This chapter is most relevant to Section F12(iii) from the 2017 CICM Primary Syllabus, which expects the exam candidates to be able to "describe the methods of measurement of oxygen and carbon dioxide tension in blood". As the clinical abilities of an intensivist are rather uncoupled from their ability to describe the construction of an electrolytic cell, this topic has not seen much air in the CICM exams, which is a refreshing trend towards sanity on the part of the examiners.
A satisfactory amount of detail about these methods is available in William L. Nastuk's 1962 textbook, "Electrophysiological Methods:Physical Techniques in Biological Research". This book was an invaluable source of reference material for elsewhere in this site as well.
Essentially, this is an electrolytic cell.
Behold an aqueous solution, which contains oxygen (represented in the diagram below by a string of childish bubbles). A reference anode and a naked platinum cathode are suspended in the solution. Between them, a potential difference is generated by a battery; the typical useful range is 600-700 mV.
The potential difference allows a reduction of the dissolved oxygen; the oxygen borrows electrons from the cathode and hydrogen ions from the water molecules of the aqueous solution.
This reaction can be represented thus:
O2 + 4H+ + 4e- → 2H2O
In actual fact, some of the oxygen is also consumed by an incomplete reduction reaction, forming hydrogen peroxide (H2O2) which - in the presence of the platinum catalyst - is immediately degraded into oxygen again, and ultimately consumed in the complete reduction reaction.
As this reaction takes place, electrons are "consumed". They are produced in the silver electrode, where silver (Ag) is oxidised.
4Ag → 4Ag+ + 4e-
The resulting silver cations join with the chloride in the KCl electrolyte, and form a crust of AgCl which must be periodically scraped off. The entire redox reaction can be depicted as a crude diagram...
... or as a mature-looking chemical equation:
4Ag + O2 + 2H2O + 4Cl- → 4AgCl + 4 OH-
Additionally, it should be mentioned that a miniscule amount of silver ions will eventually make their way towards the platinum electrode, and will deposit themselves there as a thin film of silver.
The flow of electrons through the circuit represents a current which can be measured using a galvanometer. The rate of reaction therefore governs the magnitude of the current.
This current can be represented by the following equation:
I = Sens (pO2 ) × pO2 + I0
The sensitivity of the electrode is expressed in terms of change in current per change in the partial pressure of oxygen. The modern ABG machines have a Sens(PO2) value of 5-40 pA (picoamperes) per 1 mmHg pO2. This value is calculated empirically, by calibrating the electrode with gas mixtures of known pO2.
One may plot a relationship of current, potential difference and pO2. Apparently, the plot of current and voltage is called a "polarogram", where the original Clark electrodes get their name. The graphs below have been adapted without any permission whatsoever (and with gruesome disfiguring modifications) from Philip W. Davies' chapter (Ch.3, pp 137) in the 1962 textbook by Nastuk. Instead of blood, the measurements here were taken in a 0.1 molar solution of NaCl.
The current vs voltage curve takes a sigmoid shape. At lower voltages, the reaction rate is limited by the availability of energy - few oxygen molecules are reduced at such a low voltage, and thus little current is seen. As the current is increased, a plateau develops. The plateau represents the failure of ever-increasing potential difference to drive any further oxygen reduction; at such a high voltage the rate of reaction is no longer determined by the available energy, but rather by the availability of oxygen - all available oxygen in the vicinity of the electrode is immediately reduced, and more oxygen must diffuse from elsewhere in the solution in order for the reaction to continue. Thus, the flat part of the plateau reflects conditions at which the rate of oxygen diffusion is maximal for this particular solution.
The current vs pO2 curve, for a given voltage ends up being quite linear. It would make sense to use this linear relationship to calculate a pO2 - why not just use the same voltage all the time? However, this is impossible in clinical situations. Which voltage should you use? Surely, it would be the voltage at which reduction rate is maximal (ie. limited by diffusion). But how do you know where that plateau is going to be, if you don't know the pO2? The plateau of the current vs voltage curve is determined by the pO2, as the rate of diffusional supply of O2 to the cathode is related to the partial pressure of oxygen in the sample (i.e. higher pO2, the faster the diffusion, and thus the higher the voltage required to reach the plateau).
In view of this relationship, the ABG machines tend to vary the voltage in order to find that plateau, and infer the pO2 from the required voltage.
Make note of the changes to the current which occur at the upper range of the applied voltage. Weirdness develops as one attempts to measure a pO2 greater than 150mmHg or so. Beyond a certain voltage, the plateau changes- a new peak is experienced. This is because as voltage is increased ever higher, one eventually finds that the electrode begins reducing H2O, and a new source of current is found - one entirely unrelated to the reduction of oxygen. In fact, we call this thing the "oxygen cathode", but really whether it measures oxygen or hydrogen depends only on the magnitude of the voltage. Fortunately, empirical correction formulae exist which can be applied to the numbers generated, and pO2 values can be derived from even hydrogen-polluted measurements, but their accuracy is... submaximal.
It should be mentioned (and it has already been mentioned elsewhere) that the oxygen cathode measures not the definitive pO2, but the electrical activity equivalent of oxygen tension, i.e. the redox activity of the dissolved oxygen. It is the "equivalent partial pressure". It relates closely to real partial pressure, and it can be an effective surrogate for it within the realms of biologically feasible temperatures and pressures, but we should not be deluded into believing that we are measuring the true Dalton's Law sort of fraction of mixed oxygen in the blood gas.
But wait, will say the reader with some elementary chemistry background. Is oxygen the only species being reduced here? Will current not develop due to the reduction of other elements, confounding your measurements?
Indeed, such a thing could happen. However, PW Davies hastens to point out that there is an advantage in using this electrode within the confines of biological systems. You see, oxygen is easily electro-reduceable. The other elements which are also easily reduceable are silver, copper, and lead. Under normal circumstances, these are not present in sufficient quantities in an arterial blood gas to be a major source of inaccuracy.
However, there are many other, more practical problems.
First, the issue of electrode barnacles.
There is an inherent electrode hygiene problem associated with exposing biological systems to mild current. Unfortunately, as anybody who has ever worked with temporary pacing wires will already know, any current-carrying wire exposed to living tissue will rapidly become encrusted with all sorts of ungodly filth. This will be annoying. Inaccurate low results will be produced.
The silver anode will also become encrusted (with AgCl) which is a hard scaly deposit, requiring regular scraping. Not only that, but chloride depletion will occur, with a gradual alkalinisation of the electrolyte solution.
Additionally, there is a dependence on oxygen diffusion. In a thick gooey sample, the diffusion will be slow, and in the absence of convection, all available oxygen in the vicinity of the electrode will be consumed quite rapidly. Any measurement that takes place with even a few moments delay after the circuit is completed will therefore give an inaccurately low reading (the time frame we are talking about is apparently about 25 milliseconds). The electrode, therefore, depends on a steady flow of sample.
Modern solutions to some of these 1960s problems are discussed in the chapter which deals with the matter of pO2 measurement using the Clark electrode.