A mathematical model of acid-base balance and ion transport for mammalian brain tissue and differential effects of cerebrospinal fluid composition on the control of ventilation

A model describing acid-base balance and ion transport in a nucleated mammalian cell and its associated extracellular fluid (ECF) was developed from simple biophysical concepts. The model predicts intracellular fluid (ICF) electrolyte concentrations, pH and membrane potential. Three versions of the model were constructed: in two versions, the ECF concentrations are set by the modeler before ICF variables are solved for. These versions are termed the in vitro and in vitro/Donnan models, as they most closely resemble a cell being perfused with artificial ECF. In the in vitro/Donnan model, HCO{dollar}sb3sp-{dollar} distribution is governed by a Donnan equilibrium. While the in vitro/Donnan model predicts non physiological values of ICF pH and K{dollar}sp+{dollar}, it responds to acid-base disturbances in a manner similar to actual cells. The in vitro model predicts physiological values of intracellular pH and K{dollar}sb+{dollar}, but fails to adequately describe acid-base behavior. A third version was constructed in which the ECF and ICF concentrations could be solved for simultaneously, permitting interaction between the two compartments. This model predicted physiological values for ECF ions and pH, and for ICF pH and K{dollar}sp+{dollar}, but not for ICF Na{dollar}sp+{dollar} and Cl{dollar}sp-{dollar}.; Experiments were performed in which the effects of cerebrospinal fluid (CSF) pH versus ionic composition on central respiratory chemosensitivity could be differentiated. It was established that perfusions over the ventral surface of the brain with acidic mock CSF solutions caused significant increases in both tidal volume (V{dollar}sb{lcub}rm T{rcub}{dollar}) and minute ventilation (V{dollar}sb{lcub}rm E{rcub}{dollar}). When some of the chloride in the acidic perfusate was replaced with the impermeant anion isethionate there were greater increases (p = 0.05) in both V{dollar}sb{lcub}rm T{rcub}{dollar} and V{dollar}sb{lcub}rm E{rcub}{dollar} at an identical pH. The PCO{dollar}sb2{dollar} of the fluid perfusing the brain was held constant. These findings suggest that the two acidic perfusates exert different effects on ECF H{dollar}sp+{dollar}, the putative stimulus for the chemoreceptors. When HCO{dollar}sb3sp-{dollar}/Cl{dollar}sp-{dollar} exchange was blocked with an anion transport inhibitor, the difference in V{dollar}sb{lcub}rm T{rcub}{dollar} between the two acidic perfusates was abolished, suggesting a role for this exchanger in determining central chemoreceptor input.