Some factors affecting pulmonary oxygen transport

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.

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.

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.

Multi-scale computational modelling in biology and physiology

Recent advances in biotechnology and the availability of ever more powerful computers have led to the formulation of increasingly complex models at all levels of biology. One of the main aims of systems biology is to couple these together to produce integrated models across multiple spatial scales and physical processes. In this review, we formulate a definition of multi-scale in terms of levels of biological organisation and describe the types of model that are found at each level. Key issues that arise in trying to formulate and solve multi-scale and multi-physics models are considered and examples of how these issues have been addressed are given for two of the more mature fields in computational biology: the molecular dynamics of ion channels and cardiac modelling. As even more complex models are developed over the coming few years, it will be necessary to develop new methods to model them (in particular in coupling across the interface between stochastic and deterministic processes) and new techniques will be required to compute their solutions efficiently on massively parallel computers. We outline how we envisage these developments occurring.