To incorporate the sd-PFG double diffusion encoding technique into a clinically compatible sequence, and evaluate the contrast it provides by isolating different contributions to diffusional kurtosis on phantoms and in-vivo.

We hypothesize that the contributions to diffusional kurtosis, from diffusion being restricted by cell geometry (microscopic kurtosis, μK) and indirectly due to intra-voxel heterogeneity, occurs to varying degrees in tissue and that the isolation of μK by the sd-PFG technique should provide unique contrast vs. traditional kurtosis imaging (DKI).¹ To first adapt sd-PFG double diffusion encoding for a clinically combatable sequence on a 4.7T Bruker scanner (Bruker Biospec, Billerica, MA), we utilize crusher pulses to eliminate phase-cycling and a single broadband encoding section connected to multiple slice-selective EPI acquisitions via a stimulated echo (figure 1).

The sd-PFG sequence consists of a double diffusion encoding² but utilizes a unique sampling scheme.³ It maintains the orientations of the first and second diffusion units fixed and orthogonal to each other while varying their amplitudes as $$$\cos(\phi)$$$ and $$$\sin(\phi)$$$. Direct contributions to different cumulants of the diffusion signal are isolated at distinct angular frequencies² and are extracted by decomposing the signal $$$E(b,\phi)$$$ as

$$\ln\left\{\frac{E(b,\phi)}{E_0}\right\}=E_{c,\widetilde{0}}(b)+E_{c,\widetilde{1}}(b)\cos(\phi)+E_{c,\widetilde{2}}(b)\cos\left(2\phi\right)+ \cdot\cdot\cdot++E_{s,\widetilde{1}}(b)\sin(\phi)+\cdot\cdot\cdot$$

We obtain $$$E_{c/s,\omega}$$$ by computing the Fourier transform of the logarithm of each voxel normalized to unit intensity at zero encoding strength (b-value=0), masking empty regions. Kurtosis describes the 4^th cumulant of the signal and is normalized by the diffusion coefficient. These quantities are isolated respectively at 4- and 0-cycles and μK is extracted by fitting

$$E_{c,\widetilde{4}}(b) = \frac{1}{4!}\left( E_{c,\widetilde{0}}(b) - 3 E_{c,\widetilde{4}}(b) \right)^2 K.$$

The distinct four cycle oscillation arising from Kurtosis can also be directly observed as a qualitative indicator of μK and a sd-PFG image is acquired with dense $$$\phi$$$ sampling to illustrate. (b-value=1500s/mm2, $$$\phi$$$ = {[0, 360), 47steps}, $$$\Delta$$$=25ms, fov = 52×52mm, matrix = 96×96)

The phantom consists of 3 water saturated polymer bead packs with bead diameters 10, 20 and 60μm (figure 2) in a water filled Epindorf tube. As the pores have a uniform size, this precludes heterogeneity contributing to kurtosis and the traditional and sd-PFG kurtosis maps should agree. DKI, Diffusion-weighted MRI, was acquired with spin echo (SE) EPI with 10 b-values (0, 250, 500, 750, 1000, 1250, 1500, 1750, 2000 and 2500s/mm²), gradient pulse duration/diffusion time (δ/Δ) = 6/20 ms, TR/TE = 2500/60 ms, number of average (NAE)= 4 along six directions, and sd-PFG images (b-values=50, 500, 1000,1500, 2500s/mm², $$$\phi$$$= {[0, 180), 23steps}, $$$\Delta$$$=25ms, fov = 52×52mm, matrix = 96×96) are acquired as control of the quantification of μK. Finally, to evaluate in-vivo contrast, the same sd-PFG and DKI parameters are used to image an adult Wistar rat brain.

The sd-PFG images of the control bead-pack phantom exhibits a characteristic 4-cycle oscillation indicating the presence of μK for the bead regions that is absent in the bulk water (figure 2). The computed μK maps yield ranges of kurtosis for each bead pack and the bulk water similar to the DKI data as shown by the box plot in figure 3. For the rat brain (figure 4), the μK maps yields similar values as DKI for the lateral striatum and is lower in the cortex and medial striatum, but requires additional measurements to confirm anatomical assignment.

From the phantom measurements, we have shown that the sd-PFG imaging technique yields reasonable μK maps by referencing it against DKI in a sample lacking heterogeneity contributions to kurtosis, while the μK maps of the rat brain yields unique contrast suggesting the potential of a new form of structural contrast. For this initial implementation, differences in artifacts and SNR to DKI primarily arise from requiring twice the encoding time and additional refocusing pulses for a comparable measurement. For the phantom (T₂ > 1s), these differences further sensitize sd-PFG imaging to errors in calibration that can be addressed: background gradients and pulse imperfections. For the in-vivo sample, the long encoding time strongly impacted the reconstruction quality given its T₂ (~60ms) and the encoding time (~$$$2\Delta$$$ = 50ms). Nonetheless, considerable improvements are still possible for in-vivo imaging as the noise was dominated by system instability. Hardware adjustments and fitting the oscillation components directly to signal instead of its logarithm should greatly improve both measurement stability and robustness of the reconstruction.Sd-PFG imaging shows promise as a unique form of diffusion contrast and as a research tool to understand diffusion mechanisms. Refinements in the technique to improve image quality should make it practical for routine in-vivo imaging, while additional animal studies can establish its biological interpretation.