White matter microstructure from nonparametric axon diameter distribution mapping

Abstract

We report the development of a double diffusion encoding (DDE) MRI method to estimate and map the axon diameter distribution (ADD) within an imaging volume. A variety of biological processes, ranging from development to disease and trauma, may lead to changes in the ADD in the central and peripheral nervous systems. Unlike previously proposed methods, this ADD experimental design and estimation framework employs a more general, nonparametric approach, without a priori assumptions about the underlying form of the ADD, making it suitable to analyze abnormal tissue. In the current study, this framework was used on an ex vivo ferret spinal cord, while emphasizing the way in which the ADD can be weighted by either the number or the volume of the axons. The different weightings, which result in different spatial contrasts, were considered throughout this work. DDE data were analyzed to derive spatially resolved maps of average axon diameter, ADD variance, and extra-axonal volume fraction, along with a novel sub-micron restricted structures map. The morphological information contained in these maps was then used to segment white matter into distinct domains by using a proposed k-means clustering algorithm with spatial contiguity and left–right symmetry constraints, resulting in identifiable white matter tracks. The method was validated by comparing histological measures to the estimated ADDs using a quantitative similarity metric, resulting in good agreement. With further acquisition acceleration and experimental parameters adjustments, this ADD estimation framework could be first used preclinically, and eventually clinically, enabling a wide range of neuroimaging applications for improved understanding of neurodegenerative pathologies and assessing microstructural changes resulting from trauma.

Magnetic resonance microdynamic imaging reveals distinct tissue microenvironments

“…These techniques are sensitive to features of the net displacement distribution of water molecules within the sample (Stejskal and Tanner, 1965), providing powerful tools to explore microscopic domains quantitatively (Price, 2009). In conjunction with tissue models, dMRI experiments can be used to infer macroscopic (Basser et al, 1994, 2000) and microscopic (Burcaw et al, 2015; Szczepankiewicz et al, 2015; Benjamini et al, 2016) structural features, on the basis of the type and scale of physical barriers that are present in heterogeneous biological tissue.…”

ActiveAxADD: Toward non‐parametric and orientationally invariant axon diameter distribution mapping using PGSE

“…In the field of axon diameter mapping, axons are assumed to be impermeable cylinders . The WM dMRI signal S is expressed as a weighted contribution of IA and EA signalswhere S 0 is the MRI signal without diffusion weighting, f IA is the IA volume fraction (IAVF), S IA is the restricted IA signal, S EA is the hindered EA signal, and ε is the acquisition noise.…”

“…Hollingsworth and Johns first combined it with Laplacian regularization to estimate distribution of diameters of oil droplets in water. Benjamini et al showed it could be used to provide non‐parametric ADD estimates, using double diffusion encoding (DDE) instead of PGSE to increase stability. The acquisition had to be performed perpendicularly to the axons and is considered to be orientation‐dependent .…”

“…Benjamini et al showed it could be used to provide non‐parametric ADD estimates, using double diffusion encoding (DDE) instead of PGSE to increase stability. The acquisition had to be performed perpendicularly to the axons and is considered to be orientation‐dependent . The aim of this work is to show that the orientationally invariant features of ActiveAx AMICO can be combined with Laplacian regularization into a new formulation (ActiveAx ADD ) to reconstruct orientationally invariant and non‐parametric estimates of the whole ADD using a PGSE protocol.…”

Pore size estimation from double diffusion encoding

“…Axonal diameter is also closely linked with aging [5] and certain neuropathologies [6,7]. Non-invasive estimation of the axonal diameter distribution in the human brain is nonetheless limited to specific anatomical regions, due to technical difficulties like orientation dispersion and limited gradient strength [8,9] as well as acquisition time [10]. In this context, we explore, via numerical simulations, the possibility to use double diffusion encoding (DDE) [11] to attain clinically feasible pore size estimation (see Figure 1 for a schematic representation of the effective gradient waveform of DDE).…”