A poroelastic model of the lung

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Abstract

This work is motivated by the modelling of ventilation and deformation in the lung for understanding the biomechanics of respiratory diseases. The main contribution is the derivation and implementation of a lung model that tightly couples a poroelastic model of lung parenchyma to an airway fluid network. The poroelastic model approximates the porous structure of lung parenchyma using a continuum model that allows us to naturally model changes in physiology by spatially varying material parameters, whilst conserving mass and momentum within the tissue. The proposed model will also take advantage of realistic deformation boundary conditions obtained from image registration, to drive the simulation. A finite element method is presented to discretize the equations in a monolithic way to ensure convergence of the nonlinear problem. To demonstrate the coupling between the poroelastic medium and the network flow model numerical simulations on a realistic lung geometry are presented. These numerical simulations are able to reproduce global physiological realistic measurements. We also investigate the effect of airway constriction and tissue weakening on the ventilation, tissue stress and alveolar pressure distribution and highlight the interdependence of ventilation and deformation.

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Lung tissue mechanics as an emergent phenomenon.

Béla Suki, Jason Bates (2011)

The mechanical properties of lung parenchymal tissue are both elastic and dissipative, as well as being highly nonlinear. These properties cannot be fully understood, however, in terms of the individual constituents of the tissue. Rather, the mechanical behavior of lung tissue emerges as a macroscopic phenomenon from the interactions of its microscopic components in a way that is neither intuitive nor easily understood. In this review, we first consider the quasi-static mechanical behavior of lung tissue and discuss computational models that show how smooth nonlinear stress-strain behavior can arise through a percolation-like process in which the sequential recruitment of collagen fibers with increasing strain causes them to progressively take over the load-bearing role from elastin. We also show how the concept of percolation can be used to link the pathologic progression of parenchymal disease at the micro scale to physiological symptoms at the macro scale. We then examine the dynamic mechanical behavior of lung tissue, which invokes the notion of tissue resistance. Although usually modeled phenomenologically in terms of collections of springs and dashpots, lung tissue viscoelasticity again can be seen to reflect various types of complex dynamic interactions at the molecular level. Finally, we discuss the inevitability of why lung tissue mechanics need to be complex.

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The prediction of pressure drop and variation of resistance within the human bronchial airways.

T.J. Pedley, R.C. Schroter, M.F. Sudlow (1970)

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A computational model of the topographic distribution of ventilation in healthy human lungs.

Annalisa J. Swan, Alys Clark, Merryn Tawhai (2012)

The topographic distribution of ventilation in the lungs is determined by the interaction of several factors, including lung shape, airway tree geometry, posture, and tissue deformation. Inter-species differences in lung structure-function and technical difficulty in obtaining high resolution imaging of the upright human lung means that it is not straightforward to experimentally determine the contribution of each of these factors to ventilation distribution. We present a mathematical model for predicting the topological distribution of inhaled air in the upright healthy human lung, based on anatomically structured model geometries and biophysical equations for model function. Gravitational deformation of the lung tissue is predicted using a continuum model. Airflow is simulated in anatomically based conducting airways coupled to geometrically simplified terminal acinar units with varying volume-dependent compliances. The predicted ventilation distribution is hence governed by local tissue density and elastic recoil pressure, airway resistance and acinar compliance. Results suggest that there is significant spatial variation in intrinsic tissue properties in the lungs. The model confirms experimental evidence that in the healthy lungs tissue compliance has a far greater effect than airway resistance on the spatial distribution of ventilation, and hence a realistic description of tissue deformation is essential in models of ventilation. Copyright Â© 2012 Elsevier Ltd. All rights reserved.