Fundamentals Of Alveolar Gas Diffusion: Mathematical Modeling And Visualization

Anovel mathematical model, based on transport through porous media, for simulating numerically the spatial and temporal gas-diffusion process within the alveolar region of the lung is discussed. The model depends on a representative physical property of the alveolar region termed the effective diffusivity, a function of the diffusivity, solubility, morphology and interface topography of each alveolar constituent. Unfortunately, the direct determination of the effective diffusivity of the alveolar region is impractical because of the difficulty in describing the internal geometry of each alveolar constituent. However, the transient solution of the macroscopic model can be used in conjunction with the lung-diffusing capacity (measured in a clinical setting) to determine the effective diffusivity of the alveolar region. With the effective diffusivity known, the three-dimensional effects of red blood-cell distribution on the lung-diffusing capacity can be predicted via numerical simulations. The results, obtained for normal (random), uniform, center-cluster, cornercluster, and several chain-like distributions, reveal a strong relationship between the type of red-cell distribution and the lung-diffusing capacity. The model developed has been used in order to study the impact of microscopic particles whose presence in the alveolar region may affect the lung-diffusing capacity. Clusters of particles were distributed according to the Poisson distribution with a different distribution parameter (the average number of particles per cluster). www.witpress. com, ISSN 1755-8336 (on-line) WIT Transactions on State of the Art in Science and Engineering, Vol 24, © 2006 WIT Press doi:10.2495/978-1-85312-944-5/02 32 Human Respiration Furthermore, for each of those distributions, the effect of particle concentration on the lung-diffusing capacity was investigated. Based on the results obtained by means of numerically solving the transient equations that mimic the single-breath test, volume visualization has been used for rendering the time-dependent model of the respiration process. Several video files for different RBC distributions have been created for this presentation. The streaming video version of them is available on-line at http://www.ntu. edu.sg/home/assourin/ Scivi.htm. 1 Human respiratory system Energy, necessary for the cells reproduction, growth, and survival, is produced in the course of biochemical reactions, otherwise known as metabolic activity. A typical example of such a reaction is the biochemical reaction of cellular respiration C6H12O6 (Glucose) + 6O2 (Oxygen) → 6CO2 (Carbon dioxide) + 6H2O (Water) + Energy As we can see, oxygen is an essential component in order for cellular respiration to proceed. On the other hand, one of the byproducts of the reaction is carbon dioxide – a highly toxic gas. Thus, in order for our organism to survive, oxygen must be delivered to each cell, whereas carbon dioxide must be removed. The medium that delivers oxygen to every cell in the human body is blood, and it is blood that carries with it carbon dioxide, produced in the course of cellular respiration. The respiratory system is exactly where the blood becomes enriched by oxygen and carbon dioxide (together with other toxic gases) gets transferred from the blood to the atmosphere. The main function of the human respiratory system, therefore, is to provide the blood with the amount of oxygen sufficient to conduct the cellular combustion process (respiration) together with removing toxic gases (mainly CO2) from the blood. Humans have two lungs, right and left, divided into three and two parts (lobes), respectively. The right lung is divided into superior, middle, and inferior lobes. The left lung, divided into superior and inferior lobes, is generally a little smaller than the right lung because it shares part of the thoracic cavity with the heart (cardiac notch). A schematic of the human respiratory system is presented in Fig. 1. The lungs are supported in the human body by the back-column, the back muscles, the muscles of the nape of the neck, and the diaphragm. Protected by the rib-cage, the lungs are surrounded (separated from the rest of the body) by a double-membrane called pleura. The flexible outer membrane of the pleura follows the expansion and contraction of the thoracic cavity during respiration. The inner membrane is connected to the outer membrane through an interstitial liquid. Negative pressure within the interstitial liquid keeps the lungs from collapsing. The respiratory process of inhaling (and exhaling) air is controlled by a voluntary control center in the frontal cortex of the brain. Involuntary control takes www.witpress. com, ISSN 1755-8336 (on-line) WIT Transactions on State of the Art in Science and Engineering, Vol 24, © 2006 WIT Press Fundamentals of Alveolar Gas Diffusion 33 inferior vena cava small bronchus terminal bronchiole pulmonary venule pulmonary artery trachea left main bronchus larynx Lungs