The convective-diffusive problems of oxygen and carbon dioxide in human airway at normal respiratory status were studied theoretically in the present paper. The human airway was idealized as a bifurcated(two-branch) trachea tree, based on the understanding of the physiological structure of the human airway, and on Horsfield-Wanner optimization analysis about the trachea system status. It was assumed that the gases in the airway were incompressible, viscous fluid, due mainly to the characteristics of the low pressure drop and low rate of the gases within the human airway. One dimensional, non-steady convective-diffusive equations of oxygen and carbon dioxide were solved using Lax-Wendroff finite difference method, i.e., the so called three-legged finite difference method. The boundary conditions were set up according to the two different situations, respectively. The computational results showed the reasonable distributions of the concentration of oxygen and carbon dioxide in the human airway, respectively.
Bronchi ; physiology ; Carbon Dioxide ; metabolism ; Convection ; Diffusion ; Humans ; Models, Biological ; Oxygen ; metabolism ; Trachea ; physiology

The lungs are naturally irregular and asymmetrical organ in anatomy. The conducting bronchial trees in the lungs display complex self-similar structure. We have established the host mesh coordinates of the right lung on the basis of the anatomical data from the literature. A three-dimensional fractal model of the conducting airways was set up by calculating the coordinates of the mass centers of the divided blocks, searching the branch direction and determining branch lengths with the use of the drawing tool OpenGL. Specific data of the lengths at various grades, branching angles, and capillary diameters were obtained. As a result, the computed data were identical with those of the existing statistical data. The fractal covering dimensionality obtained in the computation of this model was 2.19, which is very close to the ideal dimensionality, 2.17, from the literature. The present model has laid the foundation for further research of the gas diffusion and transfer performance in the lungs using the fractal concept, and furthermore, it helps to save the computer memories and fastening the graphic transfer.
Algorithms ; Bronchi ; anatomy & histology ; Computer Simulation ; Humans ; Imaging, Three-Dimensional ; Models, Anatomic

Based on the principles of the sheet-flow model, oxygen transport in pulmonary capillaries was considered as a process in which oxygen first enters plasma through the respiratory membranes, and then combines with the Hbc. A novel mathematical model about oxygen transport in pulmonary capillaries was established according to the relationship of the oxygen concentration inside the red blood cells with the concentration of haemoglobin and the blood saturation, and according to the basic formula for the correlation between blood saturation and oxygen partial pressure. Furthermore, we adopted the Lax-Wendroff Finite Difference Method and obtained certain valuable results under different physiological states. It was well concluded that the established model could be used to provide useful data for medical researchers as well as doctors.
Biological Transport ; physiology ; Capillaries ; physiology ; Humans ; Models, Biological ; Oxygen ; blood ; Partial Pressure ; Pulmonary Alveoli ; blood supply ; Pulmonary Circulation ; physiology ; Pulmonary Gas Exchange

A three-element model of lumped parameter based on the statistic data of Weible's symmetric model and on the reference anatomic figures of the bronchial tree of the lungs has been proposed using the fluid network theory. It was assumed that the upper five or seven generations of the twenty-four generations of the respiratory airway are asymmetric, while the rest are symmetric. GEAR method was used to solve the ordinary differential equations. The pressure and flow rate distributions in different positions of the lungs during normal respiration and partial bronchial obstruction were compared, respectively. This model has great significance in finding out the air distribution in the human bronchial tree under various physiological and pathological conditions.
Airway Resistance ; Bronchi ; anatomy & histology ; pathology ; physiology ; Humans ; Models, Biological ; Respiration ; Respiratory Mechanics ; physiology