Cortical modulation by exogenous electric fields and the dipolar nature of cortical columns

1 Cortical modulation by exogenous electric fields and the dipolar nature of cortical columns Joana Coveloa, Jaume Colomb, Julia Weinerta, Mattia D’Andolaa, Alain Destexheb and Maria V. Sanchez-Vivesa,c aInstitut d’Investigacions Biomèdiques August Pi i Sunyer (IDIBAPS), C/Rosselló 149–153, 08036 Barcelona, Spain bCentre National de la Recherche Scientifique (CNRS), Paris-Saclay University, NeuroPSI, Saclay, France cInstitució Catalana de Recerca i Estudis Avançats (ICREA), 08036 Barcelona, Spain Corresponding author: Maria V. Sanchez-Vives ([email protected]) 2 Abstract Cortical activity can be modulated by endogenous and exogenous electric fields (EFs). Recent experimental and computational data suggested that endogenous EF-mediated effects are compatible with electric dipoles, which contribute to the synchronization of neighboring cortical columns. Consistently, exogenous EFs created by means of transcranial direct-current stimulation (tDCS) have shown that the orientation of current flow determines the effect of the intervention. Here, we investigated the impact of an exogenous EF’s orientation on cortical modulation. We hypothesized that electric dipoles orthogonal to the cortical surface are responsible for the impact of the EF’s orientation on cortical modulation. We tested this hypothesis experimentally in cortical slices and in silico in a mean-field computational model of cortical columns. In the experimental setting, we applied constant exogenous EFs (−/+ 3 V/m) with different orientations (0°, 45° and 90°) to cortical slices expressing spontaneous slow oscillations (ca. 0.3 Hz). We found that DC fields orthogonal to the cortical surface had a maximum modulatory effect, while the efficacy decreased with the rotation of the EF, having a null effect when parallel to the cortical surface. These results were successfully reproduced in a computational model of a cortical column with dipolar properties. The model suggested that the effect of the exogenous EF on neuronal populations is proportional to the cosine of the angle between the direction of the applied EF and the vertical axis of the dipole. Overall, our experiments support the critical role of electric dipoles in understanding the impact of exogenous EFs on cortical activity modulation. Keywords cerebral cortex; tDCS; neuromodulation; cortical column; electric dipole; computational model 3 Introduction The recurrent interaction between neurons in the cerebral cortex generates periods of synchronized synaptic activity (Up states) followed by periods of silence (Down states) that oscillate at a frequency of ~1 Hz (Steriade et al., 1993; Stern et al., 1997; Lampl et al., 1999). These slow oscillations (SO) dominate the cortical network during slow-wave sleep (Massimini et al., 2004; Adamantidis et al., 2019) and anesthesia (Andersen and Andersson, 1968; Alkire et al., 2008; Ruiz-Mejias et al., 2011; Sarasso et al., 2015) and have been suggested to be the default emergent activity of the cortical network (Sanchez-Vives et al., 2017). During the slow-wave state, the rhythmic fluctuations in population activity are accompanied by ion fluxes that generate endogenous electric fields (EFs). Consequently, the endogenous EFs induce changes in the membrane voltage of the neurons that in turn influence the population activity, forming a feedback loop (Frohlich and McCormick, 2010; Anastassiou et al., 2011; Anastassiou and Koch, 2015). In this feedback loop, it is difficult to distinguish between the impact of EFs on neuronal activity and vice versa (Rebollo et al., 2021). To investigate the isolated effect of endogenous EFs on network activity, Rebollo et al. (2021) explored whether the endogenous EFs generated by the SO of one network could modulate or entrain the spontaneous SO of a synaptically disconnected adjacent network. Using an in vitro model of cortical slices, they observed that this modulation could occur due to the ephaptic coupling of the endogenous EF. Moreover, the endogenous EF modulation of adjacent columns exhibited properties of an electric dipole interaction. Furthermore, using a computational model of populations of electric dipoles, the authors demonstrated that the potential gradients measured experimentally across the two networks were sufficient to explain the ephaptic effects (Rebollo et al., 2021). Endogenous EF modulation also has an interaction when applying exogenous EFs to the cortical network. Considering the dipolar nature of cortical columns, it is important to take into account the orientation of an exogenously applied EF as it might be crucial for effectively modulating the network. In animal studies, the direction of current flow relative to cortical columns has been shown to determine the response to direct current (DC) (Bikson et al., 2004; Rahman et al., 2013). Specifically, current directed normally to the cortical surface, 4 which corresponds to the direction of the primary dendritic axis of the cortical pyramidal neurons (Radman et al., 2009), has been shown to induce polarity-specific (anodal/cathodal) excitability changes (Bindman et al., 1964), while an EF perpendicular to the apical-dendritic axis did not induce somatic polarization (Bikson et al., 2004). Even though the direction of the current flow in relation to the cortical columns cannot be so easily controlled in the human gyrencephalic cortex, transcranial direct current stimulation (tDCS) models suggest that controlling the direction of the current flow through the target area can improve the efficacy of the intervention, such that tDCS-induced fields orthogonal to (but not parallel with) the cortical surface modulate transcranial magnetic stimulation motor-evoked potentials (Rawji et al., 2018). In the current study, we investigated the angular orientation of exogenous EFs to assess the hypothesis that electric dipoles aligned with the cortical columns are responsible for the impact of EF direction on cortical modulation. In cortical slices expressing spontaneous SO (ca. 0.3 Hz), we applied constant exogenous EF (−/+ 3 V/m) with different orientations (approximately 0°, 45° and 90° between the cortical surface and the DC electrodes) and investigated whether the rotation of the EF correlated with the efficacy of the DC modulation. Our experimental results were reproduced in a mean-field computational model of a cortical column with dipolar characteristics, based on the assumption that the membrane potential shift created by an external EF is proportional to the cosine of the EF angle being applied. Overall, our findings clearly suggest that the angular orientation of the exogenous EF has an impact on cortical modulation due to the dipolar nature of cortical columns. 5 Experimental Procedures Preparation and maintenance of cortical slices Adult ferrets (4–8 months, either sex, n=10; Euroferret, Denmark) were deeply anaesthetized with isoflurane and sodium pentobarbital (40 mg/kg) and decapitated. The entire forebrain was rapidly removed to oxygenated cold (4–10°C) bathing medium. Acute coronal slices (400-μm-thick) were cut from the occipital cortex containing primary and secondary visual cortical areas (areas 17, 18, and 19) from both hemispheres using a Microm HM650V vibration microtome (Thermo Scientific, MA, USA). To increase tissue viability during slice preparation, we implemented an adapted sucrose-substitution technique developed by Aghajanian and Rasmussen (1989). Slices were placed in an interface-style recording chamber (Scientific Systems Design Inc., ON, Canada), and bathed for 30 min in an equal mixture of the sucrose-substituted solution and ACSF (artificial cerebro-spinal fluid). Slices were then maintained for 1 h in ACSF for recovery and in an in vivo-like modified ACSF (Latham et al., 2000) throughout the rest of the experiment. ACSF contained (in mM): NaCl, 126; KCl, 2.5; MgSO4, 2; NaH2PO4, 1; CaCl2, 2; NaHCO3, 26; dextrose, 10. The in vivo-like modified ACSF had the same ionic composition, except for different levels of (in mM): KCl, 4; MgSO4, 1 and CaCl2, 1. Solutions were aerated with 95% O2, 5% CO2 to a final pH of 7.4. The temperature was kept at 34.5–36.0°C. Electrophysiological recordings started following a recovery period of at least 40 min after changing to the in vivo-like modified ACSF. All experiments were conducted in accordance with the European Union Directive 2010/63/EU and approved by the local ethics committee. Electrophysiological recordings Extracellular local field potentials (LFP) were recorded using a multi-electrode array (MEA) with 16 gold electrodes plated with platinum black (see (Illa et al., 2015)) for further details). The electrodes were organized in diodes or triodes, covering both deep and superficial layers and three equidistant (1.5 mm) cortical columns (Fig. 1A). The signal was amplified by a factor of 100 using a PGA16 Multi Channel System amplifier (Multichannel Systems MCS, GmbH-Harvard Bioscience Inc., MA, USA), digitized using a Power 1401 CED interface (Cambridge Electronic Design, Cambridge, UK) at a sampling frequency of 10 kHz and 6 acquired with the Spike2 software (Cambridge Electronic Design). All recordings were referenced to an Ag-AgCl pellet submerged in the in vivo-like modified ACSF. Stimulation with DC electric fields The EF intensity in relation to the applied current was configured before slices were placed in the set-up. To do so, the 16-channel MEA was placed in the center between the two stimulation electrodes and a train of pulses (20 Hz, 30 s) was applied for linearly increasing currents (100–600 μA) for both polarizations. For each applied current we then computed the voltage gradient between each possible pair of vertically aligned electrode sites (n=8) as the averaged maximum difference between the signal recorded at these electrode pairs. The EF intensity was then defined for each electrode pair as the voltage gradient divided by the distance between the corresponding electrode pair. A current versus field intensity plot was then generated by averaging the EF intensities across all electrode pairs, to visually confirm a linear relationship between the applied current and the final EF intensity (see Fig. 1B). As the stability of the field intensity can only be assured as long as the relation between current and field intensity remains linear, we applied fields only in the range −5 to +5 V/m, where linearity could be approximated. Furthermore, to ensure spatial homogeneity of the field intensity (i.e., a constant voltage gradient) we interpolated the area spanned by the two stimulation electrodes based on the potentials measured at the 16 recording sites (see Fig. 1C). To test the effect of EF orientation on cortical modulation, we applied positive and negative exogenous DC fields with an intensity of 3 V/m for 200 s each, with 500 s of recovery in between the stimulation periods. The two Ag-AgCl electrodes were placed 4–8 mm in three different orientations with respect to the cortical layers: ≈ 0°, 45° and 90° between the cortical surface and the DC electrodes. EFs have been shown to induce orientation-dependent effects. Positive fields increase the excitability of pyramidal neurons, while negative fields decrease it (Purpura and McMurtry, 1965; Jefferys, 1979; Gluckman et al., 1996). Electrical stimulation protocols were defined in Spike2 (Cambridge Electronic Design), programmed using a Power1401 ADC/DAC (Cambridge Electronic Design) and converted to current through a stimulus isolator (360A, World Precision Instruments, FL, USA). 7 Data analysis Up/Down state detection We estimated the multi-unit activity (MUA) from the LFP as previously reported (Reig et al., 2010; D’Andola et al., 2018a; Barbero-Castillo et al., 2021). Briefly, the population firing rate can be reliably estimated from the power variations in the Fourier components at high frequencies of the LFP (Mattia and Del Giudice, 2002). Therefore, the MUA signal was computed as the average power of the normalized spectra of the LFP at a high-frequency band (200–1500Hz) and subsequently logarithmically scaled (logMUA) to counterbalance large fluctuations of nearby spikes. By defining duration and amplitude thresholds in the log(MUA) signal, we computed different parameters to characterize the slow wave activity (Figs 1C–F), such as the oscillatory frequency and the duration of Down states. When considered appropriate due to the noise levels, the analysis was performed directly on the LFP recordings. In this case, we computed a moving variance filter followed by the same threshold method. Data analysis was conducted using a custom-made Matlab script (MathWorks Inc.). Statistical analysis All averaged values are represented as (mean ± standard error of the mean (SEM)). The normality of the data distribution was assessed through a one-sample Kolmogorov–Smirnov test. As none of the samples followed a normal distribution, we used a Mann-Whitney U-test to check for statistically significant differences in the data. Statistical tests were performed in Matlab (MathWorks Inc.). Differences were considered statistically significant at p<0.05 (represented by *p<0.05, **p<0.01). Linear regressions were calculated resorting to the polyfit function integrated in Matlab (MathWorks Inc.). 8 Fig. 1. Experimental set-up, electric field (EF) calibration and Up state detection. (A) Scheme of the experimental set-up showing the placement of the EF towards the cortical layers and the multielectrode recording array covering deeper and upper layers. (B) Example of calibration of EF intensity based on the applied stimulation current. (C) Isopotential lines across the area spanned by the electrodes (gray bars) for 100 μA (top row) and 400 μA (bottom row) for negative (left column) and positive (right column) current application. Field intensity is measured as the difference in the field 9 potential between two vertically aligned points divided by the distance of the points. (D) Detection of Up states (red trace) was performed on the log(MUA) trace (top), obtained from the original local field potential (LFP) (bottom). Note: LFP signal was band pass filtered between 0.05 and 1500Hz (second-order Butterworth filter). (E) Relative firing rate (gray scale) for each Down/Up transition aligned at Up state onset (t=0). (F) Averaged relative firing rate of the example shown in (D+E). Computational modeling Effect of exogenous EF on membrane depolarization We applied the theory of linear cable in a polarized extracellular medium (Bédard et al., 2004) to estimate the effect of the exogenous EF on membrane depolarization. Applying the solution to the cable equation in polarized medium presented by (Anastassiou et al., 2010), the membrane potential across a dendrite 𝑉𝑚 in these conditions can be defined as 𝑉𝑚(𝑋)=𝑉𝑖(𝑋)−𝑉𝑒(𝑋)= − 𝛺2 𝛺2+1𝑠𝑖𝑛 (𝛺𝑋+ 𝜙𝑠) + 𝛺2 𝛺2+1(𝑐𝑜𝑠ℎ (𝑋) 𝑡𝑎𝑛ℎ (𝐿) 𝑐𝑜𝑠 (𝜙𝑠) − 𝑐𝑜𝑠ℎ (𝑋) 𝑠𝑖𝑛ℎ (𝐿) 𝑐𝑜𝑠 (𝛺𝐿+𝜙𝑠) −𝑠𝑖𝑛ℎ (𝑋) 𝑐𝑜𝑠 (𝜙𝑠) ) (1), The solution in dimensionless quantities is equal to 𝛺 =2𝜋𝑓𝑠𝜆𝑒𝑙 𝑋 = 𝑥 𝜆𝑒𝑙 𝑉𝑖= 𝑣𝑖−𝑣𝑟𝑒𝑠𝑡 𝑣0 (2), Considering the extracellular potential 𝑣𝑒 in terms of harmonic functions 𝑣𝑒=𝑣0𝑠𝑖𝑛 (𝛺𝑋+ 𝜙𝑠) (3) the exogenous EF is 𝐸 =− 𝑑𝑣𝑒 𝑑𝑥= −𝐸0𝑐𝑜𝑠 (𝛺𝑋+ 𝜙𝑠) (4) where 𝐸0= 𝑣0𝛺/𝜆𝑒𝑙. 16 Fig. 4 Experimental and computational data support the role of electric dipoles on the impact of both endogenous and exogenous EF in the cerebral cortex. Down state duration (top) and slow wave frequency (bottom) at approximately 0° (blue), 45° (yellow) and 90° (red) between the cortical columns and the direction of the EF, for both the mean field simulation and the EF recordings, after adjusting the model with the best parameter set (τadapt=1.4s, βτ=0.3 μV/Hz). 17 Discussion The direction of an applied field relative to the cortical columns is crucial in determining the effectiveness of DC modulation (Bikson et al., 2004; Rahman et al., 2013; Rawji et al., 2018). Here, we aimed to explore the influence of electric dipoles perpendicular to the cortical surface in shaping the effect of EFs orientation on cortical modulation. To do so, we applied constant exogenous EFs (−/+ 3 V/m) with different orientations (0°, 45° and 90°) to cortical slices expressing spontaneous slow oscillations (ca. 0.3 Hz). Our findings revealed that DC fields orthogonal to the cortical surface have a maximum modulatory effect. With the rotation of the EF, the efficacy decreased, with no modulation observed for EFs parallel to the cortical surface. By reproducing these results in a computational model of a cortical column with dipolar properties, we presented evidence supporting the critical role of electric dipoles in understanding the impact of exogenous EFs on cortical activity modulation. Previous studies have already suggested that homogeneous EFs applied perpendicular to the cortical layers can modulate not only the frequency of spontaneous SO but also the intrinsic properties of neurons, such as the firing rate (Frohlich and McCormick, 2010; Reato et al., 2010; D’Andola et al., 2019). D’Andola and colleagues have recently demonstrated the potential of direct current (DC) exogenous fields orthogonal to the cortical surface to modulate emergent activity patterns, with very precise modulation of SO (D’Andola et al., 2018b, 2019). Consistent with these findings, we were able to precisely tune slow wave activity using exogenous DC fields parallel to the cortical columns. Positive fields resulted in a significant increase of the slow wave frequency, due to a shortening of the down state, while negative fields led to a significant decrease of the slow wave frequency, through an elongation of the down state duration. However, when a field is applied to the folded cortex, there are local fluctuations in current flow intensity and direction (Rawji et al., 2018). In fact, when we applied EFs at an approximate angle of 45° in relation to the cortical columns, the degree of modulation elicited by the DC fields decreased. While still statistically significant, the observed changes in slow wave frequency and down state duration were relatively less pronounced when compared to the orthogonal case. Fields applied orthogonally to cortical columns had a null effect on cortical modulation, supporting 18 the importance of EF direction in relation to cortical columns for cortical neuromodulation (Fig. 2). As illustrated in Fig. 4, our computational results reproduced the effect of EF orientation on cortical modulation observed experimentally. The mean-field computational model, derived from the model of interacting dipoles suggested by Rebollo et al. (2021), assumes the cortical column as a vertically oriented dipole. The model proposes that the shift in 𝑉𝑚 created by an exogenous EF is proportional to the cosine of the EF angle being applied and to a constant 𝛾𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙. Therefore, a field applied at approximately 90º has no effect on cortical modulation. Similarly, Rushton has previously suggested that the threshold of depolarization of a nerve is inversely proportional to the cosine of the angle between the current and the nerve (Rushton, 1927). Applying Rushton’s cosine principle to the cortical column, Fox et al. showed that to achieve successful cortical excitation using transcranial magnetic stimulation (TMS) it is critical to consider the orientation of the induced EF relative to the columnar functional organization of the cortex (Fox et al., 2004). The hypothesis that electric dipole interactions between cortical columns can contribute to the understanding of DC stimulation orientation selectivity goes one step further from the basis suggested by Fox and colleagues. In the clinic, weak DC fields are delivered non-invasively to the brain in a technique known as tDCS, which has been reported to alter cognitive and behavioral functions (Fröhlich, 2014). Even though the resulting fields are not strong enough to trigger action potential discharges, tDCS enables shifts in the resting membrane potential, either towards polarization or depolarization. In turn, these potential fluctuations affect the probability of action potential firing (Polanía et al., 2018). Consequently, tDCS has been suggested to induce suppression of epileptiform activity (San-juan et al., 2015) by decreasing cortical excitability in humans (Rahman et al., 2013; San-juan et al., 2015) and to modulate cortical excitability in patients with disorders of consciousness (Bai et al., 2017, 2018). However, the understanding of the mechanisms of action of such intervention on cortical dynamics is still limited (D’Andola et al., 2018b; Liu et al., 2018; Sudbrack-Oliveira et al., 2021) and previous studies have pointed out an inconsistency in tDCS outcomes (López-Alonso et al., 2014; Wiethoff et al., 2014; Vergallito et al., 2022). As not all studies account for the direction selectivity of tDCS 19 effects, substantial inter-individual variability in the current direction likely contributes to the variable treatment response to tDCS (Albizu et al., 2020; Evans et al., 2022). Hence, it is of pivotal importance to understand the mechanisms underlying the differential modulation of cortical activity with the applied exogenous EF direction in tDCS to improve its efficacy. Our results shed light on these mechanisms, potentially supporting advances in the clinical application of tDCS. Our experimental and computational data support a critical role of electric dipoles in understanding the impact of exogenous EFs in the modulation of the cerebral cortex. Understanding the mechanism behind the effect of EF orientation on cortical modulation is a valuable first step towards the development of protocols and techniques for effective brain stimulation treatment strategies. Conflict of interest The authors report no conflict of interest Acknowledgments We thank Tony Donegan and Amin Samipour for critical reading and language corrections. Funding This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 860563. MVSV is funded by Project INFRASLOW PID2023-152918OB-I00 (MICIU / AEI / 10.13039/ 501100011033/FEDER, UE) and co-funded by AGAUR 2021-SGR-01165 supported by FEDER. IDIBAPS is funded by the CERCA program (Generalitat de Catalunya). MVSV and AD were funded by European Union’s Horizon 2020 Framework Programme for Research and Innovation under the Specific Grant Agreement No. 945539 (Human Brain Project SGA3). 20 References Adamantidis AR, Gutierrez Herrera C, Gent TC (2019) Oscillating circuitries in the sleeping brain. Nat Rev Neurosci 20:746–762. 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