Micro-structure diffusion scalar measures from reduced MRI acquisitions

Abstract

In diffusion MRI, the Ensemble Average diffusion Propagator (EAP) provides relevant micro-structural information and meaningful descriptive maps of the white matter previously obscured by traditional techniques like Diffusion Tensor Imaging (DTI). The direct estimation of the EAP, however, requires a dense sampling of the Cartesian q-space involving a huge amount of samples (diffusion gradients) for proper reconstruction. A collection of more efficient techniques have been proposed in the last decade based on parametric representations of the EAP, but they still imply acquiring a large number of diffusion gradients with different b-values (shells). Paradoxically, this has come together with an effort to find scalar measures gathering all the q-space micro-structural information probed in one single index or set of indices. Among them, the return-to-origin (RTOP), return-to-plane (RTPP), and return-to-axis (RTAP) probabilities have rapidly gained popularity. In this work, we propose the so-called "Apparent Measures Using Reduced Acquisitions" (AMURA) aimed at computing scalar indices that can mimic the sensitivity of state of the art EAP-based measures to micro-structural changes. AMURA drastically reduces both the number of samples needed and the computational complexity of the estimation of diffusion properties by assuming the diffusion anisotropy is roughly independent from the radial direction. This simplification allows us to compute closed-form expressions from single-shell information, so that AMURA remains compatible with standard acquisition protocols commonly used even in clinical practice. Additionally, the analytical form of AMURA-based measures, as opposed to the iterative, non-linear reconstruction ubiquitous to full EAP techniques, turns the newly introduced apparent RTOP, RTPP, and RTAP both robust and efficient to compute.

Alternative Microstructural Measures to Complement Diffusion Tensor Imaging in Migraine Studies with Standard MRI Acquisition

“…The calculation with AMURA saves a great amount of time assuming that the diffusion signal is independent from the radial direction. Details about the mathematical models and the comparison against the whole EAP can be found elsewhere [ 16 ]. The RTOP has been pointed out as a better biomarker for cellularity and diffusion restrictions in comparison with the MD [ 29 ], the RTPP as a marker of diffusion restriction in the axial direction [ 14 ] and the RTAP as a marker of diffusion restriction in the radial direction [ 14 ].…”

“…Despite the advantages of the EAP-based measures, the calculation of these scalars usually requires long execution and acquisition times, together with very large b-values and a large number of diffusion gradients, not always available in commercial scanners and clinical routine. To solve these problems, a new methodology called “Apparent Measures Using Reduced Acquisitions” (AMURA) has been developed [ 16 ]. This tool allows the estimation of the EAP-related scalars without the explicit calculation of the EAP, using a lower number of samples, even with a single-shell acquisition scheme, assuming that the diffusion signal is independent from the radial direction.…”

Apparent propagator anisotropy from single‐shell diffusion MRI acquisitions

“…This same pitfall has been recently addressed in Ref. [18] for the computation of other EAP imaging‐related markers (namely RTOP, RTPP, and RTAP). The so‐called “Apparent Measures Using Reduced Acquisitions” (AMURA) can mimic the sensitivity of EAP‐based measures to microstructural changes when a reduced amount of data distributed in a few shells (even one) is available.…”

“…First , we define an isotropic signal equivalent to the monoexponential model, . Pursuing an analogous formulation to that in AMURA, 18 we propose an alternative formulation, leading to a linear computation: for: The integration on the surface of the sphere from a limited number of samples is performed by fitting corresponding signals in the basis of spherical harmonics (SH), whose 0th order coefficient is defined as: Therefore, can be calculated as: Second , we calculate the norm of P ( R ) and under the considered assumption: …”

“…The present paper extends AMURA to the estimation of the PA. To that end, the same constrained model for radial diffusion used in Ref. [18] is adopted here, that is, the DiA is assumed to be independent of the actual b‐value of the measured shells. We use this simplification to derive alternative closed‐forms for the inner products that define the original PA that can be computed even from single‐shell acquisitions.…”