A correlative measure for processing multiangle diffusion‐weighted images

Abstract

A simple metric for the shared diffusion anisotropy between two voxels is proposed. The metric has large values when the diffusion is highly anisotropic in both voxels and oriented in the same direction. This metric can be used in several ways, three of which are illustrated in this article. First, the metric can be used to rapidly calculate a fractional anisotropy measure using an arbitrary number of measured diffusion values. Second, a simple way to exploit the metric for filtering DWI data with neighboring voxels with similar diffusion characteristics is shown. Third, the metric can be used to create color images that reflect tract orientation. The measurements from multiangle diffusion-weighted imaging (DWI) studies in white matter are rich with information and a great deal of research is being performed in extracting relevant information about diffusion anisotropy and direction for assessing white matter health and morphology (1-11).Many of these methods are based on a model of diffusion as a second-rank tensor. However, the tensor model is not always a valid approach, particularly for voxels containing multiple tracts (12). This work introduces a simple metric that does not rely on tensor assumptions and can be used to replace many of the tensor-based analysis methods. This metric can be used in various ways, three of which are given here. First, the characteristics of the metric are investigated analytically. Next, applications of this metric in calculating fractional anisotropy, filtering DWI data, and displaying tract orientation via color displays are shown. Because it does not involve reducing the data to a diffusion tensor, the information (e.g., degree of anisotropy) present in data for nontensor cases (such as overlying tracts in a single voxel) may be better preserved using the proposed metric than what is obtained in a tensor-based metric. Of course, this method cannot extract information which is not present in the source diffusion measurements.

Computation of the fractional anisotropy and mean diffusivity maps without tensor decoding and diagonalization: Theoretical analysis and validation

“…Unlike the analysis presented in the current study, these methods all involve intensive offline processing. More recent studies (36, 37) (which were published while this manuscript was under review) also reported that the icosahedral encoding scheme can provide anisotropy estimates using the DW data. The current work presents a comprehensive theoretical and experimental analysis, and a detailed comparison between the DW‐ and tensor‐based approaches.…”

Contrast-to-noise ratios for indices of anisotropy obtained from diffusion MRI: A study with standard clinical b-values at 3T

“…In addition, it has been previously shown that IVOH can be detected already at b-values as low as 1000 s/mm 2 (Tuch et al, 2002). The combination of the 63 directions used in the present study and a b-value of 1000 s/mm 2 has Table 1 Summary of the indices of anisotropy used in this study: fractional anisotropy (Basser and Pierpaoli, 1996), geodesic anisotropy (Batchelor et al, 2005), GAA (Pipe and Farthing, 2003), cumulative residual entropy (Chen et al, 2005), generalised anisotropy and scaled entropy (Ozarslan et al, 2005).…”

“…A model free approach to characterization of anisotropy was proposed by Pipe and Farthing (2003). Their definition is based on a simple correlative metric, G(A,B), for the anisotropy shared between voxels A and B (see the supplementary material for more detail).The proposed anisotropy index was called GAA because it is calculated from the correlative metric between a voxel and itself, G(A,A).…”

Investigating the structure-function relationship of the corticomotor system early after stroke using machine learning

“…An overview of the diffusion-based MRI metrics is provided in Supplementary Table 2 . Diffusion-weighted images were processed to obtain maps of fractional anisotropy, axial diffusivity, mean diffusivity, radial diffusivity, normalised eigenvalue ratio ( Armitage and Bastin 2000 ), volume fraction ( Alexander et al 2000 ), scaled relative anisotropy ( Conturo et al, 1996 , Kingsley and Monahan, 2005 ), ultimate anisotropy scaled to the diffusion ellipsoid volume, surface area, or both (UA vol , UA surf , and UA vol,surf ) ( Ulug and van Zijl, 1999 , Kingsley and Monahan, 2005 ), ellipsoidal area ratio ( Xu et al, 2009 , Kang et al, 2010 ), gamma variate anisotropy ( Armitage and Bastin 2000 ), G AA ( Pipe and Farthing, 2003 , Correia et al, 2011 ), geodesic anisotropy ( Batchelor et al, 2005 , Correia et al, 2011 ), and local diffusion homogeneity ( Gong and Zang, 2013 ). The diffusion metric maps were transformed to patient T1 space using a 6 degrees of freedom affine transformation ( Jenkinson et al 2002 ).…”