A biochemo-mechano coupled, computational model combining membrane transport and pericellular proteolysis in tissue mechanics

Numer Methods Biomed Eng

Yoshihara

Wall

2018

In this paper, we propose a finite element-based immersed method to treat the mechanical coupling between a deformable porous medium model (PM) and an immersed solid model (ISM). The PM is formulated as a homogenized, volume-coupled two-field model, comprising a nearly incompressible solid phase that interacts with an incompressible Darcy-Brinkman flow. The fluid phase is formulated with respect to the Lagrangian finite element mesh, following the solid phase deformation. The ISM is discretized with an independent Lagrangian mesh and may behave arbitrarily complex (it may, eg, be compressible, grow, and perform active deformations). We model two distinct types of interactions, namely, (1) the immersed fluid-structure interaction (FSI) between the ISM and the fluid phase in the PM and (2) the immersed structure-structure interaction (SSI) between the ISM and the solid phase in the PM. Within each time step, we solve both FSI and SSI, employing strongly coupled partitioned schemes. This novel finite element method establishes a main building block of an evolving computational framework for modeling and simulating complex biomechanical problems, with focus on key phenomena during cell migration. Cell movement is strongly influenced by mechanical interactions between the cell body and the surrounding tissue, ie, the extracellular matrix (ECM). In this context, the PM represents the ECM, ie, a fibrous scaffold of structural proteins interacting with interstitial flow, and the ISM represents the cell body. The FSI models the influence of fluid drag, and the SSI models the force transmission between cell and ECM at adhesions sites.

“…Otherwise the flux of forces would be distributed through

{\overset{Ω}{true}}_{h}^{*}

Section: Fe‐based Immersed Methodologymentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A coupled approach for fluid saturated poroelastic media and immersed solids for modeling cell‐tissue interactions

Numer Methods Biomed Eng

Yoshihara

Wall

2018

“…As presented in Section 2, modeling the fluid‐saturated rough surface domain as homogenized poroelastic media (see, eg, the work of Coussy) leads to specific requirements on the applied model. The following governing equations were developed and successfully applied in the works of Chapelle and Moireau and Vuong et al() and are capable of representing all essential physical effects, such as incompressible flow on the microscale, finite deformations of the poroelastic matrix, deformation‐dependent and variable porosity, and arbitrary strain energy functions for the skeleton. Due to the high flexibility of this formulation for the homogenized roughness layer, a broad range of different microstructures and material behavior of fluid and structures are applicable.…”

Section: Governing Equations For All Involved Physical Domainsmentioning

confidence: 99%

A consistent approach for fluid‐structure‐contact interaction based on a porous flow model for rough surface contact

Ager

Schott

Numerical Meth Engineering

et al. 2019

Summary Simulation approaches for fluid‐structure‐contact interaction, especially if requested to be consistent even down to the real contact scenarios, belong to the most challenging and still unsolved problems in computational mechanics. The main challenges are 2‐fold—one is to have a correct physical model for this scenario, and the other is to have a numerical method that is capable of working and being consistent down to a zero gap. Moreover, when analyzing such challenging setups of fluid‐structure interaction, which include contact of submersed solid components, it gets obvious that the influence of surface roughness effects is essential for a physical consistent modeling of such configurations. To capture this system behavior, we present a continuum mechanical model that is able to include the effects of the surface microstructure in a fluid‐structure‐contact interaction framework. An averaged representation for the mixture of fluid and solid on the rough surfaces, which is of major interest for the macroscopic response of such a system, is introduced therein. The inherent coupling of the macroscopic fluid flow and the flow inside the rough surfaces, the stress exchange of all contacting solid bodies involved, and the interaction between fluid and solid are included in the construction of the model. Although the physical model is not restricted to finite element–based methods, a numerical approach with its core based on the cut finite element method, enabling topological changes of the fluid domain to solve the presented model numerically, is introduced. Such a cut finite element method–based approach is able to deal with the numerical challenges mentioned above. Different test cases give a perspective toward the potential capabilities of the presented physical model and numerical approach.

“…From our experience of similar porous medium systems [37,47] along with the numerical examples of Section 4, most of the computational time is spent in resolving the coupling between the structural deformation and the fluid flow or angiogenesis, respectively. Hence, in a first step, the nonlinear coupling between these two fields (42)- (43) can be resolved monolithically while for the coupling with species transport still a partitioned scheme is employed.…”

Section: Monolithic-partitioned Schemementioning

confidence: 99%

A monolithic multiphase porous medium framework for (a-)vascular tumor growth

Kremheller

Computer Methods in Applied Mechanics and Engineering

Yoshihara

et al. 2018

Self Cite

We present a dynamic vascular tumor model combining a multiphase porous medium framework for avascular tumor growth in a consistent Arbitrary Lagrangian Eulerian formulation and a novel approach to incorporate angiogenesis. The multiphase model is based on Thermodynamically Constrained Averaging Theory and comprises the extracellular matrix as a porous solid phase and three fluid phases: (living and necrotic) tumor cells, host cells and the interstitial fluid. Angiogenesis is modeled by treating the neovasculature as a proper additional phase with volume fraction or blood vessel density. This allows us to define consistent inter-phase exchange terms between the neovasculature and the interstitial fluid. As a consequence, transcapillary leakage and lymphatic drainage can be modeled. By including these important processes we are able to reproduce the increased interstitial pressure in tumors which is a crucial factor in drug delivery and, thus, therapeutic outcome. Different coupling schemes to solve the resulting five-phase problem are realized and compared with respect to robustness and computational efficiency. We find that a fully monolithic approach is superior to both the standard partitioned and a hybrid monolithic-partitioned scheme for a wide range of parameters. The flexible implementation of the novel model makes further extensions (e.g., inclusion of additional phases and species) straightforward.