KR100530689B1 - Highly time resolved impedance spectroscopy - Google Patents

Abstract

A highly time resolved impedance spectroscopy that enhances the measurement of the dynamics of non-stationary systems with enhanced time resolution. The highly time resolved impedance spectroscopy includes an optimized, frequency rich a.c., or transient, voltage signal is used as the perturbation signal, non-stationary time to frequency transformation algorithms are used when processing the measured time signals of the voltage and current to determine impedance spectra which are localized in time; and the system-charachterizing quantities are determined from the impedance spectra using equivalent circuit fitting in a time-resolution-optimized form.

Description

Highly time resolved impedance spectroscopy

Related Applications

This application is subject to the German patent application Ser. No. 19949107.0, filed on October 12, 1999, filed on October 12, 1999, which is incorporated herein by reference, and the title "HIGHLY TIME, filed on April 15, 200. RESOLVED IMPEDANCE SPECTROSCOPY "German Patent Application No. 10018745.5 is claimed as priority.

background

1. Field of Invention

FIELD OF THE INVENTION The present invention generally relates to electrical impedance measurements, and more particularly to electrochemical impedance spectroscopy.

2. Description of related technology

Impedance spectroscopy is a procedure used to characterize the electrical and electrochemical properties and the changes over time of the studied systems. Typically, an alternating voltage signal is applied between the working electrode and the counter electrode. Where applicable, the DC bias voltage applied at the same time is monitored with a reference electrode. In addition to the current response of the system, all of the applied alternating voltage signals are measured. The complex electrical resistance of the system (referred to as impedance Z (ω)) can be calculated from the exponents of the voltage and current signals in the frequency range according to equation (1) as a function of frequency. Impedance values for multiple frequencies define the impedance spectrum.

Various electrical characteristics or electrochemical processes of the system can be obtained from the characteristics of the impedance spectrum. Especially for systems where direct current cannot flow, alternating or transient voltage signals should be used in the study. Because of the advanced information content of impedance spectroscopy, this is often used as a desirable technique for measuring impedance spectra. In electrochemistry, for example, impedance spectroscopy is a standard analytical technique for studying corrosion processes, redox reactions, liquid and solid electrolytes, thin polymer films, films, batteries, and the like. Several papers provide an overview and overview of the techniques and applications of electrochemical impedance spectroscopy. JR MacDonald: “Impedance Spectroscopy” (John Wiley & Sons, New York: 1987) and C. Gabrielli: Technical Report No. , incorporated herein by reference . 004 / 83.1983; C.Gabriell: Technical Report No. part. See No. 12860013.1990.

Impedance spectroscopy is also used to characterize semiconductor materials. A. Bard's Electrochemical Methods. (Wiley & Sons, New York: 1980); In biotechonology, BA Cornell, Braach-Maksvytis, LG King et al., "A Biosensor that Uses Ion-channel Switches." Nature. 387, pages 580-583 (1997). S. Gritsch, P. Nollert, F. Jahnig et al., "Impedance Spectroscopy of Porin and Gramicidin Pores Reconstituted into Supported Lipid Bilayers on Indiu-Tin-Oxide Electrodes." Langmuir . 14 (11), 3118-3125 (1998). All of the above referenced publications are incorporated herein by reference in their entirety.

The use of impedance spectroscopy is increasing significantly, especially in the field of biotechnology. In most cases, the electrodes are altered by chemical or physical bonding of biofunctional molecules and sets (eg, lipid membrane / protein membrane). Impedance spectroscopy is also used to detect adsorption processes.

There are two types of impedance spectroscopy methods: method I in the frequency range and method II in the time range for measuring the impedance spectrum.

Method I (Frequency Range Progression): In a first form, a sinusoidal signal at a constant frequency and amplitude is applied within a discrete period so that the complex impedance of this discrete frequency is determined. To obtain the spectrum, sinusoidal signals are applied at different frequencies. The time resolution, defined by the length of time that the determined spectra follow each other, is low in this form of impedance spectroscopy. The time for acquiring the data records making up the spectrum is the period of the plurality of lowest frequencies included in the spectrum. The exact duration also depends on the number of frequencies in the spectrum. At the next frequency change, a transition period is considered in the system to balance. The time decomposition of a conventional spectral sequence is several seconds to several minutes depending on the observed frequency band.

Method II (Time Range Progression): In a second form, a frequency rich alternating voltage signal, such as square wave pulses, structured or white noise, is applied. By using Fourier transform, the impedance spectrum can be determined from the signal data recording of the voltage and current signals over time. Thus, the impedance spectrum is limited by known Fourier transform limitations for bandwidth and frequency resolution. The measurement time is usually at least as long as one period of the lowest frequency in the spectrum of interest. Typically, the measurement period of the various periods of the lowest frequency in the spectrum is required to sufficiently improve the signal to noise ratio. The maximum time decomposition depends on the repetition rate at which data records or sets for the Fourier transform are obtained. Since the impedance of all frequencies in the spectrum is measured simultaneously in this way, time resolution is usually much better than the time resolution of the first method.

Method I is commonly used to characterize stationary systems or systems exhibiting slow dynamics. Commercial devices (frequency response analyzers (FRA)) use these measurements. Today, Method II is primarily used for measurements where the impedance spectrum includes very low frequencies, such as about 10 ⁻⁴ Hz, as required in corrosion studies.

By systems, the electrical properties of non-stationary systems, whose characteristics are not constant over time, are in many cases sufficient time resolution by method I or method II of impedance spectroscopy. Cannot be measured using. The time-averaged results of Method I (summing over several periods of all frequencies in the spectrum) and Method II (over several periods of the lowest frequency included in the spectrum) show the change in the system over a time period faster than the average time. Do not allow them to be resolved by a sequence of impedance spectra. The average time should be greatly reduced in impedance spectrometers to measure abnormal systems with sufficient time resolution. The single impedance spectrum will then represent the electrical states of the system placed in time. In addition, the individual spectra should be determined at high repetition rates to determine the amount of time lapse characterizing the system with maximum time resolution.

One example of an abnormal system that could not be measured by conventional impedance spectroscopy is integrated lipid bilayers that switch ion channels. The kinetics of many biological processes, such as opening and closing ion channels in lipid bilayers, occur on a time scale of several milliseconds. These systems are very involved in the fields of biotechnology and human physiology.

Another example of abnormal systems that could not be measured by conventional impedance spectroscopy is metal and semiconductor interfaces with liquid and solid electrolytes with highly dynamic interface processes. When characterizing semiconductors in the electrochemical field, conventional impedance spectroscopy cannot be used for many dynamic processes, such as in situ observation or relaxation of the etching process of fast electrochemical systems after a voltage jump, because the time required This is because decomposition is not possible with the required bandwidths.

From the above discussion, the need for an impedance spectroscopy method and apparatus that can measure high dynamic abnormal systems will become apparent. The present invention fulfills this need.

1 shows an example plot versus time of a structured noise voltage signal U (t).

2 shows a power spectral density plot of structured noise voltage and current signals U (f) and I (f).

3 is a plot showing examples of a sequence of impedance spectra as a function of frequency f and time τ for an abnormal system.

4 is a schematic diagram of an equivalent circuit.

5 is a block diagram illustrating one embodiment of a high time resolved impedance spectroscopy system.

FIG. 6 shows examples of parameters for structured noise signal and data processing of the simulations described in the “simulations” column and the measurements described in the “fast model” column and the “Gigaohm model” column. Table showing them.

FIG. 7 is a graph showing an example of time lapse for resistance R ₂ of the abnormal system of FIG. 4 (simulation). FIG.

8 is a graph of the extension of FIG. 7 showing a transition in the value of R ₂ ;

FIG. 9 is a graph showing an example of time lapse for the values of the equivalent circuit elements of FIG. 4 measured by high time resolved impedance spectroscopy. FIG.

10 (a) is a graph showing an example of the real part of the impedance spectrum which is the basis for two points in the time lapses of FIG.

10 (b) is a graph showing an example of an imaginary part of an impedance spectrum which is the basis for two points in the time course of FIG.

FIG. 11 is a graph showing an example of time lapse for the values of the equivalent circuit elements of FIG. 4 measured with high time resolved impedance spectroscopy. FIG.

FIG. 12A is a graph showing an example of a real part of an impedance spectrum which is the basis for a point in the time course of FIG.

FIG. 12 (b) is a graph showing an example of an imaginary part of an impedance spectrum which is the basis for a point in the time lapses of FIG.

13 is a block diagram illustrating an example of high time resolved impedance spectroscopy.

The present invention provides a method and apparatus for measuring impedance and impedance spectrum in a fast sequence. In fast sequences, the measurement of impedance and impedance spectra provides repeated or continuous characteristics of the electrical characteristics of the system under study. High time resolved impedance spectroscopy improves the measurement of the dynamics of abnormal systems due to improved time resolution.

There are three aspects of high time resolved impedance spectroscopy: (1) an optimized frequency rich alternating current or transient, voltage signal is used as a disturbing signal; (2) Unsteady time to frequency conversion algorithms are used when processing the measured time signals of voltage U (t) and current I (t) to determine the sequence of the impedance spectrum, where each spectrum is placed in time; (3) The amount of characterizing the system is determined from the impedance spectrum using an equivalent circuit suitable for a time resolved optimized form.

The present invention provides repeated or continuous features of the electrical properties of the system under study with methods and apparatus for measuring impedance and impedance spectra in fast sequences. High time resolved impedance spectroscopy can measure the dynamics of abnormal systems with improved time resolution.

There are three aspects of high time resolved impedance spectroscopy: (1) an optimized frequency rich alternating current or transient, voltage signal is used as a disturbing signal; (2) abnormal time to frequency conversion algorithms are used when processing the measured time signals of voltage U (t) and current I (t) to determine the sequence of the impedance spectrum, where each spectrum is placed in time; (3) The amount of characterizing the system is determined from the impedance spectrum using an equivalent circuit suitable for a time resolved optimized form.

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The optimized frequency rich disturbance signal may have a number of different formats. The frequency rich disturbance signal may include any desired amount of contributing frequencies that overlap one signal. For example, the frequency rich disturbance signal may be a certain number of sinusoidal vibrations, or superposition of voltage jumps, pulses and noise signals. The higher the signal-to-noise ratio of the voltage disturbance and current response signals, the lower the time extension of the database required to achieve some measurement accuracy.

Structured noise can be used as a disturbing signal of high time resolved impedance spectroscopy. Structured noise is defined as the superposition of a finite number of sinusoidal vibrations. 1 is a diagram illustrating an example plot versus time of structured noise voltage signal U (t) 18. 2 is a diagram illustrating a power spectral density plot of structured noise voltage and current signals U (f) 20 and I (f) 22. The structured noise shown in Figs. 1 and 2 can be mathematically represented by the following equation (2).

In equation (2), U _{0, i} is the amplitude of the i-th sinusoidal vibration, and the angular frequencies ω _i and φ _i are phase. A preferred signal to noise ratio can be obtained when the disturbing signal U (t) is tuned or optimized at the center of the system and measurement. The optimization of disturbance signals has been the subject of some research. Rev. Sci. Instrum by GS Popkirov and RN schindler. 63 (11), 5366-5372 (1992), entitled “A New Impedance Spectrometer for the Investigation of Electrochemical Systems”; Rev. by GS Popkirov and RN schindler . Sci. Instrum. 64 (11), 3111 to 3115 (1993), entitled " Optimization of the Perturbation Signal for Electrochemical mpedance Spectroscopy in the Time Domain. &Quot; All of the above referenced publications are incorporated herein by reference in their entirety.

Several optimization steps are aspects of high time resolved impedance spectroscopy, including the frequency band, number and frequency at which impedance is measured, and the amplitude and phase of the individual contributing frequencies. Optimization of the disturbance signal involves the selection of the frequency band in which the impedance spectrum is measured. Thus, the frequency band of the disturbing signal must be chosen to cover the maximum spectral range to be covered by the measurement. However, when evaluating the impedance spectrum, only selected frequencies of the n frequencies in the disturbing signal can be used. This aspect is discussed further below.

Further, optimization of the disturbance signal involves selecting the desired number n and frequency position ω _i of the n respective contribution frequencies. Any desired number and frequency positions of the individual frequencies can be used. This maximizes the adaptability of the high time resolved impedance spectrometer for the system under study for the user.

In one embodiment, the power applied to the sample by the structured noise signal depends on the number of frequencies in the noise signal. Since many systems exhibit linear operation with only small amplitudes or low power disturbances, it is desirable to keep the number of frequencies as low as possible. On the other hand, reproduction of the characteristic system response requires a minimum number of frequencies in the impedance spectrum. In impedance spectroscopy, since this impedance is usually determined on the order of several frequency magnitudes, the desired number of individual frequencies per frequency decade is determined unless certain system requirements require deviating from this desired number. do. In one embodiment, five individual frequencies per frequency decade are a reasonable number.

In one embodiment, the frequency position distribution of the individual frequencies is selected from a logarithmic uniform distribution over the entire frequency band. In another embodiment, the frequency position distribution of the selected individual frequencies varies in a logarithmic uniform distribution in such a way as to avoid the formation of harmonics. Avoiding harmonics helps to prevent modulation of the impedance spectrum measured by nonlinear system responses or excitation of higher harmonics.

Another aspect of the disturbing signal that can be optimized is in the amplitude U _{0, i} of the individual frequencies. The desired amplitude of any individual frequencies can be selected. In one embodiment, the amplitudes of the individual frequencies are adapted to the measurement state in order to best utilize the linear range of the measuring amplifier and to obtain an optimal signal to noise ratio for each frequency in the system. In one embodiment, the amplitudes of the individual frequencies of the disturbance signal are such that the power of the individual frequencies of the disturbance signal is constant (good for use in strong nonlinear systems). In another embodiment, the power of the current response of the excited individual frequencies is constant (reducing the effect of nonlinearity of the measurement amplifier, see FIG. 2). In another embodiment, the power of the individual frequencies of the disturbance signal and the current response reveals a minimal difference (optimum signal to noise ratio).

Another aspect of disturbance that can be optimized is in the phase φ _i of the individual frequencies. The phase angle of any desired individual frequencies can be selected. In one embodiment, the linear system response can be guaranteed by the lowest possible overall amplitude of the disturbance signal. The phases of the individual frequencies of the structured noise are selected such that the overall signal amplitude is minimized while the amplitudes of the individual frequencies are equal. Thus, the power of the individual frequencies is maintained in spite of the reduced overall amplitude, or as the overall amplitude is fixed, the power of the individual frequencies is maximized to improve the signal to noise ratio.

<Abnormal Time-to-Frequency Conversion Algorithm>

An aspect of high time resolved impedance spectroscopy lies in the determination of the time-placed impedance spectrum, with the average time reduced at high repetition rates. Unsteady time-to-frequency conversion algorithms are used in high time resolved impedance spectroscopy. The average time corresponds to the prolongation of the database required to determine the individual impedance spectra. The sequences X (ω) of the spectrum placed in time span the small time period of the measurement signal X (t) (either U (t) or I (t)) and apply window functions that repeat this procedure and , From the time signals X (t) by applying window functions shifted by short time or short intervals. These time signals, including the alternating voltage signal U (t) applied to the sample and the current response I (t) of the sample, are continuously or partially continuous over a given period of time limited only by the storage capacity of the data storage medium used. Is recorded. A partially contiguously written data set may be defined as repeated recording of finite data sets of any length with any or selected interrupt intervals between successive data sets.

Examples of anomalies, that is, time-to-frequency transformation procedures, are the sliding short time Fourier transform, the wavelet transformation, and the Wigner or Wigner-Ville distribution. . Two of these methods, namely (1) sliding short-time Fourier transform; And (2) wavelet sides will be described below.

In the sliding short-time Fourier transform, the time-to-frequency transform is performed corresponding to the equation for the continuous short-time Fourier transform.

In equation (3), x (t) corresponds to the measured time signal, and g (t) is a window function with a characteristic that is adjusted to optimize the spectrum X (τ, ω) obtained as a result of the modifying step. See Time-frequency Analysis by L. Cohen (Prentice Hall PTR, Englewood Cliffs, New York, 1995), incorporated herein by reference in its entirety. Several possible window functions have been described. See Proceedings of the IEEE 66 (1), 51-83 (1978), “On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform.” By FJ Harris, incorporated herein by reference.

The resulting impedance spectrum Z (τ, ω) is obtained according to equation (1) from the spectral indices of the voltage signal U (τ, ω) and the current signal I (τ, ω). This impedance spectrum is assigned to time τ, i.e., characterizing the sample studied at time τ of the measurement. Thus, the spectral information is placed at time tau by considering and weighting only the sections of the entire data record around time tau for time-to-frequency conversion. The impedance spectrum calculates the complex impedance depending on the angular frequency ω = 2 * π * f, where f is the frequency. The sequence of impedance spectra is obtained by iteratively calculating the impedance spectra according to the described procedure, wherein the time τ shifts by the interval Δτ for each subsequent spectrum.

3 is a plot showing examples of a sequence of real 32 and imaginary 34 impedance spectra as a function of frequency f and time τ for an abnormal system. In the manner described above, the measured data records are fully analyzed when τ shifts as much as possible from the start of measurement by the interval Δτ of the data record. If the interval Δτ is smaller than the extension of the window function g (t), it is said to be a sliding short time Fourier transform, since the window functions g (t-z) applied to the data records overlap in the sequence. The interval Δτ at which the window function shifts between each transformation defines the time decomposition procedure.

In order to obtain high time decomposition, Δτ must be correspondingly small. Similarly, the time when g (t) is not zero should be as small as possible to reduce the average time in the time-to-frequency conversion. The window function g (t) defines the maximum peak-to-peak decomposition Δt _pp of the short time Fourier transform provided by the following equation.

When the measured data records of U (t) and I (t) are in discrete form, for example in the case of computer-assisted or digitized data acquisition, the discrete algorithm of short-time Fourier transform of equation (5) is continuous Used instead of short time Fourier changes.

T _a is the sampling interval of data acquisition, n is a running variable for the number of observed data points, and N is the total number of data points. All other quantities correspond to the limitations of successive short time Fourier transforms. Typically, the shift interval Δτ is _a multiple of the total number of T _a . The frequency decomposition of the Δf of each impedance spectrum and the upper frequency limit f _max follow the sampling law expressed in equation (6). Signalverarbeitung by E. Schrufer, which is hereby incorporated by reference. (Hanser, Munich: 1990).

Where N _w is the number of data points where the window function g (nT _a ) is non-zero.

In the wavelet transform, the time-to-frequency transform is performed corresponding to the formula of the continuous wavelet transform.

O. Rioul and M. Vetterli: Title of Signal Processing Technology and Applications , edited by JG Ackenhusen (The Institute of Electrical and Electronics Engineers, Inc., New York: 1995), pages 85-109, incorporated herein by reference. Wavelet and Signal Processing ".

Instead of the variable of the angular frequency ω, the scale s is usually used for the wavelet transform. This is due to the fact that the pulse is the response of the wavelet functions h _s (t) used, as in the case where the scales with s have the base or base wavelet of the formula.

One possible form of the window function h (t) is the modulated window function g (t) as used for short-term Fourier transforms.

In equation (9), ω ₀ corresponds to the modulation frequency of the elementary or elementary wavelet. By scaling the basis function for the time-to-frequency conversion, the time decomposition is not set for the entire spectrum but changes to the analyzed frequency or scale. This has the advantage that the time average is reduced by time to frequency conversion at high frequencies by reducing the database. This allows for a substantially higher time resolution in this range by increasing time placement. In addition, the database considered at low frequencies is extended so that the contribution of these frequencies can be incorporated into spectral information. Overall, the information content of the determined sequence of impedance spectra can be significantly increased. The temporal decomposition can be best adjusted by selecting the appropriate shift interval Δτ for the sequence of impedance spectra obtained by the wavelet transform over the entire frequency bandwidth or only selected frequencies of interest.

In the case of discrete data records, the corresponding algorithm is used for discrete wavelet transform or wavelet continuous extension.

High time resolved impedance spectroscopy offers many advantages over conventional impedance spectroscopy, including the use of reduced impedance spectra. The impedance spectrum obtained by the short time Fourier transform comprises N _w / 2 + 1 frequencies, which can be reduced, for example, to n frequencies that contribute to the original structured noise. Since discrete algorithms provide impedance values for discrete equidistant frequencies, the frequencies closest to the excited frequencies are selected. This step removes most of the noise that is the background of the measurement from the impedance spectrum. Frequencies with the best signal-to-noise ratio contribute only to the impedance spectrum, resulting in a lower average time for spectral information by allowing the use of window functions to span smaller time periods.

<Equivalent Circuit Suitable for Time-Resolved Optimized Forms>

After determining the reduced impedance spectrum, the spectrum can be analyzed by adapting appropriate equivalent circuit models to determine the amount of time that characterizes the system and its time course. The elements that constitute equivalent circuits flow out of physical models for major exaggerations occurring in the system, often corresponding to the action of ideal electrical components such as resistors, capacitances and inductors. In the impedance spectrum, discrete processes adjust the system's impedance response at different ranges of frequencies. In high time resolved impedance spectroscopy, the measured and reduced impedance spectrum is evaluated completely or in certain ranges of the spectrum. In principle, one can determine whether each frequency that contributes to the reduced impedance spectrum is used for the evaluation.

The advantage of high time resolved impedance spectroscopy is that there can be multiple analyzes of the same data records with different analysis parameters, for example time resolutions Δτ. In multiple analyzes of data records, the first impedance spectrum is determined as a longer window function that leads to a long average time and a low time decomposition so that the reduced impedance spectrum can be fully evaluated. Thus, normal parameters, for example constant processes, are determined with high precision.

Impedance spectra with shorter mean window times and shorter window functions leading to high time resolution are determined in other analyzes of the same data records. When the spectrum is evaluated, the areas of the reduced spectrum are only used to characterize dynamic abnormal processes, but the parameters for static or normal processes of the equivalent circuit are set to predetermined values.

Complex impedance values may be represented in different forms. For example, the impedance can be represented by complex coordinates or polar coordinates as follows.

Likewise, an inverse impedance (referred to as admittance) or related quantity, such as a complex frequency-dependent discrete constant, can be used in coordinate forms. What is important for the individual processes in certain frequency ranges of the impedance spectrum is that it changes in the form of the coordinates used. For analysis, time resolved impedance spectroscopy can use coordinate shapes and electrical variables that significantly analyze abnormal processes in the highest frequency range. The higher frequencies at which the processes studied can be analyzed allow for the selection of a smaller time interval spanned by the window functions and a smaller shift interval Δτ for use in the sliding short time Fourier transform.

For example, a method for adapting the parameters of an equivalent circuit to the measured impedance spectrum includes complex non linear least wquare fitting methods. The problem with minimization algorithms (eg, Eevenberg-Marquardt, a method of minimizing Powell in multidimensions) for adapting an equivalent circuit to impedance data is that the algorithm often finds local minima instead of the full minima in this match. . See Numerical Recipes in C (Cambridge University Press, New York, 1992) by WH Press, SA Teukolsky, WT Vetterling et al., Which is incorporated herein by reference in its entirety.

In order to increase the probability of determining the overall minimum in coincidence, different coordinate types and variables can be combined. In high time resolved impedance spectroscopy, sequences of impedance spectra can be evaluated by automatic matching routines or procedures. As a result, the amount of time lapses characterizing the system is determined.

The procedure described above is not limited to electrical impedance, and may include mechanical measurements such as rheological measurements, magnetic and optical tweezers, quartz resonance balances and acoustic impedance measurements, as well as other procedures in which the frequency rich disturbance of the system is related to the system response. It can be used to determine the impedance spectrum.

Example Examples

One embodiment will be described in detail to help understand various aspects of high time resolved impedance spectroscopy. Although one embodiment is described in detail, high time resolved impedance spectroscopy can be implemented in other specific forms without departing from mental or inherent characteristics. This embodiment describes a scenario that facilitates the measurement or determination of the impedance of individual ion channels in supported lipid films, biofilms. In another embodiment, natural or artificial freely suspended or supported lipid substrates with or without theoretical channels can be measured. The substrates hold planar thin film microelectrodes on multi-electrode arrays that facilitate parallel and sequential multiple measurements on the substrate. Substrates can be manufactured, for example, from silicon substrates having metal or semiconductor electrodes. The substrates may be mounted to an electrochemical cell of either one or multiple measurement chambers, where the liquid may be exchanged by a manual or automatic liquid processing and control system with or without temperature control. This scenario corresponds to the measurement of the two-terminal network of electricity simplified by the circuit shown in FIG.

4 is a schematic diagram of a conventional equivalent circuit. The conventional equivalent circuit of FIG. 4 has a resistor R ₁ 42 in series with the resistors R _2a 44, R _2b 46 and C 48 in a parallel combination. The switch is in series with R ₂ 44. The excitation voltage U (t) 50 is measured across the equivalent circuit and the response current I (t) 52 flowing through this circuit is measured. Values of the conventional components may be estimated in the range of from _{R 1 ~10 0㏀, R 2a,} 2b ~1 GΩ and C~6 pF. The switching rates for the switch can be estimated to be 50 Hz for example.

5 is a schematic diagram illustrating an embodiment. The structured noise of the alternating voltage disturbance signal is calculated by the computer to generate a multiple function generator 54 (Analogic 2030A). The device generates a disturbing signal which is then patch clamp amplifier 56 (HEKA). EPC8).

When digital data records are used in a disturbing signal, the transitions between discrete contact steps should be small and smooth because it reduces the level of background noise of the disturbing signal. In order to have small steps between two consecutive values of the disturbing signal, the sampling rate at which the data record is output by the function generator must be about 10 times greater than the maximum frequency of interest in the impedance spectrum.

To facilitate the discrete steps, the disturbance signal can be filtered with a low pass filter having a corner frequency of the filter about 10 times greater than the maximum frequency of interest in the impedance spectrum. Patch clamp amplifier 56 sends an alternating voltage disturbance signal to sample 60 via external preamplifier 58 under test. This preamplification unit simultaneously measures the sample and the actual alternating voltage applied to the sample's current response. The current signal is filtered and amplified to bypass current-to-voltage conversion. Both the time signals U (t) and I (t) can be monitored as voltage signals at the corresponding outputs of the patch clamp amplifier 56. Both signals are acquired by two channels of an A / D conversion board (International Organization Lab-NB) in a measurement computer (Apple Macintosh IIfx) and saved into data records on a computer data storage medium.

The software needed to run the setup includes two programs. The first program executes data acquisition on a measurement computer with an A / D conversion board. It is data analysis software Igor Pro with an extension package of data acquisition (NIDAQ Tools). (Wave mattress). The second program performs signal processing and data analysis of the measured data records of U (t) and I (t). It is a custom C ++ program written for Windows on Macintosh and PC operating systems. The implementation algorithm of the sliding short-time Fourier transform is based on the modified Cooley-Tukey FFT algorithm.

In order to fit the equivalent circuits to the impedance spectrum, the modified minimization algorithm exits Powell's method in multiple dimensions. For the above specified application, the logarithms of the real part and negative imaginary part of the impedance spectrum (complex coordinates) are used for the data fitted by the minimization procedure. See Numerical Recipes in C (Cambridge University Press, New York, 1992) by WH Press, SA Teukolsky, WT Vetterling et al.

The performance characteristics of the described embodiment are quantized in simulations and test measurements. In simulations, the corresponding current response signals of an ideal system are computed by the computer for structured noise disturbance signals, and the generated signals U (t) and I (t) are signals of high time resolved impedance spectroscopy. Evaluated using processing and data analysis procedures. 6 is a table showing examples of parameters for structured noise signal 66 and data processing 68 in the "Simulations" column. Simulations can be accurately measured using the logarithms of the complex coordinates of the minimization procedure even in a narrow frequency band of 0.3 to 20 kHz where the membrane / ion channel system with characteristic quantities R ₁ = 100 Hz is only 6 individual frequencies. R ₂ switches between intrinsic values in the range of 0.8 to 20 GΩ and C = 6 pF. In general, in the analysis of the impedance spectrum of membrane / ion channel systems, a frequency band of 100 Gz to 100 kHz may be used.

An equivalent circuit of the membrane / ion channel system is provided by FIG. 4, where the combination of R _2a and R _2b is considered R ₂ .

In FIG. 7, the time course 72 of the switchable parallel resistor R ₂ is shown as estimated by the simulation 74 (continuous line) and determined by the high time resolved impedance spectroscopy 76 (circumference). . FIG. 8 shows one step jump 82 in R ₂ enlarged in FIG. 7. The different curves shown are produced by using different window functions g (t) in the short time Fourier transform. Window functions of the following characteristics are used: Hanning 1.0 (cos.) 84, Kaiser-Bessel (KB2) 86 with α = 2.0 and Kaiser-Bessel (KB3) 88 with α = 3.5. Time lapse analysis indicates that the amount of time lapse characterizing the system determined by the short time Fourier transform in the absence of any signal degradation corresponds to this amount of actual (ideal) time lapse using the window function. The time decomposition obtained was Δτ = 0.67 ms and the rise time τ _r was between 2.0 and 3.1 ms depending on the window function.

For test measurements, the circuit of FIG. 4 is assembled using electronic components. This circuit forms a model sample that mimics the behavior of individual ion channels in supported lipid membranes. These model samples are measured by high time resolved impedance spectroscopy.

In the first test measurement, the model was used with values of R _{2a, 2b} = 680 KΩ and C = 1 nF (no additional element for R ₁ ) and the switch was switched at a frequency of 50 Hz. 6 shows the parameters of the structured noise signal and data evaluation in the “fast model” column. In FIG. 9, the time lapses of R ₁ 92, R ₂ 94 and C 96 are determined by ideal or absolute time lapse of R ₂ 98 as well as high time resolved impedance spectroscopy.

Deviations in absolute values up to 20% result from insufficiently compensated filter effects of the setup. Changes such as the steps in R ₂ are reproduced considerably. The time decomposition obtained was 1.1 ms and the rise time was 8 ms. 10 (a) and (b), the real and negative imaginary parts of the impedance spectra 112 and 104 which are the basis for the two points in the time lapses of FIG. 9 are shown. Each of the contributing frequencies of the structured noise signal was not used for evaluation, but only in a limited range of 0.4 to 4 kHz.

In the second test measurement, the model was used with values of R _{2a, 2b} = 1 GΩ and G = 3 pF (no additional element for R ₁ ), and the switch was manually switched at irregular intervals. 6 shows the parameters of the structured noise signal and data evaluation in the "Gigaohm Model" column. In FIG. 11, time lapses of R ₁ 112, R ₂ 114, and C 116 as shown by high time resolved impedance spectroscopy are shown. Again, deviations in absolute values up to 20% result from filter effects of insufficiently compensated setup. Changes such as the step of R ₂ are also analyzed at these high impedances. The time decomposition obtained was 4.4 ms. 12 (a) and (b), the real and negative imaginary parts of the impedance spectrum underlying the point 122 in the time lapses of FIG. 11 are shown. Only five contributing frequencies in the impedance spectrum were sufficient to determine three independent, partially dynamic variables from the impedance spectrum. This proves that the information content of the measurements is quite high using high-resolution resolved impedance spectroscopy even at very limited frequency bands compared to the measurement resistance at only one frequency.

13 is a block diagram illustrating one embodiment of high time resolved impedance spectroscopy. As shown in FIG. 13, the basic setup for high time resolved impedance spectroscopy requires only a few components. The main processor 132 unit controls signal generation and data acquisition on two channels. Data for the structured noise signal is generated by the processor unit according to the stored algorithm. When stored in the memory element 134, a voltage signal is applied to the output after the D / A converter 136. The measured voltage signal U (t) undergoes A / D conversion at the converter 138 and is transmitted to the memory at the input channel. In the second input channel, the current signal I (t) is received by a signal conditioner 142 to undergo a current-to-voltage conversion in the A / D converter 144. The output of transducer 144 is sent to memory. The measured data of the voltage and current signals are processed and analyzed by routines stored in the memory element 146 and the results are saved on the data storage medium 140. In another embodiment, the two memory elements 134 and 136 are the same memory element.

As described above, the use of high time resolved impedance spectroscopy has many advantages over conventional impedance spectroscopy. Some advantages include studying substantial improvements in the time resolution of impedance spectroscopy, time resolution up to each individual frequency fraction in the impedance spectrum, continuous measurements with correct response times, real time measurements, disturbance signals and data processing and analysis. Adaptation to the system optimizes the measurement procedure, iterative analysis of measured data records adapted to the evaluation center, highly flexible technology, and impedance spectroscopy such as individual ion channels that open and close on natural or artificial magnetic fields or supported membranes There is a study of dynamic processes that cannot be measured in advance, and a greatly preferred signal to noise ratio.

The foregoing description details certain embodiments of the invention. However, no matter how detailed above, it will be apparent that the invention can be embodied in other specific forms without departing from spirit or basic characteristics. The described embodiments are to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than the foregoing. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.

Claims (35)

In high time resolved impedance spectroscopy method: Generating and applying an alternating voltage perturbation signal to the system; Recording the alternating voltage disturbance signal and a current signal generated in response to the disturbance signal; And Processing the recorded signals using an unsteady time-to-frequency conversion. The method of claim 1, wherein the abnormal time to frequency transform is a short time Fourier transform. The method of claim 1 wherein the abnormal time to frequency transform is a wavelet transform. The method of claim 1, wherein the abnormal time to frequency conversion is a Wigner distribution. The method of claim 1 wherein the recording of the alternating voltage disturbance signal is continuous. The method of claim 1 wherein the recording of the alternating voltage disturbance signal is partly continuous. The method of claim 1 wherein the AC voltage disturbance signal is structured noise. The method of claim 1 wherein the generating step uses high performance signal amplifiers such as patch clamp amplifiers. The method of claim 1 wherein the recording step uses analog-to-digital conversion of measurement signals. The method of claim 1 wherein the processing step uses data processing hardware and software for real-time analysis of the impedance spectrum. The method of claim 1 wherein the processing step detects the conductivity of a naturally or artificial free floating or substrate supported lipid membrane with or without ion channels. The method of claim 1 further comprising the use of a frequency range of about 100 Hz to 100 kHz and an algebraic analysis of the real and imaginary parts of the impedance. The method of claim 1 wherein the treating step detects mixtures in solutions having a conductivity change effect on biofilms. The method of claim 1, wherein the system is located in a measurement chamber that includes temperature control and liquid processing. The method of claim 1 further comprising the use of a complex nonlinear least squares method to fit the parameters of an equivalent circuit to the measured impedance spectrum. 15. The method of claim 14, wherein the measurement chamber comprises automatic liquid processing systems. The method of claim 1 wherein the applying or writing step comprises the use of multi-electrode arrays. 18. The method of claim 17, wherein the system is located in multiple measurement chamber systems with parallel data acquisition and analysis. 18. The method of claim 17, wherein the system is located in multiple measurement chamber systems with sequential data acquisition and analysis. The method of claim 1, further comprising the integration of automated production and process flows. In a device for measuring high-resolution resolved impedance spectra: A memory element configured to store algorithms for generating a disturbing signal and instructions for processing and evaluating measured data; At least one analog-to-digital converter configured to receive a signal representing a disturbance signal and output a digital value representing the disturbance signal and to receive a signal representing a system response to the disturbance signal and output a digital value representing the system response ; And A processor configured to receive the digital values output by the at least one analog to digital converters, and to receive instructions for processing and evaluating the algorithm and measured data from the memory element to output a disturbance signal and an impedance spectrum Including; And the instructions for processing and evaluating the measured data are an abnormal time to frequency conversion. 22. The apparatus of claim 21, wherein the abnormal time to frequency transform is a short time Fourier transform. 22. The apparatus of claim 21, wherein the abnormal time to frequency transform is a wavelet transform. 22. The apparatus of claim 21, wherein the abnormal time to frequency transformation is a Wigner distribution. 22. The apparatus of claim 21, wherein the disturbance signals are recorded continuously. 22. The apparatus of claim 21, wherein the disturbance signal is partly recorded continuously. 22. The apparatus of claim 21, wherein the disturbance signal is structured noise. 22. The apparatus of claim 21, further comprising the use of a complex nonlinear least squares method to fit parameters of an equivalent circuit to the impedance spectrum. 22. The apparatus of claim 21, wherein the apparatus comprises multi-electrode arrays. The apparatus of claim 21, wherein the apparatus comprises a measuring chamber having automatic liquid processing systems. 22. The apparatus of claim 21, wherein the apparatus comprises multiple measurement chamber systems with parallel data acquisition and analysis. 22. The apparatus of claim 21, wherein the apparatus comprises multiple measurement chamber systems with sequential data acquisition and analysis. 22. The apparatus of claim 21, further comprising a measuring cell or chamber for detecting the conductivity of a naturally or artificially free floating or substrate supported lipid membrane with or without ion channels. 22. The apparatus of claim 21, further comprising a measuring cell or chamber for detecting mixtures in solutions having a conductivity change effect on the biofilms. The apparatus of claim 21, wherein the apparatus comprises a measuring cell or chamber having temperature control and liquid treatment.