Mathematical Modeling of the Human Respiratory System

Abstract

This doctoral thesis addresses the development of novel algorithms and mathematical models to understand the role of respiratory physiology and morphology in order to diagnose the obstructive pulmonary diseases like asthma, chronic obstructive pulmonary disease (COPD) etc. A lumped parameter based approach is suggested to incorporate the mechanical phenomena associated with the governing equations in terms of an equivalent electrical circuit network. The advantage of this methodology is that by measuring the impedance of the electrical circuit, it is possible to apprise the airway obstruction level in the domain (respiratory system) contributed by various mechanical forces. Hence the developed algorithms are computationally more efficient in diagnosing the obstructive pulmonary diseases. In this doctoral thesis, both fluid flow and heat transfer mechanism are studied to under stand various physiological and patho-physiological phenomena. Forward based in-silico math ematical modeling is considered for the solution algorithm with the available clinical data as initial/boundary condition to understand the breathing mechanism. A solution approach for this algorithm is presented by by the transformation of governing equations using the lumped parame ter method describing the flow and transport mechanism fulfilling the initial/boundary conditions. The methodology has the advantage to predict and quantify the impact of local outfit over the input variables. The primary objective of the thesis is to develop a reliable and clinically relevant mathematical model of the respiratory system using lumped parameter method. The doctoral thesis consists of six chapters. Chapter 1 is the introductory section where all the preliminary information of research outputs are included to introduce the content of the thesis. Chapter 2 and 3 deal with the physiology of the human respiratory system, gas exchange and heat exchange respectively. The process of gas exchange is studied by mono-compartment based lumped parameter model while the heat exchange is studied by multi-compartment based f inite difference numerical scheme. Chapter 4 is related to the optimal morphology of the tree network for maximum flow access to provide a better understanding of the interconnected fluidics capable of providing a veritable representation of respiratory physiology. Chapter 5 is related to the quantification of the ventilation heterogeneity for the case of tidal breathing (low frequency) to predict the flow and transport throughput the system posing different difficulties. Chapter 6 is related to the derivation of lumped parameter model for the flow in elastic tube using the concept of fluid structure interaction (FSI) incorporating boundary layer and wave transmission theory, which can be further extended to study the asynchronous ventilation distribution at later stage. The overall aim of the present doctoral thesis is to develop algorithms and mathematical model to diagnose the obstructive pulmonary diseases and overcome several challenges at a level of computational modeling. However, at this stage the developed algorithm is only valid for the tidal breathing where assumption of rigid walls and unidirectional flow is physiologically valid. Furthermore, the work can be extended for the high frequency breathing to expedite the flow assess to the different parts of the respiratory system.