EP3025149A1

EP3025149A1 - Method and device for measuring the modulus of electrical impedance

Info

Publication number: EP3025149A1
Application number: EP14747544.6A
Authority: EP
Inventors: Alexandre FOUCHARD; Alain Noca
Original assignee: Commissariat a lEnergie Atomique et aux Energies Alternatives CEA
Current assignee: Commissariat a lEnergie Atomique et aux Energies Alternatives CEA
Priority date: 2013-07-24
Filing date: 2014-07-21
Publication date: 2016-06-01
Also published as: FR3009087A1; WO2015011098A1; FR3009087B1

Abstract

The invention relates to a method and device for measuring a signal amplitude in order to supply the modulus of the electrical impedance of a sample. According to the invention, the signal is sampled (step 43) at a sampling frequency lower than the Nyquist frequency. Subsequently, the samples are distributed in a histogram (step 44) and the two fullest bins of the histogram are determined (step 45) such as to calculate the amplitude of the signal (step 46). The invention provides an energy-saving bio-impedance measurement means.

Description

METHOD AND DEVICE FOR MEASURING THE MODULE OF AN ELECTRIC IMPEDANCE.

DESCRIPTION

TECHNICAL AREA

The present invention relates to the field of measurement of the module of an electrical impedance. The invention applies in particular to bioimpedance and electrical impedance tomography measurements.

STATE OF THE PRIOR ART

The principle of the measurement of impedance of a biological tissue consists in applying between two electrodes an excitation signal in the form of a voltage u (t) of small amplitude, typically of amplitude less than 100 mV. The two electrodes are placed on a sample to be studied, for example at two points of a human or animal biological tissue. The low amplitude of the voltage guarantees a linear response of the sample subjected to this voltage. This response results in a current i (t) circulating in the sample and between the two electrodes. The current i (t) is characteristic of the medium between the electrodes. This is reflected in Ohm's law:

u (t) = Z * i (t) (1) where Z is the impedance of the medium between the electrodes.

Alternatively, an excitation signal can be injected in the form of a current i (t), and a resulting voltage u (t) can be measured.

The impedance Z for a frequency f of an excitation signal is defined by a module | Z | and a phase shift φ such that:

z (f) = | () | * _e W) (2)

The module | Z | is defined as follows 1 * 1 = ¾g < ³ "

with Au (f) the peak-to-peak amplitude of the voltage across the sample and Ai (f) the peak-to-peak amplitude of the current flowing in the sample, where u (f) and i (f) are alternating signals at a frequency f. Throughout the text, the term "amplitude" refers to a peak-to-peak amplitude.

The phase φ of the impedance Z is a phase shift between the voltage u (t) and the current i (t).

Figure 1 illustrates the parameters Au, Ai and φ, to be determined to calculate the impedance Z at a predetermined frequency f.

FIG. 1 illustrates the current i (t), having an amplitude Ai, the voltage u (t), having an amplitude Au, and the phase shift φ between the voltage u (t) and the current i (t).

One of u (t) and i (t) is measured on the sample and corresponds to the response of the sample to the excitation signal. The other one of u (t) and i (t) is the excitation signal itself.

Preferably, excitation signals of small amplitude are chosen with respect to the medium studied (for example less than 100 mV or less than 100 mA, preferably less than 10 mA in the case of a biological tissue), so that that the response of the medium studied remains linear: the excitation signal and the response signal are sinusoids of the same frequency.

Au and Ai amplitudes can be exploited in the context of electrical impedance tomography. An excitation signal is then injected into the sample to be analyzed, and a response of the medium between different pairs of electrodes is then measured, the pairs of electrodes being defined from a set of at least three electrodes, for example four electrodes. These measurements are repeated for different frequencies of the excitation signal. Using these different measurements of Au, Ai and φ, we obtain a representation of the studied medium in the form of an impedance map.

We will focus here more particularly on the measurement of the module of an electrical impedance. Various methods of measuring the module of an electrical impedance are known in the prior art.

For example, patent document US 2006/0167374 discloses a bioimpedance measuring device. This apparatus sends a current at an excitation frequency, which passes through a known impedance reference object Z _ref , and an object to be studied. The voltage at the terminals of the object to be studied and the voltage at the terminals of the reference object are measured. The measured voltages are sampled at a sampling frequency by an analog-to-digital converter. The discrete Fourier transform of each of the two measured voltages is then calculated. The module of the impedance Z _obj of the object to be studied is obtained from the known module of the impedance Z _re f, and the calculated discrete Fourier transforms. The sampling frequency is chosen to be less than or equal to the frequency of the excitation signal, in order to reduce the constraints on the analog-digital converter.

The calculations implemented, however, require the use of a powerful processor, which consumes a lot of energy.

An object of the invention is to provide a method and a device for providing information relating to the electrical impedance of a sample, which are simple, robust, and consume little energy.

STATEMENT OF THE INVENTION

The present invention is defined by a method for measuring the modulus of an electrical impedance of a sample in which:

a sinusoidal excitation signal of predetermined frequency is applied to the sample, the excitation signal consisting of an excitation current or an excitation voltage;

measuring a response signal comprising a response voltage if the excitation signal is an excitation current, or a response current if the excitation signal is an excitation voltage.

The method according to the invention then comprises the following steps: the response signal is digitized at a sampling frequency lower than the Nyquist frequency, so as to obtain a series of samples of the response signal;

an amplitude histogram of the samples is constructed by distributing the series of samples in several classes, each class being associated with a voltage or current interval;

on each side of the histogram, the most full class is identified;

from the two classes identified, the amplitude of the response signal (Ai; Au) is calculated and said module is deduced from the electrical impedance. Preferably, the sampling signal is generated by a sampling clock, the excitation signal is generated by an excitation signal clock, the sampling clock and the excitation signal clock being asynchronous .

Alternatively the frequency of the excitation signal may be equal to a multiple

771

integer of the sampling frequency, plus a fraction - of the sampling frequency, where m and n are prime integers to each other and n is greater than or equal to ten.

Alternatively, the frequency of the excitation signal may be equal to an integer multiple of the sampling frequency, plus or minus a fraction of the sampling frequency less than one-tenth.

The sampling frequency is advantageously less than one tenth or one hundredth or one thousandth of the frequency of the excitation signal.

Thus, whatever the embodiment chosen, the excitation signal and the sampling signal are asynchronous.

The method according to the invention may further comprise the following steps:

the excitation signal is digitized at a sampling frequency lower than the Nyquist frequency, so as to obtain a series of samples of the excitation signal; an amplitude histogram of the samples is constructed by distributing the series of samples in several classes, each class being associated with a voltage or current interval;

on each side of the histogram, the most full class is identified;

from the two classes identified, the amplitude of the excitation signal is calculated; and

the amplitude of the excitation signal and the amplitude of the response signal are used to obtain the modulus of the electrical impedance. The method according to the invention may further comprise the steps of a method for measuring the phase of the electrical impedance, in which:

generating a first logic signal, comparing the signal and a first reference value;

generating a second logic signal, comparing the response signal and a second reference value;

combining the first logic signal and the second logic signal to obtain a third logic signal representative of a time offset between the excitation signal and the response signal;

the third logic signal is used to control the charge of a capacitor, by a constant current source of constant value, for a predetermined number of periods of the excitation signal;

the voltage at the terminals of this capacitor is measured, and said phase is deduced therefrom.

Preferably, the first reference value is equal to the second reference value, itself equal to a zero value.

The invention also relates to a device for measuring the modulus of an electrical impedance of a sample, the device comprising: means for applying to the sample a sinusoidal excitation signal of predetermined frequency, the excitation signal consisting of an excitation current or an excitation voltage;

means for measuring a response signal comprising a response voltage if the excitation signal is an excitation current, or a response current if the excitation signal is an excitation voltage.

According to the invention, the device further comprises:

a first digital to analog converter receiving as input the response signal, and outputting a series of samples of that signal, a sampling frequency being lower than the Nyquist frequency;

processing means receiving as input the series of samples of the response signal and outputting said module of the electrical impedance, these processing means being adapted to implement the following steps:

constructing a histogram of the samples, dividing the series of samples into several classes, each class being associated with a range of voltage or current;

on each side of the histogram, identification of the most filled class;

from the two classes identified, calculating the amplitude of the response signal, and using said amplitude to calculate said module.

In particular, the processing means are adapted to construct an amplitude histogram of the samples.

The excitation signal and the sampling signal are advantageously asynchronous.

The device according to the invention may further comprise a second digital analog converter receiving as input the excitation signal, the processing means receiving as input the outputs of the first and second digital analog converters and being adapted to calculate the amplitude of the signal of excitation and of the response signal, and to use these two amplitudes to calculate said module. Preferably, the device according to the invention further comprises means for measuring the phase of the electrical impedance comprising:

a first comparator receiving as input the excitation signal, comparing it with a first reference value, and outputting a first logic signal;

a second comparator receiving as input the response signal, comparing it with a second reference value, and outputting a second logic signal;

combining means receiving as input the first logic signal and the second logic signal, and outputting a third logic signal representative of a time offset between the excitation signal and the response signal;

a main switch disposed in series between a DC and constant current source and a capacitor, and controlled by said third logic signal; and

means for measuring the voltage across the capacitor.

Advantageously;

the first comparator is grounded, and is adapted to compare the excitation signal with a zero value; and

the second comparator is connected to ground, and is adapted to compare the response signal with a zero value.

The invention also relates to a portable device for measuring an electrical impedance of a human or animal tissue, comprising a device according to the invention.

The invention also relates to a portable electrical impedance tomography apparatus of a human or animal tissue, comprising a device according to the invention. BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be better understood on reading the description of exemplary embodiments given purely by way of indication and in no way limiting, with reference to the appended drawings among which:

- Figure 1 illustrates the parameters to be determined to calculate an electrical impedance Z;

Figure 2 illustrates a sampling of a sinusoidal signal and a histogram of the samples obtained;

Figure 3 illustrates a sampling according to the invention;

FIG. 4 illustrates the steps of a method according to the invention;

Figure 5 schematically illustrates a sample and a device according to the invention for measuring the modulus of an electrical impedance of the sample;

Figure 6 illustrates a first embodiment of the device according to the invention;

FIG. 7 illustrates a second device embodiment according to the invention;

Figure 8 illustrates voltage signals generated in a third embodiment of the device according to the invention;

Figure 9 schematically illustrates a detail of this third embodiment of the device according to the invention;

Figure 10 illustrates an example of this third embodiment of the device according to the invention;

Figure 11 illustrates the performance of a device according to the invention; and Figure 12 illustrates a portable measuring apparatus according to the invention.

DETAILED PRESENTATION OF PARTICULAR EMBODIMENTS

We will first describe, with reference to Figure 2, the general principle implemented according to the invention. Figure 2 illustrates a sampling of a sinusoidal signal and a histogram of the samples obtained.

The sinusoidal signal 21 is represented in a graph giving the value of the signal (y-axis) as a function of time (x-axis). We will talk about the value of the signal to designate its amplitude at a time t, to avoid any confusion with the peak-to-peak amplitude of a signal, also called "amplitude".

The sinusoidal signal 21 is sampled at regular sampling times uniformly distributed over a period of the sinusoidal signal 21 (at a multiple close to this period, that is to say after folding over a period). The samples obtained are represented by points 22. Each sample corresponds to a signal value Ai.

From the set of samples obtained, a histogram 23 is made. In this histogram, the samples are classified according to their signal value, in classes of the same width 24. Each class corresponds to a range of signal values [ A _t; A _u [. Classes are ranked in ascending or descending order of their median value.

It can be seen that the histogram 23 has a minimum in the center (the least filled class) and two maxima in the extremes (the most filled classes). Each maximum is located at one end of the histogram. The maxima are located on both sides of the median value of the histogram.

Note that in practice, the maxima do not necessarily correspond to the extrema of the histogram because the histogram can include classes corresponding to noise. Nevertheless, there will always be a maximum on each side of the histogram, so we can talk about two maxima, each located on one side of the histogram. In other words, the two most filled classes of the histogram are located on either side of a reference value.

The profile of the histogram is explained by the sinusoidal form of the signal 21:

near the maximum of the signal 21, the value of the signal varies slowly: more sampled points are in a given class; for the same reason, more sampled points are in a given class near the minimum of the signal 21.

Thus, the histogram 23 has two classes 25, 26 most filled, corresponding to the extreme value slices of the signal.

Class 25 corresponds to the interval [A _t ; A _u [of values of the signal 21, the values A _t and A _u being represented in FIG. 2.

Class 26 corresponds to an interval [A _r , A _s [(not shown) of signal values

21.

A first class corresponds to an interval of minimum values (in algebraic values) of the sinusoidal signal. A second class corresponds to an interval of maximum values (in algebraic values) of the sinusoidal signal. Thus, the difference between the two classes corresponds substantially to the amplitude of the signal.

The idea underlying the invention is to use this property to calculate the amplitude of a voltage signal or a current signal, in order to provide information relating to an electrical impedance.

Figure 2 thus illustrates this interesting property of sampling, when sampling times are uniformly distributed over a period of the signal, or in other words when sampling times are distributed according to a probability density uniform over a period of the signal. Throughout the text, a uniform probability density over a period of a signal will designate a uniform probability density over a period of the signal, at a multiple near that period, i.e. after folding over a period.

However, the invention can be implemented regardless of the sampling applied, since the classes 25, 26 corresponding to the previously described maxima have a sufficient number of occurrences relative to the other classes, so as to be distinguished from the others. classes. It is understood that the higher this number of occurrences relative to the occurrences of the other classes, the more precise the process is. This number of occurrences, for each maximum, must preferably be greater than 10, and even more preferably greater than 100. Advantageously, the sampling times are distributed according to a uniform probability density over a period of the signal. Thus, if we classify these samples in a histogram, the histogram presents a continuum of classes framed by two classes 25, 26 more filled than the others. This facilitates the identification of these two classes 25 and 26.

The histogram preferably has classes of the same width, each associated with a range of values of the signal. However, again, the invention can be implemented with classes of different widths, since the classes 25, 26 comprise a sufficient number of occurrences relative to the other classes.

For example, 3000 samples of the signal studied are acquired.

Figure 3 illustrates a sampling according to the invention. In Figure 3, there is illustrated a voltage signal V as a function of time t. The voltage signal is a sinusoidal signal i

of frequency f _ex = -. The voltage signal is sampled at a frequency

1

Sampling f _ech =.

Tech

It is recalled that the frequency of Nyquist is 2 * f _ex . In other words, when the invention is not implemented, a frequency signal f _ex will have to be sampled at a sampling frequency greater than 2 * f _ex for the sampling carried out to reconstruct the signal. without loss of information.

According to the invention, it is not necessary to reconstruct the signal. It is therefore not necessary for the sampling according to the invention to be carried out at a sampling frequency higher than the Nyquist frequency.

According to the invention, a medium is preferably excited by means of a low-amplitude excitation signal relative to the medium under study (for example less than 100 mV or less than 10 mA), and a signal is measured. reply. A low amplitude excitation signal causes a linear response of the medium studied: the response signal is therefore of known form (a sinusoid, of the same frequency as that of the excitation signal). In other words, the application of a low amplitude excitation signal makes it possible to control the shape of the response signal, the latter being similar to the shape of the excitation signal. Thus, it is even less useful to rebuild the signal.

A high sampling frequency imposes a high energy consumption of the sampling means. According to the invention, one therefore chooses not to respect the Nyquist criterion. A sampling frequency according to the invention is lower than the Nyquist frequency. A voltage (or current) signal is sampled at a sampling frequency lower than the Nyquist frequency. It is thus possible to reduce an energy consumption of a device according to the invention.

The sampling frequency is for example less than one thousandth of the frequency of the sampled signal. It can even be expected that the sampling frequency is less than one millionth of the frequency of the sampled signal. According to the invention, the sampling frequency is adjusted according to the frequency of the sampled signal. For example, the frequency of the sampled signal may vary, for example between 1 Hz and 1 MHz. In this case, the sampling frequency may be 30 kHz when the frequency of the sampled signal exceeds 20 kHz. It may be reduced to 500 Hz when the frequency of the sampled signal is in the 250 Hz range - 20 kHz, and 2 Hz when the frequency of the sampled signal is in the range 1 Hz -. 250 Hz Time period T _ech d Sampling is greater than half the T _ex period of the voltage signal, and the period of the voltage signal is fixed.

According to the invention, and considering a folding of the voltage signal modulo a period T _{ex of} said signal, it should preferably be ensured that the probability density of the sampling times is substantially uniform over a period T _ex of the signal of voltage. As specified above, the frequency of the excitation signal according to the invention is equal to the frequency of the response signal according to the invention. Thus, according to the invention, the frequency of the excitation signal and the frequency of the sampling signal are advantageously chosen so that the probability density of the sampling times is substantially uniform over a period of the excitation signal.

Such a probability density can be obtained in different ways. For example, random sampling can be simulated by selecting a sampling signal generation clock and an asynchronous voltage signal generation clock. Asynchronism then results from the natural drift in time or frequency of the distinct clocks. A signal generation clock is typically a quartz oscillator.

Even when the sample signal generation clock and the voltage signal generation clock are synchronous, a pseudo-random sampling can be simulated by an appropriate choice of the frequency ratio between the voltage signal frequency and the frequency signal. sampling signal frequency. In particular, the frequency of the voltage signal is equal to an integer multiple of the sampling frequency, plus

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a fraction- of the sampling frequency, where m and n are prime integers

not

between them and n is greater than or equal to 10. We can choose n greater than 100, and even n greater than 1000. We thus define a basic pattern of sampling. Advantageously, there will be at least n samples of the voltage signal to build a histogram. A sample number p can be used to construct a histogram, where p is an integer multiple of n.

Alternatively, the frequency of the voltage signal is equal to an integer multiple of the sampling frequency, plus a fraction less than one-tenth of the sampling frequency. The fraction may be less than one hundredth, and even less than one thousandth.

Those skilled in the art can imagine many other alternatives, for example sweep the sampling frequency between a high frequency and a low frequency, or implement pseudo-random jumps in the sampling frequency.

It is recalled that this condition on the probability density of the sampling times is not necessary, however.

The samples are used to construct a histogram as described with reference to Figure 2. The asynchronism between the excitation and sampling signals makes it possible to address the different values of a periodic signal over time, realizing sampling over a plurality of periods. Use a histogram makes it possible to dispense with isolated values to determine a signal amplitude. The invention is therefore particularly robust to measurement noise.

The sampling frequency, related to the number of samples used to build the histogram (more than 1000 samples, for example 3000), implies that the samples correspond to different periods of the signal studied. Nevertheless, the samples are taken in a short time in front of the variation of the impedance of a human or animal tissue, the latter varying between a few seconds or a few days, or even beyond, depending on the applications considered.

Moreover, the sampling over several periods of the signal is not problematic: on the contrary, it makes it possible to obtain an average of the maximum values of the signal over these few periods, which increases the robustness with regard to the measurement noise.

FIG. 4 illustrates the various steps of the method according to the invention, for measuring a module of an electrical impedance Z of a sample:

in a step 41, a sinusoidal excitation signal of predetermined frequency is applied to a sample, the excitation signal here consisting of an excitation voltage u (t);

in a step 42, the response current i (t) is measured;

in a step 43, the response current i (t) is digitized so as to obtain a series of samples of the response current. The sampling conditions implemented have been detailed previously. ;

in a step 44, a histogram of the samples is constructed by distributing the series of samples in several classes, each class being associated with a current interval. Typically, the number of classes is several tens, or several hundred classes. Preferably, the classes of the histogram all have the same width.

in a step 45, the two intervals respectively corresponding to the two most filled classes, on each side of the histogram, are identified. For this, we can define two search areas: one corresponding to a class (or channel) of low index, the other corresponding to a class of high index, the index of a class being an integer proportional to the median value of the corresponding range of values. In each zone, the most filled class is searched. We are also talking about a search for a local maximum on each zone, at each end of the histogram. Then, a value i _r , i _{t is} representative of the signal value range associated with each class thus identified. This representative value is typically the average value of the signal value range associated with each class or the value of a terminal of each class.

in a step 46, the amplitude Ai of the response current is calculated, by comparing said representative values i _r , i _t thus identified, in particular by a subtraction: Ai = i _r -i _t . The module | Z | = -. The amplitude Au of the excitation voltage can either be measured in the same way as the amplitude Ai, or be assumed to be known.

A device 50 for measuring the module according to the invention will now be described with reference to FIG. 5 and schematically.

The device 50 comprises at least two electrodes 51 for injecting a sinusoidal current i (t) into a sample 52. The current i (t) is an excitation signal. It passes through the sample between two points, from one electrode to another.

The current i (t) is provided by a source 54 emitting a sinusoidal signal of known frequency.

The signal i (t) can be determined by a measurement of the current at the output of the source 54, or by a measurement of the current after passing through the sample or by assuming that the signal theoretically emitted by the source 54 corresponds to the actual signal. issued by said source.

The two electrodes 51 also make it possible to measure the sinusoidal voltage u (t) between two points of the sample 52. The voltage u (t) is a response signal. It has the same frequency f as that of the excitation signal since the medium is assumed to be linear. The two electrodes 51 are connected to a measurement unit 55, which calculates the modulus of the electrical impedance Z of the sample between these two points (steps 43 to 46 as described with reference to FIG. 4).

Two pairs of electrodes may be provided: a pair of injection electrodes for injecting a signal into the sample, and a pair of measurement electrodes for measuring a sample response signal.

The device 50 may comprise at least three electrodes, in the context of an electrical impedance tomography.

In a variant not shown, the sinusoidal source imposes a voltage u (t) between two points of the sample 52. The voltage u (t) is then an excitation signal. This signal u (t) can be determined by measuring the voltage at the output of the source 54, or by measuring the voltage between two points of the sample or by assuming that the signal theoretically transmitted by the source 54 corresponds to the signal actually transmitted by said source. The current i (t) passing through the sample 52 is measured between the two electrodes. The current i (t) then forms a response signal.

The voltage u (t) and the current i (t) do not include an offset. In other words, the signal u (t) is centered on the abscissa axis corresponding to a zero DC voltage and the signal i (t) is centered on the abscissa axis corresponding to a zero DC current. A filtering step can be provided to retain only the AC component of the signals u (t) and i (t).

Figure 6 illustrates a first embodiment of device 100 according to the invention. According to this embodiment, a source 60 applies a voltage u (t) across the electrical impedance Z. The impedance Z symbolizes the medium studied. The voltage u (t) here forms the excitation signal.

The response of the impedance Z to the voltage u (t) is a current i (t), measured by the current measurement means 61, at the output of the impedance Z. The current i (t) here forms the signal Answer.

The current measuring means 61 are made here by a current converter circuit receiving as input the current i (t) after passing through the impedance Z, and outputting a voltage proportional to this current. Also called "trans-impedance converter" this current converter circuit.

The current i (t) converted into voltage is then digitized using an analog-digital converter 62. For example, a 12-bit analog-to-digital converter is used: the signals are therefore distributed over 2 ¹² = 4096 levels. The histogram then has 4096 classes. Advantageously, the number of classes of the histogram corresponds to the number of levels after the conversion of the analog signal into a digital signal.

As indicated with reference to FIG. 3, the digitization is performed at a sampling frequency lower than the Nyquist frequency, and preferably with a probability density of substantially uniform sampling times over a period of the excitation signal. The digitization provides a series of samples of the current i (t).

The analog-digital converter has a low opening time with respect to the frequency of the signal to be sampled, in a ratio typically 1/1000. It is associated with a conversion clock having a conversion frequency f.

In practice, the frequency of the excitation signal f _ex , starting from the conversion frequency, is chosen so that it is not an integer multiple of the conversion frequency.

For example, the conversion frequency is 500 kHz, and the frequency of the excitation signal is set at 999kHz instead of 1 Mz. Here, the sampling frequency is fech = ¾ ^{¾ 33} ' ^{3 kHz} - ^{0 naa when:}

Thus, the frequency of the excitation signal is equal to an integer multiple (29) of the

771

sampling frequency plus a fraction - of the sampling frequency, with m = 97 and n = 100 prime between them. We find one of the ways to obtain a probability density of uniform sampling times over a period of the sampling signal.

The digital analog converter 62 is connected to processing means 64 receiving as input the series of samples of the current i (t), and outputting the module of the electrical impedance Z.

The link 63 between the digital analog converter 62 and the processing means 64 is a digital link, for example of the Serial Peripheral Interface (SPI) type.

The processing means may comprise a digital or analog electronic circuit, preferably dedicated, associated with a microprocessor and / or a computer. Samples being few (for example 3000), one can use a low power microcontroller to achieve said processing means. A microcontroller is an integrated circuit which gathers the essential elements of a computer such as: processor, memories (read-only memory for storing software means, random access memory for storing input and output data of the software means), peripheral units and interfaces input-output. The peripheral units are driven by the software means, so as to perform the desired functions. This microcontroller then calculates the amplitude Ai, and deduces the module | Z | impedance Z. It also controls all the interactions between the various components forming the device 100 according to the invention.

The microcontroller is for example MSP 430 (Texas Instrument ^® ), known for its low power consumption and its ability to equip embedded circuits with a consumption constraint (of the order of 10 mW).

In the embodiment of FIG. 6, a known voltage u (t) is applied across the impedance Z. The amplitude Au of the voltage signal is assumed to be known: it is assumed that the voltage signal actually emitted by the source 60 corresponds to the voltage signal theoretically emitted by the source 60. The processing means 64 use the amplitude of the voltage Au and the amplitude of the current Ai to calculate the modulus of the electrical impedance Z. The processing means 64 may implement a tomographic reconstruction algorithm. Such an algorithm aims to estimate in three dimensions the electrical impedance distribution of a sample. In this case, the device according to the invention may comprise processing means separated into two modules:

a first processing module typically performed by a microcontroller which controls the components such as the analog-to-digital converter, and calculates at least one signal amplitude A 1, Au;

a second processing module, more powerful, which uses the amplitudes calculated in a tomographic reconstruction algorithm.

It can thus be seen that the invention offers a method and a device that consumes very little energy thanks to sampling at a frequency lower than the Nyquist frequency and to simple calculations, without the use of Fourier transforms.

Here we propose a device that can have a small footprint, and a reduced cost, since the necessary components are few in number, compact and common in the trade. In particular, the device and the method according to the invention require only a simple low-power microcontroller to drive the components of the device and perform the amplitude calculations.

Figure 7 illustrates a second embodiment of the device according to the invention. FIG. 7 will only be described for its differences with respect to FIG. 6. According to the embodiment of FIG. 7, the source 60 injects a current i (t) into the impedance Z. The current i (t) forms here the excitation signal.

The response of the impedance Z to the current i (t) is the voltage u (t) measured by the voltage measuring means 71 across the impedance Z. The voltage u (t) here forms the response signal. The voltage measuring means 71 are made here by a comparator circuit receiving as input the potential at one of the impedance Z and the potential at the other end of the impedance Z.

The voltage u (t) is then digitized by means of an analog-to-digital converter 72, as detailed with reference to FIG. 6 and about the digitization of the current i (t). The digitization provides a series of samples of the voltage u (t). The digital analog converter 72 is connected to the processing means 64 by a digital link, for example SPI. The processing means 64 implement steps 43 to 46 as defined with reference to FIG. 4, applied to the samples of the voltage u (t). The processing means 64 thus calculate the amplitude Au of the voltage and deduce therefrom the module of the impedance Z. In the embodiment of FIG. 7, a known current i (t) is injected into the impedance Z. The amplitude Ai of the current is assumed to be known: it is supposed that the current effectively emitted by the source 60 corresponds to the current theoretically emitted by the source 60.

It will be possible to imagine different variants by combining at leisure these embodiments. For example, the amplitude of the voltage can be determined by measuring the voltage across the impedance Z, as in FIG. 7, and determining the amplitude of the current by measuring the current at the output of the impedance Z as in Figure 6.

We will now describe a more complete device, taking into account another aspect of the invention, further allowing to calculate in a smart and energy efficient way the phase difference between the voltage u (t) and the current i (t).

This third embodiment of device 100 according to the invention will be described with reference to FIGS. 8, 9 and 10.

Figure 8 illustrates voltage signals generated in the third embodiment of the device according to the invention.

FIG. 9 schematically illustrates a detail of this third embodiment of the device according to the invention, in particular the part of the device according to the invention making it possible to generate and exploit the signals of FIG. 8.

A first comparator 91 compares the signal u (t) with a first reference value. The first reference value corresponds to a constant voltage, here the zero voltage. Thus, the first comparator 91 receives as input the signal u (t), and a first reference value, here a zero voltage corresponding to the mass. At the output of the first comparator, a first logic signal, said signal C1, is obtained. The signal C1 has the same frequency as the excitation signal. The signal Cl takes here a value positive (equal to unity) when u (t) is greater than or equal to zero, and a zero when u (t) is less than zero.

A second comparator 92 compares the signal representing the current i (t), converted into voltage, with a second reference value. The second reference value corresponds to a constant voltage, here the zero voltage corresponding to the mass. Thus, the second comparator 92 receives in practice the signal i (t) converted into voltage, and a second reference value, here a zero voltage. At the output of the second comparator, a second logic signal, said signal C2, is obtained. The signal C2 has the same frequency as the excitation signal. The signal C2 here takes a positive value (equal to unity) when i (t) is greater than or equal to zero, and a zero value when i (t) is less than zero.

According to the invention, the first reference value is not necessarily equal to the second reference value, and these reference values are not necessarily equal to the zero value. Nevertheless, null reference values facilitate the processing as described below, in particular when the extreme values of each of the signals to be compared, centered on the zero value because without offset, are ignored. If the extreme values of each of the signals to be compared are known, it is possible, for example, to choose the reference values so that their ratio is equal to the ratio of the peak-to-peak amplitudes of each of the signals to be compared, centered on the null value.

Then, the signals C1 and C2 are combined to form a third logic signal, representative of the time shift T _ph between the signals C1 and C2.

In the example shown in Figures 8 and 9, the signals C1 and C2 are combined to form a C1 + C2 signal. This signal has the same frequency as the excitation signal.

The signal C1 is the logical inverse of the signal C1. To generate the signal C1, a logic inverter 93 is used which is arranged at the output of the first comparator 91.

Then, to form the signal C1 + C2, a logic gate NOR 94 receiving the signal C1 and the signal C2 is used. The signal Cl + C2 is designated by the reference numeral 85. The signal 85 here takes a positive value (equal to unity) when the signal C1 is positive and the signal C2 is zero. In all other cases, the signal 85 takes the value zero. Thus, for each period corresponding to the frequency of the excitation signal, the signal 85 takes a zero value except for a time corresponding to the time shift between the signals C1 and C2, this offset being equal to the time difference between the voltage u (t ) and the current i (t). In the following, the period corresponding to the frequency of the excitation signal is called period of the excitation signal.

The idea underlying this aspect of the invention is to generate a logic signal taking the value 1 or 0, only during a time representative of the time shift T _ph between the excitation signal and the response signal, and exploit this signal so as to determine a phase shift between u (t) and i (t), while implementing a circuit that consumes less energy.

Many variants can be provided to obtain such a signal. According to a less preferred mode, an exclusive OR gate (XOR) generates a logic signal taking the value 1 for a duration equal to twice the time offset T _P during a period of the signal I excitation.

Those skilled in the art will readily be able to determine the proportionality link between the time shift between the signals C1 and C2, and the time difference between the excitation signal and the response signal, from the reference values chosen, and the case where appropriate, maximum and minimum values of the voltage signals corresponding to the reference signal and the response signal.

According to this aspect of the invention, the signal 85 is used to control the charging of a capacitor 95 by a direct current source of constant value 1 _cons , and for a predetermined number of periods of the frequency excitation signal predetermined.

For this purpose, a switch 96 is used between the constant current source 97 and the capacitor 95. The opening and closing of the switch 96, called the main switch, are controlled by the signal 85. When the signal 85 takes the zero value, the switch 96 is open. When the signal 85 takes the value equal to the unit, the switch 96 is closed and the capacitor 95 is partially loaded by the constant current source 97. In general, the idea underlying the invention is that the capacitor is charged only when the logic signal 85 takes one of two values it can take. After a predetermined number of periods of the excitation signal the voltage across the capacitor 95 is reset.

Here the capacitor 95 is charged only when the signal 85 takes the value 1.

The voltage at the terminals of the capacitor then depends on the ratio of time between the period of the signal 85 and the duration during which the signal 85 takes the value 1. This duration ratio corresponds to the ratio between the period of the excitation signal, and the offset time between the voltage u (t) and the current i (t). Thus, knowing the number of periods of the excitation signal elapsed, it is easy to connect the voltage across the switch to the phase shift φ between the voltage u (t) and the current i (t). It is noted that the phase shift φ is calculated for a given frequency of the excitation signal.

It is noted that the presence of the current source 97 makes it possible to control the charge of the capacitor 95 when the switch 96 is closed. In addition, the opening of the switch 96 between two consecutive charges of the capacitor 95 makes it possible to avoid a discharge of the capacitor. The combined use of the current source 97 and the switch 96 makes it possible to accumulate a charge, at the terminals of the capacitor 95, corresponding precisely to the accumulation of the phase shift φ for the number of periods of the elapsed excitation signal. The phase shift φ for a period is obtained by considering the voltage U _c measured across the capacitor, and the number p of elapsed periods as detailed below.

FIG. 9 shows a graph illustrating the voltage U _c across the terminals of capacitor 95 as a function of time t. The curve 99 corresponding to the voltage U _c as a function of time t is a straight line. It may be noted that this is an approximation, and that it may in fact be formed of a succession of bearings for which U _c is a constant (switch 96 open), and bearings for which U _c linearly increases (switch 96 closed). These levels correspond to the succession of null and positive values of the signal 85.

In the example shown in FIG. 9, the voltage U _C (T1), at a time T1, assuming that the capacitor 95 is initially discharged is: U _C (T1) = ^ * T _ph * p (4) where

lcons is the value of the current emitted by the current source 97;

C is the capacitance of the capacitor 95;

p is the number of periods of the excitation signal, elapsed during the time

Tl;

T _P is the average time difference between the voltage u (t) and the current i (t) over the number of periods considered (this offset here being equal to the time difference between the signals C1 and C2).

The formula (4) can be adapted according to the logic signal 85 generated. For example, if the logic signal takes the value 1 for a duration equal to twice the duration T _P , a factor 1/2 is added.

Knowing p, we find easily T _P. Then knowing T _P , we find the phase shift φ, knowing that a shift of half a period of the excitation signal corresponds to a phase shift of 180 ° (n). A precision of 1 ° is typically obtained on the measurement of phase shift φ.

The cumulative phase shift, over several periods of the excitation signal, averages the time offset measurements, which reduces the sensitivity to noise of the device and the method according to the invention.

In FIG. 9, the measurement of the voltage U _c across the capacitor is carried out using the voltmeter 98 connected in series with the capacitor.

Is expected typically more than 10 or even 100 or 1000 periods of the excitation signal before measuring the voltage across the capacitor 95. The fact of accumulating the voltage across the capacitor, over several periods, allows an easier reading of the voltage resulting, the latter being higher. The capacitor 95 is chosen so that the voltage across its terminals can increase linearly for the duration corresponding to this number of periods of the excitation signal.

For example : the frequency of the excitation signal is 1 MHz, ie a period of the excitation signal of 1 μ;;

the capacity of the capacitor is 1 nF; and

the constant current is 10 μΑ.

A phase shift of 1 ° therefore corresponds to a time shift of 2.77 ns. By integrating over 1000 periods of the excitation signal, the voltage U _c across the capacitor 95 will therefore be worth U _c = 27.7 mV.

The signals u (t) and i (t) can be obtained:

one directly at the output of the source 60, and the other by measurements on the impedance Z (see FIGS. 6 and 7), or

both by measurement on impedance Z.

This measurement of the phase shift φ makes it possible to dispense with a counter measuring an elapsed time T _P between a zero crossing of the voltage u (t) and a zero crossing of the current i (t). It is therefore not necessary to provide a counter having a particularly high clock frequency, even for a phase measurement at a high excitation signal frequency (typically greater than 10 kHz). The measurement is therefore energy efficient. The components used are inexpensive. High precision of the phase measurement and a low energy consumption are obtained at the same time. In addition, it is not necessary to adapt the components of the device implementing this measurement, depending on the frequency of the excitation signal.

Figure 10 illustrates an implementation of the third embodiment of device 100 according to the invention.

The elements of the first embodiment, as described with reference to FIG. 6, are recognized in FIG.

In addition, the excitation signal u (t) is taken at the output of the source 60, and sampled by a second analog-digital converter 108. The conditions on the sampling frequency relative to the frequency of the excitation signal are the same as those previously detailed. The digitization provides a series of samples of the voltage u (t).

The analog-digital converters 62, 108 are formed by a two-channel digital analog converter 101, connected to the processing means 64 by a single digital link 102 of the SPI type.

The processing means 64 implement steps 43 to 46 as defined with reference to FIG. 4, applied to the samples of the voltage u (t) and to the samples of the current i (t). The processing means 64 thus calculate the amplitude Au of the voltage and the amplitude Ai of the current, and deduce from this the module | Z | of the electrical impedance Z.

FIG. 10 also shows the detail shown in FIG. 9. The voltmeter 98 of FIG. 9 is replaced by an analog digital converter 103 recording the input voltage of the capacitor 95. This analog-digital converter is connected to the processing means 64. receiving as input the voltage across the capacitor, and outputting the phase shift φ between the voltage u (t) and the current i (t). The link between the digital analog converter 103 and the processing means 64 is a digital link of the SPI type.

In Figure 10, the main switch 96 is shown closed.

The device 100 comprises a secondary switch 104 for discharging the capacitor 95 when the secondary switch 104 moves from the open state to the closed state.

The device 100 also includes a counter 106 for counting a number of periods of the excitation signal. The counter 106 counts, for example, a number of high pulses of the signal 85.

When a predetermined number of periods of the excitation signal is reached: the main switch 96 is open, so as to stop the charging of the capacitor 95;

the voltage across the capacitor 95 is read by the analog-to-digital converter 103; then the secondary switch 104 is closed, so as to discharge the capacitor

95.

This aspect of the method according to the invention can then be repeated by setting counter 106 to zero, opening secondary switch 104 and then closing main switch 96.

This aspect of the method is implemented by means of control means of the secondary switch and the main switch, receiving as input a signal supplied by the counter 106. These control means are here incorporated into the processing means 64. For reasons of legibility of the figure, the connection between the processing means 64 and the counter 106, the secondary switch 104 and the main switch 96 has not been shown.

The processing means 64 also control the frequency of the excitation signal. This command is symbolized in FIG. 10 by the arrow 107. It is thus possible to vary the frequency of the excitation signal over a range from 0.1 Hz to 1 MHz. The method according to the invention is then implemented successively for several frequencies of the excitation signal, for example two per decade. It is possible to provide all the desired frequency ranges, even frequencies going beyond 1 M Hz. Preferably, the frequency of the excitation signal is greater than 10 kHz. Indeed, experience shows that for low frequencies, the implementation time of the invention may be too important. Thus, the invention is particularly suitable for high frequencies, typically greater than 10 kHz.

The invention is not limited to the embodiments described, and it may be possible to combine various variants of the several described embodiments. For example, several variants of the third embodiment of FIG. 10 can be envisaged, in particular by combining the device of FIG. 7 and that of FIG. 9.

Figure 11 illustrates the performance of the method and device according to the invention. This is a Bode diagram from the measurement of the impedance of an RC circuit, where R = 200 Q and C = 470 nF. The sampling frequency is approximately 33 kHz.

The abscissa axis corresponds to a frequency in Hz, represented in logarithmic scale. The ordinate axis corresponds to a phase in degrees, and to the left to a module in Ω represented in logarithmic scale.

Curve 111 corresponds to phase measurements φ. The curve 111 is obtained by interpolation of the measurement points, the measurements being carried out at 1 Hz, 10 Hz, 100 Hz, 1 kHz, 10 kHz, 100 kHz, 1 MHz. The aspect of the invention relating to the measurement of Phase shift has been implemented for the frequencies of 10 kHz, 100 kHz and 1 MHz. For frequencies between 1 Hz and 10 kHz, a method of the prior art has been used.

Curve 112 is the theoretical curve representing the phase of this circuit as a function of the frequency of the excitation signal.

Curve 113 corresponds to module measurements | Z | . Curve 113 is obtained by interpolation of measurement points, the measurements being carried out at 1 Hz, 10 Hz, 100 Hz, 1 kHz, 10 kHz, 100 kHz, 1 MHz. The invention has been implemented for the frequencies of 100 kHz and 1 M Hz. For frequencies between 1 Hz and 10 kHz undue, a method was used prior art. Curve 114 is the theoretical curve representing the modulus of this circuit as a function of the frequency of the excitation signal.

It can be seen that the invention offers very satisfactory results, since the curve 113 representing the measured modules is very close to the curve 114 representing the theoretical values of the module. Similarly, the curve 111 representing the measured phases is very close to the curve 112 representing the theoretical phase values.

A particularly advantageous application of the invention is that of embedded or implanted devices for measuring bioimpedance.

Figure 12 illustrates a portable apparatus 120 for measuring an electrical impedance of a human or animal tissue. Here, the studied tissue is a human tissue located at the level of the arm of a patient 122. The portable device gathers in particular a device 100 according to the invention for measuring an electrical impedance module and, if necessary, a device 121 to measure the phase of this same electrical impedance. In the case where the device 100 according to the invention makes it possible to measure both the module and the phase of the electrical impedance (see Figure 10), it is not necessary to provide a device 121 for measuring the phase of the electrical impedance.

The phase and the module are combined within the portable device, so as to provide the electrical impedance.

In a variant, the portable device 120 makes it possible to carry out an electrical impedance tomography of a human or animal tissue.

Claims

A method for measuring the modulus (| Z |) of an electrical impedance (Z) of a sample (52) in which:

a sinusoidal excitation signal (u (t); i (t)) of predetermined frequency is applied to the sample (52), the excitation signal consisting of an excitation current or an excitation voltage;

measuring a response signal (i (t); u (t)) comprising a response voltage if the excitation signal is an excitation current, or a response current if the excitation signal is an excitation voltage. excitement; characterized by the following steps:

the response signal (i (t); u (t)) is digitized at a sampling frequency lower than the Nyquist frequency, so as to obtain a series of samples of the response signal, the excitation signal and the sampling signal being asynchronous;

an amplitude histogram of the samples (23) is constructed by distributing the series of samples in several classes (24), each class being associated with a voltage or current interval;

on each side of the histogram (23), the most filled class is identified; from the two classes identified, the amplitude of the response signal (Ai; Au) is calculated and the said module (| Z |) is deduced from the electrical impedance (Z).

2. Method according to claim 1, characterized in that the sampling signal is generated by a sampling clock, the excitation signal is generated by an excitation signal clock, the sampling clock and the sampling clock. excitation clock being asynchronous.

3. Method according to claim 1, characterized in that the frequency of the excitation signal is equal to an integer multiple of the sampling frequency plus a fraction- of the sampling frequency, where m and n are prime integers between n

they and n is greater than or equal to ten.

4. Method according to claim 1, characterized in that the frequency of the excitation signal is equal to an integer multiple of the sampling frequency plus or minus a fraction of the sampling frequency less than one-tenth.

5. Method according to any one of claims 1 to 4, characterized in that the sampling frequency is less than a tenth or a hundredth or a thousandth of the frequency of the excitation signal.

6. Method according to any one of claims 1 to 5, characterized in that it further comprises the following steps:

digitizing the excitation signal (u (t); i (t)) at a sampling frequency lower than the Nyquist frequency, so as to obtain a series of samples of the excitation signal;

on each side of the histogram (23), the most filled class is identified; from the two classes identified, the amplitude of the excitation signal (Au; Ai) is calculated; and

the amplitude of the excitation signal (Au, Ai) and the amplitude of the response signal (Ai; Au) are used to obtain the modulus (| Z |) of the electrical impedance (Z).

7. Method according to any one of claims 1 to 6, characterized in that it further comprises the steps of a method for measuring the phase (φ) of the electrical impedance (Z), wherein: generating a first logic signal (C1) by comparing the excitation signal (u (t); i (t)) with a first reference value;

generating a second logic signal (C2) by comparing the response signal (i (t); u (i)) with a second reference value;

combining the first logic signal (C1) and the second logic signal (C2) to obtain a third logic signal (85; C1 + C2) representative of a time shift (T _P ) between the excitation signal and the signal of reply ;

the third logic signal (85; Cl + C2) is used to control the charging of a capacitor (95) by a constant current source (97) for a predetermined number of periods of the excitation signal ;

the voltage (U _c ) is measured at the terminals of this capacitor (95), and said phase (φ) is deduced therefrom.

8. Method according to claim 7, characterized in that the first reference value is equal to the second reference value, itself equal to a zero value.

9. Device (50; 100) for measuring the modulus (| Z |) of an electrical impedance (Z) of a sample (52), the device comprising:

means (51) for applying to the sample (52) a sinusoidal excitation signal (u (t); i (t)) of a predetermined frequency, the excitation signal being an excitation current or a voltage of excitement;

means (51) for measuring a response signal (i (t); u (t)) comprising a response voltage if the excitation signal is a driving current, or a response current if the driving signal is excitation is an excitation voltage; characterized in that it further comprises:

a first analog-to-digital converter (62; 72) receiving as input the response signal, and outputting a series of samples of that signal, a sampling frequency being less than the Nyquist frequency; processing means (64) receiving as input the series of samples of the response signal and outputting said module (| Z |) of the electrical impedance (Z), these processing means being adapted to implement the following steps :

constructing a histogram of the samples (23), distributing the series of samples into several classes (24), each class being associated with a voltage or current range;

on each side of the histogram (23), identification of the most filled class;

from the two identified classes, calculating the amplitude of the response signal (Ai; Au), and using said amplitude to calculate said module (| Z |).

10. Device (50; 100) according to claim 9, characterized in that it further comprises a second analog digital converter (108) receiving as input the excitation signal (u (t); i (t)), and in that the processing means (64) receives as input the outputs of the first and second digital analog converters and is adapted to calculate the amplitude of the excitation signal and the response signal (Au, Ai, Ai, Au). , and use these two amplitudes to calculate said module.

11. Device (50; 100) according to claim 9 or 10, characterized in that it further comprises means for measuring the phase (φ) of the electrical impedance comprising:

a first comparator (91) receiving as input the excitation signal (u (t); i (t)), comparing it with a first reference value, and outputting a first logic signal (C1);

a second comparator (92) receiving as input the response signal (i (t); u (i)), comparing it with a second reference value, and outputting a second logic signal (C2);

combining means (93, 94) receiving as input the first logic signal (C1) and the second logic signal (C2), and outputting a third signal logic (65; Cl + C2) representative of a time shift (T _ph ) between the excitation signal and the response signal;

a main switch (96) arranged in series between a DC and constant-current source (97) and a capacitor (95), and controlled by said third logic signal (85; Cl + C2); and

measuring means (98; 103) for the voltage across the capacitor

(95).

12. Device (50; 100) according to claim 11, characterized in that:

the first comparator (91) is connected to ground, and is adapted to compare the excitation signal (u (t); i (t)) with a zero value; and

the second comparator (92) is connected to ground, and is adapted to compare the response signal (i (t); u (i)) with a zero value.

13. Portable device (120) for measuring an electrical impedance (Z) of a human or animal tissue, characterized in that it comprises a device (50; 100) according to any one of claims 9 to 12.

14. Portable apparatus for electric impedance tomography of a human or animal tissue, characterized in that it comprises a device (50; 100) according to any one of claims 9 to 12.