Simple model to incorporate statistical noise based on a modified hodgkin-huxley approach for external electrical field driven neural responses

Noise activity is known to affect neural networks, enhance the system response to weak external signals, and lead to stochastic resonance phenomenon that can effectively amplify signals in nonlinear systems. In most treatments, channel noise has been modeled based on multi-state Markov descriptions or the use stochastic differential equation models. Here we probe a computationally simple approach based on a minor modification of the traditional Hodgkin-Huxley approach to embed noise in neural response. Results obtained from numerous simulations with different excitation frequencies and noise amplitudes for the action potential firing show very good agreement with output obtained from well-established models. Furthermore, results from the Mann-Whitney U Test reveal a statistically insignificant difference. The distribution of the time interval between successive potential spikes obtained from this simple approach compared very well with the results of complicated Fox and Lu type methods at much reduced computational cost. This present method could also possibly be applied to the analysis of spatial variations and/or differences in characteristics of random incident electromagnetic signals.

Intrinsic properties of primary hippocampal neurons contribute to PIP2 depletion during nsEP-induced physiological response

High-energy, short-duration electric pulses (EPs) are known to be effective in neuromodulation, but the biological mechanisms underlying this effect remain unclear. Recently, we discovered that nanosecond electric pulses (nsEPs) could initiate the phosphatidylinositol_4,5-bisphosphate (PIP₂) depletion in non-excitable cells identical to agonist-induced activation of the G_q11 coupled receptors. PIP₂ is the precursor for multiple intracellular second messengers critically involved in the regulation of intracellular Ca²⁺ homeostasis and plasma membrane (PM) ion channels responsible for the control of neuronal excitability. In this paper we demonstrate a novel finding that five day in vitro (DIV5) primary hippocampal neurons (PHNs) undergo significantly higher PIP₂ depletion after 7.5 kV/cm 600 ns EP exposure than DIV1 PHNs and day 1-5 (D1-D5) non-excitable Chinese hamster ovarian cells with muscarinic receptor 1 (CHO-hM₁). Despite the age of development, the stronger 15 kV/cm 600 ns or longer 7.5 kV/cm 12 µs EP initiated profound PIP₂ depletion in all cells studied, outlining damage of the cellular PM and electroporation. Therefore, the intrinsic properties of PHNs in concert with nanoporation explain the stronger neuronal response to nsEP at lower intensity exposures. PIP₂ reduction in neurons could be a primary biological mechanism responsible for the stimulation or inhibition of neuronal tissues.

Continuum analysis to assess field enhancements for tailoring electroporation driven by monopolar or bipolar pulsing based on nonuniformly distributed nanoparticles

Recent reports indicate that nanoparticle (NP) clusters near cell membranes could enhance local electric fields, leading to heightened electroporation. This aspect is quantitatively analyzed through numerical simulations whereby time dependent transmembrane potentials are first obtained on the basis of a distributed circuit mode, and the results then used to calculate pore distributions from continuum Smoluchowski theory. For completeness, both monopolar and bipolar nanosecond-range pulse responses are presented and discussed. Our results show strong increases in TMP with the presence of multiple NP clusters and demonstrate that enhanced poration could be possible even over sites far away from the poles at the short pulsing regime. Furthermore, our results demonstrate that nonuniform distributions would work to enable poration at regions far away from the poles. The NP clusters could thus act as distributed electrodes. Our results were roughly in line with recent experimental observations.

Picosecond Pulse Electrical Field Suppressing Spike Firing in Hippocampal CA1 in Rat In Vivo

Picosecond pulse electrical fields (psPEFs), due to their high temporal-resolution accuracy and localization, were viewed as a potential targeted and noninvasive method for neuromodulation. However, few studies have reported psPEFs regulating neuronal activity in vivo. In this paper, a preliminary study on psPEFs regulating action potentials in hippocampus CA1 of rats in vivo was carried out. By analyzing the neuronal spike firing rate in hippocampus CA1 pre- and post-psPEF stimulation, effects of frequency, duration, and dosimetry of psPEFs were studied. The psPEF used in this study had a pulse width of 500 ps and a field strength of 1 kV/mm, established by 1 kV picosecond voltage pulses. Results showed that the psPEF suppressed spike firing in hippocampal CA1 neurons. The suppression effect was found to be significant except for 10 s, 10 Hz. For short-duration stimulation (10 s), the inhibition rate of spike firing increased with frequency. At longer stimulation durations (1 and 2 min), the inhibition rate increased and decreased alternately as the frequency increased. Despite this, the inhibition rate at high frequencies (5 and 10 kHz) was significantly larger than that at 10 and 100 Hz. A cumulative effect of psPEF on spike firing inhibition was found at low frequencies (10 and 100 Hz), which was saturated when frequency reached 500 Hz or higher. This paper conducts a study on psPEF regulating spike firing in hippocampal CA1 in vivo for the first time and guides subsequent study on psPEF achieving noninvasive neuromodulation. © 2020 Bioelectromagnetics Society.

ns Pulsed Electric Field-Induced Action Potentials in the Circuital Model of an Axon

Pulsed electric fields with duration in the sub- and ns time scale (nsPEFs) increase the permeability of cell membranes, enabling the transport of normally impermeant molecules into or out of the cell (electroporation). Such effect is associated to intracellular alterations and indicates nsPEFs as a new stimulus to modulate cell functions. In particular, studies dealing with the application of nsPEFs to excitable cells suggest their use for the stimulation/inhibition of cell excitation. In this paper, the circuital model per surface unit of the plasma membrane of an axon was developed to implement the Hodgkin and Huxley equations, describing the action potential activation process. For the first time, a power electronics circuital simulator was adopted. The model was first validated with conventional microsecond stimuli, and then it was employed to identify the conditions for cell excitation by nsPEFs. The results demonstrated the possibility of electrostimulation by nsPEFs at depolarization levels far below those required for inducing electroporation, and with ionic current dynamics similar to that induced by conventional stimuli, confirming recent experimental findings. Moreover, by using a power electronics tool, easier integration of the cell modeling with the design and optimization of pulse generation systems can be gained.

Rhodamine B as an optical thermometer in cells focally exposed to infrared laser light or nanosecond pulsed electric fields

The temperature-dependent fluorescence property of Rhodamine B was used to measure changes in temperature at the cellular level induced by either infrared laser light exposure or high intensity, ultrashort pulsed electric fields. The thermal impact of these stimuli were demonstrated at the cellular level in time and contrasted with the change in temperature observed in the extracellular bath. The method takes advantage of the temperature sensitivity of the fluorescent dye Rhodamine B which has a quantum yield linearly dependent on temperature. The thermal effects of different temporal pulse applications of infrared laser light exposure and of nanosecond pulsed electric fields were investigated. The temperature increase due to the application of nanosecond pulsed electric fields was demonstrated at the cellular level.

Towards electroporation based treatment planning considering electric field induced muscle contractions

The electric field threshold for muscle contraction is two orders of magnitudes lower than that for electroporation. Current electroporation treatment planning and electrode design studies focus on optimizing the delivery of electroporation electric fields to the targeted tissue. The goal of one part of this study was to investigate the relation between the volumes of tissue that experience electroporation electric fields in a targeted tissue volume and the volumes of tissue that experience muscle contraction inducing electric fields around the electroporated tissue volume, (V(MC)), during standard electroporation procedures and for various electroporation electrodes designs. The numerical analysis shows that conventional electroporation protocols and electrode design can generate muscle contraction inducing electric fields in surprisingly large volumes of non-target tissue, around the electroporation treated tissue. In studying various electrode configurations, we found that electrode placement in a structure we refer to as a "Current Cage" can substantially reduce the volume of non-target tissue exposed to electric fields above the muscle contraction threshold. In an experimental study on a tissue phantom we compare a commercial two parallel needle electroporation system with the Current Cage design. While tissue electroporated volumes were similar, V(MC) of tissue treated using the Current Cage design electrodes was an order of magnitude smaller than that using a commercially available system. An important aspect of the entire study is that it suggests the benefit of including the calculations of V(MC) for planning of electroporation based treatments such as DNA vaccination, electrochemotherapy and irreversible electroporation.

Numerical study of lipid translocation driven by nanoporation due to multiple high-intensity, ultrashort electrical pulses

The dynamical translocation of lipids from one leaflet to another due to membrane permeabilization driven by nanosecond, high-intensity (>100kV/cm) electrical pulses has been probed. Our simulations show that lipid molecules can translocate by diffusion through water-filled nanopores which form following high voltage application. Our focus is on multiple pulsing, and such simulations are relevant to gauge the time duration over which nanopores might remain open, and facilitate continued lipid translocations and membrane transport. Our results are indicative of a N(½) scaling with pulse number for the pore radius. These results bode well for the use of pulse trains in biomedical applications, not only due to cumulative behaviors and in reducing electric intensities and pulsing hardware, but also due to the possibility of long-lived thermo-electric physics near the membrane, and the possibility for pore coalescence.

Case for applying subnanosecond high-intensity, electrical pulses to biological cells

In this paper, model analysis into the time-dependent transmembrane potential at the outer cell membrane is presented, for applied high-intensity electric pulses having durations in the nanosecond range or smaller. It is argued that the frequency-dependent dielectric response of cell membranes could be used to advantage for stronger bioeffects by employing shorter pulses. Our model calculations predict faster transmembrane voltages and larger electroporation densities for a given external energy with pulse durations in the subnanosecond regime. This temporal regime would be used, for example, in the electrotherapy of mixed cell ensembles having different dielectric response properties.

Effects of nanosecond pulsed electric fields on the activity of a Hodgkin and Huxley neuron model

The cell membrane poration is one of the main assessed biological effects of nanosecond pulsed electric fields (nsPEF). This structural change of the cell membrane appears soon after the pulse delivery and lasts for a time period long enough to modify the electrical activity of excitable membranes in neurons. Inserting such a phenomenon in a Hodgkin and Huxley neuron model by means of an enhanced time varying conductance resulted in the temporary inhibition of the action potential generation. The inhibition time is a function of the level of poration, the pore resealing time and the background stimulation level of the neuron. Such results suggest that the neuronal activity may be efficiently modulated by the delivery of repeated pulses. This opens the way to the use of nsPEFs as a stimulation technique alternative to the conventional direct electric stimulation for medical applications such as chronic pain treatment.

Synergistic effects of local temperature enhancements on cellular responses in the context of high-intensity, ultrashort electric pulses

Results of self-consistent analyses of cells show the possibility of temperature increases at membranes in response to a single nanosecond, high-voltage pulse, at least over small sections of the membrane. Molecular Dynamics simulations indicate that such a temperature increase could facilitate poration, which is one example of a bio-process at the plasma membrane. Our study thus suggests that the use of repetitive high-intensity voltage pulses could open up possibilities for a host of synergistic bio-responses involving both thermal and electrically driven phenomena.

Analysis of cell membrane permeabilization mechanics and pore shape due to ultrashort electrical pulsing

Cell membrane permeabilization mechanics and the resulting shape of nanopores in response to electrical pulsing are probed based on a continuum approach. This has implications for electropermeabilization and cell membrane transport. It is argued that small pores resulting from high-intensity (approximately 100 kV/cm), nanosecond pulsing would have an initial asymmetric shape. This would lead to asymmetric membrane current-voltage characteristics, at least at early times. The role of the cytoskeleton is ignored here, but can be expected to additionally contribute to such asymmetries. Furthermore, we show that the pore shape and membrane conduction would be dynamic, and evolve toward a symmetric characteristic over time. This duration has been shown to be in the micro-second range.

Cellular apoptosis by nanosecond, high-intensity electric pulses: model evaluation of the pulsing threshold and extrinsic pathway

A simple, bistable rate-equation based model is used to predict trends of cellular apoptosis following electric pulsing. The caspase-8 extrinsic pathway with inherent delays in its activation, cytochrome c release, and an internal feedback mechanism between caspase-3 and cleavage of Bid are incorporated. Results obtained were roughly in keeping with the experimental cell-survival data and include an electrical pulse-number threshold followed by a near-exponential fall-off. The extrinsic caspase-8 mechanism is predicted to be more sensitive than the mitochondrial intrinsic pathway for electric pulse induced cell apoptosis. Also, delays of about an hour are predicted for detectable molecular concentration increases following electrical pulsing. Finally, our results suggest that multi-needle electrode systems with adjustable field orientations would likely enhance apoptosis in the context of pulsed voltage-induced inactivation of tumor cells.

Transmembrane voltage analyses in spheroidal cells in response to an intense ultrashort electrical pulse

Self-consistent evaluations of both the transmembrane potential (TMP) and possible electroporation density across membrane of spheroidal cells in response to ultrashort, high-intensity pulses are reported and discussed. Most treatments in the literature have been based on spherical cells, and this represents a step towards more realistic analyses. The present study couples the Laplace equation with Smoluchowski theory of pore formation, to yield dynamic membrane conductivities that influence the TMP. It is shown that the TMP induced by pulsed external voltages can be substantial higher in oblate spheroids as compared to spherical or prolate spheroidal cells. Flattening of the surface area in oblate spheroids leads to both higher electric fields seen by the membrane, and allows a great fraction of the surface area to be porated. This suggests that biomedical applications such as drug delivery and electrochemotherapy could work best for flatter-shaped cells, and secondary field-enabled orienting would be beneficial. Results for arbitrary field orientations and different cell sizes have also been presented.