MATHEMATICAL MODELING OF RESPIRATORY MECHANICS

Abstract

The respiratory system as a mechanical system, has studied by engineers, physicists, and mathematicians for decades. Indeed, the field of respiratory mechanics is now mature and highly quantitative making wide use of sophisticated mathematical and computational methods. Accordingly, methods of applied mathematics, including basic calculus and differential equations have been used as a tool to solve the problem related to respiratory mechanics. 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, 10, 52, 54]. Yet, no recognized unifying hypothesis presently exists. Much of the uncertainty exists 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 also necessary 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 close enough to exchange oxygen and carbon dioxide. The mechanical properties of the lungs therefore ii conclude how muscular pressures, airway flows, and lung volumes are connected. The field of respiratory mechanics is concerned with the study of these properties. Present thesis entitled Mathematical Modeling of Respiratory Mechanics deals with different types of Mathematical models of blood partial pressure, asthmatic bifurcation and particle deposition in the human nasal cavity, vocal fold modeling, lung ventilation modeling. 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 Respiratory 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 have considered mathematical model letting for blood partial pressure in arterial and venous system. In this model two simultaneous differential equation used, arterial system and venous system are depending upon the heart rate and ventilation. Heart rate and ventilation play a measure role to control blood partial pressure. The study shows numerical results for blood partial pressure of arterial system and venous system. The numerical results of the model presented for three cases, named walking, jogging and running fast. In Chapter 3, we consider the human nasal cavity particle deposition based on simple mechanical principles, to build a mathematical model of fluid motion as well as particle motion. The aim of this work is to study the velocity of fluid as well as velocity of particle in the human nasal cavity. We have calculated skin friction on the wall numerically.We have also included the number density effect on skin friction. This work gives the details of airflow iii particle dynamics in human nasal cavity for normal breathing. Lower value of skin friction shows the size of the nature of suspension. In Chapter 4, we have studied the asthmatic lung at inlet and outlet positions. we have calculated the velocity profile at different generations. Symmetric airways bifurcations corresponding to generation 12-23 of Weibles were investigated through numerical simulation. The effect of size of the lumen area and the number of folds on particle deposition and the pressure drop were investigated In Chapter 5, we studied the mathematical lung ventilation model for radioactive tidal breathing. We have taken Radon gas for this study because Radon gas is present in the atmosphere in small quantity. Radon particle goes in our body with the oxygen when we inhale or breath. These particles are very dangerous to our body, and may cause lung cancer. In this study the lung counts is find to be very high with respect to time when we inhale normally. Otherwise it decreases and tends to zero as we exhale. In this work we are getting different -different types of parameters like regional lung ventilation and volume parameters. In Chapter 6, we have study a mathematical model of vocal fold. Since our body is not pure elastic, but hyper elastic, a hyper elasticity approach is included in this work. The present work concerns with strain energy function and extension ratios. We have calculated strain energy function in terms of extension ratio.