Volume 3 (2012): Issue 1 (January 2012)

Using the fractional calculus approach, we present the Laplace analysis of an equivalent electrical circuit for a multilayered system, which includes distributed elements of the Cole model type. The Bode graphs are obtained from the numerical simulation of the corresponding transfer functions using arbitrary electrical parameters in order to illustrate the methodology. A numerical Laplace transform is used with respect to the simulation of the fractional differential equations. From the results shown in the analysis, we obtain the formula for the equivalent electrical circuit of a simple spectrum, such as that generated by a real sample of blood tissue, and the corresponding Nyquist diagrams. In addition to maintaining consistency in adjusted electrical parameters, the advantage of using fractional differential equations in the study of the impedance spectra is made clear in the analysis used to determine a compact formula for the equivalent electrical circuit, which includes the Cole model and a simple RC model as special cases.

In this study, three-electrode based electric cell-substrate impedance sensing (ECIS) devices were used to study the electrical properties of blood and its constituents using electrochemical impedance spectroscopy. The three-electrode based ECIS devices were fabricated by using micromachining technology with varying sizes for working, reference and counter electrodes. The blood and its constituents such as serum, plasma, and red blood cells (RBCs) were prepared by conventional methods and stored for impedance measurement using fabricated microdevices. Equivalent circuits for blood, serum, plasma and RBCs were proposed using the software package ZSimpWin to validate the experimental data. The proposed equivalent circuit models of blood and its components have excellent agreement up to a frequency of 1 MHz. It is evident from the experimental results that blood and its components have specific impedance signatures that decrease with the increase of frequency. Blood shows higher impedance than the other samples in the lower frequency range (<50 kHz). It was also found that above 50 kHz, the impedance value of RBCs is nearly the same as whole blood. The impedance of serum and plasma steadily decreases with the increase of frequency up to 100 kHz and flattens out after that. The minimum impedance value achieved for serum and plasma is much less than the value obtained for whole blood.

In this paper, we propose an equation and define the Isopotential Interface Factor (IIF) to quantify the contribution of electrode polarization impedance in two tetrapolar electrode shapes. The first tetrapolar electrode geometry shape was adjacent and the second axial concentric, both probes were made of stainless steel (AISI 304). The experiments were carried out with an impedance analyzer (Solartron 1260) using a frequency range between 0.1 Hz and 8 MHz. Based on a theoretical simplification, the experimental results show a lower value of the IIF in the axial concentric tetrapolar electrode system which caused a lower correction of interface value. The higher value of the IIF in the adjacent electrode system was K_EEI (1Hz, 0.28 mS/cm) = 1.41 and decreased when the frequency and conductance were increased, whereas in the axial concentric electrode system was K_EEI (1Hz, 0.28 mS/cm) = 0.08. The average isopotential interface factor throughout the whole range of conductivities and frequencies was 0.23 in the adjacent electrode system and 0.02 in the axial concentric electrode system. The index of inherent electrical anisotropy (IEA) was used to present an analysis of electrical anisotropy of biceps brachii muscle in vitro using the corrections of both tetrapolar electrode systems. A higher IEA was present in lower frequency where the variation below 1 kHz was 15 % in adjacent electrode configuration and 26 % in the axial concentric probe with respect to full range. The IIF is then shown that it can be used to describe the quality of an electrode system.

A model for current-voltage nonlinearity and asymmetry is a good starting point for explaining the electrical behavior of nanopores in synthetic or biological membranes. Using a Nernst-Planck model, we found three behaviors for the calculated current density in a membrane's pore as a function of voltage: a quasi-ohmic, slow rising linear current at low voltages; a nonlinear current at intermediate voltages; and a non-ohmic, fast rising linear current at large voltages. The slope of the quasi-ohmic current depends mainly on the height of the energy barrier inside the pore, w, through an exponential term, e^w. The magnitude of the non-ohmic linear current is controlled by the potential energy gradient at the pore entrance, w/r. The current-voltage relationship is asymmetric if the ion's potential energy inside the pore has an asymmetric triangular profile. The model has only two assumed parameters, the energy barrier height, w, and the relative size of the entrance region of the pore, r, which is a useful feature for fitting and interpreting experimental data.

Electrical impedance measurements of a suspension have to take into account the double layer impedance that results from a very thin charged layer formed at the electrode-electrolyte interface. A dedicated measuring cell that enables variation of the distance between the electrodes was developed to investigate the electrical properties of suspensions using two-electrode impedance measurements. By varying the distance between the electrodes it is possible to separate the double layer and the suspension impedance from the measured data. Electrical ‘lumped’ models have been developed from measured and extracted impedances. The error of non-inclusion of the double layer impedance has been analyzed. The error depends on the frequency of the measurement as well as the distance between the electrodes.

Electrical impedance spectroscopy (EIS) allows for the study and characterization of tissue alterations and properties associated with the skin. Here, the potential application of EIS to estimate the thickness of the stratum corneum is explored in the form of a mathematical model for EIS, which is analyzed in the limit of 1 kHz and closed-form analytical solutions derived. These analytical expressions are verified with the numerical solution of the full set of equations and validated with an EIS study comprising 120 subjects: overall, good agreement is found in the frequency range 1-100 kHz, where the impedance is governed by the stratum corneum. Combining the closed-form expression for the thickness of the stratum corneum predicted by the model with the experimental EIS measurements, a distribution for the stratum corneum thickness of the subjects is found with a mean and standard deviation that agree well with reported stratum corneum thicknesses from other experimental techniques. This, in turn, suggests that EIS could be employed to measure the thickness of the stratum corneum with reasonable accuracy. In addition, the electrical properties relevant to EIS – conductivity and relative permittivity – of the stratum corneum can be estimated with the closed form expressions if the stratum corneum thickness is known.

In March of 2011, a magnitude 9.0 earthquake and subsequent 14 meter high tsunami caused major damage to the Fukushima Daiichi nuclear power plant in Japan. The release of radiation, along with other uncontrolled releases elsewhere, revealed the necessity of a portable high throughput minimally invasive biological dosimetry modality. Immediate and early radiation effects on vasculature could be used as a dosimetry modality. To test whether non-coronary vasculature exhibited transient perturbation in barrier function, video microscopy studies and electric cell-substrate impedance sensing (ECIS) technology were used to probe very subtle changes in primary human vascular endothelium. In our studies, human umbilical vein endothelial cell (HUVEC) monolayers exhibited a transient, significant decrease (p = 0.017) in monolayer resistance three hours after irradiation with 5.0 Gy of γ rays. Radiation induced perturbations in HUVEC monolayer permeability are similar in magnitude and kinetics to those observed in coronary arterial endothelium. Therefore, at least two types of endothelia respond to radiation on ECIS arrays with an early transient disruption in permeability. This finding supports the use of early passage HUVECs for use in bioelectric dosimetry studies of vasculature and suggests that permeability changes in superficial vessels and sequellae could potentially serve as biological dosimetry tools.

Multifrequency Electrical Bioimpedance (MEB) has been widely used as a non-invasive technique for characterizing tissues. Most MEB systems use wideband current sources for injecting current and instrumentation amplifiers for measuring the resultant potential difference. To be viable current sources should have intrinsically high output impedance for a very wide frequency range. Most contemporary current sources in MEB systems are based on the Howland circuit. The objective of this work is to compare the Mirrored Modified Howland Current Source (MMHCS) with three Operational Transconductance Amplifier (OTA) based voltage controlled current sources (i.e., class-A, class-AB and current conveyor). The results show that both current conveyor and class-AB OTA-based current sources have a wider output current frequency response and an output impedance of 226% larger than the MMHCS circuit at 1 MHz. The presented class-AB OTA circuit has a power consumption of 4.6 mW whereas current conveyor consumed 1.6 mW. However, the MMHCS circuit had a maximum total harmonic distortion of 0.5% over the input voltage from -0.5 to +0.5 V. The OTA-based current sources are going to be integrated in a semiconductor process. The results might be useful for cell impedance measurements and for very low power bioimpedance applications.

The memristor (short for memory resistor) is a yet quite unknown circuit element, though equally fundamental as resistors, capacitors, and coils. It was predicted from theory arguments nearly 40 years ago, but not realized as a physical component until recently. The memristor shows many interesting features when describing electrical phenomena, especially at small (molecular or cellular) scales and can in particular be useful for bioimpedance and bioelectricity modeling. It can also give us a richer and much improved conceptual understanding of many such phenomena. Up until today the tools available for circuit modeling have been restricted to the three circuit elements (RLC) as well as the widely used constant phase element (CPE). However, as one element has been missing in our modeling toolbox, many bioelectrical phenomena may have been described incompletely as they are indeed memristive. Such memristive behavior is not possible to capture within a traditional RLC framework. In this paper we will introduce the memristor and look at bioelectrical memristive phenomena. The goal is to explain the new memristor’s properties in a simple manner as well as to highlight its importance and relevance. We conclude that memristors must be included as a readily used building block for bioimpedance and bioelectrical data analysis and modeling.

Between 1910 and 1913 Rudolf Höber presented proof that the interiors of red blood cells and muscle cells contain conducting electrolytes, and that each conducting core is contained within an insulating membrane. He did this by demonstrating, in a series of remarkable electrical experiments, that the conductivity of compacted cell samples at low frequencies (~150 Hz) was about ten-times less than the value obtained at ~5 MHz. On perforation of the membrane, the low-frequency conductivity increased to a value approaching that exhibited at MHz frequencies. Apart from representing a major milestone in the development of cell biology and electrophysiology, Höber’s work was the first description of what we now call the dielectric β-dispersion exhibited by cell suspensions and fresh tissue.