Lung mechanics: a systematic review of mechanical elasticity in lung parenchyma

Abstract

The lung functions as the main organ of the respiratory system. Its primary purposeis to facilitate the physiological operation of gas exchange. This process is commonly referred to as breathing. Mechanically, breathing may be described as the cyclic application of stresses acting against the surface of the lung. In order to offset theseforces, lung tissue displays prominent stress-bearing components. These components are a direct result of the mechanical elastic properties of the alveolar septa or the lung parenchyma. Various studies have been dedicated to understanding the macro-scopic behaviour of either the alveolar septa or layers of lung parenchyma. This has been achieved through analysis of pressure-volume (P-V) plots, numerical methods, as well as the development of constitutive equations or strain-energy functions. In lung mechanics, constitutive equations are capable of describing the elastic behaviour exhibited by lung parenchyma for example, through the relationship between the macroscopic stress and the macroscopic strain. These equations have been modelled under both the classical and non-classical theories of elasticity. The research conducted within lung mechanics around the elastic and resistive properties of the lung has allowed for scientists to develop new methods and equipment for evaluating and treating pulmonary pathogens. Thus, the aim of this research is to establish a descriptive and systematic review of mathematical studies conducted within the field of lung mechanics. This review shall be centered on the development and implementation of elasticity to the understanding of the mechanical functions and components of the lung. Elastic theory has had a significant contribution in these studies. Under the classical theory of elasticity, the lung is said to behave as an isotropic elastic continuum undergoing small deformations. However, the lung actually displays in-homogeneous behaviour associated with large deformations. Therefore, particular focus is placed on the assumptions and development of the various models, their subsequent mechanical influence on lung physiology, and more importantly, the development of constitutive equations through the classical and non-classical theory ofelasticity. Note that airway resistance is not considered in this dissertation. The primary focus is on nonlinear elastic theory within the domain of continuum mechanicsand not on fluid mechanics.