Elsevier

Journal of Theoretical Biology

Volume 332, 7 September 2013, Pages 136-140
Journal of Theoretical Biology

Heterogeneous distribution of mechanical stress in human lung: A mathematical approach to evaluate abnormal remodeling in IPF

https://doi.org/10.1016/j.jtbi.2013.04.038Get rights and content

Highlights

  • Modeling nonlinear viscoelastic dynamics in human lung.

  • Correspondence between early lesions and anatomical distribution of mechanical stress.

  • Interplay between mathematics-mechanics and physiology of human lung.

Abstract

Idiopathic pulmonary fibrosis (IPF) is the most common and severe form of idiopathic interstitial pneumonia. A recently proposed pathogenic model suggests that the concurrent action of cell senescence, exposure to cigarette smoke and mechanical stress due to respiratory lung movements lead to a localized exhaustion of tissue renewal capacity with eventual alveolar loss and abnormal lung remodeling. In this study we have compared the distribution of IPF lesions, as shown by TC radiological images, with the hypothetical distribution of maximal mechanical stress obtained by a simplified mathematical model. The geometry and distribution of stress as determined by our simulation are closely similar to those demonstrated in vivo in the lungs of patients with idiopathic pulmonary fibrosis using high resolution CT scan radiological imaging. These data argue in favor of the recently proposed contribution of mechanical stress to progressive damage and remodeling of lung parenchyma in IPF. The parameters of the model can be tuned on the age of the patients.

Introduction

Idiopathic pulmonary fibrosis (IPF) is the most common and severe form of idiopathic interstitial pneumonia, and its median survival is 3–4 years (American Thoracic Society, 2000, Fernandez Perez et al., 2010). New concepts have been recently proposed regarding the biology and pathogenesis of this devastating disease, suggesting that the abnormal remodeling of lung parenchyma in IPF is not related to inflammatory mechanisms as previously considered, but is rather the effect of a series of pathologic events including epithelial alveolar cell injury, and deranged activation of lung reparative processes (Selman et al., 2001, Selman et al., 2008, Chilosi et al., 2010, Chilosi et al., 2012). Accumulating evidence is available that in IPF the abnormal re-epithelialization after injury can be related to a progressive stem-cell exhaustion due to intrinsic cellular defects either related to a predisposing genetic background (familial IPF is a well recognized entity), or to the aging-related accumulation of metabolic alterations (e.g. due to toxic effects of smoking, pollution, metabolic abnormalities, or other causes) (Chilosi et al., 2010). The remodeling process in this scheme is likely related to the abnormal triggering at sites of disease progression of different molecular pathways crucial to lung tissue development and regeneration, including the Wnt-beta-catenin pathway, TGF-beta, NOTCH, BMP, and others (Chilosi et al., 2003, Knigshoff et al., 2008, Knigshoff et al., 2009).

A relevant missing point in this pathogenic scenario is related to the peculiar localization of IPF lesions, that typically start at the posterior bases of the lower lobes, progressively extending in a caudal-cranial mode (American Thoracic Society, 2000). Several lines of evidence suggest that these anatomical parts of the lung are in fact sites where mechanical forces can be particularly concentrated, thus triggering the formation of microscopic tears in the alveolar structure, which may result in repetitive small scarring events (fibroblast foci), and eventual honeycomb changes (Dail, 2001, Leslie, 2012). The microscopic damages due to chronic mechanical stress located in these areas can in fact cooperate in a sequence of pathogenic events, including:

  • 1.

    localized accelerated pneumocyte turnover, with eventual increase of replicative senescence;

  • 2.

    occurrence of a senescence-induced secretive phenotype (SASP) within these parts of the lung parenchyma;

  • 3.

    abnormal activation of reparative molecular pathways (e.g. Wnt-pathway), leading to abnormal remodeling of the lung parenchyma (Chilosi et al., 2010, Chilosi et al., 2003, Coppe et al., 2010).

A limited number of mathematical studies are available addressing these issues, that suggest that mechanical forces during respiration can in fact be heterogeneously distributed within the lung parenchyma (Karakaplan et al., 1980, Denny and Schroter, 2000, Fung, 1975, Mead et al., 1970, Maksym et al., 1998, Yuan et al., 1999). Nevertheless, evidence of a close correspondence existing between the early IPF lesions and the anatomical distribution of mechanical stress in human lung is still incomplete.

In this study we have compared the distribution of IPF lesions, determined on HRTC images, with the hypothetical distribution of maximal mechanical stress obtained by a simplified mathematical model, which is presented in Section 2. Simulations and biological interpretations are proposed in Section 3. The modeling approach is developed within the general framework of system biology (Deutsch and Dormann, 2004, Bellomo and Carbonaro, 2011, Coscia et al., 2011) with the aim of decomposing the overall system into simple subsystems consistent with the objectives the specific research program under consideration. The result is encouraging enough, as we shall see, to motivate the development of more sophisticated models.

Section snippets

The mathematical mechanical model

A mathematical-mechanical model is derived in the following to describe the dynamics of the lung in order to detect the areas that are more susceptible to stretch overload in the pulmonary parenchyma. The lung is viewed, in the model, as a two-dimensional surface compacted into the thoracic space. Really, the lung is a three dimensional organ, however our simple approach is sufficient to investigate on the aforesaid problem.

The derivation involves some principal issues including the analysis of

Simulations and biological interpretation

In this section we present our numerical simulations concerning the lung dynamics in order to identify the areas more susceptible to loss of elasticity.

Its initial configuration (see Fig. 3) is such that the coordinates of all nodes of hexagons have been chosen according to the unstressed lengths of the springs, so that the baseline network configuration is uniform. Starting from this initial configuration, we have applied to the left and to the bottom border nodes the external forces

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    This work was supported by the European Union FP7 Health Research Grant Number HEALTH-F4-2008-202047 Resolve Chronic Inflammation and Achieve Healthy Ageing by Understanding Non-regenerative Repair.

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