Is the lung an optimal gas exchanger? (original) (raw)
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Mathematics and Biosciences in Interaction, 2005
We investigate oxygen transport to and across alveolar membranes in the human lung, the last step in the chain of events that takes oxygen through the bronchial airways to the peripheral, acinar airways. This step occurs by diffusion. We carry out analytic and numerical computations of the oxygen current for fractal, space-filling models of the acinus, based on morphological data of the acinus and appropriate values for the transport constants, without adjustable parameters. The computations address the question whether incoming oxygen reaches the entire available membrane surface (reaction-limited, unscreened oxygen current), a large part of the surface (mixed reaction/diffusion-limited, partly screened current), or only the surface near the entrance of the acinus (diffusion-limited, completely screened current). The analytic treatment identifies the three cases as sharply delineated screening regimes and finds that the lung operates in the partial-screening regime, close to the transition to no screening, for respiration at rest; and in the no-screening regime for respiration at exercise. The resulting currents agree well with experimental values. We test the analytic treatment by comparing it with numerical results for two-dimensional acinus models and find very good agreement. The results provide quantitative support for the conclusion, obtained in other work, that the space-filling fractal architecture of the lung is optimal with respect to active membrane surface area and minimum power dissipation. At the level of the bronchial tree, we show that the space-filling architecture provides optimal slowing down of the airflow from convection in the bronchial airways to diffusion in the acinar airways.
PLoS Computational Biology, 2010
The space-filling fractal network in the human lung creates a remarkable distribution system for gas exchange. Landmark studies have illuminated how the fractal network guarantees minimum energy dissipation, slows air down with minimum hardware, maximizes the gas-exchange surface area, and creates respiratory flexibility between rest and exercise. In this paper, we investigate how the fractal architecture affects oxygen transport and exchange under varying physiological conditions, with respect to performance metrics not previously studied. We present a renormalization treatment of the diffusion-reaction equation which describes how oxygen concentrations drop in the airways as oxygen crosses the alveolar membrane system. The treatment predicts oxygen currents across the lung at different levels of exercise which agree with measured values within a few percent. The results exhibit wide-ranging adaptation to changing process parameters, including maximum oxygen uptake rate at minimum alveolar membrane permeability, the ability to rapidly switch from a low oxygen uptake rate at rest to high rates at exercise, and the ability to maintain a constant oxygen uptake rate in the event of a change in permeability or surface area. We show that alternative, less than space-filling architectures perform sub-optimally and that optimal performance of the space-filling architecture results from a competition between underexploration and overexploration of the surface by oxygen molecules.
Entropy Production and the Pressure-Volume Curve of the Lung
Frontiers in physiology, 2016
We investigate analytically the production of entropy during a breathing cycle in healthy and diseased lungs. First, we calculate entropy production in healthy lungs by applying the laws of thermodynamics to the well-known transpulmonary pressure-volume (P-V) curves of the lung under the assumption that lung tissue behaves as an entropic spring similar to rubber. The bulk modulus, B, of the lung is also derived from these calculations. Second, we extend this approach to elastic recoil disorders of the lung such as occur in pulmonary fibrosis and emphysema. These diseases are characterized by particular alterations in the P-V relationship. For example, in fibrotic lungs B increases monotonically with disease progression, while in emphysema the opposite occurs. These diseases can thus be mimicked simply by making appropriate adjustments to the parameters of the P-V curve. Using Clausius's formalism, we show that entropy production, ΔS, is related to the hysteresis area, ΔA, enclos...
Diffusion of gases into the lung: How physics can help to understand physiology
Pramana, 2008
In the human lung, the gas transfer between air and blood is achieved in terminal units that are called 'acini'. Whereas convection is still the predominant transport phenomenon at the acinus entrance, most of the acinar surface is in fact accessed by diffusion. The transition between convection and diffusion, and thus the size of the diffusion unit, depends on the air velocity at the acinus entrance. In this paper, we present a gas transport model which takes into account both the diffusion into the acinus and the diffusion across the alveolar membrane. It is shown that the physiological sizes of the diffusion unit in the lung, at rest or at exercise, can be explained by physical arguments. In that sense, diffusion is the 'dimensioning criterion' of the lung at the acinar level. This approach shows that, due to diffusional screening at inspiration and at rest, there exists a permanent spatial inhomogeneity of oxygen and carbon dioxide partial pressure which reduces the effective surface efficiency of the human acinus to a value of only 30 to 40%. This model casts a new light on the properties of this physiological transport system. It permits in particular to understand how several diseases among which pulmonary edema may remain asymptomatic in their early stages.
Computational Analyses of Airway Flow and Lung Tissue Dynamics
Image-Based Computational Modeling of the Human Circulatory and Pulmonary Systems, 2010
The function of the mammalian respiratory system is the facilitation the transfer of gas exchange between the organism's environment and its internal transport medium, the blood. Evolutionary processes have optimized the anatomic structure of the lung as a tree-like branching network of airways terminating in thinwalled elastic ducts and alveoli, where this gas exchange occurs. Both dissipative and elastic properties of the respiratory system contribute to its unique static and dynamic mechanical behavior. In this chapter, we will explore the various structural and functional relationships of the respiratory system, and review several computational and modeling analyses that provide insight into the pathophysiology of common respiratory diseases. Particular emphasis is placed on studies that utilize imaging to help understand and/or validate the distributed regional nature of lung function.
A revised model of gas transport in human lungs
Applied Mathematical Modelling, 1979
A critical reappraisal is made of the boundary conditions assumed in contemporary models of gas transport in the human lungs. It is demonstrated that the previously assumed zero concentration gradient at the alveolar wall does not guarantee zero flux for an insoluble tracer gas at this point and, more importantly, causes an unrealistically rapid equilibration of gaseous concentrations to occur. In view of these major shortcomings, a revised set of boundary conditions are proposed which are shown to yield results in close agreement with experimental findings.
Open Access Animal Physiology, 2014
Acquisition of molecular oxygen (O 2 ) from the external fluid media (water and air) and the discharge of carbon dioxide (CO 2 ) into the same milieu is the primary role of respiration. The functional designs of gas exchangers have been considerably determined by the laws of physics which govern the properties and the flux of gases and the physicochemical properties of the respiratory fluid media (water or air and blood). Although the morphologies of gas exchangers differ greatly, certain shared structural and functional features exist. For example, in all cases, the transfer of O 2 and CO 2 across the water/air-blood (tissue) barriers occurs entirely by passive diffusion along concentration gradients. In the multicellular organisms, gas exchangers have developed either by evagination or invagination. The arrangement, shape, and geometries of the airways and the blood vessels determine the transport and exposure of the respiratory media and, consequently, gas exchange. The thickness of the water/air-blood (tissue) barrier, the respiratory surface area, and volume of pulmonary capillary blood are the foremost structural parameters which determine the diffusing capacity of a gas exchanger for O 2 . In fish, stratified design of the gills and internal subdivision of the lungs increase the respiratory surface area: the same adaptive property is realized by different means. A surface active phospholipid substance (surfactant) lines the respiratory surface. Adaptive specializations of gas exchangers have developed to meet individual survival needs.
A novel modelling approach to energy transport in a respiratory system
International journal for numerical methods in biomedical engineering, 2016
In this paper, energy transport in a respiratory tract is modelled using the finite element method for the first time. The upper and lower respiratory tracts are approximated as a 1-dimensional domain with varying cross-sectional and surface areas, and the radial heat conduction in the tissue is approximated using the 1-dimensional cylindrical coordinate system. The governing equations are solved using 1-dimensional linear finite elements with convective and evaporative boundary conditions on the wall. The results obtained for the exhalation temperature of the respiratory system have been compared with the available animal experiments. The study of a full breathing cycle indicates that evaporation is the main mode of heat transfer, and convection plays almost negligible role in the energy transport. This is in-line with the results obtained from animal experiments.