The conduction velocity (CV) of action potentials along axons is a key neurophysiological property central to neural communication. The ability to estimate CV in humans in vivo from non-invasive MRI methods would therefore represent a significant advance in neuroscience. However, there are 2 major challenges that this paper aims to address: (1) much of the complexity of the neurophysiology of action potentials cannot be captured with currently available MRI techniques. Therefore, we seek to

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... blish the variability in CV that can be captured when predicting CV purely from parameters that can be estimated from MRI (axon diameter and g-ratio); and (2) errors inherent in existing MRI-based biophysical models of tissue will propagate through to estimates of CV, the extent to which is currently unknown. Issue (1) is investigated by performing a sensitivity analysis on a comprehensive model of axon electrophysiology and determining the relative sensitivity to various morphological and electrical parameters. The investigations suggest that 89.2 % of the variance in CV is accounted for by variation in AD and g-ratio. The observed dependency of CV on AD and g-ratio is well characterised by a previously reported model by Rushton. Issue (2) is investigated through simulation of diffusion and relaxometry MRI data for a range of axon morphologies, applying models of restricted diffusion and relaxation processes to derive estimates of axon volume fraction (AVF), AD and g-ratio and estimating CV from the derived parameters. The results show that errors in the AVF have the biggest detrimental impact on estimates of CV, particularly for sparse fibre populations (AVF< 0.3). CV estimates are most accurate (below 5% error) where AVF is above 0.3, g-ratio is between 0.6 and 0.85 and AD is below 10 m. Fortunately, these parameter bounds are typically satisfied by most myelinated axons. In conclusion, we demonstrate that accurate CV estimates can be inferred in axon populations across a range of configurations, except in some exceptional cases or where axonal density is low. As a proof of concept, for the first time, we generated an in vivo map of conduction velocity in the human corpus callosum with estimates consistent with values previously reported from invasive electrophysiology in primates.