A mathematical model of blood-interstitial acid-base balance: application to dilution acidosis and acid-base status

Abstract

We developed mathematical models that predict equilibrium distribution of water and electrolytes (proteins and simple ions), metabolites, and other species between plasma and erythrocyte fluids (blood) and interstitial fluid. The models use physicochemical principles of electroneutrality in a fluid compartment and osmotic equilibrium between compartments and transmembrane Donnan relationships for mobile species. Across the erythrocyte membrane, the significant mobile species Cl⁻ is assumed to reach electrochemical equilibrium, whereas Na(+) and K(+) distributions are away from equilibrium because of the Na(+)/K(+) pump, but movement from this steady state is restricted because of their effective short-term impermeability. Across the capillary membrane separating plasma and interstitial fluid, Na(+), K(+), Ca²(+), Mg²(+), Cl⁻, and H(+) are mobile and establish Donnan equilibrium distribution ratios. In each compartment, attainment of equilibrium by carbonates, phosphates, proteins, and metabolites is determined by their reactions with H(+). These relationships produce the recognized exchange of Cl(-) and bicarbonate across the erythrocyte membrane. The blood submodel was validated by its close predictions of in vitro experimental data, blood pH, pH-dependent ratio of H(+), Cl⁻, and HCO₃⁻ concentrations in erythrocytes to that in plasma, and blood hematocrit. The blood-interstitial model was validated against available in vivo laboratory data from humans with respiratory acid-base disorders. Model predictions were used to gain understanding of the important acid-base disorder caused by addition of saline solutions. Blood model results were used as a basis for estimating errors in base excess predictions in blood by the traditional approach of Siggaard-Andersen (acid-base status) and more recent approaches by others using measured blood pH and Pco₂ values. Blood-interstitial model predictions were also used as a basis for assessing prediction errors of extracellular acid-base status values, such as by the standard base excess approach. Hence, these new models can give considerable insight into the physicochemical mechanisms producing acid-base disorders and aid in their diagnoses.

Whole body acid-base and fluid-electrolyte balance: a mathematical model

“…This assumption differs from that of DeLand and Bradham (12), who simulated Na ϩ and K ϩ distribution across erythrocyte and cellular membranes using a constant, standard-free-energy pump. In contrast, our previously validated IPE model (39) used the erythrocyte model of Raftos et al (31) who found that besides K ϩ , Na ϩ was also effectively impermeable to this membrane (assumption 5). Na ϩ and other small ions not shown, such as Ca 2ϩ , Mg 2ϩ , Pi Ϫ , and lac Ϫ , distribute at equilibrium across the I-P microvascular membrane, with the latter two also entering erythrocytes.…”

“…This assumption will be explored in detail in the present study. H ϩ is assumed to follow equilibrium conditions in the other compartments (assumption 8) as we verified previously (39). The concentration of HCO 3 Ϫ in each compartment (shown for compartment I) is determined by the Henderson-Hasselbalch equilibrium relation using compartment concentrations of dissolved CO 2 and H ϩ as we described previously (39).…”

“…The steady-state, three-compartment, interstitial (I), plasma (P), erythrocyte (E) model that Wolf and DeLand developed previously (39) was based on the original steady-state, whole body fluid, and electrolyte model of DeLand and Bradham (12). In addition to the three compartments listed above, they included a fourth compartment, cells (C).…”

“…H ϩ is assumed to follow equilibrium conditions in the other compartments (assumption 8) as we verified previously (39). The concentration of HCO 3 Ϫ in each compartment (shown for compartment I) is determined by the Henderson-Hasselbalch equilibrium relation using compartment concentrations of dissolved CO 2 and H ϩ as we described previously (39). Although CO2 is assumed to be freely diffusible throughout the model fluid compartments, its water-dissolved concentrations are different because of different CO 2 solubilities in each compartment.…”

“…Hence, the aims of the present study were to expand and modify the previous IPE model (39) by 1) adding a parenchymal cell compartment, 2) incorporating a more explicit description of the forces leading to plasma-interstitial water distribution, 3) providing much more extensive validation of both water and electrolyte distribution, and 4) examining the predictions of the model relative to understanding dilution (saline) acidosis, effects of infusion of acidic, and basic solutions and to explore the role of potassium, a primary intracellular ion, in acid-base balance.…”