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(PC-4) Calculating Blood Gases - SlideRule - 03-30-2021 11:12 PM
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 ^{+}] [HCO_{3}^{-}] } / [H_{2}CO_{3}]Solving the equation for [H ^{+}] - the hydrogen concentration in nanograms (10^{-9} or one billionth of a gram) per liter – we have[H ^{+}] = K { [H_{2}CO_{3}] / [HCO_{3}^{-}] }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/log _{10} of both sides of the equation results in the familiar Henderson-Hasselbalch equation:pH = pK + log _{10} { [HCO_{3}^{-}] / [H_{2}CO_{3}] }where pK is the dissociation constant, 6.1. Back to the original: [H ^{+}] = { K [H_{2}CO_{3}] } / [HCO_{3}^{-}]H _{2}CO_{3} breaks down to CO_{2} and water. Thus, the numerator H_{2}CO_{3} is proportional to the CO_{2} dissolved in the blood. The solubility constant of CO_{2} in the blood is 0.51, and that calculates out to 0.03 mmol CO_{2}/mm Hg partial pressure of CO_{2}. Thus, we have[H ^{+}] = { K (0.03)(pCO_{2}) } / [HCO_{3}^{-}]Because 0.03 is a constant. K X 0.03 is also a constant and enables us to express the equation as [H ^{+}] = { K (pCO_{2}) } / [HCO_{3}^{-}]The new constant K is 0.03 multiplied by antilog _{10} 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(pCO_{2}) / [HCO_{3}^{-}]Since the normal pCO _{2} is 40 and the normal bicarbonate concentration is 24. it is easy to see that with normal values[H ^{+}] = (24×40) / 24 = 40And 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 { pCO_{2} / [HCO_{3}^{-}] }[HCO _{3}^{-}] = K { pCO_{2} / [H^{+}]}pCO _{2} = { [H^{+}] [HCO_{3}^{-}] } / KFussing 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 grams60 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, 10 ^{9}*10^{-p}, but PC-4 hastrouble 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 RE: (PC-4) Calculating Blood Gases - Ren - 04-08-2021 05:18 PM
OTOH (on the other hand), it is amazing how much intestinal gas can be generated by one Lima bean. B^) |