SPHERIOUSLY? The challenges of estimating spherical pore size non-invasively in the human brain from diffusion MRI

Abstract

The Soma and Neurite Density Imaging (SANDI) three-compartment model was recently proposed to disentangle cylindrical and spherical geometries, attributed to neurite and soma compartments, respectively, in brain tissue. The approach could also enable estimation of microstructure parameters such as the apparent size (radius) of the soma. There are some recent advances in diffusion-weighted MRI signal encoding and analysis (including the use of multiple so-called b-tensor encodings and analysing the signal in the frequency-domain) that have not yet been applied in the context of SANDI. In this work, using: (i) ultra-strong gradients; (ii) a combination of linear, planar, and spherical b-tensor encodings; and (iii) analysing the signal in the frequency domain, three main challenges to robust estimation of soma size were identified: First, the Rician noise floor in magnitude-reconstructed data biases estimates of soma properties in a non-uniform fashion. It may cause overestimation or underestimation of the soma size and density. This can be partly ameliorated by accounting for the noise floor in the estimation routine. Second, even when using the strongest diffusion-encoding gradient strengths available for human MRI, there is an empirical lower bound on the spherical signal fraction and pore-size that can be detected and estimated robustly. For the experimental setup used here, the lower bound on the signal fraction was approximately 10%. We employed two different ways of establishing the lower bound for spherical radius estimates in white matter. The first, examining power-law relationships between the DW-signal and diffusion weighting in empirical data, yielded a lower bound of 7 m, while the second, pure Monte Carlo simulations, yielded a lower limit of 3 m and in this low radii domain, there is little differentiation in signal attenuation. Third, if there is sensitivity to the transverse intra-cellular diffusivity in cylindrical structures, e.g., axons and cellular projections, then trying to disentangle two diffusion-time-dependencies using one experimental parameter (i.e., change in frequency-content of the encoding waveform) makes spherical pore-size estimates particularly challenging. We conclude that due to the aforementioned challenges spherical pore size estimates may be biased when the corresponding signal fraction is low, which must be considered when using them as biomarkers in clinical/research studies.