Algorithms for Reconstruction of Impedance Spectra from Non-uniformly Sampled Step Responses.

Fast and reliable bioimpedimetric measurements are of growing importance in many practical applications. In this work we used a measurement method in time domain by processing the step response of the biological system under test. In order to decrease the data volume and computation time while retaining all relevant information the step response is sampled non-uniformly. Consequently, fast Fourier transform cannot be directly used for spectrum calculation and non-conventional data processing algorithms for transforming measured data into the frequency domain are required. In this paper we present corresponding computational methods. They are split into two groups. The first group is oriented on calculating the local approximation of the measured step response with a set of proper functions and calculating its spectrum via analytical Fourier transform, thus yielding a relatively versatile approach for estimating the impedance spectrum. In this case, the choice of approximating functions that suit known a priori properties of the measured signals are of great importance. A second group of methods relies on the evaluation of important signal parameters directly in the time domain. In this case we use a priori information about the measurement object in the form of an underlying model. After that the model is fitted to the measured data and thus, parameter values are extracted. Practical aspects, advantages and drawbacks of all considered data processing steps are revealed when applying them to the measurements made with real biological objects.

Multichannel Cell Detection in Microcompartments by Means of True Parallel Measurements using the Solartron S-1260.

Designing proper frontend electronics is critical in the development of highly sophisticated electrode systems. Multielectrode arrays for measuring electrical signals or impedance require multichannel readout systems. Even more challenging is the differential or ratiometric configuration with simultaneous assessment of measurement and reference channels. In this work, an eight-channel frontend was developed for contacting a 2×8 electrode array (8 measurement and 8 reference electrodes) with a large common electrode to the impedance gain-phase analyzer Solartron 1260 (S-1260). Using the three independent and truly parallel monitor channels of the S-1260, impedance of trapped cells and reference material was measured at the same time, thereby considerably increasing the performance of the device. The frontend electronics buffers the generator output and applies a potentiostatic signal to the common electrode of the chip. The applied voltage is monitored using the current monitor of the S-1260 via voltage/current conversion. The frontend monitors the current through the electrodes and converts it to a voltage fed into the voltage monitors of the S-1260. For assessment of the 8 electrode pairs featured by the chip, a relay-based multiplexer was implemented. Extensive characterization and calibration of the frontend were carried out in a frequency range between 100 Hz and 1 MHz. Investigating the influence of the multiplexer and the frontend electronics, direct measurement with and without frontend was compared. Although differences were evident, they have been negligible below one per cent. The significance of measurement using the complex S-1260-frontend-electrode was tested using Kohlrausch's law. The impedance of an electrolytic dilution series was measured and compared to the theoretical values. The coincidence of measured values and theoretical prediction serves as an indicator for electrode sensitivity to cell behavior. Monitoring of cell behavior on the microelectrode surface will be shown as an example.

Evaluation of electrical broad bandwidth impedance spectroscopy as a tool for body composition measurement in cows in comparison with body measurements and the deuterium oxide dilution method.

Body fatness and degree of body fat mobilization in cows vary enormously during their reproduction cycle and influence energy partitioning and metabolic adaptation. The objective of the study was to test bioelectrical impedance spectroscopy (BIS) as a method for predicting fat depot mass (FDM), in living cows. The FDM is defined as the sum of subcutaneous, omental, mesenteric, retroperitoneal, and carcass fat mass. Bioelectrical impedance spectroscopy is compared with the prediction of FDM from the deuterium oxide (DO) dilution method and from body conformation measurements. Charolais × Holstein Friesian (HF; = 18; 30 d in milk) crossbred cows and 2 HF (lactating and nonlactating) cows were assessed by body conformation measurements, BIS, and the DO dilution method. The BCS of cows was a mean of 3.68 (SE 0.64). For the DO dilution method, a bolus of 0.23 g/kg BW DO (60 atom%) was intravenously injected and deuterium (D) enrichment was analyzed in plasma and whey by stabile isotope mass spectrometry, and total body water content was calculated. Impedance measurement was performed using a 4-electrode interface and time domain-based measurement system consisting of a voltage/current converter for applying current stimulus and an amplifier for monitoring voltage across the sensor electrodes. For the BIS, we used complex impedances over three frequency decades that delivers information on intra- and extracellular water and capacity of cell membranes. Impedance data (resistance of extra- and intracellular space, cell membrane capacity, and phase angle) were extracted 1) by simple curve fit to extract the resistance at direct current and high frequency and 2) by using an electrical equivalent circuit. Cows were slaughtered 7 d after BIS and D enrichment measurements and dissected for the measurement of FDM. Multiple linear regression analyses were performed to predict FDM based on data obtained from body conformation measurements, BIS, and D enrichment, and applied methods were evaluated by cross-validation. The FDM varied widely between cows and was correlated to D enrichment in plasma ( = 0.91, < 0.05). Prediction of FDM by body size measurements was less precise ( = 0.84), but FDM prediction was more accurate using D enrichment in plasma ( = 0.90) and BIS ( = 0.99) data. Therefore, both BIS and D enrichment analysis resulted in similarly good predictions of FDM in cows, and we conclude that BIS could have the potential to predict FDM in dairy cows from 40 to 380 kg.

Broadband excitation for short-time impedance spectroscopy.

Frequency domain impedance measurements are still the common approach in assessing passive electrical properties of cells and tissues. However, due to the time requirements for sweeping over a frequency range for performing spectroscopy, they are not suited for recovering fast impedance changes of biological objects. The use of broad bandwidth excitation and monitoring the response as a function of time will greatly reduce the measurement time. The widespread usage of a square wave excitation is simple but not always the best choice. Here we consider different waveforms for excitation and discuss not only the advantages but also their limitations. Measurements in a miniaturized chamber where frequency and time domain measurements are compared show the suitability of different waveforms as excitation signals for the measurements of bio-impedance. The chirp excitation has been found to be most promising in terms of frequency range, signal-to-noise ratio and crest factor.

High electrical field effects on cell membranes.

Electrical charging of lipid membranes causes electroporation with sharp membrane conductance increases. Several recent observations, especially at very high field strength, are not compatible with the simple electroporation picture. Here we present several relevant experiments on cell electrical responses to very high external voltages. We hypothesize that, not only are aqueous pores created within the lipid membranes, but that nanoscale membrane fragmentation occurs, possibly with micelle formation. This effect would produce conductivity increases beyond simple electroporation and display a relatively fast turn-off with external voltage. In addition, material loss can be expected at the anode side of cells, in agreement with published experimental reports at high fields. Our hypothesis is qualitatively supported by molecular dynamics simulations. Finally, such cellular responses might temporarily inactivate voltage-gated and ion-pump activity, while not necessarily causing cell death. This hypothesis also supports observations on electrofusion.

Prediction of intramuscular fat by impedance spectroscopy.

Multiple multi-frequency impedance measurements during the computer controlled passage of a probe through the M. longissimus dorsi in pork and beef were applied. It was expected that the variability in impedance would correlate with the intramuscular fat (IMF) due to the inhomogeneous distribution of electrolytes and fat. We conducted our experiments in pig carcasses at different, well defined times post-mortem in varying directions of puncture (Experiment 1) and predicted the intramuscular fat in pork and beef by regression (Experiment 2). The highest correlations were obtained in experiment 1 for parameters characterising the variability of the impedance 24h post-mortem and insertion of the probe through the back fat and muscle towards the body cavity (r=0.54-0.79, P<0.001). Both of these were chosen for the measurements in experiment 2. Regression for the prediction of IMF in pork and beef in experiment 2 resulted in R(2) values of 0.12 and 0.48, respectively; and in RMSE values of 0.67 and 0.64, respectively. The correlation between the predicted and the IMF analysed by n-hexane extraction or Near Infrared Transmission varied from 0.28 to 0.69 (P<0.001) depending on species and breed. A selection of the carcasses for high IMF (above a certain threshold) using the impedance measurements agreed poorly with the analysed IMF. Depending on the level of IMF within a breed, low IMF contents were often over-predicted (3.4-92.7%) or high IMF contents were estimated as too low (0-80.9%). Breed specific regression equations could improve the accuracy. These data indicate that the selectivity of the impedance method in the configuration presented here is not yet sufficient for practical use.

Local and transient structural changes in stratum corneum at high electric fields: contribution of Joule heating.

Electroporation of skin is accompanied by local heating, such that thermally induced structural changes of the stratum corneum (SC) accompany the field effect. Comparing on the time scale, the local changes in structure, temperature and conductance of the SC, during and after the pulse, it is seen that Joule heating also facilitates the subsequent molecular transport. It is found that the transport of medium-sized, ionic molecules occurs through localized transport regions (LTR). The size of a LTR increases with the pulse length, whereas the density of the LTRs increases with increasing voltage, for instance at U(SC=)80 V, the LTR cover approximately 0.02--1% of the surface area. The state of low resistance within the LTR is long-lived. During high voltage application, the center of the LTR is heated above the phase transition temperature of the SC lipids (70 degrees C) and the heat front propagates outwards. Inside the SC, the pulse causes aggregates of small-sized vesicles. At a higher temperature, the aggregate formation and their disappearance are delayed. Multiple pulses with the applied voltage of U(appl)=80 V induce the formation of long-lasting vesicle aggregates with a diameter of slashed circle=1--30 microm, covering 0.05--0.5% of the total sample area. The electric energy dissipated within the LTR during high voltage application is apparently sufficient to raise the temperature well above the phase transition temperature of the lipids of the SC, accounting for the conformational changes from the multi-lamella to the vesicular structures.

Prediction of carcass composition by impedance spectroscopy in lambs of similar weight.

Previous research on impedance measurements for the prediction of carcass composition was predominantly carried out on animals that varied widely in body weight, breed, or sex. The high accuracy for the estimated lean or fat mass was mainly obtained by including the body weight in the regression equations. The objective of this study was the prediction of carcass composition in lambs of similar weight. We used 70 male German Merino Mutton lambs and 70 male German Blackheaded Mutton lambs with 35 and 45kg live weight each. Impedance measurements with different electrode placements were carried out in vivo and on carcasses 20min and 24h postmortem. The carcass composition was ascertained by dissection of the left carcass side into lean, fat, and bone. R(2)-values for prediction of lean mass by impedance and body weight ranged between 0.11 and 0.71 within breeds and weight groups and between 0.84 and 0.89in the total material. Lean percentage was estimated with R(2)=0.18-0.48 within breeds and weight groups. The corresponding values for the total material varied from 0.23 to 0.37. We conclude that the impedance method is not suitable for the prediction of lean or fat percentage, neither in lambs of similar weight nor in heterogeneous animals.

Surface area involved in transdermal transport of charged species due to skin electroporation.

The electroporative effect on the stratum corneum (SC) is highly localized. However, the fractional area for the transport of small ions and larger ionic species differs considerably during and after high voltage (HV) application. Electroporation of SC creates new aqueous pathways, accessible for small ions, such as Cl(-) and Na(+) ions. The pores are distributed across the skin surface yielding a fractional area for current flow during electroporation of up to 0.1%. An increased permeability after high voltage application persists within a fractional area on the order of 10(-3)%. The permeabilization of SC for larger, charged molecules (M > 200 g/mol) involves Joule heating and a phase transition of the long chain sphingolipids within local transport regions (LTR). The transport area for these molecules (approximately 10(-3)%) changes only negligibly after high voltage application.

Prediction of lamb carcass composition by impedance spectroscopy.

The objective of this study was to compare impedance spectroscopy with resistance measurements at a single frequency (50 kHz) for the prediction of lamb carcass composition. The impedance spectrum is usually recorded by measuring the complex impedance at various frequencies (frequency domain); however, in this study, we also applied the faster and simpler measurement in the time domain (application of a current step and measurement of the voltage response). The study was carried out on 24 male, German Black-headed Mutton lambs with an average BW of 45 kg. Frequency- and time domain-based impedance measurements were collected at 20 min and 24 h postmortem with different electrode placements. Real and imaginary parts at various frequencies were calculated from the locus diagram. Left sides were dissected into lean, fat, and bone, and right sides were ground to determine actual carcass composition. Crude fat, crude protein, and moisture were chemically analyzed on ground samples. Frequency- and time domain-based measurements did not provide the same absolute impedance values; however, the high correlations (P < 0.001) between these methods for the "real parts" showed that they ranked individuals in the same order. Most of the time domain data correlated higher to carcass composition than did the frequency domain data. The real parts of impedance showed correlations between -0.37 (P > 0.05) and -0.74 (P < 0.001) to water, crude fat, lean, and fatty tissue, whereas the relations to CP were much lower (from 0.00 to -0.47, P < 0.05). Electrode placements at different locations did not substantially improve the correlations with carcass composition. The "imaginary parts" of impedance were not suitable for the prediction of carcass composition. The highest accuracy (R2 = 0.66) was reached for the estimation of crude fat percentage by a regression equation with the time domain-based impedance measured at 24 h postmortem. Furthermore, there was not a clear superiority of measurements in a wide frequency range over a single frequency measurement at 50 kHz for the prediction of carcass composition. Even though we calculated the impedance at 50 kHz based on the locus diagram, which allowed for a high precision for predicting this impedance trait, single-frequency impedance devices typically used in practice cannot record the locus diagram and, therefore, exhibit a greater amount of uncertainty.

Electroporation of subcutaneous mouse tumors by rectangular and trapezium high voltage pulses.

The artificial electrotransfer of bioactive agents such as drugs, peptides or therapeutical nucleic acids and oligonucleotides by membrane electroporation (MEP) into single cells and tissue cells requires knowledge of the optimum ranges of the voltage, pulse duration and frequency of the applied pulses. For clinical use, the classical electroporators appear to necessitate some tissue specific presetting of the pulse parameters at the high voltage generator, before the actual therapeutic pulsing is applied. The optimum pulse parameters may be derived from the kinetic normal mode analysis of the current relaxations due to a voltage step (rectangular pulse). Here, the novel method of trapezium test pulses is proposed to rapidly assess the current (I)/voltage (U) characteristics (IUC). The analysis yields practical values for the voltage U(app) between a given electrode distance and pulse duration t(E) of rectangular high voltage (HV) pulses, to be preset for an effective in vivo electroporation of mouse subcutaneous tumors, clamped between two planar plate electrodes of stainless steel. The IUC of the trapezium pulse compares well with the IUC of rectangular pulses of increasing amplitudes. The trapezium pulse phase (s) of constant voltage and 3 ms duration, following the rising ramp phase (r), yields a current relaxation which is similar to the current relaxation during a rectangular pulse of similar duration. The fit of the current relaxation of the trapezium phase (s) to an exponential function and the IUC can be used to estimate the maximum current at a given voltage. The IUC of the falling edge (phase f) of the trapezium pulse serves to estimate the minimum voltage for the exploration of the long-lived electroporation membrane states with consecutive low-voltage (LV) pulses of longer duration, to eventually enhance electrophoretic uptake of ionic substances, initiated by the preceding HV pulses.

Joule heating during solid tissue electroporation.

The application of high-voltage pulses to biological tissue causes not only electroporation, a non-thermal phenomenon of pore creation within a lipid membrane due to an elevated electric field, but also significant heating. Once a biological membrane is porated, the current density increases several times, causing Joule heating. A combined experimental and theoretical study is reported. The theoretical temperature rise for a 1.25 kV cm(-1), 6 ms pulse is about 11.2 K for a tissue conductivity of 0.5 S m(-1) (i.e. myocardial tissue) during high-voltage application. Owing to the inhomogeneous electric field obtained with the use of needle electrodes, the temperature rises first at the electrodes, where the field strength reaches a maximum. Only for highly conductive tissue such as muscle was a temperature effect primarily observed in the bulk. Even if the temperature effect is biologically insignificant, it can affect the creation of stabile aqueous pathways by electroporation. The calculation of temperature distribution during high-voltage application, taking the electric field strength and the heat transfer into account, can be a useful tool for electrode optimisation.

P(y)-a parameter for meat quality.

The P(y) is a parameter which assesses the integrity of the cell membranes. It is a direct indicator for the volume fraction of cells surrounded by insulating cell membranes. The P(y) has been shown to correlate well with meat quality parameters like the drip loss or pH. It is a useful parameter for the discrimination between normal suited meat and PSE meat. The measurement is instantaneous and nondestructive. Due to aging of meat, P(y) depends on the time post mortem. It shows the highest significance between 4 and 24 h p.m.

Non-linearity of molecular transport through human skin due to electric stimulus.

The multilamellar bilayer system of the skin's stratum corneum (SC) provides the main barrier to transdermal transport of ions and charged molecules. Electrically driven transport of charged species at low trans-SC voltages (U(SC)<5 V) occurs predominantly via pre-existing aqueous pathways. In contrast, high voltage, (HV; U(SC)>50 V) has been hypothesized to involve electroporation within the SC's multilamellar bilayer membranes, creating new aqueous pathways that contribute to a rapid, large increase in transport. Thus, it might be expected that HV-pulses would always increase subsequent iontophoresis. Here we show, however, that for some charged molecules the opposite occurs, because the low skin resistance due to new aqueous pathways leads to an actual decrease in U(SC) for the same applied current, and the transport of some, highly charged molecules has a highly nonlinear dependence on U(SC).

Perturbation of human skin due to application of high voltage.

Electroporation is believed to be the effect that greatly enhances the transport of water-soluble molecules across the stratum corneum (SC) by application of short high voltage pulses. However, electroporation was originally a phenomenon investigated at the level of cell and model membranes, which is only partially comparable to the complicated structure of the stratum corneum. Here, we show, that electroporation is accompanied by other effects, which may be primarily involved in creation of new pathways and altering existing pathways, respectively. Experimental evidence shows that the dramatic increase in skin permeability is due to synergistic effect of electric field and heating by high local current density. Heating starts at small spots, not related to a visible skin structure and results in a propagating heat front. The phase transition of the SC lipids plays a major role in skin permeability during the pulse. The permeability after a high voltage pulse correlates well with the surface area showing a permanent low electrical resistance after pulsing. The main transport of water-soluble molecules is facilitated by the electric field due to the electrophoretic driving force in conjunction with the high permeability due to the breakdown of the multilamellar system of the SC lipids.

Overcoming electrically induced artifacts in penetration studies with fluorescent tracers.

The use of model molecules in transdermal transport studies reveals transport behavior while providing an economical setup by detection of readily measured quantities such as fluorescence, radioactivity or absorbance of low-cost substances. Water soluble fluorescent tracers such as calcein have been repeatedly used as model molecules in transdermal transport studies. However, if electrically enhanced calcein transport across the human skin barrier is measured, artifacts due to interaction between calcein and electrode byproducts influence the result. Here, we describe an experimental setup which avoids known artifacts and makes calcein or other fluorescent tracers a suitable model for transdermal transport studies.

Evaluation of fast time-domain based impedance measurements on biological tissue.

Bio-impedance measurements are widely used for characterization of biological objects. Although the measured impedance of such objects is independent of the measurement method used, slight differences between measurements in the frequency and time domain are found. For many practical applications time domain based measurements are advantageous, but they are often rejected as not accurate. In order to show their suitability for bio-impedance measurements we used a special arrangement of time domain and frequency domain based measurements at the same biological specimen (canine liver) with the same electrodes. A reasonable coincidence in the measurement results could be shown. Moreover we used only a fraction of the time domain measurement data in order to demonstrate a significant reduction in measurement time while maintaining a reasonable accuracy. An algorithm for fast processing of the time domain data without transformation into the frequency domain is provided.

Mechanistic studies of skin electroporation using biophysical methods.

The mechanism by which high-voltage pulses transiently disrupt lipid bilayers in cell membranes has been the subject of controversy since electroporation was first observed almost three decades ago. Determining the mechanism by which such pulses permeabilize the complex, multilamellar bilayer structures in skin poses an even greater challenge. To address this issue, a range of methods have been employed to perform biophysical characterization for skin electroporation studies. In this chapter, we provide an overview of these methods and highlight representative findings which biophysical characterization has yielded.

Electrical impedance spectroscopy for rapid and noninvasive analysis of skin electroporation.

Transient disruption of skin's barrier properties using high-voltage pulses involves complex changes in skin microstructure believed to be due to electroporation. Electroporation of cell membranes is a well known phenomenon which has found extensive use as a method of DNA transfection in biological laboratories (1-3). More recently, it has been shown that the multilamellar lipid bilayer membranes found in skin can also be electroporated (4-17). The dramatic and reversible increases in skin permeability caused by electroporation indicate that drugs might be delivered transdermally at significantly enhanced rates. Especially for macromolecules, such as protein- and gene-based drugs, electroporation-mediated transdermal drug delivery could be an important pharmaceutical approach.