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

4.2.2. Interface as an Electrical Circuit

An array of parallel RC circuits that for simplicity are usually lumped into one RC network is frequently used to model the electrode-electrolyte interface (Figure 4.1). Its main components are the electrolytic medium resistance Rm, to account for ionic conduction in the solution bulk, the double layer capacitance Cdl formed by ionic accumulation and/or by polarized particles which give rise to the half-cell potential (the other half is located at the companion electrode completing the circuit), the charge transference resistance Rct to model the hindrance faced by the electrons when moving to and from the electrodes, and the diffusion impedance Zw, also called the Warburg impedance after the investigator who proposed it back in 1899; the latter considers how difficult is for the charges to diffuse towards the interface. Often, the electric elements of similar kind are lumped into a single one (say, the Warburg resistance is combined with the transference resistance) but conceptually this is not quite correct because different phenomena are being mixed even though it is electrically

to amplifier

Rfl

Figure 4.1. ELECTRODE-ELECTROLYTE INTERFACE EQUIVALENT CIRCUIT.

Rct or charge transfer resistance; Cdl or double layer capacitance. These components together are called polarization elements. Ehc or half-cell potential and Rfl or resistive faradic leak, the latter to provide for the dc and low frequency interface behavior. The return electrode (lower part of figure) is similar so that the two points called 1 are immersed in the electrolytic solution with a resistance Rm. Points 2 are connected to the input amplifier. In general, both electrodes will have different values of the equivalent circuit elements.

simpler. The Warburg impedance has a complex nature, for a resistance in series with a capacitance forms it. These components vary with the frequency of the signal applied to the interface. Besides, it must be underlined that the half-cell potential is characteristic of each metalelectrolyte combination and is not able to sustain any current. The total voltage between a pair of electrode terminals is the algebraic sum of the two half-cell potentials; usually, they are numerically different, and they may even display opposite signs depending on the metals the electrodes are made of. If the metal is the same for both electrodes and since the half-cell potentials appear in series, at least theoretically, they should tend to cancel out. Changes in acidity (a desired signal in pH-meters), bacterial growth (also a desired change in impedance microbiology), movements of the electrodes (undesired in ECG or in EMG records) modify the half-cell potentials, which are detected and amplified by the recording system. To measure a single half-cell potential is impossible; thus, an arbitrary standard electrode has been chosen (the hydrogen electrode) and electrode potentials are measured and tested against it in electrochemistry laboratories. There are other types of reference electrodes. The bibliography describing constructive and technical details is abundant (Geddes and Baker, 1989).

Emil Daniel Warburg (1846–1931) was one of the first to investigate the components of the electrode-electrolyte interface. He was a German physicist connected to several other physicists of great accomplishments and prestige, like Kohlrausch, Einstein and Planck (students: find out who they were). Warburg postulated that the capacitance of an elec- trode-electrolyte interface varies inversely with the square root of frequency, i.e., C = Kf–α, where K is a constant depending on the metal species, electrolyte concentration and temperature. Experimentally, it has been found that many times the exponent α ranges between 0.22 and 0.79 (Geddes, 1972).

Student task: Search for information about the hydrogen electrode. Describe it. Search for other types, such as the calomel and the silver-silver chloride electrodes.

The circuit shown in Figure 4.1 holds only for ideally smooth interfaces and does not take into account electrode rugosities. Thus, such model can be used in a few experimental situations, as the case may be with a mercury electrode. Some authors (Geddes & Baker, 1989; Webster, 1992) often make use of purely empirical models for the interface, calling it Zi, the interface impedance, or Zp, the polarization impedance, usually composed of a resistance and a reactance in series plus a battery, also in se-

made through the interface. To make electrodes rougher is common practice when bioelectric signals such as EEG or ECG are recorded. An important benefit is a significant decrease in the unavoidable impedance interposed between the source (heart, brain or other) and the electronic amplifier. As example, Figure 4.3 shows a platinum wire electrode roughened by using low frequency square-wave potential perturbations (Pajkossy, 1991).

This kind of electrodes has interface impedance 10 to 100 times lower than those that are untreated. Only recently the structures of this figure were approximately modelled by fractals (fractional elements). The concept, introduced by Mandelbrot (1975), has self-similarity as principal characteristic, that is, no matter how much an imaginary microscope power is increased to observe a given pattern, the pattern keeps being similar to itself. Fractal structures seem to be part of our inner biological nature, be it blood flow cerebral distribution (Nagao et al., 2001) or the helicoidal DNA. A true challenge was for physicists and electrochemists the development of the equations to predict, at least qualitatively, the behavior of a rough electrode-electrolyte interface (Liu, 1985; Nyikos & Pajkossy, 1985). The subject goes beyond the objectives of the book and suffice it just this short mention for the curious student.

Student Task: Fractal legumes. Buy a cauliflower and analyze its parts as you cut it into smaller and smaller pieces. Looking at it with a lens might help. Search in INTERNET for more information.

Figure 4.3. ROUGHENED PLATINUM WIRE TIP. Images were obtained using a scanning electron microscope. Left view: scale 100 µm. Right view scale 10 µm. Reproduced with permission from Electrochemistry at fractal surfaces, J. Electroanal. Chem., 300 (1991), pp:1–11.

The interface does not embrace only the surface metal and its rugosities; as mentioned previously, it includes also the associated electric charges. Hence, an ideally smooth electrode (with an interface width anywhere between 10–9 and 10–10 meters), but submerged in diluted saline solution, increases its interface width up to 10–6 meters. In high concentration solutions, instead, the double-layer size is much smaller than the rugosities of the electrode metal. The above-mentioned interface width is defined as the perpendicular distance to the electrode measured from the deepest metallic valley to the last molecular level associated with the interface.

4.2.3. Useful and Annoying Interfaces

An electrode-electrolyte interface (EEI) may in some cases supply useful information while in others may act as a disturbance.

The first situation, from an electrochemical point of view and being somewhat repetitious, includes the measurement of pH, CO2 and/or O2 concentration, say, in blood or plasma. These physiological parameters are essential in clinical practice and during surgical interventions (Peura, 1992). Currently there are in the literature a great variety of gages, called biosensors, where an electrochemical transducer is combined with enzymes, nucleic acids, cellular receptors, antibodies or intact cells so producing myriads of gadgets to measure glucose, cholesterol, urea, lactate, creatinine or other substances (Zhang et al., 2000). In impedance microbiology the interface is a natural ally too, providing quantitative and qualitative information about microorganisms growth (Felice & Valentinuzzi, 1999). In the dairy industry, evaluation of either the reactive or the resistive components or both of cow milk samples using a bipolar technique can be used to assess possible contamination (Felice, Madrid, Olivera et al., 1999).

In the second situation, instead, the interface impedance is not wanted for it interferes with the desired signal, as exemplified in the recording of the ECG, EEG, EMG, or other similar signals; the biopotential appears in series with the EEI and, thus, the latter tends to modify the former both in amplitude and in shape.

The EEI must also be either avoided or decreased in biomass measurements. Electrodes are introduced in fermentators where high concentrations of microorganisms, fungii, yeasts or other types of living cells are present (Davey, Davey & Kell, 1993). The best way to avoid it is by

Leslie Geddes, Herman Schwan and their collaborators carefully studied the EEI as function of current density. Their many contributions, classics in the literature, are frequently used for bioinstrumentation design (Schwan, 1968; Ragheb and Geddes, 1991; Mayer, Geddes, Bourland et al., 1992; Geddes, 1997; Geddes and Roeder, 2001).

4.2.5.Bioelectric Signals Picked Up with Electrodes: Four Different

Situations

For the sake of illustration, in this section we describe four interface bioengineering applications: pH measurement (when the generated dc potential difference at the interface is used to quantitate hydrogen ion concentration), interface impedance measurement during bacterial growth (to quantitate bacterial concentration), continuous membrane potential measurements (when the pH dc potential becomes a disturbance), and finally, measurement of classical variable bioevents (when the interface impedance appears also as a disturbing phenomenon). In brief: in two situations the interface is welcome and in the other two it is declared as nondesirable.

4.2.5.1. Measurement of pH (dc signal at the interface)

Let us first review as introduction the concept of pH. The following paragraph can be skipped if the student is already familiar with these basic concepts. Søren Peter Lauritz Sørensen (1868–1939), Danish biochemist, introduced it as a convenient way to quantitate the acidity of a solution. A numerical scale can be established by taking the negative logarithm of hydrogen ion concentration. The letters pH stand for “pondus hydrogenii” (literally hydrogen weight, in Latin), as acidity is caused by a predominance of hydrogen ions [H+]. Originally, Sørensen wrote both letters with capitals, but W. M. Clark (inventor of the oxygen electrode that carries his name), in 1920, suggested the current notation “pH” for typographical convenience; as an extension, “p-functions” have also been adopted for other concentrations and concentration-related numbers. For example, a pH of 4.5 refers to a molar H ion concentration of 3.2x104 and a pCa = 5.0 means a concentration of calcium ions of 10–5 M. Thus, in its original description, the acid potential of aqueous solutions is expressed in terms of the pH scale, where the symbol “p” means “take the negative logarithm of whatever follows in the formula”, say, for pH, pOH, or p[anything], i.e., pH = –log [H+] = log {1/[H+]}. Note that the hydrogen ion concentration must be ascertained before the pH can be calculated. Tremendous swings in hydrogen ion or hydronium ion concentration occur in water when acids or bases are mixed in it (see below for the conceptual chemical difference between the two terms). These changes can be as big as 1 x 1014 meaning that concentrations can change by multiples as big as one hundred trillion. The pH

scale is a logarithmic scale. Every multiple of ten in H+ concentration equals one unit on the logarithm scale. Physically, the pH is intended to tell what the acid “potential or weight” is for a solution. In a sense, the system is inverted; so, a low pH value indicates a great acid potential while a high pH indicates a low acid potential (this is upside down and counterintuitive.)

A more modern definition makes use of the molar concentration of hydronium ions [H3O+] in solution, that is, pH = – log([H3O+]). Pure water autoionizes to produce equal concentrations of hydronium and hydroxide ions [OH–]. This is described by, 2 H2O = H3O+ + OH– whose equilibrium obeys the law of mass action in the form Kw = [H3O+] [OH–] = 1.0×10–14 (at 25ºC). This modern form of the equation for water autoionization recognizes that protons do not exist in solution but instead are bound to an electron lone pair in water: H+ + H2O = H3O+. The obsolete term hydrogen ion and its concentration [H+] have been replaced by “hydronium ion” and [H3O+] but we continue to use pH (and not pH3O). Since the hydronium ion concentration and the hydroxide ion concentration are equal in pure water, it follows that [H3O+] = [OH–] = 1.0×10–7. Then, the pH of pure water is pH = – log(1.0×10–7) = 7.00. In dilute acid solution the hydronium ion concentration is higher; e.g., in micromolar hydrochloric acid, 10–6 M HCl, the hydronium ion concentration is [H3O+] = 10–6 mol/L so that the pH = 6.00. That is, one step lower (higher) on the pH scale represents 10 times higher (or lower) hydronium ion concentration. In a similar way to pH, the concentration of hydroxide ion is also expressed on a logarithmic negative power scale: pOH = – log([OH–]). Further, since water autoionization equilibrium relates [H3O+] to [OH–], the pH and pOH are related: [H3O+] [OH–] = 1.0×10–14, so that –log([H3O+]) – log([OH–]) = –14.00 or pH + pOH = 14.00. The hydrogen ion concentration in pure water around room temperature is about 1.0×10–7 M. A pH of 7 is considered “neutral”, because the concentration of hydrogen ions is exactly equal to the concentration of hydroxide (OH–) ions produced by dissociation of the water. Increasing the concentration of hydrogen ions above 1.0×10–7 M produces a solution with a pH of less than 7, and the solution is considered “acidic”. Decreasing the concentration below 1.0×10–7 M produces a solution with a pH above 7, and the solution is considered “alkaline” or “basic”.

In 1906, Max Cremer found that a difference in hydrogen ionic concentration caused a difference of potential across a glass membrane. The circuit contains two Ag/AgCl reference electrodes and a glass membrane sensitive to hydrogen ions (Figure 4.5). There are two interfaces at stake: one between the glass and the electrolyte within the bulb (left electrode in Figure 4.5) sustaining a constant potential difference and another between the glass and the sample with a potential related to its acidity. The interface potentials of the two reference electrodes are constant because of the high concentration of HCl and KCl. Thus, any change in the sample solution has negligible effect on them. Moreover, the electrode metal within that electrolyte must have a very low drift, so giving good stabil-

Figure 4.5. BASIC SYSTEM TO MEASURE pH OF A SOLUTION. White points at the EEI’s mark dc interface potentials; their sum E is given at the voltmeter VM output. The double circle area at the glass membrane is the only interfacial potential that changes with hydrogen ion concentration. The rest remains constant.

ity to the system. The electrode in HCl is separated from the sample by a glass membrane sensitive to H+. The other electrode, really the reference in this circuit, is separated from the sample by an orifice covered with a porous filter that lets the electric current flow but it prevents mixing of the electrolytes.

The liquid-liquid interface at the filter sustains a minute potential due to two reasons, on one hand, the sample ionic concentration is much lower than K+ or Cl– concentration within the electrode; thus, it does not generate an apreciable difusión potential as ions traverse the porous filter towards the KCl solution. On the other hand, K+ and Cl– difusión to the sample through the filter does not generate significant electrical potential because they involve charges of equal magnitude and mobility.

In summary, the voltmeter records the algebraic sum of all interface potentials but the only one that varies with the hydrogen ionic concentration originates at the glass-sample interface.

4.2.5.2. Bacterial concentration (ac signals at the interface)

In this application the interface impedance is continuously measured with electrodes immersed in innoculated broth cultures. The growth of microorganisms leads to proton and/or ionic production causing an increment of the interface capacity Ci. Such parameter better follows bacterial development than monitoring the broth ohmic resistance (Noble, Dziuba, Harrison et al.,1999; Felice, Madrid, Olivera et al., 1999; Felice & Valentinuzzi, 1999). Figure 4.6 shows this capacitance for different microorganism concentrations in raw cow milk, where contamination is

Time [hr]

Figure 4.6. INTERFACE CAPACITANCE Ci GROWTH CURVES. Two stainless steel electrodes immersed in culture broth. Assorted set from different cells. From Felice, Madrid, Olivera et al. (1999), experimental data obtained at the Department of Bioengineering, UNT.

well known and composed of several bateria. The upward inflexión point is used to estimate the initial bacterial concentration; a documented law states that the lower the initial concentration, the higher the initial contamination.

4.2.5.3. Membrane potential (dc signal through the interface)

The resting membrane potential of an excitable tissue is a dc signal measured by a very small electrode (microelectrode) piercing the membrane to get into electrical contact with the intracellular fluid against a big return electrode placed in the extracellular fluid. The inside is about 80 to 90 mV negative to the outside. Since the interface half-cell potentials interfere and tend to heavily distort the desired electrophysiological signal, they must be balanced out with a previous short-circuit procedure, otherwise, there is no way to separate them out (Geddes & Baker, 1989). The bibliography is abundant and the student is encouraged to search for more information regarding the subject.

4.2.5.4. ECG, EMG and EEG (ac signals through the interface)

This application has been already been dealt with in a preceding chapter. We only emphasize here that these physiologycal signals are of the ac type that traverse the electrode-electrolyte interfaces; thus, changes in electrode impedance introduce distortion, especially when the latter is