The article is a brief summary of the fundamental principles of EEG system design. It is based on almost twenty-year experience in the creation of systems of functional diagnostics and contains strict and clear interpretation of the main technical terms, which characterize the quality of electroencephalographic systems. Although the article requires special knowledge from the reader, it is of interest for professionals in the field of electroencephalography, as well as for system engineers, who independently develop a system of functional diagnostics. Taking into account that many terms used in the article require explanations, the article is completed with a simplified glossary. Harshness of some definitions of the author is an inevitable reaction to the real state of the matter with electroencephalographic equipment in Ukraine.

Recording an EEG in the routine version of examination is not a technically difficult task. However, obtained results are far from always of high diagnostic value. It is connected not only with physiological limitations of the method, but often also with the quality of recording, which not only shows no increase, but in a number of cases evokes associations from the domain of obscene vocabulary.

The reason lies not only in the degradation of electroencephalographic equipment in Ukraine (sic!), but also in the absence of the stuff training and frequent complete dilettantism of the doctor.

Really, if twenty years ago the devices from respected companies - NIHON_KOHDEN, ORION, etc. were used, completed with proprietary electrodes and expendable materials, than now they use computers, "home-made" by Ukrainian companies and certified a la Ukraine. The masterpiece of squalor, if one may say so, is their completion with homemade iron electrodes wrapped in rags to be moistened with physiological solution. It is clear that, dumping at tenders, these companies compete in reducing the cost of production and as a consequence, in reducing the quality of EEG recording. Naturally, producing more and more "full-featured" software they try to play the fool with the doctor. They offer thereat either nonexistent methods of analysis, or methods for removing the artifacts, born by, let's say it flat out, a shitty electroencephalograph. Most often they manage to draw the wool over the doctor's eyes, because for almost 20 years there were no full value courses in this specialty. Eventually the most eye-popping results are achieved in commercial polyclinics, where the main requirement to the equipment is the availability of a system of automatic diagnostics in it.

But, in spite of our nationally isolated, cheap at tenders, domestic collective farm, the technical progress in the world goes on, and the quality of electroencephalographs of the world leaders grows up. And thereat not only doctors, but some domestic developers of medical diagnostic equipment are convinced that such pure recordings cannot exist, and bourgeoises have invented some trick, by means of which they draw such nice electroencephalograms, electrocardiograms, etc. Generally speaking, the ghost of second-rateness and provinciality is tacitly, but menacingly present at any discussion of the problems of electrophysiological signal recording in our domestically developing consciousness. The best evidence of this thesis will be the fact that nobody even thinks of using homebred Ukrainian EEG junk for diagnosing the death of the brain (it is not just telling users and patients horror fairy tales, "everything you say can be used against you"). Or for operation with a connected artificial lung1 (it's obvious that the device will produce nothing but interference), and for any serious examination at all. But, regardless the local (featherbed!) state of the matter, it is necessary to strive to improve the quality of recording, even disregarding the fact that not competition, not doctors and not patients require this. The worse the users, the better the equipment must be. And, if earlier only the Big League dealt with electroencephalography, now there will be nobody except sleeping on the go dumb Dora Nakenavel as the nurse and a prescriber of biological food additives as the doctor. There are lucky exceptions (very few of them), but they are still exceptions.

Theoretically the problem of EEG recording is a problem of multichannel synchronous recording of microvolt infra-low frequency2 signals with a typical internal resistance of the signal source between several and hundreds of kiloohms. One must take thereat into account the a priori presence of additive3 systematic noise with the mains frequency with the signal-to-noise ratio worse than a unit, additive white Gaussian4 noise (AWGN) of the electrodes, zero-frequency component in the form of electrochemical polarization potential, trends caused by changes in osmotic pressure5 if electrode liquid, and multiplicative noise caused by changes in electrode resistance. Perhaps, we must place systematic and radio-frequency noise in a separate group, as well as physiological artifacts.

Historically, this problem was rather successfully solved by means of differential amplifiers7 with a large common-mode rejection ratio (CMRR8) and high input impedance. No other solution was proposed up till now. And even now, in spite of all impressive progress of electronics, the majority of devices are designed in the same way. Beautycraft in the form of widened dynamic range9 or decimation10 after high-frequency digitization is presented as a revolutionary breakthrough to the shining heights. Especially good (particularly for a psychiatrist) are the statements on achieving the CMRR of more than 140 decibel (160 dB11 - I saw it with my own eyes in one advertising booklet of an Ukrainian manufacturer). Amazingly, there is no such equipment either in Germany, or the USA, or Japan. The declared specifications of their devices are tragically inferior to the Ukrainian ones, and it is not clear, what insidious Japan specialists do in the field of industrial espionage.

However, in order to understand the process of development of equipment for EEG examinations, it is expedient to recollect its history with unforgettable tube Alvars, the nostalgia for which clings to the good old guard, going into oblivion.

So, let us take as an axiom the requirement of high impedance and common-mode rejection ratio of the input amplifier. Paradoxically, but tube circuits met this requirement in the best way, especially in a nuvistor12 low-noise version. The reason is simple (although it is ignored by contemporary developers) - these stages preserved high CMRR up to the frequencies much higher than the working ones and had very insignificant (almost unreachable even up till now) input capacitance. So, as a consequence, the device successfully filtered all HF components of external interference and physiological artifacts. And an irremovable drawback was a parametric trend, that is, these assemblies required fine adjustment and were not a LIS13 system. At present it is difficult to imagine an electroencephalographist adjusting the CMRR (!), he has very vague notion even about the operation of the device's filters (the better cars, the worse the drivers :).

The development of semiconductor technology has predetermined the appearance of electroencephalographs with field-effect transistors at the input and the input amplifier balanced at the factory. In spite of the development of special-purpose chip assemblies of type KPS 104, these devices were inferior to tube ones by all parameters (except dimensions, mass and energy consumption). Higher flicker14, the necessity to protect the inputs from static discharges and impossibility of adjustment after repair and replacement of components have made these devices non-competitive. As a consequence, parametric input amplifiers (PIA15) began to appear, where the main gain in current was provided by a stage based on varicaps16. High characteristics in the working band were combined in them with low efficiency of HF interference rejection and complexity of circuitry. But the necessity to space apart the working frequencies of the electroencephalograph amplifiers has become the main problem. That is why such devices were manufactured only in versions with small number of channels.

First attempts to build the amplifiers on integrated17 operational amplifiers have shown that everything is far from good with internal noises and input impedance. And, in spite of special methods for suppressing flicker (passivation18 of the crystal by silicon nitride, etc.), only recently the attempts to achieve the desired characteristics succeeded. Nevertheless, the problem of drift of the main parameters as frequencies approach the boundary ones still persists even in operational amplifiers manufactured by AD, Burr-Brown and other. That is exactly why the designing of a modern electroencephalograph somewhat differs as to complexity from assembling a LEGO toy. Utilization of good components by no means guarantees the good quality of the device (NB!).

Modem operational amplifiers19 in the integrated circuit version have turned out to be suitable for utilization as the electroencephalograph input stages. Disregarding rather modest figures of the main parameters declared by the manufacturer (chip 140UD13), they ensured reliable and stable operation without the drift of characteristics throughout the entire period of operation. However, some peculiar features have floated up. For example, it is not possible to use electrodes with polyurethane foam filler - "bridges"20 - due to the device's response to periodical changes of the active and reactive components of their total impedance. The reason is simple - the modem operational amplifier pumps the RF energy "back" through the spurious capacitance21 of the modulator gates22. Unfortunately, this fact is ignored by some Ukrainian manufacturers, who have obtained the device in "solid-drawn" form. The results of polyurethane foam bridge application are horrible for the user, but wonderful for the manufacturer - it's cheap, cool, and nothing is clear.

Our experiments have shown that the attempt to build modem amplifiers on small-scale integrated circuits in order to increase the channel area of field-effect transistor and, as a consequence, to reduce internal noise, have yielded excellent results in separate specimens and demonstrated complete inadequacy for mass production. We have obtained the peak-to-peak noise23 reduced to the input less than 0.35 ?V with CMRR not less than 115 dB and differential input impedance not less than 20 MOhm. But a multichannel electroencephalograph built on this principle required enormously large labor consumption for adjustment and tuning.

Out of the hardware exotics, we must note commutation amplifiers24, which, according to the results of investigation in our laboratory, remain promising, although problematic (internal noise grows proportionally to the square root of the number of channels). But one cannot exclude that application of optimum circuitry solutions can help to solve this problem, that is to lower the noise to acceptable values.

Among the loss-making products of the Goodwin's factory of magical articles (this factory was recently renamed in one of Ukrainian companies), we can name circuits with "flying" capacity25, which simulate a high CMRR by means of lowering the differential input impedance of the stage (the energy of commutation noise is compensated due to continuous recharging of capacitor). Namely for this purpose the specifications of interest to a psychiatrist were proclaimed. According to the user's response such devices never operated properly.

At present the development of the EEG circuitry has halted on operational amplifiers. Virtually all modern electroencephalographs use precision26 operational amplifiers as the main scaling27 amplifier. And taking into account the choice of their types, we can say for sure that an amplified EEG is present at the output terminals of the operational amplifiers. In this connection the question arises, why the majority of homemade electroencephalographs work so bad and how they manage to create such problems at routine recording?

The explanation can be the only one - the device has not been designed for operation under the conditions of actual noise. In this connection let us examine the situation with external interference in more detail.

Undoubtedly, the most important and maximal as to level is the noise with the mains frequency - 50 Hz. It is caused by pickups from power supply wires, including current loops, in which the device and patient can find themselves. Very simply said, the value of the noise can be considered proportional to the capacitance of the system patient-device in respect to the power supply wires. One must thereat keep in mind that when a device with internal power supply is grounded, the noise increases proportionally to the increase in capacitance (the ground/mains capacitance is always larger than the patient/mains capacitance). Of course, we speak not only about the common-mode component. Its antiphase (to be specific - out-of-phase) value is determined by the asymmetry of the system of electrode placement. Naturally, the more symmetrical is the system of electrode placement, the lower is the out-of-phase component of the noise, which arrives at the input of the electroencephalograph. According to the data, obtained in our laboratory, in order to obtain the amplifier's CMRR of 80 dB, it is necessary to balance the system of electrode placement up to the value not less than 40 dB. Otherwise the operation outside a shielded chamber will become problematic.

However, this requirement does not exist for an infinitive dynamic band of the input amplifiers and ideal elimination filter28. Surely, nothing is perfect in the world, and an electroencephalograph with infinitive CMRR and asymmetrical system of electrode placement will not work. Even at very small external noise. Generally speaking, one must take into account that asymmetrical systems were designed at ancient times (but sound and professional) - only for the conditions of operation in "Faraday cage". As it is impossible to use it under unscreened conditions, we can with good reason attribute it to the realm of the designer's idiocy. Conclusion for the buyer: being offered a device with whatever-you-want hardware calculators of the system of electrode placement - know: some of them will never work in a not screened room, even disregarding the outstanding specifications of the amplifiers.

Well, what will happen to an electroencephalograph when the noise exceeds the value of the margin, determined by the dynamic range? The answer is quite simple - "dirty" electroencephalogram will periodically appear and then disappear, and the "sections of silence" will be slightly shifted with respect to each other in various channels (Fig.1).

Fig.1. Appearance of "sections of silence" on EEG

Namely, the 50 Hz noise is not seen, it has been shamefacedly cut off by the rejector. But if we turn it off, the beauty of the designer's ideas will manifest itself in full volume (Fig.2).

Fig.2.EEG with filters turned off

But it is possible to solve the 50 Hz problem in he absolute version. With full symmetry of the system of electrode placement and equal patient/ground and patient/mains capacitances it (i.e. noise) tends to zero in its out-of-phase version. Naturally, the provision of such conditions require the infinitive input impedance of the device, no grounding and complete symmetry of the inputs. No problem is to eliminate grounding by means of digital telemetry. But the other conditions are both unreachable and mutually exclusive. It is impossible to balance the input under the conditions of very large impedances of the input resistive array, and it is impossible to obtain infinitive values of resistance for a precision array due to physical reasons. Do not thereat forget that the noise EMF30 grows as the input resistance increases. Nevertheless, an approximate (and particular) solution exists in the form of the transfer of calculations into a strong-current or digital domain, naturally, at a sufficient dynamic range. As a result, the noise will be not filtered, but eliminated primordially, that is the condition of external noise rejection will be met. Developing this theme, we can offer also other solutions within the scope of the "External Noise Rejection" (ENR39) principle. As an illustration, we can show the electroencephalogram of the same patient, recorded in the same premises and under the same recording conditions (Fig.3).

Fig.3.Gain 50 чV /10mm, sweep speed 30 mm/s, HFF-OFF, LFF 70 Hz. (EEG is scaled, 50 чV, 1 s are shown)

Pay attention that the elimination filter is off, and the bandwidth is limited to 70 Hz. That is, noise is not filtered, it is eliminated primordially. This is very important also because high values of the noise signal are not multiplied inside the amplifier with the useful signal (such multiplication is caused by nonideality of the voltage-current characteristic of any physically feasible amplifier). Besides, the absence of a band-rejection filter ensures high fidelity of signal transmission, as an IPC31-eliminator always "clinks" at pulse interference, and an FPC32-system has in the time domain a preceding and succeeding response, caused by the shape of the data window (obviously, specialists do not need illustrations).

We must also keep in mind that, apart from the 50 Hz noise, its harmonics exist, especially when fluorescent lamps, thyristor power controllers and other similar devices are used. Therefore the electroencephalograph's immunity to other systematic noise must be ensured as well.

Most generally speaking, we can say that an ideal device must not register any physical artifacts at all.

When analyzing a group of artifacts it makes sense not to analyze each of them separately in the time domain, but investigate the spectrum of all possible interferences and compare it to the spectrum of electroencephalogram. This work was carried out in 70s in the New York Medical College and it has immediately become as near as dammit a classical one. It has been shown that the EEG signal in many cases "dives under the noise" at frequencies below one Hertz and above 70 Hertz. And one can say nothing about the electroencephalogram below and above the indicated frequency boundaries when analyzing it visually. At the same time, if the signal and the noise are not spaced apart in time and the spectra of the noise and the signal overlap, its complete separation is impossible. This is one of the most general and fundamental postulates of the theory of informatics and attempt to bypass it is akin to the desire to cheat the force of gravity. However, such exercises still go on and are caused not so much by dilettantism, as by efforts to invent (a perpetuum mobile?).

Taking into account two facts - the required bandpass of the amplifier and requirement to minimize noise within the band, it is obvious, that a properly designed amplifier limits the bandpass, and the nearer to the input amplification states, the better, and tends to limit the spatial filtering at the input for the noise within the bandwidth. Otherwise there is no way to cut them off from the signal. That is, the ENR principle quite logically follows from the main task of designing.

It must be acknowledged, that the majority of devices with to the utmost open bandwidth, redundant digitization at the dynamic range determined by the gain of the first (upstream of the ADC) stages, are designed improperly. Herewith the increase of the ADC digit capacity can be used for advertising purposes only. The actual tolerance of the device to noise will the smaller, the larger its bandwidth, and the dynamic range will be "jammed" the earlier, the more open is the band from the lower side. But the most substantial will be the contribution of the noise passed through an asymmetrical system of electrode placement.

Besides, the problem of adequate discretization of input signals still has no rigorous solution and is rather a technical compromise, completely subordinated to posed problems. Even if we orient exceptionally at sigma-delta converters33, we must acknowledge, that the frequency response of the channel (Fig. 4) is far from the one intended to cope with high-amplitude interference in a wide frequency band (Fig. 5).

Obviously, the simplest addition in the form of implementation of Hamming polynomials makes it possible to obtain a much better protected digitizer. At the same time, discretization by the sigma-delta method has no advantages, except a lower intrinsic noise, against a trivial "voltage-frequency" converter (VFC34), which uses the temporal aperture of the discretization period, and, taking into account the possibility to use in a VFC the temporal data window, is inferior to it. And even primitive solutions in the form of the hardware Bartlett window35 ensures the victory of the VFC over the sigma-delta digitizer (it is hardly its fault - it has been designed not for these purposes). Nevertheless, both the designers and advertisers of the device always demonstrate the euphoria on the occasion of total interference immunity of their device, which implements all gimmicks of the modern component base.

If we actually subjugate the digitizer technical requirements to specific features of the hardware, which has to operate under the conditions of a priori unknown interference, we must first of all ensure the maximum out-of-band attenuation at a linear frequency response in the band and realization of necessary band-rejection filters, which are combined with the digitization procedure and do not use infinite pulse characteristics. Please pay attention that in this case the requirements to the dynamic band become substantially lower (it becomes realistic) and the possibility appears to raise the gain of first stages. In its turn, this, as a consequence, lowers their intrinsic noise (NB!). In this case there is no necessity to increase the number of ADC digits, it can be subordinated to the requirements of a specified digitization error within the scope of the entire project (but not competitive advertising).

Fig.6. Death of the brain. Infant 1 year old, the seventh day of artificial lung operation. Throughout the entire recording no phenomena with amplitude above 1.5 чV were registered. Ag/AgCl gel electrodes. Telemetric electroencephalograph. Gain 25 чV/cm in the main image and 6.25 чV/cm in the enhanced one. The image is scaled, +-1,5 чV is indicated with arrows in the enhanced EEG.

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