Characterization of anisotropy via diffusion MRI reveals fiber crossings in a substantial portion of voxels within the white-matter (WM) regions of the human brain. A considerable number of such voxels could exhibit asymmetric features such as bends and junctions. However, widely employed reconstruction methods yield symmetric Orientation Distribution Functions (ODFs) even when the underlying geometry is asymmetric. In this paper, we employ inter-voxel directional filtering approaches through a cone model to reveal more information regarding the cytoarchitectural organization within the voxel. The cone model facilitates a sharpening of the ODFs in some directions while suppressing peaks in other directions, thus yielding an Asymmetric ODF (AODF) field. We also show that a scalar measure of AODF asymmetry can be employed to obtain new contrast within the human brain. The feasibility of the technique is demonstrated on in vivo data obtained from the MGH-USC Human Connectome Project (HCP) and Parkinson's Progression Markers Initiative (PPMI) Project database. Characterizing asymmetry in neural tissue cytoarchitecture could be important for localizing and quantitatively assessing specific neuronal pathways.