MATHEMATICAL MODELING OF LUNG MECHANICS

Abstract

Viewing the lungs as a mechanical system has intrigued engineers, physicists, and mathematicians for decades. Indeed, the field of lung mechanics is now mature and highly quantitative making wide use of sophisticated mathematical and computational methods. Accordingly, some familiarity with the methods of applied mathematics, including basic calculus and differential equations is assumed. Usual Hemodynamic is concerned with the measurement of pressure, flow and resistance. Current Biofluid mechanics, on the other hand, concerns itself with the local, time-dependent velocity and flow measurements in blood vessels, the lungs, the lymph and other body fluids together with the micro-circulation. Mechanical changes in lung structure throughout respiration, also known as lung mechanics, have been extensively discussed in the literature e.g. [2, 4, 7-9]. Yet, no recognized unifying hypothesis presently exists. Much of the uncertainty has been due to the difficulties in documenting alveolar and capillary mechanics, given the small size and large movement during breathing. Breathing is basically a mechanical procedure in which the muscles of the thorax and abdomen, working jointly, generate the pressures necessary to inflate the lung. These pressures must be enough to conquer the tendencies of the lung and chest wall tissues to recoil, a lot similar to blowing up a balloon. Pressure is cJnecessary to drive air along the pulmonary airways, a classification of branching conduits that starts at the mouth and ends deep in the lungs at the point where air and blood are S 1e+I Meto exchange oxygen and carbon dioxide. The mechanical properties of the lungs therefore conclude how muscular pressures, airway flows, and lung volumes are connected. The field of lung mechanics is concerned with the study of these properties. Present thesis entitled Mathematical Modeling of Lung Mechanics deals with different types of Mathematical models of gas exchange, blast wave propagation and particle deposition in the lungs. Numerical solutions are obtained using finite difference method. Results are displayed in the form of graphs in Origin (6.0) and behavior of fluid particles is visualized by images generated in MATLAB. The whole work is presented in the form of six chapters, as follows: Chapter 1 is introductory in nature. Besides stating the relevant definitions it gives an introduction to Lung Mechanics. It gives a brief account for human respiratory system, disease, air flow in capillaries and gas exchange process. At the end of the chapter, summary of the whole work embodied in the thesis is given. In Chapter 2, we use a mathematical model letting for both time and spatial distributions of partial pressure of an inert gas inside a body section. The axisymmetric model developed is a two-dimensional model as a function of time that incorporates convectivediffusion processes in a more fundamental manner by simultaneously solving the convectiondiffusion equation. This study existing numerical results for an unsteady partial pressure of inert gas by the generalized diffusion equations. The computational results of the model presented here predict that the partial pressure of inert gas in the lung tissue in asphyxia environment diminishes along the capillary axis from arteriolar end to venular end. In Chapter 3, we consider the lung as a porous permeable medium, based on simple mechanical principles, to build a mathematical model of wave propagation in the lung that is able of describing the main features of lung injury. The aim of this work is: (1) to include porosity in the linear model of blast wave propagation in the course of the lung tissue; and (2) to learn relationships between special physical wave parameters and one type of lung injury— edema. Criterion is that the curves for rigidly and freely supported lungs should overlap well. Eli Our results show that maximal tensile stress and strains can be considered as good criteria for edema formation. is In Chapter 4, the discussion concentrates on biofiltration technology whichpreferred as a pollutant removal technique due to its low investment and operating cost, high removal efficiency, reliable operating stability and low amount of secondary pollution. Here we consider an appropriate momentum equation in cylindrical polar coordinates with the entire body force because of the existence of porous media and particle number density. The purpose is to examine the effect of Darcy number and porosity on air removal efficiency to get a better act of biofilter. In Chapter 5, we studied the determination of effective area average concentration and dispersion coefficient associated with unsteady flow through a small-diameter tube where a solute goes through first order chemical reaction both inside the fluid and at the boundary. To understand the dispersion, the governing equations along by the reactive boundary conditions are explained numerically using the Finite Difference Method (FDM). The resultant equation explains how the dispersion coefficient is inclined by the first order chemical reaction. The effects of a variety of dimensionless parameters e.g., Da (the Damkohler number), a (phase partitioning number) and F (dimensionless absorption number) on dispersion are discussed. One of the results exposes that the dispersion coefficient may move toward its steady-state limit in a short period at a high value of Damkohler number (say Da > 10) and a little but non-zero value of absorption rate (say F 0.5). In Chapter 6, a mathematical model for nanoparticle deposition in the alveolar ducts of the human lung airways is proposed. The present work concerns with pulsatile flow of dusty fluid through a pipe consisting of axisymmetric distributed constrictions described by the wall radius R. The governing equations are explained numerically by using a finite lii lbsiraii difference scheme so as to get the velocities of fluid and dust particles. An extensive quantitative study is performed through numerical computations of the preferred quantities having physiological importance through their graphical representation so as to certify the applicability of the present model.