A first principles calculation of the oxygen uptake in the human pulmonary acinus at maximal exercise

Revisiting Airflow and Aerosol Transport Phenomena in the Deep Lungs with Microfluidics

The dynamics of respiratory airflows and the associated transport mechanisms of inhaled aerosols characteristic of the deep regions of the lungs are of broad interest in assessing both respiratory health risks and inhalation therapy outcomes. In the present review, we present a comprehensive discussion of our current understanding of airflow and aerosol transport phenomena that take place within the unique and complex anatomical environment of the deep lungs, characterized by submillimeter 3D alveolated airspaces and nominally slow resident airflows, known as low-Reynolds-number flows. We exemplify the advances brought forward by experimental efforts, in conjunction with numerical simulations, to revisit past mechanistic theories of respiratory airflow and particle transport in the distal acinar regions. Most significantly, we highlight how microfluidic-based platforms spanning the past decade have accelerated opportunities to deliver anatomically inspired in vitro solutions that capture with sufficient realism and accuracy the leading mechanisms governing both respiratory airflow and aerosol transport at true scale. Despite ongoing challenges and limitations with microfabrication techniques, the efforts witnessed in recent years have provided previously unattainable in vitro quantifications on the local transport properties in the deep pulmonary acinar airways. These may ultimately provide new opportunities to explore improved strategies of inhaled drug delivery to the deep acinar regions by investigating further the mechanistic interactions between airborne particulate carriers and respiratory airflows at the pulmonary microscales.

Modeling of Gas Exchange in the Lungs

This overview presents the recent progress in our understanding of gas transfer by the lungs during the respiratory cycle and during breath holding. Different phenomena intervene in gas transfer, convection and diffusion in the gas, dissolution, diffusion across the alveolar-capillary membrane, diffusion across blood plasma, and finally diffusion and reaction with hemoglobin inside blood cells. The different gases, O₂ , CO, and NO, have very different reaction times with hemoglobin ranging from a few microseconds to tens of milliseconds. This is leading to different outcomes. For O₂ , the solutions to the coupled nonlinear gas and blood equations are obtained at the acinus level. They include the fact that the acinar internal ventilation is strongly heterogeneous due to the arborescent structure. Also, in the dynamic calculation, one takes care of the delay between the start of inhalation and arrival of fresh air in the acinus. This "dead" time is the dynamic equivalent of the dead space ventilation. The question of the dependence of Vo₂ on ventilation and perfusion takes a different form. The results show that Vo₂ is not only a function of the ventilation/perfusion ratio but also depends on the variables: acinar ventilation VE_ac and perfusion Q_ac . The ratio VE_ac /Q_ac roughly determines arterial O₂ saturation and arterial and alveolar O₂ partial pressure. The classic Roughton-Forster interpretation of DLCO (separation between independent membrane and blood resistance) was a mathematical conjecture. It was shown recently that this conjecture was violated. This article presents an alternative interpretation that uses time concepts instead of resistance. © 2021 American Physiological Society. Compr Physiol 11:1289-1314, 2021.

Lung Structure and the Intrinsic Challenges of Gas Exchange

Structural and functional complexities of the mammalian lung evolved to meet a unique set of challenges, namely, the provision of efficient delivery of inspired air to all lung units within a confined thoracic space, to build a large gas exchange surface associated with minimal barrier thickness and a microvascular network to accommodate the entire right ventricular cardiac output while withstanding cyclic mechanical stresses that increase several folds from rest to exercise. Intricate regulatory mechanisms at every level ensure that the dynamic capacities of ventilation, perfusion, diffusion, and chemical binding to hemoglobin are commensurate with usual metabolic demands and periodic extreme needs for activity and survival. This article reviews the structural design of mammalian and human lung, its functional challenges, limitations, and potential for adaptation. We discuss (i) the evolutionary origin of alveolar lungs and its advantages and compromises, (ii) structural determinants of alveolar gas exchange, including architecture of conducting bronchovascular trees that converge in gas exchange units, (iii) the challenges of matching ventilation, perfusion, and diffusion and tissue-erythrocyte and thoracopulmonary interactions. The notion of erythrocytes as an integral component of the gas exchanger is emphasized. We further discuss the signals, sources, and limits of structural plasticity of the lung in alveolar hypoxia and following a loss of lung units, and the promise and caveats of interventions aimed at augmenting endogenous adaptive responses. Our objective is to understand how individual components are matched at multiple levels to optimize organ function in the face of physiological demands or pathological constraints.

Time-based understanding of DLCO and DLNO

Capture of CO and NO by blood requires molecules to travel by diffusion from alveolar gas to haemoglobin molecules inside RBCs and then to react. One can attach to these processes two times, a time for diffusion and a time for reaction. This reaction time is known from chemical kinetics and, therefore, constitutes a unique physical clock. This paper presents a time-based bottom-up theory that yields a simple expression for DLCO and DLNO that produces quantitative predictions which compare successfully with experiments. Specifically, when this new approach is applied to DLCO experiments, it can be used to determine the value of the characteristic diffusion time, and the value of capillary volume (Vc). The new theory also provides a simple explanation for still unexplained correlations such as the observed proportionality between the so-called membrane conductance DM and Vc of Roughton and Forster's interpretation. This new theory indicates that DLCO should be proportional to the haematocrit as found in several experiments.

Unsteady diffusional screening in 3D pulmonary acinar structures: from infancy to adulthood

Diffusional screening in the lungs is a physical phenomenon where the specific topological arrangement of alveolated airways of the respiratory region leads to a depletion, or 'screening', of oxygen molecules with increasing acinar generation. Here, we revisit diffusional screening phenomena in anatomically-inspired pulmonary acinar models under realistic breathing maneuvers. By modelling 3D bifurcating alveolated airways capturing both convection and diffusion, unsteady oxygen transport is investigated under cyclic breathing motion. To evaluate screening characteristics in the developing lungs during growth, four representative stages of lung development were chosen (i.e. 3 months, 1 year and 9 months, 3 years and adulthood) that capture distinct morphological acinar changes spanning alveolarization phases to isotropic alveolar growth. Numerical simulations unveil the dramatic changes in O2 transport occurring during lung development, where young infants exhibit highest acinar efficiencies that rapidly converge with age to predictions at adulthood. With increased ventilatory effort, transient dynamics of oxygen transport is fundamentally altered compared to tidal breathing and emphasizes the augmented role of convection. Resolving the complex convective acinar flow patterns in 3D acinar trees allows for the first time a spatially-localized and time-resolved characterization of oxygen transport in the pulmonary acinus, from infancy to adulthood.

Pharmacokinetic analysis of the chronic administration of the inert gases Xe and Ar using a physiological based model

Background

New gas therapies using inert gases such as xenon and argon are being studied, which would require chronically administered repeating doses. The pharmacokinetics of this type of administration has not been addressed in the literature.

Methods

A physiologically based pharmacokinetics (PBPK) model for humans, pigs, mice, and rats has been developed to investigate the unique aspects of the chronic administration of inert gas therapies. The absorption, distribution, metabolism and excretion (ADME) models are as follows: absorption in all compartments is assumed to be perfusion limited, no metabolism of the gases occurs, and excretion is only the reverse process of absorption through the lungs and exhaled.

Results

The model has shown that there can be a residual dose, equivalent to constant administration, for chronic repeated dosing of xenon in humans. However, this is not necessarily the case for small animals used in pre-clinical studies.

Conclusions

The use of standard pharmacokinetics parameters such as area under the curve would be more appropriate to assess the delivered dose of chronic gas administration than the gas concentration in the delivery system that is typically reported in the scientific literature because species and gas differences can result in very different delivered doses.

Analytical theory of oxygen transport in the human placenta

We propose an analytical approach to solving the diffusion-convection equations governing oxygen transport in the human placenta. We show that only two geometrical characteristics of a placental cross-section, villi density and the effective villi radius, are needed to predict fetal oxygen uptake. We also identify two combinations of physiological parameters that determine oxygen uptake in a given placenta: (i) the maximal oxygen inflow of a placentone if there were no tissue blocking the flow and (ii) the ratio of transit time of maternal blood through the intervillous space to oxygen extraction time. We derive analytical formulas for fast and simple calculation of oxygen uptake and provide two diagrams of efficiency of oxygen transport in an arbitrary placental cross-section. We finally show that artificial perfusion experiments with no-hemoglobin blood tend to give a two-orders-of-magnitude underestimation of the in vivo oxygen uptake and that the optimal geometry for such setup alters significantly. The theory allows one to adjust the results of artificial placenta perfusion experiments to account for oxygen-hemoglobin dissociation. Combined with image analysis techniques, the presented model can give an easy-to-use tool for prediction of the human placenta efficiency.

A new approach to the dynamics of oxygen capture by the human lung

Oxygen capture in the lung results from the intimate dynamic interaction between the space- and time-dependent oxygen partial pressure that results from convection-diffusion and oxygen extraction from the alveolar gas and the space and time dependence of oxygen trapping by the red blood cells flowing in the capillaries. The complexity of the problem can, however, be reduced due to the fact that the systems obey different time scales: seconds for the gas phase transport and tenths of seconds for oxygen trapping by blood. This results first from a dynamical study of gas transport in a moving acinus and second from a new theory of dynamic oxygen trapping in the capillaries. The global solution can be found only through a self-consistent iterative approach linking the two systems. This has been accomplished and used to quantify oxygen capture in various situations: at rest, during exercise, ventilation-perfusion mismatching, high altitude and pulmonary edema.

Theoretical analysis of the determinants of lung oxygen diffusing capacity

The process of pulmonary oxygen uptake is analyzed to obtain an explicit equation for lung oxygen diffusing capacity in terms of hematocrit and pulmonary capillary diameter. An axisymmetric model with discrete cylindrical erythrocytes is used to represent radial diffusion of oxygen from alveoli through the alveolar-capillary membrane into pulmonary capillaries, through the plasma, and into erythrocytes. Analysis of unsteady diffusion due to the passage of the erythrocytes shows that transport of oxygen through the alveolar-capillary membrane occurs mainly in the regions adjacent to erythrocytes, and that oxygen transport through regions adjacent to plasma gaps can be neglected. The model leads to an explicit formula for diffusing capacity as a function of geometric and oxygen transport parameters. For normal hematocrit and a capillary diameter of 6.75 μm, the predicted diffusing capacity is 102 ml O₂ min⁻¹ mmHg⁻¹. This value is 30-40% lower than values estimated previously by the morphometric method, which considers the total membrane area and the specific uptake rate of erythrocytes. Diffusing capacity is shown to increase with increasing hematocrit and decrease with increasing capillary diameter and increasing thickness of the membrane. Simulations of pulmonary oxygen uptake in humans under conditions of exercise or hypoxia based show closer agreement with experimental data than previous models, but still overestimate oxygen uptake. The remaining discrepancy may reflect effects of heterogeneity of perfusion and ventilation in the lung.

Variability in uptake efficiency for pulsed versus constant concentration delivery of inhaled nitric oxide

Background

Nitric oxide (NO) is currently administered using devices that maintain constant inspired NO concentrations. Alternatively, devices that deliver a pulse of NO during the early phase of inspiration may have use in optimizing NO dosing efficiency and in extending application of NO to long-term use by ambulatory, spontaneously breathing patients. The extent to which the amount of NO delivered for a given pulse sequence determines alveolar concentrations and uptake, and the extent to which this relationship varies with breathing pattern, physiological, and pathophysiological parameters, warrants investigation.

Methods

A mathematical model was used to analyze inhaled nitric oxide (NO) transport through the conducting airways, and to predict uptake from the alveolar region of the lung. Pulsed delivery was compared with delivery of a constant concentration of NO in the inhaled gas.

Results

Pulsed delivery was predicted to offer significant improvement in uptake efficiency compared with constant concentration delivery. Uptake from the alveolar region depended on pulse timing, tidal volume, respiratory rate, lung and dead space volume, and the diffusing capacity of the lung for NO (D_LNO). It was predicted that variation in uptake efficiency with breathing pattern can be limited using a pulse time of less than 100 ms, with a delay of less than 50 ms between the onset of inhalation and pulse delivery. Nonlinear variation in uptake efficiency with D_LNO was predicted, with uptake efficiency falling off sharply as D_LNO decreased below ~50-60 ml/min/mm Hg. Gas mixing in the conducting airways played an important role in determining uptake, such that consideration of bulk convection alone would lead to errors in assessing efficiency of pulsed delivery systems.

Conclusions

Pulsed NO delivery improves uptake efficiency compared with constant concentration delivery. Optimization of pulse timing is critical in limiting intra- and inter-subject variability in dosing.