Ultrafast and hypersensitive phase imaging of propagating internodal current flows in myelinated axons and electromagnetic pulses in dielectrics

Abstract

Many ultrafast phenomena in biology and physics are fundamental to our scientific understanding but have not yet been visualized owing to the extreme speed and sensitivity requirements in imaging modalities. Two examples are the propagation of passive current flows through myelinated axons and electromagnetic pulses through dielectrics, which are both key to information processing in living organisms and electronic devices. Here, we demonstrate differentially enhanced compressed ultrafast photography (Diff-CUP) to directly visualize propagations of passive current flows at approximately 100 m/s along internodes, i.e., continuous myelinated axons between nodes of Ranvier, from Xenopus laevis sciatic nerves and of electromagnetic pulses at approximately 5 × 10⁷ m/s through lithium niobate. The spatiotemporal dynamics of both propagation processes are consistent with the results from computational models, demonstrating that Diff-CUP can span these two extreme timescales while maintaining high phase sensitivity. With its ultrahigh speed (picosecond resolution), high sensitivity, and noninvasiveness, Diff-CUP provides a powerful tool for investigating ultrafast biological and physical phenomena.

Fig. 1. Diff-CUP system.

a Schematic of the Diff-CUP system. Amp amplifier, BS beamsplitter, CCD charge-coupled device camera, DG delay generator, HWP half-wave plate, LN lithium niobate crystal, OB objective lens, PBS polarizing beamsplitter, PG pulse generator, SC streak camera, Sync synchronization. b Delivery of an EMP, $E\left(t\right)$, to the LN crystal through a custom-designed microstrip transmission line. c Spatiotemporal electric field distribution of the signal propagating in the LN crystal simulated using a finite element model. Green curve represents the Gaussian-shaped pulse in a snapshot. $W$, width of the LN crystal; $v$, propagation speed of the signal; $w_s$, pulse width of the signal. d Spatiotemporal phase changes resulted from the propagating signal in the LN crystal operating in different modes (conventional CUP, uncoded or coded). Yellow lines indicate the pulse width, and green lines represent the temporal intensity in the middle of the FOV.

Fig. 2. Phase sensitivity of Diff-CUP.

a Spatiotemporal interferograms of a 2.6-ns EMP in the LN crystal captured by the streak camera and simulated by the electric field and phase distribution model, and the corresponding temporal phase averaging over the x direction. Horizontal scale bars, 300 µm. Vertical scale bars, 500 ps. b Experimental interferogram of a 150-ps propagating EMP and the corresponding temporal correlation of Fringes 1–4. D is the spatial distance between Fringes 1 and 4. The inset at the bottom right shows the approach to calculate the propagation time, T, of the EMP through the LN (top right). Horizontal scale bar, 300 µm. Vertical scale bar, 50 ps. c Quantification of phase-sensitivity of uncoded Diff-CUP by inducing EMPs with different amplitudes in the LN crystal. Each curve represents a reconstructed pulse shape with a different amplitude, where the corresponding phase change is shown above the curve. Black arrows denote the pulse width of the EMP. d Spatiotemporal interferograms of a weak EMP propagating in the LN crystal. Left, unprocessed interferogram, i.e., control group. Middle, interferogram processed with the temporal correlation (TC) and template matching (TM) methods. Right, interferogram processed with the TC, TM, and differential approach. Black dashed lines denote the regions of the EMP. Horizontal scale bars, 300 µm. Vertical scale bars, 20 ps. e Reconstruction of the pulse shape of the weak EMP using the three interferograms in (d).

Fig. 3. Uncoded Diff-CUP imaging of propagating internodal current flows in myelinated axons.

a Setup for imaging propagating internodal current flows in the sample arm of Diff-CUP’s Mach–Zehnder interferometer. $E\left(t\right)$ is the transient field stimulation applied to the parallel bipolar microelectrodes. b Schematic of the equivalent double cable internodal circuit. IN internode, PN paranode, NOR node of Ranvier, MS myelin sheath; ${\mathrm{R}}_{\mathrm{a}}$, axonal axial resistivity; ${\mathrm{R}}_{\mathrm{pa}}$, periaxonal resistivity; ${\mathrm{R}}_{\mathrm{pn}}$, paranodal resistivity; ${\mathrm{R}}_{\mathrm{m}}$ and ${\mathrm{C}}_{\mathrm{m}}$, specific membrane resistance and capacitance; ${\mathrm{R}}_{\mathrm{my}}$ and ${\mathrm{C}}_{\mathrm{my}}$, specific myelin sheath resistance and capacitance. c, Spatiotemporal interferograms of a propagating internodal current flow in a myelinated axon captured by uncoded Diff-CUP (400 interferograms) under different conditions. The horizontal and vertical axes of the interferogram denote $x$ and $z$, respectively, where $z=nd+y$, $x$ and $y$ are the two spatial axes, $n$ stands for the $n$-th axon image in the time series, and $d$ denotes the FOV in the $y$ dimension. From left to right: interference, unprocessed interferogram; LN, interferogram captured with a synchronous EMP induced in the LN crystal, where the strong Pockels effect caused by the EMP is used as a time reference for locating the starting time point of the current flow; control, interferogram captured without field stimulation; stimulus, interferogram captured with field stimulation; simulation, interferogram overlaid with a “virtual” stimulus generated by the NEURON simulation environment. Black box denotes the FOV of the axon. Gray electrode symbols denote when the stimulation is applied. Horizontal scale bars, 25 µm. Vertical scale bars, 3 µs. d–g Reconstructions based on the LN (d), control (e), stimulus (f), and simulation (g) interferograms in (c). Each reconstructed correlation curve corresponds to a segment of the FOV, labeled with numbers 1–8. Scale bars show the normalized correlation values. The regions corresponding to these segments are marked in the axon’s CCD image on the right of (f). Black dashed lines indicate the peak time of the synchronous EMP (d) or the signal region of the internodal current flow (e–g). T is the propagation time of the internodal current flow within the FOV of the axon.

Fig. 4. Coded Diff-CUP imaging of propagating EMPs in an LN crystal.

a Lossless-encoding CUP setup in the Diff-CUP system. DMD, digital micromirror device; OB, objective lens; SC, streak camera; BS, beamsplitter. b Operation principle of lossless-encoding CUP. The DMD spatially encodes spatiotemporal scenes with a pseudorandom binary pattern by reflecting the incident light to either +12° (+) or –12° (–), creating two beams encoded with complementary patterns. c Quantification of temporal resolution in Diff-CUP. An 800-nm, 50-fs laser pulse (Libra-HE, Coherent) is split by the Mach–Zehnder interferometer into a reference pulse and a signal pulse. The temporal resolution of the system is measured as the minimum, distinguishable temporal distance between the two pulses with a 6 dB contrast-to-noise ratio. d Correlation between each frame and the first frame in the reconstructed movies of EMPs propagating in the LN crystal acquired by conventional CUP and coded Diff-CUP. The correlation curves indicate the phase change induced by the propagating EMPs. Data are presented as mean values ± standard errors of the means (n = 50). e Dependence of the maximum correlation change ($△$C/C with C equals to one) in (d) on the number of interferograms used for coded Diff-CUP reconstruction. f Representative snapshots from the reconstructed movie of a 150-ps EMP (launched from left to right) propagating in the LN crystal acquired by coded Diff-CUP (20 interferograms). Shown below are the relative phase changes induced by the EMP obtained by subtracting the first frame from each frame in the movie. Numbers 1–4 denote the four interference fringes in the FOV. Yellow arrows indicate the propagating direction of the EMP. Scale bar, 500 µm. g Spatiotemporal profile of the propagating EMP revealed by processing the interference fringes 1–4 in (f) with the correlation and TM methods. Dashed line indicates the time shift of the EMP peaks. Black arrows denote the pulse width of the EMP.