Revisiting the interpretation of axon diameter mapping using higher-order signal representations

Diffusion-weighted Magnetic Resonance Imaging (dMRI) has emerged as an imaging modality of interest to measure axon diameters noninvasively. The previously observed <i>b</i> ^-½ power law scaling suggests that high <i>b</i>-value dMRI signals originate from water confined within "stick" geometries, representing impermeable cellular processes. A key assumption is that any deviation from this power law at high <i>b-</i>values-modeled as a non-zero perpendicular intracellular diffusivity-must be specifically axonal in origin. Recent developments in axon diameter mapping build upon such assumptions, thereby neglecting the possibility that other cellular structures, such as glial processes, may also exhibit similar "stick"-like characteristics. This explorative study investigates the validity of axon diameter mapping by evaluating its robustness to experimental variation. In particular, it compares the mapping of the axon diameter using the zeroth- (spherical mean) and second-order (spherical variance) rotationally invariant spherical harmonic (RISH) features. As a condition for validity, axon diameter should be robust to such variations in RISH order. A novel log-linear estimator with a closed-form solution for computationally efficient axon diameter mapping is introduced, which can be applied with a minimum of two high <i>b-</i>value measurements. Using this estimator, it was observed that axon diameter measurements vary with RISH order, suggesting that high <i>b</i>-value signals from non-axonal cellular sources may confound axon diameter mapping. Monte Carlo simulations show that such dependence on RISH order could be explained by the presence of glial processes. Overall, these results highlight the need for caution in the interpretation of dMRI-derived "<i>axon</i>" diameter.