  Biophysical modeling is the mediator of evaluating the cellular structure of
biological tissues using diffusion-weighted MRI. It is however the bottleneck
of microstructural MRI. Beyond the complexity of diffusion, the current
development is hindered by the fact that biophysical models heavily rely on
diffusion-specific properties of diverse cellular compartments that are still
unknown and must be measured in vivo. Obtaining such parameters by
straightforward fitting is hindered by the degenerated landscape of the
likelihood functions, in particular, the signal obtained for multiple diffusion
directions and moderate diffusion weighting strength is not enough to estimate
these parameters: different parameter constellations explain the signal equally
well. The aim of this study is to measure the central parameter of white matter
models, namely the intra-axonal water diffusivity in the normal human brain.
Proper estimation of this parameter is complicated due to (i) the presence of
both intra- and extra-axonal water compartments and (ii) the orientation
dispersion of axons. Our measurement involves an efficient suppression of
extra-axonal space and all cellular processes oriented outside a narrow cone
around the principal fiber direction. This is achieved using a planar water
mobility filter -- a strong diffusion weighting that suppresses signal from all
molecules that are mobile in the plane transverse to the fiber bundle.
Following the planar filter, the diffusivity in the remaining compartment is
measured using linear and isotropic weighting. We find the specifically
averaged intra-axonal diffusivity $D_0 = 2.25\pm 0.03{\,\rm \mu m^2/ms}$ for
the timing of the applied gradients. Extrapolation to the infinite diffusion
time gives $D_\infty \approx 2.0{\,\rm \mu m^2/ms}$. This result imposes a
strong limitation on the parameter selection for biophysical modeling of
diffusion-weighted MRI.
