Biomechanical Modelling for Lung Tissue Viscoelasticity at Extracellular Level

Abstract

Nearly all lung diseases begin with alteration of the composition of the extracellular matrix (ECM) components, which eventually results in a change in the structural and mechanical properties of the lung tissue. This research develops a viscoelastic network model for the mechanical properties of the lung from the extracellular level to the tissue level. The ECM is modelled to represent the effects of three major load-bearing components of the extracellular matrix: elastin, collagen, and proteoglycans (PGs). The model helps us to better understand the role of the extracellular matrix components in the mechanical lung properties related to health and diseases. Determining the specific contribution of ECM components to these mechanical properties can reveal the mechanical pathways of respiratory diseases. Previous experimental studies have facilitated understanding of the effect of selective digestion of ECM fibres at the tissue level. Despite the fruitful results of these experimental studies, the impact of the ECM fibres across the scale is still not well understood. The model developed in this thesis mimics the alveolar network of lung parenchyma using a hexagonal network. The elements of the network represent the alveolar walls, which are modelled using a parallel, nonlinear, spring-dashpot configuration. The effect of collagen fibres are modelled with a nonlinear spring in concert with a linear spring representing elastin. A Maxwell model, included to represent the surrounding matrix, is utilised to complement the viscoelastic properties for the tissue. The model has been used to link the amount of collagen, elastin, PGs, and the tissue's mechanical properties. The model parameters were set according to the area fraction of elastin and collagen within the alveolar wall. Subsequently, the ratio of collagen-to-elastin was altered to investigate the impact of material heterogeneity within the elements of the network. Additional hypothetical cross-diagonal elements were adjoined to the network to stabilise it. The results of the model were validated using data from the literature. Finally, an airway was built using the model to investigate the impact of interdependent forces between the airway and alveolar network. The heterogeneity in the geometric structure, similar to the real lung’s alveolar network, is introduced to the network by randomly moving the network nodes. The results indicated that increasing the geometric heterogeneity of the model increased the heterogeneity of the stress distribution amongst the individual alveolar walls. The reduction of the volume fraction of any one of the three ECM components resulted in a decrease of the tissue’s stiffness. However, this reduction was only observed in the higher strain due to the consideration of the ECM components independent of each other. After embedding an airway inside the network, the pattern of stress distribution was altered following a 35% biaxial strain. An increase in the stress on the elements attaching the network to the airway wall was observed. Following an increase in airway wall stiffness from 20 N/cm2 (considered normal) to 100 N/cm2 led to a 37% reduction in the airway lumen area at a 35% biaxial strain. When the number of airways in the simulated lung tissue strip increased from one to nine airways, the required stress at 35% biaxial strain increased. Furthermore, increasing the airway stiffness led to increased stresses being exerted on the adjacent alveolar network, which is hypothesised to increase the likelihood of breakage in the alveolar wall. Subsequently, the tissue destruction in emphysema was simulated by diminishing the alveolar wall elements with the highest stress at 35% strain. This two-dimensional network model enabled us to investigate how alterations in the ECM’s composition and structural properties affected the tissue’s mechanical response. There are several limitations to the model developed in this thesis, and resolving them would improve its accuracy. One of the most important limitations is that the ECM components were modelled independently, meaning that reducing the effect one of them would not affect the mechanical properties of the others. Using a cross-diagonal format was problematic when simulating the progression of emphysema. This model can be upgraded to a three-dimensional network that could be scaled up to link ECM composition to regional and whole organ lung function.