The principal eigenvector of the tensor, which is the primary direction of diffusion, is V1. The magnitude of that vector is L1, i.e., AD.

The normal vector of a surface is a vector perpendicular to the tangent plane to the surface at a certain point. It's a characteristic of a surface, rather than a characteristic of diffusion, so you won't find it among the outputs of the diffusion tensor fit.
From: freesurfer-bounces@nmr.mgh.harvard.edu <freesurfer-bounces@nmr.mgh.harvard.edu> on behalf of Zeng, Qi <qi.zeng@icahn.mssm.edu>
Sent: Friday, August 19, 2022 1:55 PM
To: Freesurfer support list <freesurfer@nmr.mgh.harvard.edu>
Subject: [Freesurfer] primary diffusion direction & surface normal vector
 

        External Email - Use Caution        

Hi Freesurfer experts, 

After DTI tensor fitting, usually we obtain primary, secondary, and tertiary eigenvectors (V1, V2, V3) and eigenvalues (L1, L2, L3). So what do we use to describe the primary diffusion direction, FA or AD(=L1)? I read the term "surface normal vector" from a paper and the formula r=[Vn * e1|. V presents the surface normal vector, which can be computed using the cross-product between edges. Where can I find this information? 
The paper named: "Surface-based analysis of diffusion orientation for identifying architectonic domains in the in vivo human cortex"
Thank you so much!


Best, 
Qi

--

Ph.D. candidate 
Icahn School of Medicine at Mount Sinai