bioRxiv | 2019
Direction-Averaged Diffusion-Weighted MRI Signal using different Axisymmetric B-tensor Encoding Schemes “Submitted to Magnetic Resonance in Medicine”
Abstract
Purpose: It has been shown previously that for a very specific form of diffusion-encoding, i.e., the conventional Stejskal-Tanner pulsed gradient, or linear tensor encoding (LTE), and in tissue in which diffusion exhibits a stick-like geometry, the diffusion-weighted MRI signal at extremely high b-values follows a power law. Specifically, the signal decays as a 1/√b. Here, the asymptotic behaviour of the direction-averaged signal for arbitrary diffusion encoding waveforms is considered to establish whether power-law behaviours occur with other encoding wave-forms and for other (non stick-like) diffusion geometries. Theory and Methods: We consider the asymptotic form of the signal decay for high b-values for encoding geometries ranging from 2-dimensional planar tensor encoding (PTE), through isotropic or spherical tensor encoding (STE) to linear tensor encoding. When a power-law behaviour was suggested, this was tested using in silico simulations and in vivo using an ultra-strong gradient (300 mT/m) Connectom scanner. Results: Our theoretical derivation shows that a power law only exists for two scenarios: For stick-like geometries, (i) the already-discovered LTE case; and (ii) for pure planar encoding. In this latter case, to first order, the signal decays as 1/b. Our in silico and in vivo experiments confirm this 1/b relationship. Conclusion: A complete analysis of the power-law dependencies of the diffusion-weighted signal at high b-values has been performed. Only two forms of encoding result in a power-law dependency, pure linear and pure planar tensor encoding and when the diffusion geometry is 9stick-like9. The different exponents of these encodings could be used to provide independent validation of the presence of stick-like geometries in vivo.