Download Dear colleagues, the article published on “Scandinavian Journal of

Dear colleagues, the article published on “Scandinavian Journal of Clinical and Laboratory
Investigation”, demonstrates how to simulate the acid-base status of a patient. It is able to calculate the
pH of a solution, knowing the total stoichiometric concentrations of acids, bases and ampholytes.
Usually, however, the real unknown variable is the concentration of metabolizable acid related to some
organic metabolizable acids as lactic acid, acetic acid, acetoacetic acid, fumaric acid, etc., usually not
directly measurable. I wanted to expose some examples to simplify the matter as possible.
Description of the program.
The solver of Excel:
1. How to load the Excel solver: see https://www.youtube.com/watch?v=Q3ciB1ED4_A
2. How to set the solver Excel. Note: in my Excel the “?Solver” is displayed in Italian language:
“?Risolutore”.
The program is divided into a part dedicated to the plasma, in a second part dedicated to the interstitial
fluid and in a third section for urine. In column “A”, the ingredients of the plasma solution are
expressed in millimoles / liter: sodium hydroxide, potassium hydroxide, calcium hydroxide,
magnesium hydroxide; hydrochloric acid, o - phosphoric acid, sulfuric acid; while PCO2 in mmHg, etc.
The box “A9” contains the concentration of sulfuric acid in plasma. If your laboratory is not able to
measure it, it can be estimated directly from the plasma BUN concentration (mg/dL), placed in the
“G3” box. For example, for a BUN equal to 100 milligrams / deciliter, the sulfuric acid will be equal to
2.26 millimoles / liter.
The box “A12” contains the concentration of a generic metabolizable organic acid, with an “average”
pKA value of 4.76. This type of acid can be considered as a jolly to be utilized for calculating the
concentration of metabolizable acid other than Albumin – related titratable hydrogen ions. Next to each
compound we can find the pKA values, except for strong acids and bases (complete
dissociation/protonation). The pKA values can be changed arbitrarily. In fact, some authors, who follow
the approach of Stewart, prefer to assign a value of 1.91 to the first group of orthophosphoric acid; a
value of 6.66 for the second and a value of 11.78 for the third.
Column "S" contains the concentration of non-metabolizable base, NB, managed by the kidney, the
concentration of metabolizable acid, MA, managed by intermediary metabolism, and the concentration
of titratable carbonic acid, CA, managed by the lung.
For "non-metabolizable base" we mean the net stoichiometric concentration of non-metabolizable
hydroxide ions, measured by titration to pH 7.40. For "metabolizable acid" we refer to the net
stoichiometric concentration of metabolizable hydrogen ions, measured by titration to pH 7.40. For
"titratable carbonic acid", instead, we refer to the stoichiometric concentration of carbonic hydrogen
ions, measured by titration to pH 7.40.
Further below, the values of plasma and whole blood base excess are shown.
By dissolving the total mass of hemoglobin in a distribution volume equal to the extracellular fluid, the
whole blood base excess, BE(B), turns into standard BE, recommended by Siggaard-Andersen to
distinguish between respiratory and non-respiratory disorders. For example, if the blood volume is
approximately 5 liters, while the extracellular volume is 15 liters, the hemoglobin concentration (A22
box) will change as well: (cHb x 5)/15 = cHb/3. The same apply for hematocrit (A23 box): (Hct x 5)/15
= Hct/3.
Box "S9" contains the plasma buffer value. Further, “S11” and “S12” boxes show the PCO2 values
before and after a ventilatory variation ("start", "end"). This allows us to calculate the pH associated
with fluctuations in PCO2 and, consequently, the NB–related variations especially due to chloride
redistribution between red blood cell, plasma and interstitial fluid.
Let's take an example. After pressing "Ctrl + q", and "OK" three times, we get a normal electrolytic
and acid – base status.
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Now, let's change the "hydrochloric acid" box, A7, from 102.5 to 98. Open the Excel solver. Click on
"solve" and "ok". The pH value changes from 7.400 to 7.469. Now simultaneously press "Ctrl + z" and
click "OK" three times.
Pay attention to column "S", where plasma non – metabolizable base, NB(P), increased from a value of
about 41 mmol/l to 45.78 mmol/l; plasma metabolizable acid, MA(P), remains unchanged: 17.18
mmol/l. This latter value is composed of titratable hydrogen ions released by albumin, 10.27 mmol/l
(box “P3”), and titratable H+ ions released by different organic metabolizable acids, 6.92 mmol/l (box
“P5”). Plasma titratable carbonic acid, CA(P), rose to 28.04 mmol/l (isocapnic CO2 retention). Plasma
base excess (BE(P)) rose to +4.5 mmol/l, while whole blood base excess, BE(B), reaches +5.13
mmol/l. In interstitial fluid, isf (see column "AB"), non – metabolizable base, normally equal to 35.45
mmol/l, rose to 40.19 mmol/l, metabolizable acid (released by metabolizable molecules other than
albumin) remains unchanged, 8.12 mmol/l, while CA rose to 31.71 mmol/l. The interstitial base excess,
BE(isf), reaches +4.74 mmol/l.
This condition is compatible with a NB – alkalosis related to a gain of non – metabolizable base (e.g.
NB overload). Otherwise this is also interpretable as a NA – alkalosis, due to a loss of non –
metabolizable acid, NA (vomit).
Now, pay attention to “S17” box, which contains the estimated PCO2 value in the case of respiratory
compensation: 44.51 mmHg. Enter this value in "S12" box: the pH of the "S13" box will reduce from
7.469 to 7.433. Place this latter value, 7.433, into "A19" box, while put the compensatory PCO 2, 44.51
mmHg, into "A11" box. For consistency, put the PCO2 value of "S12" box into "S11" box. Now, open
the solver: in the cell "by changing the variable cells" select "$A$7", and click on "solve" and on "ok".
The value of HCl changes from 98 to 97.49 mmol/l (mild NB redistribution from red blood cells to
plasma, and from plasma into interstitial fluid). Push "Ctrl + z" and then "ok" three times. The picture
that emerges is compatible with a NB - alkalosis compensated by the lungs (mild compensatory
hypercapnia).
By changing the hemoglobin value from 15 g/dl to 5 g/dl, and Hematocrit from 40% to 13%, we obtain
the standardized base excess. In fact, BE(B) changes from +4.79 to +4.95 mmol/l.
Second example. Acute hypercapnic acidosis: the "in vivo CO2 titration", i.e., the redistribution of
non-metabolizable base between erythrocytes, plasma and interstitial fluid.
Press "Ctrl + q" to reset. Put “100” into "S12" box. The pH of “S13" box reaches 7.092. Put this latter
value in "A19" box. Finally, you must put the PCO2 value equal to “100” mmHg in "A11" box. Once
that is done, put the value of "S12", 100, into "S11" box, to maintain a pH value equal to 7.092 in
"S13" box.
Open the solver: in the cell "changing ..." selected "$A$7", then click "solve" and then "ok". The value
of HCl decreases from 102.5 to 98.68 mmol/l (considerable redistribution of non-metabolizable base
from red blood cells into plasma and from plasma into interstitial fluid). Press "Ctrl + z" and then “ok”
three times.
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Note that plasma non-metabolizable base, NB(P), and interstitial non-metabolizable base, NB(isf),
increase. This is not in agreement with a NB-alkalosis, because the increase in NB is secondary to
hypercapnia. NOTE: BE(isf), box "AB6", is equal to +6.01 mmol/l, BE(P), in box "S6", is equal to
+3.82 mmol/l, while BE(B) is even negative: -4.77 mmol/l. This highlights the redistribution of nonmetabolizable base between red blood cell (which loses alkalinity), plasma and interstitial (which gain
alkalinity). At this point Siggaard-Andersen suggests to correct the hemoglobin and hematocrit values
from 15 to 5 g/dL and from 40% to 13%, respectively. BE(B), which now represents standardized base
excess, increases from -4.77 mmol/l to +0.95 mmol/l. In a nutshell, the standardized BE helps the less
experienced doctor to put the correct diagnosis of pure hypercapnic acidosis, bypassing reasoning on
the physiological redistribution of NB in response to hypercapnia. The same reasoning, but in reverse,
apply in the case of acute hypocapnia, during which the plasma and interstitial NB are reduced, the
BE(isf) will be negative, as for plasma BE, but more markedly, while BE(B) (Hb=15 g/dl and
Hct=40%) will be positive. The standardized BE will instead be next to zero.
Third example. Mixed non carbonic acidosis: MA + NA acidosis (metformin poisoning and acute
renal injury).
Use the following data:
cBUN(P) 75 mg/dl
cNa+(P) 135 mmol/l
cK+(P) 6.40 mmol/l
ctCa2+(P) 2.56 mmol/l
cMg2+(P) 0.90 mmol/l
cCl-(P) 107 mmol/l
cPi(P) 2.11 mmol/l
cSO42-(P) 1.75 mmol/l
PCO2(B) 12.8 mmHg
cLactic Acid(P) 9.3 mmol/l
cAlb.(P) 26.46 g/l
pH(B) 6.846
Hb 10 g/dL
Hct 31.3%
ctPr(P) 44 g/l
Open the solver: in the cell "changing ..." select "$A$12", click "solve" and then "ok". Push "Ctrl + z"
and "OK" three times. See column "S": NB(P) is low, due to an accumulation of phosphoric, sulfuric
and chloride acid. MA(P) is high not only in relation to hyperlactatemia, but also for the increased
concentration of other organic metabolizable acids that, evidently, rise during metformin intoxication.
The interstitial fluid detects the same situation: MA - acidosis + NA - acidosis. Standardized BE(B),
turns from -32.31 mmol/l to -27.15 mmol/l.
Good fun!
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