A nested dynamic multi-scale approach for 3D problems accounting for micro-scale multi-physics

Wiechert, Lena; Wall, Wolfgang A.

doi:10.1016/j.cma.2009.09.017

Cited by 18 publications

(8 citation statements)

References 32 publications

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“…For this reason we are working on including the presented simulations within a multiscale approach for alveolar ensemble. 33 This allows us to project the global parenchymal deformation down to the level of a single alveolar ensemble in order to provide realistic boundary conditions. This method has the advantage that we will be able to measure local alveolar strain fields in large geometries, for example living precision cut rat lung slices (PCLS).…”

Section: Discussionmentioning

confidence: 99%

Local Strain Distribution in Real Three-Dimensional Alveolar Geometries

et al. 2011

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Mechanical ventilation is not only a life saving treatment but can also cause negative side effects. One of the main complications is inflammation caused by overstretching of the alveolar tissue. Previously, studies investigated either global strains or looked into which states lead to inflammatory reactions in cell cultures. However, the connection between the global deformation, of a tissue strip or the whole organ, and the strains reaching the single cells lining the alveolar walls is unknown and respective studies are still missing. The main reason for this is most likely the complex, sponge-like alveolar geometry, whose three-dimensional details have been unknown until recently. Utilizing synchrotron-based X-ray tomographic microscopy, we were able to generate real and detailed three-dimensional alveolar geometries on which we have performed finite-element simulations. This allowed us to determine, for the first time, a three-dimensional strain state within the alveolar wall. Briefly, precision-cut lung slices, prepared from isolated rat lungs, were scanned and segmented to provide a three-dimensional geometry. This was then discretized using newly developed tetrahedral elements. The main conclusions of this study are that the local strain in the alveolar wall can reach a multiple of the value of the global strain, for our simulations up to four times as high and that thin structures obviously cause hotspots that are especially at risk of overstretching.

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Section: Discussionmentioning

confidence: 99%

Local Strain Distribution in Real Three-Dimensional Alveolar Geometries

et al. 2011

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“…Unit cell models have been used to analyze the response of idealized polyhedral cells to mechanical loading (Ko, 1965;Takishima and Mead, 1972;Wilson and Bachofen, 1982). Unit cell models of lung parenchyma have been proposed by Kimmel and co-workers (Kimmel and Budiansky, 1990;Kimmel et al, 1987), who analyzed a pentagonal dodecahedral cell, and by Denny and Schroter (1995, 2000, who analyzed tetrakaidecahedral cells, and more recently by Wiechert and Wall (2010), who used micro scale multi-physics approach to analyze tetrakaidecahedral cells. Here we present an analysis of random Voronoi structure that is likely to represent more accurately the human lung in both the healthy and injured states, and compare it with results from hexagonal honeycombs and continuum approximations.…”

Section: Strainmentioning

confidence: 99%

Stress concentration around an atelectatic region: A finite element model

Makiyama

Gibson

Harris

et al. 2014

Respiratory Physiology & Neurobiology

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Lung parenchyma surrounding an atelectatic region is thought to be subjected to increased stress compared with the rest of the lung. Using 37 hexagonal cells made of linear springs, Mead et al. (1970) measured a stress concentration greater than 30% in the springs surrounding a stiffer central cell. We re-examine the problem using a 2D finite element model of 500 cells made of thin filaments with a non-linear stress-strain relationship. We study the consequences of increasing the central stiff region from one to nine contiguous cells in regular hexagonal honeycombs and random Voronoi honeycombs. The honeycomb structures were uniformly expanded with strains of 15%, 30%, 45% and 55% above their resting, non-deformed geometry. The curve of biaxial stress vs. fractional area change has a similar shape to that of the pressure-volume curve of the lung, showing an initial regime with relatively flat slope and a final regime with decreasing slope, tending toward an asymptote. Regular honeycombs had little variability in the maximum stress in radially oriented filaments adjacent to the central stiff region. In contrast, some filaments in random Voronoi honeycombs were subjected to stress concentration approximately 16 times the average stress concentration in the radially oriented filaments adjacent to the stiff region. These results may have implications in selecting the appropriate strategy for mechanical ventilation in ARDS and defining a "safe" level of alveolar pressure for ventilating atelectatic lungs.

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“…As already mentioned before, the algorithms discussed in Sections 2 and 3 are by no means restricted to any specific discretization scheme or solution technique. Furthermore, arbitrary constitutive laws including poroelastic models (cf., for instance, ) and multi‐scale approaches (see, e.g., ) may be utilized to describe the behavior of the tissue under consideration as accurately as possible.…”

Section: Discussionmentioning

confidence: 99%

A combined fluid–structure interaction and multi–field scalar transport model for simulating mass transport in biomechanics

Yoshihara

Coroneo

Comerford

et al. 2014

Numerical Meth Engineering

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SUMMARYMass transport processes are known to play an important role in many fields of biomechanics such as respiratory, cardiovascular, and biofilm mechanics. In this paper, we present a novel computational model considering the effect of local solid deformation and fluid flow on mass transport. As the transport processes are assumed to influence neither structure deformation nor fluid flow, a sequential one‐way coupling of a fluid–structure interaction (FSI) and a multi‐field scalar transport model is realized. In each time step, first the non‐linear monolithic FSI problem is solved to determine current local deformations and velocities. Using this information, the mass transport equations can then be formulated on the deformed fluid and solid domains. At the interface, concentrations are related depending on the interfacial permeability. First numerical examples demonstrate that the proposed approach is suitable for simulating convective and diffusive scalar transport on coupled, deformable fluid and solid domains. Copyright © 2014 John Wiley & Sons, Ltd.

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A nested dynamic multi-scale approach for 3D problems accounting for micro-scale multi-physics

Cited by 18 publications

References 32 publications

Local Strain Distribution in Real Three-Dimensional Alveolar Geometries

Local Strain Distribution in Real Three-Dimensional Alveolar Geometries

Stress concentration around an atelectatic region: A finite element model

A combined fluid–structure interaction and multi–field scalar transport model for simulating mass transport in biomechanics

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