Mapping axon diameters and conduction velocity in the rat brain - different methods tell different stories of the structure-function relationship

The structure-function relationship of nerve fibers describes an empirically determined linear relationship between axon diameter, myelin thickness (i.e., g-ratio), and conduction velocity. We investigated the structure-function relationship with different modalities in axons projecting through the corpus callosum of the rodent brain. We measured transcallosal conduction times using optogenetically evoked local field potentials (LFP) and estimated conduction velocity after measuring the callosal length with diffusion magnetic resonance imaging (dMRI) based tractography. Tractography followed the same projection as the fluorescently labeled axons in the corpus callosum. In the same animal, axon diameters were quantified using transmission electron microscopy (TEM) and dMRI. Axon distributions of TEM indicated a bimodal population, where the larger axons shrink more than the smaller ones, when comparing the modes with cryo-TEM. When applying shrinkage-correction to axon diameters from TEM of dehydrated tissue, they were better aligned with estimates from dMRI obtained in the same animal. Measured LFPs predicted axon diameters that agree with the primary mode of the axon distribution, whereas the large axons estimated by dMRI predicted latencies too short to be measured by LFPs. Different modalities show different degrees of variations, being low between animals, suggesting that the variation is methodologically dominated - not anatomically. Our results show that modalities have different sensitivity profiles to the whole axon diameter distribution. Therefore, caution must be taken when interpreting a method's prediction of a metric, as it may not represent the full but only a sub-part of the structure-function relationship of an axonal projection. ### Competing Interest Statement HRS has received honoraria as a speaker and consultant from Lundbeck Pharma A/S, Denmark, and as editor in chief (Neuroimage Clinical) from Elsevier Publishers, Amsterdam, The Netherlands. HRS has received royalties as a book editor from Springer Publishers, Stuttgart, Germany, and Gyldendal Publishers, Copenhagen, Denmark, Oxford University Press, Oxford, UK.