The ion sensitive electrodes in the ABG machine measure the concentrations of potassium, sodium, calcium, chloride and lactatem as well as non-ionised glucose. Similar principles of operation apply to each electrode, and they are coupled into a "electrode chain" in the blood gas analyser.
For a detailed reference on this topic, I refer the readers to Nallanna Lakshminarayanaiah's Membrane Electrodes (2012)- it is a thorough treatment of this subject. Martin Frant has also published two excellent articles detailing the ascent of the ion selective electrode as a tool of point-of-care measurement.
Generally speaking, this potentiometric instrument requires two electrodes. One is a reference electrode, and and the other is an electrode suspended in an ion-selective enviornment. This environment can be a pool of electrolyte solution with a calibrated reference concentration, or an ion-selective PVC membrane which acts as an ion carrier. Either way, a potential difference develops between the two, which is proportional to the log of the difference in ion concentration between the reference solution and the sample.
Thus, if the reference solution and the sample both have the same concentration of ions, the potential difference between the electrodes should theoretically be 0mV.
Obviously, selectivity is imperfect. In the foggy uncertainty of the atomic scale, ions of the same charge resemble one another. In a perfect world, one would expect a totally linear response of potential difference (mV) to ion concentration (log aI). Unfortunately in reality at lower limits of in concentration all the other ions of the same charge are going to start to confuse the electrode. Even when the concentration of the Ion Of Interest drops to zero, there will be a non-zero voltage between the electrodes because minute concentrations of similarly charged ions will be migrating around the membrane. Similarly, at the upper reaches of concentration, the competition from ions of the opposite charge becomes a problem, placing an upper limit on the measurement. For example, for the potassium electrode, this interference seems to come mainly from sodium and ammonium ions.
Thus, though an electrode might be 200-1000 times more selective for its ion of interest, there is a certain detection limit beyond which it becomes nonselective. For instance, for the potassium electrode in the local blood gas analyser, the detection limits seem to be between 0.5 and 12 mmol/L. This imperfect device remains clinically useful simply because this sensitivity spectrum encompasses the "survivable" potassium concentration range. Weirdly, the Radiometer brand of sodium electrode (model E755) remains sensitive well outside the normal physiological range; it can go as low as 10mmol/L, and as high as 250mmol/L.
Thus, the real trick in making these electrodes truly "ion selective" is in the design of the membrane.
The ion-selective membranes are sufficiently awesome to deserve their own chapter, where their various properties are discussed in greater detail; in brief, the selectivity of such membranes is conferred by "ionophore" molecules (ie. ion-selective molecules which act as carriers). For instance, the potassium-selective PVC membranes have for a long time been impregnated with valinomycin, a macrolide antibiotic with a ring structure. The ring happens to have a gap in it which fits the potassium ion very precisely, and is therefore a useful "carrier", allowing the potassium ions to slowly exchange across the membrane. Apparently, an electrode with a valinomycin-impregnated PVC membrane can be up to 5000 times more selective for potassium when compared to sodium.
The electrode chain in the blood gas analyser consists of the Ag/AgCl reference electrode and all the electrolyte electrodes. Strictly speaking, the chain consists of a circuit which comprises the sample solution, a membrane, a reference electrolyte, a measuring electrode, a reference electrode suspended in a reference solution, and a voltmeter to measure the total potential between the two electrodes.
Thus, Etot is the sum of the potential differences at each section of the circuit.
The specific potential difference one is interested in is Esample which is the potential difference across the membrane of the ion-selective electrode; this is the membrane across which the ion of interest will migrate, and the potential generated by this migration is proportional to the concentration of that ion.
In other words, one can subtract the known potentials from the total potential across the electrode chain to calculate the potential across the ion-selective membrane.
One can then use a rearranged Nernst equation to relate this potential difference to the activity of an ion, which in turn is related to its concentration:
The activity of an ion is related to its concentration (cion) by the equation aion = γcion where γ is a certain "activity coefficient" for a given species under the measurement conditions (and in an ideal situation, this value is 1.0 - i.e. activity equals concentration). For the maintenance of sanity, the blood gas analyser does the heavy lifting for you, and represents ionic activity as a concentration automatically.
Specific ion-selective electrodes, and curious peculiarities of their design, are discussed in greater depths individually.