Insights and improvements in correspondence between axonal volume fraction measured with diffusion-weighted MRI and...

Biophysical diffusion-weighted imaging (DWI) models are increasingly used in neuroscience to estimate the axonal water fraction ( $f_{\text{AW}}$ ), which in turn is key for noninvasive estimation of the axonal volume fraction ( $f_A$ ). These models require thorough validation by comparison with a reference method, for example, electron microscopy (EM). While EM studies often neglect the unmyelinated axons and solely report the fraction of myelinated axons, in DWI both myelinated and unmyelinated axons contribute to the DWI signal. However, DWI models often include simplifications, for example, the neglect of differences in the compartmental relaxation times or fixed diffusivities, which in turn might affect the estimation of $f_{\text{AW}}$ . We investigate whether linear calibration parameters (scaling and offset) can improve the comparability between EM- and DWI-based metrics of $f_A$ . To this end, we (a) used six DWI models based on the so-called standard model of white matter (WM), including two models with fixed compartmental diffusivities (e.g., neurite orientation dispersion and density imaging, NODDI) and four models that fitted the compartmental diffusivities (e.g., white matter tract integrity, WMTI), and (b) used a multimodal data set including ex vivo diffusion DWI and EM data in mice with a broad dynamic range of fibre volume metrics. We demonstrated that the offset is associated with the volume fraction of unmyelinated axons and the scaling factor is associated with different compartmental $T_2$ and can substantially enhance the comparability between EM- and DWI-based metrics of $f_A$ . We found that DWI models that fitted compartmental diffusivities provided the most accurate estimates of the EM-based $f_A$ . Finally, we introduced a more efficient hybrid calibration approach, where only the offset is estimated but the scaling is fixed to a theoretically predicted value. Using this approach, a similar one-to-one correspondence to EM was achieved for WMTI. The method presented can pave the way for use of validated DWI-based models in clinical research and neuroscience.