF ) is a quantitative tissue property mapping technique1. In MRF acquired signal evolutions shaped by pseudo-random flip angles and repetition times are matched to a set of expected signal evolutions in a dictionary. The target dictionary is free from system imperfections and any noise sources known to effect MRF data acquisition. MRF data are typically acquired with heavily undersampled spiral trajectories where the spiral arm rotation order is fixed and repeated throughout data acquisition, using either a linear or golden-angle approach. Thus, undersampling artifacts from reconstruction form cyclic patterns in time which are not simulated in the dictionary. However, it is well known that some parts of the signal evolution allow better separation between the tissues than others, which could result in some interleaves with a greater ability to distinguish different tissues than others, which could result in residual artifacts in the final maps. Here we propose a new approach to reorder spiral trajectories based on the variance across the tissue dimension of the dictionary instead of a fixed order. This ensures similar separability for all spiral readouts, and thus reduced artifacts.


The first step in determining the optimized order is to calculate the variance of the dictionary along the tissue dimension at each time point (Figure 1c). While there are potentially many ways to arrange these spirals, we chose a greedy algorithm. Starting at the first timepoint, the next readout is assigned to the spiral arm with the lowest cumulative variance. The cumulative variance is updated and we move to the next timepoint. If the dictionary variance is taken as a measure of the separability of dictionary entries, the optimized order aims to distribute the separability power evenly between spiral arms. Phantom2,3 and in vivo (with IRB approval and after prior written consent) data were acquired using a FISP based MRF acquisition4 at 3T scanner (Skyra, Siemens) using a head coil with the following parameters; FA: 5°-75° (Figure 1a), 1.2x1.2x5 mm3 resolution, TR: 10-13 ms (Figure 1b), 2000 time points. Data were acquired twice with the same acquisition parameters but with different spiral arm (n=48) orders; first with sequential order (1,2,…48,1,2,…48,1,2,..) and then with variance optimized order. Data were reconstructed retrospectively with fewer time points (N=100/200/300/500/750/1000/1500/2000) to observe the effects of different sampling choices.


Phantom data results in Figure 2 and 3 show that the standard sequential order breaks down with 100 time points whereas optimized order can still produce images with minimal artifacts. If maps with 2000 time points are taken as gold standard, difference maps can give some clues on the speed of convergence with different spiral arm orders. In comparison to sequential ordering the optimized order consistently achieved smaller differences with respect to full time series maps for both T1 and T2 across all the reconstructions with shorter time series (rows 2 and 4 in Figure 2 and 3). In vivo results do not immediately display a clear benefit such as observed with phantom data. T1 (row 1&3) and T1 difference (row 2&4) maps in Figure 4 are similar for all reconstructions. On the other hand, optimized order converges faster for T2 for regions around CSF.


It is important to note that the suggested variance based spiral arm ordering scheme can be applied to any MRF FA and TR pattern combination. Once the dictionary is calculated, signal differences for every time point will dictate which spiral arm to acquire. This optimized order method also provides flexibility on tuning the sensitivity of a given MRF sequence to certain tissue properties by calculating variance with only certain parts of the dictionary. One can focus on dictionary entries where T1 is fixed but T2 is allowed to vary to make the acquisition more sensitive to T2. Optimized order does not limit or preclude other types of MRF optimization. It can also be taken into account separately as the last step after optimizing other MRF sequence parameters.


The acquisition order of precalculated spiral trajectories can be optimized by considering dictionary variance along the tissue dimension for a given MRF pulse sequence. The optimized order converges faster to expected tissue property maps when tested for different levels of shortening of MRF time series. Regardless of employing other optimization strategies and choice of sequence parameters, optimized order can be applied to any MRF sequence.


The authors would like to acknowledge funding from Siemens Healthcare and NIH grants 1R01EB016728-01A1 and 5R01EB017219-02.


1. Ma D, Gulani V, Seiberlich N, et al. Magnetic resonance fingerprinting. Nature 2013;495: 187–192.

2. Russek SE, Boss M, et al. Characterization of NIST/ISMRM MRI system phantom. In Proceedings of the 20th Annual Meeting of ISMRM, Melbourne, Australia, 2012. Abstract 2456.

3. https://collaborate.nist.gov/mriphantoms/bin/view/MriPhantoms/MRISystemPhantom

4. Jiang Y, Ma D, Seiberlich N, et al. MR Fingerprinting Using Fast Imaging with Steady State Precession (FISP) with Spiral Readout. Magn Reson Med 2015;74:1621-1631.


Figure 1. Flip angle (a) and TR (b) pattern for FISP MRF sequence. In (c) dictionary variance along the tissue dimension is plotted for all time points. It is evident that time points with higher variance contribute more for differentiation of dictionary entries and mapping true values with dictionary matching.

Figure 2. Phantom T1 results when matching is done with various number of time points. N500 with optimized order maps T1 with limited artifacts. Across all reconstructions, optimized order would require fewer time points for similar image quality.

Figure 3. Phantom T2 results when matching is done with various number of time points. T1 converges faster than T2. With the same number of time points optimized order generates maps which are closer to gold standard of N2000.

Figure 4. In vivo T1 results when matching is done with various number of time points. T1 in vivo does not show any apparent benefits for optimized order. It appears that CSF voxels need more time points to converge for both ordering schemes.

Figure 5. In vivo T2 results when matching is done with various number of time points. Various regions around CSF (pointed with arrows) with long T2 benefit from the optimized order.

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