One can find an excellent overview of calcium in the Electrolyte Quintet series from the Lancet. It is an article you migth have to pay for. The freegan can instead avail themselves of the excellent calcium chapter from the free-to-view Chapter 143 from the 3rd edition of Clinical Methods: The History, Physical, and Laboratory Examinations. Furthermore, one can observe the thought processes of pioneers in this 1935 paper by McLean and Hastings. As far as modern measurement methods go, the calcium-sensitive electrode is an interesting device, and gets its own chapter. Factors which influence the behaviour of calcium ions in human body fluids are explored elsewhere. The distribution of calcium in the body fluid compartments is briefly discussed in the electrolyte section of this site.
As is discussed elsewhere, the majority of bound calcium travels around in the circulation in a complex with albumin. It binds reversibly to twelve of the sixteen exposed imidazoline binding sites on the albumin molecule.
Of these available cation-binding sites, only 10-15% are occupied (i.e. only one or two sites). This means there are plenty of available sites to bind other cations (eg. magnesium) and the divalent cation species rarely enter into binding site competition with one another, particularly as there are so few of them (1-2mmol/L). On the other hand, the hydrogen (or hydronium) cation is a constant source of competition. The positively charged water molecule species work to displace calcium from its binding sites.
For each 0.1 decrease in pH, ionised calcium rises by about 0.05 mmol/L.
The local unit uses the following formula:
Of course, similar adjustments can be made for all other ions which bind to proteins, as their binding is also typically affected by pH. For instance, if one were a pedant inclined to acts of biochemical masochism, one might try to correct serum magnesium values for pH. In case one is interested, the ionised fraction of Mg2+ increased by 0.12mmol/L for every point of pH increase.
Like the action of correcting total calcium for albumin, this practice may seem to be an atavism. If you are going to correct total calcium for protein, you should probably include pH in that calculation, to acknowledge the fact that protein binding is affected by it. However, even in the 1970s it was known that these formulae tend to generate crappy numbers. The formulae were never as accurate as the calcium-sensisitve electrode.
Furthermore, there is a certain argument from bedside utility. Say the patient has a plasma pH of 6.9. Who cares what their calcium would be at a normal pH? That corrected number would have zero relevance to the reality of the patient's current state.
And on the topic of obsessive correction, if one were going to submerge this far into nerdy chemistry, one might also want to correct their ionised calcium for temeperature (it decreases with increasing temeperature, albeit slightly- the early pioneers reported that at 38°C, it is about 0.2mmol/L higher than at 25°). And one could try to correct for the presence of all the other calcium binding species, such as lactate, phosphate, bicarbonate...
Mockery aside, there are several reasons as to why one might want to have a pH-corrected value:
When might one want to look at the pH-corrected ionised calcium level?
Preprocessing sampling errors are an argument for pH correction which may not be obvious to the spoilt inner-city intensivist, who is accustomed to having a rapidly effective ABG analyser within shouting distance of the patient's artery. It is more relevant in smaller units, where one might have to send the ABG across the hospital to get analysed, and then wait for the lab guy to recalibrate the machine. During its travel time, the pH of the sample drifts down. Furthermore, each trip might be different (one time the wardsman stopped for a cigarette?) and the pH will drift down by a different amount each time. In such circumstances, one would wish to have their calcium corrected to a standard pH, so that one is able to compare between samples.
Sample CO2 is a notable influence on ionised calcium measurement. The evaporation of CO2 from an "aerobic" (open-to-air) sample results in a sample alkalosis, which will decrease the ionised fraction.
Another historical argument for the correction of ionised calcium for pH stems from the fact that in the bad old days, the ionised calcium analyser was a completely separate device. The measurements of pH and iCa2+ were not simultaneous. In such a situation, one might wish for a pH-standardised measurement, so that one is able to make decisions about management without confusing the process by acknowledging momentary pH fluctuations.