Quantitative assessment of dielectric parameters for membrane lipid bi-layers from RF permittivity measurements

The Importance of Subcellular Structures to the Modeling of Biological Cells in the Context of Computational Bioelectromagnetics Simulations

Numerical investigation of the interaction of electromagnetic fields with eukaryotic cells requires specifically adapted computer models. Virtual microdosimetry, used to investigate exposure, requires volumetric cell models, which are numerically challenging. For this reason, a method is presented here to determine the current and volumetric loss densities occurring in single cells and their distinct compartments in a spatially accurate manner as a first step toward multicellular models within the microstructure of tissue layers. To achieve this, 3D models of the electromagnetic exposure of generic eukaryotic cells of different shape (i.e. spherical and ellipsoidal) and internal complexity (i.e. different organelles) are performed in a virtual, finite element method-based capacitor experiment in the frequency range from 10 Hz to 100 GHz. In this context, the spectral response of the current and loss distribution within the cell compartments is investigated and any effects that occur are attributed either to the dispersive material properties of these compartments or to the geometric characteristics of the cell model investigated in each case. In these investigations, the cell is represented as an anisotropic body with an internal distributed membrane system of low conductivity that mimics the endoplasmic reticulum in a simplified manner. This will be used to determine which details of the cell interior need to be modeled, how the electric field and the current density will be distributed in this region, and where the electromagnetic energy is absorbed in the microstructure regarding electromagnetic microdosimetry. Results show that for 5 G frequencies, membranes make a significant contribution to the absorption losses. © 2023 The Authors. Bioelectromagnetics published by Wiley Periodicals LLC on behalf of Bioelectromagnetics Society.

Strobe photography mapping of cell membrane potential with nanosecond resolution

The ability to directly observe membrane potential charging dynamics across a full microscopic field of view is vital for understanding interactions between a biological system and a given electrical stimulus. Accurate empirical knowledge of cell membrane electrodynamics will enable validation of fundamental hypotheses posited by the single shell model, which includes the degree of voltage change across a membrane and cellular sensitivity to external electric field non-uniformity and directionality. To this end, we have developed a high-speed strobe microscopy system with a time resolution of ~ 6 ns that allows us to acquire time-sequential data for temporally repeatable events (non-injurious electrostimulation). The imagery from this system allows for direct comparison of membrane voltage change to both computationally simulated external electric fields and time-dependent membrane charging models. Acquisition of a full microscope field of view enables the selection of data from multiple cell locations experiencing different electrical fields in a single image sequence for analysis. Using this system, more realistic membrane parameters can be estimated from living cells to better inform predictive models. As a proof of concept, we present evidence that within the range of membrane conductivity used in simulation literature, higher values are likely more valid.

Microwave characterization of low-molecular-weight antioxidant specific biomarkers

Antioxidants play a crucial role in the life sciences, as the regulators of biochemical reactions. We studied the dielectric properties of the low-molecular weight antioxidant specific biomarkers sodium ascorbate and glutathione in solutions of different concentrations. The biomarkers are multifunctional metabolites relevant to the reactive oxygen species (ROS) scavenging system of cells. The newly developed high-Q microwave whispering-gallery-mode (WGM) dielectric resonator based technique was applied. The technique allows investigation of liquids of nanoliter volumes filled in microfluidic channel within several milliseconds. The revealed peculiarities in the dependence of permittivity on concentrations of the sodium ascorbate and glutathione solutions are explained by differences in relaxation times and loses introduced by molecules of different shapes. We suggest that this novel approach offers the potential for the detection and characterization of ROS-relevant biomarkers with millisecond-time resolution.

Stimulation Strategies for Tinnitus Suppression in a Neuron Model

Tinnitus is a debilitating perception of sound in the absence of external auditory stimuli. It may have either a central or a peripheral origin in the cochlea. Experimental studies evidenced that an electrical stimulation of peripheral auditory fibers may alleviate symptoms but the underlying mechanisms are still unknown. In this work, a stochastic neuron model is used, that mimics an auditory fiber affected by tinnitus, to check the effects, in terms of firing reduction, of different kinds of electric stimulations, i.e., continuous wave signals and white Gaussian noise. Results show that both white Gaussian noise and continuous waves at tens of kHz induce a neuronal firing reduction; however, for the same amplitude of fluctuations, Gaussian noise is more efficient than continuous waves. When contemporary applied, signal and noise exhibit a cooperative effect in retrieving neuronal firing to physiological values. These results are a proof of concept that a combination of signal and noise could be delivered through cochlear prosthesis for tinnitus suppression.

Sine wave electropermeabilization reveals the frequency-dependent response of the biological membranes

The permeabilization of biological membranes by electric fields, known as electroporation, has been traditionally performed with square electric pulses. These signals distribute the energy applied to cells in a wide frequency band. This paper investigates the use of sine waves, which are narrow band signals, to provoke electropermeabilization and the frequency dependence of this phenomenon. Single bursts of sine waves at different frequencies in the range from 8 kHz-130 kHz were applied to cells in vitro. Electroporation was studied in the plasma membrane and the internal organelles membrane using calcium as a permeabilization marker. Additionally, a double-shell electrical model was simulated to give a theoretical framework to our results. The electroporation efficiency shows a low pass filter frequency dependence for both the plasma membrane and the internal organelles membrane. The mismatch between the theoretical response and the observed behavior for the internal organelles membrane is explained by a two-step permeabilization process: first the permeabilization of the external membrane and afterwards that of the internal membranes. The simulations in the model confirm this two-step hypothesis when a variable plasma membrane conductivity is considered in the analysis. This study demonstrates how the use of narrow-band signals as sine waves is a suitable method to perform electroporation in a controlled manner. We suggest that the use of this type of signals could bring a simplification in the investigations of the very complex phenomenon of electroporation, thus representing an interesting option in future fundamental studies.

Theoretical analysis of transmembrane potential of cells exposed to nanosecond pulsed electric field

PURPOSE

Intracellular electroporation occurs when the cells are exposed to nanosecond pulsed electric field (nsPEF). It is believed the electroporation (formation and extension of pores on the membrane induced by external electric field) is affected significantly by the transmembrane potential. This paper analyzed transmembrane potential induced by nsPEF in the term of pulse frequency spectrum, aiming to provide a theoretical explanation to intracellular bio-effects.

METHODS

Based on the double-shelled spherical cell model, the frequency dependence of transmembrane potential was obtained by solving Laplace's equation, while the time course of transmembrane potential was obtained by a method combined with discrete Fourier transform and Laplace transform. First-order Debye equation was used to describe the dielectric relaxation of the cell medium.

RESULTS

Frequency-domain analysis showed that when the electric field frequency was higher than 10⁵ Hz, the transmembrane potential on the organelle membrane (ΔΦ_o) was increasing to exceed the transmembrane potential on the cellular membrane (ΔΦ_c). In the time-domain analysis, transmembrane potentials induced by four nsPEF (short trapezoid, long trapezoid, bipolar and sine shapes) with the same field strength were compared with each other. It showed that ΔΦ_o is obviously larger than ΔΦ_c if the curve of the normalized frequency spectrum of the pulse is more similar with the curve of normalized ΔΦ_o in frequency domain. Pulses with major frequency components higher than 10⁸ Hz lead to both small ΔΦ_o and ΔΦ_c. This may explain why high power pulsed microwave lead to unobvious bio-effects of cells than nsPEF with trapezoid form.

CONCLUSION

Through the pulse frequency spectrum it is clearer to understand the relationship between nsPEF and the transmembrane potential.

A Microdosimetric Study of Electropulsation on Multiple Realistically Shaped Cells: Effect of Neighbours

Over the past decades, the effects of ultrashort-pulsed electric fields have been used to investigate their action in many medical applications (e.g. cancer, gene electrotransfer, drug delivery, electrofusion). Promising aspects of these pulses has led to several in vitro and in vivo experiments to clarify their action. Since the basic mechanisms of these pulses have not yet been fully clarified, scientific interest has focused on the development of numerical models at different levels of complexity: atomic (molecular dynamic simulations), microscopic (microdosimetry) and macroscopic (dosimetry). The aim of this work is to demonstrate that, in order to predict results at the cellular level, an accurate microdosimetry model is needed using a realistic cell shape, and with their position and packaging (cell density) characterised inside the medium.

Relaxation dynamics of liposomes in an aqueous solution

The gel–liquid crystal phase transition has been studied by the temperature and frequency dependent dielectric relaxation behavior of liposomes in an aqueous solution (40 g L⁻¹ DPPC–water mixture).

The Design and Operation of Ultra-Sensitive and Tunable Radio-Frequency Interferometers

Dielectric spectroscopy (DS) is an important technique for scientific and technological investigations in various areas. DS sensitivity and operating frequency ranges are critical for many applications, including lab-on-chip development where sample volumes are small with a wide range of dynamic processes to probe. In this work, we present the design and operation considerations of radio-frequency (RF) interferometers that are based on power-dividers (PDs) and quadrature-hybrids (QHs). Such interferometers are proposed to address the sensitivity and frequency tuning challenges of current DS techniques. Verified algorithms together with mathematical models are presented to quantify material properties from scattering parameters for three common transmission line sensing structures, i.e., coplanar waveguides (CPWs), conductor-backed CPWs, and microstrip lines. A high-sensitivity and stable QH-based interferometer is demonstrated by measuring glucose-water solution at a concentration level that is ten times lower than some recent RF sensors while our sample volume is ~1 nL. Composition analysis of ternary mixture solutions are also demonstrated with a PD-based interferometer. Further work is needed to address issues like system automation, model improvement at high frequencies, and interferometer scaling.

Nanometer-resolved radio-frequency absorption and heating in biomembrane hydration layers

Radio-frequency (RF) electromagnetic fields are readily absorbed in biological matter and lead to dielectric heating. To understand how RF radiation interacts with macromolecular structures and possibly influences biological function, a quantitative description of dielectric absorption and heating at nanometer resolution beyond the usual effective medium approach is crucial. We report an exemplary multiscale theoretical study for biomembranes that combines (i) atomistic simulations for the spatially resolved absorption spectrum at a single planar DPPC lipid bilayer immersed in water, (ii) calculation of the electric field distribution in planar and spherical cell models, and (iii) prediction of the nanometer resolved temperature profiles under steady RF radiation. Our atomistic simulations show that the only 2 nm thick lipid hydration layer strongly absorbs in a wide RF range between 10 MHz and 100 GHz. The absorption strength, however, strongly depends on the direction of the incident wave. This requires modeling of the electric field distribution using tensorial dielectric spectral functions. For a spherical cell model, we find a strongly enhanced RF absorption on an equatorial ring, which gives rise to temperature gradients inside a single cell under radiation. Although absolute temperature elevation is small under conditions of typical telecommunication usage, our study points to hitherto neglected temperature gradient effects and allows thermal RF effects to be predicted on an atomistically resolved level. In addition to a refined physiological risk assessment of RF fields, technological applications for controlling temperature profiles in nanodevices are possible.

Microdosimetric study for nanosecond pulsed electric fields on a cell circuit model with nucleus

Recently, scientific interest in electric pulses, always more intense and shorter and able to induce biological effects on both plasma and nuclear membranes, has greatly increased. Hence, microdosimetric models that include internal organelles like the nucleus have assumed increasing importance. In this work, a circuit model of the cell including the nucleus is proposed, which accounts for the dielectric dispersion of all cell compartments. The setup of the dielectric model of the nucleus is of fundamental importance in determining the transmembrane potential (TMP) induced on the nuclear membrane; here, this is demonstrated by comparing results for three different sets of nuclear dielectric properties present in the literature. The results have been compared, even including or disregarding the dielectric dispersion of the nucleus. The main differences have been found when using pulses shorter than 10 ns. This is due to the fact that the high spectral components of the shortest pulses are differently taken into account by the nuclear membrane transfer functions computed with and without nuclear dielectric dispersion. The shortest pulses are also the most effective in porating the intracellular structures, as confirmed by the time courses of the TMP calculated across the plasma and nuclear membranes. We show how dispersive nucleus models are unavoidable when dealing with pulses shorter than 10 ns because of the large spectral contents arriving above 100 MHz, i.e., over the typical relaxation frequencies of the dipolar mechanism of the molecules constituting the nuclear membrane and the subcellular cell compartments.

Novel passive element circuits for microdosimetry of nanosecond pulsed electric fields

Microdosimetric models for biological cells have assumed increasing significance in the development of nanosecond pulsed electric field technology for medical applications. In this paper, novel passive element circuits, able to take into account the dielectric dispersion of the cell, are provided. The circuital analyses are performed on a set of input pulses classified in accordance with the current literature. Accurate data in terms of transmembrane potential are obtained in both time and frequency domains for different cell models. In addition, a sensitivity study of the transfer function for the cell geometrical and dielectric parameters has been carried out. This analysis offers a new, simple, and efficient tool to characterize the nsPEFs' action at the cellular level.

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.

Microdosimetry applied to nanosecond pulsed electric fields: a comparison on a single cell between real and ideal waveforms

A microdosimetric analysis using ideal and real pulses was carried out in this paper. To perform this goal, authors employed an algorithm developed recently for nsPEF based on Laplace's equation and able to take into account cell compartment dispersivity. A comparison between biphasic real and ideal waveforms was carried out. The ideal pulse induced the highest pore density efficiency, hence evidencing that a device optimization to avoid waveform degradation and losses has a fundamental impact on the performances of the delivered pulses at the single cell level.

Microdosimetry for nanosecond pulsed electric field applications: a parametric study for a single cell

A microdosimetric study of nanosecond pulsed electric fields, including dielectric dispersivity of cell compartments, is proposed in our paper. A quasi-static solution based on the Laplace equation was adapted to wideband signals and used to address the problem of electric field estimation at cellular level. The electric solution was coupled with an asymptotic electroporation model able to predict membrane pore density. An initial result of our paper is the relevance of the dielectric dispersivity, providing evidence that both the transmembrane potential and the pore density are strongly influenced by the choice of modeling used. We note the crucial role played by the dielectric properties of the membrane that can greatly impact on the poration of the cell. This can partly explain the selective action reported on cancerous cells in mixed populations, if one considers that tumor cells may present different dielectric responses. Moreover, these kinds of studies can be useful to determine the appropriate setting of nsPEF generators as well as for the design and optimization of new-generation devices.

Effective dielectric properties of biological cells: generalization of the spectral density function approach

We suggest an extension of the spectral density function approach to describe the complex dielectric response of suspensions of arbitrarily shaped particles having a thin shell, in particular, biological cells. The approach is shown to give analytical results in some simple but practically important cases. In the general case, for the 3-phase systems it reduces to determination of the spectral density function for the suspension of a certain kind. Prospects and limitations of the approach, as well as practical examples, are also considered.