Effect of ventilation-perfusion inhomogeneity and N(2)O on oxygenation: physiological modeling of gas exchange

The safety of nitrous oxide: glass half-full or half-empty?

A systematic review of clinical trials confirms that including nitrous oxide in the gas mixture for general anaesthesia has minor short-term benefits and does not impact most patient safety outcomes. However, no risk-benefit analysis of nitrous oxide should ignore its known environmental effects. If continued nitrous oxide use is supported, strategies to minimise and monitor the contribution of medical nitrous oxide to global warming are vital.

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.

A modal definition of ideal alveolar oxygen

In the three-compartment model of lung ventilation-perfusion heterogeneity (VA/Q scatter), both Bohr dead space and shunt equations require values for central "ideal" compartment O2 and CO2 partial pressures. However, the ideal alveolar gas equation most accurately calculates mixed (ideal and alveolar dead space) PAO2 . A novel "modal" definition has been validated for ideal alveolar CO2 partial pressure, at the VA/Q ratio in a lung distribution where CO2 elimination is maximal. A multicompartment computer model of physiological, lognormal distributions of VA and Q was used to identify modal "ideal" PAO2 , and find a modification of the alveolar gas equation to estimate it across a wide range of severity of VA/Q heterogeneity and FIO2 . This was then validated in vivo using data from a study of 36 anesthetized, ventilated patients with FIO2 0.35-80. Substitution in the alveolar gas equation of respiratory exchange ratio R withmodalR = R - 1 - PEtC O 2 / P aCO 2 $$ \kern0.5em \mathrm{modalR}=\mathrm{R}\hbox{--} \left(1\hbox{--} \mathrm{PEtC}{\mathrm{O}}_2/\mathrm{P}{\mathrm{aCO}}_2\right) $$ achieved excellent agreement (r2  = 0.999) between the calculated ideal PAO2 and the alveolar-capillary Pc'O2 at the modal VO2 point ("modal" Pc'O2 ), across a range of log standard deviation of VA 0.25-1.75, true shunt 0%-20%, overall VA/Q 0.4-1.6, and FIO2 0.18-1.0, where the modeled PaO2 was over 50 mm Hg. Modal ideal PAO2 can be reliably estimated using routine blood gas measurements.

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.

European Society of Anaesthesiology Task Force on Nitrous Oxide: a narrative review of its role in clinical practice

Nitrous oxide (N₂O) is one of the oldest drugs still in use in medicine. Despite its superior pharmacokinetic properties, controversy remains over its continued use in clinical practice, reflecting in part significant improvements in the pharmacology of other anaesthetic agents and developing awareness of its shortcomings. This narrative review describes current knowledge regarding the clinical use of N₂O based on a systematic and critical analysis of the available scientific literature. The pharmacological properties of N₂O are reviewed in detail along with current evidence for the indications and contraindications of this drug in specific settings, both in perioperative care and in procedural sedation. Novel potential applications for N₂O for the prevention or treatment of chronic pain and depression are also discussed. In view of the available evidence, we recommend that the supply of N₂O in hospitals be maintained while encouraging its economic delivery using modern low flow delivery systems. Future research into its potential novel applications in prevention or treatment of chronic conditions should be pursued to better identify its role place in the developing era of precision medicine.

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.

Between prediction, education, and quality control: simulation models in critical care

Today, computer-aided strategies in social sciences are an indispensable component of teaching programs. In recent years, microsimulation modeling has gained attention in its ability to represent predicted physiological developments visually, thus providing the user with a full understanding of the impacts of a proposed scheme. There are several microsimulation models in human medicine, and they can be either dynamic or static. If the model is dynamic the course of variables changes over time; in contrast, in the static case time constancy is assumed. In critical care there have been several approaches to implement microsimulation models to predict outcome. This commentary describes current approaches for predicting disease progression by using dynamic microsimulation in pneumonia-related sepsis.

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.

Persisting concentrating and second gas effects on oxygenation during N2O anaesthesia

Theoretical modelling predicts that the concentrating effect of nitrous oxide (N2O) uptake on alveolar oxygenation is a persisting phenomenon at typical levels of ventilation - perfusion (V/Q) inhomogeneity under anaesthesia. We sought clinical confirmation of this in 20 anaesthetised patients. Arterial oxygen pressure (P(aO2)) was measured after a minimum of 30 min of relaxant general anaesthesia with an inspired oxygen (F(I O2)) of 30%. Patients were randomly allocated to two groups. The intervention group had N2O introduced following baseline blood gas measurements, and the control group continued breathing an identical F(I O2) in nitrogen (N2). The primary outcome variable was change in P(aO2). Mean (SD) in P(aO2) was increased by 1.80 (1.80) kPa after receiving a mean of 47.5 min of N2O compared with baseline conditions breathing O2/N2 (p = 0.01). This change was significantly greater (p = 0.03) than that in the control group: + 0.09 (1.37) kPa, p = 0.83 and confirms the presence of significant persisting concentrating and second gas effects.

Large volume N 2 O uptake alone does not explain the second gas effect of N 2 O on sevoflurane during constant inspired ventilation †

BACKGROUND

The second gas effect (SGE) is considered to be significant only during periods of large volume N(2)O uptake (VN(2)O); however, the SGE of small VN(2)O has not been studied. We hypothesized that the SGE of N(2)O on sevoflurane would become less pronounced when sevoflurane administration is started 60 min after the start of N(2)O administration when VN(2)O has decreased to approximately 125 ml min(-1), and that the kinetics of sevoflurane under these circumstances would become indistinguishable from those when sevoflurane is administered in O(2).

METHODS

Seventy-two physical status ASA I-II patients were randomly assigned to one of six groups (n=12 each). In the first four groups, sevoflurane (1.8% vaporizer setting) administration was started 0, 2, 5 and 60 min after starting 2 litre min(-1) O(2) and 4 litre min(-1) N(2)O, respectively. In the last two groups, sevoflurane (1.8 or 3.6% vaporizer setting) was administered in 6 litre min(-1) O(2). The ratios of the alveolar fraction of sevoflurane (Fa) over the inspired fraction (Fi), or Fa/Fi, were compared between the groups.

RESULTS

Sevoflurane Fa/Fi was larger in the N(2)O groups than in the O(2) groups, and it was identical in all four N(2)O groups.

CONCLUSIONS

We confirmed the existence of a SGE of N(2)O. Surprisingly, when using an Fa of 65% N(2)O, the magnitude of the SGE was the same with large or small VN(2)O. The classical model and the graphical representation of the SGE alone should not be used to explain the magnitude of the SGE. We speculate that changes in ventilation/perfusion inhomogeneity in the lungs during general anaesthesia result in a SGE at levels of VN(2)O previously considered by most to be too small to exert a SGE.

Continuous measurement of cardiac output by inert gas throughflow: comparison with thermodilution

OBJECTIVE

The throughflow method is a new technique for continuous and minimally invasive measurement of cardiac output by the Fick principle, which uses ventilation of the 2 lungs with unequal inspired gas concentrations by means of a double-lumen endobronchial tube. It exploits steady-state gas exchange and thus permits rapid repetition of measurement.

DESIGN

Comparison of paired measurements by the throughflow method using N(2)O exchange with bolus thermodilution.

SETTING

Departments of anesthesiology in 2 university teaching hospitals.

PARTICIPANTS

Nine patients undergoing cardiac surgery in the precardiopulmonary bypass period.

INTERVENTIONS

Patients intubated with a double-lumen endobronchial tube were ventilated with 45% nitrous oxide (N(2)O) to the left lung (zero to the right lung). Arterial blood gas samples were taken to measure alveolar deadspace to allow correction for the alveolar-arterial N(2)O difference and to correct for the presence of unmeasured shunt perfusion.

MEASUREMENTS AND MAIN RESULTS

Throughflow measurements correlated with thermodilution (r = 0.719, p < 0.05) with a mean bias of -0.208 L/min (-5.2%). The standard error of the bias was 0.060 L/min, with 95% confidence limits for the bias of -0.088 L/min and -0.328 L/min. The limits of agreement between the 2 methods were +0.960 L/min and -1.376 L/min.

CONCLUSIONS

The throughflow method showed good agreement with thermodilution. It permits continuous cardiac output measurement without the need for sampling of mixed venous blood, using techniques of lung isolation, which are readily available in clinical anesthetic practice.

Anesthetic uptake of sevoflurane and nitrous oxide during an inhaled induction in children

The uptake of sevoflurane and nitrous oxide (N(2)O) was characterized during the mask induction of anesthesia in healthy children. We assessed concentration and second gas effects by determining the influence of two different inspiratory N(2)O concentrations on the rate at which the estimated alveolar concentration (FA) increased to the inspired gas concentration (FI). Eighteen children aged 4-12 yr old were randomly assigned to receive a 6% sevoflurane mixture with either a large or a small N(2)O concentration with balance O(2). End-tidal and inspiratory concentrations of respiratory and anesthetic gases were continuously assessed during the induction. The FA/FI for the small N(2)O was 0.87 +/- 0.09 (mean +/- SD) and increased to 0.92 +/- 0.08 for the large N(2)O (P < 0.01). Both groups differed significantly at 3, 4, and 5 min. The FA/FI for sevoflurane increased but more slowly than for N(2)O. The mean only differed significantly at 3 min. Equilibration between FA and FI for N(2)O and sevoflurane was attained rapidly. Consistent with their respective blood/gas partition coefficients, the FA/FI for N(2)O increased more rapidly than that for sevoflurane. Increasing FI-N(2)O produced a leftward shift in gas equilibration curves. A concentration effect was confirmed with N(2)O and a brief second gas effect, probably explained by the higher solubility of sevoflurane.

Variation of venous admixture, SF6 shunt, PaO2, and the PaO2/FIO2 ratio with FIO2

BACKGROUND

Measures of impairment of oxygenation can be affected by the inspired oxygen fraction.

METHODS

We used a mathematical model of an inhomogenous lung to predict the effect of increasing inspired oxygen concentration (FIO2) on: (1) venous admixture (Qva/Qt); (2) arterial oxygen partial pressure (PaO2); (3) the PaO2/FIO2 index of hypoxaemia; and (4) sulphur hexafluoride (SF6) retention (often taken to be true right-to-left shunt). This model predicts whether or not atelectasis will occur.

RESULTS

For lungs with regions of low V/Q, increasing the inspired oxygen concentration can cause these regions to collapse. In the absence of atelectasis, the model predicts that Qva/Qt will decrease and arterial oxygen partial pressure increase as FIO2 is increased. However, when atelectasis occurs, Qva/Qt rises to a constant value, whilst PaO2 falls at first, but then begins to rise again, with increasing FIO2. The SF6 retention increased markedly in some cases at high FIO2.

CONCLUSIONS

Venous admixture will estimate true right-to-left shunt at high FIO2, even when oxygen consumption is raised. This model can explain the way that the Pa/Fl ratio changes with increasing inspired oxygen concentration.

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.

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

Ventilation-perfusion (VA/Q) inhomogeneity was modeled to measure its effect on overall gas exchange during maintenance-phase N(2)O anesthesia with an inspired O(2) concentration of 30%. A multialveolar compartment computer model was used based on physiological log normal distributions of VA/Q inhomogeneity. Increasing the log standard deviation of the distribution of perfusion from 0 to 1.75 paradoxically increased O(2) uptake (VO(2)) where a low mixed venous partial pressure of N(2)O [high N(2)O uptake (VN(2)O)] was specified. With rising mixed venous partial pressure of N(2)O, a threshold was observed where VO(2) began to fall, whereas VN(2)O began to rise with increasing VA/Q inhomogeneity. This phenomenon is a magnification of the concentrating effects that VO(2) and VN(2)O have on each other in low VA/Q compartments. During "steady-state" N(2)O anesthesia, VN(2)O is predicted to paradoxically increase in the presence of worsening VA/Q inhomogeneity.