Numerical simulation of a compound capsule in a constricted microchannel

Gounley, John; Draeger, Erik W.; Randles, Amanda

doi:10.1016/j.procs.2017.05.209

Cited by 30 publications

(16 citation statements)

References 30 publications

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“…A no-slip boundary condition is enforced on geometry surfaces by a halfway bounce-back boundary, while Zou-He boundary conditions are used at inlets and outlets with a fixed velocity profile at the inlet and a fixed pressure at the outlet [15]. Collision kernel from previous HARVEY implementations is extended to include an external force distribution F derived from an external force g [13–14, 34–36].…”

Section: Methodsmentioning

confidence: 99%

“…The cell membrane is numerically described by 20480 flat triangular face elements [21]. The triangulated grid for the membrane is created by taking successive subdivisions of an icosahedron, which produces a favorable regularity and isotropy, and projecting onto the cell initial spherical shape [15, 21]. Shear and dilational elastic responses to a strain of cell membrane are governed by a Skalak constitutive law, Where I 1 , I 2 are strain invariants, E is shear elastic modulus, and C is ratio of dilational to shear elastic moduli ( C = 1 to model the cell membrane as an area compressible biological membrane) [21].…”

Section: Methodsmentioning

confidence: 99%

“…We have conducted simulations with HARVEY [13–14], a massively parallel computational fluid dynamics solver based on the lattice Boltzmann method to investigate the local hemodynamics around DCC migrating within microvasculature. In this study, we leverage fluid-structure-interaction functionality implemented via the immersed boundary method to couple a finite element model for DCC with the fluid model [15]. To the best of our knowledge, no previous study investigated the hemodynamic conditions in the vicinity of migrating DCC within the microvasculature.…”

Section: Introductionmentioning

confidence: 99%

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Role of deformable cancer cells on wall shear stress-associated-VEGF secretion by endothelium in microvasculature

Dabagh

Randles

2019

PLoS ONE

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Endothelial surface layer (glycocalyx) is the major physiological regulator of tumor cell adhesion to endothelium. Cancer cells express vascular endothelial growth factor (VEGF) which increases the permeability of a microvessel wall by degrading glycocalyx. Endothelial cells lining large arteries have also been reported, in vitro and in vivo , to mediate VEGF expression significantly under exposure to high wall shear stress (WSS) > 0.6 Pa. The objective of the present study is to explore whether local hemodynamic conditions in the vicinity of a migrating deformable cancer cell can influence the function of endothelial cells to express VEGF within the microvasculature. A three-dimensional model of deformable cancer cells (DCCs) migrating within a capillary is developed by applying a massively parallel hemodynamics application to simulate the fluid-structure interaction between the DCC and fluid surrounding the DCC. We study how dynamic interactions between the DCC and its local microenvironment affect WSS exposed on endothelium, under physiological conditions of capillaries with different diameters and flow conditions. Moreover, we quantify the area of endothelium affected by the DCC. Our results show that the DCC alters local hemodynamics in its vicinity up to an area as large as 40 times the cancer cell lateral surface. In this area, endothelium experiences high WSS values in the range of 0.6–12 Pa. Endothelial cells exposed to this range of WSS have been reported to express VEGF. Furthermore, we demonstrate that stiffer cancer cells expose higher WSS on the endothelium. A strong impact of cell stiffness on its local microenvironment is observed in capillaries with diameters <16 μm. WSS-induced-VEGF by endothelium represents an important potential mechanism for cancer cell adhesion and metastasis in the microvasculature. This work serves as an important first step in understanding the mechanisms driving VEGF-expression by endothelium and identifying the underlying mechanisms of glycocalyx degradation by endothelium in microvasculature. The identification of angiogenesis factors involved in early stages of cancer cell-endothelium interactions and understanding their regulation will help, first to develop anti-angiogenic strategies applied to diagnostic studies and therapeutic interventions, second to predict accurately where different cancer cell types most likely adhere in microvasculature, and third to establish accurate criteria predisposing the cancer metastasis.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Role of deformable cancer cells on wall shear stress-associated-VEGF secretion by endothelium in microvasculature

Dabagh

Randles

2019

PLoS ONE

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“…The simulation of different kinds of biological cells going through small narrowings has attracted notable attention in recent years [90,25,91,92]. This kind of problem is a good way of testing how robust an immersed FSI method is when it comes to deal with large distortions of the Lagrangian mesh.…”

Section: Red Blood Cell Passing Through a Constrictionmentioning

confidence: 99%

Non-body-fitted fluid–structure interaction: Divergence-conforming B-splines, fully-implicit dynamics, and variational formulation

Casquero

Zhang

Bona-Casas

et al. 2018

Journal of Computational Physics

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Immersed boundary (IB) methods deal with incompressible visco-elastic solids interacting with incompressible viscous fluids. A long-standing issue of IB methods is the challenge of accurately imposing the incompressibility constraint at the discrete level. We present the divergence-conforming immersed boundary (DCIB) method to tackle this issue. The DCIB method leads to completely negligible incompressibility errors at the Eulerian level and various orders of magnitude of increased accuracy at the Lagrangian level compared to other IB methods. Furthermore, second-order convergence of the incompressibility error at the Lagrangian level is obtained as the discretization is refined. In the DCIB method, the Eulerian velocitypressure pair is discretized using divergence-conforming B-splines, leading to inf-sup stable and pointwise divergence-free Eulerian solutions. The Lagrangian displacement is discretized using non-uniform rational B-splines, which enables to robustly handle large mesh distortions. The data transfer needed between the Eulerian and Lagrangian descriptions is performed at the quadrature level using the same spline basis functions that define the computational meshes. This conduces to a fully variational formulation, sharp treatment of the fluid-solid interface, and a 0.5 increase in the convergence rate of the Eulerian velocity and the Lagrangian displacement measured in L 2 norm in comparison with using discretized Dirac delta functions for the data transfer. By combining the generalized-α method and a block-iterative solution strategy, the DCIB method results in a fully-implicit discretization, which enables to take larger time steps. Various two-and three-dimensional problems are solved to show all the aforementioned properties of the DCIB method along with mesh-independence studies, verification of the numerical method by comparison with the literature, and measurement of convergence rates.

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“…For example, HemeLB, a large‐scale LBM solver, has been extensively applied to study vascular modeling and angiogenesis . Additionally, several LBM solvers have been coupled with fluid‐structure interaction models and used for biologically relevant problems like modeling cancer cell transport . In spite of the increasing number of applications of LBM in blood flow analysis, there does not exist a unified scheme for implementing inlet and outlet boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Suitability of lattice Boltzmann inlet and outlet boundary conditions for simulating flow in image‐derived vasculature

Feiger

Vardhan

Gounley

et al. 2019

Numer Methods Biomed Eng

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The lattice Boltzmann method (LBM) is a popular alternative to solving the Navier-Stokes equations for modeling blood flow. When simulating flow using the LBM, several choices for inlet and outlet boundary conditions exist. While boundary conditions in the LBM have been evaluated in idealized geometries, there have been no extensive comparisons in image-derived vasculature, where the geometries are highly complex. In this study, the Zou-He (ZH) and finite difference (FD) boundary conditions were evaluated in image-derived vascular geometries by comparing their stability, accuracy, and run times. The boundary conditions were compared in four arteries: a coarctation of the aorta, dissected aorta, femoral artery, and left coronary artery. The FD boundary condition was more stable than ZH in all four geometries. In general, simulations using the ZH and FD method showed similar convergence rates within each geometry. However, the ZH method proved to be slightly more accurate compared with experimental flow using three-dimensional printed vasculature. The total run times necessary for simulations using the ZH boundary condition were significantly higher as the ZH method required a larger relaxation time, grid resolution, and number of time steps for a simulation representing the same physiological time. Finally, a new inlet velocity profile algorithm is presented for complex inlet geometries. Overall, results indicated that the FD method should generally be used for large-scale blood flow simulations in image-derived vasculature geometries. This study can serve as a guide to researchers interested in using the LBM to simulate blood flow. KEYWORDS boundary conditions, finite difference, hemodynamics, image-derived vasculature, lattice Boltzmann method, Zou-He Int J Numer Meth Biomed Engng. 2019;35:e3198.wileyonlinelibrary.com/journal/cnm

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Numerical simulation of a compound capsule in a constricted microchannel

Cited by 30 publications

References 30 publications

Role of deformable cancer cells on wall shear stress-associated-VEGF secretion by endothelium in microvasculature

Role of deformable cancer cells on wall shear stress-associated-VEGF secretion by endothelium in microvasculature

Non-body-fitted fluid–structure interaction: Divergence-conforming B-splines, fully-implicit dynamics, and variational formulation

Suitability of lattice Boltzmann inlet and outlet boundary conditions for simulating flow in image‐derived vasculature

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