Abstract
Acquisition, analysis, and visualization of diffusion tensor magnetic resonance imaging (DT-MRI) is still an evolving technology. This article reviews the fundamentals of the data acquisition process and the pipeline leading to visual results that are interpretable by physicians in their clinical practice. The limitations of common approaches for visualizing the retrieved data are discussed and a new statistical method is presented to assess the reliability of the acquired tensor field. A novel visualization method is proposed which is discussed in light of neurophysiological considerations of the perception of colored patterns. It is argued that this method is more accurate for medical data while providing a nearly optimal visual stimulus. The method is evaluated on a patient study with a brain tumor.
Notes
1Such regions are sometimes called “degenerate features of a tensor field.” However, care needs to be taken about the term “degenerate” here: “degenerate eigenvalues” denote multiple eigenvalues, which may or may not be due to multiple eigenvectors. On the other hand, a “degenerate matrix” refers to a singular, that is, non-invertible matrix which does not have full rank. This term is more common for bilinear forms or metric tensor fields. Such a “degenerate tensor” (corresponding to the cs = 0 line in the barycentric shape factor diagram) does not imply “degenerate eigenvalues (which are the cp = 0 and cl = 0 edges of the shape factor triangle), nor vice versa. As can be easily seen at cl = 0 and cp = 0, an invertible (non-degenerate) matrix may possess two different eigenvectors with same (degenerate) eigenvalues (spanning an full eigen space), and a non-invertible (degenerate) matrix at cs = 0 may have three unique (non-degenerate) eigenvalues. Only at the corners with cl = 0, cs = 0 and cp = 0, cs = 0 both flavors of “;degeneracy”; coincide.
2Including the similarly named method of “tensor splatting” (Bhalerao & Westin, Citation2003).
3Diagonal 1700 is approximately pixel, makes 100 pixels per inch on a 17″ screen, that is, 100 dpi. Seen from a distance of 57″, one degree is exactly one inch, as one radiant is 57°. These are 100 pixels. From a third the distance, ca. 20″, one degree covers 30 pixels and a tenth corresponding to 10 cpd results in three pixels.