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Fast quantitative T₂ mapping at ultra-high field using sparse sampling and dictionary-based reconstruction

Jochen Schmidt^1,2, Dvir Radunsky³, Patrick Scheibe¹, Noam Ben-Eliezer^3,4,5, Robert Trampel¹, and Nikolaus Weiskopf^1,6
¹Neurophysics, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany, ²International Max Planck Research School on Neuroscience of Communication: Function, Structure and Plasticity, Leipzig, Germany, ³Biomedical Engineering, Tel Aviv University, Tel Aviv, Israel, ⁴Sagol School of Neuroscience, Tel Aviv University, Tel Aviv, Israel, ⁵Center for Advanced Imaging Innovation and Research (CAI2R), New York University Langone Medical Center, New York, NY, United States, ⁶Felix Bloch Institute for Solid State Physics, Leipzig University, Leipzig, Germany

Synopsis

Keywords: Quantitative Imaging, Sparse & Low-Rank Models

Quantitative T₂ mapping at ultra high-field via multi-echo spin-echo acquisitions suffers from bias introduced by pronounced transmit field inhomogeneities. Hence, accurate signal modeling is vital. Futhermore, high-resolution imaging results in longer scan times, which need to be compensated by k-space undersampling. Conventional undersampling schemes for multi-echo approaches skip identical phase encoding areas for all echo readouts. Image reconstruction quality might be improved by varying the sampling across echoes and using a low rank reconstruction approach. A multi-echo acquisition combining sparse undersampling with a dictionary modelling method was successfully used to acquire accurate T2 at 7T with a high acceleration.

Introduction

Robust and accurate quantification of the relaxation parameters T₁, T₂* and T₂ is vital for studying the microstructural composition of the human brain in vivo^1,2. With the development of ultra-high-field (UHF ≥ 7T) MRI it has become possible to obtain relaxation parameter maps at high spatial resolution³. However, inhomogeneity of the (B₁⁺) transmit field is pronounced at UHF⁴. This is especially a problem for estimating the transverse relaxation time T₂, since commonly used multi-echo spin-echo (MESE)^5,6 approaches suffer from the formation of stimulated echo pathways when subject to an inhomogeneous B₁⁺and the inherent variation of B₁⁺ across the slice profile. Compensation methods, using either the extended-phase-graph (EPG) formalism⁷ or Bloch equation simulations⁸, are needed for robust and reliable estimation of high-resolution T₂ maps by accurate signal modeling at UHF⁹. High spatial resolution requires long scan times, typically compensated by standard parallel imaging techniques like GRAPPA¹⁰, where skipping of phase encode lines outside of a central fully sampled auto-calibrated (AC) k-space region is used. The penalty in signal-to-noise ratio (SNR) might be decreased by using more effective k-space undersampling schemes or improved image reconstruction. AC-LORAKS¹¹ reconstruction was shown to efficiently reconstruct random under-sampled k-space data with an AC region. Additionally, LORAKS benefits from exploitation of image information shared between echoes when using joint echo reconstruction¹². To obtain accurate high-resolution T₂ maps in feasible time, we developed a MESE sequence variant, which combines sparse undersampling with AC-LORAKS reconstruction. The echo signal was modeled by the echo-modulation curve (EMC)⁸ approach. As quantitative reference, we used a fully sampled SE, and a GRAPPA accelerated standard MESE sequence.

Methods

We developed a python package¹³ for the EMC method. A database, tailored to the exact experimental parameters of each sequence, was simulated for a range of input parameters (Fig. 1). The Siemens product MESE sequence (SEMC) samples identical phase encode lines for all contrasts, when using GRAPPA acceleration. Better conditioning of the reconstruction problem might be achieved by utilizing different k-space regions per contrast and sharing the information across contrasts. We set up a MESE sequence variant (TMC) via pypulseq^14,15 to cover a central AC region with 42 lines, identical to the SEMC sequence. However, we employed phase encode steps between successive readouts for k-space lines outside of the AC region (Fig. 2). Measurements were conducted on a Magnetom Terra 7T (Siemens Healthineers, Erlangen, Germany) using an 8Tx/32Rx radio-frequency (RF) head coil (Nova Medical, Wilmington MA, USA). The sequence was tested on a phantom (Gold standard phantoms, Rochester, UK) containing vials with various concentrations of a MnCl2 solution. We used (0.7mm)³ isotropic resolution for all MESE scans and 1.05 x 1.05 x 0.7 mm³ resolution for the SE acquisitions. A TR of 4000ms was used in all scans to avoid T₁ saturation effects. We used the following echo times: TE=k*9.4ms for the TMC, TE=k*10ms for the SEMC scans (k=1,2,…,6) and TE=10ms,25ms,50ms for the SE acquisitions. Total scan times were 4:58min for the TMC sequence (acceleration = 4), 6:18min / 10:39min for the SEMC sequence with GRAPPA 4 / 2, respectively, and a total of ~33min for the fully sampled SE scans (Fig. 3). We used standard GRAPPA reconstruction for the datasets acquired with SEMC. The resulting magnitude images exhibit non-central χ noise due to the multi-channel coil combinations and non-linear operations¹⁶. Hence, a majorize-minimize algorithm was deployed for denoising¹⁷. The TMC acquired data was reconstructed using AC-LORAKS (reconstruction parameters: rank=200, λ=0.0, R=3, Type=C) and noise filtered per channel before combination. A best match of the decay curve per voxel to the respective pre-calculated EMC database was used for all MESE data. SE acquisitions were subjected to noise filtering and a mono-exponential signal fit.

Results

A 6.6-fold reduction in scan time compared to an un-accelerated SE acquisition (with 3 echoes) was achieved using the TMC sequence with AC-LORAKS reconstruction and higher image resolution, while maintaining the overall image data quality (Fig. 3). We achieved similar speed-up (5.2-fold) using the SEMC sequence, but it was less robust to B₁⁺ inhomogeneities (Figs. 3 and 4). T₂ maps were obtained after database matching (Fig. 4) and comparable to the SE reference. However, the TMC approach appeared to underestimate T2 somewhat (Fig. 5).

Discussion

The estimated T₂ showed quantitative comparability to the SE data (Fig. 5). However, MESE acquisitions still suffer from a B₁⁺ bias which is not completely accounted for by EMC database fitting. This behavior is pronounced in regions with low SNR making it dependent on the acceleration factor. Notice the mitigation of B₁⁺ bias effects in the TMC approach compared to the SEMC technique when a similar acceleration was employed. This presumably stems from the more homogeneous k-space coverage and LORAKS reconstruction performance. However, the TMC approach is sensitive to fold-over artifacts when highly undersampling k-space. The reconstruction might be enhanced by further optimizing the k-space sampling pattern.

Conclusion

We acquired (0.7mm)³ high-resolution quantitative T₂ maps in feasible scan time. The acceleration enabled by the TMC approach might translate to higher coverage for in vivo scans. Future work will include tests in volunteers, randomized sampling in the accelerated TMC phase encoding and implementing pTx pulses for compensating the remaining B₁⁺ bias.

Acknowledgements

We like to acknowledge the Institutes MTAs for aiding most of the scan sessions. And also Niklas Wehkamp, from Department of Radiology, University Medical Center Freiburg, Germany and Kerrin Pine, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany, for the help with setting up scanning with pulseq.

Nikolaus Weiskopf has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n° 616905; from the European Union's Horizon 2020 research and innovation programme under the grant agreement No 681094; from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project no. 347592254 (WE 5046/4-2); from the Federal Ministry of Education and Research (BMBF) under support code 01ED2210.

The Max Planck Institute for Human Cognitive and Brain Sciences has an institutional research agreement with Siemens Healthcare. NW holds a patent on acquisition of MRI data during spoiler gradients (US 10,401,453 B2). NW was a speaker at an event organized by Siemens Healthcare and was reimbursed for the travel expenses.

References

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Figures

Figure 1: Exemplary signal response curves for a range of T₂ values and two different transmit field efficiencies (pink vs green). The formation and characteristics of stimulated echoes causes a clear deviation from a mono-exponential decay.

Figure 2: Exemplary echo trains of the MESE - TMC sequence (A,B). The acquired k–space data is zero-filled and concatenated in frequency encode direction (C). An acquisition with identical phase encoding for all echo readouts (A) results in one central line. Phase encode ‘blips’ implement the k-space shifts between echo readouts for lines outside the central region (B) and result in a spread of sampled lines in k-space. The complementary sampling scheme (D) accentuates sampled lines for visibility.

Figure 3: Top Row: Reconstructed echo magnitude images for the first echo readout. Signal bias due to the inhomogeneous B₁⁺ transmit field profile is apparent in all acquisitions (red arrows). Bottom row: corresponding scan time for the acquisition of respective echo magnitude images.

Figure 4: Top row: Estimated T₂ maps for each sequence. Inefficient B₁⁺ (red arrows) results in erratic T₂ for MESE acquisitions. The severity is dependent on the acceleration factor. B₁⁺ related bias was lower in the TMC approach although similar acceleration was used (~12% faster acquisition compared to the SEMC GRAPPA 4). However, T₂ values were underestimated. Bottom row: Signal curves for voxels marked in the images (top row) show the deviation from a mono-exponential decay and the need for the EMC signal modeling approach.

Figure 5: A: MnCl₂ concentrations for all 24 vials. Each concentration is found in two vials at different locations to evaluate position independent performance of the methods, as indicated in the top right image (C). B: Estimated T₂ values in milliseconds including standard deviations for circular regions of interest set concentrically into respective vials. Since low echo times were used (TE ≤ 70ms), all methods show low accuracy for high T₂ estimates. C: Vial locations for phantom adjusted to the orientation of the acquired images. D: SE T₂ map for reference.

Proc. Intl. Soc. Mag. Reson. Med. 31 (2023)

1786

DOI: https://doi.org/10.58530/2023/1786