Stimulation-induced changes at the electrode–tissue interface and their influence on deep brain stimulation

Stimulation electrodes were implanted into the left STN of 16 adult male naïve Wistar rats. Rat were chosen for their size and availability. Animals were operated in blocks with random group allocation within each block into either the stimulation group which received high frequency DBS starting 3 days after surgery (stimulation group, n= 9) or a control group in which the electrode remained inactive (no-stimulation group, n= 7). To provide histological controls, a stab incision or a craniotomy only was performed in the second hemisphere. Impedance measurements (described in section 2.1.5) were performed during surgery, daily for the first week and three times per week thereafter. After 8 weeks, rats were perfused with formalin and brains harvested for histological assessment. Analysis of the histological slides was fully or semi-automated. Blinding and assessment by two researchers was employed in operator dependent tasks. The sample size calculation with a power of 80% and α-level of 0.05 was based on a previously published impedance data by Williams et al [15] and the estimated effect of stimulation. In two additional rats, electrodes were implanted bilaterally to record the stimulation pulse and short-term changes in impedance during cessation and initiation of stimulation. All animal work was approved by the UCD Animal Research Ethics Committee (AREC 17–22) and licenced by the Health Product Regulatory Authority Ireland (AE18982-P122). The primary outcome measures were impedance, astrocyte density, microglial activation, neuronal loss and axonal damage. The animal comprised the experimental unit for impedance assessment and each hemisphere for histological assessment. Only animal completing the 8 weeks study period were included and welfare issues and technical failure resulted in exclusion.

Rats were housed in stable pairs with the following exceptions. After surgery rats were housed singly for up to 24 h to recover from the procedure and then reintroduced to their former cage-mate. Rats in the stimulation group had to be separated in the same cage, which facilitated visual, olfactory, auditory and limited tactile contact, during the lights-off period to prevent gnawing damage to the headstage. They were housed together during the lights-on period. These housing arrangements reflect a recent refinement in animal welfare for rats with cranial implants. The Rat Grimace Scale [22] and a facility specific health score system including weight checks were used for welfare assessments. These were carried out daily in the week following surgery and three times per week thereafter. Rats were assessed and treated in no set order.

General housing condition in a specific pathogen free facility included a 12/12 h light-dark cycle in a temperature (21.8 °C, SEM 0.02 °C, SD 0.21 °C) and humidity (49%, SEM 0.19%, SD 2.53%) controlled environment with access to water and standard rodent diet ad libitum. Cages contained wood chip bedding, paper shreds and enrichment (wooden balls or sticks). Rats were fed on the ground because metal food dispensers were incompatible with the inductive charging system. Cages were cleaned three times per week.

At the time of surgery rats weighted 430 g (mean, 51 g (SD), 13 g (SEM)), and were 9 weeks (2.5 weeks, 0.5 weeks) old. Stereotaxic surgery using non-rupture ear bars was performed under gaseous anaesthesia (induction with 4.5% Isoflurane in 4 l min⁻¹ oxygen and maintenance with 1.2%–1.8% Isoflurane in 1 l min⁻¹ oxygen). The depth of anaesthesia was monitored continuously using the pedal withdrawal reflex, corneal reflex and breathing. Surgical practice included temperature control, an aseptically prepared surgical field, subcutaneous (s.c.) antibiosis (pre- and 4 days post-op; Metronidazole (20 mg kg⁻¹) and Gentamicin (6 mg kg⁻¹) QD), tear replacement ointment (Vidisic, Chem.-pharm. Fabrik GmbH, Germany), local anaesthesia at the skin incision (maximum 0.05 ml 0.5% Lidocaine, diluted from Lidocaine 1%, Hameln Pharmaceuticals Ltd, UK), anaesthetic cream at the ear bars (Emla 5% cream, AstraZeneca, UK), fluid replacement and analgesia (Buprenorphine 1 h pre- and 4 days post-op (0.015–0.03 mg kg⁻¹ s.c., BID)). The analgesic dose administered depended on the rat grimace score. Warmth was provided in part of the cage for 18 h post-surgery.

For implantation, a midline skin incision was made from between the eyes to between the ears which included some skin resection. The reference points Bregma and Lambda were exposed. Three bone screws (1.59 mm, Stoelting, Ireland) were inserted into drill holes. Due to instability of headstages in the first rats operated the number of holding cranial screws was increased to four. The left and right STN location was stereotaxically defined (location −3.6 mm craniocaudal and −2.5 mm mediolateral from Bregma and −7.6 mm dorsoventral from the dura). The actual size of the rat's skull was considered and if necessary controlled for. The following procedures were performed after random allocation:

• (a)  
  Insertion of stimulation electrode for future DBS or insertion of electrode (SNEX-100, Microprobes for Life Science, Gaithersburg, USA).
• (b)  
  Insertion and immediate removal of electrode (stab incision) or craniotomy only.

During electrode insertion, local field potentials (LFPs) were recorded to help localise the STN. LFPs were recorded through a pre-amplifier (NL844) and amplifier-filter system (Neurolog, both Digitimer Ltd, UK) between the two electrode contacts with the ground electrode located at the skin incision and recorded using Spike 2 (C.E.D.) after AD conversion (1401, C.E.D.). Once positioned, the electrode was fixed with cyanoacrylic glue (Loctite, Henkel, Germany) and the skull was covered with a cap of dental cement (Dentalon plus, Heraeus Kulzer GmbH, Germany), enveloping the connector for the headstage and forming a platform to secure the headstage. The skin was re-aligned cranially and caudally using an intra-dermal suture (Vicyl 4–0, Ethicon Inc., USA).

In four rats the headstage dislodged prematurely due to infection (n = 1; excluded from the study) or mechanical dislodgement (n = 3, at 4, 6 and 6 weeks; data presented but excluded from histology and analysis). In another rat technical failure of the headstage occurred at 6 weeks (excluded from analysis). Minor side effects noted included itchiness (n = 2), bites from a cage mate (n = 2) and need for re-attachment of the stimulator (n = 2).

Two rats were implanted bilaterally in order to record the extracellular DBS pulse waveform. The voltage at the right electrode during stimulation of the left electrode was recorded at 8 weeks with a sampling frequency of 50 kHz. In one rat (rat 25), stimulation was applied for 1 h at the 4 and 8 weeks time points.

DBS was delivered using a wirelessly programmable and inductively powered headstage (S-series, Triangle BioSystems International, USA) with an inductive coil fitted around the rats' home cage to provide continuous charging of the headstage. The stimulation parameters were based on those used clinically for Parkinson's disease [23] and for therapeutic DBS in rats [24–26]. Bipolar constant current stimulation was delivered at a frequency of 130 Hz with anodic biphasic, rectangular, balanced pulses with a stimulating pulse of 60 µs duration and a charge balancing pulse of 120 µs duration with an amplitude half that of the stimulating pulse. The stimulation amplitude was set individually for each rat at the minimum of either 100 µA (six rats) or 80% of the amplitude that caused involuntary jerky forepaw movements (80 µA in two rats). The concentric electrodes were configured with an active PtIr contact (0.078 mm²) and stainless-steel reference contact (0.34 mm²) 0.5 mm apart throughout the study. The applied stimulation lies within the effective range reported for suppression of motor symptoms in 6-OHDA rats in the literature [24–26]. Pulse charge per phase and charge density were calculated for the maximal amplitude pulse. Continuous stimulation was delivered mean 6:57 h d⁻¹ (SEM 0.01 h, SD 0.19 h). Continuous stimulation for 24 h d⁻¹ was not possible due to technical limitations of the inductive charging system.

Impedance of the electrode and surrounding tissue was measured using the two-electrode technique using a precision LCR Meter (E4980AL, Keysight, USA). Impedance was measured at >80 frequencies in the range from 20 Hz to 300 kHz at an amplitude of 20 µA. Impedance was measured daily in the morning for 1 week and three times a week, thereafter, in the home cage. Stimulation was discontinued during impedance recordings. To assess the reversibility of these changes, DBS was stopped in a rat receiving DBS at 6 weeks and was applied for 1 h in a rat that did not previously receive DBS at 4 and again at 8 weeks.

At the end of 8 weeks rats were anaesthetised (induction with 4.5% Isoflurane in 4 l min⁻¹ oxygen; maintenance with 1.2%–1.8% Isoflurane in 1 l min⁻¹ oxygen). A final impedance spectrum was recorded. Anaesthesia was deepened until the pedal withdrawal reflex was completely abolished and the animal was trans-cardially perfused with phosphate buffered saline (Sigma-Aldrich), followed by 10% formalin (Sigma-Aldrich), after administration of heparine (625 IU/rat, INNOHEP 2500 IU, LEO Pharma, Denmark). The headstage and electrode were removed after fixation. The brain was harvested, and each hemisphere cut to allow horizontal slicing of the electrode tract at the level of the two contacts.

The brain tissue was paraffin embedded and 3.5 µm slices were cut for standard haematoxylin & eosin staining and immunocytochemistry for glial fibrillary acidic protein (GFAP) for astrocytes, Iba1 to for microglia, neuron specific enolase (NSE) for neurons and neurofilament (NF) for axons and dendrites. Slices were first dewaxed and rehydrated (Leica autostainer, Leica, Germany). Histological slides were examined by a veterinary pathologist (HJ). Five hemispheres with electrodes that were stimulated, seven hemispheres with electrodes that were not stimulated, four hemispheres with a stab incision and eight control hemispheres were available but some slides were lost due to technical problems.

Heat mediated antigen retrieval was required for Iba1 (heating for 20 min in pre-heated 0.01 M tri-sodium citrate at pH 6.0) and NSE (heating for 10 min in pre-heated 0.01 M tri-sodium citrate at pH 6.0). An endogenous peroxidase block was performed using 3% H₂O₂ in ethanol. For GFAP a Proteinase K step was included (Digest-All, Invitrogen). Blocking was performed with normal horse serum for 30 min at room temperature (ImmPRESS^TM Kit, Vectorlabs, USA). Then the slides were incubated with the primary and following secondary antibody. For astrocytes anti-GFAP (polyclonal rabbit anti-GFAP, Z033401, DAKO, Denmark) was used at 1:400 dilution for 60 in at 37 °C with an ImmPRESS^TM VR Reagent Kit anti-rabbit IgG (MP-6401, Vectorlabs) as secondary antibody and detection system. For microglia anit-Iba1 (goat anti-human plyclonal AIF1/Iba1, LS-B2402 LSBio, USA) was used at 1:500 for 60 min at room temperature with an ImmPRESS^TM HRP Reagent Kit anti-goat IgG (MP-7405, Vectorlabs). For neurons anti-NSE (anti-rabbit polyclonal NSE, ab53025, Abcam, UK) was used at 1:100 for 24 h at 4 °C with an ImmPRESS^TM VR Reagent Kit anti-rabbit IgG (MP-6401, Vectorlabs). For neural processes NF (monoclonal mouse anti-NF, M0762, DAKO) was used at 1:125 for 60 min at room temperature with an ImmPRESS^TM VR Reagent Kit anti-mouse IgG (MP-6402, Vectorlabs). The secondary antibody was applied for 30 min at room temperature. Fast acting 3,3'-diaminobenzidine (Sigma-Aldrich) was used for detection. Slides were counterstained with haematoxylin before dehydration and cover slipping. Slices were then scanned at 40× magnification (ScanScope XT, Aperio Technologies, USA).

Scanned images of immunocytochemistry slides were computationally analysed using custom developed code in MATLAB (Mathworks, USA). For GFAP, the density of stained pixels as a function of distance from the electrode edge was quantified as the percentage difference in the number of stained pixels per unit area compared with a control area in the same slide. For Iba1, individual cells were identified using a custom developed machine learning model to differentiate full microglia from partial cells and noise. All cells in the area of interest (600 µm from electrode centre) were automatically identified based on their shapes and colour for a subset of images. A graphical user interface presented the segmented cells in a random and blinded fashion and cells were then classified by two operators (JE and HJ) into activated (bushy or amoeboid) and inactive (ramified) microglia to create a training set. The training set was then used to automatically segment the cells in the rest of the images into the activated and inactive categories. Total microglia profiles, activated and inactive microglia were compared for each group. For NSE, the location of NSE positive cells was marked computer assisted and the number of neuron profiles in relation to distance from the electrode edge counted. For NF, the density of stained pixel as a function of distance from the electrode edge was quantified as the percentage difference in the number of stained pixels compared with a control area in the same slide. For all the segmentation methods mentioned above, image contrast was first enhanced using a quaternion based approach before using the red, green and blue (RGB) channels of the image to find the stained areas.

In vivo impedance data were analysed using a three-way repeated-measures analysis of variance (ANOVA) with the factors stimulation group (between subjects), time and frequency (within subjects) including ten frequencies (20 Hz, 50 Hz, 100 Hz, 500 Hz, 1 kHz, 5 kHz, 10 kHz, 50 kHz, 100 kHz and 300 kHz) and 12 time points (baseline, mean of day 2 and 3, day 3 and 5, day 6 and 7, day 8 and 9, day 10 and 12, week 3, week 4, week 5, week 6, week 7 and week 8) (MATLAB, Mathworks). Post-test used the Tukey–Kramer correction. In vitro impedance recordings at 14 days and immunohistochemistry results were similarly analysed using a two-way repeated-measures ANOVA with the factors frequency and group or distance and group, respectively (MATLAB, Mathworks). A power of 80% and criterion for statistical significance of p < 0.05 were used.

The EDL of the concentric bipolar electrodes (SNEX-100, Microprobes for Life Science) was characterised in saline solution. Electrode impedance was measured using electrochemical impedance spectroscopy with the electrode in 0.9% saline solution, following immersion for 24 h, using a precision LCR Meter (E4980AL, Keysight). Impedance measurements were performed using the two-electrode technique in the range from 20 Hz to 300 kHz with an applied current amplitude of 20 µA in five electrodes. Impedance was also recorded in 0.2 mg ml⁻¹ albumin bovine serum albumin (BSA, Sigma-Aldrich) in 0.9% saline solution over 14 days with (n= 6) and without (n= 10) the application 130 Hz stimulation using the same balanced pulse as in vivo (rectangular biphasic, 100 µA, 60 µs, balancing pulse of half the amplitude).

SNEX-100 electrodes immersed in protein solution for 14 days with (n= 4) or without (n= 3) stimulation with a rectangular balanced pulse of 130 Hz frequency, 60 µs pulse duration and 100 µA amplitude were stained with a universal protein stain. A Pierce Silver Stain Kit (2612, ThermoScientific, Dublin, Ireland) was used for the stain. Staining was performed as per instructions. After washes with 10% ethanol and ultrapure water, 1 min incubation in the Sensitizer Working solution was performed, followed by 30 min incubation in the Stain working solution (silver nitrate) and development for 2 min which was stopped with 5% acetic acid. Electrodes were imaged with a stereomicroscope (SZR-180, Opticamicroscopes Italy, Italy). Semi-quantitative analysis of the electrode area covered in protein was performed (MATLAB). Two images were taken for each electrode contact, one of each side. In each image, half of the electrode was assumed to be visible (covered or not), the outline of the contact was semi-manually segmented by an operator blinded to group allocation and the ratio of pixels covered to pixels not covered in the segmented area was computed and converted to mm² using the known surface of the contacts.

A 3D-piecewise heterogeneous FEM of the rat brain was used in combination with the in vitro and in vivo impedance data to estimate the electrical properties of the ETI in the stimulated and unstimulated conditions. The EDL equivalent circuit parameters were calculated using the impedance spectrometry data for the active electrode in saline solution. Equivalent double layer properties were then applied using a thin layer approximation in the FEM and a parametric sweep method was applied to estimate the dispersive (frequency-dependent) properties of the encapsulation tissue surrounding the chronically implanted electrode under stimulated conditions. Assuming that the electrical conductivity and permittivity of the encapsulation tissue did not change with stimulation, the properties of the EDL during unstimulated conditions were then estimated by iteratively solving for the impedance at the electrode using FEM to converge on the experimentally recorded impedance values for the unstimulated condition. Finally, the FEM was coupled to a population of multicompartment neuron axon models representing branching axon collaterals within the STN [27, 28], to estimate the influence of stimulation-induced changes in the ETI on the extent of neural activation under stimulated and unstimulated conditions.

To estimate the equivalent EDL parameters in vitro, the impedance spectrum of the electrode in physiological solution was fit to a circuit model similar to that proposed by McAdams et al [29]. The equivalent impedance of a 10 nm thick EDL was represented as a parallel combination of a constant phase angle element, ${Z_{{\text{cpe}}}}$, and the overpotential independent form of the charge transfer resistance, ${R_{{\text{ct}}}}$,

$$\begin{equation}{Z_{{\text{cpe}}}} = K{\left(\, {j\omega } \right)^{ - \beta }}\end{equation} \tag{ 1 }$$

$$\begin{equation}{R_{{\text{ct}}}} = \frac{{RT}}{{nF{I_0}}}\end{equation} \tag{ 2 }$$

where $K$ and $\beta$ are constants denoting the magnitude of the impedance of the EDL and inhomogeneities at the surface of the electrode, respectively; $R$ is the universal gas constant, $F$ Faraday's constant, $\,T\,$ temperature, $\,n$ the number of electrons per molecule, and ${I_0}$ the exchange current density. In this case, the electrode was considered as a partially polarizable electrode where the electrode behaves as a pseudocapacitor and the faradic component was assumed to be zero due to electrode reaction being infinitely slow.

A heterogeneous rat model with geometrical structures comprising a cerebrospinal fluid (CSF), STN, grey and white matter of the brain was created using image segmentation of Waxholm Space atlas of the Sprague Dawley rat Brain (WSSD) atlas [30]. The segmented masks of the different brain tissues were converted to a geometric model using Simpleware ScanIP software (Synopsys, USA). The microelectrode was positioned within the STN with the aid of WSSD atlas as shown in figure 1(b). Finally, a surrounding layer of tissue of 100 μm and 200 μm thickness as indicated by the extent of the glial scar in the histological analysis was created in the geometry to represent the encapsulation layer for chronic conditions under unstimulated and stimulated conditions, respectively, see figure 3.

The potential within the FEM was calculated using the time harmonic electric-quasi static Laplace equation, where magnetic and wave propagation effects were neglected [31–33]:

$$\begin{equation}\nabla \cdot \left[ {\left( {\sigma \left( \omega \right) + \omega {\varepsilon _0}{\varepsilon _r}\left( \omega \right)} \right)\nabla \phi } \right] = {\text{0}}{\text{.}}\end{equation} \tag{ 3 }$$

$\sigma \left( \omega \right){ }$ and ${\varepsilon _r}\left( \omega \right)$ are the electrical conductivity and relative permittivity, $\omega$ is angular frequency, ${\varepsilon _0}$ permittivity of free space, and ϕ scalar potential. Maxwell's equation in this form considers the frequency dependent conductivity and permittivity, where both conductivity and permittivity were described using the Cole–Cole equation representation.

Dispersive electrical properties of the rat brain grey matter, white matter and encapsulation tissue were incorporated in the FEM using the four pole Cole–Cole model with parameters described by Gabriel et al [34]:

$$\begin{equation}{\varepsilon _r}\left( \omega \right) = {{{\varepsilon }}_\infty } + \sum\limits_{n = 1}^4 \frac{{{{\Delta }}{\varepsilon _n}}}{{1 + {{\left(\, {jwt} \right)}^{\left( {1 - \alpha } \right)}}}} + \frac{\sigma }{{j\omega {\varepsilon _0}}}\end{equation} \tag{ 4 }$$

where, $\Delta {\varepsilon _n}$ is difference between the static relative permittivity and high frequency relative permittivity for pole n, ${\varepsilon _\infty }$ is the high frequency relative permittivity, $\omega$ is the angular frequency, $\alpha$ is a distribution parameter for pole n, $\sigma$ is ionic conductivity, and $\tau$ is the relaxation time of pole n. The Pt/Ir active contact, stainless steel ground contact and polyimide insulation were purely conductive with electrical conductivity $4.5\; \times \;{10^6}$, $9 \times {10^5}\,$ and $1 \times {10^{ - 6}}{ }$ S m⁻¹ [35], respectively.

During bipolar stimulation in the computational model, the platinum–iridium contact of the microelectrode was assigned as the active terminal to which a constant voltage or current was applied, the stainless-steel contact was assigned as ground. Neumann boundary conditions were applied to the insulating parts of the electrode and outer surface of the skull [32].

The ETI was implemented using the thin layer approximation for both voltage-controlled stimulation and current controlled stimulation [36]. With thin layer approximation, it was assumed that total current density passing through the ETI layer is equal to the normal component of finite thickness layer:

$$\begin{equation}n.J = \frac{{\left( {\sigma + i\omega {\varepsilon _0}{\varepsilon _r}} \right)\left( {{\text{dV}}} \right)}}{t}\end{equation} \tag{ 5 }$$

where, $\,n.J$ is the normal current density at electrode surface, ${\text{dV}}$ is the voltage across a layer of thickness $t$. The intrinsic properties and thickness of ETI were replaced with total admittance calculated from equivalent circuit parameters:

$$\begin{equation} - n.J = \left( {{\text{dV}}} \right){Y_{{\text{ETI}}}}\end{equation} \tag{ 6 }$$

where, ${Y_{{\text{ETI}}}}$ is the inverse of the estimated impedance, ${Z_{{\text{cpe}}}}$.

A parametric sweep method was used to estimate the electrical properties of the encapsulation tissue where the Cole–Cole parameters of the encapsulation tissue were swept between the established values for white matter and 175% of the white matter properties [34]. Solving the finite element model for each set of parameters, the parameters for which the deviation between the experimentally recorded and simulated impedance data, across the frequency range from 20 Hz to 300 kHz, was minimised were identified. Assuming linearity at the EDL interface [37], the impedance at the electrode, $Z$, can be calculated using Ohm's law:

$$\begin{equation}Z = \frac{V}{{{{\mathop \smallint \nolimits }}{{}}{I_{\text{d}}}{\text{.d}}s}}\end{equation} \tag{ 7 }$$

where V is the electric potential calculated using the Laplace equation over active surface area, and ${I_{{\text{d }}}}$ is the normal current density around active electrode and ds the electrode surface area.

The piecewise heterogeneous rat brain model with DBS electrode was meshed using Simpleware Simpleware ScanIP (Synopsys). The model consisted of 5 million tetrahedral elements. A quadratic interpolation function was used on each tetrahedral element to approximate the scalar potential. Finally, the discretised FEM was solved using COMSOL Multiphysics (COMSOL, USA) using the BiCGStab iterative solver with a geometric multigrid preconditioner.

To incorporate the influence of dispersive tissue properties on the stimulation waveform in the surrounding tissue, the electrical potential was estimated for 800 harmonics of the fundamental stimulation frequency (130 Hz), equation (1), to obtain the transfer function of the tissue at these frequencies. The square wave stimulus pulse train, with pulse duration 60 μs and stimulation frequency of 130 Hz, was transformed to the frequency domain using the fast Fourier transformation (FFT). The FFT of the stimulus pulse train was then multiplied by the transfer function estimated at a given point within the surrounding tissue to obtain a frequency domain estimate of the potential at that point before taking the inverse FFT of the resulting signal to obtain the time domain voltage at the point of interest:

$$\begin{equation}{Y_{p\left( {x,y,z} \right)}}\left( \omega \right) = {V_{{f_{p\left( {x,y,z} \right)}}}}\left( \omega \right) \times {\text{FFT}}\left( {x\left( t \right)} \right)\end{equation} \tag{ 8 }$$

$$\begin{equation}{y_{p\left( {x,y,z} \right)}}\left( t \right) = {\text{IFFT}}\left( {Y\left( \omega \right)} \right)\end{equation} \tag{ 9 }$$

where, ${Y_{p\left( {x,y,z} \right)}}\left( \omega \right)$ is the Fourier transform of extracellular potential at a point $p\left( {x,y,z} \right)$ in the STN, ${V_{{f_{p\left( {x,y,z} \right)}}}}\left( \omega \right){ }$ is the potential at point $p$ due to a unit source at the electrode calculated using the finite element model, $x\left( t \right)$ is the applied DBS pulse train and ${y_{p\left( {x,y,z} \right)}}\left( t \right)$ is the extracellular potential at point $p$ due to the DBS pulse train.

To determine the extent of activation by STN DBS of afferent collaterals within the STN, 1000 idealised multi-compartment cable models of an axon and branching collateral were positioned inside the STN. Axon collaterals were positioned within the STN, parallel to one another, and orientated to project in the direction. The axon and collateral model was based on that used previously by Lowery and Kang [27, 38] with membrane parameters based on an experimental study in mice developed by Foust et al [39]. This model captures the threshold of activation of the axon and collateral by considering the properties of the model neuron along with the electrode geometry, the ETI, and the heterogeneity and electrical properties of brain tissue incorporated in the rat DBS FEM model. Multi-compartment axon collaterals were simulated to be 500 µm long with a diameter of 0.5 µm and were comprised of 11 segments with ten nodes. Each collateral was connected to a myelinated axon comprised of ten nodes each of length of 2 μm and diameter of 0.5 μm separated by ten internodes of length 500 μm and diameter 1.2 μm [39]. At each instant in time, the time dependent extracellular potential computed from the FEM model was applied to each node of each collateral segment in NEURON using the extracellular mechanism. The activation threshold of each collateral was defined as the minimum current or voltage at which action potential propagation was observed. The neuron models were simulated in the NEURON simulation environment [40] and implemented in Python using the PyNN API package [41]. The model was numerically integrated using the Crank–Nicholson method with a 0.01 ms timestep.