  Designing novel diffusion-weighted pulse sequences to probe tissue
microstructure beyond the conventional Stejskal-Tanner family is currently of
broad interest. One such technique, multidimensional diffusion MRI, has been
recently proposed to afford model-free decomposition of diffusion signal
kurtosis into terms originating from either ensemble variance of isotropic
diffusivity or microscopic diffusion anisotropy. This ability rests on the
assumption that diffusion can be described as a sum of multiple Gaussian
compartments, but this is often not strictly fulfilled. The effects of
nongaussian diffusion on single shot isotropic diffusion sequences were first
considered in detail by de Swiet and Mitra in 1996. They showed theoretically
that anisotropic compartments lead to anisotropic time dependence of the
diffusion tensors, which causes the measured isotropic diffusivity to depend on
gradient frame orientation. Here we show how such deviations from the multiple
Gaussian compartments assumption conflates orientation dispersion with ensemble
variance in isotropic diffusivity. Second, we consider additional contributions
to the apparent variance in isotropic diffusivity arising due to
intracompartmental kurtosis. These will likewise depend on gradient frame
orientation. We illustrate the potential importance of these confounds with
analytical expressions, numerical simulations in simple model geometries, and
microimaging experiments in fixed spinal cord using isotropic diffusion
encoding waveforms with 7.5 ms duration and 3000 mT/m maximum amplitude.
