Label-free nanoscale optical metrology on myelinated axons in vivo

In the mammalian nervous system, myelin provides electrical insulation for the neural circuit by forming a highly organized, multilayered thin film around the axon fibers. Here, we investigate the spectral reflectance from this subcellular nanostructure and devise a new label-free technique based on a spectroscopic analysis of reflected light, enabling nanoscale imaging of myelinated axons in their natural living state. Using this technique, we demonstrate three-dimensional mapping of the axon diameter and sensing of dynamic changes in the substructure of myelin at nanoscale. We further reveal the prevalence of axon bulging in the brain cortex in vivo after mild compressive trauma. Our novel tool opens new avenues of investigation by creating unprecedented access to the nanostructural dynamics of live myelinated axons in health and disease.

phospholipid protein, PLP) 3 . Periaxonal space is reported to be ~12 nm measured by transmission electron microscopy 4 . Myelin cytoplasm is reported to be 3 nm, formed by compaction mediated by myelin basic protein (MBP) 5 . Extracellular layer is set to 5 nm, considering that spatial period of each myelin layer is about 18 nm 6 . Structural parameters used in the simulation are summarized in Supplementary Table 1.

Number of myelin layer
The g-ratio is defined as the ratio of the inner axonal diameter (d) to the total outer diameter (D).

− =
If the g-ratio is 0.7, the myelin thickness can be expressed as follows.
In our geometric model, the myelin thickness has a discrete value determined by the number of myelin layers, N (Supplementary Fig. 2  Lastly, refractive index for extracellular space (n e ) is estimated. Refractive index of the myelin sheath is consistently reported to be ~1.45 8,15 . Each myelin layer (18 nm in thickness) is composed of 2 layers of membrane (10 nm in thickness), a single layer of cytosol (3 nm in thickness) and extracellular space (5 nm in thickness) as described in Supplementary Fig. 1.
As fractional volume for each layer is proportional to each thickness, overall refractive index of the myelin sheath can be written as linear weighted summation (Eq. 3) Solving Eq. 3 yields n e ~ 1.35 16,17 . We used the same index for periaxonal space. Structural parameters for each substructure is summarized in Supplementary Table 1.

Supplementary Note 2. Wave simulation
Numerical simulation based on the theory of electromagnetic waves was performed in order to estimate and predict the spectral reflectance from the myelinated axons of various structures. The distribution of the electric-field reflected from the myelinated axons can be explained by the thin-film matrix theory 18 , since myelin layers can be considered as dielectric multilayers. By thin-film matrix theory, matrix components of myelin layers can be defined as, where b is optical admittance for S and P polarization at given angle of the ray and b is the phase delay at the layer. S polarization is perpendicular and P polarization is parallel to the meridional plane, which is defined by plane of incidence. Film matrix b is composed of two polarization states since Fresnel reflection coefficient of the medium is dependent on the polarization of the incident light. Then the amplitude reflection coefficient of the myelin is expressed as where, \ is the optical admittance at the extracellular region.
Focusing the incident wave into myelin layers at high NA and collecting the reflected light at epi-detection configuration can be described by the wave diffraction theory. The electric field at the position on the image plane focused by an objective lens is described by a general scalar form 19 .
, is the given electric field at the pupil plane of the objective lens, for example, Thereby, the distribution and polarization of electromagnetic wave focused into multilayered thin-films can be properly described, whereas it cannot be explained in scalar diffraction theory.
The local polarization variation can be described by polarization decomposition factor ‰QŠ , where is the initial polarization state, corresponds to the local S, P coordinate The intensity distribution of the focused beam is given by ()* = ()*ˆ. In order to demonstrate the rotation of local polarization, the contour maps of intensity distribution via each local polarization states S and P are indicated in the lower panel of Figure SN, for the given incident Gaussian wave at polarization.
The electric field reflected from multi-layers of myelin can be derived by multiplying the reflection coefficient into the decomposed electric field at each local polarization state, where * is the point spread function of the collection system involving confocal detection.
Hence, the total reflectance from the myelin at the optical system is given by