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

Abstract

In this work, we present an experimental design and analytical framework to measure the nonparametric joint radius-length (R-L) distribution of an ensemble of parallel, finite cylindrical pores, and more generally, the eccentricity distribution of anisotropic pores. Employing a novel 3D double pulsed-field gradient acquisition scheme, we first obtain both the marginal radius and length distributions of a population of cylindrical pores and then use these to constrain and stabilize the estimate of the joint radius-length distribution. Using the marginal distributions as constraints allows the joint R-L distribution to be reconstructed from an underdetermined system (i.e., more variables than equations), which requires a relatively small and feasible number of MR acquisitions. Three simulated representative joint R-L distribution phantoms corrupted by different noise levels were reconstructed to demonstrate the process, using this new framework. As expected, the broader the peaks in the joint distribution, the less stable and more sensitive to noise the estimation of the marginal distributions. Nevertheless, the reconstruction of the joint distribution is remarkably robust to increases in noise level; we attribute this characteristic to the use of the marginal distributions as constraints. Axons are known to exhibit local compartment eccentricity variations upon injury; the extent of the variations depends on the severity of the injury. Nonparametric estimation of the eccentricity distribution of injured axonal tissue is of particular interest since generally one cannot assume a parametric distribution a priori. Reconstructing the eccentricity distribution may provide vital information about changes resulting from injury or that occurred during development.

Magnetic resonance microdynamic imaging reveals distinct tissue microenvironments

“…Reexamination of the relationships between the 1D and higher-dimension distributions (Benjamini and Basser, 2014) laid the groundwork for addressing the primary issue precluding multidimensional REDCO biological and clinical applications in conjunction with imaging. Briefly, one can regard the 2D REDCO spectrum as a joint probability distribution of two variables, each with its own 1D marginal distribution of the 2D spectrum.…”

White matter microstructure from nonparametric axon diameter distribution mapping

“…We used N =160 such that the number of observations (i.e., Ωs) would be roughly 10 times the number of dependent parameters (i.e., diameters) in accordance with previous publications (Katz and Nevo, 2014; Benjamini and Basser, 2014). The mixing time, τ m , was kept at zero.…”

NMR signal for particles diffusing under potentials: From path integrals and numerical methods to a model of diffusion anisotropy

“…Indeed, several different pulse sequences have been studied in recent years employing pulsed [8,[39][40][41] and continuous [42][43][44] waveforms. Especially in the context of modeling local diffusion anisotropy, one is faced with the choice between the Gaussian diffusion tensor model [37,45], and restricted capped cylinder model [25,46]. Although, the restricted character of the model is desirable, the capped cylinder model had two limitations, which may have prompted some studies to adopt the diffusion tensor model instead: (i) it has only two size parameters, so is more limited than the diffusion tensor model, (ii) the solutions are rather complicated.…”