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Modelling and Simulating the Adhesion and Detachment of Chondrocytes in Shear Flow Jian Hao 1 , Tsorng-Whay Pan 1 , and Doreen Rosenstrauch 2 1 Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA jianh@math.uh.edu, pan@math.uh.edu 2 The Texas Heart Institute and the University of Texas Health Science Center at Houston, Houston, TX 77030, USA Doreen.Rosenstrauch@uth.tmc.edu 1 Introduction Chondrocytes are typically studied in the environment where they normally reside such as the joints in hips, intervertebral disks or the ear. For example, in [SKE + 99], the effect of seeding duration on the strength of chondrocyte adhesion to articulate cartilage has been studied in shear flow chamber since such adhesion may play an important role in the repair of articular defects by maintaining cells in positions where their biosynthetic products can contribute to the repair process. However, in this investigation, we focus mainly on the use of auricular chondrocytes in cardiovascular implants. They are abundant, easily and efficiently harvested by a minimally invasive technique. Auricular chondrocytes have ability to produce collagen type-II and other important extracellular matrix constituents; this allows them to adhere strongly to the artificial surfaces. They can be genetically engineered to act like endothelial cells so that the biocompatibility of cardiovascular prothesis can be improved. Actually in [SBBR + 02], genetically engineered auricular chondrocytes can be used to line blood-contacting luminal surfaces of left ventricular assist device (LVAD) and a chondrocyte-lined LVAD has been planted into the tissue-donor calf and the results in vivo have proved the feasibility of using autologous auricular chondrocytes to improve the biocompatibility of the blood-biomaterial interface in LVADs and cardiovascular prothesis. Therefore, cultured chondrocytes may offer a more efficient and less invasive means of covering artificial surface with a viable and adherent cell layer. In this chapter, we first develop the model of the adhesion of chondrocytes to the artificial surface and then combine the resulting model with a Lagrange multiplier based fictitious domain method to simulate the detachment of chondrocyte cells in shear flow. The chondrocytes in the simulation are treated as neutrally buoyant rigid particles. As argued in [KS06] that the scaling estimates show that for typical parameter values for cell elasticity, deformations
210 J. Hao et al. due to shear flow and lubrication forces are small, the cells can be treated as rigid. The Newtonian incompressible viscous flow is modeled by the Navier– Stokes equations since the inertial effect is crucial for the lift-off of the cells; in most studies of cell adhesion, the Stokes flow is considered since the rolling of cells on the surface and then the capture of cells, like white blood cells, are the main interest, e.g., see [KS06, KH01, SZD03]. 2 Model for Cell Adhesion Cell adhesion to the extracellular matrix (ECM) plays key roles in the assembly of cells into functional multicellular organisms. Chondrocytes produce collagen type-II and other important extracellular matrix constituents; this allows them to adhere strongly to the artificial surfaces. Chondrocyte cells are responsible for the synthesis and maintenance of a viable ECM which is suitably adapted to cope with the physical pressures of its environment. On the lined surface of LVAD, a monolayer of cells formed on the surface was reported in [SBBR + 02]. Adhesive interactions between chondrocytes and ECM occur via a variety of molecular systems (e.g., see discussion for cell-matrix adhesion in [ZBCAG04]). Zaidel et al. have shown in [ZBCAG04] that cell-associated hyaluronan plays a central role in mediating early stages in the attachment of chondrocytes to the surfaces. Their results indicate that chondrocytes establish, initially, “soft contact” to the surface through a hyaluronan-based coat. The surface adhesion, mediated by the hyaluronan coat, occurs within seconds after the cell first encounters the surface. Then within a few tens of secondsto-minutes, the hyaluronan-mediated adhesion is replaced by integrin-based interactions which is actually a sequential formation starting from dot-shaped focal complexes (FXs), then changing to focal adhesions (FAs) and finally becoming fibrillar adhesions (FBs). In [ZBCAG04] chondrocytes were allowed to adhere to a serum coated glass coverslip for 10–25 minutes and exposed to shear flow, they drifted under flow for quite a distance (compared to their diameters) before detachment from the surface. In [SKE + 99] chondrocytes were seeded on the surface of a piece of articular cartilage for specific durations (5–40 minutes) and then were exposed to shear flow in a flow chamber. It was observed that the increase in resistance to shear stress-induced cell detachment with increasing seeding duration. But in [SBBR + 02], chondrocytes were allowed to have 24 hours for seeding process on the luminal surfaces of LVADs and then 4 days in incubator for promoting ECM synthesis to maximize the adherence of cells. When using flow loop to precondition seeded cells in order to promote good cell adherence, the cell loss during the process did not exceed 12%. The results in [SKE + 99] suggest that chondrocytes adhere to the surface mainly via hyaluronan gel and the numbers of integrin-based interactions are not high enough since the durations are comparable to the one used in [ZBCAG04]. But in [SBBR + 02], the results indicate that adhesions are mainly integrin-mediated interactions
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Partial Differential Equations
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Partial Differential Equations Mode
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Dedicated to Olivier Pironneau
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VIII Preface computers has been at
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Contents List of Contributors .....
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List of Contributors Yves Achdou UF
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List of Contributors XV Claude Le B
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Discontinuous Galerkin Methods Vive
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Discontinuous Galerkin Methods 5 2
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Discontinuous Galerkin Methods 7 g
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Discontinuous Galerkin Methods 9 (
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Discontinuous Galerkin Methods 15 W
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Let a h and b h denote the bilinear
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Discontinuous Galerkin Methods 19 t
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Discontinuous Galerkin Methods 21 l
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Table 1. Primal DG for transport Di
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Discontinuous Galerkin Methods 25 [
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Mixed Finite Element Methods on Pol
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Mixed FE Methods on Polyhedral Mesh
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4 Hybridization and Condensation Mi
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is symmetric and positive definite,
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with some coefficient α ∈ R wher
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44 E.J. Dean and R. Glowinski so fa
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46 E.J. Dean and R. Glowinski 2 A L
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50 E.J. Dean and R. Glowinski minim
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54 E.J. Dean and R. Glowinski Fig.
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56 E.J. Dean and R. Glowinski and
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60 E.J. Dean and R. Glowinski Fig.
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62 E.J. Dean and R. Glowinski Assum
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Higher Order Time Stepping for Seco
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u n+1 h Optimal Higher Order Time D
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124 R. Sanders and A.M. Tesdall 8.6
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126 R. Sanders and A.M. Tesdall 0.3
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128 R. Sanders and A.M. Tesdall [TR
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136 S. Lapin et al. Ω R γ Fig. 3.
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138 S. Lapin et al. 4 Energy Inequa
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140 S. Lapin et al. 5 Numerical Exp
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Domain Decomposition and Electronic
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Domain Decomposition Approach for C
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