Putting aside diffusion time dependency for a moment, isotropic diffusion encoding is specific to the average and spread of isotropic diffusivities across all sub-compartments of a given voxel content. It is therefore sensitive to the mean diffusivity of the voxel content (at low b-value) and to the variance of isotropic diffusivities (at higher b-values). While the former informs on average cell density, the latter reports on the variance of cell densities.
Let us now discuss diffusion-time dependent effects. We know that cell boundaries give rise to restricted diffusion, which could be probed over an appropriate range of diffusion times. At too short diffusion times, one can only measure the bulk diffusivity of the diffusion environment. At too long diffusion times, one probe the stationary Gaussian diffusion regime. While time-dependent effects have been detected in, e.g., white matter, spinal cord and prostate, these effects appear to be quite minimal in the brain when using sequences that are not specifically designed to probe a wide range of diffusion times.
That being said, let us come back to spherical encoding and discuss what could happen in a time-dependent case. A spherically encoded gradient waveform is typically made up of three orthogonal orientation-specific gradient waveforms (along general x, y and z axes). While the combination of these gradient waveforms amounts to a spherical b-tensor in principle, there is no obligation that the waveforms share identical frequency contents (if you were to Fourier transform them independently, obtaining their respective encoding spectra). This means that these waveforms may probe different diffusion times along the x, y and z axes. If these diffusion times venture in the range associated with the restricted diffusion in a given tissue (because of cell sizes for instance), then isotropic encoding becomes... anisotropic. Another problem can arise when two different gradient waveforms (e.g., one linear and one spherical) do not share similar frequency contents. Indeed, this can imply that both waveforms probe, for instance, different mean diffusivities at low b-value, which would create inconsistencies in parameter estimations (typically a higher microscopic anisotropy). Preventing such issue led to the concept of spectral tuning of the gradient waveform. Fortunately, this deepened understanding of arbitrary gradient waveforms is giving birth to quite insightful work linked to biological structure sizes, such as this one related to axon diameter.

Putting aside diffusion time dependency for a moment, isotropic diffusion encoding is specific to the average and spread of

across all sub-compartments of a given voxel content. It is therefore sensitive to the mean diffusivity of the voxel content (at low b-value) and to the variance of isotropic diffusivities (at higher b-values). While the former informs on average cell density, the latter reports on the variance of cell densities. Let us now discuss diffusion-time dependent effects. We know that cell boundaries give rise to restricted diffusion, which could be probed over an appropriate range of diffusion times. At too short diffusion times, one can only measure the bulk diffusivity of the diffusion environment. At too long diffusion times, one probe the stationary Gaussian diffusion regime. While time-dependent effects have been detected in,isotropic diffusivitiese.g.,white matter,spinal cordandprostate, these effects appear to bequite minimal in the brainwhen using sequences that are not specifically designed to probe a wide range of diffusion times. That being said, let us come back to spherical encoding and discuss what could happen in a time-dependent case. A spherically encoded gradient waveform is typically made up of three orthogonal orientation-specific gradient waveforms (along generalx,yandzaxes). While the combination of these gradient waveforms amounts to a spherical b-tensor in principle, there is no obligation that the waveforms share identical frequency contents (if you were to Fourier transform them independently, obtaining their respectiveencoding spectra). This means that these waveforms may probe different diffusion times along thex,yandzaxes. If these diffusion times venture in the range associated with the restricted diffusion in a given tissue (because of cell sizes for instance), then isotropic encoding becomes... anisotropic. Another problem can arise when two different gradient waveforms (e.g., one linear and one spherical) do not share similar frequency contents. Indeed, this can imply that both waveforms probe, for instance, different mean diffusivities at low b-value, which would create inconsistencies in parameter estimations (typically a higher microscopic anisotropy). Preventing such issue led to the concept ofspectral tuningof the gradient waveform. Fortunately, this deepened understanding of arbitrary gradient waveforms is giving birth to quite insightful work linked to biological structure sizes, such asthis one related to axon diameter.