Multiscale modelling and simulations of tissue perfusion using the Biot-Darcy-Brinkman model

Rohan, Eduard; Turjanicová, Jana; Lukeš, Vladimír

doi:10.1016/j.compstruc.2020.106404

Cited by 8 publications

(6 citation statements)

References 47 publications

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“…Instead, the sinusoidal microporosity geometry can be respected in the context of the hierarchical homogenization by a locally periodic ultrastructure associated with a subscale, as proposed e.g . in [ 39 ], cf. [ 46 ].…”

Section: Discussionmentioning

confidence: 99%

“…It has been demonstrated, how the LRPC is applied in the perfusion modelling based on the Double-Darcy model of the homogenized periodic structure. Alternative models can be considered, such as [ 38 , 39 , 41 ], which employ a similar homogenization concept, although a convenient model accounting correctly for the fluid-structure interaction and the blood rheology in the transition between the precapillary vessels and the sinusoidal porosity remains an open problem. As an advantage over the phenomenological approaches, such as the model based on the multi-network poroelasticity theory [ 50 , 51 ], by virtue of the effective model parameters computed using the characteristic responses of the micromodel defined in the LRPC geometry, the homogenization method enables to respect the geometrical features of the parenchyma.…”

Section: Discussionmentioning

confidence: 99%

“…Our approach is different. We aim to treat the perfusion as the two-scale problem, so that the macroscopic and microscopic phenomena are coupled by virtue of the homogenization method [ 36 , 38 , 39 ]. The macroscopic pressures associated with the terminal PV and HV branches may vary with the macroscopic position at the organ level, even though the lobular structure is described as a periodic lattice generated by the LRPC.…”

Section: Methods and Modelsmentioning

confidence: 99%

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Geometrical model of lobular structure and its importance for the liver perfusion analysis

2021

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A convenient geometrical description of the microvascular network is necessary for computationally efficient mathematical modelling of liver perfusion, metabolic and other physiological processes. The tissue models currently used are based on the generally accepted schematic structure of the parenchyma at the lobular level, assuming its perfect regular structure and geometrical symmetries. Hepatic lobule, portal lobule, or liver acinus are considered usually as autonomous functional units on which particular physiological problems are studied. We propose a new periodic unit—the liver representative periodic cell (LRPC) and establish its geometrical parametrization. The LRPC is constituted by two portal lobulae, such that it contains the liver acinus as a substructure. As a remarkable advantage over the classical phenomenological modelling approaches, the LRPC enables for multiscale modelling based on the periodic homogenization method. Derived macroscopic equations involve so called effective medium parameters, such as the tissue permeability, which reflect the LRPC geometry. In this way, mutual influences between the macroscopic phenomena, such as inhomogeneous perfusion, and the local processes relevant to the lobular (mesoscopic) level are respected. The LRPC based model is intended for its use within a complete hierarchical model of the whole liver. Using the Double-permeability Darcy model obtained by the homogenization, we illustrate the usefulness of the LRPC based modelling to describe the blood perfusion in the parenchyma.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Methods and Modelsmentioning

confidence: 99%

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Geometrical model of lobular structure and its importance for the liver perfusion analysis

2021

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“…In multiscale and multiphysical simulations (the principal application of SfePy), e.g. in the field of biomechanics (Rohan et al, 2021), it is often necessary to implement several new weak forms (called terms in the code), and while it is not very difficult, still it is a hurdle for users with non-programmer background.…”

Section: Introductionmentioning

confidence: 99%

Leveraging Python tensor contraction packages for evaluating finite element weak forms

Cimrman¹

2022

Engineering Mechanics

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A new implementation of finite element matrix evaluation functions in the finite element code SfePy is introduced, leveraging several Python tensor contraction packages that implement a general function for evaluating expressions given using the Einstein summation convention. An example of the new weak form implementation is shown, and then results of a numerical study are presented comparing performance of the new implementation, the original implementation, and FEniCS suite.

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“…Systems exhibiting free flow coupled with porous medium flow are ubiquitous in nature appearing in numerous environmental, industrial (see e.g. [29] and references therein), and medical applications [60] . Discretization of the Stokes-Darcy problem is challenging with many finite element (e.g.…”

mentioning

confidence: 99%

Robust monolithic solvers for the Stokes-Darcy problem with the Darcy equation in primal form

Boon¹,

Koch²,

Kuchta³

et al. 2021

Preprint

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We construct mesh-independent and parameter-robust monolithic solvers for the coupled primal Stokes-Darcy problem. Three different formulations and their discretizations in terms of conforming and non-conforming finite element methods and finite volume methods are considered. In each case, robust preconditioners are derived using a unified theoretical framework. In particular, the suggested preconditioners utilize operators in fractional Sobolev spaces. Numerical experiments demonstrate the parameter-robustness of the proposed solvers.

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Multiscale modelling and simulations of tissue perfusion using the Biot-Darcy-Brinkman model

Cited by 8 publications

References 47 publications

Geometrical model of lobular structure and its importance for the liver perfusion analysis

Geometrical model of lobular structure and its importance for the liver perfusion analysis

Leveraging Python tensor contraction packages for evaluating finite element weak forms

Robust monolithic solvers for the Stokes-Darcy problem with the Darcy equation in primal form

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