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

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.

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

“…As increases, the SGE increases in blood but decreases in the gas phase (black arrows). This is in line with our previous findings (11).…”

“…The augmentation-solubility relationship. A useful measure of the magnitude of the SGE is the augmentation ratio (AR), which is defined as the partial pressure of the second gas in the relevant phase (gas or blood) in the presence of N 2O divided by the partial pressure the second gas would have in that phase in the absence of N2O, with all other factors being held constant (7,11). When AR ϭ 1, there is no SGE, so when the SGE does occur, its magnitude is given by the amount by which AR exceeds unity.…”

“…Here, k is a variable that depends primarily on the solubility of the second gas in blood () and the degree of mismatch between ventilation and blood flow () (10,11). Equation 9 explains how it is possible for the degree of ventilation-perfusion mismatch to influence the magnitude of the SGE provided that ⌬V /V A, the relative volume change associated with N 2O uptake, remains greater than zero.…”

A Second Look at the Second Gas Effect

“…In this issue, Korman et al 1 provide data from a model of the second gas effect on arterial partial pressures of volatile anesthetic agents. Most readers might wonder what this information adds, some will struggle to remember what the second gas effect is, and others will query the value of modeling rather than "real data."…”

“…The key steps are transfer from the breathing circuit to alveolar gas, from the alveoli to plasma, and then from plasma to the "effect-site." Separating the two steps between breathing circuit and plasma helps us understand both the second gas effect and the message underlying the paper by Korman et al 1 While the classical model of the concentration effect and second gas effect persists in most textbooks and teaching, aspects of this description have been challenged for more than 20 yr. In 1997, Korman and Mapleson 5 identified shortcomings in the "standard model" of the concentration and second gas effects, which assume constant lung volume.…”