Biological Driven Phase Transitions in Fully or Partly Saturated Porous Media: A Multi-Component FEM Simulation Based on the Theory of Porous Media

Ricken, Tim; Thom, Andrea; Gehrke, T.; Denecke, Martin; Widmann, Renatus; Schulte, Marcel; Schmidt, Thorsten C.

doi:10.1007/978-3-030-49267-0_8

Cited by 7 publications

(5 citation statements)

References 30 publications

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“…To describe flow and transport of microscopic substances, we extend this approach to include microscopic solutes in blood and liver tissue. To simulate exchange processes between different components, the TPM has been extended with mass exchange processes for miscible [56, 57] and non-miscible substances [58, 59, 60, 61, 62].…”

Section: Methodsmentioning

confidence: 99%

Simulation of zonation-function relationships in the liver using coupled multiscale models: Application to drug-induced liver injury

Gerhäusser,

Lambers,

Mandl

et al. 2024

Preprint

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Multiscale modeling requires the coupling of models on different scales, often based on different mathematical approaches and developed by different research teams. This poses many challenges, such as defining interfaces for coupling, reproducible exchange of submodels, efficient simulation of the models, or reproducibility of results. Here, we present a multiscale digital twin of the liver that couples a partial differential equation (PDE)-based porous media approach for the hepatic lobule with cellular-scale ordinary differential equation (ODE)-based models. The models based on the theory of porous media describe transport, tissue mechanical properties, and deformations at the lobular scale, while the cellular models describe hepatic metabolism in terms of drug metabolism and damage in terms of necrosis. The resulting multiscale model of the liver was used to simulate perfusion-zonation-function relationships in the liver spanning scales from single cell to the lobulus. The model was applied to study the effects of (i) protein zonation patterns (metabolic zonation) and (ii) drug concentration dependence on spatially heterogeneous liver damage in the form of necrosis. Depending on the zonation pattern, different liver damage patterns could be reproduced, including periportal and pericentral necrosis as seen in drug-induced liver injury (DILI). Increasing the drug concentration led to an increase in the observed damage pattern. A key point for the success was the integration of domain-specific simulators based on standard exchange formats, i.e., libroadrunner for the high-performance simulation of ODE-based systems and FEBio for the simulation of the continuum-biomechanical part. This allows a standardized and reproducible exchange of cellular scale models in the Systems Biology Markup Language (SBML) between research groups.

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Section: Methodsmentioning

confidence: 99%

Simulation of zonation-function relationships in the liver using coupled multiscale models: Application to drug-induced liver injury

Gerhäusser,

Lambers,

Mandl

et al. 2024

Preprint

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“…The extended Theory of Porous Media (eTPM) as presented in 24,26 provides an approach to treat miscible substances ϕ β present in the immiscible macro phases ϕ α α α , see also 27 . The complex mixture body ϕ consists of κ κ κ macroscopic phases denoted as ϕ α α α , with α α α = 1, ...,κ κ κ.…”

Section: Theoretical Basis -Extended Theory Of Porous Mediamentioning

confidence: 99%

“…In the following, the required equations and derivatives are provided, which are finally inserted into the basic form of the entropy inequality (26). After further transformations the final form of the entropy inequality is obtained, from which the energy conserving and the dissipative restrictions evolve.…”

Section: Author Contributions Statementmentioning

confidence: 99%

A continuum multi-phase and multi-component description of the freezing process of seawater to porous sea ice

Ricken,

Thom,

Pathak

et al. 2023

Preprint

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Formation of porous 'pancake' ice floes in the Antarctic Marginal Ice Zone (MIZ) is a complex phenomenon associated with interactions between the saline seawater and temperature. Ocean warming and future environmental conditions in the Southern Ocean will most likely have an impact on the porous microstructure and thus, also on the connected biogeochemical processes which are closely related to the ice formation. Hence, it becomes important to realistically model the phase transition phenomena. In this paper, a biphasic model of solid ice and saline sea water is presented within the framework of the extended Theory of Porous Media (eTPM) using a continuum mechanical multi-phase and multi-component treatment. The phase transition between ice and brine is modeled using an interfacial mass transfer approach where the mass transferred is assumed as a jump across an interface which separates the phases. The mass production, hence, depends on the heat fluxes, specific enthalpies and the interfacial area. Moreover, the freezing point depression due to changing salinities can be implemented yielding a more detailed simulation. The system of equations results in a high-fidelity model and is simulated using the Finite Element Method (FEM). As proof of concept academic examples are presented.

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“…Within the extended TPM (eTPM), cf. [4] or [6], each macroscopic phase can further be composed of ν miscible compounds ϕ β , so that the overall body is described via the generalized approach ϕ = α α α ϕ α α α = α α α β ϕ αβ . Herein, ϕ αβ allocates the solute β to its solvent ϕ α α α .…”

Section: Model Approachmentioning

confidence: 99%

Towards a physical model of Antarctic sea ice microstructure including biogeochemical processes using the extended Theory of Porous Media

Thom

Ricken

2019

Proc Appl Math and Mech

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Predictive numerical climate models include an ocean modeling system as an important module, which comprises the components of ocean and sea ice physics as well as the coupled biogeochemical processes occuring in the ocean and sea ice, respectively. Whereas large‐scale, physical sea ice models are well represented, a new thrust for climate modeling is to include the sea ice biogeochemistry (BGC) as a strong influencing factor. For that reason, a demanding challenge is to develop a numerical model for the sea ice microstructure, which considers all relevant physical parts, like the evolution of salinity, thermodynamic properties and mechanical deformation, as well as the biological and chemical conversion processes. The model should be able to quantify phytoplankton biomass, nutrient sources and utilization as well as carbon content and export in connection to the underlying physical and biogeochemical driven mechanisms. A thermodynamically consistent derived continuum mechanical model is developed and prepared by means of a standard GALERKIN procedure to be implemented and solved with the finite element method (FEM). The governing equations and constitutive relations are set up in the framework of the homogenization approach of the extended Theory of Porous Media (eTPM).

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Biological Driven Phase Transitions in Fully or Partly Saturated Porous Media: A Multi-Component FEM Simulation Based on the Theory of Porous Media

Cited by 7 publications

References 30 publications

Simulation of zonation-function relationships in the liver using coupled multiscale models: Application to drug-induced liver injury

Simulation of zonation-function relationships in the liver using coupled multiscale models: Application to drug-induced liver injury

A continuum multi-phase and multi-component description of the freezing process of seawater to porous sea ice

Towards a physical model of Antarctic sea ice microstructure including biogeochemical processes using the extended Theory of Porous Media

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