  Measuring fibre dispersion in white matter with diffusion magnetic resonance
imaging (MRI) is limited by an inherent degeneracy between fibre dispersion and
microscopic diffusion anisotropy (i.e., the diffusion anisotropy expected for a
single fibre orientation). This means that estimates of fibre dispersion rely
on strong assumptions, such as constant microscopic anisotropy throughout the
white matter or specific biophysical models. Here we present a simple approach
for resolving this degeneracy using measurements that combine linear
(conventional) and spherical tensor diffusion encoding.
  To test the accuracy of the fibre dispersion when our microstructural model
is only an approximation of the true tissue structure, we simulate
multi-compartment data and fit this with a single-compartment model. For such
overly simplistic tissue assumptions, we show that the bias in fibre dispersion
is greatly reduced ($\sim$5x) for single-shell linear and spherical tensor
encoding data compared with single-shell or multi-shell conventional data. In
in-vivo data we find a consistent estimate of fibre dispersion as we reduce the
b-value from 3 to 1.5 ms/$\mu$m$^2$, increase the repetition time, increase the
echo time, or increase the diffusion time. We conclude that the addition of
spherical tensor encoded data to conventional linear tensor encoding data
greatly reduces the sensitivity of the estimated fibre dispersion to the model
assumptions of the tissue microstructure.
