Bicarbonate kinetics in humans: Identification and validation of a three- compartment model

A model of bicarbonate kinetics is crucial to a correct interpretation of experiments for measuring oxidation in vivo of carbon-labeled compounds. The aim of this study is to develop a compartmental model of bicarbonate kinetics in humans from tracer data by devoting particular attention to model identification and validation. The data base consisted of impulse-dose studies of ¹⁴C-labeled bicarbonate in nine normal subjects. The decay curve of specific activity of CO₂ in expired air (sa(CO₂)/(R)) was frequently sampled for 4-7 h. In addition, endogenous production of CO₂, V̇(CO₂), was measured by indirect calorimetry. A model of data, i.e., an exponential model, analysis of decay curves of sa(CO₂)/(R) showed first that three compartments are necessary and sufficient to describe bicarbonate tracer kinetics. Compartmental models were then used as models of system. To correctly describe the input-output configuration, labeled CO₂ flux in the expired air, Φ(CO₂)/(R) (= sa(CO₂)/(R) · V̇(CO₂)), has been used as measurement variable in tracer model identification. A mammillary three- compartment model with a respiratory and a nonrespiratory loss has been studied. Whereas there is good evidence that respiratory loss takes place in the central compartment, whether nonrespiratory loss is taking place in the central compartment or in one of the two peripheral compartments is uncertain. Thus three competing tracer models were considered. Using a model- independent analysis of data, based on the body activity variable, to calculate mean residence time in the system, we have been able to validate a specific model structure, i.e., with the two irreversible losses taking place in the central compartment. This validated tracer model was then used to quantitate bicarbonate masses in the system. Because there is uncertainty about where endogenous production enters the system, lower and upper bounds of masses of bicarbonate in the body are derived.