Finite element simulation of fluid dynamics and CO $$_2$$ 2 gas exchange in the alveolar sacs of the human lung

Caucha, Luis Jhony; Frei, Stefan; Rubio, Obidio

doi:10.1007/s40314-018-0692-5

Cited by 5 publications

(2 citation statements)

References 47 publications

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“…Partial differential equations (PDEs) posed on moving domains are significant in many areas of science and engineering. They arise for example in flow problems around moving structures, such as pumps [4], wind or water turbines [55], within moving objects [15], or as sub-problems in fluid-structure interactions or multiphase flows. Fluid-structure interactions arise in aerodynamical applications like flow around airplanes or parachutes [59], in biomedical problems such as blood flow through the cardiovascular system [25,54,61] or the airflow within the respiratory system [63] and even in tribological applications [47].…”

Section: Introductionmentioning

confidence: 99%

An Implicitly Extended Crank–Nicolson Scheme for the Heat Equation on a Time-Dependent Domain

Frei,

Singh

2024

J Sci Comput

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We consider a time-stepping scheme of Crank–Nicolson type for the heat equation on a moving domain in Eulerian coordinates. As the spatial domain varies between subsequent time steps, an extension of the solution from the previous time step is required. Following Lehrenfeld and Olskanskii (ESAIM: M2AN 53(2):585–614, 2019), we apply an implicit extension based on so-called ghost-penalty terms. For spatial discretisation, a cut finite element method is used. We derive a complete a priori error analysis in space and time, which shows in particular second-order convergence in time under a parabolic CFL condition. Finally, we present numerical results in two and three space dimensions that confirm the analytical estimates, even for much larger time steps.

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Section: Introductionmentioning

confidence: 99%

An Implicitly Extended Crank–Nicolson Scheme for the Heat Equation on a Time-Dependent Domain

Frei,

Singh

2024

J Sci Comput

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“…Roth et al 11 used a simplified parameterized model of lung microstructures to study ventilator-induced lung injury. Caucha et al 12 presented a numerical framework based on continuum models for fluid dynamics and CO 2 gas distribution in the alveolar sacs of the human lung during expiration and inspiration, including gas exchange to the cardiovascular system. This study did not consider the shape change of the geometry, and it only considers the computational fluid dynamics and transport simulation.…”

Section: Introductionmentioning

confidence: 99%

A preliminary study of dynamic interactive simulation and computational CT scan of the ideal alveolus model

Liu,

Li,

Huang

et al. 2023

Medical Physics

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BackgroundWhile the development of CT imaging technique has brought cognition of in vivo organs, the resolution of CT images and their static characteristics have gradually become barriers of microscopic tissue research.PurposePrevious research used the finite element method to study the airflow and gas exchange in the alveolus and acinar to show the fate of inhaled aerosols and studied the diffusive, convective, and sedimentation mechanisms. Our study combines these techniques with CT scan simulation to study the mechanisms of respiratory movement and its imaging appearance.MethodsWe use 3D fluid‐structure interaction simulation to study the movement of an ideal alveolus under regular and forced breathing situations and ill alveoli with different tissue elasticities. Additionally, we use the Monte Carlo algorithm within the OpenGATE platform to simulate the computational CT images of the dynamic process with different designated resolutions. The resolutions show the relationship between the kinematic model of the human alveolus and its imaging appearance.ResultsThe results show that the alveolus and the wall thickness can be seen with an image resolution smaller than 15.6 μm. With ordinary CT resolution, the alveolus is expressed with four voxels.ConclusionsThis is a preliminary study concerning the imaging appearance of the dynamic alveolus model. This technique will be used to study the imaging appearance of the dynamic bronchial tree and the lung lobe models in the future.

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Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains

2022

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This article is concerned with the discretisation of the Stokes equations on time-dependent domains in an Eulerian coordinate framework. Our work can be seen as an extension of a recent paper by Lehrenfeld and Olshanskii (ESAIM: M2AN 53(2):585–614, 2019), where BDF-type time-stepping schemes are studied for a parabolic equation on moving domains. For space discretisation, a geometrically unfitted finite element discretisation is applied in combination with Nitsche’s method to impose boundary conditions. Physically undefined values of the solution at previous time-steps are extended implicitly by means of so-called ghost penalty stabilisations. We derive a complete a priori error analysis of the discretisation error in space and time, including optimal $$L^2(L^2)$$ L 2 ( L 2 ) -norm error bounds for the velocities. Finally, the theoretical results are substantiated with numerical examples.

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Finite element simulation of fluid dynamics and CO $$_2$$ 2 gas exchange in the alveolar sacs of the human lung

Cited by 5 publications

References 47 publications

An Implicitly Extended Crank–Nicolson Scheme for the Heat Equation on a Time-Dependent Domain

An Implicitly Extended Crank–Nicolson Scheme for the Heat Equation on a Time-Dependent Domain

A preliminary study of dynamic interactive simulation and computational CT scan of the ideal alveolus model

Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains

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