Selective extracellular stimulation of individual neurons in ganglia

Experimental methods

Aplysia californica weighing 200–450 g (Marinus Scientific, Garden Grove, CA) were maintained in an aerated aquarium containing artificial seawater (Instant Ocean; Aquarium Systems, Mentor, OH) kept at 18±1 °C.

Extracellular stimulating electrodes were made from single-barrelled capillary glass (catalogue #6150; A-M Systems, Everett, WA) pulled on a Flaming-Brown micropipette puller (model P-80/PC; Sutter Instruments, Novato, CA). Electrodes were backfilled with Aplysia saline (460 mM NaCl, 10 mM KCl, 22 mM MgCl₂, 33 mM MgSO₄, 10 mM CaCl₂, 10 mM glucose, 10 mM MOPS, pH 7.4–7.5), and placed in the saline above the surface of the ganglion. Their inner diameters were about 40 µm, and their resistances were about 0.1 MΩ. Currents were supplied by a stimulus isolator (model A-360, WPI).

Intracellular recording electrodes were also made from single-barrelled capillary glass (catalogue #6150; A-M Systems, Everett, WA) pulled on a Flaming-Brown micropipette puller (model P-80/PC; Sutter Instruments, Novato, CA). Electrodes were backfilled with 3 M potassium acetate, and their resistances were 3–6 MΩ. The bridge was balanced for both stimulation and recording. Intracellular signals were amplified using a DC-coupled amplifier (model 1600; A-M Systems).

Nerve recording electrodes were made from polyethylene tubing (catalogue #427421; Becton Dickinson, Sparks, MD; outer diameter 1.27 mm; inner diameter 0.86 mm). Electrodes were backfilled with Aplysia saline. Nerve recording signals were amplified using an AC-coupled differential amplifier (model 1700; A-M Systems) and filtered using a 300 Hz high-pass filter and a 1 kHz low-pass filter.

To study the responses of neurons to extracellular stimulation near the cell bodies, animals were anesthetized, and the buccal ganglia were dissected out. The buccal ganglia were pinned caudal side up in Aplysia saline. The nerve of interest was suctioned into the tapered end of the nerve recording electrode and recorded simultaneously as the extracellular stimulation was applied (figure 1, right side schematic). When intracellular recordings were also performed, ganglia were desheathed to expose the cell bodies of the neurons. The cell body of each neuron of interest was impaled by an intracellular electrode for recording, while it was simultaneously stimulated by an extracellular electrode (figure 1, left side schematic). During extracellular cathodic stimulation, we used the same intracellular recording electrode to induce multiple action potentials at a certain frequency by injecting a depolarizing current into the cell body.

To measure the real membrane potential changes during extracellular stimulation, we subtracted the stimulation artefact from the intracellular recordings. The membrane potential is the difference between the internal and external voltages of the cell. Because the bath is grounded, the external voltage is normally zero, so the recording of the internal voltage of the cell can be used to represent the membrane potential. However, an extracellular current source will create an external voltage gradient, so in this case we cannot assume that the external voltage is zero. Thus, to obtain a more accurate value of the membrane potential during stimulation, we needed to estimate the external voltage as we recorded intracellularly. We first recorded the voltage in the bath near the soma with the intracellular electrode while applying extracellular stimulation at the current levels for every 100 µA in the range of 100–1000 µA. Then we penetrated the cell and measured the internal voltage during identical extracellular stimulation for every current level. Lastly, we subtracted the external voltage from the internal voltage that was recorded when applying the identical extracellular current, which we will refer to as the artefact subtracted recording. Changes in the intracellular electrode resistance were negligible compared to the impedance of the amplifier and were therefore neglected.

In addition, to study the effects of the sheath on the neurons, we compared the minimum currents (i.e., threshold currents) needed to change neural activity when the sheath was intact and after the sheath was removed. We placed the extracellular stimulating electrode above the sheath to stimulate the cell bodies underneath (figure 1, right schematic diagram). Because the sheath blocked access of intracellular electrodes to the neurons, we instead recorded from the buccal nerve containing the axon of the targeted neuron. We first measured the threshold currents at different stimulating electrode locations when the sheath was intact. Afterwards, we removed the sheath partially or entirely and measured the threshold currents again at different stimulating electrode locations. Because we were not able to directly measure the electrode-to-soma distances with the sheath covering the neuron, we estimated them by adding the thickness of the sheath to the distances from the electrode to the sheath immediately covering the targeted neuron using the reticle of the microscope. We measured the thickness of the sheath that was removed as well as the thickness of the remaining sheath. We added these two values to estimate the original thickness of the sheath. The threshold currents before and after removing the sheath were nearly identical at the electrode locations in the range of 150–300 µm away from the neuron (for details, see Results section). Thus, the sheath of the buccal ganglion has a negligible effect on the threshold currents of neurons for extracellular ganglionic stimulation.

To estimate the resistivity of Aplysia saline, we performed a four-wire (Kelvin) resistance measurement (figure 2) (Light 1997). We applied 100 µA alternating positive and negative 3 ms current pulses at 200 Hz using two stimulus isolators (model A-360, WPI). We varied the separations of the two recording electrodes in a conductance cell and obtained the slope of the changing voltage versus separation. The resistivity of Aplysia saline was calculated by dividing the slope by the current amplitude and multiplying by the cross-sectional area of the conductance cell.

NEURON model simulations

To understand the mechanisms of extracellular ganglionic stimulation and study its spatial and temporal specificity, we developed models using the NEURON software package.

An unmyelinated neuron was simulated using the NEURON software package (Hines and Carnevale 1997), based on the simplified geometry of the Aplysia buccal neurons B4/B5. The parameters describing the geometry of this NEURON model are listed in table 1. Aplysia neurons do not have dendrites surrounding the cell bodies; rather, the dendrites emerge from the axons in the central neuropil (Kreiner et al 1987). Thus, we modelled the axon and dendrites as a single cylinder and modelled the soma as a sphere (figure 3A). The soma diameter was set to 200 µm based on a reticle measurement of B4/B5 using a microscope. The axon diameter was set to 15 µm based on the relative size of the soma and axon (Kreiner et al 1987). The axon length was set to about 20 mm based on a rough estimation of the nerve length. The soma sphere was divided into 100 segments of equal length (figure 3A, schematic diagrams 1 and 2). To increase the homogeneity of the electrical field across the soma as the electrode was moved through different angles, the soma segments were automatically rotated according to the stimulating electrode positions to remain perpendicular to the line between the electrode tip and the soma centre (figure 3A, schematic diagrams 1 and 2). As a consequence, the connection location between the soma and the axon changed. When the 100^th soma segment was connected to the axon, there was only one closed end at the 1^st soma segment. However, when the 100^th soma segment was not connected to the axon, there would be two closed ends at both the 1^st and 100^th soma segments. In order to eliminate this special case, we attached an additional very short soma segment (1/1000 the length of other soma segments) to the 100^th segment as a small branch which would always act as the second closed end of the soma. When multiple electrodes were used to stimulate neurons (figure 14C1), the soma segments were rotated to point to the weighed average position of the electrodes. Then the axon was divided into 200 segments of equal length except the 1^st axon segment whose length was the mean of one regular soma and axon segments. Increasing the number of segments by a factor of 10 while maintaining the overall neuronal geometry changed threshold currents by less than 0.1%.

The simulated neuron was represented by an equivalent electrical circuit (figure 3B). The midpoint of each segment was chosen to be a representation of the electrical node. The internal potential at the n^th electrical node was represented by V_i(n). The axial resistance of the n^th electrical nodes was represented by R_a (n), which was equal to

where l(n) was the length of the n^th segment, diam (n) was the diameter of the n^th segment and ρ_a was the resistivity of the intracellular fluid of the neuron, which was estimated to be 200 Ω·cm based on McIntyre and Grill (2002) and was in the range from 86 Ω·cm to 410 Ω·cm calculated from Hovey et al (1972). The electrical parameters of this NEURON model are listed in table 2. The dynamics of the fast sodium, slow potassium and leakage channels in the membrane were a modification of those originally described in the squid giant axon membrane by Hodgkin and Huxley (1952). We did not attempt to match the specific electrical parameters of the single-compartment model of B4/B5 (Ziv et al 1994), because we wished to generalize the NEURON models to many other excitable cells. The maximum conductances of fast Na⁺ and slow K⁺ channels, ${\overline{g}}_{\text{Na}}$ and ${\overline{g}}_{\mathrm{K}}$, as well as the conductance of leakage channels, g_L, remained the same in the axon membrane as those in the Hodgkin-Huxley model. The reversal potential of the leakage channels was set to be −65 mV. To simulate the lower densities of Na⁺ and K⁺ channels in the soma compared to the axon, ${\overline{g}}_{\text{Na}}$ and ${\overline{g}}_{\mathrm{K}}$ were reduced by a factor of five in the soma. The time constants of the Na⁺ and K⁺ channels were increased by linear scaling factors based on the ratios of the time constants of the Hodgkin-Huxley model to the time constants of Aplysia sensory neurons (Baxter et al 1999).

Extracellular stimulation was modelled by a point current source that was applied within an infinite homogeneous saline medium (McIntyre and Grill 1999), in which the X-axis was oriented along the axon, and the Y-axis was perpendicular to the axon. The stimulating electrode was placed at (X_elec, Y_elec) relative to the centre of the soma at (0, 0). We assumed that the presence of the neuron did not affect the extracellular field created by this current source and that the extracellular potentials generated by the membrane currents of the neuron were negligible. We also assumed that the extracellular saline medium was homogeneous, with its resistivity estimated to be 19.3 Ω · cm based on the measurements described above. In addition, we demonstrated that the sheath of the buccal ganglia had negligible effect on the threshold currents of neurons during extracellular stimulation (see previous Methods section and Results section below). Therefore, we used the same NEURON model to simulate neurons with or without the protective sheath.

Stimulation was modelled with an approach similar to Rattay (1989). The external voltage V_ext(n) at any electrical node of the simulated neuron was determined by equation (2) (Rattay 1989),

where I is the magnitude of the applied extracellular current, σ_e is the conductivity of the extracellular medium (σ_e = 1/ρ_e) and r is the distance from the point current source to the n^th node (r = ((X_elec − X(n))² + (Y_elec − Y(n))²)^1/2). The ground electrode was assumed to be an infinite distance away. Therefore, these external voltages V_ext(n) could be converted to the equivalent intracellular injected currents I_int(n) at each node according to equation (3) (McIntyre and Grill 1999),

These currents were applied to the neuron in monophasic pulses using the NEURON software package to view cellular voltages, including action potentials, over time. During extracellular cathodic stimulation, we injected additional depolarizing monophasic intracellular current pulses into the soma to induce multiple action potentials.

To investigate the spatial specificity when stimulating multiple cells, we added two more identical neurons to create a multiple-cell NEURON model. The centre of the middle neuron was set at (0, 0), and the centres of the neighbouring neurons were set at positions (0, −200) and (0, 200), respectively, with their axons parallel and pointing in the same direction. This simulated the geometry of the ganglion in which cell bodies are clustered together near the surface. The X-axis was along the axons and the Y-axis was perpendicular to the axons. The stimulating electrode was again placed at (X_elec, Y_elec) relative to the centre of the middle neuron at (0, 0). During cathodic inhibition, we injected depolarizing currents intracellularly into the cell bodies of all three neurons to induce a train of action potentials in each neuron.

To test the applicability of the technique to vertebrate neurons, we reconstructed a previously-published model of cat spinal motorneurons (McIntyre and Grill 2000). Parameters of the model are presented in table 3. Qualitatively, results are similar to those obtained for the generic model of invertebrate neurons presented here. Results for this model are shown at the end of the paper (figure 18).

Analytical model

To generalize predictions of spatial specificity to arbitrary neurons that have various sizes and geometric configurations, and to provide a way to readily predict the magnitude of the threshold currents needed to stimulate a neuron, we created a steady-state analytical model. We represented the neuron as a semi-infinite axon in this model. The tip of the new axon was placed at the centre of the original soma, based on the work of Lee and Grill (2005) showing that the cytoplasmic potential in an isolated cell stimulated by a point source will approach the potential at its equator. The new axon was capped with a resistor equivalent to the total membrane resistance of the original soma.

We then examined the influence of an extracellular electric field on this new axon. A point current source was placed at a negative position along the X axis. We assumed the effects of the neuron on the extracellular electric field were negligible, and used a steady-state form of the cable equation to model the membrane potential in the axon (see Appendix A for detailed derivation). We will refer to this model as the full analytical model.

While the resulting equation needed to be evaluated numerically, we found that we were able to approximate it with less than 6% error using the following equation when the current source was placed over the range of one to three length constants (or one-fifth to three length constants if γ, the normalized soma resistance, was greater than one) away from the tip of the new axon:

where κ_th is the normalized threshold current (the threshold current divided by −4πσ_e E_m, where σ_e is the conductivity of the extracellular medium and E_m is the resting membrane potential), α is the normalized distance from the centre of the soma to the extracellular stimulating electrode (α = d/λ, where λ is the length constant of the axon and d is the distance from the centre of the soma to the point current source), γ is the normalized soma resistance (γ = r_s/(r_iλ), where r_s is the total resistance across the membrane of the soma and r_i is the internal resistance per unit length in the axon), ν_th is the normalized threshold potential (ν_th = −V_th/E_m, where V_th is the threshold potential) and θ is the angle between the axon and the line drawn from the current source to the axon (see Appendix A). We will refer to equation (4) as the simplified analytical model.

We performed two sets of simulations to determine the constants for the simplified analytical model when comparing it with the NEURON model. First, we determined the length constant λ by injecting a small intracellular current into the NEURON model axon and measuring the rate of membrane potential decrease with distance. For example, the length constant was about 514 µm for the simulated neuron with the soma diameter of 200 µm and the axon diameter of 15 µm, and the length constant was 351 µm for the neuron with half the soma and axon diameters. Second, we estimated ν_th by measuring the threshold currents using the NEURON model when extracellularly stimulating the neuron along the axonal axis at distances of 100–300 µm and fitting the results to the simplified analytical model.

Mechanisms of extracellular ganglionic stimulation

Previous work demonstrated that a neuron can respond to extracellular stimulation in different ways and in different regions depending on its position relative to the stimulating electrode (McIntyre and Grill 2002, Iles 2005 and Tehovnik et al 2006). Anodic stimulation on the side of the soma opposite to the axon had a lower threshold for exciting the cell than cathodic current (Ranck 1975, Rattay 1999), which is the opposite of what is seen in periaxonal stimulation. Similarly, cathodic stimulation from this side could induce inhibition of the cell. To examine quantitatively the voltage changes resulting from either anodic or cathodic extracellular stimulation, we constructed a NEURON model. We first examined how the same neuronal segment (e.g., the axon hillock) responds differently to extracellular stimulation depending on the electrode position. We measured the membrane potential changes of the axon hillock as we moved the stimulating electrode along the axonal axis from (−500, 200) to (2000, 200). The effects of extracellular electrical fields on axon membrane potentials have been well described (Rattay 1989). It is well known that anodic currents hyperpolarize the area immediately below the electrode (figure 4A, schematics 2 and 3; note red areas in the axon) while depolarizing the distal area (figure 4A, schematics 2 and 3; note blue areas in the axon). Therefore, when the electrode is placed near the axon hillock (figure 4A, schematic 2), anodic currents strongly hyperpolarize the axon hillock so that the suppression will dominate. When the electrode is placed far away from the axon hillock (figure 4A, schematic 3), anodic currents weakly depolarize the axon hillock which will not overcome the suppression due to strong hyperpolarization in the axonal areas immediately below the electrode. Furthermore, anodic currents applied on the side of the soma opposite to the axon (figure 4A, schematic 1) weakly depolarize the axon hillock while strongly hyperpolarizing the soma. However, unlike the effects of distal axon stimulation (figure 4A, schematic 3), this depolarization in the axon hillock will dominate because the axon hillock contains many more voltage-gated sodium channels than does the soma.

The effects of cathodic stimulation on a neuron are the reverse. Cathodic currents strongly depolarize the axon hillock when applied near it (figure 4B, schematic 2). In contrast, cathodic currents weakly hyperpolarize the axon hillock as the electrode is placed far away from it (figure 4B, schematics 1 and 3). While stimulating the distal axon, the weak hyperpolarization of the axon hillock cannot suppress the neuron’s excitatory response to the distal axon depolarization. However, when stimulating on the side of the soma opposite to the axon, the weak hyperpolarization in the axon hillock can inhibit the neuron because of the high density of voltage-gated sodium channels in the axon hillock.

We then examined how various neuronal segments respond differently to extracellular ganglionic stimulation with the same current source. We measured the membrane potential changes along the neuron as we fixed the electrode position at (−150, 0). Anodic stimulation hyperpolarizes the proximal and middle parts of the soma, while depolarizing the distal soma and the proximal axon segments (figure 5A). Thus, a sufficiently large depolarization could initiate action potentials in the proximal axon segments, which then propagate throughout the rest of the neuron. This is consistent with the earlier modelling studies of Rattay (1999) who noted that spike initiation occurred in the proximal axon, but not at the hillock itself. Because of the low density of voltage-gated sodium channels, the hyperpolarization in the local soma segments will not be able to suppress the neuron’s activity. The effects of cathodic currents on the neuronal segments are the reverse (figure 5B). Cathodic stimulation depolarizes the proximal and middle parts of the soma, while hyperpolarizing the distal soma and the proximal axon segments. Because the axon contains many more voltage-gated sodium channels than does the soma, the hyperpolarization in the proximal axon would dominate, and thus inhibit the neuron. Therefore, we used anodic currents to activate neurons and cathodic currents to inhibit neurons during ganglionic stimulation on the side of the soma opposite to the axon.

Qualitative comparisons between experimental results and the NEURON model’s predictions

To experimentally validate the effects of extracellular currents applied on the side of the soma opposite to the axon, we compared the neural responses obtained from in vitro electrophysiological experiments with those predicted by the NEURON model.

The NEURON model predicted that anodic currents would activate a neuron when applied on the side of the soma opposite to the axon. A 6 msec anodic current pulse was applied to the simulated neuron. Anodic stimulation strongly hyperpolarized the tip of the soma and weakly hyperpolarized the middle of the soma (figure 6A; three black arrows point to the peaks of action potentials; the two top grey arrows indicate the hyperpolarization). However, the initial part of the axon was depolarized to generate an action potential, which then propagated back to the soma (figure 6A; the bottom grey arrow indicates the depolarization). Because of the high density of voltage-gated sodium channels in the initial axon segments, the hyperpolarization of the soma could not suppress the neuron’s activation.

To demonstrate anodic activation experimentally, we intracellularly recorded from both the tip and the middle of a soma in a desheathed ganglion as we simultaneously applied a 6 msec anodic current pulse above the soma. The intracellular recordings showed that the neuron was excited to fire an action potential at both sites of the soma (figure 6B, the two left black arrows point to the peaks of action potentials). However, the real polarization of the neuron at each soma site was embedded in the stimulation artefact. Thus, we subtracted the artefact from the intracellular recordings to show both the action potentials and polarizations of the neuron (for details, see Methods section). We found that the tip of the soma was strongly hyperpolarized while the middle of the soma was only weakly hyperpolarized due to anodic stimulation (figure 6B; the two grey arrows indicate the hyperpolarization; the two middle black arrows point to the peaks of action potentials). In addition, the action potentials occurred despite the hyperpolarization in both sites of the soma. Therefore, the experimental results qualitatively validate the NEURON model’s prediction that anodic activation is likely to be due to depolarization of the initial axon segments.

The NEURON model also predicted that cathodic currents would inhibit a neuron when applied on the side of the soma opposite to the axon. A 300 ms intracellular current pulse was injected into both the tip and the middle of the simulated neuron to generate multiple action potentials. Then a 100 msec cathodic extracellular current pulse was also applied to the simulated neuron (figure 7A). Cathodic currents hyperpolarized the initial part of the axon, blocking action potentials, whereas they strongly depolarized the tip of the soma and weakly depolarized the middle of the soma (figure 7A; note grey lines, indicating the steady-state membrane potential in response to the intracellular current alone). Thus, cathodic currents inhibit the neuron by directly hyperpolarizing the initial axon segments.

To demonstrate cathodic inhibition experimentally, we again recorded intracellularly from both the tip and the middle of the soma. We applied a 3 sec intracellular current pulse into both soma sites to induce action potentials, and then applied a 1 sec cathodic current pulse immediately above the soma in a desheathed ganglion (figure 7B). The intracellular recordings showed that action potentials were completely blocked during cathodic extracellular stimulation at both sites in the soma. In the artefact subtracted recordings, the tip of the soma was significantly depolarized during extracellular stimulation, whereas the middle of the soma was only slightly depolarized (figure 7B; grey lines correspond to the steady-state membrane potential in response to the intracellular current alone). Thus, the experimental results qualitatively validate the NEURON model’s prediction that cathodic hyperpolarization of the initial axon segment will inhibit nerve cells.

Threshold currents

Stimulation specificity requires that a single neuron can be selectively activated or inhibited among a group of neurons (spatial specificity) or that single spikes can be selectively added to or removed from a firing pattern of an individual neuron (temporal specificity). To obtain stimulation specificity, we need to employ the minimum currents that are necessary for effective stimulation. Therefore, we defined the threshold current for anodic activation to be the minimum current required to activate an individual neuron to generate at least one action potential. The threshold current for cathodic inhibition was defined to be the minimum current needed to totally block all action potentials in an individual neuron driven by a fixed input (e.g., intracellular depolarizing current or synaptic input) during the inhibitory pulse.

To predict threshold currents at various electrode positions, we studied the relationship between threshold currents and the distances from the stimulating electrode to the soma via intracellular recordings (figure 1, left side schematic). Consistent with previous studies (Stoney et al 1968, Nowak and Bullier 1996), the square root of threshold current for both anodic activation and cathodic inhibition increased as we moved the stimulating electrode away from the soma (figures 8A and 8B; n = 3; p < 0.05) The NEURON model also suggested qualitatively similar linear relationships between the square root of the threshold current and the electrode-to-soma distance (p < 0.05 for the linear fits of the square root transformations of both the cathodic and anodic model data). We noticed that the threshold currents could be relatively low (e.g., 30–60 µA) when the electrode was placed very close to the cell bodies (e.g., at around 5 µm) based on the linear fits from the experimental data.

Do we need more current to stimulate neurons when the protective sheath of the ganglia is intact, which is very important if this technique is to be applied in vivo? To investigate this, we compared the threshold currents for anodic activation of a single neuron when the sheath was intact and after the sheath was removed. We applied anodic stimulation to the soma of the targeted neuron through the sheath and simultaneously recorded from the buccal nerve containing its axon (figure 1, right side schematic). We measured threshold currents at various stimulating electrode positions and estimated the electrode-to-soma distances (for details, see Methods section). The threshold currents of the same neuron were very close when the sheath was intact and after the sheath was removed (figure 9; n = 3). However, we noticed that we did need more current to activate a neuron in an intact animal because the stimulating electrode cannot be placed very close to the neuron when the sheath is intact.

Selective activation and inhibition of an individual neuron

Can we selectively activate or inhibit an individual neuron by extracellular ganglionic stimulation? As shown in figure 8 and figure 9, the threshold currents of a neuron increase with the electrode-to-soma distance. As an electrode is moved along the surface of the ganglion, it will be closer to the cell bodies of some neurons and further from others. Thus, if we position the electrode over a certain range, extracellular currents should be able to selectively stimulate a single neuron.

To demonstrate selective activation, we intracellularly recorded simultaneously from the cell bodies of three adjacent neurons as we applied anodic extracellular currents above the soma of the targeted middle neuron in a desheathed ganglion (figure 10A; n = 8). The intracellular recordings showed that at the threshold current, the middle neuron fired an action potential following the stimulating artefact (figure 10B; note the black arrow pointing to the action potential). However, this current was not enough to activate the other two neurons. When 386% of the threshold current was applied, both the left and the middle neuron were excited to generate at least one action potential during or following the stimulation (figure 10C; note the black arrows pointing to the action potentials). Finally, as we increased the current to 471% of the threshold current of the middle neuron, all three neurons were excited, and generated at least one action potential during or following the stimulation (figure 10D; note the black arrows pointing to the action potentials). Therefore, an individual neuron can be selectively activated without activating its neighbours.

To demonstrate selective inhibition of an individual neuron, we again recorded intracellularly from the cell bodies of three adjacent neurons simultaneously. A depolarizing current was injected into each soma to induce a train of action potentials. A cathodic extracellular current was applied above the soma of the targeted middle neuron (figure 11A; n = 3). At the threshold current, cathodic stimulation only eliminated the action potentials in the middle neuron (figure 11B). With 208% of the threshold current of the middle neuron, both the left and the middle neuron were inhibited during the stimulation (figure 11C). Finally, as we increased the current to 358% of the threshold current of the middle neuron, all three neurons were inhibited during the stimulation (figure 11D). Therefore, an individual neuron can be inhibited selectively without suppressing the neighbouring neurons.

Spatial specificity for multiple neurons

The ability to selectively stimulate a single neuron among multiple neurons is one of the most important aspects of our technique, which we refer to as spatial specificity. It requires that the minimum current necessary to stimulate a given neuron is less than that needed to stimulate any other neuron by a reasonably large and reliable margin. In order to quantify the current window of spatial specificity, we defined it to be I_adjacent − I_neuron/I_adjacent, where I_adjacent was the threshold current for an adjacent neuron and I_neuron was the threshold current for the neuron of interest. In figure 10 and figure 11, we show large current windows of spatial specificity, which are 286% for anodic activation and 108% for cathodic inhibition.

To investigate the characteristics of spatial specificity, we created a multiple-cell NEURON model consisting of three adjacent neurons as described in the Methods section (figure 12A and figure 13A). We defined the X-axis to be along the axons and the Y-axis to be perpendicular to the axons. The X-coordinate of the stimulating electrode was fixed at 200 µm away from the centres of the cell bodies. The electrode was then moved along the Y-axis from the centre of the bottom neuron at Y_elec = −200 µm to the centre of the top neuron at Y_elec = 200 µm. At each point, the threshold currents of all three neurons were recorded and normalized to be the percentage of the minimum threshold current of the targeted middle neuron. When the electrode was placed between Y_elec = −99 µm and Y_elec = 99 µm, the normalized threshold currents of the middle neuron were lower than those of the other two neurons for both anodic activation and cathodic inhibition (figure 12B and figure 13B; the symmetric lines). As a consequence, the middle neuron could be activated and inhibited selectively over this range. At Y_elec = 0 µm, we could obtain the maximum current windows of spatial specificity, which were 88.8% for anodic activation and 113.7% for cathodic inhibition. In addition, the sizes of these maximum current windows fell quickly (approximately as the inverse square of the electrode-to-soma distance) as the stimulating electrode was moved away (figure 12C and figure 13C).

How general are the spatial specificity results as the neuron geometry varies, in particular, as one neuron is further from the surface than the surrounding neurons? To address this question, we developed a steady-state analytical model (for details, see Methods section and Appendix A) to predict the spatial specificity of arbitrary neurons that have various sizes and geometric configurations. We found that for the distances of interest (about one-third to three length constants from the soma), the simplified analytical model described in equation (4) provides an excellent approximation to the threshold current values from the NEURON model (figures 14A2, 14B2 and 14C2; note the lines for the analytical model and the symbols for the NEURON model).

How does the spatial specificity change if the neurons of interest have different sizes? Since a small neuron has a higher threshold current than a large neuron, it might be difficult to stimulate a small neuron selectively if it is surrounded by large neurons. To explore this problem, we considered the case where a small neuron was surrounded by two large neurons. The parameters of the large neurons were the same as those used in the previous multiple-cell NEURON model containing three identical adjacent neurons (figure 12A). The soma and axon diameters of the small neuron were 100 µm and 7.5 µm, respectively, which were both half of those of the large neurons. We first examined the neural responses when all three neurons were aligned at the tips of their cell bodies with their axons parallel to each other (figure 14A1). We did the same measurements of threshold currents to determine spatial specificity. The targeted small middle neuron could be selectively activated. For example, the maximum current window was 11.2% when the stimulating electrode was 200 µm away along the X-axis from the tips of the cell bodies (figure 14A2; note the arrow pointing down). Although it is smaller than the maximum current window shown above (figure 12), it is still sufficient for reliable selective stimulation. Similarly, the maximum current window was largest when the stimulating electrode was close to the neurons along the X-axis, and it fell as the electrode was moved away (data not shown).

How does specificity change if the neurons of interest have both different sizes and geometric configurations? One extreme case would occur if the targeted neuron was both smaller and further away from the surface. For example, the targeted small neuron and its neighbours could be aligned at their hillocks with their axons parallel to each other (figure 14B1). In fact, we observed that spatial specificity was now much worse: the targeted small neuron could not be selectively activated (figure 14B2; note the arrow pointing up). In order to regain the spatial specificity of the targeted small neuron, we had to place the electrode immediately above it and between the two large adjacent neurons. For example, when the X-coordinate of the electrode was 50 µm from the tip of the small neuron, the maximum specificity window was about 75% of its minimum threshold current (data not shown). Previous work by Tarler and Mortimer (2004) studying axon stimulation showed that if one suppresses activity in neighbouring axons, it was possible to regain spatial specificity. Based on this idea, we were able to restore the spatial specificity of the middle small neuron by adding two cathodic current sources directly above the two large adjacent neurons (figure 14C).

Temporal Specificity for an individual neuron

In many applications, it is also crucial to control the firing frequency of a neuron by adding or removing specific spikes at precise times, which we refer to as temporal specificity. At the threshold current for anodic stimulation, one can use a low-frequency pulse train to generate a single action potential during or immediately following each single pulse. This makes it possible to control the firing frequency of the neuron by adding one action potential per pulse (figure 15). However, a higher current or pulse frequency may induce more than one action potential per pulse, making the neuron’s firing frequency unpredictable. For example, we found that we could reliably drive B4/B5 to fire at frequencies up to 45 Hz using anodic pulse trains (data not shown), but not at higher frequencies. We were also able to add specific spikes to the firing pattern of B4/B5 (figure 15).

Similarly, at the threshold current for cathodic stimulation, we can also use a low-frequency pulse train to block a single action potential during a single pulse. This also allows the control of firing frequency by removing one action potential per pulse (figure 16). However, the pulse should be long enough to cover the duration of an action potential so that each pulse can eliminate one action potential. For example, we were able to control the spiking rates of B4/B5 when it was firing at frequencies lower than 45 Hz. We were also able to remove specific spikes during repetitive firing of B4/B5.

Generalization of the technique

To explore whether this technique can be generalized to neurons having varying morphologies in vertebrates, we examined the stimulation mechanisms under different conditions. First, we examined whether the size of the neuron would affect the mechanisms of extracellular ganglionic stimulation by comparing the membrane polarization along the neuron as we varied the soma and axon diameters. We found that in the simulated neuron with the original soma diameter of 200 µm and axon diameters of 15 µm, the maximum membrane polarization occurred at the second axon segment, which would be the initiation site for generating or inhibiting action potentials (figure 17; black solid lines in both (A) and (B)). We fixed the axon diameter, and then increased or reduced the soma diameter (figure 17A; the gray solid line and black dashed line). Note that as we reduced the soma diameter to 41.2 µm, which was the value for a cat spinal motorneuron model developed by McIntyre and Grill (2000), the site of maximum membrane polarization shifted towards the end of the axon by a few axon segments (figure 17A; the black dashed line). In contrast, as we reduced the axon diameter to 9.6 µm, also obtained from the same model, the site of maximum membrane polarization shifted towards the axon hillock (figure 17B; the gray solid line). These quantitative changes will affect the predicted threshold currents. However, the overall profile of membrane polarization along the neuron did not vary qualitatively with the soma and axon diameters. Therefore, the mechanisms of extracellular ganglionic stimulation will still be valid for various sized neurons when it is applied on the side of the soma opposite to the axon.

What are the effects of dendritic trees on the extracellular stimulation technique? How does the myelination of the axon affect the response to extracellular stimulation applied on the side of the soma opposite to the axon? Since vertebrate neurons have extensive dendritic trees and myelinated axons, this could affect their response. To address these questions, we modified our NEURON model using new geometric parameters of the cat spinal motorneuron from McIntyre and Grill (2000), and replaced the unmyelinated axon with a myelinated axon including nodes of Ranvier and myelinated internodes (figure 18A; table 3). We measured the membrane polarization along the neuron in this modified model with or without the myelination of the axon as we placed the stimulating electrode both on-axis at (−221, 0) and off-axis at (−71, 50) (figure 18B; gray dashed and gray solid lines). We then added three dendritic trees surrounding the soma (McIntyre and Grill 2000; table 3). The dendritic trees only had leakage channels in the membrane. We again measured the membrane polarization along the neuron in models that had dendritic trees with or without the myelination of the axon as we placed the stimulating electrode at the identical locations (−221, 0) and (−71, 50) (figure 18B; black dashed and black solid lines). Lastly, we compared the results under these four conditions. The overall profile of the membrane polarization did not vary qualitatively after adding the dendritic trees on the soma side or after replacing the unmyelinated axon with the myelinated one. However, the site of maximum membrane polarization shifted by one to three axon segments towards the axon hillock. Therefore, the mechanisms of extracellular ganglionic stimulation will still be valid for neurons having various morphologies. As a consequence, this technique could be applicable to vertebrate peripheral ganglia that have cell bodies of neurons clustering near the surface of the ganglia.

Limitations of the NEURON and analytical models

The NEURON and analytical models used in this study had three primary limitations. First, the extracellular saline medium used in both the NEURON and analytical models was assumed to be homogeneous. In the actual ganglion, there are several sources of inhomogeneity: the sheath, the neuropil including the other embedded cells and the extracellular fluid medium within the ganglion. Some direct experimental evidence supports the hypothesis of homogeneity. In particular, the experimental results showed that the presence of the protective sheath only affected the threshold currents slightly (figure 9). If the assumption of extracellular homogeneity were invalid, the results would be quantitatively different. However, the overall results would still be qualitatively valid.

Second, both the NEURON and analytical models made several simplifying assumptions that may not apply when the electrode is very close to the soma. For example, both models assumed that the extracellular field was not affected by the neuron, which is not likely to be true at sufficiently short distances (Lee and Grill 2005). In addition, both models did not include the 3-D extent of the neuron, which may have different external voltages at different locations surrounding each segment and thus may cause a threshold current error. McIntyre and Grill (1999) showed that the results of the 3-D model corresponded closely to the simplified 2-D model, with only a 5–10% increase in the relative threshold current value for electrodes positioned over the soma. We have also partially compensated for this potential error by rotating the segments of the soma segments to remain perpendicular to the line connecting the stimulating electrode to the centre of the soma. Furthermore, in the analytical model, we assumed that any line drawn from the stimulating electrode to any point on the axon met the axon at approximately the same angle. This is unlikely to be true at short distances or when the axon curves. Although all of these effects may be significant at very short electrode-to-neuron distances, they are less relevant at the distances that are likely to be used in experiments.

Finally, the simplified analytical model (equation (4)) is a fit of the full analytical model over a relatively limited range of stimulation distances, from about one to three length constants. Above or below this range, equation (4) starts to deviate significantly from the results of the full analytical model. This limitation can be circumvented by using the full analytical model, or by fitting the full analytical model over a different range.

Potential applications of the technique

The ability to selectively stimulate single neurons could allow for many scientific and medical applications. Experimentally, extracellular ganglionic stimulation could be used to study the causal role of an individual neuron on an animal’s behaviour. For example, buccal interneurons B4/B5 are strongly activated during rejection in Aplysia, whereas they are moderately activated during swallowing, and weakly activated during biting (Warman and Chiel 1995, Ye et al 2006). By implanting electrodes into freely moving Aplysia, one could stimulate B4/B5 selectively, and thus deduce its causal role in the feeding behaviours of Aplysia in vivo.

To minimize the difficulties of positioning the electrodes over the surface of ganglia, in current studies in our laboratory, we are developing a multi–electrode device for specific stimulation of individual neurons in any ganglion with cell bodies near its surface. While multi-electrode array devices have been developed for stimulation in the central nervous system, e.g., cortex (McCreery et al 2006), spinal cord (Falowski et al 2008) and retina (Sekirnjak et al 2006), as well as peripheral nerves (Kovacs et al 1992), no such device for peripheral ganglia (e.g., autonomic ganglia) has been constructed to date.

Previous work by Tarler and Mortimer (2004) suggested that such a multi-electrode device applied to axons could be used to provide better spatial specificity than a single electrode. Our results suggest that similar specificity could be used to target neuron cell bodies. For example, if a targeted neuron is much smaller than its neighbours with their hillocks aligned, anodic stimulation by a single electrode will lose spatial specificity when the electrode is placed far away from the neurons (figure 14B). However, with a multi-electrode device, one could inject anodic currents via the electrode adjacent to the targeted small neuron while injecting cathodic currents via the electrodes adjacent to the neighbouring large neurons, and significantly improve spatial specificity (figure 14C). In addition, by combining the spatial and temporal specificity of our technique, such a multi-electrode device could be very useful for selective stimulation of multiple neurons and shaping their firing patterns in different ways, thus generating or switching motor patterns.

Clinically, this technique could be applied to peripheral ganglia to control the activity of the neurons whose cell bodies are near the surface of the ganglion. The pseudounipolar geometry of sensory neurons in these ganglia closely resembles the geometry of the unipolar neurons used in this study (Williams et al 1995). In addition, although postsynaptic sympathetic motor neurons have a more extensive dendritic tree, it is likely that it will be possible to selectively stimulate these neurons if their cell bodies are near the surface and their axons are oriented towards the centre of the ganglia (Williams et al 1995; figure 18). This may allow greater stimulation specificity than can be achieved by nerve stimulation (Navarro et al 2005).

One potential application of the technique described in this paper could be stimulation of the sensory neurons of the vagal ganglia. Vagal nerve stimulation is currently used as a treatment for epilepsy and refractory depression (Shafique and Dalsing 2006). However, its mechanism of action is not well understood, and there are a number of side effects of treatment (e.g. hoarseness, coughing, or difficulty breathing). Several of these side effects may be due to the lack of specificity of the stimulation. For example, the current procedure stimulates vagal fibres that branch off to form the recurrent laryngeal nerve. The greater specificity of our technique could allow for equal efficacy with fewer side effects. In addition, it could provide a useful tool for identifying the subpopulation of neurons responsible for the clinical effects of this treatment.

The technique could also be used for many other clinical applications. For example, our extracellular stimulation technique could allow selective inhibition of sensory neurons in dorsal root ganglia for the treatment of chronic pain in conditions such as post-herpetic neuralgia (Holsheimer 1997). Stimulation of postsynaptic neurons in sympathetic ganglia could also be useful in conditions such as urinary incontinence and diabetic autonomic neuropathy (Pedrini and Magnoni 2007).