Christian Guenthner^{1}, Thomas Amthor^{2}, Sebastian Kozerke^{1}, and Mariya Doneva^{2}

Magnetic Resonance Fingerprinting (MRF) and triple-echo steady-state (TESS) are two sequences that both allow for the simultaneous quantification of T1 and T2. While MRF relies on the transient response of tissue and noise-like under-sampling artifacts, TESS acquires the two lowest order SSFP-FIDs and the lowest order SSFP-Echo in the steady-state of a rapid, spoiled SSFP sequence.

In this work, we compare the performance of the two sequences in a phantom study, where imaging parameters and total acquisition duration between the two scan techniques were matched. In addition, a slice-profile correction for TESS is proposed and included in the comparsion.

Magnetic Resonance Fingerprinting (MRF) allows for the simultaneous quantification of tissue parameters by matching the transient response to a series of varying flip-angles (FA) and repetition times (TR) to a pre-calculated dictionary.^{1,2} Another technique for rapid relaxometry is the triple-echo steady state (TESS) sequence, which allows for the simultaneous estimation of T1 and T2 through acquisition of the two lowest order SSFP-FID$$$\;F_{+1,0}\;$$$and the lowest order SSFP-Echo$$$\;F_{-1}\;$$$in a rapid SSFP sequence with constant TR and FA.^{3} While MRF heaviliy relies on spatio-temporal correlations and noise-like undersampling artifacts, TESS requires the acquisition of consistent, high SNR images to allow fitting of a fully analytic signal model.

In this work, we propose a slice profile correction for TESS and compare the performance of MRF and TESS in a phantom study, where imaging parameters and total acquisition duration between the two scan techniques were matched.

Cartesian TESS^{3} (Fig.1) and spiral FISP-MRF^{2} (Fig.2) were implemented on a 3T Philips Ingenia system (Philips, Best, The Netherlands) and data was acquired using an 8-channel head coil. The measurements were performed on a phantom (High Precision Devices, Inc., Model 130) with 14 samples of differing T1 and T2 values. Both sequences were set up with equal imaging parameters: 240mm square FOV, 1.5mm isotropic resolution, single-slice excitation, 5mm slice thickness, spoiling in through-plane direction of Δk_{S}=4·2π/5mm and in the case of TESS also with additional in-plane spoiling of Δk_{x}=2π/1.5mm spoiling area in both measurement and phase-encode direction (Fig.1b), and identical sinc-Gauss excitation pulse. The slice profile was determined using the hardpulse approximation. In addition,$$$\;B_1^+(\vec{r})\;$$$ was determined using actual flip angle imaging.^{4}

**TESS:** The three spoiled magnetization states were acquired in successive TR periods by adding a respective re-phasing gradient before the readout and ensuring equal total spoiling in each TR (Fig.1).^{5} Sequence timing is depicted as part of Figure 1. Each echo was sampled three times to increase SNR and to match the acquisition duration of TESS and the MRF scan to 16s.

T1/T2 were simultaneously recovered using a least-squares minimization of the signal ratios$$S_{T1}\left(T_1,T_2\right)=\frac{F_{-1}}{F_0-F_1}\quad\text{and}\quad{}S_{T_2}\left(T_1,T_2\right)=\frac{F_{1}}{F_0}$$using an analytic signal model.^{6} The local$$$\;B_1^+\;$$$was included by per-pixel calculation of the effective FA. Moreover, a slice profile correction (SPC) for TESS was devised, which takes the finite spoiling$$$\;\Delta{}k_S\;$$$over the slice of thickness$$$\;\Delta{}s\;$$$into account. The corrected echo amplitudes are given by$$F_n^\text{SPC}=\sum_{k,z}F_+\left(z;k\right)e^{-\text{i}z\cdot\Delta{}k_S\cdot\left(k-n\right)}\cdot\text{sinc}\left(\frac{\Delta{}z\Delta{}k_S\cdot\left(k-n\right)}{2}\right),$$where$$$\;n\;$$$is the echo order ($$$n=-1\dots{}1$$$),$$$\;k\;$$$the contributing configuration states (here$$$\;k=-25\dots{}25\;$$$) and$$$\;z\;$$$the position within the discretized slice with bin width$$$\;\Delta{}z$$$. The configuration states$$$\;F_+\left(z;k\right)\;$$$were evaluated for each bin separately using the FA given by the product of local slice profile, B_{1}^{+}, and nominal FA.

Additional in-plane spoiling simplifies the slice profile correction to averaging over the profile according to$$F_n^\text{SPC, in-plane}=\sum_{z}F_+\left(z;n\right).$$

**MR Fingerprinting:** The MRF signal evolution was acquired using a single shot, 15-fold undersampled spiral acquisition with conjugate phase reconstruction to account for B_{0} inhomogeneity. The acquisition of 1000 time-points was preceded by an adiabatic inversion pulse with 20ms delay. A constant TR of 16ms and a varying FA up to 70° was used (Fig.2).

Parameter maps were obtained by matching of the temporal response to a pre-calculated dictionary using the EPG formulation.^{7,8,9} Two dictionaries were created, one only accounting for T1/T2 and a second dictionary accounting for B_{1}^{+} and slice-profile determined prior to matching. Details are given in Fig.2c-d.

Fig.3 shows the dependency on T1/T2 of the TESS signal ratios$$$\;S_{T_1}\;$$$and$$$\;S_{T_2}\;$$$without and with SPC for in-plane and additional through-plane spoiling. TESS without SPC leads to underestimation of T1.$$$\;S_{T_1}\;$$$is equivalent for all models below a T2 of approx. 75ms, thus small T2 are expected to be unaffected by slice profile effects.

Fig.4 shows mean and standard deviation of T1/T2 values obtained with MRF and TESS against vendor-provided ground-truth (GT) values. MRF allows to recover T1 over the whole investigated range and underestimates T2 especially for values below 50ms. TESS without SPC underestimates T1 by a factor 2, which is in accordance with the findings of Fig.3. TESS with SPC and through-plane spoiling, allows to recover T1 up to 1250ms, however, minimization becomes unstable at low T1 values. Independent of SPC, TESS is in excellent agreement with GT for T2 values below 50ms. The discrepancy of TESS with additional in-plane spoiling compared to through-plane spoiling only, indicates that the simplified SPC model is not accounting for all slice-profile effects.

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