NUMERICAL STUDY OF AIRFLOW, DUST PARTICLES TRANSPORT AND DEPOSITION IN HUMAN AIRWAYS

Abstract

The human respiratory system consists of a set of organs to take in oxygen from the environment and remove carbon dioxide from the blood through a combination of breathing and gas exchange processes. Like other fluid flows, the airflow in the respiratory tract is governed by mass, momentum and energy conservation laws which are expressed by nonlinear partial differential equations. To understand the airflow characteristics in the respiratory tract, solutions of the governing equations are required. Complete analytic solutions are not currently available for these equations. Because of complex structure of airways and flow conditions, numerical simulations of the airflow have been carried out in physical models of airways involving small subregions of the respiratory tract. The two major numerical discretization techniques being used are finite volume and finite element methods. Respiratory airflow varies in the same person under different conditions such as type of activity (rest, sleep, exercise), environmental conditions (temperature, humidity, altitude, barometric pressure), age (infancy, childhood, adolescence, adulthood), pathological conditions (chronic obstructive pulmonary disease, asthma), medication and drugs. These variations occur due to the fact that such conditions cause change in breathing parameters or dimensions of airways. It is essential to investigate breathing patterns and airflow characteristics in the airways for a better understanding of physiological changes occur in respiratory system under abovementioned conditions. When we breath in air, airborne particles present in surrounding enter our respiratory tract. Some of these inhaled particles are deposited on airway walls depending on their size, density, shape, surface properties and the respiratory airflow of an individual. Unfavourable conditions are formed on human respiratory system in response to the deposition of these particles. Deposition of harmful particles leads to many respiratory health risk and may damage the airways. On the other hand, pharmaceutical particle transport through airways is beneficial for treatment of respiratory diseases. Understanding the transport and deposition of air pollutant particles in human airways is important to reduce risk of respiratory disorders. In this work, numerical investigations of airflow were carried out in different subregions of human respiratory tract under different conditions. Finite volume method was used to solve the governing equations for airflow in simplified and CT-scan airway models. A finite volume based computational fluid dynamics (CFD) software ANSYS Fluent 19.0/18.2 was employed to perform numerical simulations. The simplified airway models in tracheobronchial airways were constructed by SOLIDWORKS 2013 software. In addition to airflow, motion and deposition distribution of dust particles were studied numerically in a subregion of the tracheobronchial tree. Eulerian–Lagrangian approach was implemented to simulate two-phase gas–particle flow. A mathematical model of alveolar-capillary oxygen gas exchange under normal condition was also developed. Fick’s Law and Henry’s Law were used to construct the model. Numerical solution of the model was obtained using MATLAB. The findings of this study quantitatively revealed changes in human respiratory airflow dynamics under different conditions. The type of physical activity we do, the altitude in which we live, our age and airways narrowing by asthma attack significantly affect our respiratory airflow dynamics. The possibility of inhaled dust particles to be deposited in human tracheobronchial airways is high. The oxygen gas partial pressure in a pulmonary capillary blood versus time is expressed mathematically during gas exchange process. This study can provide insights on airflow and particle deposition under different conditions at different subregions of the respiratory tract which can be used in the delivery of respiratory care. The whole work is presented in six chapters as follows. Chapter 1 provides introduction about human respiratory system, geometric modeling techniques of human respiratory airways and secondary flow in curved pipes. Preliminary mathematical concepts from literature in fluid flow equations, modeling of turbulent flows and boundary layer flow in circular pipes are presented. Finite volume discretization of transport and momentum equations is discussed. These mathematical concepts are used in numerical simulations of airflow in human airways in the study. Chapter 2 treats computer implementation of finite element and finite volume methods which are the most commonly used numerical methods in fluid dynamics. MATLAB codes for simulations of lid-driven cavity and channel (2D circular pipe) flows are developed to implement such methods. ANSYS Fluent 18.2 was also used to simulate the flows and results of the corresponding simulations were compared. From the simulations, it was observed that finite volume method has good memory usage and computing speed than the finite element method. Home-made codes help users to gain insights on how to use commercial codes successfully and more understandingly.Chapter 3 discusses numerical simulations of airflow in human airways under different conditions (i) in response to different levels of physical activity (ii) during exercise at sea level and high altitude (iii) in growth and development from infancy to adulthood and (iv) normal health and asthma conditions. Based on these, this chapter is divided into four sections. The airway geometric model(s), governing equations, boundary conditions and numerical methods used were presented in each section. In the first section, statistical data for spirometric measurement of subjects’ breathing parameters at rest and in response to different levels physical activity is provided. Each section presents numerical characterization of flow parameters (velocity, streamlines, pressure, wall shear stress) in the airway models for related and comparable conditions. The results quantitatively show that there are significant variations in breathing patterns, airflow characteristics or flow pattern under the different conditions considered in each section. Chapter 4 deals with numerical simulation of a two-phase flow of air and dust particles in a human tracheobronchial airway model. The result showed that the dust particles trajectories followed the airflow streamlines and the influence of secondary flow was high on the motion of the particles. The transport and deposition fraction of dust particles in the airway model were presented. It is found that if dust particles are inhaled by humans and pass the larynx, the possibility of deposition of the particles in upper part of tracheobronchial airways is high. The simulation results can provide awareness on deposition of dust particles and enhance prevention of their entry into the respiratory system. It can also contribute a convenient way on the location of deposition of particles of a given type in human respiratory tract to be used in respiratory care efforts. Chapter 5 provides a mathematical model of oxygen pulmonary gas exchange in human respiratory system. Numerical solution of the model obtained using Runge–Kutta algorithm (MATLAB R2015a function ode45) is presented. The oxygen gas partial pressure in a pulmonary capillary blood versus time is expressed mathematically. The diffusion of oxygen continues until the oxygen partial pressure equilibrium is attained between alveoli gas and the pulmonary capillary blood. The application of mathematics in describing biological processes may be appreciated. Chapter 6 gives summary and conclusions of the study. The limitations of the study are presented. Possible suggestions to alleviate the limitations are provided for better research works on human respiratory system in the future.