Stability analysis for a new model of multi-species convection-diffusion-reaction in poroelastic tissue

Vilaca, Luis Miguel De Oliveira; Gómez-Vargas, Bryan; Kumar, Sarvesh; Ruiz–Baier, Ricardo; Verma, Nitesh

doi:10.1016/j.apm.2020.04.014

Cited by 18 publications

(12 citation statements)

References 27 publications

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“…Recent applications of biphasic poroelasticity theory, e.g., in traumatic brain injuries [18], swelling of hydrogels [19], and cartilage biosynthesis [20], show the need for suitable numerical schemes that are able to solve consolidation problems in complex geometries. This requirement is even more urgent when the role of the interface is of importance since quantitative analytical advancement in the description of the interfacial zone is only possible in simplified settings [17].…”

Section: Introductionmentioning

confidence: 99%

Coupling Stokes flow with inhomogeneous poroelasticity

Taffetani,

Ruiz-Baier,

Waters

2021

Preprint

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We investigate the behaviour of a system where a single phase fluid domain is coupled to a biphasic poroelastic domain. The fluid domain consists of an incompressible Newtonian viscous fluid while the poroelastic domain consists of a linear elastic solid filled with the same viscous fluid. The properties of the poroelastic domain, i.e. permeability and elastic parameters, depend on the inhomogeneous initial porosity field. The theoretical framework highlights how the heterogeneous material properties enter the linearised governing equations for the poroelastic domain. To couple flows through this domain with a surrounding Stokes flow, we show case a numerical implementation based on a new mixed formulation where the equations in the poroelastic domain are rewritten in terms of three fields: displacement, fluid pressure and total pressure.Coupling single phase and multiphase flow problems are ubiquitous in many industrial and biological applications, and here we consider an example from in-vitro tissue engineering. We consider a perfusion system, where a flow is forced to pass from the single phase fluid to the biphasic poroelastic domain. We focus on a simplified two dimensional geometry with small aspect ratio, and perform an asymptotic analysis to derive analytical solutions for the displacement, the pressure and the velocity fields. Our analysis advances the quantitative understanding of the role of heterogeneous material properties of a poroelastic domain on its mechanics when coupled with a fluid domain. Specifically, (i) the analytical analysis gives closed form relations that can be directly used in the design of slender perfusion systems; (ii) the numerical method is validated by comparing its result against selected theoretical solutions, opening towards the possibility to investigate more complex geometrical configurations.

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Section: Introductionmentioning

confidence: 99%

Coupling Stokes flow with inhomogeneous poroelasticity

Taffetani,

Ruiz-Baier,

Waters

2021

Preprint

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“…Examples include the interaction between soft permeable tissue and blood flow, or the study of biofilm growth and distribution near fluids (see [33,68]). Recent applications of poroelastic consolidation theory to the poromechanical characterisation of soft living tissues include oxygen diffusivity in cartilage [51], swelling of hydrogels [76], feather and scale development [10], tumour localisation and biomass growth [67], cardiac perfusion [11,23,29], chemically-controlled cell motion [53], lung characterisation [14], traumatic brain injury [31], the formation of inflammatory oedema in the context of blood-brain barrier failure [48], and immune systems for small intestine [70,75] as well as for myocarditis [38].…”

Section: Introductionmentioning

confidence: 99%

Finite element methods for large-strain poroelasticity/chemotaxis models simulating the formation of myocardial oedema

Nicolas¹,

Gómez-Vargas²,

Lourenço³

et al. 2021

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In this paper we propose a novel coupled poroelasticity-diffusion model for the formation of extracellular oedema and infectious myocarditis valid in large deformations, manifested as an interaction between interstitial flow and the immune-driven dynamics between leukocytes and pathogens. The governing partial differential equations are formulated in terms of skeleton displacement, fluid pressure, Lagrangian porosity, and the concentrations of pathogens and leukocytes. A five-field mixed-primal finite element scheme is proposed for the numerical approximation of the problem, and we provide the stability analysis for a simplified system emanating from linearisation. We also discuss the construction of an adequate, Schur complement based, nested preconditioner. The produced computational tests exemplify the properties of the new model and of the mixed schemes.

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“…Mechanical properties of different cell types indicate diverse behaviour, including elastic [15,18,45], poroelastic [14,37,50,51], or nonlinear and nonlocal characteristics [36,56] but more predominantly, viscoelastic effects [2,8,10,20,29,47,57]. The specific constitutive rheological model to adopt in a tissue depends on the characteristics of each constituent cell, on the properties inherent to distinct biological states, on the nature and intensity of the stresses and strains that are to be applied, and on the spatio-temporal scales involved.…”

Section: Introductionmentioning

confidence: 99%

Mechanochemical models for calcium waves in embryonic epithelia

Kaouri¹,

Méndez²,

Ruiz–Baier³

2021

Preprint

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In embryogenesis, epithelial cells, acting as individual entities or as coordinated aggregates in a tissue, exhibit strong coupling between chemical signalling and mechanical responses to internally or externally applied stresses. Intercellular communication in combination with such coordination of morphogenetic movements can lead to drastic modifications in the calcium distribution in the cells. In this paper we extend the recent mechanochemical model in [K.

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Stability analysis for a new model of multi-species convection-diffusion-reaction in poroelastic tissue

Cited by 18 publications

References 27 publications

Coupling Stokes flow with inhomogeneous poroelasticity

Coupling Stokes flow with inhomogeneous poroelasticity

Finite element methods for large-strain poroelasticity/chemotaxis models simulating the formation of myocardial oedema

Mechanochemical models for calcium waves in embryonic epithelia

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