Effects of N O elimination on the elimination of second gases in a two-step mathematical model of heterogeneous gas exchange.

We have investigated the elimination of inert gases in the lung during the elimination of nitrous oxide (N O) using a two-step mathematical model that allows the contribution from net gas volume expansion, which occurs in Step 2, to be separated from other factors. When a second inert gas is used in addition to N O, the effect on that gas appears as an extra volume of the gas eliminated in association with the dilution produced by N O washout in Step 2. We first considered the effect of elimination in a single gas-exchanging unit under steady-state conditions and then extended our analysis to a lung having a log-normal distribution of ventilation and perfusion.

Elucidating the roles of solubility and ventilation-perfusion mismatch in the second gas effect using a two-step model of gas exchange.

The second gas effect occurs when high inspired concentrations of a first gas, usually nitrous oxide, enhance the uptake of other gases administered simultaneously. The second gas effect is greater in blood than in the gas phase, persists well into the period of nitrous oxide maintenance anesthesia, increases as the degree of ventilation-perfusion mismatch increases, and is most pronounced with the low soluble agents in current use. Yet, how low gas solubility and increased ventilation-perfusion mismatch can combine to improve gas transfer remains unclear, which is the focus of the present study.

Effect of net gas volume changes on alveolar and arterial gas partial pressures in the presence of ventilation-perfusion mismatch.

The second gas effect (SGE) occurs when nitrous oxide enhances the uptake of volatile anesthetics administered simultaneously. Recent work shows that the SGE is greater in blood than in the gas phase, that this is due to ventilation-perfusion mismatch, that as mismatch increases, the SGE increases in blood but is diminished in the gas phase, and that these effects persist well into the period of nitrous oxide maintenance anesthesia. These modifications of the SGE are most pronounced with the low soluble agents in current use.

Can Mathematical Modeling Explain the Measured Magnitude of the Second Gas Effect?

Background: Recent clinical studies suggest that the magnitude of the second gas effect is considerably greater on arterial blood partial pressures of volatile agents than on end-expired partial pressures, and a significant second gas effect on blood partial pressures of oxygen and volatile agents occurs even at relatively low rates of nitrous oxide uptake. We set out to further investigate the mechanism of this phenomenon with the help of mathematical modeling.

Methods: Log-normal distributions of ventilation and blood flow were generated representing the range of ventilation-perfusion scatter seen in patients during general anesthesia.

Simple accurate mathematical models of blood HbO2 and HbCO2 dissociation curves at varied physiological conditions: evaluation and comparison with other models.

Purpose: Equations for blood oxyhemoglobin (HbO2) and carbaminohemoglobin (HbCO2) dissociation curves that incorporate nonlinear biochemical interactions of oxygen and carbon dioxide with hemoglobin (Hb), covering a wide range of physiological conditions, are crucial for a number of practical applications. These include the development of physiologically-based computational models of alveolar-blood and blood-tissue O2–CO2 transport, exchange, and metabolism, and the analysis of clinical and in vitro data.

Methods And Results: To this end, we have revisited, simplified, and extended our previous models of blood HbO2 and HbCO2 dissociation curves (Dash and Bassingthwaighte, Ann Biomed Eng 38:1683–1701, 2010), validated wherever possible by available experimental data, so that the models now accurately fit the low HbO2 saturation (SHbO2) range over a wide range of values of PCO2, pH, 2,3-DPG, and temperature.