Original paper| Volume 105, 102514, January 2023

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# Optimisation of data acquisition towards continuous cardiac Magnetic Resonance Fingerprinting applications

Open AccessPublished:January 04, 2023

## Highlights

• Various Magnetic Resonance Fingerprinting schemes were analysed.
• Evaluation were performed in simulations, phantoms and in-vivo.
• T2-preparation pulses led to a modest improvement in T2 accuracy.
• Accuracy of T1 was shown to be very robust for different scan parameters.

## Abstract

### Purpose

Assess and optimise acquisition parameters for continuous cardiac Magnetic Resonance Fingerprinting (MRF).

### Methods

Different acquisition schemes (flip angle amplitude, lobe size, T2-preparation pulses) for cardiac MRF were assessed in simulations and phantom and demonstrated in one healthy volunteer. Three different experimental designs were evaluated using central composite and fractional factorial designs. Relative errors for T1 and T2 were calculated for a wide range of realistic T1 and T2 value combinations. The effect of different designs on the accuracy of T1 and T2 was assessed using response surface modelling and Cohen’s f calculations.

### Results

Larger flip angle amplitudes lead to an improvement of T2 accuracy and precision for simulations and phantom experiments. Similar effects could also be shown qualitatively in in-vivo scans. Accuracy and precision of T1 were robust to different design parameters with improved values for faster flip angle variation. Cohen’s f showed that T2-preparation pulses influence the accuracy of T2. The number of pulses used is the most important parameter. Without T2-preparation pulses, RMSE were 3.0 ± 8.09 % for T1 and 16.24 ± 14.47 % for T2. Using those pulses reduced the RMSE to 2.3 ± 8.4 % for T1 and 14.11 ± 13.46 % for T2. Nonetheless, even if the improvement is significant, RMSE are still too high for reliable quantification.

### Conclusion

In contrast to previous study using triggered MRF sequences using < 30° flip angles, large flip angle amplitudes led to better results for continuous cardiac MRF sequences. T2-preparation pulse can improve the accuracy of T2 estimation but lead to longer scan times.

## Introduction

Magnetic Resonance Imaging (MRI) is an important medical imaging modality frequently used in cardiology. Commonly, qualitative images are obtained, which require a contrast between healthy and pathological tissue for diagnosis. Quantitative MRI is becoming more and more important as it directly provides (bio)-physical parameters that can be easily compared to reference values.
Several quantitative multiparametric methods applied to cardiovascular imaging have been recently reported in literature. Those sequences aim to quantify several biomarkers in only one acquisition, while addressing cardiac imaging challenges, such as motion and ECG-triggering. Among those techniques, multiparametric SASHA combines T1 and T2 mapping using a single saturation recovery-based sequence. Nine images are acquired during a triggered sequence covering eleven heartbeats [
• Chow K.
• Hayes G.
• Flewitt J.A.
• Feuchter P.
• Lydell C.
• et al.
Improved accuracy and precision with three-parameter simultaneous myocardial T1 and T2 mapping using multiparametric SASHA.
]. Another notable multiparametric technique is Magnetic Resonance Multitasking applied to cardiovascular imaging. This method considers motion as multiple time dimensions that can be resolved using a low-rank tensor method. This framework allows for a free-breathing acquisition without ECG-triggering however acquisition time is longer than quantitative acquisitions under breathhold (88 s) [
• Christodoulou A.G.
• Shaw J.L.
• Nguyen C.
• Yang Q.
• Xie Y.
• Wang N.
• et al.
Magnetic resonance multitasking for motion-resolved quantitative cardiovascular imaging.
].
This study focuses on Magnetic Resonance Fingerprinting (MRF) another multiparametric quantitative MRI technique, which can yield multiple parameters such as T1, T2, the extracellular volume fraction or also the fat fraction. Those parameters can provide potentially complimentary diagnostic information for a range of human diseases [
• Ma D.
• Gulani V.
• Seiberlich N.
• Liu K.
• Sunshine J.L.
• Duerk J.L.
• et al.
Magnetic resonance fingerprinting.
,
• Liu Y.
• Hamilton J.
• Rajagopalan S.
• Seiberlich N.
Cardiac Magnetic Resonance Fingerprinting: Technical Overview and Initial Results.
,
• Bipin Mehta B.
• Coppo S.
• Frances McGivney D.
• Ian Hamilton J.
• Chen Y.
• Jiang Y.
• et al.
Magnetic resonance fingerprinting: a technical review.
,
• Assländer J.
A perspective on MR fingerprinting.
].
In contrast to a classic MR acquisition, MRF acquisition parameters are not fixed during a scan but are varied in order to create unique (i.e. different for different values of T1 and T2) temporal signal curves. These temporal signal curves are called “fingerprints” and are then voxel-wise matched to a predetermined dictionary, simulating the signal evolution for various tissue types. Machine and deep learning can also be applied to MRF to reconstruct acquired data and match the fingerprints [
• Montalt-Tordera J.
• Muthurangu V.
• Hauptmann A.
• Steeden J.A.
Machine learning in Magnetic Resonance Imaging: Image reconstruction.
,
• Barbieri M.
• Brizi L.
• Giampieri E.
• Solera F.
• Manners D.N.
• Castellani G.
• et al.
A deep learning approach for magnetic resonance fingerprinting: Scaling capabilities and good training practices investigated by simulations.
]. To be sensitive to different T1 and T2 times, an inversion pulse is normally applied at the beginning of the sequence and the flip angle amplitude is varied during the scan. Although original MRF techniques for the brain used flip angles larger than 70° [
• Jiang J.Y.
• Ma D.
• Seiberlich N.
• Gulani V.
• Griswold M.A.
MR fingerprinting using fast imaging with steady state precession (FISP) with spiral readout.
], so far for cardiac MRF flip angles below 30° have been used to help reducing B1 errors [
• Liu Y.
• Hamilton J.
• Rajagopalan S.
• Seiberlich N.
Cardiac Magnetic Resonance Fingerprinting: Technical Overview and Initial Results.
,
• Hamilton J.I.
• Jiang Y.
• Eck B.
• Griswold M.
• Seiberlich N.
Cardiac cine magnetic resonance fingerprinting for combined ejection fraction, T1 and T2 quantification.
]. Most studies on cardiac MRF use T2-preparation pulses to increase the sensitivity of the MRF signal to different T2 values and compensate for those small flip angles values [
• Hamilton J.I.
• Jiang Y.
• Eck B.
• Griswold M.
• Seiberlich N.
Cardiac cine magnetic resonance fingerprinting for combined ejection fraction, T1 and T2 quantification.
,
• Cruz G.
• Jaubert O.
• Qi H.
• Bustin A.
• Milotta G.
• Schneider T.
• et al.
3D free-breathing cardiac magnetic resonance fingerprinting.
,
• Hamilton J.I.
• Jiang Y.
• Chen Y.
• Ma D.
• Lo W.C.
• Griswold M.
• et al.
MR fingerprinting for rapid quantification of myocardial T1, T2, and proton spin density.
,
• Jaubert O.
• Cruz G.
• Bustin A.
• Schneider T.
• Lavin B.
• Koken P.
• et al.
Water-fat Dixon cardiac magnetic resonance fingerprinting.
].
One challenge of cardiac MRF is the motion of the heart due to breathing. This leads to ghosting and blurring artefacts on resulting images and errors in quantitative maps. Commonly, one 2D cMRF slice is acquired during a single breathhold, limiting the available scan time to 10–15 s. In addition, the motion due to beating of the heart also needs to be considered. Cardiac triggering is frequently applied, and this restricts the data acquisition to a predefined phase (e.g. mid-diastole) of the cardiac cycle. This method is effective but using it means that only a small percentage (10 – 20 %) of the heart cycle is used to acquire diagnostic information [
• Messroghli D.R.
• Kozerke S.
• Higgins D.M.
• Sivananthan M.U.
• Ridgway J.P.
Modified Look-Locker inversion recovery (MOLLI) for high-resolution T1 mapping of the heart.
]. The majority of previously proposed cardiac MRF approaches have been optimised for cardiac triggering [
• Assländer J.
A perspective on MR fingerprinting.
,
• Lima da Cruz G.J.
• Velasco C.
• Lavin B.
• Jaubert O.
• Botnar R.M.
• Prieto C.
Myocardial T1, T2, T2*, and fat fraction quantification via low-rank motion-corrected cardiac MR fingerprinting.
,
• Cruz G.
• Qi H.
• Jaubert O.
• Kuestner T.
• Schneider T.
• Botnar R.M.
• et al.
Generalized low-rank nonrigid motion-corrected reconstruction for MR fingerprinting.
,
• Jaubert O.
• Cruz G.
• Bustin A.
• Hajhosseiny R.
• Nazir S.
• Schneider T.
• et al.
T1, T2, and Fat Fraction Cardiac MR Fingerprinting: Preliminary Clinical Evaluation.
]. Cardiac motion correction was also proposed by Cruz et al. in [
• Lima da Cruz G.J.
• Velasco C.
• Lavin B.
• Jaubert O.
• Botnar R.M.
• Prieto C.
Myocardial T1, T2, T2*, and fat fraction quantification via low-rank motion-corrected cardiac MR fingerprinting.
,
• Cruz G.
• Qi H.
• Jaubert O.
• Kuestner T.
• Schneider T.
• Botnar R.M.
• et al.
Generalized low-rank nonrigid motion-corrected reconstruction for MR fingerprinting.
], using cardiac motion-fields with a low-rank reconstruction to correct for parts of the cardiac cycle [
• Lima da Cruz G.J.
• Velasco C.
• Lavin B.
• Jaubert O.
• Botnar R.M.
• Prieto C.
Myocardial T1, T2, T2*, and fat fraction quantification via low-rank motion-corrected cardiac MR fingerprinting.
]. In [
• Cruz G.
• Qi H.
• Jaubert O.
• Kuestner T.
• Schneider T.
• Botnar R.M.
• et al.
Generalized low-rank nonrigid motion-corrected reconstruction for MR fingerprinting.
], the same method is used but this time an extended acquisition window of ∼ 480 ms is applied. This last technique admits that there is no longitudinal motion in the selected long acquisition window [
• Cruz G.
• Qi H.
• Jaubert O.
• Kuestner T.
• Schneider T.
• Botnar R.M.
• et al.
Generalized low-rank nonrigid motion-corrected reconstruction for MR fingerprinting.
].
To further improve efficiency, cardiac motion correction has been proposed, where data is acquired continuously during the cardiac cycle (100 % efficiency) and motion correction is carried out during image reconstruction to ensure high image quality, minimize motion artefacts and provide accurate parameter estimation [
• Batchelor P.G.
• Atkinson D.
• Irarrazaval P.
• Hill D.L.
• Hajnal J.
• Larkman D.
Matrix description of general motion correction applied to multishot images.
,
• Becker K.M.
• Blaszczyk E.
• Funk S.
• Nuesslein A.
• Schulz-Menger J.
• Schaeffter T.
• et al.
Fast myocardial T1 mapping using cardiac motion correction.
,
• Gatefait C.G.F.
• et al.
Cardiac motion-corrected image reconstruction for Cardiac Magnetic Resonance Fingerprinting, 1553.
].
The aim of this study is to evaluate different MRF acquisition schemes for continuous cardiac MRF sequences which can be combined with cardiac motion correction. In this study, only T1 and T2 maps are retrieved from MRF acquisitions. Different flip angle patterns with varying maximal flip angle amplitude are compared and the effect of T2-preparation pulses on the accuracy of T1 and T2 estimation is evaluated. Numerical simulations, phantom experiments and in-vivo scans in a healthy volunteer are carried out.

## Materials and methods

Based on the results of previous simulation studies for triggered cardiac MRF sequences [
• Liu Y.
• Hamilton J.
• Rajagopalan S.
• Seiberlich N.
Cardiac Magnetic Resonance Fingerprinting: Technical Overview and Initial Results.
,
• Hamilton J.I.
• Jiang Y.
• Eck B.
• Griswold M.
• Seiberlich N.
Cardiac cine magnetic resonance fingerprinting for combined ejection fraction, T1 and T2 quantification.
], this study evaluates the accuracy and precision of estimated T1 and T2 values for MRF sampling schemes specified by varying values of maximum flip angle ($αmax)$, lobe size (L) and number of T2-preparation pulses (see Fig. 1). Numerical simulations were used to compare different cardiac MRF approaches. Phantom experiments and in-vivo scans were carried out for acquisition parameters which showed strong effects on the accuracy and precision of T1 and T2 estimates in the numerical simulations.

### Numerical and physical phantom

To ensure a good comparability between numerical simulation and phantom experiments, a virtual twin was created to mimic a phantom specifically designed for cardiac T1 and T2 mapping applications with and without contrast agent [
• Captur G.
• Gatehouse P.
• Keenan K.E.
• Heslinga F.G.
• Bruehl R.
• Prothmann M.
• et al.
A medical device-grade T1 and ECV phantom for global T1 mapping quality assurance-the T1 Mapping and ECV Standardization in cardiovascular magnetic resonance (T1MES) program.
]. Nine tubes with different combinations of T1 and T2 values were included. These tubes correspond to different tissue types, for example tubes 1 and 4 represent blood and native myocardium, respectively. The values of T1 and T2 used for each tube are listed in Table 1.
Table 1T1 and T2 values of the numerical phantom in each tube simulated for a 3 T MR scanner.
Tube 1Tube 2Tube 3Tube 4Tube 5Tube 6Tube 7Tube 8Tube 9
T1 (ms)1770.0560.0580.01385.0430.0430.01060.0340.0295.0
T2 (ms)190.030.0120.037.032.0120.031.033.0115.0
Moreover, the coil sensitivity map of the 32-channel cardiac coil (Siemens Healthineers, Erlangen, Germany) used was acquired and implemented in the simulation framework to improve its consistency. Finally, complex gaussian noise was added to the simulated k-space data along the 1500 datapoints.

### Evaluation of the flip angle pattern

Sequence parameters optimization is an important need in MRF, as a good encoding capability inherently leads to robust parameter estimation. Different studies aimed to evaluate and predict the encoding abilities of a sequence using, for example, the Monte Carlo method or the Cramér-Rao Bound method [
• Sommer K.
• Amthor T.
• Doneva M.
• Koken P.
• Meineke J.
• Börnert P.
Towards predicting the encoding capability of MR fingerprinting sequences.
,
• Zhao B.o.
• Haldar J.P.
• Liao C.
• Ma D.
• Jiang Y.
• Griswold M.A.
• et al.
Optimal Experiment Design for Magnetic Resonance Fingerprinting: Cramér-Rao Bound Meets Spin Dynamics.
,
• Lee P.K.
• Watkins L.E.
• Anderson T.I.
• Buonincontri G.
• Hargreaves B.A.
Flexible and efficient optimization of quantitative sequences using automatic differentiation of Bloch simulations.
]. However, it has not been applied for continuous cardiac MRF techniques yet.
Following the approach of a previous study for triggered cardiac MRF [
• Hamilton J.I.
• Jiang Y.
• Ma D.
• Lo W.C.
• Gulani V.
• Griswold M.
• et al.
Investigating and reducing the effects of confounding factors for robust T1 and T2 mapping with cardiac MR fingerprinting.
], we designed a flip angle pattern using multiple sinusoidal lobes with varying amplitudes (Fig. 1a).The flip angle pattern was defined using two parameters: the maximum flip angle ($αmax$) and the lobe size (L). L is defined as a number of repetitions, the duration of each lobe in ms is L * TR, with TR the repetition time. The length of the flip angle train is equal to 1500 repetitions and is kept constant throughout the acquisition.
The maximum flip angle was defined as the highest flip angle in the entire flip angle pattern. The relative amplitude differences between the different lobes were kept constant. L was defined as the duration of one sinusoidal lobe. The larger the L, the fewer the lobes that were used in the flip angle pattern as the total duration (i.e., number of k-space samples) of the flip angle pattern was kept constant.
Data was acquired with the parameters defined in a central composite design (design A) with three centre points and two replicates for each design point, giving a total of 22 runs. Two examples of parameter combinations are presented in Fig. 2A. The acquisition order of the 22 experiments was randomized. Each experiment is replicated twice, except for the central point, which is repeated six times. Details of the central composite design are presented in Supplemental table 1.

### Evaluation of T2 preparation pulses

T2-preparation pulse modules are a combination of rectangular 90° and 180° pulses which modify the longitudinal magnetisation as a function of T2 and hence yield signals which are sensitive to different T2-times [
• Brittain J.H.
• Hu B.S.
• Wright G.A.
• Meyer C.H.
• Macovski A.
• Nishimura D.G.
Coronary angiography with magnetization-prepared T2 contrast.
,
• Nezafat R.
• Stuber M.
• Ouwerkerk R.
• Gharib A.M.
• Desai M.Y.
• Pettigrew R.I.
B1-insensitive T2 preparation for improved coronary magnetic resonance angiography at 3 T.
]. They are also used for standard cardiac T2 mapping [
• Giri S.
• Chung Y.C.
• Merchant A.
• Mihai G.
• Rajagopalan S.
• Raman S.V.
• et al.
T2 quantification for improved detection of myocardial edema.
]. Combining T2-preparation pulses with a continuous cardiac MRF scan leads to several parameters which can be optimised: the number of T2-preparation pulses ($NT2$), the duration of the T2-preparation pulses ($DT2$) (shorter or longer duration leads to an increase in sensitivity to shorter or longer T2 times, respectively) and when these T2-preparation pulses are applied during the scan ($TPT2$). T2-preparation pulses were only used in the simulation framework. Thus, applied pulses were considered perfect.
In order to evaluate the effect of these parameters, two different factorial designs, design B and design C, were used to generate statistically meaningful combinations of parameters to test. Differences between the two designs are presented on Fig. 2B and 2C. Designs B and C are summarized in Supplemental tables 2 and 3.
For design B, owing to operational changes in pulse setting, pulse angle is confounded with number of pulses to give a four-factor complete factorial design [
• Montgomery D.C.
Design and Analysis of Experiments.
], each with two levels: flip angle (55 and 65), lobe size (70 and 90), repetition number (Low and High), and Pulse/Duration (0 and 40–60). Its experimental objective was to determine whether $αmax$, L and $TPT2$ have a significant effect on the accuracy of T1 and T2. $NT2$ and $DT2$ were not separately evaluated but combined as one parameter ($NT2DT2$).
Based on the results of design B, design C, a full factorial design, was created to evaluate effects of different combinations of $NT2$ and $DT2$. L and $αmax$ were restricted to a certain range based on the results of design A in order to reduce the number of possible parameter combinations.

### Experiments

MRF data acquisition was carried out with a gradient-spoiled gradient echo sequence and golden-angle radial k-space sampling. An adiabatic non-selective inversion pulse was applied at the beginning of the scan. In order to achieve a similar acquisition time compared to standard clinical mapping sequences, 1500 radial lines were acquired in a single breath hold. Each radial line is imaged with a different flip angle according to the FA pattern. Used parameters were a constant TE of 4 ms and a constant TR of 8.2 ms leading to a total acquisition time (TA) of 12 s.
Signal reception was carried out with a 32-channel cardiac coil (Siemens Healthineers, Erlangen, Germany) on a 3 T MR scanner (Verio, Siemens Healthineers, Erlangen, Germany). The same coil was use for both phantom and in-vivo acquisitions.
A sliding-window approach was implemented to accelerate the reconstruction process and improve the quality of the image series used for dictionary matching [
• Cao X.
• Liao C.
• Wang Z.
• Chen Y.
• Ye H.
• He H.
• et al.
Robust sliding-window reconstruction for Accelerating the acquisition of MR fingerprinting.
]. For the phantom scans each image was reconstructed using a non-uniform fast Fourier transform [
• O'Sullivan J.D.
A fast sinc function gridding algorithm for Fourier inversion in computer tomography.
].
A dictionary was created using an Extended-Phase-Graph approach [
• Weigel M.
Extended phase graphs: dephasing, RF pulses, and echoes - pure and simple.
]. The simulated entries of the dictionary (fingerprints) were then matched with the acquired data to obtain T1 and T2 maps. In order to realize the matching, dot-products between fingerprints from the dictionary and signal curves from the reconstructed images were calculated. The fingerprint with the maximum dot-product value was considered the best match.
For the numerical simulations, MR signals were simulated from the parameters of the numerical phantom using the Extended-Phase-Graph approach. MR data acquisition was simulated using the same parameters as those used for the experiments. Realistic coil maps obtained from a phantom scan were applied. Image reconstruction was also carried out in the same way as for the phantom experiments.
The desired flip angle amplitude can be defined for each sequence. However, the actual flip angle ($αact)$ seen by the tissue, depends on the interaction between the object and the applied RF-field and can deviate from the desired flip angle $αmax$ [
• Ma D.
• Coppo S.
• Chen Y.
• McGivney D.F.
• Jiang Y.
• Pahwa S.
• et al.
Slice profile and B1 corrections in 2D magnetic resonance fingerprinting.
], leading to quantitative parameters underestimations [
• Buonincontri G.
• Sawiak S.J.
MR fingerprinting with simultaneous B1 estimation.
]. To evaluate, the impact of the slice profile imperfection, the numerical simulations for the designs B and C were carried out using an ideal setting (i.e. $αact=αmax$) and a realistic setting (i.e. $αact<αmax$). In this study, $αact$ was defined as:
$αact=0.85∗αmax$
(1)

For the phantom experiments, reference measurements were carried out using spin echo (SE) sequences. To estimate T1, SE images at different time points TI after an inversion pulse were acquired (acquisition time of 161:42 min). TI was selected as [25, 50, 300, 600, 1200, 2400, 4800] with TR = 8000 ms. For T2, SE images with different echo times TE were obtained (acquisition time of 61:29 min). TE was selected as [24, 50, 100, 200, 400, 800, 1000] with TR = 3000 ms. Both gold standard pulse sequences were 2D and acquired with a resolution of 0.8x0.8x5 mm3.
As a proof-of-principle, in-vivo cardiac MRF scans of selected designs were carried out in one healthy volunteer (1 female, aged 27y). The subject gave written informed consent before participation, in accordance with the institutional ethical committee.
Data was acquired in a short-axis view of the heart. ECG triggering was used to start the acquisition during diastole, data was then acquired continuously without further triggering. In order to evaluate the effect of through-plane motion on the parameter estimation, we compared MRF reconstruction using all the data to discarding systolic phases based on the recorded ECG as suggested by [
• Becker K.M.
• Blaszczyk E.
• Funk S.
• Nuesslein A.
• Schulz-Menger J.
• Schaeffter T.
• et al.
Fast myocardial T1 mapping using cardiac motion correction.
] for T1 mapping. This led to an efficiency for this scan of 75 %. For comparison, data was also reconstructed as proposed by Cruz et al [
• Cruz G.
• Qi H.
• Jaubert O.
• Kuestner T.
• Schneider T.
• Botnar R.M.
• et al.
Generalized low-rank nonrigid motion-corrected reconstruction for MR fingerprinting.
] using a 450 ms gating window in diastole with application of motion-correction. In addition, the data was also reconstructed simulating a standard cardiac triggered acquisition with a gating window of 190 ms place in end-diastole [
• Messroghli D.R.
• Kozerke S.
• Higgins D.M.
• Sivananthan M.U.
• Ridgway J.P.
Modified Look-Locker inversion recovery (MOLLI) for high-resolution T1 mapping of the heart.
], without motion-correction. The duration of the gating window was chosen to match the in-vivo reference bSFFP T2-prep and MOLLI scans.
The pynufft package was used for iterative non-Cartesian sensitivity encoding reconstruction with twenty iterations [
• Pruessmann K.P.
• Weiger M.
• Börnert P.
• Boesiger P.
Advances in sensitivity encoding with arbitrary k-space trajectories.
, ]. Moreover, non-rigid motion correction was applied to correct for cardiac movement. For this, the MRF data was retrospectively separated into 15 cardiac phases based on the recorded ECG signal to obtain cine data. With the MIRTK toolkit [
• Rueckert D.
• Sonoda L.I.
• Hayes C.
• Hill D.L.
• Leach M.O.
• Hawkes D.J.
Nonrigid registration using free-form deformations: application to breast MR images.
] non-rigid motion fields were estimated to a reference diastole frame from the cine images. They are then used to correct for cardiac motion during the MRF image reconstruction [
• Jaubert O.
• Cruz G.
• Bustin A.
• Schneider T.
• Lavin B.
• Koken P.
• et al.
Water-fat Dixon cardiac magnetic resonance fingerprinting.
].
The SE-based reference measurements could not be used for in-vivo evaluation due to their long scan time of several hours. Instead, clinically used sequences were applied to obtain T1 and T2 estimates [
• Petitjean C.
• Rougon N.
• Cluzel P.
Assessment of myocardial function: a review of quantification methods and results using tagged MRI.
]. For T1, a Modified look-locker inversion recovery (MOLLI) sequence was used [
• Messroghli D.R.
• Moon J.C.
• Ferreira V.M.
• Grosse-Wortmann L.
• He T.
• Kellman P.
• et al.
Clinical recommendations for cardiovascular magnetic resonance mapping of T1, T2, T2* and extracellular volume: A consensus statement by the Society for Cardiovascular Magnetic Resonance (SCMR) endorsed by the European Association for Cardiovascular Imaging (EACVI).
]. T2 maps were obtained using a balanced stead-state-free-precession with multiple T2-preparation pulses technique (T2prep-bSSFP) [
• Messroghli D.R.
• Kozerke S.
• Higgins D.M.
• Sivananthan M.U.
• Ridgway J.P.
Modified Look-Locker inversion recovery (MOLLI) for high-resolution T1 mapping of the heart.
]. Nevertheless, as these methods can have biased estimated T1 and T2 values, the resulting maps were used for a qualitative comparison in this study [
• Piechnik S.K.
• Jerosch-Herold M.
Myocardial T1 mapping and extracellular volume quantification: an overview of technical and biological confounders.
].

### Mapping analysis

To evaluate the obtained T1 and T2 parameter maps, circular regions of interests (ROIs) were drawn in each tube for both the numerical and the physical phantoms. The average T1 and T2 values (V) in each ROI were calculated. The designs were then compared based on the relative error E between ground truth or gold standard T1 and T2 times (VRef) and the T1 and T2 times estimated with the current MRF design (VMRF):
$E=VMRF-VRefVRef$
(2)

E was evaluated separately for T1 and T2 and separately for each tube. For the final evaluation the root-mean-square-error (RMSE) over all tubes was also calculated.
Cohen’s f was used to compare standardised effect size [
• Cohen J.E.
Statistical Power Analysis for the Behavioral Sciences.
]. Cohen’s f is a measure of relative variance contributed by a particular variable relative to the residual variance. It is calculated from a particular effect sum of squares Si and the residual sum of squares Sres of the previously calculated relative error E in an analysis of variance (ANOVA) table as:
$f=ηi21-ηi2$
(3)

where
$ηi2=SiSi+Sres$

A high value of f indicates a large between-group difference. For multiple factors, factors with larger f make a larger difference than factors with small f. An example of ANOVA table is shown in Supplemental table 4.

## Results

### Evaluation of the flip-angle pattern

Fig. 3, Fig. 4 show reconstructed T1 and T2 maps from the simulations and the phantom scans for selected parameter combinations. A first inspection shows higher noise (i.e. poorer reproducibility) of T2 for small $αmax$ and L.
Fig. 5 shows T1 and T2 maps from the T1MES phantom obtained with the gold standard Spin-Echo reference sequences, the in-vivo reference sequences, MOLLI and T2-prepared bSSFP, and the proposed MRF sequence ($αmax$ = 70°, L = 150). Fig. 5 compares the calculated T1/T2 values from in to vivo references sequences and MRF measurements to the reference T1/T2 values in the T1MES phantom. Results show that the MOLLI sequence leads to high accuracy and precision. They also confirm the previously reported overestimation of T2 values with a T2-prepared bSSFP [
• Chow K.
• Hayes G.
• Flewitt J.A.
• Feuchter P.
• Lydell C.
• et al.
Improved accuracy and precision with three-parameter simultaneous myocardial T1 and T2 mapping using multiparametric SASHA.
]. However, the proposed MRF sequence leads to high precision and accuracy for both T1 and T2 values.
T1 and T2 maps obtained from an in-vivo scans for different values of $αmax$ and L are shown in Fig. 6.
As blood is constantly flowing, the retrieved values in the myocardial blood pool may differ depending on the blood-flow-dynamics during the data acquisition.
Fig. 7 shows the resulting maps for different acquisition windows for an MRF acquisition with L = 250 and $αmax$ = 40°. All maps lead to comparable results for T1 and T2, however more noise is present for reconstructions with large and short diastolic windows as respectively, only 45 % and 20 % of the whole dataset are used.
All maps present a similar behaviour in the numerical simulations, in the phantom scans and for in-vivo acquisitions. Larger $αmax$ lead to an improved T2 estimation and higher signal-to-noise ratio.
Fig. 8, Fig. 9 compare the estimated T1/T2 values from simulation and phantom measurements to the reference T1/T2 values. As Gaussian noise and an experimental coil sensitivity maps were used in the simulation framework, simulated results may differ from the identity and adopt a behaviour closer to the experimental results. Results confirm that smaller $αmax$ lead to a poor precision for T2. T1 shows high accuracy and high precision for a wide range of parameters.
Fig. 10 shows Cohen’s f, a measure of the variance contributed by each parameter, for $αmax$ and L and their quadratic transforms. The size of each box describes within effect variability. The median, the black line across a box, represents the importance of the main effect.
Cohen’s f doesn’t show a strong predominance of either factor except for the effect of flip angle on T1 error in simulations, where two outliers with unusually large effects relative to others can be identified. For the majority of other effects, also for phantom acquisitions, both angle and duration seem to be important as first or second-order terms. The principal common feature is that the two-way interaction is rarely important, indicating that the two factors do not interact strongly in the parameter range examined. Low interaction can be practically useful as it suggests that parameters can, to a good approximation, be optimised individually in modest ranges.
In addition to Cohen’s f boxplots, the relative T1 and T2 errors as a function of $αmax$ and L were plotted as contours. Contours for the ideal simulation and the phantom experiments are presented on Fig. 11. Again, similar results between the simulation and the scanner acquisitions can be observed. Reviewing those figures show that small values of $αmax$ lead to high errors in T2 estimation. Moreover, T1 and T2 seem to be optimized for low and intermediate values of L.

### T2-preparation pulses evaluation

#### Design B

Similar to design A, Cohen’s f values were plotted for designs B. Results for the ideal and realistic simulations are presented in the Supplemental Fig. 1. This design aims to evaluate the application of T2-preparation pulses combined with varying L and $αmax$ and inspection shows that L and $αmax$ present the largest effect sizes for the simulated T1 and T2 estimations. NT2DT2 is also important for the estimated T2, which is expected as T2-preparation pulses aim to improve the encoding sensitivity of T2. Few interactions are important compared to the stronger main effects.

#### Design C

Similar to above, Cohen’s f plot for design C is shown in the Supplemental Fig. 2. Whereas design B was evaluating the parameters L, $αmax$ and TPT2, design C focuses on NT2 and DT2, which were previously combined as one parameter. T2-preparation pulses are applied in every run of this design, either two or four times. Reviewing Cohen’s f plot, the strongest effect for T1 and T2 in both an ideal and a realistic setting is the effect of L. The NT2 and NT2:L size interaction are also important; the interaction indicates that changes in NT2 moderate the effects of L and vice versa. DT2 contributes less to the variation in most cases, and other interactions are essentially minor except for one larger effect for the L: NT2 interaction on T2 for the realistic simulation. The relatively good precision for the simulations leads to a large number of statistically significant effects. Consideration of the relative contribution of different parameters indicates that the most important effect is L, with NT2 and the NT2:L size interaction also moderately important.
The influence of the chosen parameters can be further analysed by looking at the improvement of the averaged error over all runs using either zero, two or four T2-preparation pulses (Supplemental Fig. 3). The data shows an improvement between the runs without and the runs with T2-preparation pulses.
The simulated data being normally distributed, a Student t-test can be applied to evaluate the error difference between acquisitions with zero, two or four T2-preparation pulses [

Student (1908). The probable error of a mean. Biometrika, 1–25.

]. A 2-sample t-test using a null hypothesis was performed. A significant difference between two groups is considered by a p-value ≤ 0.05. Most p-values obtained after performing the t-tests are all under this threshold for T2 RMSE, thus showing that the null hypothesis is rejected and that the difference between the groups is significant. Significance is indicated on Fig. 10, * corresponds to p-value ≤ 0.05, ** to p-value ≤ 0.01 and *** to p-value ≤ 0.001 However, the significance is strongly dependant on the combination of T1 and T2 values of the considered tube.

## Discussion

The results of the in-vivo reconstruction (Fig. 7) utilizing different parts of the cardiac cycle suggest that the proposed cardiac motion-correction framework provides reliable T1 and T2 values. Further studies in patients are required, to verify the proposed motion correction framework in the presence of small pathologies in the myocardium. The proposed simulation is simplified and further effects, such as the slice profile, would need to be considered for a more detailed analysis.
We compared the accuracy of T1 and T2 maps for flip angle patterns with different $αmax$ and L. The main conclusion of this evaluation is the confirmation that accurate T2 estimation requires high $αmax$ [
• Cao X.
• Liao C.
• Wang Z.
• Chen Y.
• Ye H.
• He H.
• et al.
Robust sliding-window reconstruction for Accelerating the acquisition of MR fingerprinting.
]. Previous studies on cardiac MRF have mainly used low flip angles. However, to encode T2, these studies utilized T2 preparation modules. Based on the previous results, it can be hypothesized that the sensitivity of these sequences to different T2 values is mainly given by the T2-preparation pulses rather than the flip angle variations.
In the case of design B, Cohen’s f in Fig. 9 shows that lobe size (L) and the compound NT2DT2 parameter show the largest effect sizes for T2. The maximum flip angle $αmax$ also appears moderately important. Few interactions are important compared to the stronger main effects. Analysis of Cohen’s f from design C confirms these results and also shows that the number of pulses is important whereas the duration of the pulses is of less importance.
Nevertheless, the impact on the accuracy of the T2-preparation pulses on T1 and T2 is very small. For the ideal case in design B the relative error without T2-preparation pulses is 3.08 ± 8.09 % for T1 and 16.24 ± 14.47 % for T2 and 2.37 ± 8.4 % for T1 and 14.11 ± 13.46 % using T2-preparation pulses.
For the realistic scenario the relative errors are 2.37 ± 9.0 % for T1 and 43.48 ± 20.41 % for T2 without T2-preparation pulses and 1.92 ± 8.6 % for T1 and 39.36 ± 22.0 % using T2-preparation pulses.
In design C up to four T2-preparation pulses are used, which further improves T2 estimation to error ranges of 36.28 ± 20.52 % for the realistic case.
The main disadvantage of T2-preparation pulses is that they require a certain duration in order of the T2 values of interest and hence much longer than the repetition time. T2-preparation pulses used in this study have values between 40 ms and 60 ms. This is not a problem for standard triggered cardiac T2-mapping or cardiac MRF, because in each cardiac cycle only a single image is acquired. A T2-preparation pulse can be carried out prior to each of these images without a time penalty. For continuous data acquisition on the other hand, T2-preparation pulses come with a considerable time penalty equal to NT2*(DT2 + 10) ms. With four T2-preparation pulses, the relative error over all the nine tubes is reduced by 24.2 % ± 13.7 %. Nonetheless, the overall T2 relative error with four T2-preparation pulses equals 36.22 % ± 19.8 % and remains too high for a reliable parameter estimation.
This study aimed to evaluate the influence of T2-preparation pulses for an application where the applied flip-angle is inaccurate. Nevertheless, even for the case of using 4 T2-preparation pulses, the overall error remains high for this case. Thus, it can be supposed that the value of the RF-pulse applied need to be known accurately. This can be realised by increasing the bandwidth-time product, leading to longer RF-pulses, or also modelling the slice profile imperfection in the reconstruction framework [
• Ma D.
• Coppo S.
• Chen Y.
• McGivney D.F.
• Jiang Y.
• Pahwa S.
• et al.
Slice profile and B1 corrections in 2D magnetic resonance fingerprinting.
].
The small effect of the T2-preparation pulse is probably due to the fact, that the effect of any T2-preparation pulse is short lived and hence has little impact on a continuous cardiac MRF sequence. Myocardial T2 values at 3 T are usually equal to 45 ± 5 ms [
• von Knobelsdorff-Brenkenhoff F.
• Prothmann M.
• Dieringer M.A.
• Wassmuth R.
• Greiser A.
• Schwenke C.
• et al.
Myocardial T1 and T2 mapping at 3 T: reference values, influencing factors and implications.
], preparation pulses have then to be in this range of values to improve the T2-encoding sensitivity of the sequence.
T1 showed low dependence on $αmax$ in our investigation. The sensitivity to T1 of the MRF sequence used in this study is strongly determined by the initial inversion pulse. After the inversion pulse the MR Signal recovers proportional to T1 hence this initial signal variation allows for accurate T1 estimation for very different flip angle patterns. L did have an influence on T1 estimation and smaller L showed better performance than larger L.
One limitation of this study is that only one set of TE and TR were used in this study. Nevertheless, as both of these parameters are kept constant during the MRF acquisition, they will have an impact on the overall image quality but not on the sensitivity of the sequence to changes in T1 and T2. Therefore, different TE and TR values could change the overall error but are not expected to change the shape of the surface plots.
Furthermore, in this study we only varied two parameters of the flip angle pattern but of course the flip angle pattern could be changed in many other ways. Previous studies have shown the actual shape or order of the different flip angle lobes has very little impact on the accuracy of T2 [
• Batchelor P.G.
• Atkinson D.
• Irarrazaval P.
• Hill D.L.
• Hajnal J.
• Larkman D.
Matrix description of general motion correction applied to multishot images.
]. As long as the flip angle is not constant or completely random, T2 with an error below 10 % could be estimated. Therefore, we believe that $αmax$ and L are the most important parameters which needed to be analysed.

## Conclusion

• Sommer K.
• Amthor T.
• Doneva M.
• Koken P.
• Meineke J.
• Börnert P.
Towards predicting the encoding capability of MR fingerprinting sequences.
,
• Hamilton J.I.
• Jiang Y.
• Ma D.
• Lo W.C.
• Gulani V.
• Griswold M.
• et al.
Investigating and reducing the effects of confounding factors for robust T1 and T2 mapping with cardiac MR fingerprinting.
,
• Ma D.
• Coppo S.
• Chen Y.
• McGivney D.F.
• Jiang Y.
• Pahwa S.
• et al.
Slice profile and B1 corrections in 2D magnetic resonance fingerprinting.
,
• Buonincontri G.
• Sawiak S.J.
MR fingerprinting with simultaneous B1 estimation.
], our study confirmed that the temporal pattern of the flip angle is important to achieve accurate T1 and T2 estimation. We carried out a central composite design for different parameters of the flip angle pattern. Our results suggest that large flip angles and high number of flip angle lobes allow for most accurate parameter estimation. T2-preparation pulse improve the accuracy of T1 and T2. Nevertheless, the improvement of T2 accuracy was for our designs very small. For the realistic case (i.e. overestimation of $αact$) adding even four T2-preparation pulses only reduced the mean error of T2 from 43.48 ± 20.41 % to 36.28 ± 20.52 % compared to no T2-preparation pulses. This indicates that for continuous cardiac MRF acquisitions, the flip angle needs to be known accurately and even small inaccuracies lead to large errors and cannot be compensated for by T2-preparation pulses.

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgment

The results presented here have been developed in the framework of the 18HLT05 QUIERO Project. This project has received funding from the EMPIR programme co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme.

## Appendix A. Supplementary data

• Supplementary data 1
• Supplementary data 2
• Supplementary data 3
• Supplementary data 4
• Supplementary data 5
• Supplementary data 6
• Supplementary data 7

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