(PC-4) Calculating Blood Gases

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Calculating Blood Gases on a Pocket Computer, CHARLES HARRIS

Figuring pH and blood gases on a $20 scientific calculator or a $75 hand-held pocket computer can be fun and educational. But first. a brief review of the blood gas equation is in order. It derives from the fact that the equilibrium between components of a weak acid or base is constant. In the case of carbonic acid, the equation is
       K = { [H⁺] [HCO₃^-] } / [H₂CO₃]
  Solving the equation for [H⁺] - the hydrogen concentration in nanograms (10^-9 or one billionth of a gram) per liter – we have
       [H⁺] = K { [H₂CO₃] / [HCO₃^-] }
remembering that 1/K is also constant.
  Anyone who ever worked in an intensive care unit recognizes that the denominator of the equation is the basic bicarbonate ion. The negative logarithm to the base 10, or 1/log₁₀ of both sides of the equation results in the familiar Henderson-Hasselbalch equation:
       pH = pK + log₁₀ { [HCO₃^-] / [H₂CO₃] }
where pK is the dissociation constant, 6.1.
  Back to the original:
       [H⁺] = { K [H₂CO₃] } / [HCO₃^-]
  H₂CO₃ breaks down to CO₂ and water. Thus, the numerator H₂CO₃ is proportional to the CO₂ dissolved in the blood. The solubility constant of CO₂ in the blood is 0.51, and that calculates out to 0.03 mmol CO₂/mm Hg partial pressure of CO₂. Thus, we have
       [H⁺] = { K (0.03)(pCO₂) } / [HCO₃^-]
  Because 0.03 is a constant. K X 0.03 is also a constant and enables us to express the equation as
       [H⁺] = { K (pCO₂) } / [HCO₃^-]
  The new constant K is 0.03 multiplied by antilog₁₀ of 6.1 (10^-6.1), which turns out to be 23.8 ng mmol/mm Hg. (Let's round it out to 24.)
       [H⁺] = 24(pCO₂) / [HCO₃^-]
  Since the normal pCO₂ is 40 and the normal bicarbonate concentration is 24. it is easy to see that with normal values
       [H⁺] = (24×40) / 24 = 40
And the negative log of 40×10^-9 is - guess what? 7.3979, or the normal pH of blood.
  Of course, the trick here is to begin to appreciate or guess the pH of various hydrogen concentrations. Figure it out on your calculator. To find the pH of a hydrogen concentration of any number (let's take 40), press in the following order: 40; exp; 9; ⁺/_-; log.
  This should yield 4.07×10^-8 or 40 ng/L of hydrogen. The equation can be used to solve any of the variables:

       [H⁺] = K { pCO₂ / [HCO₃^-] }

       [HCO₃^-] = K { pCO₂ / [H⁺]}

       pCO₂ = { [H⁺] [HCO₃^-] } / K

  Fussing with the equation and the calculator will enable you to second-guess your laboratory equipment or, in case one value is missing, to make the appropriate calculations.
  The equations can be set up in a pocket computer (I used a TRS 80 syntax for the PC-4).
  Try it. It's fun and instructive. Sure, all the data are continually spit out of complex high-tech machines, but these computations will force you to think, which can't be all bad.
  Also, the trend will be to express hydrogen ion concentration in nanograms per liter, which may doom pH for future generations. But in case you never see the term again and wonder whence pH was derived, it is Gallic, pure French, and stands for puissance Hydrogen - the power of hydrogen! What could be more appropriate? After all, the term "pH" has dominated thinking about acids and bases for a long time. Only computers and calculators that can deal easily with terms like "0.00000004" could logically dispatch "pH" to that realm where scientific relics repose.

         Program for Calculating Blood Gases
  5 VAC                            This vacates prior data entries
10 PRINT "GASES"               File name
20 PRINT "FIND PH"
30 INPUT"PC02=" ,A
35 IFA=OTHEN90                Skips pH and goes to "FIND C02"
40 INPUT "BASE=" ,B
50 H = (24*A/B)/109           Expresses [H⁺] in grams
60 PRINT "H CONC=" ;H
70 P=LOG H
80 PRINT "PH=" ;P
90 PRINT "FIND C02"
100 INPUT "PH=" ,P
110 IF P = 0 THEN 160        Allows escape to bases
120 INPUT "BASE=" ,B
130 H = 109 /10P               Actually, 10⁹*10^-p, but PC-4 has
                                      trouble with negative exponents
                                      over (-4) in program equations
140 C = B*H/24
150 PRINT "C02=" ;A
160 PRINT "FIND BASE"
170 INPUT "PH=" ,P
180 INPUT "C02=" ,A
190 H = 1/10P
200 B = (24*C*10P)/109     Equal to 24*C/H
210 PRINT "BASE=" ;B
220 GOTO 5                      Starts program over again

BEST!
SlideRule

[Ren]

OTOH (on the other hand),
it is amazing how much intestinal gas can be generated by one Lima bean.
B^)