A quasi-static poromechanical model of the lungs

Abstract

The lung vital function of providing oxygen to the body heavily relies on its mechanical behavior, and the interaction with its complex environment. In particular, the large compliance and the porosity of the pulmonary tissue are critical for lung inflation and air inhalation, and the diaphragm, the pleura, the rib cage and intercostal muscles all play a role in delivering and controlling the breathing driving forces. In this paper, we introduce a novel poromechanical model of the lungs. The constitutive law is derived within a general poromechanics theory via the formulation of lung-specific assumptions, leading to a hyperelastic potential reproducing the volume response of the pulmonary mixture to a change of pressure. Moreover, physiological boundary conditions are formulated to account for the interaction of the lungs with their surroundings, including a following pressure and bilateral frictionless contact. A strategy is established to estimate the unloaded configuration from a given loaded state, with a particular focus on ensuring a positive porosity. Finally, we illustrate through several realistic examples the relevance of our model and its potential clinical applications.

Pressure-driven micro-poro-mechanics: A variational framework for modeling the response of porous materials

“…Interestingly, under the same assumptions (a closed-cell composite and extending P to the fluid domain) and with some algebraic manipulations, this equation can be related to the stationary condition Equation (2.16), which is generated by considering the macroscopic strain as a variable of the problem. The relationship between pressure-driven and deformation-driven formulations has profound consequences on the modeling of free-breathing versus ventilated-breathing, for instance in the context of lung mechanical simulations (Hurtado et al, 2020;Patte et al, 2020Patte et al, , 2019Tawhai & Lin, 2010).…”

Estimation of Regional Pulmonary Compliance in Idiopathic Pulmonary Fibrosis Based on Personalized Lung Poromechanical Modeling

“…The lung poromechanical model used in this study has been described in details in [Patte, 2020;Patte et al, 2022]. We only recall here the main points used in the present work.…”

“…We recently proposed a lung biomechanical model, based on a novel poromechanics behavior law, and specific boundary conditions [Patte et al, 2019;Patte, 2020;Patte et al, 2022]. The constitutive framework relies on the general formulation of poromechanics detailed in [Chapelle and Moireau, 2014] and based on [Biot and Temple, 1972;Coussy, 2004], describing the lung tissue as a mixture of "solid" (tissue & blood) and fluid (air).…”

“…The boundary conditions contain the (negative) pleural pressure that inflates the lungs, and frictionless bilateral contact with the thorax. The model focuses on the end-exhalation and end-inhalation states (which are assumed to be at static equilibrium), and has been shown to adequately reproduce many elements of lung physiology [Patte, 2020;Patte et al, 2022].…”

“…In Section 2.1, we detail the clinical data that is routinely acquired on IPF patients and can be used to personalize a biomechanical model. Then, in Section 2.2, we briefly recall the main components of our pulmonary poromechanics model, which was fully detailed in [Patte, 2020;Patte et al, 2022]. In Section 2.3, we describe the personalization pipeline, which is the main technical novelty of this paper.…”