Direction-averaged diffusion-weighted MRI signal using different axisymmetric B-tensor encoding schemes

Abstract

Purpose: It has been shown, theoretically and in vivo, that using the Stejskal-Tanner pulsed-gradient, or linear tensor encoding (LTE), and in tissue exhibiting a "stick-like" diffusion geometry, the direction-averaged diffusion-weighted MRI signal at high b-values ( $7000<b<10000s/{\mathrm{mm}}^2$ ) follows a power-law, decaying as $1/\sqrt{b}$ . It has also been shown, theoretically, that for planar tensor encoding (PTE), the direction-averaged diffusion-weighted MRI signal decays as 1/b. We aimed to confirm this theoretical prediction in vivo. We then considered the direction-averaged signal for arbitrary b-tensor shapes and different tissue substrates to look for other conditions under which a power-law exists.

Methods: We considered the signal decay for high b-values for encoding geometries ranging from 2-dimensional PTE, through isotropic or spherical tensor encoding to LTE. When a power-law behavior was suggested, this was tested using in silico simulations and, when appropriate, in vivo using ultra-strong (300 mT/m) gradients.

Results: Our in vivo results confirmed the predicted 1/b power law for PTE. Moreover, our analysis showed that using an axisymmetric b-tensor a power-law only exists under very specific conditions: (a) "stick-like" tissue geometry and purely LTE or purely PTE waveforms; and (b) "pancake-like" tissue geometry and a purely LTE waveform.

Conclusions: A complete analysis of the power-law dependencies of the diffusion-weighted signal at high b-values has been performed. Only three specific forms of encoding result in a power-law dependency, pure linear and pure PTE when the tissue geometry is "stick-like" and pure LTE when the tissue geometry is "pancake-like". The different exponents of these encodings could be used to provide independent validation of the presence of different tissue geometries in vivo.

Keywords: B-tensor encoding; diffusion-weighted MRI; direction-averaged diffusion signal; high b-value; power-law.