Lucas Soustelle^{1}, Paulo Loureiro de Sousa^{1}, Julien Lamy^{1}, Mathieu D. Santin^{2}, François Rousseau^{3}, and Jean-Paul Armspach^{1}

Imaging of the very-short T_{2} tissues in the head is challenging in that the signals decay very rapidly (T_{2} < 1 ms), as well as their signal quantity being often overwhelmed by long-T_{2} relaxing components (fat, free-water). In this work, we explore the feasibility of short-T_{2} quantification in the white matter and in the cortical bone using a novel method for long-T_{2} suppression based on diffusion and coherence effects in a steady-state 3D-UTE sequence.

The pulse sequence employed (fig. 1) consists in a long ($$$\gg$$$$$$T_2^{short}$$$) saturation rectangular-pulse followed by a short one, whose flip angle will be computed to maximize the short-T_{2} signal. Gradient spoiling, RF spoiling and delays are optimized to ensure a steady-state of the long-T_{2} component to be suppressed, and a minimal impact of potential static gradients (e.g. B_{0} inhomogeneities)^{7,8}.

Given a first flip angle $$$\alpha_1$$$ = 90°, $$$\alpha_2$$$ ($$$\leq$$$ 90°) is computed to maximize the short-T_{2} component by using the Bloch equations (accounting for relaxation occurring during excitation^{9}), and using myelin semi-solid T_{1} and T_{2}* values found in [4]. Then, using the expression of configuration states in [6], the signal to be suppressed can be written:

$$F_0^+=\cos(\alpha_2/2)^2F_{0}^-+e^{2i\Phi}\sin(\alpha_2/2)^2F_0^{-*}-ie^{i\Phi}\sin(\alpha_2)Z_{0}^{-},$$

with $$$F_0$$$ and $$$Z_0$$$ being functions of $$$\alpha_1,\alpha_2$$$, RF-phase $$$\Phi,n=TR_2/TR_1,TR_2,TR_1,T_1^{long},T_2^{long}$$$ and diffusion coefficient $$$D$$$. Since no trivial analytical expression exists for the $$$F_0^-$$$ and $$$Z_0^-$$$ states in steady-state, we numerically explored the tissues and sequence parameters space in order to assess whether the diffusion effect induced by the spoiling gradients would combine the $$$F_0^-$$$ and $$$Z_0^-$$$ states in order to satisfy $$$|F_0^+|=0$$$, corresponding to a signal cancellation. This condition has been met in simulations using an EPG implementation (fig. 2).

1. Horch, R. et al., Origins of the ultrashort-T2 1H NMR signals in myelinated nerve: A direct measure of myelin content?, MRM 2011; 66:24-31

2. Wilhelm, M. et al., Direct MR detection of myelin and prospects for quantitative imaging of myelin density, PNAS 2012; 109:9605-9610

3. Du, J. et al., Ultrashort echo time (UTE) magnetic resonance imaging of the short T2 components in white matter of the brain using a clinical 3T scanner, NeuroImage 2014; 87:32-41

4. Du, J. et al., Measurement of T1 of the Ultrashort T2* Components in White Matter of the Brain at 3T, 2014 PLoS ONE; 9:e103296

5. Larson, P. et al., Designing long-T2 suppression pulses for ultrashort echo time imaging, MRM 2006; 56:94-103

6. Weigel, M., Extended phase graphs: Dephasing, RF pulses, and echoes - pure and simple, JMRI 2015; 41:266-295

7. Yarnykh, V. et al., Actual flip-angle imaging in the pulsed steady state: A method for rapid three-dimensional mapping of the transmitted radiofrequency field, MRM 2007; 57:192-200

8. Nehrke, K., On the steady-state properties of actual flip angle imaging (AFI), MRM 2009; 61:84-92

9. Sussman, M., Design of practicalT2-selective RF excitation (TELEX) pulses, MRM 1998; 40:890-899

10. Chen, J. et al., Fast volumetric imaging of bound and pore water in cortical bone using 3D-UTE and inversion recovery UTE sequences, NMR in Biomedicine 2016; 29:1373-1380

Pulse sequence

Simulated signal vs. spoiling gradient amplitude. Explored parameters are T_{2}, T_{1}, D, TR and B_{1}, with TR_{2}/TR_{1}=5 and $$$t_{Spoil}$$$=3/15 ms. Signal pit occurrences have a monotonic behavior with respect to the value of every parameter. As T_{2} is increasing, the diffusion effect prevails, making the pit position shifts less. T_{1} doesn’t have a significant impact in the tested range, unlike D as the latter controls the damping. TR also has an impact due to its involvement in the steady-state evolution through relaxation effects. B_{1} deviations also shift the pit, and even multiply occurrences for low gradient amplitudes.

Coronal (a-f) and axial (g-i) views of the mouse head using the proposed method. (a), (b) and (g-i) show CC, parts of the anterior commissure and internal capsule. Striatum, superior commisure, cerebellar peduncle, fimbria and optic tract can be found in figures (c-f). Cortical bone is well highlighted due to its relatively high proton density and longer T_{2}*.

With a single exponential non-linear fitting, T_{2}* value in CC was found to be 62.1 $$$\mu$$$s, and 260.1 $$$\mu$$$s in CB, with respective tight confidence interval. CB signal and corresponding fitted curve were divided by a factor of 3 for display purpose.