  Biophysical models of diffusion in white matter are based on what is now
commonly referred to as the "Standard Model" (SM) of non-exchanging anisotropic
Gaussian compartments. In this work, we focus on diffusion MRI in gray matter,
which requires rethinking basic microstructure modeling blocks. In particular,
at least three contributions beyond the SM need to be considered: water
exchange across the cell membrane - between neurites and the extracellular
space; non-Gaussian diffusion along neuronal and glial processes - resulting
from structural disorder; and signal contribution from soma. For the first
contribution, we propose Neurite Exchange Imaging (NEXI) as an extension of the
SM of diffusion, which builds on the anisotropic K\"arger model of two
exchanging compartments. Using datasets acquired at multiple diffusion
weightings (b) and diffusion times (t) in the rat brain in vivo, we show that
for the investigated diffusion time window (~10-45 ms) there is minimal
diffusivity time-dependence and more pronounced kurtosis decay with time in
gray matter, which is well fit by the exchange model. Moreover, we observe
lower signal for longer diffusion times at high b. In light of these
observations, we identify exchange as the mechanism that best explains these
signal signatures in both low-b and high-b regime, and thereby propose NEXI as
the minimal model for gray matter microstructure mapping. We finally highlight
multi-b multi-t acquisitions protocols as being best suited to estimate NEXI
model parameters reliably. Using this approach, we estimate the
inter-compartment water exchange time to be 15 - 60 ms in the rat cortex and
hippocampus in vivo, which is of the same order or shorter than the diffusion
time in typical diffusion MRI acquisitions. This suggests water exchange as an
essential component for interpreting diffusion MRI measurements in gray matter.
