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. Method 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 PO2, PCO2, pH, 2,3-DPG, and temperature. Our new equations incorporate a novel PO2-dependent variable cooperativity hypothesis for the binding of O2 to Hb, and a new equation for P50 of O2 that provides accurate shifts in the HbO2 and HbCO2 dissociation curves over a wide range of physiological conditions. The accuracy and efficiency of these equations in computing PO2 and PCO2 from the SHbO2 and SHbCO2 levels using simple iterative numerical schemes that give rapid convergence is a significant advantage over alternative SHbO2 and SHbCO2 models. Conclusion The new SHbO2 and SHbCO2 models have significant computational modeling implications as they provide high accuracy under non-physiological conditions, such as ischemia and reperfusion, extremes in gas concentrations, high altitudes, and extreme temperatures.

During induction with high inspired concentrations of nitrous oxide, net uptake of gas produces a contraction in volume and a concentrating effect. In turn, this results in concentration and second gas effects. Most explanations of these effects are based on the common "rectangle" diagram devised by Stoelting and Eger and contain several inconsistencies which are explored here in order to produce a more accurate description. It is shown that in the standard diagram gas uptake is incomplete, there is ambiguity over functional residual capacity (FRC), equilibration with blood is inadequately represented and there is no representation of recirculation of anaesthetic. Compensation for loss of volume may be by means of an increased inspired ventilation, decreased expired ventilation or reduction in lung volume. Numerous accounts in the literature (including those based on the standard diagram) focus on the former mechanism at constant FRC. This has produced an unbalanced picture in which it is often implied that extra gas is routinely drawn into the lungs to replace that taken up. Significant compensation by this means cannot occur, for example when a constant volume ventilator is used. In discussing concentration and second gas effects, it is necessary to give a balanced view of the alternative mechanisms of compensation or to revert, as above, to a simple statement of the principle of conservation of volume.

No abstract

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. Mixtures of nominal delivered concentrations of volatile agents (desflurane, isoflurane and diethyl ether) with and without 70% nitrous oxide were mathematically modeled using steady state mass-balance principles, and the magnitude of the second gas effect calculated as an augmentation ratio for the volatile agent, defined as the partial pressure in the presence to that in the absence of nitrous oxide. Results Increasing the degree of mismatch increased the second gas effect in blood. Simultaneously, the second gas effect decreased in the gas phase. The increase in blood was greatest for the least soluble gas, desflurane, and least for the most soluble gas, diethyl ether, while opposite results applied in the gas phase. Conclusions Modeling of ventilation-perfusion inhomogeneity confirms that the second gas effect is greater in blood than in expired gas. Gas-based minimum alveolar concentration readings may therefore underestimate the depth of anesthesia during nitrous oxide anesthesia with volatile agents. The effect on minimum alveolar concentration is likely to be most pronounced for the less soluble volatile agents in current use.

Gas exchange in the lung can always be represented as the sum of two components: gas exchange at constant volume followed by gas exchange on volume correction. Using this sequence to study the second gas effect, low gas solubility and increased ventilation-perfusion mismatch are shown to act together to enhance second gas uptake. While appearing to contravene classical concepts of gas exchange, a detailed theoretical analysis shows it is fully consistent with these concepts.

No abstract

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. We investigate further the effect of net gas volume loss during nitrous oxide uptake on low concentrations of other gases present using partial pressure-solubility diagrams. The steady-state equations of gas exchange were solved assuming a log-normal distribution of ventilation-perfusion ratios using Lebesgue-Stieltjes integration. It was shown that under these conditions the classical partial pressure-solubility diagram must be modified, that for currently used volatile anesthetic agents the alveolar-arterial partial pressure difference is less than that predicted in the past, and that the alveolar-arterial partial pressure difference may even be reversed during uptake in the case of highly insoluble gases such as sulfur hexafluoride. Comparing this with the situation described previously for nitrogen in steady-state air breathing, we show that for nitrogen, the direction of the alveolar-arterial gradient is opposite to the direction of net gas volume movement. Although gas uptake with ventilation-perfusion inequality exceeding that when matching is optimal is shown to be possible, it is less likely than alveolar-arterial partial pressure reversal. NEW & NOTEWORTHY Net uptake of gases administered with nitrous oxide may proceed against an alveolar-arterial partial pressure gradient. The alveolar-arterial gradient for nitrogen in the steady-state breathing air depends not only on the existence of a distribution of ventilation-perfusion ratios in the lung but also on the presence of a net change in gas volume and is opposite in direction to the direction of net gas volume uptake.

No abstract