Linking Parenchymal disease progression to changes in lung mechanical function by percolation

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.