Modeling extracellular matrix viscoelasticity using smoothed particle hydrodynamics with improved boundary treatment

Heck, Tommy; Smeets, Bart; Vanmaercke, Simon; Bhattacharya, Pinaki; Odenthal, Tim; Ramón, Herman; Oosterwyck, Hans Van; Liedekerke, Paul Van

doi:10.1016/j.cma.2017.04.031

Cited by 18 publications

(21 citation statements)

References 32 publications

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“…Φ J is the shape function in the cell mesh ( = ) or ECM mesh ( = ), respectively, which is associated with node J contained in one of the corresponding sets of nodes   h or   h . Vector fields are discretized analogously by applying (16) to each component. Note that in the sequel, we refer to each cell node in the immersed mesh by I ∈   h and to each ECM node in the background mesh by B ∈   h .…”

Section: Spatial Fe Discretizationmentioning

confidence: 99%

“…Farsad and Vernerey presented a chemo‐mechanical approach for cell adhesion, contraction, and spreading using a combined extended FE and level‐set approach to track the cell boundary in a one‐dimensional axisymmetric setup. Recently, a novel approach for modeling cell‐ECM interactions in 3D was proposed, where the ECM is modeled by a viscoelastic smoothed particle hydrodynamics model . Unlike in earlier works, in this paper, we adopt a purely mesoscopic point of view, with individual homogenized FE models for the cell and the ECM in 3D.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, a novel approach for modeling cell-ECM interactions in 3D was proposed, where the ECM is modeled by a viscoelastic smoothed particle hydrodynamics model. 16 Unlike in earlier works, in this paper, we adopt a purely mesoscopic point of view, with individual homogenized FE models for the cell and the ECM in 3D. In this context, the ISM represents a single biological cell and the PM represents the surrounding tissue.…”

Section: Introductionmentioning

confidence: 99%

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

Vuong

Yoshihara

Wall

2018

Numer Methods Biomed Eng

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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.

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Section: Spatial Fe Discretizationmentioning

confidence: 99%

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

Vuong

Yoshihara

Wall

2018

Numer Methods Biomed Eng

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“…Therefore, inertial 171 forces can be omitted from the conservation of momentum equation, resulting in the 172 non-inertial SPH (NSPH) method. As described before [20,31], the conservation of 173 momentum for ECM particle i in contact with neighboring particles j becomes:…”

mentioning

confidence: 97%

“…with m the mass, ρ the density, µ the dynamic viscosity, v the velocity, x the position, 175 σ the stress tensor, ∇ i W ij the derivative of the smoothing kernel W , η = 0.01h 2 a 176 correction factor that prevents singularity when particles approach each other and F b i 177 body forces. The detailed implementation of this method as described before [20,31] is 178 summarized in S2 Text. The ECM is modeled as a circular domain with a radius of 179 150 µm, fixed displacement at the boundary and a particle distance dp = 2 µm.…”

mentioning

confidence: 99%

The role of actin protrusion dynamics in cell migration through a degradable viscoelastic extracellular matrix: Insights from a computational model

Heck

Vargas

Smeets

et al. 2019

Preprint

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Actin protrusion dynamics plays an important role in the regulation of three-dimensional (3D) cell migration. Cells form protrusions that adhere to the surrounding extracellular matrix (ECM), mechanically probe the ECM and contract in order to displace the cell body. This results in cell migration that can be directed by the mechanical anisotropy of the ECM. However, the subcellular processes that regulate protrusion dynamics in 3D cell migration are difficult to investigate experimentally and therefore not well understood. Here, we present a computational model of cell migration through a degradable viscoelastic ECM. The cell is modeled as an active deformable object that captures the viscoelastic behavior of the actin cortex and the subcellular processes underlying 3D cell migration. The ECM is regarded as a viscoelastic material, with or without anisotropy due to fibrillar strain stiffening, and modeled by means of the meshless Lagrangian smoothed particle hydrodynamics (SPH) method. ECM degradation is captured by local fluidization of the material and permits cell migration through the ECM. We demonstrate that changes in ECM stiffness and cell strength affect cell migration and are accompanied by changes in number, lifetime and length of protrusions. Interestingly, directly changing the total protrusion number or the average lifetime or length of protrusions does not affect cell migration. A stochastic variability in protrusion lifetime proves to be enough to explain differences in cell migration velocity. Force-dependent adhesion disassembly does not result in faster migration, but can make migration more efficient. We also demonstrate that when a number of simultaneous protrusions is enforced, the optimal number of simultaneous protrusions is one or two, depending on ECM anisotropy. Together, the model provides non-trivial new insights in the role of protrusions in 3D cell migration and can be a valuable contribution to increase the understanding of 3D cell migration mechanics. Author summaryThe ability of cells to migrate through a tissue in the human body is vital for many processes such as tissue development, growth and regeneration. At the same time, abnormal cell migration is also playing an important role in many diseases such as July 5, 2019 2/38 cancer. If we want to be able to explain the origin of these abnormalities and develop new treatment strategies, we have to understand how cells are able to regulate their migration. Since it is challenging to investigate cell migration through a biological tissue in experiments, computational modeling can provide a valuable contribution. We have developed a computational model of cell migration through a deformable and degradable material that describes both mechanics of the cell and the surrounding material and subcellular processes underlying cell migration. This model captures the formation of long and thin protrusions that adhere to the surrounding material and that pull the cell forward. It provides new non-trivial insights in the role of these protrus...

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Simulating bubble dynamics in a buoyant system

Arai

Villafranco

Grace

et al. 2019

Numerical Methods in Fluids

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Multiphase flows are critical components of many physical systems; however, numerical models of multiphase flows with large parameter gradients can be challenging. Here, two different numerical methods, volume of fluid (VOF) and smoothed particle hydrodynamics (SPH), are used to model the buoyant rise of isolated gas bubbles through quiescent fluids for a range of Bond and Reynolds numbers. The VOF is an Eulerian grid-based method, whereas the SPH is Lagrangian and mesh free. Each method has unique strengths and weaknesses, and a comparison of the two approaches as applied to multiphase phenomena has not previously been performed. The VOF and SPH simulations are compared, verified, and validated. Results using two-dimensional VOF and SPH simulations are similar to each other and are able to reproduce numerical benchmarks and experimental results for sufficiently large Morton and Reynolds numbers. It is also shown that at low Reynolds numbers, the two methods, SPH and VOF, diverge in the transient regime of the bubble rise. Regimes that require simulations capable of representing three-dimensional drag are identified as well as regimes in which results from VOF and SPH diverge. KEYWORDS bubble dynamics, buoyant systems, multiphase flows, rising bubble dynamics, smoothed particle hydrodynamics (SPH), volume of fluid (VOF) Re = vL ,

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Modeling extracellular matrix viscoelasticity using smoothed particle hydrodynamics with improved boundary treatment

Cited by 18 publications

References 32 publications

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

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

The role of actin protrusion dynamics in cell migration through a degradable viscoelastic extracellular matrix: Insights from a computational model

Simulating bubble dynamics in a buoyant system

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