Linking Parenchymal Disease Progression to Changes in Lung Mechanical Function by Percolation

Abstract

Rationale: The mechanical dysfunction accompanying parenchymal diseases such as pulmonary fibrosis and emphysema may follow a different course from the progression of the underlying microscopic pathophysiology itself, particularly in the early stages. It is tempting to speculate that this may reflect the geographical nature of lung pathology. However, merely ascribing mechanical dysfunction of the parenchyma to the vagaries of lesional organization is unhelpful without some understanding of how the two are linked. Objectives: We attempt to forge such a link through a concept known as percolation, which has been invoked to account for numerous natural processes involving transmission of events across complex networks. Methods: We numerically determined the bulk stiffness (corresponding to the inverse of lung compliance) of a network of springs representing the lung parenchyma. We simulated the development of fibrosis by randomly stiffening individual springs in the network, and the development of emphysema by preferentially cutting springs under the greatest tension. Measurements and Main Results: When the number of stiff springs was increased to the point that they suddenly became connected across the network, the model developed a sharp increase in its bulk modulus. Conversely, when the cut springs became sufficiently numerous, the elasticity of the network fell to zero. These two conditions represent percolation thresholds that we show are mirrored structurally in both tissue pathology and macroscopic computed tomography images of human idiopathic fibrosis and emphysema. Conclusions: The concept of percolation may explain why the development of symptoms related to lung function and the development of parenchymal pathology often do not progress together.

In silico modeling of interstitial lung mechanics: implications for disease development and repair

“…Nevertheless, merely ascribing mechanical dysfunction of the parenchyma to the vagaries of lesional organization is unhelpful without an understanding of how the two are linked. Our above results show that such a link can be forged through the concept of percolation [12], which has been invoked previously to account for numerous natural processes involving transmission of events across networks [26,27,30,31]. These simulations suggest that tissue undergoes a sharp change in its macroscopic mechanical properties at the percolation threshold, which may correspond to the point in the disease course when patients experience a sudden downturn in clinical symptoms.…”

“…Extending this approach to large networks, we have recently shown that a sudden change in macroscopic tissue stiffness occurs when the isolated lesions become numerous enough to connect in a contiguous pathway across a large expanse of tissue [12]. This is an emergent phenomenon known to occur at the so called percolation threshold [26], and may explain why the time-course of degradation in lung function does not always mirror the progression of underlying pathology in diseases of the lung parenchyma.…”

“…This is an emergent phenomenon known to occur at the so called percolation threshold [26], and may explain why the time-course of degradation in lung function does not always mirror the progression of underlying pathology in diseases of the lung parenchyma. Below, we first review percolation thresholds in elastic networks [27] as models of parenchymal disease progression [12], and then explore how the reverse process might be exploited to study the efficacy of targeted parenchymal repair…”

“…In other words, alterations in elasticity are emergent phenomena that arise from the way in which the lesions of disease are arranged spatially. Computer models have proven essential for investigating how such phenomena develop, both in emphysema [6,11] and fibrosis [12]. However, as far as we are aware, there has not yet been any attempt to use computer models to explore how these diseases might be treated most effectively.…”

“…We have previously developed a network model of the lung to mimic the progression of the parenchymal destruction caused by emphysema and the remodeling due to fibrosis [12]. In this perspective, we will first briefly review this model and then show how it can be used in reverse to provide an in silico approach for the rational design of strategies for the targeted delivery of therapies for treating lung parenchymal disease.…”