面向血液葡萄糖测量的生物组织阻抗模型

本文推导了细胞膜电容与血糖浓度之间的关系,并将这种关系应用到Pauly和Schwan提出的弛豫模型中,再将弛豫模型应用于多重Cole-Cole介电模型,最后通过介电模型得出阻抗模型,建立起人体血糖浓度与组织介电谱,阻抗谱之间的联系。通过分析发现,细胞膜电容随着血糖浓度增加而增大,且当血糖浓度趋于无穷大时,细胞膜电容等于血糖浓度为0时细胞膜电容的1.53倍。对介电谱的仿真得出,当外加信号频率小于1 MHz时,介电常数实部随着葡萄糖浓度改变而发生明显变化。阻抗谱的研究结果表明,随着葡萄糖浓度的升高,阻抗的实部减小,阻抗虚部模增大,且分别在频率为1.48 MHz和0.55 MHz时变化得最快。本文建立的模型为血糖无创检测提供了一种新的方法和手段。     

The Transient Response and Impedance Locus of a Mobile Site Membrane

The kinetic properties of a mobile site membrane are analyzed theoretically and the results are compared with experimental data obtained from a simple model system. In the model system the measured response to a step change in electric current is a single relaxation process, in excellent agreement with the theoretically predicted behavior. To this relaxation process corresponds an anomalous capacitance whose properties are obtained by performing a frequency analysis of the system. By plotting the impedance locus of this mobile site membrane, the locus is shown to exhibit a 45° phase angle at high frequencies, a phenomenon which is generally associated with depletion layers.     

Impedance of goat lens as a function of frequency at DC voltages 0, 50, 100, 200 mV

Impedance characteristics of lens tissue has been studied using the AC impedance system (EG&G PARC, model 318) at different low voltage excitations using a Cole-Cole Plot. The extracellular resistance (Re), intracellular resistance (Ri), depressed angle (theta), total impedance (/Z/), and phase angle (phi) of the tissue were measured. The impedance locus between the real part (Z') and imaginary part (Z') of the complex impedance of lens was examined at discrete frequencies ranging from 10 mHz to 10 Hz. A decrease in extra-cellular resistance (Re) and increase in distribution of the factor (alpha) of 56.8 KOmega, 48.1 KOmega, 32.8 KOmega, 13.4 KOmega, and 0.40, 0.43, 0.46, 0.53 were found at 0 mV, 50 mV, 100 mV, and 200 mV, respectively. The total impedance (/Z/) and phase angle (phi) were also evaluated and the observed frequency dependent for the frequency range was tested as a function of excitation voltage. An attempt has been made to explain the effect of voltage stress on lens impedance.     

Frequency dependence of the frog skin impedance

At frequencies between 20 Hz and 1 kHz the impedance locus of the isolated frog skin is circular; below 20 Hz the resistive component of the impedance is frequently greater than would be expected from extrapolation of the high-frequency locus. At frequencies greater than twice the highest frequency at which there are deviations from the circular locus the variation of impedance Z with angular frequency ω is closely described by the equation Z = r₁ + r₀/[1+(jωτ)^1-α], where j is √?1, r¹ and r⁰ are resistance, τ is a time constant and α a constant in the range 0.02–0.14.     

An experimental study of the dielectric dispersion of solutions of cytochrome c at medium ionic strengths

In this paper, the results are presented of measurements of the dielectric dispersions of horse heart cytochrome c molecules in various buffers. The data are fitted to the Cole-Cole relaxation model. The influence of the concentration and the ionic strength on the parameters that result from the Cole-Cole model is determined. The measured data are compared with calculations based on the model presented previously. Good agreement is found between the model and the observed data.     

PGE(2) activation of apical membrane Cl(-) channels in A6 epithelia: impedance analysis.

Measurements of transepithelial electrical impedance of continuously short-circuited A6 epithelia were made at audio frequencies (0.244 Hz to 10.45 kHz) to investigate the time course and extent to which prostaglandin E(2) (PGE(2)) modulates Cl(-) transport and apical membrane capacitance in this cell-cultured model epithelium. Apical and basolateral membrane resistances were determined by nonlinear curve-fitting of the impedance vectors at relatively low frequencies (<50 Hz) to equations (P?unescu, T. G., and S. I. Helman. 2001. Biophys. J. 81:838--851) where depressed Nyquist impedance semicircles were characteristic of the membrane impedances under control Na(+)-transporting and amiloride-inhibited conditions. In all tissues (control, amiloride-blocked, and amiloride-blocked and furosemide-pretreated), PGE(2) caused relatively small (< approximately 3 microA/cm(2)) and rapid (<60 s) maximal increase of chloride current due to activation of a rather large increase of apical membrane conductance that preceded significant activation of Na(+) transport through amiloride-sensitive epithelial Na(+) channels (ENaCs). Apical membrane capacitance was frequency-dependent with a Cole-Cole dielectric dispersion whose relaxation frequency was near 150 Hz. Analysis of the time-dependent changes of the complex frequency-dependent equivalent capacitance of the cells at frequencies >1.5 kHz revealed that the mean 9.8% increase of capacitance caused by PGE(2) was not correlated in time with activation of chloride conductance, but rather correlated with activation of apical membrane Na(+) transport.     

Microwave absorption in oligomers of ethylene glycol

The dielectric properties of biologically and pharmaceutically important low-molecular weight ethylene glycols H(-OCH2CH2-)n -OH (n = 1,2,4,6) were investigated to clarify the effect of chain length on the dielectric properties. The measurement of dielectric constant and dielectric loss was carried out over the frequency range 200 MHz to 20 GHz at temperatures of 25 degrees C to 55 degrees C. It is found that in these molecules microwave dielectric losses are significant. The dispersion behaviour of these molecules can be represented by Cole-Cole equation. The dielectric properties of these homologous ethylene glycols are discussed in terms of the effects of chain length and intermolecular hydrogen bonds regarding the molecular conformations. These wide frequency range dielectric data have also been discussed in view of the suitable selection of the oligomer of ethylene glycol for cosmetic preparations and other pharmaceutical applications with the intention of protection of the skin from weak microwave radiations present in the surrounding environment. These systematic microwave dielectric data with frequency and temperature variation are not available and are provided in this paper.     

Effects of freeze-thaw injury on parameters of distributed electrical circuits of stems and needles of Scots pine seedlings at different stages of acclimation

Frost hardening and frost injury of both the stems and needlesof Scots pine (Pinus sylvestris L.) seedlings were studied byelectrical impedance analysis. This impedance analysis was basedon equivalent circuits with distributed circuit elements (DCE).A double-DCE model for stems and two single-DCE models for needlesprovided excellent fit to the experimental impedance data. However,the single-DCE model for needles which takes into account theasymmetry of the impedance arc proved more appropriate thanthe symmetric model. Several parameters changed in proportionto frost injury. In stems, extracellular resistance and onerelaxation time decreased with increasing damage, whereas intracellularresistance remained relatively unchanged. In needles, the overallpattern for extracellular resistance and relaxation time wassimilar to that in the stem. Intracellular resistance remainedapproximately constant in the case of the symmetric DCE model.During frost hardening, both extracellular and intracellularresistance increased in stems. In needles, extracellular resistanceincreased but relaxation time decreased with hardening. Theskewness of the impedance spectra in the Cole-Cole plot forneedles increased with hardening. The coefficient for distributionof the relaxation time(s) did not change in either stems orneedles with frost hardening but some changes were found withfrost damage. Key words: Pinus sylvestris L, electrical impedance, equivalent circuit, frost hardening, frost injury     

Some observations on the dielectric properties of hemoglobin's suspending medium inside human erythrocytes.

Dielectric permittivity and conductivity data for human erythrocytes exhibit two consecutive dispersions with frequency in the range from 0.1 to 250 MHz. The dispersion observed above 50 MHz yields a circle in the complex impedance plane with its center on the real axis, suggesting a Debye relaxation, for the erythrocyte interior medium, centered in the microwave frequency range as for bulk water. Moreover, the Maxwell mixture equation, indicates that this "free" water forms most of the suspending medium of hemoglobin macromolecules. These results extend to lower frequencies (earlier results obtained by Schwan) with biological tissues such as muscles, skin, or liver at microwaves frequencies.     

cAmp activation of apical membrane Cl(-) channels: theoretical considerations for impedance analysis.

Transepithelial electrical impedance analysis provides a sensitive method to evaluate the conductances and capacitances of apical and basolateral plasma membranes of epithelial cells. Impedance analysis is complicated, due not only to the anatomical arrangement of the cells and their paracellular shunt pathways, but also in particular to the existence of audio frequency-dependent capacitances or dispersions. In this paper we explore implications and consequences of anatomically related Maxwell-Wagner and Cole-Cole dielectric dispersions that impose limitations, approximations, and pitfalls of impedance analysis when tissues are studied under widely ranging spontaneous rates of transport, and in particular when apical membrane sodium and chloride channels are activated by adenosine 3',5'-cyclic monophosphate (cAMP) in A6 epithelia. We develop the thesis that capacitive relaxation processes of any origin lead not only to dependence on frequency of the impedance locus, but also to the appearance of depressed semicircles in Nyquist transepithelial impedance plots, regardless of the tightness or leakiness of the paracellular shunt pathways. Frequency dependence of capacitance precludes analysis of data in traditional ways, where capacitance is assumed constant, and is especially important when apical and/or basolateral membranes exhibit one or more dielectric dispersions.     

Dielectric response of some biological tissues

The dielectric properties of two freshly excised mice tissue samples (kidney, skeletal muscle) and also freshly excised Ehrlich solid tumor were measured in the frequency range from 20 Hz to 100 kHz using RLC bridges. The data were fitted to a summation of multiple Cole-Cole dispersion and also to the constant power law which is related formally to the fractal geometries of tissues using a genetic algorithm for optimization developed by the author. The data were in good agreement with the Cole-Cole equation for the three samples.     

Dielectric relaxation of DNA solutions. II

Real and imaganiry parts of complex dielectric constant of dilute solutions of DNA in 10^?3M NaCl with molecular weight ranging from 0.4 × 10⁶ to 4 × 10⁶ were measured at frequencies from 0.2 Hz to 30 kHz. Dielectric increments Δε were obtained from Cole-Cole plots and relaxation times τ_D from the loss maximum frequency. The τ_D of all samples agrees well with twice of the maximum viscoelastic relexation time in the Zimm theory, indicating that the low-frequency dielectric relaxiation should be ascribed to be the rotation of DNA. The rms dipole moment, which was obtained from Δε, agree well with that calculated from the counterion fluctuation theory. The dielectric increment was found to be greatly depressed in MgCl₂, which is resonably interpreted in terms of a strong binding of Mg⁺⁺ ions with DNA.     

Microwave dielectric studies on proteins,tissues, and heterogeneous suspensions

We summarize the results of several of our recent studies on the dielectric properties of protein solutions, tissues, and nonionic microemulsions at microwave frequencies extending to 18 GHz. The data in all cases are analyzed using the Maxwell mixture theory to determine the dielectric properties of the suspending water and the amount and dielectric properties of the water of hydration associated with the suspended phase. The dielectric data from the protein solutions and tissues are broadly consistent with the results of previous studies at UHF frequencies; they indicate hydration values in the range of 0.4–0.6 g water/g protein. There is evidence of a dielectric relaxation process occurring at low-GHz frequencies that can be attributed in part to dielectric relaxation of the “bound” water in the system. The remaining solvent water appears to have dielectric properties close to, if not precisely the same as, those of pure water. The average relaxation frequency of the suspending water in the microemulsions is reduced from that of pure water, evidently reflecting an average of that of the water of hydration (～5–6 GHz) and that of pure water. This reduced average relaxation frequency implies an increased average viscosity of the water and (by Walden's rule) accounts for the unexpectedly low ionic conductivity of the preparations.     

Passive electrical properties of the membrane and cytoplasm of cultured rat basophil leukemia cells. I. Dielectric behavior of cell suspensions in 0.01-500 MHz and its simulation with a single-shell model

Frequency dependence of relative permittivity (dielectric constant) and conductivity, or the 'dielectric dispersion', of cultured cells (RBL-1 line) in suspension was measured using a fast impedance analyzer system capable of scanning 92 frequency points over a 10 kHz-500 MHz range within 80 s. Examination of the resulting dispersion curves of an improved reliability revealed that the dispersions consisted of at least two separate components. The low-frequency component (dispersion 1) had a permittivity increment (delta epsilon) of 10(3)-10(4) and a characteristic frequency (fc) at several hundred kHz; for the high-frequency component (dispersion 2), delta epsilon was smaller by a factor of 10(2) and fc = 10-30 MHz. Increments delta epsilon for both components increased with the volume fraction of cell suspension, while fc did not change appreciably as long as the conductivity of suspending medium was fixed. By fitting a model for shelled spheres (the 'single-shell' model) to the data of dispersion 1, the dielectric capacity of the plasma membrane phase (Cm) was estimated to be approx. 1.4 microF/cm2 for the cells in an isotonic medium. However, simulation by this particular shell model failed to reproduce the entire dispersion profile leaving a sizable discrepancy between theory and experiment especially at frequencies above 1 MHz where dispersion 2 took place. This discrepancy could not be filled up even by taking into consideration either the effect of cell size distribution actually determined or that of possible heterogeneity in the intracellular conductivity. The present data strongly indicate the need for a more penetrating model that effectively accounts for the behavior of dispersion 2.     

Dielectric behavior of DNA solution at radio and microwave frequencies (at 20 degrees C).

The dielectric constant and conductivity of calf thymus DNA were investigated at frequencies between 0.1 MHz and 70 GHz. This work is to investigate the dielectric properties of DNA in low gigahertz region and also to study whether the dielectric behavior of the water is affected by the presence of highly charged DNA. The results of these measurements indicate the presence of two anomalous dispersions, the one between 1 MHz and 1 GHz and the second one above 1 GHZ. The dispersion at low frequencies is likely to arise from polar groups in the DNA molecule. The relaxation behavior of unbound water in DNA solution is only slightly affected by the presence of DNA at concentrations below 1%.     

Dynamics of water in supercooled aqueous solutions of glucose and poly(ethylene glycol)s as studied by dielectric spectroscopy

The dielectric behaviour of aqueous solutions of glucose, poly(ethylene glycol)s (PEGs) 200 and 600, and poly(vinyl pyrrolidone) (PVP) has been examined at different concentrations in the frequency range of 10(6)-10(-3) Hz by dielectric spectroscopy and by using differential scanning calorimetry down to 77 K from room temperature. The shape of the relaxation spectra and the temperature dependence of the relaxation rates have been critically examined along with temperature dependence of dielectric strength. In addition to the so-called primary (alpha-) relaxation process, which is responsible for the glass-transition event at T(g), another relaxation process of comparable magnitude has been found to bifurcate from the main relaxation process on the water-rich side, which continues to the sub-T(g) region, exhibiting relaxation at low frequencies. The sub-T(g) process dominates the dielectric measurements in aqueous solutions of higher PEGs, and the main relaxation process is seen as a weak process. The sub-T(g) process was not observed when water was replaced by methanol in the binary mixtures. These observations suggest that the sub-T(g) process in the aqueous mixtures is due to the reorientational motion of the 'confined' water molecules. The corresponding dielectric strength shows a noticeable change at T(g), indicating a hindered rotation of water molecules in the glassy phase. The nature of this confined water appears to be anomalous compared to most other supercooled confined liquids.     

The AC Impedance of Frog Skin and Its Relation to Active Transport

The AC electrical impedance of frog skin was measured in the range 1 cycle/second to 50 kc/second by injecting current sinusoidally at low current density. The behavior of the skin was found to be linear so the usual concepts of impedance could be validly employed. In the range 1 cycle/second to 5 kc/second, the impedance traces out a circular arc locus with its center off the real axis; thus the skin could be represented by a series resistance and a parallel combination of a conductance and a phase shift element. The phase shift element has an impedance angle of about 80 degrees , current leading voltage, with an equivalent capacitance of about 2 muf/cm(2). The phase shift and the equivalent capacitance were independent of the experimental conditions. The parallel conductance, which was responsible for most of the low frequency impedance, could be subdivided into two approximately equal conductances, one associated with sodium ion current and the other associated with chloride ion current. Both currents were determined mainly by the concentrations of the respective ions bathing the outside of the skin. The response to changes in concentration and the response to CO(2) indicated that the chloride current was passive, but the sodium current appeared to be associated with the active transport mechanism; little sodium could pass through the skin unless associated with active transport.     

Temperature-dependent dielectric properties of slightly hydrated horn keratin

With an aim to reveal the mechanism of protein-water interaction in a predominantly two phase model protein system this study investigates the frequency and temperature dependence of dielectric constant epsilon' and loss factor epsilon' in cow horn keratin in the frequency range 30 Hz to 3 MHz and temperature range 30-200 degrees C at two levels of hydration. These two levels of hydration were achieved by exposing the sample to air at 50% relative humidity (RH) at ambient temperature and by evacuating the sample for 72 h at 105 degrees C. A low frequency dispersion (LFD) and an intermediate frequency alpha-dispersion were the two main dielectric responses observed in the air-dried sample. The LFD and the high frequency arm of the alpha-dispersion followed the same fractional power law of frequency. Within the framework of percolation cluster model these dispersions, respectively have been attributed to percolation of protons between and within the clusters of hydrogen-bonded water molecules bound to polar or ionizable protein components. The alpha-dispersion peak, which results from intra-cluster charge percolation conformed to Cole-Cole modified Debye equation. Temperature dependence of the dielectric constant in the air-dried sample exhibited peaks at 120 and 155 degrees C which have been identified as temperatures of onset of release of water bound to polar protein components in the amorphous and crystalline regions, respectively. An overall rise in the permittivity was observed above 175 degrees C, which has been identified as the onset of chain melting in the crystalline region of the protein.     

Microwave dielectric measurements of erythrocyte suspensions.

Complex dielectric constants of human erythrocyte suspensions over a frequency range from 45 MHz to 26.5 GHz and a temperature range from 5 to 40 degrees C have been determined with the open-ended coaxial probe technique using an automated vector network analyzer (HP 8510). The spectra show two separate major dispersions (beta and gamma) and a much smaller dispersion between them. The two major dispersions are analyzed with a dispersion equation containing two Cole-Cole functions by means of a complex nonlinear least squares technique. The parameters of the equation at different temperatures have been determined. The low frequency behavior of the spectra suggests that the dielectric constant of the cell membrane increases when the temperature is above 35 degrees C. The real part of the dielectric constant at approximately 3.4 GHz remains almost constant when the temperature changes. The dispersion shifts with temperature in the manner of a thermally activated process, and the thermal activation enthalpies for the beta- and gamma-dispersions are 9.87 +/- 0.42 kcal/mol and 4.80 +/- 0.06 kcal/mol, respectively.     

Counterion fluctuation and dielectric dispersion in linear polyelectrolytes

The thermal fluctuation in the concentration of counterions bound to a rodlike polyion was analyzed by expanding the fluctuation in a Fourier series along the rod. The amplitude and the relaxation time of fluctuations of various wave lengths were obtained as functions of the charge density and the length of the polyion. From these results the real and imaginary parts of the dielectric constant of the polyelectrolyte solution were derived as the sum of contributions of fluctuations of different modes. The dielectric dispersion curve or the Cole-Cole plot obtained was found to be in good agreement with experimental data.