Creeping Flow past a Solid Sphere in a Porous Medium

Ganapathy, R.

doi:10.1002/zamm.19970771113

Cited by 25 publications

(16 citation statements)

References 5 publications

(3 reference statements)

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“…The only limitation in this process is our ability to find the associated integrals in Eq. (8). Here we consider a blob with exponential decay and / 0 d ð0Þ ¼ 0 (for symmetry) / d ðrÞ ¼ ðr þ 2dÞ 2 224pd 5 e Àr=d whose exponential form allows the analytical computation of the integrals related to B d .…”

Section: Finding G D By First Selecting the Blobmentioning

confidence: 99%

Computation of three-dimensional Brinkman flows using regularized methods

Cortez

Cummins

Leiderman

et al. 2010

Journal of Computational Physics

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Section: Finding G D By First Selecting the Blobmentioning

confidence: 99%

Computation of three-dimensional Brinkman flows using regularized methods

Cortez

Cummins

Leiderman

et al. 2010

Journal of Computational Physics

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“…We introduced a 60-Pa pressure gradient across the 2 mg/mL collagen gel to drive flow with a mean velocity of 4.6 μm/s, as measured along the center line of the device. The total fluid drag force imparted on a spherical cell can be estimated from the solution for drag on a sphere within a Brinkman medium (21), and for our experimental setup, a 16.8 pN integrated shear force and 235 pN integrated pressure force are imparted on a 20-μm-diameter cell (SI Appendix, Eq. S5).…”

Section: Significancementioning

confidence: 99%

Mechanotransduction of fluid stresses governs 3D cell migration

Polacheck

German

Mammoto

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

228

215

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Solid tumors are characterized by high interstitial fluid pressure, which drives fluid efflux from the tumor core. Tumor-associated interstitial flow (IF) at a rate of ∼3 μm/s has been shown to induce cell migration in the upstream direction (rheotaxis). However, the molecular biophysical mechanism that underlies upstream cell polarization and rheotaxis remains unclear. We developed a microfluidic platform to investigate the effects of IF fluid stresses imparted on cells embedded within a collagen type I hydrogel, and we demonstrate that IF stresses result in a transcellular gradient in β1-integrin activation with vinculin, focal adhesion kinase (FAK), FAK PY397 , F actin, and paxillindependent protrusion formation localizing to the upstream side of the cell, where matrix adhesions are under maximum tension. This previously unknown mechanism is the result of a force balance between fluid drag on the cell and matrix adhesion tension and is therefore a fundamental, but previously unknown, stimulus for directing cell movement within porous extracellular matrix.mechanobiology | breast cancer | metastasis I ntegrins and associated focal adhesion (FA) proteins form a tension-sensitive mechanical link between the extracellular matrix (ECM) and the cytoskeleton, and serve as key components in the signaling cascade by which cells transduce mechanical signals into biological responses (mechanotransduction) (1, 2). Contractile stresses generated by the cell are balanced by tractions at cell-substrate adhesions, and the FA protein vinculin accumulates at regions of high substrate stress (3, 4). The FA protein paxillin colocalizes with vinculin (4) and mediates β1-integrin FA turnover through interaction with FA kinase (FAK) (5). The FAK-paxillin signaling axis recruits vinculin to β1 integrins at regions of high matrix adhesion tension (6), and paxillin-a key mechanosensor (7)-mediates protrusion formation at regions of high stress on 2D substrates (8), and FAK-paxillin-vinculin signaling is required for mechanosensing and durotaxis (9).The tumor microenvironment imparts mechanical and chemical signals on tumor and stromal cells (10), and advanced breast carcinomas are characterized by high interstitial fluid pressure (11), an indicator of poor prognosis (12). This elevated fluid pressure drives interstitial flow (IF) and alters chemical transport within the tumor (13), and IF influences tumor cell migration through the generation of autocrine chemokine gradients (14). Equally important, although not as well understood, is the physical drag imparted on the ECM and constitutive cells (15) by IF, which is analogous to the FA-activating shear stresses generated on endothelial cells by hemodynamic forces (16). With endothelial cells, shear stress can be the dominant mechanical stimulus that induces FAK activation and cytoskeletal remodeling; however, for cells embedded within a porous matrix scaffold, the ratio of the force due to the pressure drop across the cell to the total shear force is inversely proportional to hydrogel p...

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“…Once K is known for a given matrix, whether via direct measurement in an experiment or by using a theoretical relationship like those above, the Brinkman equation can be used to estimate the average shear stress on the surface of the sphere, as well as the fluid drag on the sphere from a given average flow velocity U 0 . Ganapathy's form of the shear stress on a sphere in a Brinkman medium is (Ganapathy, 1997):…”

Section: Theorymentioning

confidence: 99%

Cells in 3D matrices under interstitial flow: Effects of extracellular matrix alignment on cell shear stress and drag forces

Pedersen

Lichter

Swartz

2010

Journal of Biomechanics

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a b s t r a c tInterstitial flow is an important regulator of various cell behaviors both in vitro and in vivo, yet the forces that fluid flow imposes on cells embedded in a 3D extracellular matrix (ECM), and the effects of matrix architecture on those forces, are not well understood. Here, we demonstrate how fiber alignment can affect the shear and pressure forces on the cell and ECM. Using computational fluid dynamics simulations, we show that while the solutions of the Brinkman equation accurately estimate the average fluid shear stress and the drag forces on a cell within a 3D fibrous medium, the distribution of shear stress on the cellular surface as well as the peak shear stresses remain intimately related to the pericellular fiber architecture and cannot be estimated using bulk-averaged properties. We demonstrate that perpendicular fiber alignment of the ECM yields lower shear stress and pressure forces on the cells and higher stresses on the ECM, leading to decreased permeability, while parallel fiber alignment leads to higher stresses on cells and increased permeability, as compared to a cubic lattice arrangement. The Spielman-Goren permeability relationships for fibrous media agreed well with CFD simulations of flow with explicitly considered fibers. These results suggest that the experimentally observed active remodeling of ECM fibers by fibroblasts under interstitial flow to a perpendicular alignment could serve to decrease the shear and drag forces on the cell.

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Creeping Flow past a Solid Sphere in a Porous Medium

Cited by 25 publications

References 5 publications

Computation of three-dimensional Brinkman flows using regularized methods

Computation of three-dimensional Brinkman flows using regularized methods

Mechanotransduction of fluid stresses governs 3D cell migration

Cells in 3D matrices under interstitial flow: Effects of extracellular matrix alignment on cell shear stress and drag forces

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