Predicting alveolar ventilation heterogeneity in pulmonary fibrosis using a non-uniform polyhedral spring network model

Abstract

Pulmonary Fibrosis (PF) is a deadly disease that has limited treatment options and is caused by excessive deposition and cross-linking of collagen leading to stiffening of the lung parenchyma. The link between lung structure and function in PF remains poorly understood, although its spatially heterogeneous nature has important implications for alveolar ventilation. Computational models of lung parenchyma utilize uniform arrays of space-filling shapes to represent individual alveoli, but have inherent anisotropy, whereas actual lung tissue is isotropic on average. We developed a novel Voronoi-based 3D spring network model of the lung parenchyma, the Amorphous Network, that exhibits more 2D and 3D similarity to lung geometry than regular polyhedral networks. In contrast to regular networks that show anisotropic force transmission, the structural randomness in the Amorphous Network dissipates this anisotropy with important implications for mechanotransduction. We then added agents to the network that were allowed to carry out a random walk to mimic the migratory behavior of fibroblasts. To model progressive fibrosis, agents were moved around the network and increased the stiffness of springs along their path. Agents migrated at various path lengths until a certain percentage of the network was stiffened. Alveolar ventilation heterogeneity increased with both percent of the network stiffened, and walk length of the agents, until the percolation threshold was reached. The bulk modulus of the network also increased with both percent of network stiffened and path length. This model thus represents a step forward in the creation of physiologically accurate computational models of lung tissue disease.

A scale-free model of acute and ventilator-induced lung injury: a network theory approach inspired by seismology

“…This theory has been bolstered in subsequent computational analyses employing, e.g., finite element spring networks ( Wilson and Bachofen, 1982 ; Makiyama et al, 2014 ; Albert et al, 2019 ) or systems of differential equations ( Ma et al, 2023 ) to show that stress accumulates heterogeneously in the lung parenchyma, with the largest stresses found near areas with greater extents of injury. Other spring network simulations have shown that tethering (or stiffening) has both localized and longer length-scale effects on the distribution of lung stress and strain ( Ma et al, 2013 ; Ma et al, 2015 ; Hall et al, 2023 ). Probabilistic methods, based on experimental data, have also been employed to understand the forces contributing to injury propagation, the mechanisms of injury heterogeneity, and the rich-get-richer mechanisms of VILI pathogenesis and offer a complementary perspective to deterministic mechanical models ( Mattson et al, 2022 ; Mattson and Smith, 2023 ).…”

Elucidating the interaction between stretch and stiffness using an agent-based spring network model of progressive pulmonary fibrosis

“… Suki et al, 2020 developed a self-healing model on a 2D hexagonal network, however induced fibrosis required a constant perturbation of the agents, rather than fibrosis induced from a single insult. Bates et al, 2007 and Hall et al, 2023 explored fibrosis on 2D hexagonal networks and 3D non-uniform networks, respectively, and both observed clustering and mechanics seen in PF, but neither included rupture, gradient in agent behavior, or self-healing.…”

“…We created a non-uniform spring network to represent the parenchymal tissue using a method we have described previously ( Hall et al, 2023 ). Briefly, Poisson Disk Sampling was used to create a semi-organized 2D Voronoi diagram.…”

“…This initial configuration of the network was not at equilibrium, however. The equilibrium configuration was found by simulated annealing in which the nodes were moved in random directions by progressively decreasing amounts until the net force on each node was minimized, similar to the energy optimization method we have described previously ( Cavalcante et al, 2005 ; Hermann, 2021 ; Hall et al, 2023 ) As the model simulations progressed, the continually changing values of throughout the network caused its equilibrium configuration to change. Simulated annealing was used to determine the new configuration at each time step.…”

“…The above considerations suggest that lung parenchymal homeostasis is maintained via a balance of mechanotransduction signals related to substrate stiffness and stretch, and that when the system is perturbed sufficiently, the self-healing nature of tissue is overpowered by progressive stiffening, leading to PF. We have previously developed several computational models of PF pathogenesis that support this hypothesis ( Wellman et al, 2018 ; Suki et al, 2020 ; Suki et al, 2020 ; Hall et al, 2023 ). In these models, elastic spring networks mimic the structure and mechanics of the parenchymal tissue, while autonomous agents mimic the cellular processes that act on the tissue.…”