ENCODING OF ANISOTROPIC DIFFUSION WITH TETRAHEDRAL GRADIENTS - A GENERAL MATHEMATICAL DIFFUSION FORMALISM AND EXPERIMENTAL RESULTS

A diffusion imaging method with a tetrahedral sampling pattern has bee n developed for high-sensitivity diffusion analysis. The tetrahedral g radient pattern consists of four different combinations of x, y, and z gradients applied simultaneously at full strength to uniformly measur e diffusion in four different directions, Signal-to-noise can be incre ased by up to a factor of about three using this approach, compared wi th diffusion measurements made using separately applied x, y, and z gr adients, A mathematical formalism is presented describing six fundamen tal parameters: the directionally averaged diffusion coefficient (D) o ver bar and diffusion element anisotropies eta and epsilon which are r otationally invariant, and diffusion ellipsoid orientation angles thet a, phi, and psi which are rotationally variant, These six parameters c ontain all the information in the symmetric diffusion tensor D. Princi pal diffusion coefficients, reduced anisotropies, and other rotational invariants are further defined, It is shown that measurement of off-d iagonal tensor elements is essential to assess anisotropy and orientat ion, and that the only parameter which can be measured with the orthog onal method is (D) over bar. In cases of axial diffusion symmetry (e.g ., fibers), the four tetrahedral diffusion measurements efficiently en able determination of (D) over bar, eta, theta, and phi which contain all the diffusion information, From these four parameters, the diffusi on parallel and perpendicular to the symmetry axis (D-parallel to and D-perpendicular to) and the axial anisotropy A can be determined, In m ore general cases, the six fundamental parameters can be determined wi th two additional diffusion measurements. Tetrahedral diffusion sequen ces were implemented on a clinical MR system, A muscle phantom demonst rates orientation independence of (D) over bar, D-parallel to, D-perpe ndicular to, and A for large changes in orientation angles, Sample bac kground gradients and diffusion gradient imbalances were directly meas ured and found to be insignificant in most cases.