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.
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.
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