Comprehensive diagnosis of whole-body acid–base and fluid-electrolyte disorders using a mathematical model and whole-body base excess

Abstract

A mathematical model of whole-body acid–base and fluid-electrolyte balance was used to provide information leading to the diagnosis and fluid-therapy treatment in patients with complex acid–base disorders. Given a set of measured laboratory-chemistry values for a patient, a model of their unique, whole-body chemistry was created. This model predicted deficits or excesses in the masses of Na⁺, K⁺, Cl⁻ and H₂O as well as the plasma concentration of unknown or unmeasured species, such as ketoacids, in diabetes mellitus. The model further characterized the acid–base disorder by determining the patient’s whole-body base excess and quantitatively partitioning it into ten components, each contributing to the overall disorder. The results of this study showed the importance of a complete set of laboratory measurements to obtain sufficient accuracy of the quantitative diagnosis; having only a minimal set, just pH and PCO₂, led to a large scatter in the predicted results. A computer module was created that would allow a clinician to achieve this diagnosis at the bedside. This new diagnostic approach should prove to be valuable in the treatment of the critically ill.

Appendices

Appendix 1

The model used in the present study has been updated from that formulated previously [8] in the following ways:

• 1. The pK for intracellular proteins has been changed from 6.5 to 5.5 to achieve more realistic buffering.

• 2. The standard-state interstitial albumin concentration was set to the concentration that would achieve a standard-state colloid osmotic pressure of 14 mmHg. This value resulted from a total albumin concentration of 28.8 g/l corrected to 38.4 g/l because of a 25 % protein exclusion volume in the standard-state interstitial space.

• 3. Changing the pK and standard-state interstitial colloid osmotic pressure, above, required solving the model again to achieve the standard state. As described previously [8], the new values of six constants had to be determined to be consistent with the model changes. Table 6 shows the new values.

  Table 6 Selected standard-state data

• 4. Net unmeasured anions (XA⁻) were added to the model. The concentration in interstitial fluid was assumed to be the plasma concentration as corrected for the plasma protein volume and the Donnan-distribution effect. These effects amounted to about a 12 % interstitial concentration increase above that in plasma in the standard state.

• 5. Plasma glucose concentrations above the standard value of 5.3 mmol/l_W resulting from glucose impermeability in diabetes mellitus were assumed to osmotically draw water from cells.

• 6. A model of human respiratory physiology [23] was used to generate data which led to a mathematical relationship (SigmaPlot computer program. Systat Software, Point Richmond CA) that was used to convert arterial PCO₂ values to those in venous blood. The relationship was,

  $$PvCO_{2} = - 0.0000291 \times X^{3} + 0.00586 \times X^{2} + 0.67 \times X + 0.586$$

  where X stands for PaCO₂.

Appendix 2

The screenshots of Figs. 4, 5, 6 were from a computer module that a scientist/clinical diagnostician can obtain from this author and run free of charge using downloadable Vissim-Viewer software from Visual Solutions Inc. The subject information and laboratory-chemistry values are entered in the left column. Model solution results and normal values are shown in the middle column. WBBE values and QDVs from other diagnostic approaches are shown in the right column.

Instructions for using the software and program will be provided with the software. All that is required are that the values for the patient’s laboratory chemistry be entered into the left column of the display.