Compartment shape anisotropy (CSA) revealed by double pulsed field gradient MR

Abstract

The multiple scattering extensions of the pulsed field gradient (PFG) experiments can be used to characterize restriction-induced anisotropy at different length scales. In double-PFG acquisitions that involve two pairs of diffusion gradient pulses, the dependence of the MR signal attenuation on the angle between the two gradients is a signature of restriction that can be observed even at low gradient strengths. In this article, a comprehensive theoretical treatment of the double-PFG observation of restricted diffusion is presented. In the first part of the article, the problem is treated for arbitrarily shaped pores under idealized experimental conditions, comprising infinitesimally narrow gradient pulses with long separation times and long or vanishing mixing times. New insights are obtained when the treatment is applied to simple pore shapes of spheres, ellipsoids, and capped cylinders. The capped cylinder geometry is considered in the second part of the article where the solution for a double-PFG experiment with arbitrary experimental parameters is introduced. Although compartment shape anisotropy (CSA) is emphasized here, the findings of this article can be used in gleaning the volume, eccentricity, and orientation distribution function associated with ensembles of anisotropic compartments using double-PFG acquisitions with arbitrary experimental parameters.

Studying neuroanatomy using MRI

“…A recent method 125 aims to estimate "per-axon" diffusivities and anisotropy ("microscopic anisotropy"), which are inherently free from orientation homogeneity/heterogeneity assumptions and focus solely on microscopic features of interest. Variations in the gradients used for diffusion encoding, primarily involving double diffusion encoding approaches such as double-pulse diffusion sensitisation or oscillating gradients, offer alternative approaches for estimating compartment shape and size, as "diffraction" measurements of zero-crossings are robust to heterogeneities of the imaged system 124,126,127 . Such sequences are also promising to better characterise restricted diffusion and probe anisotropy within a bulk isotropic voxel (e.g.…”

Joint radius-length distribution as a measure of anisotropic pore eccentricity: An experimental and analytical framework

“…The current framework allows a direct measurement of the anisotropy variation within the sample in the form of cylinder eccentricity distribution. If we follow Özarslan's definition of the finite cylinder's eccentricity, = L/(2R), 20 then the eccentricity probability distribution, ( ) can be determined from (R, L). After defining an eccentricity matrix…”

“…1), as previously proposed. 20 The partial volumetric fraction vector, , was then obtained by implementing a non-negative least-square algorithm with an added constraint, that i i = 1 (and for the joint distribution, the additional equality constraint in Eq. (14)), using the lsqlin Matlab function.…”

“…The restricting nature of pores can result in estimates of average pore size 18 or macroscopic anisotropy. 19 Special attention was given to different types of anisotropy by Özarslan, 20 as well as experimental and analytical strategies to measure them. The compartment shape anisotropy (CSA) of a capped cylinder geometry can be measured using a variant of the s-PFG MR experiment, the double-PFG (d-PFG).…”

“…In the case of a capped cylinder geometry, both radius and length would provide an exact estimate of eccentricity. 20 In most cases, the MR signal is generated from an ensemble of polydisperse pores. Estimating the PSD with an assumed parametric distribution has a long history.…”