Figure 1.

The Simulated Cube of a Diffusion Tensor Field FA values on the section triangle, ABC, form a representative snapshot of all possible FA values in this cube. This triangle thus provides a context in which we can compare the values of FA with values of EAR for the tensors within the cube. X corresponds to eigenvalue λ₁ (L1), Y to λ₂ (L2), and Z to λ₃ (L3). The tetrahedron OADF occupies 1/6 of the cube, the region in which λ₁ ≥ λ₂ ≥ λ₃. The FA value for the tensor at P(a,b,c) is the trigonometric Sin operator (multiplied by a constant) of the angle between lines PO and OF. Thus, the tensors at P and Q have identical FA values, as do the tensors at P′ and Q′. Indeed, all tensors (except the tensor on origin O) that lie on a single line passing through the origin O will have identical FA values.