Modeling diffusion limitation of gas exchange in lungs containing perfluorocarbon

We reportedchanges in alveolar-arterial PO₂ gradient,ventilation-perfusion heterogeneity, and arterial-alveolarPCO₂ gradient during partial liquid ventilation(PLV) in healthy piglets (E. A. Mates, P. Tarczy-Hornoch, J. Hildebrandt, J. C. Jackson, and M. P. Hlastala. In: OxygenTransport to Tissue XVII, edited by C. Ince. New York: Plenum,1996, vol. 388, p. 585-597). Here we develop two mathematicalmodels to predict transient and steady-state (SS) gas exchangeconditions during PLV and to estimate the contribution of diffusionlimitation to SS arterial-alveolar differences. In the simplest model,perfluorocarbon is represented as a uniform flat stirred layer and, ina more complex model, as an unstirred spherical layer in a ventilatedterminal alveolar sac. Time-dependent solutions of both models showthat SS is established for various inert and respiratory gases within5-150 s. In fluid-filled unventilated terminal units, all times toSS increased sometimes by hours, e.g., SF₆ exceeded 4 h. SSsolutions for the ventilated spherical model predicted minorend-capillary disequilibrium of inert gases and significantdisequilibrium of respiratory gases, which could explain a largeportion of the arterial-alveolar PCO₂ gradient measured during PLV (14). We conclude that, during PLV, diffusion gradients for gases are generally small, except for CO₂.

     

Simplified models for gas exchange in the human lungs

This paper presents a hierarchy of models with increasing complexity for gas exchange in the human lungs. The models span from a single compartment, inflexible lung to a single compartment, flexible lung with pulmonary gas exchange. It is shown how the models are related to well-known models in the literature. A long-term purpose of this work is to study nonlinear phenomena seen in the cardio-respiratory system (for example, synchronization between ventilation rate and heart rate, and Cheyne-Stokes respiration). The models developed in this paper can be regarded as the controlled system (plant) and provide a mathematical framework to link between "molecular-level", and "systems-level" models. It is shown how changes in molecular level affect the alveolar partial pressure. Two assumptions that have previously been made are re-examined: (1) the hidden assumption that the air flow through the mouth is equal to the rate of volume change in the lungs, and, (2) the assumption that the process of oxygen binding to hemoglobin is near equilibrium. Conditions under which these assumptions are valid are studied. All the parameters in the models, except two, are physiologically realistic. Numerical results are consistent with published experimental observations.     

Regional volume changes in canine lungs suspended in air

The purpose of this study was to determine the effect of the absence of a pleural pressure gradient (simulating the presumed condition found in microgravity) upon regional expansion of the lung. We attempted to produce a uniform pressure over the surface of the lung by suspending excised lungs in air. Such studies should help determine whether or not absence of a pleural pressure gradient leads to uniform ventilation. A preparation in which there is no pleural pressure gradient should also be useful in studying non-gravitational effects on ventilation distribution.     

Impact of axial diffusion on nitric oxide exchange in the lungs.

Nitric oxide (NO) appears in the exhaled breath and is a potentially important clinical marker. The accepted model of NO gas exchange includes two compartments, representing the airway and alveolar region of the lungs, but neglects axial diffusion. We incorporated axial diffusion into a one-dimensional trumpet model of the lungs to assess the impact on NO exchange dynamics, particularly the impact on the estimation of flow-independent NO exchange parameters such as the airway diffusing capacity and the maximum flux of NO in the airways. Axial diffusion reduces exhaled NO concentrations because of diffusion of NO from the airways to the alveolar region of the lungs. The magnitude is inversely related to exhalation flow rate. To simulate experimental data from two different breathing maneuvers, NO airway diffusing capacity and maximum flux of NO in the airways needed to be increased approximately fourfold. These results depend strongly on the assumption of a significant production of NO in the small airways. We conclude that axial diffusion may decrease exhaled NO levels; however, more advanced knowledge of the longitudinal distribution of NO production and diffusion is needed to develop a complete understanding of the impact of axial diffusion.     

Caterpillars have evolved lungs for hemocyte gas exchange

Since insect blood usually lacks oxygen-carrying pigments it has always been assumed that respiratory needs are met by diffusion in the gas-filled lumen of their tracheal systems. Outside air enters the tracheal system through segmentally arranged spiracles, diffuses along tubes of cuticle secreted by tracheal epithelia and then to tissues through tracheoles, thin walled cuticle tubes that penetrate between cells. The only recognized exceptions have been blood cells (hemocytes), which are not tracheated because they float in the hemolymph. In caterpillars, anoxia has an effect on the structure of the hemocytes and causes them to be released from tissues and to accumulate on thin walled tracheal tufts near the 8th (last) pair of abdominal spiracles. Residence in the tufts restores normal structure. Hemocytes also adhere to thin-walled tracheae in the tokus compartment at the tip of the abdomen. The specialized tracheal system of the 8th segment and tokus may therefore be a lung for hemocytes, a novel concept in insect physiology. Thus, although as a rule insect tracheae go to tissues, this work shows that hemocytes go to tracheae.     

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.     

Quantitative aspects of oxygen and carbon dioxide exchange through the lungs in Ocypode ceratophthalmus (Crustacea: Decapoda) during rest and exercise in water and air

Ghost crabs Ocypode ceratophthalmus were exercised in air and water to measure CO₂ and O₂ exchange rates using the method of instantaneous measurements of oxygen consumption rate (MO₂) where applicable. Average heart rate increased from 100 to nearly 400 pulses per minute after five minutes of exercise on a treadmill at a run rate of 0.133 m s^?1. It took less than a minute for oxygen taken up through the lung epithelium from the air inside the branchial cavity to reach the maximal oxygen consumption rate of 26.1 mmol O₂ kg^?1 h^?1. Resting MO₂ was 4.06 mmol O₂ kg^?1 h^?1 in air, but decreased to 3.37 mmol O₂ kg^?1 h^?1 in seawater. Radioactive CO₂ from injected l-lactate is released linearly by the lung. The percent accumulated 14-CO₂ in exhaled air, plotted against time, intersects zero time on the x -axis, indicating rapid gas exchange at the lung surface. The P ₅₀ values for native haemocyanin of 4.89 mm Hg before exercise, and 8.99 mm Hg after exercise, are typical of a high-affinity haemocyanin usually associated with terrestrial crabs. The current notion that Ocypode ceratophthalmus drown when submerged in seawater was not substantiated by our experiments. MO₂ in seawater increased from 3.37 mmol O₂ kg^?1 h^?1 for resting crabs to 5.72 mmol O₂ kg^?1 h^?1 during exercise. When submerged by wave-seawater in the natural environment and during exercise in respirometer-seawater O. ceratophthalmus do not swim but, having a specific density of 1.044, float nearly weightless with a minimum of body movements.