Diffusion MRI measurements in challenging head and brain regions via cross-term spatiotemporally encoding

Cross-term spatiotemporal encoding (xSPEN) is a recently introduced imaging approach delivering single-scan 2D NMR images with unprecedented resilience to field inhomogeneities. The method relies on performing a pre-acquisition encoding and a subsequent image read out while using the disturbing frequency inhomogeneities as part of the image formation processes, rather than as artifacts to be overwhelmed by the application of external gradients. This study introduces the use of this new single-shot MRI technique as a diffusion-monitoring tool, for accessing regions that have hitherto been unapproachable by diffusion-weighted imaging (DWI) methods. In order to achieve this, xSPEN MRI’s intrinsic diffusion weighting effects are formulated using a customized, spatially-localized b-matrix analysis; with this, we devise a novel diffusion-weighting scheme that both exploits and overcomes xSPEN’s strong intrinsic weighting effects. The ability to provide reliable and robust diffusion maps in challenging head and brain regions, including the eyes and the optic nerves, is thus demonstrated in humans at 3T. New avenues for imaging other body regions are also briefly discussed.

are first calculated, and then combined with the diffusion model discussed by Karlicek and Lowe (1) according to which the diffusion-derived attenuation imposed by gradients throughout an NMR sequence is summarized by a b-value where is a wavenumber encompassing the action of all gradients up to a particular time t'. As shown in (2,3), the application of frequency swept pulses under the action of gradients as done in SPEN/xSPEN, results in a spin dephasing which, by contrast to the assumptions leading to Eq.
[S1], is neither linear in space, nor independent of position. To account for this we preserve Eq.
[S1] but re-express the K-wavenumber in terms of a local spatial dispersion K local , describing the dephasing experienced by the spins within a neighboring region that is relevant in terms of the diffusion length scale (2,4). A Taylor expansion allows one to describe this wavenumber in proximity to an arbitrary r 0 as dr , an expression that becomes identical to the Karlicek-Lowe formulation if ϕ's dephasing has been imparted solely by a linear gradient.
Using this formalism for calculating the diffusion-driven signal attenuation as a function of time and position, the decays expected for the xSPEN sequences described in Figure 1 of the main text, were estimated. For simplicity, we only took into consideration the imaging gradients ∫ along the xSPEN-relevant (y,z)-axes, disregarding the effects of the rapidly-oscillating RO (xaxis) gradient, and assuming that the diffusion gradients (greyed G d s in Fig. 1) were initially null.
The relevant manipulations therefore include a slice-selective 90˚ excitation followed by two identical frequency-swept inversion pulses acting in synchrony with a bipolar ±G y -all of this imparted while in the presence a constant G z , which stays active throughout the course of an acquisition lasting a duration T a . Referring to tas the time in which spins positioned at a given is the signal in the absence of diffusion-follows.   In general, displacement measurements require extending the above calculations to account for the presence of diffusion gradients G d applied along multiple, non-coincident spatial orientations (6-8). These gradients can be introduced in the xSPEN scheme as illustrated in the manuscript's Fig. 1a, which places a PGSE block during a built-in (T a +p 1 )/2 free evolution delay introduced for the sake of achieving full refocusing. These pulsed magnetic field gradients G d , acting along arbitrary orientations for a duration δ and separated by a diffusion-sensitizing time Δ, can be accounted by extending the K local -based formalism that lead to Eq. [S2] to the tensorial where b is now a matrix dictated by products of the localized phase derivatives of ϕ(t ', r 0 ) , given by both the imaging and the diffusion gradients. The resulting b tensor will be both space-and time-dependent, and by contrast to common PGSE measurements, it will have usually two dominant eigenvalues that define it. Complexities of this behavior are further illustrated in Extended Data Figure S1, which describes how the various tensorial b-components vary for different positions along the imaged axis, over the course of an xSPEN acquisition.

B. Gradient scheme validations.
The reliability of the various gradient schemes discussed in the main text's Figure 2 were tested on a set of 2601 "synthetic tissues", where each of these samples was assigned a random proton density and axially-symmetric diffusion tensors with randomized directionality and eigenvalues spanning realistic FA (0-1 arbitrary) and ADC (0.4-1.8x10 -3 ) values. The signals arising from these different tissues under the action of the various gradient schemes were simulated using the Bloch-Torrey formalism (10), and Gaussian noise was added to these calculated signals so that the mean b 0 -image SNR would be 7%. Based on these synthetic sets, FA and ADC values were then estimated, and both mean absolute differences (which can be appreciated in Fig. 2 as deviations from the red-lined unity slopes graphed) and r 2 values, were calculated against the ground truth FAs and ADCs for the various tested gradient schemes. The Extended Data Figure   S2 illustrates an experimental validation of the resulting b o -including "double-cone" approach, conducted on a water phantom in a clinical 3T MRI machine, showing essentially the same reliability as EPI-based maps. This latter gradient scheme was adopted for the human ADC and DTI xSPEN mapping.
Extended Data - Figure S1. Extended Data Figure S2. Experimental validation of the "b o -enhanced double-cone" gradient scheme introduced in the main text Figs. 1b and 2d, on a water phantom examined in a 3T clinical scanner. The xSPEN pulse sequence in Fig. 1b was used to derive the ADC and FA maps. In the left-hand column these were derived under the assumption that the diffusion-driven signal attenuation solely arise due to the effects of the G d diffusion gradients (11); in the righthand column maps accounted for both the xSPEN imaging and the PGSE bipolar gradients as per the analytical calculation deriving from Eqs. [S1]-[S4].