The Figge-Fencl Quantitative Physicochemical Model
of Human Acid-Base Physiology (Version 3.0):
Application Program.

by James J. Figge, MD, MBA, FACP

Copyright 2003 - 2013 James J. Figge.
Published 8 October, 2012; updated on 28 April, 2013; updated on 27 October, 2013;
on www.Figge-Fencl.org and www.acid-base.org.

Introduction to the Application Program.

The application program is designed to demonstrate the effects of changing independent variables on the pH of plasma-like solutions containing albumin.

The following computer program, written in Visual Basic, will solve the function:

pH = fpH { SID, PCO2, [ Pitot ], [ Albumin ] }


Default values for independent variables are SID = 39 mEq / L; PCO2 = 40 Torr; [ Pitot ] = 1.15 mmol / L; and [ Albumin ] = 4.4 g /dL.

Running the program with the default values will give the following output:

Figge-Fencl Model Version 3.0 (8 October, 2012; www.Figge-Fencl.org).

pH = f { SID, PCO2, [ Pi tot ], [ Albumin ] }

pH = f { 39 , 40 , 1.15 , 4.4 } = 7.4




Any combination of legitimate values for the independent variables can be entered into the program. For example, SID = 25 mEq / L; PCO2 = 20 Torr; [ Pitot ] = 1.15 mmol / L; and [ Albumin ] = 2.2 g /dL.

Running the program with these values will give the following output:

Figge-Fencl Model Version 3.0 (8 October, 2012; www.Figge-Fencl.org).

pH = f { SID, PCO2, [ Pi tot ], [ Albumin ] }

pH = f { 25 , 20 , 1.15 , 2.2 } = 7.524



Notice:
The program may be downloaded free of charge for academic and educational use only. This program is not intended for clinical use or for the care of human subjects in clinical trials. The program applies to plasma-like solutions containing albumin. The program does not account for the contribution of plasma globulins, and has not been tested with clinical data; hence the program is not suitable for clinical use.
The easiest way to use the program is to highlight and copy the program text below, and then paste the program into a Visual Basic editor. The program can then be run from the editor. For example, Microsoft Office Excel has a Visual Basic editor that can run this program. The editor can usually be accessed from Excel by clicking on "Tools" or "View" and then "Macro" or "Macros". It may be necessary to adjust security settings to enable macros.

Computer Program.

Sub CalcPH()

Rem: Figge-Fencl Quantitative Physicochemical Model
Rem: of Human Acid-Base Physiology Version 3.0 (8 October, 2012; www.Figge-Fencl.org).
Rem:
Rem: Copyright 2003 - 2013 James J. Figge. Update published 28 April, 2013;
Rem: Update published 27 October, 2013.
Rem:
Rem: The program may be downloaded free of charge for academic and educational use only.
Rem: This program is not intended for clinical use or for the care of human subjects in clinical trials.
Rem: This program applies to plasma-like solutions containing albumin.
Rem: The program does not account for the contribution of plasma globulins, and has not been tested with clinical data; hence
Rem: the program is not suitable for clinical use.

Rem: Kc1 is derived from the parameters in the Henderson-Hasselbalch
Rem: equation. pK = 6.1; a = 0.230 mM / kPa; 1 Torr = 0.13332236842105 kPa
Rem: The value of Kc1 is 2.44E-11 (Eq / L)^2 / Torr.

Rem: Kc2 is calculated from Harned and Scholes (1941) for 37 degrees C and ionic
Rem: strength 0.15 M. The value of Kc2 is 5.5E-11 mol / L x 2 = 1.1E-10 Eq / L.

Rem: K1, K2, and K3 for the phosphoric acid - phosphate system are from Sendroy and
Rem: Hastings (1927). pK1 = 1.915; pK2 = 6.66; pK3 = 11.78.

Close #1

Const kw = 0.000000000000044

Const Kc1 = 0.0000000000244
Const Kc2 = 0.00000000011

Const K1 = 0.0122
Const K2 = 0.000000219
Const K3 = 0.00000000000166

Rem: Enter desired values for SID, PCO2, [ Pi tot ], and [ Albumin ] in the next four lines.
SID = 39
PCO2 = 40
Pi = 1.15
alb = 4.4

Worksheets("Sheet1").Activate

High = 14
Low = 1

calculatepH:
pH = (High + Low) / 2
H = 10 ^ -pH

HCO3 = Kc1 * PCO2 / H
CO3 = Kc2 * HCO3 / H

FNX = K1 * H * H + 2 * K1 * K2 * H + 3 * K1 * K2 * K3
FNY = H * H * H + K1 * H * H + K1 * K2 * H + K1 * K2 * K3
FNZ = FNX / FNY
P = Pi * FNZ

Netcharge = SID + 1000 * (H - kw / H - HCO3 - CO3) - P

Rem: NB accounts for histidine pK shift due to the NB transition
NB = 0.4 * (1 - (1 / (1 + 10 ^ (pH - 6.9))))

Rem: Calculate charge on albumin
Rem: alb2 accumulates results

Rem: cysteine residue
alb2 = -1 * (1 / (1 + 10 ^ (-(pH - 8.5))))

Rem: glutamic acid and aspartic acid residues
alb2 = alb2 - 98 * (1 / (1 + 10 ^ (-(pH - 3.9))))

Rem: tyrosine residues
alb2 = alb2 - 18 * (1 / (1 + 10 ^ (-(pH - 11.7))))

Rem: arginine residues
alb2 = alb2 + 24 * (1 / (1 + 10 ^ (pH - 12.5)))

Rem: lysine residues
alb2 = alb2 + 2 * (1 / (1 + 10 ^ (pH - 5.8)))
alb2 = alb2 + 2 * (1 / (1 + 10 ^ (pH - 6.15)))
alb2 = alb2 + 2 * (1 / (1 + 10 ^ (pH - 7.51)))
alb2 = alb2 + 2 * (1 / (1 + 10 ^ (pH - 7.685)))
alb2 = alb2 + 1 * (1 / (1 + 10 ^ (pH - 7.86)))

alb2 = alb2 + 50 * (1 / (1 + 10 ^ (pH - 10.3)))

Rem: 16 different histidine residues
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 7.12 + NB)))
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 7.22 + NB)))
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 7.1 + NB)))
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 7.49 + NB)))
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 7.01 + NB)))
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 7.31)))
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 6.75)))
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 6.36)))
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 4.85)))
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 5.76)))
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 6.17)))
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 6.73)))
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 5.82)))
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 5.1)))
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 6.7)))
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 6.2)))

Rem: amino terminus
alb2 = alb2 + (1 / (1 + 10 ^ (pH - 8)))

Rem: carboxyl terminus
alb2 = alb2 - 1 * (1 / (1 + 10 ^ (-(pH - 3.1))))

alb2 = alb2 * 1000 * 10 * alb / 66500

Netcharge = Netcharge + alb2

If Abs(Netcharge) < 0.0000001 Then GoTo complete
If Netcharge < 0 Then High = pH
If Netcharge > 0 Then Low = pH
GoTo calculatepH

complete:

Rem: Enter output file name in next line.

Open "PH Calculation" For Output As #1

Print #1, "Figge-Fencl Model Version 3.0 (8 October, 2012; www.Figge-Fencl.org)."
Print #1, " "
Print #1, "pH = f { SID, PCO2, [ Pi tot ], [ Albumin ] }"
Print #1, " "
Print #1, "pH = f { "; SID; ", "; PCO2; ", "; Pi; ", "; alb; " } = "; Round(pH, 3)
Print #1, " "

Close #1

End Sub

Link to Figge-Fencl Model Version 3.0

Link to Statistical Validation of Model Version 3.0

Link to Albumin Titration Curve (Model Version 3.0)

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