Biophysical modeling of the electric field magnitude and distribution induced by electrical stimulation with intracerebral electrodes.

Intracranial electrodes are used clinically for diagnostic or therapeutic purposes, notably in drug-refractory epilepsy (DRE) among others. Visualization and quantification of the energy delivered through such electrodes is key to understanding how the resulting electric fields modulate neuronal excitability, i.e. the ratio between excitation and inhibition. Quantifying the electric field induced by electrical stimulation in a patient-specific manner is challenging, because these electric fields depend on a number of factors: electrode trajectory with respect to folded brain anatomy, biophysical (electrical conductivity / permittivity) properties of brain tissue and stimulation parameters such as electrode contacts position and intensity. Here, we aimed to evaluate various biophysical models for characterizing the electric fields induced by electrical stimulation in DRE patients undergoing stereoelectroencephalography (SEEG) recordings in the context of pre-surgical evaluation. This stimulation was performed with multiple-contact intracranial electrodes used in routine clinical practice. We introduced realistic 3D models of electrode geometry and trajectory in the neocortex. For the electrodes, we compared point (0D) and line (1D) sources approximations. For brain tissue, we considered three configurations of increasing complexity: a 6-layer spherical model, a toy model with a sulcus representation, replicating results from previous approaches; and went beyond the state-of-the-art by using a realistic head model geometry. Electrode geometry influenced the electric field distribution at close distances (∼3 mm) from the electrode axis. For larger distances, the volume conductor geometry and electrical conductivity dominated electric field distribution. These results are the first step towards accurate and computationally tractable patient-specific models of electric fields induced by neuromodulation and neurostimulation procedures.

A physical neural mass model framework for the analysis of oscillatory generators from laminar electrophysiological recordings.

Cortical function emerges from the interactions of multi-scale networks that may be studied at a high level using neural mass models (NMM) that represent the mean activity of large numbers of neurons. Here, we provide first a new framework called laminar NMM, or LaNMM for short, where we combine conduction physics with NMMs to simulate electrophysiological measurements. Then, we employ this framework to infer the location of oscillatory generators from laminar-resolved data collected from the prefrontal cortex in the macaque monkey. We define a minimal model capable of generating coupled slow and fast oscillations, and we optimize LaNMM-specific parameters to fit multi-contact recordings. We rank the candidate models using an optimization function that evaluates the match between the functional connectivity (FC) of the model and data, where FC is defined by the covariance between bipolar voltage measurements at different cortical depths. The family of best solutions reproduces the FC of the observed electrophysiology by selecting locations of pyramidal cells and their synapses that result in the generation of fast activity at superficial layers and slow activity across most depths, in line with recent literature proposals. In closing, we discuss how this hybrid modeling framework can be more generally used to infer cortical circuitry.

Towards a mesoscale physical modeling framework for stereotactic-EEG recordings.

Objective.Stereotactic-electroencephalography (SEEG) and scalp EEG recordings can be modeled using mesoscale neural mass population models (NMMs). However, the relationship between those mathematical models and the physics of the measurements is unclear. In addition, it is challenging to represent SEEG data by combining NMMs and volume conductor models due to the intermediate spatial scale represented by these measurements.Approach.We provide a framework combining the multi-compartmental modeling formalism and a detailed geometrical model to simulate the transmembrane currents that appear in layer 3, 5 and 6 pyramidal cells due to a synaptic input. With this approach, it is possible to realistically simulate the current source density (CSD) depth profile inside a cortical patch due to inputs localized into a single cortical layer and the induced voltage measured by two SEEG contacts using a volume conductor model. Based on this approach, we built a framework to connect the activity of a NMM with a volume conductor model and we simulated an example of SEEG signal as a proof of concept.Main results.CSD depends strongly on the distribution of the synaptic inputs onto the different cortical layers and the equivalent current dipole strengths display substantial differences (of up to a factor of four in magnitude in our example). Thus, the inputs coming from different neural populations do not contribute equally to the electrophysiological recordings. A direct consequence of this is that the raw output of NMMs is not a good proxy for electrical recordings. We also show that the simplest CSD model that can accurately reproduce SEEG measurements can be constructed from discrete monopolar sources (one per cortical layer).Significance.Our results highlight the importance of including a physical model in NMMs to represent measurements. We provide a framework connecting microscale neuron models with the neural mass formalism and with physical models of the measurement process that can improve the accuracy of predicted electrophysiological recordings.

Signal processing and computational modeling for interpretation of SEEG-recorded interictal epileptiform discharges in epileptogenic and non-epileptogenic zones.

Objective.In partial epilepsies, interictal epileptiform discharges (IEDs) are paroxysmal events observed in epileptogenic zone (EZ) and non-epileptogenic zone (NEZ). IEDs' generation and recurrence are subject to different hypotheses: they appear through glutamatergic and gamma-aminobutyric acidergic (GABAergic) processes; they may trigger seizures or prevent seizure propagation. This paper focuses on a specific class of IEDs, spike-waves (SWs), characterized by a short-duration spike followed by a longer duration wave, both of the same polarity. Signal analysis and neurophysiological mathematical models are used to interpret puzzling IED generation.Approach.Interictal activity was recorded by intracranial stereo-electroencephalography (SEEG) electrodes in five different patients. SEEG experts identified the epileptic and non-epileptic zones in which IEDs were detected. After quantifying spatial and temporal features of the detected IEDs, the most significant features for classifying epileptic and non-epileptic zones were determined. A neurophysiologically-plausible mathematical model was then introduced to simulate the IEDs and understand the underlying differences observed in epileptic and non-epileptic zone IEDs.Main results.Two classes of SWs were identified according to subtle differences in morphology and timing of the spike and wave component. Results showed that type-1 SWs were generated in epileptogenic regions also involved at seizure onset, while type-2 SWs were produced in the propagation or non-involved areas. The modeling study indicated that synaptic kinetics, cortical organization, and network interactions determined the morphology of the simulated SEEG signals. Modeling results suggested that the IED morphologies were linked to the degree of preserved inhibition.Significance.This work contributes to the understanding of different mechanisms generating IEDs in epileptic networks. The combination of signal analysis and computational models provides an efficient framework for exploring IEDs in partial epilepsies and classifying EZ and NEZ.

A personalizable autonomous neural mass model of epileptic seizures.

Work in the last two decades has shown that neural mass models (NMM) can realistically reproduce and explain epileptic seizure transitions as recorded by electrophysiological methods (EEG, SEEG). In previous work, advances were achieved by increasing excitation and heuristically varying network inhibitory coupling parameters in the models. Based on these early studies, we provide a laminar NMM capable of realistically reproducing the electrical activity recorded by SEEG in the epileptogenic zone during interictal to ictal states. With the exception of the external noise input into the pyramidal cell population, the model dynamics are autonomous. By setting the system at a point close to bifurcation, seizure-like transitions are generated, including pre-ictal spikes, low voltage fast activity, and ictal rhythmic activity. A novel element in the model is a physiologically motivated algorithm for chloride dynamics: the gain of GABAergic post-synaptic potentials is modulated by the pathological accumulation of chloride in pyramidal cells due to high inhibitory input and/or dysfunctional chloride transport. In addition, in order to simulate SEEG signals for comparison with real seizure recordings, the NMM is embedded first in a layered model of the neocortex and then in a realistic physical model. We compare modeling results with data from four epilepsy patient cases. By including key pathophysiological mechanisms, the proposed framework captures succinctly the electrophysiological phenomenology observed in ictal states, paving the way for robust personalization methods based on NMMs.

Modeling implanted metals in electrical stimulation applications.

Objective. Metal implants impact the dosimetry assessment in electrical stimulation techniques. Therefore, they need to be included in numerical models. While currents in the body are ionic, metals only allow electron transport. In fact, charge transfer between tissues and metals requires electric fields to drive electrochemical reactions at the interface. Thus, metal implants may act as insulators or as conductors depending on the scenario. The aim of this paper is to provide a theoretical argument that guides the choice of the correct representation of metal implants in electrical models while considering the electrochemical nature of the problemApproach.We built a simple model of a metal implant exposed to a homogeneous electric field of various magnitudes. The same geometry was solved using two different models: a purely electric one (with different conductivities for the implant), and an electrochemical one. As an example of application, we also modeled a transcranial electrical stimulation (tES) treatment in a realistic head model with a skull plate using a high and low conductivity value for the plate.Main results. Metal implants generally act as electric insulators when exposed to electric fields up to around 100 V m-1and they only resemble a perfect conductor for fields in the order of 1000 V m-1and above. The results are independent of the implant's metal, but they depend on its geometry. tES modeling with implants incorrectly treated as conductors can lead to errors of 50% or more in the estimation of the induced fieldsSignificance.Metal implants can be accurately represented by a simple electrical model of constant conductivity, but an incorrect model choice can lead to large errors in the dosimetry assessment. Our results can be used to guide the selection of the most appropriate model in each scenario.

Modeling Methods for Treatment Planning in Overlapping Electroporation Treatments.

OBJECTIVE: Irreversible electroporation (IRE) is a non-thermal tissue ablation therapy which is induced by applying high voltage waveforms across electrode pairs. When multiple electrode pairs are sequentially used, the treatment volume (TV) is typically computed as the geometric union of the TVs of individual pairs. However, this method neglects that some regions are exposed to overlapping treatments. Recently, a model describing cell survival probability was introduced which effectively predicted TV with overlapping fields in vivo. However, treatment overlap has yet to be quantified. This study characterizes TV overlap in a controlled in vitro setup with the two existing methods which are compared to an adapted logistic model proposed here. METHODS: CHO cells were immobilized in agarose gel. Initially, we characterized the electric field threshold and the cell survival probability for overlapping treatments. Subsequently, we created a 2D setup where we compared and validated the accuracy of the different methods in predicting the TV. RESULTS: Overlap can reduce the electric field threshold required to induce cell death, particularly for treatments with low pulse number. However, it does not have a major impact on TV in the models assayed here, and all the studied methods predict TV with similar accuracy. CONCLUSION: Treatment overlap has a minor influence in the TV for typical protocols found in IRE therapies. SIGNIFICANCE: This study provides evidence that the modeling method used in most pre-clinical and clinical studies seems adequate.

Pulsed radiofrequency for chronic pain: In vitro evidence of an electroporation mediated calcium uptake.

Pulsed radiofrequency (PRF) treatments for chronic pain consist in the delivery of a train of sinusoidal electric bursts to the targeted nerve. Despite numerous clinical evidence of its efficiency, the mechanism of action of PRF remains unclear. Since most of the reported biological effects of PRF can be initiated by a calcium influx into the neurons, we hypothesized that PRF may induce a mild electroporation effect causing a calcium uptake. To test this hypothesis, HEK-293 cells were exposed to PRF bursts and cytosolic calcium and Yo-Pro-1 uptake were monitored. After a single burst, calcium peaks were observed for electric fields above 480 V/cm while the uptake of Yo-pro-1 was insignificant. After a train of 120 bursts, the electric fields required to induce a calcium and Yo-pro-1 uptake decreased to 330 V/cm and 880 V/cm respectively. Calcium peaks were not detected when cells were treated in calcium free media. The temperature increase during the treatments was lower than 5 °C in all cases. Finally, the cell response for different burst frequencies and extracellular media conductivities correlated with the induced transmembrane voltage calculated with a numerical model. Our results support the hypothesis of an electroporation mediated calcium influx.

EView: An electric field visualization web platform for electroporation-based therapies.

BACKGROUND AND OBJECTIVES: Electroporation is the phenomenon by which cell membrane permeability to ions and macromolecules is increased when the cell is briefly exposed to high electric fields. In electroporation-based treatments, such exposure is typically performed by delivering high voltage pulses across needle electrodes in tissue. For a given tissue and pulsing protocol, an electric field magnitude threshold exists that must be overreached for treatment efficacy. However, it is hard to preoperatively infer the treatment volume because the electric field distribution intricately depends on the electrodes' positioning and length, the applied voltage, and the electric conductivity of the treated tissues. For illustrating such dependencies, we have created EView (https://eview.upf.edu), a web platform that estimates the electric field distribution for arbitrary needle electrode locations and orientations and overlays it on 3D medical images. METHODS: A client-server approach has been implemented to let the user set the electrode configuration easily on the web browser, whereas the simulation is computed on a dedicated server. By means of the finite element method, the electric field is solved in a 3D volume. For the sake of simplicity, only a homogeneous tissue is modeled, assuming the same properties for healthy and pathologic tissues. The non-linear dependence of tissue conductivity on the electric field due to the electroporation effect is modeled. The implemented model has been validated against a state of the art finite element solver, and the server has undergone a heavy load test to ensure reliability and to report execution times. RESULTS: The electric field is rapidly computed for any electrode and tissue configuration, and alternative setups can be easily compared. The platform provides the same results as the state of the art finite element solver (Dice = 98.3 ± 0.4%). During the high load test, the server remained responsive. Simulations are computed in less than 2 min for simple cases consisting of two electrodes and take up to 40 min for complex scenarios consisting of 6 electrodes. CONCLUSIONS: With this free platform we provide expert and non-expert electroporation users a way to rapidly model the electric field distribution for arbitrary electrode configurations.

Interleaved intramuscular stimulation with minimally overlapping electrodes evokes smooth and fatigue resistant forces.

OBJECTIVE: It is known that multi-site interleaved stimulation generates less muscle fatigue compared to single-site synchronous stimulation. However, in the limited number of studies in which intramuscular electrodes were used, the fatigue reduction associated with interleaved stimulation could not consistently be achieved. We hypothesize that this could be due to the inability to place the intramuscular electrodes used in interleaved stimulation in locations that minimize overlap amongst the motor units activated by the electrodes. Our objective in the present study was to use independent intramuscular electrodes to compare fatigue induced by interleaved stimulation with that generated by synchronous stimulation at the same initial force and ripple. APPROACH: In the medial gastrocnemius muscle of an anesthetized rabbit (n = 3), ten intramuscular hook wire electrodes were inserted at different distances from the nerve entry. Overlap was measured using the refractory technique and only three electrodes were found to be highly independent. After ensuring that forces obtained by both stimulation modalities had the same ripple and magnitude, fatigue induced during interleaved stimulation across three independent distal electrodes was compared to that obtained by synchronously delivering pulses to a single proximal electrode. MAIN RESULTS: Contractions evoked by interleaved stimulation exhibited less fatigue than those evoked by synchronous stimulation. Twitch force recruitment curves collected from each of the ten intramuscular electrodes showed frequent intermediate plateaus and the force value at these plateaus decreased as the distance between the electrode and nerve entry increased. SIGNIFICANCE: The results indicate that interleaved intramuscular stimulation is preferred over synchronous intramuscular stimulation when fatigue-resistant and smooth forces are desired. In addition, the results suggest that the large muscle compartments innervated by the primary intramuscular nerve branches give rise to progressively smaller independent compartments in subsequent nerve divisions.

Dynamics of Cell Death After Conventional IRE and H-FIRE Treatments.

High-frequency irreversible electroporation (H-FIRE) has emerged as an alternative to conventional irreversible electroporation (IRE) to overcome the issues associated with neuromuscular electrical stimulation that appear in IRE treatments. In H-FIRE, the monopolar pulses typically used in IRE are replaced with bursts of short bipolar pulses. Currently, very little is known regarding how the use of a different waveform affects the cell death dynamics and mechanisms. In this study, human pancreatic adenocarcinoma cells were treated with a typical IRE protocol and various H-FIRE schemes with the same energized time. Cell viability, membrane integrity and Caspase 3/7 activity were assessed at different times after the treatment. In both treatments, we identified two different death dynamics (immediate and delayed) and we quantified the electric field ranges that lead to each of them. While in the typical IRE protocol, the electric field range leading to a delayed cell death is very narrow, this range is wider in H-FIRE and can be increased by reducing the pulse length. Membrane integrity in cells suffering a delayed cell death shows a similar time evolution in all treatments, however, Caspase 3/7 expression was only observed in cells treated with H-FIRE.

In vitro study on the mechanisms of action of electrolytic electroporation (E2).

Electrolytic Electroporation (E2) is the combination of reversible electroporation and electrolysis. It has been proposed as a novel treatment option to ablate tissue percutaneously. The present in vitro study in cells in suspension was performed to investigate the underlying mechanisms of action of E2. Different types of experiments were performed to isolate the effects of the electrolysis and the electroporation components of the treatment. Additionally, thermal simulations were performed to determine whether significant temperature increase contributes to the effect. The results indicate that E2's cell killing efficacy is due to a combinational effect of electrolysis and reversible electroporation that takes place within the first two minutes after E2 application. The results further show that cell death after E2 treatment is significantly delayed. These observations suggest that cell death is induced in permeabilized cells due to the uptake of electrolysis species. Thermal simulations revealed a significant but innocuous temperature increase.

Successful Tumor Electrochemotherapy Using Sine Waves.

OBJECTIVE: The purpose of this work is to assess the ability of sine waves to perform electrochemotherapy (ECT) and to study the dependence of the frequency of the applied sine wave on the treatment efficacy. METHODS: A subcutaneous tumor model in mice was used, and the electric field was delivered in combination with bleomycin. Sinusoidal electric fields of different frequencies, amplitudes, and durations were compared to square waves. Computer simulations were additionally performed. RESULTS: The results confirmed the ability of a sinusoidal electric field to obtain successful ECT responses. A strong dependence on frequency was obtained. The efficacy of the treatment decreased when the frequency of the sine waves was increased. At low sinusoidal frequency, the efficacy of the treatment is very similar to that obtained with a square wave. The collateral effects such as skin burns and muscle contractions decreased for the highest frequency assayed. CONCLUSION: The use of sine wave burst represents a feasible option for the treatment of cancer by ECT. SIGNIFICANCE: These results could have important implications for the treatment of cancer in the clinical world where ECT is performed with dc square pulses.

Avoiding neuromuscular stimulation in liver irreversible electroporation using radiofrequency electric fields.

Electroporation-based treatments typically consist of the application of high-voltage dc pulses. As an undesired side effect, these dc pulses cause electrical stimulation of excitable tissues such as motor nerves. The present in vivo study explores the use of bursts of sinusoidal voltage in a frequency range from 50 kHz to 2 MHz, to induce irreversible electroporation (IRE) whilst avoiding neuromuscular stimulation. A series of 100 dc pulses or sinusoidal bursts, both with an individual duration of 100 µs, were delivered to rabbit liver through thin needles in a monopolar electrode configuration, and thoracic movements were recorded with an accelerometer. Tissue samples were harvested three hours after treatment and later post-processed to determine the dimensions of the IRE lesions. Thermal damage due to Joule heating was ruled out via computer simulations. Sinusoidal bursts with a frequency equal to or above 100 kHz did not cause thoracic movements and induced lesions equivalent to those obtained with conventional dc pulses when the applied voltage amplitude was sufficiently high. IRE efficacy dropped with increasing frequency. For 100 kHz bursts, it was estimated that the electric field threshold for IRE is about 1.4 kV cm-1 whereas that of dc pulses is about 0.5 kV cm-1.

Effect of applied voltage, duration and repetition frequency of RF pulses for pain relief on temperature spikes and electrical field: a computer modelling study.

BACKGROUND: The thermal and electrical effects of pulsed radiofrequency (PRF) for pain relief can be controlled by modifying the characteristics of the RF pulses applied. Our goal was to evaluate the influence of such modifications on the thermal and electric performance in tissue. METHODS: A computational model was developed to compare the temperature and electric field time courses in tissue between a standard clinical protocol (45 V pulses, 20 ms duration, 2 Hz repetition frequency) and a new protocol (55 V pulses, 5 ms duration, 5 Hz repetition frequency) with a higher applied electric field but a smaller impact on temperature alterations in tissue. The effect of including a temperature controller was assessed. Complementarily, an agar-based experimental model was developed to validate the methodology employed in the computer modelling. RESULTS: The new protocol increased the electric field magnitude reached in the tissue by around +20%, without increasing the temperature. The temperature controller was found to be the fundamental factor in avoiding thermal damage to the tissue and reduced the total number of pulses delivered by around 67%. The experimental results matched moderately well with those obtained from a computer model built especially to mimic the experimental conditions. CONCLUSIONS: For the same delivered energy, the new protocol significantly increases the magnitude of the applied electric field, which may be the reason why it is clinically more effective in achieving pain relief.

Avoiding nerve stimulation in irreversible electroporation: a numerical modeling study.

Electroporation based treatments consist in applying one or multiple high voltage pulses to the tissues to be treated. As an undesired side effect, these pulses cause electrical stimulation of excitable tissues such as nerves and muscles. This increases the complexity of the treatments and may pose a risk to the patient. To minimize electrical stimulation during electroporation based treatments, it has been proposed to replace the commonly used monopolar pulses by bursts of short bipolar pulses. In the present study, we have numerically analyzed the rationale for such approach. We have compared different pulsing protocols in terms of their electroporation efficacy and their capability of triggering action potentials in nerves. For that, we have developed a modeling framework that combines numerical models of nerve fibers and experimental data on irreversible electroporation. Our results indicate that, by replacing the conventional relatively long monopolar pulses by bursts of short bipolar pulses, it is possible to ablate a large tissue region without triggering action potentials in a nearby nerve. Our models indicate that this is possible because, as the pulse length of these bipolar pulses is reduced, the stimulation thresholds raise faster than the irreversible electroporation thresholds. We propose that this different dependence on the pulse length is due to the fact that transmembrane charging for nerve fibers is much slower than that of cells treated by electroporation because of their geometrical differences.

Dependence of Electroporation Detection Threshold on Cell Radius: An Explanation to Observations Non Compatible with Schwan's Equation Model.

It is widely accepted that electroporation occurs when the cell transmembrane voltage induced by an external applied electric field reaches a threshold. Under this assumption, in order to trigger electroporation in a spherical cell, Schwan's equation leads to an inversely proportional relationship between the cell radius and the minimum magnitude of the applied electric field. And, indeed, several publications report experimental evidences of an inverse relationship between the cell size and the field required to achieve electroporation. However, this dependence is not always observed or is not as steep as predicted by Schwan's equation. The present numerical study attempts to explain these observations that do not fit Schwan's equation on the basis of the interplay between cell membrane conductivity, permeability, and transmembrane voltage. For that, a single cell in suspension was modeled and the electric field necessary to achieve electroporation with a single pulse was determined according to two effectiveness criteria: a specific permeabilization level, understood as the relative area occupied by the pores during the pulse, and a final intracellular concentration of a molecule due to uptake by diffusion after the pulse, during membrane resealing. The results indicate that plausible model parameters can lead to divergent dependencies of the electric field threshold on the cell radius. These divergent dependencies were obtained through both criteria and using two different permeabilization models. This suggests that the interplay between cell membrane conductivity, permeability, and transmembrane voltage might be the cause of results which are noncompatible with the Schwan's equation model.