Understanding the Human Machine - A Primer for Bioengineering - Max E. Valentinuzzi

i.e., to return to the normal operating range? This is the recovery time. By and large, it depends on the transient characteristics (amplitude and duration) and also on the overall amplifier frequency response features. It can reach several seconds. There are protecting circuits, which automatically disconnect the amplifier once an overload is detected.

Suggested exercise: Find examples where the concept may (or may not apply). Hints: A force suddenly applied to a body; the lag time of a muscle to respond to a stimulus. Design possible experiments. It does not matter whether they are or not realizable. Discuss critically. Einstein used to imagine experiments and his results were highly productive.

5.5. Noise and Interference

The weed always has to be separated out from the good herb; besides, never mix two good herbs, choose only one; otherwise, you may get a tummy ache. Old Mother Rose's advice.

The input signal to a biological amplifier has several components: The desired biopotential to be measured plus unwanted disturbances, such as noise or interference of different characteristics — usually originated in external sources different from the biological system — interference from other normal and always present biopotentials, and the ever present potentials at the electrode-electrolyte interface (see the preceding Chapter). The latter could reach amplitudes significantly higher than the desired signal and may become particularly annoying with motion (the so called movement artifact).

Generally speaking, any unwanted signal mixed with or superimposed on the desired one is called noise or interference or disturbance. We will not make any distinction among these three words although, under certain circumstances, noise could be differentiated from interference or disturbance (the first would be a continuous random signal of very wide frequency content, while the second could be manifested as single or multiple pulses of undetermined shape and duration). Its origins recognize a variety of sources:

External sources are located outside of the biological system and of the amplifier. They usually come from electrical and electronic appliances, but the atmospheric discharge is also possible.

Internal sources are located within the biological system and, most of the time, produce normal potentials which do not belong to the desired biological signal.

Intrinsic sources essentially refer to the amplifier itself. It is noise of the integrated circuits and its associated circuitry.

An adequate amplifier design must tend to fully eliminate or at least minimize all the above-mentioned disturbances.

5.5.1. Coupling of External Interference

First, we will recall three fundamental physics postulates, which permit the modeling of noisy systems:

Electric fields are confined within capacitors; Magnetic fields are confined within inductors;

Circuit dimensions are always much smaller than the noise wavelengths. If for some reason they do not hold, or the analyst does not want to make use of them, the situation changes drastically transforming the system enormously more complex and essentially impossible to resolve. Models are the only way to approach complex systems and, as such, models must turn to simplifying assumptions and hypotheses, sometimes even oversimplifications. Remember what was said about models in the preceding chapter.

According to the way a disturbance gets into the amplifier, we can consider different types of coupling: conductive, capacitive, inductive and by electromagnetic radiation.

5.5.1.1. Noise counductively coupled

It is a very common situation. A cable laid on the floor of a room may pick up noise. The wiring from the power supply to its amplifiers is an easy route. A common resistor or impedance taking current from two different circuits can introduce interference from one to the other and vice-versa. Figure 5.7 depicts such situation: The current due to the second circuit modulates voltage VG1, developed by the first current. Conversely, the first one also modulates voltage VG2, developed by the second circuit. The net result is mutual introduction of noise from one to the

Figure 5.7. CONDUCTIVELY COUPLED NOISE.

other. Since the pathway is a line or a wire or resistor network, either overtly or covertly (the latter may no be easy to uncover), this kind of coupling noise is called conductive.

5.5.1.2. Noise capacitively coupled

As the word indicates, the culprit here is a capacitor but … it is not a well-behaved “touchable” capacitor built by man, it is a stray capacitance (called also distributed or parasitic) formed by wires, connections, the animal or the patient and the noise source. Typical values, to illustrate, of interest to the biomedical engineer in the medical environment are:

Human subject standing up on an insulator, between the subject and the noise source

Adapter of ac input power to ±15V dc output, between primary and secondary

Shielded two-wire cable, between both wires, per foot

Between one wire and shield, per foot

Coaxial cable (RG58), between central conductor and shield, per foot,

Optic isolator, photodetector LED, between input and output

Resistor, 1/2 w, tip to tip

Figure 5.8 gives a simple model visualizing a capacitive coupling between two conductors when there is a generator connected to one of the wires and a resistive load to the other. The reference is ground. Voltage

V1 and conductor 1 act as interference source while conductor 2 is its receptor. There is a stray capacitance, C12, coupling the first to the second. C1G and C2G are capacitances from each wire to ground. The second conductor has a load R. The noise voltage VN can be calculated by considering the complex voltage divider (see Figure 5.8) formed between V1 and VN via impedances Z1G and Z2G, respectively, offered by the stray capacitance C12 and the parallel combination of C2G and the load R; hence, obtain first the ratio Z2G (Z12 + Z2G ), and work it out algebraically to find,

where, interestingly enough, capacitance C1G does not play a part. Besides, if the load resistance has a much lower value than the combined impedance presented by C12 + C2G, a rather common situation in practice, the equation of above reduces to

In conclusion: The noise voltage due to capacitive coupling is a function of the amplitude and frequency of the noise source and also of the coupling capacitance and the resistance to ground of the affected circuit. Since the first two parameters usually cannot be controlled, the only way of reducing noise y by acting on the two latter.

The student is urged to work out the last derivation. First divide through by jω, thereafter,

Figure 5.8. INDUCTIVE COUPLING. The circuit to the right is an equivalent representation of the two wires to the left.

Figure 5.9. CAPACITIVE COUPLING, A PATHWAY TO NOISE. Impedance Z12 is represented by the stray capacitance C12 between the two wires while impedance Z2G appears as the parallel combination of the load R and the stray capacitance to ground

C2G.

multiply through by R, and in the new expression apply the above-mentioned simplification. We use the words resistor and resistance, capacitor and capacitance, inductor and inductance. Pay attention how they are placed in the sentence recalling that those ending in -or refer to the physical element containing the electrical property whose English term ends in - ance. Very rarely, if ever, we can hold in our hands, say, a resistor showing pure resistance, for it is always contaminated by the other two properties!

5.5.1.3. Noise coupled inductively (or magnetically)

Current flowing into a circuit generates a magnetic field that, in turn, may induce voltages in a neighbor circuit via a mutual inductance. Let us consider Figure 5.9, where such situation is depicted. Magnetic flux is Φ = L1I1 , partially transferred to the second circuit by the mutual induc-

tance M12 so inducing, by Faraday's law, the noise voltage VN = jωM12 I1 . An equivalent circuit (a model) is also shown.

The mutual inductance depends on the geometry of the system and on the magnetic properties of the medium (most probably air in the physiology laboratory or the hospital environment). As in the previous capacitive case, the source amplitude and frequency directly influence the amount of noise induced. The only way to reduce it is by reducing the mutual coupling. The task may face great practical difficulties though, especially

when there are power distribution lines, transformers and ac machinery in the proximity of the working place.

5.5.1.4. Noise coupled by electromagnetic radiation

Physiology laboratories, intensive care units, coronary units, catheterization labs an other medical departments placed in the neighborhood of radio (either AM or FM), TV or radar stations, are prone to nicely blur their records with this very annoying interference. With due high respect, we should unload the original responsibility to Maxwell, Herz, Tesla, Marconi and many other wireless communication pioneers and, at the same time, recognize the interference as part of the price we pay for living the luxury of an almost simultaneous world. However, and do no take it all on these fine men, electrocautery and diathermy equipments (which use RF in the MHz range) may also be powerful and very close sources of disturbing signals. Some piece of the medical equipment acts as a de facto antenna (perhaps the cables hooked to the patient) while, somehow, the amplifier acts as an unwilling detector. Techniques to reduce this disturbance are complex, not easy to implement, require a good physical construction of the operating theater along with a good arrangement of the instruments within it, plus adequate filtering.

5.5.2. Network Interference

Take a deep breath, buddy, 'cause this is gonna be a thorny morsel to swallow

The domestic urban power line is without doubt the main source of interference detected by our biosignal systems. Instrumentation amplifiers are specifically designed to reject, as much as possible, this 60 or 50 Hz (frequency depends on the country) disturbance coupled either capacitively or inductively or both to either the patient or the experimental animal.

Let us consider an ECG recording via surface electrodes. Figure 5.10 schematizes a usual arrangement, where always the right leg is grounded. Coupling possibilities in the hospital or laboratory environment are manifold. Just merely think of the countless ac-lines crossing walls, ceilings and floors, getting into power supplies, equipments of all sorts, including those located in the very working place and other as pedestrian as vac-

Figure 5.10. INTERFERENCE

PICKED UP BY AN ELECTRO-

CARDIOGRAPHIC SYSTEM.

uum cleaners or floor-polishers, and easily you will realize that our poor biological amplifier is literally swimming in a noise-sea. In fact, you may even believe the successful measurement of what you want, say, the ECG, is an impossible mission. Well, for the Biomedical Engineer no mission is impossible.

A little gossiping to relax you: Do you remember or have you ever seen a replay of Mission Impossible, that breath-holding TV series of the sixties? For that team no mission was impossible. Lalo Schiffrin, a great and talented Argentine-born musician and composer, wrote

— in a not common rhythm (5/4 time signature, i.d., five quart beats in a measure) — its background beautiful music. He was high-school classmate of this book's author (MEV), and once, as teenagers, he played in MY piano (still in my hands and in excellent conditions); that is the best musical accomplishment found in my cv!

5.5.2.1. Capacitively Coupled Interference

Figure 5.11 intends to represent Figure 5.10 in a slightly more real world: The patient is replaced by a volume conductor holding the biological generator (for example, the heart in this case), VBIOL, which develops surface potentials A, B, and C, detected by the electrode leads. Between these points and the generator there are resistances, RA, RB and RC, materialized by the body fluids. Their values can be in the order of 500 Ω. Besides, Ze1, Ze2 and ZeG, represent the respective contact electrode impedances, that is, the impedance between the patient's skin and the electrode metal; expected values lie somewhere between 1 KΩ and 20 KΩ. The amplifier receives the signal (any, the good and the bad one) with its two input impedances, the differential Zd and the common mode one Zcm. It would be a good idea to go back in the chapter to review these concepts.

Figure 5.11. MODEL TO ANALYZE CAPACITIVE PATHWAYS. The circle represents a volume conductor (the patient) with the heart in its center (the biological generator). Surface electrodes A, B and C pick up a fraction of that signal. Currents ic1 (through capacitor C1), id1 and id2 return as iG to ground; they do contribute to interference, but whatever currents may traverse C2 and C3 do not. Besides, they are usually rather small. See text for more details.

The possible capacitive coupling pathways are defined as follows: Ce2 and Ce1, between the power line and the lead wires;

C1, between the power line and the patient; C2, between the patient and the reference;

C3, between the power line and the equipment case.

Coupling magnitude depends on how close the active and ground conductors are with respect to the measuring system and patient. Capacitive stray elements, respectively, offer pathways for currents id1, id2 and ic1, returning to ground as iG via ZeG; the latter is always lower than the impedance offered by C2 while the differential input impedance to the amplifier is very high. The other two stray capacitive pathways, C2 and C3, are not interference contributors. Hence, the total current through the return connection is,

Moreover, since the patient's impedance is much lower than the electrode impedance, the net interference voltage applied to the amplifier appears expressed as,

leading to the unfortunate but not surprising conclusion that there is a noise differential voltage at the amplifier's input due to capacitive coupling. At the output, it is reflected as,

Well … after a regret sigh, the question springing up right away is, and how big this nasty interference can actually be? Let us make some estimates of a hypothetical but possible situation. Biomedical engineers, as any other engineer, always have to play with numbers to get an idea of where they really stand.

Let us consider a unipolar cable, 9 m long, with which a current id ≈ 6 nA was measured in a given medical office. Even though theoretically the electrode impedance should be equal for the pair, experience has taught us that there is always a difference. Perfect matching does not exist. Assuming a good installation of the electrodes (good electrolytic paste, good pressure, clean surface), the difference can range from 1 KΩ (excellent contact) to 20 KΩ (poor contact), producing 6 µV < (VM – VN ) < 120 µV, as the probable range of the undesirable signal. Some authors cite differences even above 50 KΩ. We think it is way to high, … or the technician installing the electrodes did not know what he/she was doing! The typical ECG input signal competing with the intruder is in the order of 1 to 2 mV, that is, interference is about 1 % to 10 % of the signal to measure. The first level is barely acceptable, the second is definitely not because at the output, if the gain is 500, we would be getting from 0.3 mV to 60 mV … of noise! We seem to be almost “kinda stuck”. What do we do then? Experience from many people, careful analysis of labs, operating rooms, coronary units and similar working shops in many places can be summarized in a few advices, and beware, because there is for the time being no other way out,

•worsen the coupling conditions by decreasing the input cable length, increasing the distance between the input cable and the power line, shielding the input cable, and grounding the shield;

•decrease the electrode impedance by improving the electrodes, cleaning them well, using adequate paste and, very important, installing them properly.

Still we have the common mode signals entering the system by the very same capacitive coupling. Our amplifier is well prepared for them with a high rejection ratio, typically 80 dB (see above). The common mode potential between any point over the patient and ground is,

The latter equation is based on the fact that biological impedances are always much lower than contact impedances. That common mode interference, taking into account the voltage divisors shown in Figure 5.11, produces a difference between points M and N that can be written as,

but, since both electrode impedances are much smaller than Zcm, the latter equations reduces to,

Verify the latter equation, but be careful how you do it. Hint: Fully develop the fraction within the brackets in (5.40).

In brief, equations (5.37) and (5.38) describe the differential interference while (5.39) and (5.41) deal with common mode noise; both types are capacitively coupled.

To illustrate now the latter, let us assume iG = 0.5µA and ZeG = 10 kΩ, leading to Vcm = 5 mV by applying equation (5.39). If the electrode impedance imbalance is (Ze2 – Ze1) = 5 kΩ and Zcm = 1 MΩ, the amp would be presented with VM – VN = 5 mV [5 kΩ/1 MΩ ] = 25 µV, after equation (5.40). This is a border value. If you play a little with possible numbers, easily the unwanted signal may reach 100 µV or even more, which is unacceptable or at least objectionable. To reduce the level of interference still sneaking in, in spite of the common mode rejection, we have to,

•increase the CMR of the amplifier;

•use low impedance electrodes trying to decrease the imbalance.