from dti (lower fa and md) differentiate healthy adults from those with carpal tunnel syndrome research early in the development of dti based tractography, a number of researchers pointed out a flaw in the diffusion tensor model. the tensor analysis assumes that there is a single ellipsoid in each imaging voxel— as if all of the axons traveling through a voxel traveled in exactly the same direction. this is often true, but it can be estimated that in more than 30% of the voxels in a standard resolution brain image, there are at least two different neural tracts traveling in different directions that pass through each other. in the classic diffusion ellipsoid tensor model, the information from the crossing tract just appears as noise or unexplained decreased anisotropy in a given voxel. david tuch was among the first to describe a solution to this problem. the idea is best understood by conceptually placing a kind of geodesic dome around each image voxel. this icosahedron provides a mathematical basis for passing a large number of evenly spaced gradient trajectories through the voxel—each coinciding with one of the apices of the icosahedron. basically, we are now going to look into the voxel from a large number of different directions (typically 40 or more). we use "n-tuple" tessellations to add more evenly spaced apices to the original icosahedron (20 faces)—an idea that also had its precedents in paleomagnetism research several decades earlier. we just want to know which direction lines turn up the maximum anisotropic diffusion measures. if there is a single tract, there will be just two maxima pointing in opposite directions. if two tracts cross in the voxel, there will be two pairs of maxima, and so on. we can still use tensor math to use the maxima to select groups of gradients to package into several different tensor ellipsoids in the same voxel, or use more complex higher rank tensors analyses, or we can do a true "model free" analysis that just picks the maxima and go on about doing the tractography. the q-ball method of tractography is an implementation in which david tuch provides a mathematical alternative to the tensor model. instead of forcing the diffusion anisotropy data into a group of tensors, the mathematics used deploys both probability distributions and a classic bit of geometric tomography and vector math developed nearly 100 years ago—the funk radon transform. summary for dti, it is generally possible to use linear algebra, matrix mathematics and vector mathematics to process the analysis of the tensor data. in some cases, the full set of tensor properties is of interest, but for tractography it is usually necessary to know only the magnitude and orientation of the primary axis or vector. this primary axis—the one with the greatest length—is the largest eigenvalue and its orientation is encoded in its matched eigenvector. only one axis is needed as it is assumed the largest eigenvalue is aligned with the main axon direction to accomplish tractography.