Ventilation-perfusion inhomogeneity increases gas uptake: theoretical 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.

Integrative Computational Models of Lung Structure-Function Interactions

Anatomically based integrative models of the lung and their interaction with other key components of the respiratory system provide unique capabilities for investigating both normal and abnormal lung function. There is substantial regional variability in both structure and function within the normal lung, yet it remains capable of relatively efficient gas exchange by providing close matching of air delivery (ventilation) and blood delivery (perfusion) to regions of gas exchange tissue from the scale of the whole organ to the smallest continuous gas exchange units. This is despite remarkably different mechanisms of air and blood delivery, different fluid properties, and unique scale-dependent anatomical structures through which the blood and air are transported. This inherent heterogeneity can be exacerbated in the presence of disease or when the body is under stress. Current computational power and data availability allow for the construction of sophisticated data-driven integrative models that can mimic respiratory system structure, function, and response to intervention. Computational models do not have the same technical and ethical issues that can limit experimental studies and biomedical imaging, and if they are solidly grounded in physiology and physics they facilitate investigation of the underlying interaction between mechanisms that determine respiratory function and dysfunction, and to estimate otherwise difficult-to-access measures. © 2021 American Physiological Society. Compr Physiol 11:1501-1530, 2021.

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.

Integrative approaches for modeling regulation and function of the respiratory system

Mathematical models have been central to understanding the interaction between neural control and breathing. Models of the entire respiratory system-which comprises the lungs and the neural circuitry that controls their ventilation-have been derived using simplifying assumptions to compartmentalize each component of the system and to define the interactions between components. These full system models often rely-through necessity-on empirically derived relationships or parameters, in addition to physiological values. In parallel with the development of whole respiratory system models are mathematical models that focus on furthering a detailed understanding of the neural control network, or of the several functions that contribute to gas exchange within the lung. These models are biophysically based, and rely on physiological parameters. They include single-unit models for a breathing lung or neural circuit, through to spatially distributed models of ventilation and perfusion, or multicircuit models for neural control. The challenge is to bring together these more recent advances in models of neural control with models of lung function, into a full simulation for the respiratory system that builds upon the more detailed models but remains computationally tractable. This requires first understanding the mathematical models that have been developed for the respiratory system at different levels, and which could be used to study how physiological levels of O2 and CO2 in the blood are maintained.

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.

Effects of methacholine on small airway function measured by forced oscillation technique and multiple breath nitrogen washout in normal subjects

The multiple breath nitrogen washout (MBNW) can be analysed to produce the parameters Scond and Sacin as measures of ventilation heterogeneity in conductive and acinar airways, respectively. The derivation of these parameters is based on a model of pulmonary ventilation and results of similar modelling suggest that respiratory system conductance (Grs) measured by forced oscillation technique (FOT) is also sensitive to heterogeneity and to airway closure. Therefore, Scond, the volume of gas trapping at FRC (VtrappedFRC) and Grs may be inter-related parameters. These relationships were examined in 12 normals under baseline and bronchoconstricted states. Specific Grs was measured at 5Hz (sGrs5=Grs5/FRC) and Scond, Sacin and VtrappedFRC by MBNW, before and after methacholine challenge. Scond was independently predicted by VtrappedFRC and FRC in a multivariate model (R2=0.68, p=0.002). Post methacholine challenge, Scond related only to VtrappedFRC (R2=0.79, p<0.0001). The absolute change in Scond induced by methacholine challenge were predicted by the changes in VtrappedFRC and sGrs5 in a multivariate model (R2=0.82, p=0.0002). Sacin was unrelated to VtrappedFRC and sGrs5 before and after methacholine challenge. In conclusion, Scond and sGrs5 are measurements that are sensitive to changes occurring to the function of peripheral conducting airways, in particular heterogeneity and airway closure, while Sacin and presumably heterogeneity in terminal airways, are independent of these. Scond is also related to lung size. We review the current state of knowledge of FOT and MBNW in obstructive lung diseases and discuss future research directions.

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.