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This article presents the potential problems arising from the use of "axial" and "radial" diffusivities, derived from the eigenvalues of the diffusion tensor, and their interpretation in terms of the underlying biophysical properties, such as myelin and axonal density. Simulated and in vivo data are shown. The simulations demonstrate that a change in "radial" diffusivity can cause a fictitious change in "axial" diffusivity and vice versa in voxels characterized by crossing fibers. The in vivo data compare the direction of the principle eigenvector in four different subjects, two healthy and two affected by multiple sclerosis, and show that the angle, ␣, between the principal eigenvectors of corresponding voxels of registered datasets is greater than 45°in areas of low anisotropy, severe pathology, and partial volume. Also, there are areas of white matter pathology where the "radial" diffusivity is 10% greater than that of the corresponding normal tissue and where the direction of the principal eigenvector is altered by more than 45°compared to the healthy case. This should strongly discourage researchers from interpreting changes of the "axial" and "radial" diffusivities on the basis of the underlying tissue structure, unless accompanied by a thorough investigation of their mathematical and geometrical properties in each dataset studied. Since the early publications by Basser et al. (1,2), diffusion tensor imaging (DTI) has evolved and expanded noticeably its application to clinical studies moving toward modeling the tissue microstructure (3-5) and reconstructing white matter tracts (6 -8).While the elements of the tensor matrix are different for each system of coordinates, the DT can be diagonalized to extract its three eigenvalues, 1 , 2 , and 3 , which can be combined to define quantitative parameters such as mean diffusivity (MD) and fractional anisotropy (FA), which are rotationally invariant and independent of eigenvalue sorting.Since Song et al. (9) published their article where they look at the "axial diffusivity," i.e., the principal eigenvalue of the DT, and at the "radial diffusivity," i.e., the average of the second and third eigenvalues of the DT, in an animal model, and where they link the radial diffusivity with myelin content, studies reporting comparisons of these indices are becoming very frequent (e.g., 10 -14). It is important to underline the fact that the direction of the principal eigenvector with eigenvalue 1 , i.e., the direction of the "axial" diffusivity, is not always preserved in pathological tissue and is not always aligned with the underlying expected tissue architecture (15).It has been thoroughly shown (e.g., 28) that the direction and the magnitude of the eigenvalues and eigenvectors are physical measures that are affected by the noise, the shape of the calculated diffusion ellipsoid, and pathology. With this study we do not claim to propose a new method for interpreting DTI data or for solving the problem of the sorting bias already extensively investigated (16 -18). Here we wo...

Purpose: To establish a general methodology for quantifying streamline-based diffusion fiber tracking methods in terms of probability of connection between points and/or regions. Materials and Methods:The commonly used streamline approach is adapted to exploit the uncertainty in the orientation of the principal direction of diffusion defined for each image voxel. Running the streamline process repeatedly using Monte Carlo methods to exploit this inherent uncertainty generates maps of connection probability. Uncertainty is defined by interpreting the shape of the diffusion orientation profile provided by the diffusion tensor in terms of the underlying microstructure.Results: Two candidates for describing the uncertainty in the diffusion tensor are proposed and maps of probability of connection to chosen start points or regions are generated in a number of major tracts. Conclusion:The methods presented provide a generic framework for utilizing streamline methods to generate probabilistic maps of connectivity.

Magnetic resonance imaging (MRI) is being used to probe the central nervous system (CNS) of patients with multiple sclerosis (MS), a chronic demyelinating disease. Conventional T2-weighted MRI (cMRI) largely fails to predict the degree of patients' disability. This shortcoming may be due to poor specificity of cMRI for clinically relevant pathology. Diffusion tensor imaging (DTI) has shown promise to be more specific for MS pathology. In this study we investigated the association between histological indices of myelin content, axonal count and gliosis, and two measures of DTI (mean diffusivity [MD] and fractional anisotropy [FA]), in unfixed post mortem MS brain using a 1.5-T MR system. Both MD and FA were significantly lower in post mortem MS brain compared to published data acquired in vivo. However, the differences of MD and FA described in vivo between white matter lesions (WMLs) and normal-appearing white matter (NAWM) were retained in this study of post mortem brain: average MD in WMLs was 0.35 × 10− 3 mm2/s (SD, 0.09) versus 0.22 (0.04) in NAWM; FA was 0.22 (0.06) in WMLs versus 0.38 (0.13) in NAWM. Correlations were detected between myelin content (Trmyelin) and (i) FA (r = − 0.79, p < 0.001), (ii) MD (r = 0.68, p < 0.001), and (iii) axonal count (r = − 0.81, p < 0.001). Multiple regression suggested that these correlations largely explain the apparent association of axonal count with (i) FA (r = 0.70, p < 0.001) and (ii) MD (r = − 0.66, p < 0.001). In conclusion, this study suggests that FA and MD are affected by myelin content and – to a lesser degree – axonal count in post mortem MS brain.