Richard Buschbeck^{1}, Ezequiel Farrher^{1}, Kuan-Hung Cho^{2}, Ming-Jye Chen^{2}, Seong Dae Yun^{1}, Chang-Hoon Choi^{1}, Li-Wei Kuo^{2,3}, and N. Jon Shah^{1,4,5,6}

Initial phantom and in vivo results of a multi-echo Stejskal-Tanner EPI sequence are presented demonstrating the feasibility of rapid measurements for diffusion tensor and T_{2} correlations. The diffusion and T_{2} maps are artefact-free and are found to be very similar to the ones derived from the conventional individual-echo methods. However, the data tend to display slightly overestimated diffusivities and T_{2}, which need to be investigated further.

Compared to the standard method, the proposed multi-echo sequence reduces the scan time by a factor of five, which is necessary to make multidimensional diffusion techniques feasible in clinical settings.

Multidimensional MRI methods have recently been used in a variety of in vivo investigations, offering a non-invasive characterisation of tissue heterogeneity with an unprecedented level of detail. In particular, it has been demonstrated that simultaneously measuring diffusion and transverse relaxation (D-T_{2}) properties can provide valuable information on the underlying microstructure^{1}. Moreover, it has been shown that this kind of analysis leads to a more accurate, precise and robust estimation of the model parameters^{2}, such as in case of the free water elimination (FWE) method^{3}. However, measuring D-T_{2} properties simultaneously requires long scan times.

In this work, we propose a multi-echo Stejskal-Tanner EPI sequence to acquire D-T_{2} data more efficiently, drastically reducing the scan time. A complete five-echo D-T_{2} protocol was acquired in ~7min and the performance was compared to the standard single-echo procedure acquired in ~35min.

A multi-echo Stejskal-Tanner sequence acquiring five spin-echo (SE) EPI readouts per repetition time (Fig. 1) was implemented on a 3T PRISMA scanner (Siemens Healthineers, Germany). The sequence was compared to the conventional approach of acquiring each echo individually (“individual-echo” approach).

The sequence was first tested on a diffusion fibre phantom composed of five parallel-fibre tubes^{4}, doped with different concentrations of MgCl_{2}$$$\cdot$$$6H_{2}O: 0, 1.35, 2.30, 3.01, 3.55mol/l. In vivo measurements were performed on a healthy male 34-year-old volunteer from whom written informed consent was obtained in line with legal requirements prior to the measurements.

The sequence parameters for the phantom experiments were: TE = 66, 166, 266, 366 and 466ms; diffusion gradient duration and separation, δ=14ms and Δ=36ms; b-values(directions) = 0(8), 0.625(12) and 1.25(26)ms/μm^{2}; matrix-size=128⨉128⨉8; voxel-size=2^{3}mm^{3}.

For the in vivo experiments: TE=58, 86, 114, 142 and 170ms; δ=14ms and Δ=31ms; b-values(directions) = 0(8), 0.4(12) and 0.8(26)ms/μm^{2}; matrix-size=96⨉96⨉40; voxel-size=2.5^{3}mm^{3}.

Additionally, a conventional single-echo spin-echo sequence to obtain reference T_{2} values was employed. Echo-times for the phantom were: TE=12, 62, 112, 212, 312, 412 and 512ms. For the in vivo experiments: TE=12, 32, 52, 82 and 122ms. The repetition-time in all experiments was TR=9s.

Individual- and multi-echo data were processed using the method assuming anisotropic, Gaussian diffusion (DTI) and monoexponential transverse relaxation (DTIT_{2}), in which the signal, S, is expressed as:

$$S(\mathrm{TE},b,\mathbf{n})=S_0e^{-\frac{\mathrm{TE}}{\mathrm{T_2}}e^{-b\mathbf{n}^\mathrm{T}\mathbf{D}\mathbf{n}}}~~~~~~~~(1)$$

where S_{0}, T_{2} and **D** are the proton density, the transverse relaxation time and diffusion tensor, respectively; b and n are the diffusion weighting strength and direction.

Model parameters, $$$\boldsymbol{\hat{\theta}}=[\ln(S_0),\mathrm{D}_{11},\mathrm{D}_{12},…,\mathrm{D}_{33},1/\mathrm{T_2} ]^\mathrm{T}$$$, were estimated by fitting Eq. 1 to the experimental datasets, using the weighted-linear least-squares method:

$$\boldsymbol{\hat{\theta}}=(\mathbf{X}^\mathrm{T}\mathbf{wX})^{-1}\mathbf{X}^\mathrm{T}\mathbf{wy}~~~~~~~~(2)$$

where **y** is a column vector whose elements are given by *y _{i}*=ln(

Fig. 2 shows AD, RD and T_{2} maps for the individual-echo and the multi-echo approaches. The maps acquired using multi-echo acquisition are in agreement with those with individual-echo acquisition. Small differences are visible in T_{2} between 3 and 5 echoes in the multi-echo case.

Fig. 3 shows a comparison of the mean AD, RD and T_{2} in six regions of interest (ROIs), five in the tubes and one in the bulk.

In vivo FA, MD and T_{2} maps shown in Fig. 4 demonstrate that the multi-echo approach provides comparable results.

Fig. 5 shows the histograms of FA, MD and T_{2} for the whole FOV, each compared to the reference and the individual-echo method. In the multi-echo case, FA is shifted towards lower values, whereas MD and T_{2} become shifted towards larger values, in line with the phantom results (Figs. 2-3).

The results demonstrate that the proposed sequence produces reasonable results while reducing the scan time. However, it tends to slightly overestimate T_{2} and diffusivity, which needs to be further investigated. In the phantom case, the fitting instability of bulk T_{2} values is due to its extremely long values (>2.5s), which are not present in vivo.

In the current implementation in vivo, only 3 echoes are usable as echo 4 and 5 show low SNR values and are affected by several artefacts, probably due to the accumulation of imperfect RF refocusing effects. Other phase cycling approaches, as well as the use of parallel-excitation methods could be used to improve the RF refocusing.

1 de Almeida Martins, João P. and Topgaard, Daniel (2018) ‘Multidimensional correlation of nuclear relaxation rates and diffusion tensors for model-free investigations of heterogeneous anisotropic porous materials’. Scientific Reports, 8(1).

2 Veraart, Jelle, Novikov, Dmitry S. and Fieremans, Els (2018) ‘TE dependent Diffusion Imaging (TEdDI) distinguishes between compartmental T2 relaxation times’. NeuroImage, 182, pp. 360–369.

3 Collier, Q, Veraart, J, den Dekker, AJ, Vanhevel, F, et al. (2017) ‘Solving the free water elimination estimation problem by incorporating T2 relaxation properties’, in Proceedings of 25th Annual Meeting of ISMRM, Honolulu, Hawaii, USA, p. 1783.

4 Farrher, Ezequiel, Lindemeyer, Johannes, Grinberg, Farida, Oros-Peusquens, Ana-Maria and Shah, N. Jon (2017) ‘Concerning the matching of magnetic susceptibility differences for the compensation of background gradients in anisotropic diffusion fibre phantoms’ Jiang, Q. (ed.). PLOS ONE, 12(5), p. e0176192.

5 Basser, Peter J. and Pierpaoli, Carlo (2011) ‘Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI’. Journal of Magnetic Resonance, 213(2), pp. 560–570.

6 Nagy, Zoltán, Thomas, David L and Weiskopf, Nikolaus (2014) ‘Orthogonalizing crusher and diffusion-encoding gradients to suppress undesired echo pathways in the twice-refocused spin echo diffusion sequence’. Magnetic Resonance in Medicine, 71(2), pp. 506–515.

7 Bernstein, Matt A, King, Kevin F and Zhou, Xiaohong Joe (2004) Handbook of MRI pulse sequences, Elsevier.

Figure 1: Schematic of the multi-echo Stejskal-Tanner diffusion EPI sequence. The duration and the separation of the diffusion gradients (grey shaded) can be chosen freely. Five identical EPI readouts at equidistantly spaced echo times were acquired. The SE signal is refocused by multiple 180° RF pulses each of which are accompanied by symmetrical crusher gradients (not shown) providing four times the phase dispersion of the readout gradients. The crusher directions were chosen orthogonal to the diffusion directions as suggested by Nagy et al.^{6} To mitigate the effect of imperfections in the refocusing pulses, a CPMG phase cycling scheme was used.^{7}

Figure 2: AD (first row), RD (second row) and T_{2} maps (third row) for the individual-echo (first and second columns) and the multi-echo (third and fourth columns) approaches. In the tubes, the results are very comparable between the individual-echo and the multi-echo approach as well as the cases of 3 and 5 echoes. Only in the T_{2} maps in the bulk water, the results appear different, probably due to the extremely long T_{2} times.

Figure 3: Comparison of AD, RD and T_{2} in six ROIs, five in the tubes and one in bulk water.

The plots show the diffusion parameters AD (top row) and RD (middle row) from DTIT2 (multi-echo and individual-echo experiments) versus the same parameters from conventional DTI (single-echo).

Bottom row: comparison of T_{2} from DTIT_{2} versus the reference T_{2} from the SE sequence.The derived values are similar to the reference methods, although they tend to be overestimated. The overestimation becomes larger the more echoes are used in the analysis.

Figure 4: Maps of FA (first row), MD (second row) and T_{2} (third row) for the individual-echo (first column) and the multi-echo (second column) approach. Based on visual inspection, the results appear very comparable.

Figure 5: Histograms comparing the distribution of FA, MD and T_{2} values in the whole brain. The black curves represent the reference (DTI for FA and MD, SE for T_{2}); the blue and red curves represent the individual-echo and the multi-echo techniques, respectively.

FA, MD and T_{2} from DTIT_{2} analysis appear shifted compared to the same maps from conventional DTI (FA and MD) and SE (T_{2}) analyses.