Volkert Roeloffs^{1}, Nick Scholand^{1,2}, and Martin Uecker^{1,2,3}

^{1}Institute for Diagnostic and Interventional Radiology, University Medical Center Göttingen, Goettingen, Germany, ^{2}DZHK (German Centre for Cardiovascular Research), Partner Site Göttingen, Germany, Goettingen, Germany, ^{3}Campus Institute Data Science (CIDAS), University of Göttingen, Göttingen, Germany, Goettingen, Germany

Sensitivity to T1 and T2 in frequency-modulated SSFP sequences can be increased by choosing a higher modulation speed without prolonging the repetition time. In this work, we assess the boost in sensitivity by Cramér-Rao-bound analysis, combine the sequence with stack-of-stars sampling and subspace-constrained reconstruction, and demonstrate joint T1/T2/B1/off-resonance mapping in phantom and in vivo study. The results render fast-sweep frequency-modulated SSFP an excellent candidate for comprehensive 3D multi-parametric mapping.

In this work, we investigate the increased sensitivity of the "fast-sweep" fmSSFP, combine this novel sequence with a stack-of-stars sampling scheme, and demonstrate joint T1/T2/B1/off-resonance mapping in phantom and in vivo.

$$\phi(n)= 180^\circ n + 360^\circ \frac{n^2}{2P}$$

where $$$P$$$ is the period of the generated signal and controls the sweeping speed. Two representative signal time courses are shown in Fig. 1 with periods $$$P$$$=50000 (slow sweep, left column) and $$$P$$$=1616 (fast sweep, right column). To assess the sensitivity of the respective Bloch responses, a relative Cramér-Rao-bound (rCRB) analysis was performed similar to [4]:

$$ \text{rCRB(}M_0\text{)} = \sigma^{-2} T_\text{exp} \left[I^{-1}(\theta)\right]_{11} $$

$$ \text{rCRB(}R_1\text{)} = \sigma^{-2} R^2_1 T_\text{exp} \left[I^{-1}(\theta)\right]_{22} $$

$$ \text{rCRB(}R_2\text{)} = \sigma^{-2} R^2_2 T_\text{exp} \left[I^{-1}(\theta)\right]_{33} $$

with noise variance $$$\sigma^2$$$, Fisher-Information matrix $$$I(\theta)=\sigma^{-2}(DS)^{H}(DS)$$$, total duration of the sweep $$$T_\text{exp}$$$, and Jacobi matrix of the signal $$$DS$$$.

By increasing the modulation speed of the fmSSFP signal, the sensitivities of both T1 and T2 can be increased as relaxation effects are introduced into the signal time course, resulting in asymmetries that decouple the partial derivatives of R1 and R2 (Fig. 1).

Image reconstruction is performed in the low-frequency Fourier subspace as detailed in [6,7] using BART [8] utilizing coil estimation by ESPIRIT [9] and gradient delay correction with RING [10].

For fast-sweep fmSSFP, in contrast to phase-cycled bSSFP, no closed-form signal models are available so far. Therefore, we modeled the signal time course within the framework of Extended Phase Graphs (EPG, [11]) and projected to the low-frequency Fourier subspace subsequently.

The presented approach was validated in a phantom study (NIST system standard model 130, TR=5.0 ms, FA=15°, 1×1×3 mm

Figure 3 shows reconstructed subspace coefficient maps, fitting results and fit residuals for the brain study. Fitting accuracy is excellent except for regions with subcutaneous fat or flowing CSF.

A synthesized time series can be computed from the reconstructed subspace coefficient maps and is shown in Figure 4.

Figure 5 shows parameter maps of the brain study similar to Fig 2. A ROI-based analysis for white and gray matter showed good agreement for both T1 and T2 with literature findings [12,13]. Similar to the phantom study, a coupling between M0 and relative B1 can be observed.

Several properties render this sequence very attractive for 3D multi-parametric mapping, which are a) continuous data acquisition without intermediate preparation phases, b) off-resonance-resolved reconstruction, and c) availability of a subspace model.

Initial results are promising and we believe fast-sweep fmSSFP to be an excellent candidate for fast and comprehensive multi-parametric mapping. As a next step, the observed coupling between $$$M_0$$$ and relative $$$B_1$$$ needs to be analyzed and eventually overcome.

A future integration of this signal model into a non-linear model-based reconstruction could help to better decouple individual parameter maps (e.g. $$$M_0$$$ from relative $$$B_1$$$) by incorporating prior knowledge and advanced regularization.

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[2] Shcherbakova et al., "PLANET: an ellipse fitting approach for simultaneous T1 and T2 mapping using phase‐cycled balanced steady‐state free precession." MRM 79.2 (2018)

[3] Foxall et al., "Frequency‐modulated steady‐state free precession imaging", MRM 48.3 (2002)

[4] Assländer et al., "Optimized quantification of spin relaxation times in the hybrid state" MRM 82.4 (2019)

[5] Wundrak et al., "Golden ratio sparse MRI using tiny golden angles." MRM 75.6 (2016)

[6] Roeloffs et al., "Frequency‐modulated SSFP with radial sampling and subspace reconstruction: A time‐efficient alternative to phase‐cycled bSSFP." MRM 81.3 (2019)

[7] Roeloffs et al., "Joint T1/T2 mapping with frequency-modulated SSFP, radial sampling, and subspace reconstruction.", Proc. ISMRM 2018, 3702

[8] BART 0.6.00 Toolbox for Computational Magnetic Resonance Imaging, DOI: 10.5281/zenodo.3934312

[9] Uecker et al.. "ESPIRiT—an eigenvalue approach to autocalibrating parallel MRI: where SENSE meets GRAPPA", MRM 71.3 (2014)

[10] Rosenzweig et al., "Simple auto‐calibrated gradient delay estimation from few spokes using Radial Intersections (RING).", MRM 81.3 (2019)

[11] Hennig et al., "Echoes—how to generate, recognize, use or avoid them in MR‐imaging sequences. Part I: Fundamental and not so fundamental properties of spin echoes" Concepts in Magnetic Resonance 3.3 (1991)

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[14] Shcherbakova et al., "On the accuracy and precision of PLANET for multiparametric MRI using phase‐cycled bSSFP imaging", MRM 81.3 (2019)

Fig 1: Signal time course and derivatives w.r.t. R1 and R2 for
slow-sweep ($$$P$$$=50000) and fast-sweep fmSSFP ($$$P$$$=1616). The fast-sweep
fmSSFP signal exhibits a pronounced asymmetry and results in reduced relative
Cramér-Rao-bound, especially for R2. Note that the derivative w.r.t. $$$M_0$$$ is
proportional to the signal itself (upper row). Other simulation parameters were
TR=5.0 ms, FA=15°, T1=800 ms, T2=50 ms

Fig 2: Parameter maps obtained after pixelwise fitting of
subspace-constrained reconstruction (top) along with quantitative
comparison to reference data (bottom).

Fig 3: Coefficient maps of the subspace-constrained reconstruction (top,
magnitude only) are fitted with the EPG signal model (center). Major
differences appear only in the subcutaneous fat or in compartments with
flowing CSF.

Fig 4: Synthesized time series after subspace-constrained reconstruction
with intensity-coded magnitude and color-coded phase. Frame rate equals
acquisition rate (8s sweep duration).

Fig 5: Parameter maps obtained after pixelwise fitting of
subspace-constrained reconstruction.