Effect of shape on the dielectric properties of biological cell suspensions

Using the Probability Density Function-Based Channel-Combination Bloch-Siegert Method Realizes Permittivity Imaging at 3T

Magnetic resonance electrical properties tomography (MR EPT) can retrieve permittivity from the B1+ magnitude. However, the accuracy of the permittivity measurement using MR EPT is still not ideal due to the low signal-to-noise ratio (SNR) of B1+ magnitude. In this study, the probability density function (PDF)-based channel-combination Bloch-Siegert (BSS) method was firstly introduced to MR EPT for improving the accuracy of the permittivity measurement. MRI experiments were performed using a 3T scanner with an eight-channel receiver coil. The homogeneous water phantom was scanned for assessing the spatial distribution of B1+ magnitude obtained from the PDF-based channel-combination BSS method. Gadolinium (Gd) phantom and rats were scanned for assessing the feasibility of the PDF-based channel-combination BSS method in MR EPT. The Helmholtz-based EPT reconstruction algorithm was selected. For quantitative comparison, the permittivity measured by the open-ended coaxial probe method was considered as the ground-truth value. The accuracy of the permittivity measurement was estimated by the relative error between the reconstructed value and the ground-truth value. The reconstructed relative permittivity of Gd phantom was 52.413, while that of rat leg muscle was 54.053. The ground-truth values of relative permittivity of Gd phantom and rat leg muscle were 78.86 and 49.04, respectively. The relative error of average permittivity was 33.53% for Gd and 10.22% for rat leg muscle. The results indicated the high accuracy of the permittivity measurement using the PDF-based channel-combination BSS method in MR EPT. This improvement may promote the clinical application of MR EPT technology, such as in the early diagnosis of cancers.

The dielectric spectroscopy of human red blood cells during 37-day storage: β-dispersion parameterization

This study exploits dielectric spectroscopy to monitor the kinetics of red blood cells (RBC) storage lesions, focusing on those processes linked to cellular membrane interface known as β-dispersion. The dielectric response of RBC suspensions, exposed to blood-bank cold storage for 37 days, was studied using time-domain dielectric spectroscopy in the frequency range 500 kHz to 200 MHz. The measured dielectric processes are characterized by their dielectric strength (Δε) and their relaxation times (τ). Changes in the dielectric properties of the RBC suspensions, due to storage-related biophysical changes, were evaluated. For a quantitative characterization of RBC vitality, we characterized the shape of fresh and stored RBC and measured their deformability as expressed by their average elongation ratio, which was achieved under a shear stress of 3.0 Pa. During the second week of storage, an increment in the evolution of the relaxation times and in the dielectric permittivity strength of about 25% was observed. We propose that the characteristic increment of ATP, during the second and third weeks of storage, is responsible for the raise of the specific capacitance of cell membrane, which in turn explains the changes observed in the dielectric response when combined with the influence of the shape changes.

A Novel Efficient FEM Thin Shell Model for Bio-Impedance Analysis

In this paper, a novel method for accelerating eddy currents calculation on a cell model using the finite element method (FEM) is presented. Due to the tiny thickness of cell membrane, a full-mesh cell model requires a large number of mesh elements and hence intensive computation resources and long time. In this paper, an acceleration method is proposed to reduce the number of mesh elements and therefore reduce the computing time. It is based on the principle of replacing the thin cell membrane with an equivalent thicker structure. The method can reduce the number of mesh elements to 23% and the computational time to 17%, with an error of less than 1%. The method was verified using 2D and 3D finite element methods and can potentially be extended to other thin shell structures. The simulation results were validated by measurement and analytical results.

On Modeling Diversity in Electrical Cellular Response: Data-Driven Approach

Electrical properties of biological cells and tissues possess valuable information that enabled numerous applications in biomedical engineering. The common foundation behind them is a numerical model that can predict electrical response of a single cell or a network of cells. We analyzed the past empirical observations to propose the first statistical model that accurately mimics biological diversity among animal cells, yeast cells, and bacteria. Based on membrane elasticity and cell migration mechanisms, we introduce a more realistic three-dimensional geometry generation procedure that captures membrane protrusions and retractions in adherent cells. Together, they form a model of diverse electrical response across multiple cell types. We experimentally verified the model with electrical impedance spectroscopy of a single human cervical carcinoma (HeLa) cell on a microelectrode array. The work is of particular relevance to medical diagnostic and therapeutic applications that involve exposure to electric and magnetic fields.

In silico validation procedure for cell volume fraction estimation through dielectric spectroscopy

Dielectric spectroscopy has proved to be a good tool for analyzing the passive electrical properties of biological tissues as well as those of inhomogeneous materials. This technique promises to be a valid alternative to the classical ones based on metabolites to monitor the growth and cell volume fraction of cell cultures in a simple and minimally invasive way. In order to obtain an accurate estimation of the cell volume fraction as a function of the permittivity of the suspension, a simple in silico procedure is proposed. The procedure is designed to perform homogenization from the micro-scale to the macro-scale using simple analytical models and simulation setups hypothesizing the properties of diluted suspension (cell volume fraction less than 0.2). Results obtained show the possibility to overcome some trouble involving the analytical treatment of the cellular shape by considering a sphere with the same permittivity in the quantitative analysis of the cell volume fraction. The entire study is based on computer simulations performed in order to verify the correctness of the procedure. Obtained data are used in a cell volume fraction estimation scenario to show the effectiveness of the procedure.

A novel approach for using dielectric spectroscopy to predict viable cell volume (VCV) in early process development

Online monitoring of viable cell volume (VCV) is essential to the development, monitoring, and control of bioprocesses. The commercial availability of steam-sterilizable dielectricspectroscopy probes has enabled successful adoption of this technology as a key noninvasive method to measure VCV for cell-culture processes. Technological challenges still exist, however. For some cell lines, the technique’s accuracy in predicting the VCV from probepermittivity measurements declines as the viability of the cell culture decreases. To investigate the cause of this decrease in accuracy, divergences in predicted vs. actual VCV measurements were directly related to the shape of dielectric frequency scans collected during a cell culture. The changes in the shape of the beta dispersion, which are associated with changes in cell state, are quantified by applying a novel “area ratio” (AR) metric to frequency-scanning data from the dielectric-spectroscopy probes. The AR metric is then used to relate the shape of the beta dispersion to single-frequency permittivity measurements to accurately predict the offline VCV throughout an entire fed-batch run, regardless of cell state. This work demonstrates the possible feasibility of quantifying the shape of the beta dispersion, determined from frequency-scanning data, for enhanced measurement of VCV in mammalian cell cultures by applying a novel shape-characterization technique. In addition, this work demonstrates the utility of using changes in the shape of the beta dispersion to quantify cell health.

Dielectric properties of microvillous cells simulated by the three-dimensional finite-element method

Most of biological cells have microvilli on their surfaces, which significantly influence their dielectric properties. The complex permittivity of a cubical system containing a spherical cell model with cylindrical projections was calculated over a frequency range of 10 kHz to 100 MHz using the three-dimensional finite-element method. The spectra of the complex permittivity consisted of low- and high-frequency relaxation processes which were respectively attributed to the polarization of the membranes covering the projections and the spherical body. Conventional analysis based on the spherical shell model was applied to the simulated spectra to discuss the effects of cell surface morphology on the electric parameters estimated for the plasma membrane and the cytoplasm.

A novel broadband impedance method for detection of cell-derived microparticles

A novel label-free method is presented to detect and quantify cell-derived microparticles (MPs) by the electrochemical potential-modulated electrochemical impedance spectroscopy (EIS). MPs are present in elevated concentrations during pathological conditions and play a major role in the establishment and pathogenesis of many diseases. Considering this, accurate detection and quantification of MPs is very important in clinical diagnostics and therapeutics. A combination of bulk solution electrokinetic sorting and interfacial impedance responses allows achieving detection limits as low as several MPs per μL. By fitting resulting EIS spectra with an equivalent electrical circuit, the bulk solution electrokinetic and interfacial impedance responses were characterized. In the bulk solution two major relaxations were prominent-β-relaxation in low MHz region due to the MP capacitive membrane bridging, and α-relaxation at ∼10 kHz due to counter ions diffusion. At low frequencies (10-0.1 Hz) at electrochemical potentials exceeding -100 mV, a facile interfacial Faradaic process of oxidation in MPs coupled with diffusion and non-Faradaic double layer charging dominate, probably due to oxidation of phospholipids and/or proteins on the MP surface and MP lysis. Buffer influence on the MP detection demonstrated that a relatively low conductivity Tyrode's buffer background solution is preferential for the MP electrokinetic separation and characterization. This study also demonstrated that standard laboratory methods such as flow cytometry underestimate MP concentrations, especially those with smaller average sizes, by as much as a factor of 2-40.

Polarizability of spherical biological cells in the presence of localized surface charge distributions at the membrane interfaces

The electrical polarizability α(ω) of a biological cell in the presence of a layer of localized, partially bounded, charges at the two cell membrane interfaces has been calculated within the dipolar approximation. The cell is modeled in the light of the single-shell spherical model, but the results can be easily extended to shelled particles of more complex shape. Under the influence of an external electric field, the presence of these charge distributions, which added to the ones originated by the mismatch of the complex dielectric constants of the different media, produces a further dielectric relaxation, besides the one due to the usual Maxwell-Wagner effect. We explicitly find the contribution that must be added to the electrical polarizability α(ω) in order to take into account the surface electrical currents originated by the localized charges free to move on the membrane surfaces. Our results, maintaining their validity whatsoever the values of the surface charge distributions and, moreover, whatsoever the values of the membrane conductivity are, extend the applicability of the model recently proposed by Prodan [Biophys. J. 95, 4174 (2008)], who developed an analytical solution which offers reliable results only in the case of weak surface charge distributions and, moreover, for negligible small values of the membrane conductivity. Our approach, removing these constrains, represents a valuable improvement toward more realistic biological cell models and widens the use of dielectric relaxation methods to a larger class of biological systems.

Linear dielectric response of clustered living cells

The dielectric behavior of a linear cluster of two or more living cells connected by tight junctions is analyzed using a spectral method. The polarizability of this system is obtained as an expansion over the eigenmodes of the linear response operator, showing a clear separation of geometry from electric parameters. The eigenmode with the second largest eigenvalue dominates the expansion as the junction between particles tightens, but only when the applied field is aligned with the cluster axis. This effect explains a distinct low-frequency relaxation observed in the impedance spectrum of a suspension of linear clusters.

Quantifying the membrane potential during E. coli growth stages

The presence of the resting membrane potential has a strong effect on the dielectric behavior of cell suspensions. Using this observation and a well-established theoretical model, the low frequency dielectric dispersion curves of E. coli cell suspensions are de-convoluted to obtain the resting membrane potential of E. coli cells at various growth stages. Four regions of the exponential growth stage are investigated and the measurements indicate that the membrane depolarizes from -220mV in the early exponential phase to -140mV in the late exponential phase. The conductivity of the cell suspension is also found to decrease as the cells progress from the early to the late exponential phases.

Dielectric screening of early differentiation patterns in mesenchymal stem cells induced by steroid hormones

In the framework of this study, target identification and localization of differentiation patterns by means of dielectric spectroscopy is presented. Here, a primary pre-osteoblastic bone marrow-derived MBA-15 cellular system was used to study the variations in the dielectric properties of mesenchymal stem cells while exposed to differentiation regulators. Using the fundamentals of mixed dielectric theories combined with finite numerical tools, the permittivity spectra of MBA-15 cell suspensions have been uniquely analyzed after being activated by steroid hormones to express osteogenic phenotypes. Following the spectral analysis, significant variations were revealed in the dielectric properties of the activated cells in comparison to the untreated populations. Based on the differentiation patterns of MBA-15, the electrical modifications were found to be highly correlated with the activation of specific cellular mechanisms which directly react to the hormonal inductions. In addition, by describing the dielectric dispersion in terms of transfer functions, it is shown that the spectral perturbations are well adapted to variations in the electrical characteristics of the cells. The reported findings vastly emphasize the tight correlation between the cellular and electrical state of the differentiated cells. It therefore emphasizes the vast abilities of impedance-based techniques as potential screening tools for stem cell analysis.

The role of GLUT1 in the sugar-induced dielectric response of human erythrocytes

We propose a key role for the glucose transporter 1 (GLUT1) in mediating the observed changes in the dielectric properties of human erythrocyte membranes as determined by dielectric spectroscopy. Cytochalasin B, a GLUT1 transport inhibitor, abolished the membrane capacitance changes in glucose-exposed red cells. Surprisingly, D-fructose, known to be transported primarily by GLUT5, exerted similar membrane capacitance changes at increasing D-fructose concentrations. In order to evaluate whether the glucose-mediated membrane capacitance changes originated directly from intracellularly bound adenosine triphosphate (ATP) or other components of the glycolysis process, we studied the dielectric responses of swollen erythrocytes with a decreased ATP content and of nucleotide-filled ghosts. Resealed ghosts containing physiological concentrations of ATP yielded the same glucose-dependent capacitance changes as biconcave intact red blood cells, further supporting the finding that ATP is the effector of the glucose-mediated dielectric response where the ATP concentration is also the mediating factor in swollen red blood cells. The results suggest that ATP binding to GLUT1 elicits a membrane capacitance change that increases with the applied concentration gradient of D-glucose. A simplified model of the membrane capacitance alteration with glucose uptake is proposed.