A mathematical evaluation of the alveolar amplitude response technique

Analysis of the effect of inert gas on alveolar/venous blood partial pressure by using the operator splitting method

This study aims to investigate how inert gas affects the partial pressure of alveolar and venous blood using a fast and accurate operator splitting method (OSM). Unlike previous complex methods, such as the finite element method (FEM), OSM effectively separates governing equations into smaller sub-problems, facilitating a better understanding of inert gas transport and exchange between blood capillaries and surrounding tissue. The governing equations were discretized with a fully implicit finite difference method (FDM), which enables the use of larger time steps. The model employed partial differential equations, considering convection-diffusion in blood and only diffusion in tissue. The study explores the impact of initial arterial pressure, breathing frequency, blood flow velocity, solubility, and diffusivity on the partial pressure of inert gas in blood and tissue. Additionally, the effects of anesthetic inert gas and oxygen on venous blood partial pressure were analyzed. Simulation results demonstrate that the high solubility and diffusivity of anesthetic inert gas lead to its prolonged presence in blood and tissue, resulting in lower partial pressure in venous blood. These findings enhance our understanding of inert gas interaction with alveolar/venous blood, with potential implications for medical diagnostics and therapies.

Noninvasive cardiac output monitoring in a porcine model using the inspired sinewave technique: a proof-of-concept study

Background

Cardiac output (Q˙) monitoring can support the management of high-risk surgical patients, but the pulmonary artery catheterisation required by the current ‘gold standard’—bolus thermodilution (Q˙T)—has the potential to cause life-threatening complications. We present a novel noninvasive and fully automated method that uses the inspired sinewave technique to continuously monitor cardiac output (Q˙IST).

Methods

Over successive breaths the inspired nitrous oxide (N₂O) concentration was forced to oscillate sinusoidally with a fixed mean (4%), amplitude (3%), and period (60 s). Q˙IST was determined in a single-compartment tidal ventilation lung model that used the resulting amplitude/phase of the expired N₂O sinewave. The agreement and trending ability of Q˙IST were compared with Q˙T during pharmacologically induced haemodynamic changes, before and after repeated lung lavages, in eight anaesthetised pigs.

Results

Before lung lavage, changes in Q˙IST and Q˙T from baseline had a mean bias of –0.52 L min⁻¹ (95% confidence interval [CI], –0.41 to –0.63). The concordance between Q˙IST and Q˙T was 92.5% as assessed by four-quadrant analysis, and polar plot analysis revealed a mean angular bias of 5.98° (95% CI, –24.4°–36.3°). After lung lavage, concordance was slightly reduced (89.4%), and the mean angular bias widened to 21.8° (–4.2°, 47.6°). Impaired trending ability correlated with shunt fraction (r=0.79, P<0.05).

Conclusions

The inspired sinewave technique provides continuous and noninvasive monitoring of cardiac output, with a ‘marginal–good’ trending ability compared with cardiac output based on thermodilution. However, the trending ability can be reduced with increasing shunt fraction, such as in acute lung injury.

The inspired sine-wave technique: A novel method to measure lung volume and ventilatory heterogeneity

NEW FINDINGS

What is the central question of this study? We present a new non-invasive medical technology, the inspired sine-wave technique, which involves inhalation of sinusoidally fluctuating concentrations of a tracer gas. The technique requires only passive patient cooperation and can monitor different cardiorespiratory variables, such as end-expired lung volume, ventilatory heterogeneity and pulmonary blood flow. What is the main finding and its importance? In this article, we demonstrate that the measurements of end-expired lung volume are repeatable and accurate, in comparison to whole-body plethysmography, and the technique is sensitive to the changes in ventilatory heterogeneity associated with advancing age. As such, it has the potential to provide clinically valuable information.

ABSTRACT

The inspired sine-wave technique (IST) is a new method that can provide simple, non-invasive cardiopulmonary measurements. Over successive tidal breaths, the concentration of a tracer gas (i.e. nitrous oxide, N₂ O) is sinusoidally modulated in inspired air. Using a single-compartment tidal-ventilation lung model, the resulting amplitude/phase of the expired sine wave allows estimation of end-expired lung volume (ELV), pulmonary blood flow and three indices for ventilatory heterogeneity (VH; ELV₁₈₀ /FRC_pleth , ELV₁₈₀ /FRC_pred and ELV₆₀ /ELV₁₈₀ ). This investigation aimed to determine the repeatability and agreement of ELV with FRC_pleth and, as normal ageing results in well-established changes in pulmonary structure and function, whether the IST estimates of ELV and VH are age dependent. Forty-eight healthy never-smoker participants (20-86 years) underwent traditional pulmonary function testing (e.g. spirometry, body plethysmography) and the IST test, which consisted of 4 min of quiet breathing through a face mask while inspired N₂ O concentrations were oscillated in a sine-wave pattern with a fixed mean (4%) and amplitude (3%) and a period of either 180 or 60 s. The ELV₁₈₀ /FRC_pleth and ELV₁₈₀ /FRC_pred were age dependent (average decreases of 0.58 and 0.48% year^-1 ), suggesting an increase in VH with advancing age. The ELV showed a mean bias of -1.09 litres versus FRC_pleth , but when normalized for the effects of age this bias reduced to -0.35 litres. The IST test has potential to provide clinically useful information necessitating further study (e.g. for mechanically ventilated or obstructive lung disease patients), but these findings suggest that the increases in VH with healthy ageing must be taken into account in clinical investigations.

Modelling mixing within the dead space of the lung improves predictions of functional residual capacity

Routine estimation of functional residual capacity (FRC) in ventilated patients has been a long held goal, with many methods previously proposed, but none have been used in routine clinical practice. This paper proposes three models for determining FRC using the nitrous oxide concentration from the entire expired breath in order to improve the precision of the estimate. Of the three models proposed, a dead space with two mixing compartments provided the best results, reducing the mean limits of agreement with the FRC measured by whole body plethysmography by up to 41%. This moves away from traditional lung models, which do not account for mixing within the dead space. Compared to literature values for FRC, the results are similar to those obtained using helium dilution and better than the LUFU device (Dräger Medical, Lubeck, Germany), with significantly better limits of agreement compared to plethysmography.

Inert gas transport in blood and tissues

This article establishes the basic mathematical models and the principles and assumptions used for inert gas transfer within body tissues-first, for a single compartment model and then for a multicompartment model. From these, and other more complex mathematical models, the transport of inert gases between lungs, blood, and other tissues is derived and compared to known experimental studies in both animals and humans. Some aspects of airway and lung transfer are particularly important to the uptake and elimination of inert gases, and these aspects of gas transport in tissues are briefly described. The most frequently used inert gases are those that are administered in anesthesia, and the specific issues relating to the uptake, transport, and elimination of these gases and vapors are dealt with in some detail showing how their transfer depends on various physical and chemical attributes, particularly their solubilities in blood and different tissues. Absorption characteristics of inert gases from within gas cavities or tissue bubbles are described, and the effects other inhaled gas mixtures have on the composition of these gas cavities are discussed. Very brief consideration is given to the effects of hyper- and hypobaric conditions on inert gas transport.

A Non-Invasive Method for Estimating Cardiopulmonary Variables Using Breath-by-Breath Injection of Two Tracer Gases

Conventional methods for estimating cardiopulmonary variables usually require complex gas analyzers and the active co-operation of the patient. Therefore, they are not compatible with the crowded environment of the intensive care unit (ICU) or operating theatre, where patient co-operation is typically impossible. However, it is these patients that would benefit the most from accurate estimation of cardiopulmonary variables, because of their critical condition. This paper describes the results of a collaborative development between an anesthesiologists and biomedical engineers to create a compact and non-invasive system for the measurement of cardiopulmonary variables such as lung volume, airway dead space volume, and pulmonary blood flow. In contrast with conventional methods, the compact apparatus and non-invasive nature of the proposed method allow it to be used in the ICU, as well as in general clinical settings. We propose the use of a non-invasive method, in which tracer gases are injected into the patient's inspired breath, and the concentration of the tracer gases is subsequently measured. A novel breath-by-breath tidal ventilation model is then used to estimate the value of a patient's cardiopulmonary variables. Experimental results from an artificial lung demonstrate minimal error in the estimation of known parameters using the proposed method. Results from analysis of a cohort of 20 healthy volunteers (within the Oxford University Hospitals NHS Trust) show that the values of estimated cardiopulmonary variables from these subjects lies within the expected ranges. Advantages of this method are that it is non-invasive, compact, portable, and can perform analysis in real time with less than 1 min of acquired respiratory data.

Assessment of lung function using a non-invasive oscillating gas-forcing technique

•

We propose a compact and non-invasive system for the measurement and monitoring of lung function.

•

We develop a novel tidal ventilation model using a non-invasive oscillating gas-forcing technique.

•

We compare a conventional continuous ventilation model with the proposed tidal ventilation model.

•

The proposed technique has several advantages over conventional methods, and can be used to assess patient lung function.

Conventional methods for monitoring lung function can require complex, or special, gas analysers, and may therefore not be practical in clinical areas such as the intensive care unit (ICU) or operating theatre. The system proposed in this article is a compact and non-invasive system for the measurement and monitoring of lung variables, such as alveolar volume, airway dead space, and pulmonary blood flow. In contrast with conventional methods, the compact apparatus and non-invasive nature of the proposed method could eventually allow it to be used in the ICU, as well as in general clinical settings. We also propose a novel tidal ventilation model using a non-invasive oscillating gas-forcing technique, where both nitrous oxide and oxygen are used as indicator gases. Experimental results are obtained from healthy volunteers, and are compared with those obtained using a conventional continuous ventilation model. Our findings show that the proposed technique can be used to assess lung function, and has several advantages over conventional methods such as compact and portable apparatus, easy usage, and quick estimation of cardiopulmonary variables.

A tidal breathing model of the inert gas sinewave technique for inhomogeneous lungs

The tidal breathing model conservation of mass equations for the sinewave technique have been described for a homogeneous alveolar compartment by Gavaghan and Hahn, 1996 [Gavaghan, D.J., Hahn, C.E.W., 1996. A tidal breathing model of the forced inspired gas sinewave technique. Respir. Physiol. 106, 209-221]. We develop these equations first to a multi-discrete alveolar compartment lung model and then to a lung model with a continuous distribution of volume, ventilation and perfusion. The effect on the output parameters of a multi-compartment model is discussed, and the results are compared to those derived from the conventional continuous-ventilation model. Using the barely soluble gas argon as the tracer gas, an empirical index of alveolar inhomogeneity is presented which uses the end-expired and mixed-expired partial pressures on each breath. This index distinguishes between a narrow unimodal distribution of ventilation-volume, a wide unimodal distribution of ventilation-volume and a bimodal distribution of ventilation-volume. By using Monte Carlo simulations, this index is shown to be stable to experimental error of realistic magnitude.

Modelling inert gas exchange in tissue and mixed-venous blood return to the lungs

Inert gas exchange in tissue has been almost exclusively modelled by using an ordinary differential equation. The mathematical model that is used to derive this ordinary differential equation assumes that the partial pressure of an inert gas (which is proportional to the content of that gas) is a function only of time. This mathematical model does not allow for spatial variations in inert gas partial pressure. This model is also dependent only on the ratio of blood flow to tissue volume, and so does not take account of the shape of the body compartment or of the density of the capillaries that supply blood to this tissue. The partial pressure of a given inert gas in mixed-venous blood flowing back to the lungs is calculated from this ordinary differential equation. In this study, we write down the partial differential equations that allow for spatial as well as temporal variations in inert gas partial pressure in tissue. We then solve these partial differential equations and compare them to the solution of the ordinary differential equations described above. It is found that the solution of the ordinary differential equation is very different from the solution of the partial differential equation, and so the ordinary differential equation should not be used if an accurate calculation of inert gas transport to tissue is required. Further, the solution of the PDE is dependent on the shape of the body compartment and on the density of the capillaries that supply blood to this tissue. As a result, techniques that are based on the ordinary differential equation to calculate the mixed-venous blood partial pressure may be in error.

Noninvasive monitoring of nonshunted pulmonary capillary blood flow in the acute respiratory distress syndrome

OBJECTIVE

Noninvasive monitoring of nonshunted pulmonary capillary blood flow, using the alveolar amplitude response technique (AART) in a porcine model of the acute respiratory distress syndrome.

DESIGN

Experimental animal study.

SETTING

University center for animal experiments.

INTERVENTIONS

In 12 mechanically ventilated pigs, the nonshunted pulmonary capillary blood flow was varied by means of lung lavages and the application of positive end-expiratory pressure.

MEASUREMENTS AND MAIN RESULTS

Nonshunted pulmonary capillary blood flow was determined by AART. Cardiac output (determined by the thermodilution method) corrected for venous admixture was used for comparison (r2 varied between .58 and .94; p < .01). The trend in the development of nonshunted pulmonary capillary blood flow as measured with AART was in agreement with the trend detected by cardiac output corrected for venous admixture in 92% of all events.

CONCLUSIONS

We conclude that AART can be used to monitor changes in nonshunted pulmonary capillary blood flow in cases of acute respiratory distress syndrome noninvasively and continuously.

A real-time algorithm to improve the response time of a clinical multigas analyser

OBJECTIVE

An algorithm to improve the response time of a clinical respiratory multigas analyser is presented.

METHODS

The algorithm involves the application of a second order differential equation to the analyser gas output signals in real-time. The adjusted analyser output signals are compared with those of a quadrupole respiratory mass spectrometer sampling and analysing simultaneously.

RESULTS

Our results show a close correlation between the adjusted clinical gas analyser and the mass spectrometer signals. Lung volumes derived from a non-invasive sinusoidal inert gas forcing technique, in a model test lung, using the adjusted clinical gas analyser and the mass spectrometer signals demonstrated comparable results.

CONCLUSIONS

The algorithm provides an improvement on the relatively slow response times of the clinical gas analyser for breath-by-breath time-dependent applications. The same algorithm can also be applied to other instruments which have slow response times.

A tidal breathing model of the forced inspired inert gas sinewave technique

We have shown previously that it is possible to assess the cardio-respiratory function using sinusoidally oscillating inert gas forcing signals of nitrous oxide and argon (Hahn et al., 1993). This method uses an extension of a mathematical model of respiratory gas exchange introduced by Zwart et al. (1976), which assumed continuous ventilation. We investigate the effects of this assumption by developing a mathematical model using a single alveolar compartment and incorporating tidal ventilation, which must be solved using numerical methods. We compare simulated results from the tidal model with those from the continuous model, as the governing ventilatory and cardiac parameters are varied. The mathematical model is designed to be the basis of an on-line, non-invasive, cardio-respiratory measurement method, and will only be useful if the associated parameter recovery techniques are both reliable and robust. We demonstrate, in the presence of simulated measurement errors, that: (a) accurate recovery of the ventilatory parameters end-tidal volume, VA, and airways series dead-space, VD, are possible using the tidal breathing model; and (b) that a robust technique for recovery of pulmonary blood flow, QP, can be obtained using the more familiar continuous ventilation model.