A model evaluation of estimates of breath-to-breath alveolar gas exchange

A mathematical model has been implemented for evaluation of methods for estimating breath-to-breath alveolar gas exchange during exercise in humans. This model includes a homogeneous alveolar gas exchange compartment, a dead space compartment, and tissue spaces for CO2 (alveolar and dead space). The dead space compartment includes a mixing portion surrounded by tissue and an unmixed (slug flow) portion which is partitioned between anatomical and apparatus contributions. A random sinusoidal flow pattern generates a breath-to-breath variation in pulmonary stores. The Auchincloss algorithm for estimating alveolar gas exchange (Auchincloss et al., J. Appl. Physiol. 21: 810-818, 1966) was applied to the model, and the results were compared with the simulated gas exchange. This comparison indicates that a compensation for changes in pulmonary stores must include factors for alveolar gas concentration change as well as alveolar volume change and thus implies the use of end-tidal measurements. Although this algorithm yields reasonable estimates of breath-to-breath alveolar gas exchange, it does not yield a "true" indirect measurement because of inherent error in the estimation of a homogeneous alveolar gas concentration at the end of expiration.     

Evaluation of estimates of alveolar gas exchange by using a tidally ventilated nonhomogenous lung model

Busso, Thierry, and Peter A. Robbins. Evaluation ofestimates of alveolar gas exchange by using a tidally ventilated nonhomogenous lung model. J. Appl.Physiol. 82(6): 1963-1971, 1997.The purposeof this study was to evaluate algorithms for estimatingO₂ andCO₂ transfer at thepulmonary capillaries by use of a nine-compartment tidallyventilated lung model that incorporated inhomogeneities inventilation-to-volume and ventilation-to-perfusion ratios.Breath-to-breath O₂ andCO₂ exchange at the capillary level and at the mouth were simulated by using realistic cyclical breathing patterns to drive the model, derived from 40-min recordings in six resting subjects. The SD of the breath-by-breath gas exchange atthe mouth around the value at the pulmonary capillaries was 59.7 ± 25.5% for O₂ and 22.3 ± 10.4% for CO₂. Algorithmsincluding corrections for changes in alveolar volume and for changes in alveolar gas composition improved the estimates of pulmonary exchange, reducing the SD to 20.8 ± 10.4% forO₂ and 15.2 ± 5.8% forCO₂. The remaining imprecision ofthe estimates arose almost entirely from using end-tidal measurementsto estimate the breath-to-breath changes in end-expiratory alveolar gasconcentration. The results led us to suggest an alternative method thatdoes not use changes in end-tidal partial pressures as explicitestimates of the changes in alveolar gas concentration. The proposedmethod yielded significant improvements in estimation for the modeldata of this study.

     

A mathematical model of alveolar gas exchange in partial liquid ventilation

In partial liquid ventilation (PLV), perfluorocarbon (PFC) acts as a diffusion barrier to gas transport in the alveolar space since the diffusivities of oxygen and carbon dioxide in this medium are four orders of magnitude lower than in air. Therefore convection in the PFC layer resulting from the oscillatory motions of the alveolar sac during ventilation can significantly affect gas transport. For example, a typical value of the Péclet number in air ventilation is Pe approximately 0.01, whereas in PLV it is Pe approximately 20. To study the importance of convection, a single terminal alveolar sac is modeled as an oscillating spherical shell with gas, PFC, tissue and capillary blood compartments. Differential equations describing mass conservation within each compartment are derived and solved to obtain time periodic partial pressures. Significant partial pressure gradients in the PFC layer and partial pressure differences between the capillary and gas compartments (P(C)-Pg) are found to exist. Because Pe> 1, temporal phase differences are found to exist between P(C)-Pg and the ventilatory cycle that cannot be adequately described by existing non-convective models of gas exchange in PLV The mass transfer rate is nearly constant throughout the breath when Pe>1, but when Pe<1 nearly 100% of the transport occurs during inspiration. A range of respiratory rates (RR), including those relevant to high frequency oscillation (HFO) +PLV, tidal volumes (V(T)) and perfusion rates are studied to determine the effect of heterogeneous distributions of ventilation and perfusion on gas exchange. The largest changes in P(C)O2 and P(C)CO2 occur at normal and low perfusion rates respectively as RR and V(T) are varied. At a given ventilation rate, a low RR-high V(T) combination results in higher P(C)O2, lower P(C)CO2 and lower (P(C)-Pg) than a high RR-low V(T) one.     

Breath-by-breath alveolar gas exchange

A method is described for breath-by-breath measurement of alveolar gas exchange corrected for changes of lung gas stores. In practice, the subject inspires from a spirometer, and each expired tidal volume is collected into a rubber bag placed inside a rigid box connected to the same spirometer. During the inspiration following any given expiration the bag is emptied by a vacuum pump. A computer monitors inspiratory and expiratory tidal volumes, drives four solenoid valves allowing appropriate operation of the system, and memorizes end-tidal gas fractions as well as mixed expired gas composition analyzed by mass spectrometer. Thus all variables for calculating alveolar gas exchange, based on the theory developed by Auchincloss et al. (J. Appl. Physiol. 21: 810-818, 1966), are obtained on a single-breath basis. Mean resting and steady-state exercise gas exchange data are equal to those obtained by conventional open-circuit measurements. Breathing rates up to 30 X min-1 can be followed. The breath-to-breath variability of O2 uptake at the alveolar level is less (25-35%) than that measured at the mouth as the difference between the inspired and expired volumes, both at rest and during exercise up to 0.7 of maximum O2 consumption.     

A new method for breath-to-breath determination of oxygen flux across the alveolar membrane

A new method for breath-to-breath determination of the oxygen flux across the alveolar membrane is described. The principle of the method is to integrate the product of oxygen concentration and flow in the respiratory gas over an interval, which covers a complete respiratory cycle. The result is corrected for the change in oxygen content of the lungs through a formula, which, in contrast to those used in other methods, is independent of the residual capacity of the lungs. The method was evaluated with respect to repeatability by repetitive measurement of oxygen flux in twenty volunteer subjects, and with respect to accuracy by comparing the measured oxygen fluxes with those obtained by the gas collection method. The coefficient of variation was found to be 8% and the breath to breath determinations were, on an average, 6% lower than those of the gas collection method.     

Breath-by-breath assessment of alveolar gas stores and exchange.

The volume of O(2) exchanged at the mouth during a breath (Vo(2,m)) is equal to that taken up by pulmonary capillaries (Vo(2,A)) only if lung O(2) stores are constant. The latter change if either end-expiratory lung volume (EELV), or alveolar O(2) fraction (Fa(O(2))) change. Measuring this requires breath-by-breath (BbB) measurement of absolute EELV, for which we used optoelectronic plethysmography combined with measurement of O(2) fraction at the mouth to measure Vo(2,A) = Vo(2,m) - (DeltaEELV x Fa(O(2)) + EELV x DeltaFa(O(2))), and divided by respiratory cycle time to obtain BbB O(2) consumption (Vo(2)) in seven healthy men during incremental exercise and recovery. To synchronize O(2) and volume signals, we measured gas transit time from mouthpiece to O(2) meter and compared Vo(2) measured during steady-state exercise by using expired gas collection with the mean BbB measurement over the same time period. In one subject, we adjusted the instrumental response time by 20-ms increments to maximize the agreement between the two Vo(2) measurements. We then applied the same total time delay (transit time plus instrumental delay = 660 ms) to all other subjects. The comparison of pooled data from all subjects revealed r(2) = 0.990, percent error = 0.039 +/- 1.61 SE, and slope = 1.02 +/- 0.015 (SE). During recovery, increases in EELV introduced systematic errors in Vo(2) if measured without taking DeltaEELV x Ca(O(2))+EELV x DeltaFa(O(2)) into account. We conclude that optoelectronic plethysmography can be used to measure BbB Vo(2) accurately when studying BbB gas exchange in conditions when EELV changes, as during on- and off-transients.     

Off-pump coronary bypass surgery adversely affects alveolar gas exchange

While the introduction of off-pump myocardial revascularization (OPCAB) has initially shown promise in reducing respiratory complications inherent to conventional coronary surgery, it has failed to eradicate them. Our study focused on quantifying the lactate release from the lungs and the dysfunction at the level of the alveolar-capillary membrane precipitated by OPCAB at different time points after the insult. Furthermore, we aimed to determine the impact of pulmonary lactate production on systemic lactic acid concentrations. The study was conducted in a prospective observational fashion. Forty consecutive patients undergoing OPCAB were analyzed. The mean patient age was 60 +/- 10 years. The mean EUROScore was 3.8 +/- 2.9. The alveolar-arterial O2 gradient increased from 19 [range 9 to 30] to 26 [range 20 to 34] kPa (P < 0.001) and remained elevated up to 6 hours after surgery. It rapidly declined again by 18 hours postoperatively. The observed increase in the pulmonary lactate release (PLR) from a baseline value of 0.022 [range -0.074 to 0.066] to 0.089 [range 0.016 to 0.209] mmol/min/m2 at six hours postoperatively did not reach statistical significance (P = 0.105). The systemic arterial lactate (Ls) concentration increased from 0.94 [range 0.78 to 1.06] to 1.39 [range 0.97 to 2.81] mmol/L (P < 0.001). The venoarterial pCO2 difference showed no significant change in comparison to baseline values. The mortality in the studied group was 2.5% (1/40). The pulmonary lactate production showed a statistically significant correlation with the systemic lactate concentration (R = 0.46; P = 0.003). Pulmonary injury following off pump myocardial revascularization was evidenced by a prompt increase in the alveolar-arterial oxygen gradient. The alveolar-arterial O2 gradient correlated with the duration of mechanical ventilation.     

Effect of regional alveolar hypoxia on gas exchange in dogs

We studied the effects of left lower lobe (LLL) alveolar hypoxia on pulmonary gas exchange in anesthetized dogs using the multiple inert gas elimination technique (MIGET). The left upper lobe was removed, and a bronchial divider was placed. The right lung (RL) was continuously ventilated with 100% O2, and the LLL was ventilated with either 100% O2 (hyperoxia) or a hypoxic gas mixture (hypoxia). Whole lung and individual LLL and RL ventilation-perfusion (VA/Q) distributions were determined. LLL hypoxia reduced LLL blood flow and increased the perfusion-related indexes of VA/Q heterogeneity, such as the log standard deviation of the perfusion distribution (log SDQ), the retention component of the arterial-alveolar difference area [R(a-A)D], and the retention dispersion index (DISPR*) of the LLL. LLL hypoxia increased blood flow to the RL and reduced the VA/Q heterogeneity of the RL, indicated by significant reductions in log SDQ, R(a-A)D, and DISPR*. In contrast, LLL hypoxia had little effect on gas exchange of the lung when evaluated as a whole. We conclude that flow diversion induced by regional alveolar hypoxia preserves matching of ventilation to perfusion in the whole lung by increasing gas exchange heterogeneity of the hypoxic region and reducing heterogeneity in the normoxic lung.     

A three-dimensional multiscale model for gas exchange in fruit

Respiration of bulky plant organs such as roots, tubers, stems, seeds, and fruit depends very much on oxygen (O2) availability and often follows a Michaelis-Menten-like response. A multiscale model is presented to calculate gas exchange in plants using the microscale geometry of the tissue, or vice versa, local concentrations in the cells from macroscopic gas concentration profiles. This approach provides a computationally feasible and accurate analysis of cell metabolism in any plant organ during hypoxia and anoxia. The predicted O2 and carbon dioxide (CO2) partial pressure profiles compared very well with experimental data, thereby validating the multiscale model. The important microscale geometrical features are the shape, size, and three-dimensional connectivity of cells and air spaces. It was demonstrated that the gas-exchange properties of the cell wall and cell membrane have little effect on the cellular gas exchange of apple (Malus×domestica) parenchyma tissue. The analysis clearly confirmed that cells are an additional route for CO2 transport, while for O2 the intercellular spaces are the main diffusion route. The simulation results also showed that the local gas concentration gradients were steeper in the cells than in the surrounding air spaces. Therefore, to analyze the cellular metabolism under hypoxic and anoxic conditions, the microscale model is required to calculate the correct intracellular concentrations. Understanding the O2 response of plants and plant organs thus not only requires knowledge of external conditions, dimensions, gas-exchange properties of the tissues, and cellular respiration kinetics but also of microstructure.     

A mathematical model of pulmonary gas exchange under inflammatory stress

During a severe local or systemic inflammatory response, immune mediators target lung tissue. This process may lead to acute lung injury and impaired diffusion of gas molecules. Although several mathematical models of gas exchange have been described, none simulate acute lung injury following inflammatory stress. In view of recent laboratory and clinical progress in the understanding of the pathophysiology of acute lung injury, such a mathematical model would be useful. We first derived a partial differential equations model of gas exchange on a small physiological unit of the lung (≈25 alveoli), which we refer to as a respiratory unit (RU). We next developed a simple model of the acute inflammatory response and implemented its effects within a RU, creating a single RU model. Linking multiple RUs with various ventilation/perfusion ratios and taking into account pulmonary venous blood remixing yielded our lung-scale model. Using the lung-scale model, we explored the predicted effects of inflammation on ventilation/perfusion distribution and the resulting pulmonary venous partial pressure oxygen level during systemic inflammatory stresses. This model represents a first step towards the development of anatomically faithful models of gas exchange and ventilation under a broad range of local and systemic inflammatory stimuli resulting in acute lung injury, such as infection and mechanical strain of lung tissue.     

Rapid and straightforward estimates of photosynthetic characteristics using a portable gas exchange system

Procedures are described for estimating photosynthetic characteristics using a portable infra-red gas analysis (IRGA) system. Once the effects of stomatal limitation on CO2 assimilation have been established, up to ten parameters of photosynthesis can be estimated for a single leaf within 2 h, including: photosynthetic efficiency and capacity on both photon and CO2 bases; compensation irradiances and CO2 compensation concentrations; and light and dark respiration rates. These measurements can be made in the laboratory, glasshouse or field with relative ease. Methods for obtaining near instantaneous ("snapshot") measurements of leaf photosynthesis are also described, using carefully pre-set conditions within the leaf cuvette. Representative results are shown for Phaseolus vulgaris L. Important aspects of the procedure's experimental design, assumptions made in the analysis, and limitations of this approach are analysed. This revised version was published online in June 2006 with corrections to the Cover Date.     

Rapid and straightforward estimates of photosynthetic characteristics using a portable gas exchange system

Procedures are described for estimating photosynthetic characteristics using a portable infra-red gas analysis (IRGA) system. Once the effects of stomatal limitation on CO2 assimilation have been established, up to ten parameters of photosynthesis can be estimated for a single leaf within 2 h, including: photosynthetic efficiency and capacity on both photon and CO2 bases; compensation irradiances and CO2 compensation concentrations; and light and dark respiration rates. These measurements can be made in the laboratory, glasshouse or field with relative ease. Methods for obtaining near instantaneous ("snapshot") measurements of leaf photosynthesis are also described, using carefully pre-set conditions within the leaf cuvette. Representative results are shown for Phaseolus vulgaris L. Important aspects of the procedure's experimental design, assumptions made in the analysis, and limitations of this approach are analysed.     

Effects of human pregnancy and aerobic conditioning on alveolar gas exchange during exercise

This study examined the effects of aerobic conditioning during the second and third trimesters of human pregnancy on ventilatory responses to graded cycling. Previously sedentary pregnant women were assigned randomly to an exercise group (n = 14) or a nonexercising control group (n = 14). Data were collected at 15-17 weeks, 25-27 weeks and 34-36 weeks of pregnancy. Testing involved 20 W.min-1 increases in work rate to a heart rate of 170 beats.min-1 and (or) volitional fatigue. Breath-by-breath ventilatory and alveolar gas exchange measurements were compared at rest, a standard submaximal .VO2 and peak exercise. Within both groups, resting .V(E), .V(A), and V(T)/T(I) increased significantly with advancing gestation. Peak work rate, O2 pulse (.VO2/HR), .V(E), .V(A) respiratory rate, V(T)/T(I), .VO2, .VCO2, and the ventilatory threshold (T(vent)) were increased after physical conditioning. Chronic maternal exercise has no significant effect on pregnancy-induced changes in ventilation and (or) alveolar gas exchange at rest or during standard submaximal exercise. Training-induced increases in T(vent) and peak oxygen pulse support the efficacy of prenatal fitness programs to improve maternal work capacity.