you can read more about these written by their own protagonists on:

the Siggaard-Andersen homepage

and an excellent website about the BE approach (event though very critical of the Stewart approach .... ): Alan W. Grogono's homepage.

the bicarbonate approach, also called the "physiological approach", is well described by Adrogué, even though he has little good to say about our favourite theory, either:

a recent article by Adrogué

Adrogué HJ, Gennari FJ, Galla JH, Madias NE; Assessing acid-base disorders; Kidney Int 2009 Oct 7

quoting James Figge from page 224 in "Stewart's Textbook of Acid-Base", advertised on this website: "Base Excess is defined by Siggaard-Andersen as the negative value of the concentration of titrable hydrogen in blood or plasma." the formula is given as:

BE = [HCO

[HCO

ß

the crucial point with this is, that it assumes normal values for albumin and phosphate. as long as this condition is met, the Stewart approach gives results completely equivalent to the Siggaard-Andersen method.

not many of our ICU-patients do meet this condition -

BUT: the base excess approach is the only one taking into account the modifying ("buffering") effects of both the red blood cell intracellular fluid and the interstitial fluid, giving you an idea about how much you have to change the SID to normalise the pH (if you elect to do so) - with the same caveat, though, that it assumes normal values for the weak acids and for the volume ratios between these different fluid spaces, too.

on the Siggaard-Andersen homepage you will find the complete version of the "van Slyke equation":

the "van Slyke equation"

this actually includes a way of calculating albumin's contribution to the acid-base behaviour of plasma:

quoting from that page:

the same page even offers a way of unifying the concepts of "buffer base" and SID:

**Strong ion difference (SID) **is defined as the concentration of non-buffer
cations minus the concentration of non-buffer anions. SID of plasma therefore is
the sum of the concentrations of Na^{+}, K^{+}, Ca^{2+}, Mg^{2+} minus the sum of
the concentrations of Clˉ,
SO^{2+}, and
certain organic anions, which also represent non-buffer anions at physiological
pH.

BBˉ and SID are obviously numerically equal, because the sum of all cations must equal the sum of all anions (law of electroneutrality)."

you can find more information about BE and other acid-base related matters at Radiometer's website (obviously, not a website dedicated to Stewart's physiochemical approach .... ).