Ventilation-perfusion inhomogeneity increases gas uptake in anesthesia: computer modeling of gas exchange

Effects of N2 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 (N2 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 N2 O, the effect on that gas appears as an extra volume of the gas eliminated in association with the dilution produced by N2 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. A further increase in inert gas elimination was demonstrated with gases of low solubility in the presence of the increased ventilation-perfusion mismatch that is known to occur during anesthesia. These effects are transient because N2 O elimination depletes the input of that gas from mixed venous blood to the lung, thereby rapidly reducing the magnitude of the diluting action.

Arterial and Mixed Venous Kinetics of Desflurane and Sevoflurane, Administered Simultaneously, at Three Different Global Ventilation to Perfusion Ratios in Piglets with Normal Lungs

BACKGROUND

Previous studies have established the role of various tissue compartments in the kinetics of inhaled anesthetic uptake and elimination. The role of normal lungs in inhaled anesthetic kinetics is less understood. In juvenile pigs with normal lungs, the authors measured desflurane and sevoflurane washin and washout kinetics at three different ratios of alveolar minute ventilation to cardiac output value. The main hypothesis was that the ventilation/perfusion ratio (VA/Q) of normal lungs influences the kinetics of inhaled anesthetics.

METHODS

Seven healthy pigs were anesthetized with intravenous anesthetics and mechanically ventilated. Each animal was studied under three different VA/Q conditions: normal, low, and high. For each VA/Q condition, desflurane and sevoflurane were administered at a constant, subanesthetic inspired partial pressure (0.15 volume% for sevoflurane and 0.5 volume% for desflurane) for 45 min. Pulmonary arterial and systemic arterial blood samples were collected at eight time points during uptake, and then at these same times during elimination, for measurement of desflurane and sevoflurane partial pressures. The authors also assessed the effect of VA/Q on paired differences in arterial and mixed venous partial pressures.

RESULTS

For desflurane washin, the scaled arterial partial pressure differences between 5 and 0 min were 0.70 ± 0.10, 0.93 ± 0.08, and 0.82 ± 0.07 for the low, normal, and high VA/Q conditions (means, 95% CI). Equivalent measurements for sevoflurane were 0.55 ± 0.06, 0.77 ± 0.04, and 0.75 ± 0.08. For desflurane washout, the scaled arterial partial pressure differences between 0 and 5 min were 0.76 ± 0.04, 0.88 ± 0.02, and 0.92 ± 0.01 for the low, normal, and high VA/Q conditions. Equivalent measurements for sevoflurane were 0.79 ± 0.05, 0.85 ± 0.03, and 0.90 ± 0.03.

CONCLUSIONS

Kinetics of inhaled anesthetic washin and washout are substantially altered by changes in the global VA/Q ratio for normal lungs.

EDITOR’S PERSPECTIVE

Effect of Global Ventilation to Perfusion Ratio, for Normal Lungs, on Desflurane and Sevoflurane Elimination Kinetics

BACKGROUND

Kinetics of the uptake of inhaled anesthetics have been well studied, but the kinetics of elimination might be of more practical importance. The objective of the authors' study was to assess the effect of the overall ventilation/perfusion ratio (VA/Q), for normal lungs, on elimination kinetics of desflurane and sevoflurane.

METHODS

The authors developed a mathematical model of inhaled anesthetic elimination that explicitly relates the terminal washout time constant to the global lung VA/Q ratio. Assumptions and results of the model were tested with experimental data from a recent study, where desflurane and sevoflurane elimination were observed for three different VA/Q conditions: normal, low, and high.

RESULTS

The mathematical model predicts that the global VA/Q ratio, for normal lungs, modifies the time constant for tissue anesthetic washout throughout the entire elimination. For all three VA/Q conditions, the ratio of arterial to mixed venous anesthetic partial pressure Part/Pmv reached a constant value after 5 min of elimination, as predicted by the retention equation. The time constant corrected for incomplete lung clearance was a better predictor of late-stage kinetics than the intrinsic tissue time constant.

CONCLUSIONS

In addition to the well-known role of the lungs in the early phases of inhaled anesthetic washout, the lungs play a long-overlooked role in modulating the kinetics of tissue washout during the later stages of inhaled anesthetic elimination. The VA/Q ratio influences the kinetics of desflurane and sevoflurane elimination throughout the entire elimination, with more pronounced slowing of tissue washout at lower VA/Q ratios.

EDITOR’S PERSPECTIVE

Ideal alveolar gas defined by modal gas exchange in ventilation-perfusion distributions

Under the three-compartment model of ventilation-perfusion (V_A/Q) scatter, Bohr-Enghoff calculation of alveolar deadspace fraction (V_DA/V_A) uses arterial CO₂ partial pressure measurement as an approximation of "ideal" alveolar CO₂(ideal P_ACO₂). However, this simplistic model suffers from several inconsistencies. Modelling of realistic physiological distributions of V_A and Q instead suggests an alternative concept of "ideal" alveolar gas at the V_A/Q ratio where uptake or elimination rate of a gas is maximal. The alveolar-capillary partial pressure at this "modal" point equals the mean of expired alveolar and arterial partial pressures, regardless of V_A/Q scatter severity or overall V_A/Q. For example, modal ideal P_ACO₂ can be estimated from Estimated modal ideal P_ACO₂ = (P_ACO₂+P_aCO₂)/2 Using a multicompartment computer model of log normal distributions of V_A and Q, agreement of this estimate with the modal ideal P_ACO₂ located at the V_A/Q ratio of maximal compartmental VCO₂ was assessed across a wide range of severity of V_A/Q scatter and overall V_A/Q ratio. Agreement of V_DA/V_A for CO₂ from the Bohr equation using modal idealPCO₂ with that using the estimated value was also assessed. Estimated modal ideal P_ACO₂ agreed closely with modal ideal P_ACO₂, intraclass correlation (ICC) > 99.9%. There was no significant difference between V_DA/V_ACO₂ using either value for ideal P_ACO₂. Modal ideal P_ACO₂ reflects a physiologically realistic concept of ideal alveolar gas where there is maximal gas exchange effectiveness in a physiological distribution of V_A/Q, which is generalizable to any inert gas, and is practical to estimate from arterial and end-expired CO₂ partial pressures.

End-tidal to Arterial Gradients and Alveolar Deadspace for Anesthetic Agents

BACKGROUND

According to the "three-compartment" model of ventilation-perfusion ((Equation is included in full-text article.)) inequality, increased (Equation is included in full-text article.)scatter in the lung under general anesthesia is reflected in increased alveolar deadspace fraction (VDA/VA) customarily measured using end-tidal to arterial (A-a) partial pressure gradients for carbon dioxide. A-a gradients for anesthetic agents such as isoflurane are also significant but have been shown to be inconsistent with those for carbon dioxide under the three-compartment theory. The authors hypothesized that three-compartment VDA/VA calculated using partial pressures of four inhalational agents (VDA/VAG) is different from that calculated using carbon dioxide (VDA/VACO2) measurements, but similar to predictions from multicompartment models of physiologically realistic "log-normal" (Equation is included in full-text article.)distributions.

METHODS

In an observational study, inspired, end-tidal, arterial, and mixed venous partial pressures of halothane, isoflurane, sevoflurane, or desflurane were measured simultaneously with carbon dioxide in 52 cardiac surgery patients at two centers. VDA/VA was calculated from three-compartment model theory and compared for all gases. Ideal alveolar (PAG) and end-capillary partial pressure (Pc'G) of each agent, theoretically identical, were also calculated from end-tidal and arterial partial pressures adjusted for deadspace and venous admixture.

RESULTS

Calculated VDA/VAG was larger (mean ± SD) for halothane (0.47 ± 0.08), isoflurane (0.55 ± 0.09), sevoflurane (0.61 ± 0.10), and desflurane (0.65 ± 0.07) than VDA/VACO2 (0.23 ± 0.07 overall), increasing with lower blood solubility (slope [Cis], -0.096 [-0.133 to -0.059], P < 0.001). There was a significant difference between calculated ideal PAG and Pc'G median [interquartile range], PAG 5.1 [3.7, 8.9] versus Pc'G 4.0[2.5, 6.2], P = 0.011, for all agents combined. The slope of the relationship to solubility was predicted by the log-normal lung model, but with a lower magnitude relative to calculated VDA/VAG.

CONCLUSIONS

Alveolar deadspace for anesthetic agents is much larger than for carbon dioxide and related to blood solubility. Unlike the three-compartment model, multicompartment (Equation is included in full-text article.)scatter models explain this from physiologically realistic gas uptake distributions, but suggest a residual factor other than solubility, potentially diffusion limitation, contributes to deadspace.

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

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.

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. 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.

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. 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.

A tidally breathing model of ventilation, perfusion and volume in normal and diseased lungs †

BACKGROUND

To simulate the short-term dynamics of soluble gas exchange (e.g. CO2 rebreathing), model structure, ventilation-perfusion (VA/Q) and ventilation-volume (VA/VA) parameters must be selected correctly. Some diseases affect mainly the VA/Q distribution while others affect both VA/Q and VA/VA distributions. Results from the multiple inert gas elimination technique (MIGET) and multiple breath nitrogen washout (MBNW) can be used to select VA/Q and VA/VA parameters, but no method exists for combining VA/Q and VA/VA parameters in a multicompartment lung model.

METHODS

We define a tidally breathing lung model containing shunt and up to eight alveolar compartments. Quantitative and qualitative understanding of the diseases is used to reduce the number of model compartments to achieve a unique solution. The reduced model is fitted simultaneously to inert gas retentions calculated from published VA/Q distributions and normalized MBNWs obtained from similar subjects. Normal lungs and representative cases of emphysema and embolism are studied.

RESULTS

The normal, emphysematous and embolism models simplify to one, three and two alveolar compartments, respectively.

CONCLUSIONS

The models reproduce their respective MIGET and MBNW patient results well, and predict disease-specific steady-state and dynamic soluble and insoluble gas responses.

Ventilation-perfusion inhomogeneity increases gas uptake: theoretical modeling of gas exchange

Ventilation-perfusion (VA/Q) inhomogeneity was modeled to measure its effect on gas exchange in the presence of inspired mixtures of two soluble gases using a two-compartment computer model. Theoretical studies involving a mixture of hypothetical gases with equal solubility in blood showed that the effect of increasing inhomogeneity of distributions of either ventilation or blood flow is to paradoxically increase uptake of the gas with the lowest overall uptake in relation to its inspired concentration. This phenomenon is explained by the concentrating effects that uptake of soluble gases exert on each other in low VA/Q compartments. Repeating this analysis for inspired mixtures of 30% O(2) and 70% nitrous oxide (N(2)O) confirmed that, during "steady-state" N(2)O anesthesia, uptake of N(2)O is predicted to paradoxically increase in the presence of worsening VA/Q inhomogeneity.