A new volume selective sequence for single-shot diffusion-weighting by the trace of the diffusion tensor

Introduction Diffusion-weighted (DW) spectroscopy is a unique tool for exploring the intracellular micro-environment in vivo [1]. In living systems, diffusion is generally anisotropic, since biological membranes may exhibit some anisotropic orientation, and signal attenuation generally depends on the orientation of the gradients relative to the cellular orientation, diffusion being characterized by the diffusion tensor D. Measuring the trace of the diffusion tensor Dav=1/3×(Dxx+Dyy+Dzz) may be particularly interesting. Indeed, since the trace of a tensor is invariant under rotation of the reference frame, Dav is independent of cellular orientation within the gradient frame. This might allow the characterization of intrinsic diffusion properties of the intracellular microenvironment without bias induced by the cellular orientation. In this work, a volume selective DW-sequence allowing single-shot measurement of Dav is proposed. Cross-terms between diffusion gradients and other gradients (including background gradients) are all cancelled out. In addition, an adiabatic version (similar to the LASER sequence [2], with additional diffusion gradients) is derived, which provides partial immunity to cross-terms. Proof of concept is performed on anisotropic tissues (ex vivo chicken muscle), by varying tissue orientation and intra-voxel shim. Theory Cancellation of cross-terms: Let’s consider the sequence in Fig. 1A, consisting in a non-selective 90° excitation followed by two identical slice selection blocks, each block consisting in a 180° pulse with a slice selection gradient Gslice, surrounded by spoilers Gspoil. Refocusing is assumed to occur at the center of the pulse. Diffusion-weighting is achieved using two gradient lobes of duration δ and amplitude Gdiff with opposite polarities, located outside the two slice selection blocks and separated by the delay Δ. A B0 inhomogeneity gradient G0 is also considered. As shown graphically in Fig. 1, the particular symmetry of the sequence results in a null integral for kdiffkspoil, kdiffkslice and kdiffk0, i.e. cross-terms between diffusion gradients and other gradients cancel out: signal is only weighted by the diagonal term of D in the direction of Gdiff. Single-shot Dav measurement: Following the above analysis performed for a single diffusion block, it is straightforward to derive a volume selective DW-sequence made of one non-selective 90° pulse followed by three successive orthogonal blocks built by circular permutation of the gradient axes, such as shown on Fig. 2. Because the phase induced by diffusion gradients is refocused (kdiff=0) at the end of each block, these blocks are temporally isolated from each other and diffusion-weighting arising from the three blocks simply adds up: