Fig 1.
Cross-sectional slice of the extracellular field generated by the electrode.
Cross-sectional slice of the extracellular field generated by the electrode over the model Nerve 1 at the middle of its length (z = 5000 μm), where the stimulation pad (blue diamond) is situated, and at the time step following the onset of the stimulating pulse. The RN assumes the field is constant over the surface of each tessellation polygon. The contours of the nerve and the fascicles are indicated with a black solid line for better identification. Axons are not shown in this figure. Although the maximum value of |vE|, situated at the active site, is 2413.62 mV, the colorbar was cut at 1000 mV in order to facilitate the visualisation of the spatial details of the field.
Fig 2.
Longitudinal profile of the extracellular field generated by the electrode.
Longitudinal profile (z-axis) of the extracellular field (absolute value, logarithmic scale) generated by the electrode over the model Nerve 1, along the length of the cuff electrode, at three different points on the x-y plane: the position of the active pad (x = 250 μm, blue), the position of the central-most axon in the nerve (x = −3 μm, green), and the farthest point from the active pad (x = −250 μm, red). All three points are located at y = 0 μm.
Fig 3.
Scaled recruitment curves for all the fascicles and the whole nerve. Black lines correspond to SEC and blue lines correspond to SNOEC simulations. Red lines show the difference between the two. The horizontal axis indicates the pulse amplitudes exerted on the electrode’s active pad. Pulses are always negative in the simulations, but they have been represented as absolute values in this figure for clarity.
Fig 4.
For one particular axon, randomly chosen as an example, central panel shows the time evolution of the extracellular potential (vE) on the node of Ranvier lying closer to the electrode’s active pad for both simulations (blue for SNOEC, black for SEC), and left panel shows the time evolution of the transmembrane potential (vm, same location and legend). Note in this panel how the EC produces an AP earlier than in SNOEC. Right panel: Time evolution of the endogenous fields () for all the axons (thin black lines) on the nodes lying closer to the active pad. Red lines indicate the mean of these fields (averaged for each time step, middle thick line) with their standard deviation (thin lines). The two black vertical lines indicate the start and finish of the pulse.
Fig 5.
Selectivity for Fascicle 1 for the various pulse amplitudes in use.
Fig 6.
Propagation: Action potential trajectories.
Trajectories of the axons on the t-z space for SNOEC and SEC. Each trajectory is coloured according to its corresponding fiber’s diameter. These results correspond to Bundle 1.
Fig 7.
Propagation: Conduction velocities.
CVs of the fibers in the simulation SEC, scaled over their respective values in SNOEC, which are stationary. CVs are obtained from a linear regression on the (t, z) points of the trajectories, using a window of 11 nodes or Ranvier, so the curves do not span the whole simulation. Error margins are not shown in order to aid a clearer visualisation. These data correspond to Bundle 1.
Fig 8.
Propagation in a bundle with a natural fiber diameter distribution: Action potential trajectories.
Trajectories of the axons on the t-z space. Each trajectory is coloured according to its corresponding fiber’s diameter. These results correspond to Bundle 2.
Fig 9.
Strength of ephaptic coupling with inter-axonal distance.
Maximum variation of vm above vr (resting potential, −80 mV) along the unstimulated axons, represented against the distance to the stimulated axon. Left: Bundle 3; right: Nerve 2, which contains seven fascicles separated by a perineurium, same as Nerve 1.
Table 1.
Geometrical and electrical properties of the models.
Fig 10.
Histograms for fiber diameters.
Histograms for fiber diameters of the nerve and bundle models used in this study, except for models without diameter variability (Bundle 4 and Nerve 2). Horizontal axes indicate diameter values in μm and vertical axes indicate the number of axons for each bin of the histograms. Note that although all histograms have the same number of bins (39), they do not necessarily share any horizontal or vertical axes. The corresponding model names are indicated on the top of each histogram.
Table 2.
Parameters used for the RN.
Fig 11.
Resistor network connecting two myelinated fibers ephaptically.
Example of RN connecting two myelinated fibers ephaptically. Conceptual (not to scale) representations of two myelinated fibers are shown as axons (green) wrapped by the myelin sheaths (dark yellow). Thick black line segments represent purely resistive connections. Grey boxes represent membrane compartments, either nodal or internodal (in which case, they also include the myelin sheath in series). The periaxonal space of the double-cable model is not shown in this figure for simplicity, but it is important to hold in mind that it is present in the models. The y-axis has been used on the ordinate axis in this figure for simplicity, but given our model, this can be any direction co-planar with the x-y plane.
Table 3.
Variables used for the RN.
Fig 12.
Power diagram and Delaunay triangulation of the nerve’s cross-section (Nerve 1).
Discretisation of a nerve model’s cross-section Nerve 1 in polygons using a power diagram (green). Grey circles indicate the locations and diameters of the axons, which are embedded in seven fascicles (the blue labels number the fascicles). Black dots indicate points resulting from a Delaunay triangulation to discretise the epineurium, indicating the locations of NAELC. The dual Delaunay triangulation to the power diagram representing the connections with transverse resistors is represented with solid red thin segments. Note that while the nerve’s contour contains NAELC, the fascicles contours do not. This model is used in simulations in this work (see Nerve 1 in Fig 10 and Table 1).
Fig 13.
Power diagram and Delaunay triangulation of the nerve’s cross-section (zoomed).
Cross-sectional view of a random fascicle including the tessellation (green lines) and the triangulation (red). Additional information is used to display the details of the connection between two randomly chosen nearest-neighbouring fibers k and l. The coloured areas represent the extracellular area assigned to the calculation of the longitudinal extracellular resistance of each fiber (green for fiber k and blue for fiber l).