Tissue Eng Lecture_102413

Bmc sys biol 2011 24 ned hspg gra the model that

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Unformatted text preview: rstitial VEGF/Protease Transport and Reactions t generating an VEGF biochemical reactions and transport processes are s. As with pro- described by partial differential equations with appropriate first-order rate boundary conditions. The computational domain consists was done with of two components: the interstitium, into which VEGF is on affects only secreted, and a sprout surfaceolecular-detailed reactionComputational methods: m layer, on which VEGF capation” model); ture by the receptors is modeled. Upon secretion from the diffusion edge of the -bound VEGF leading model domain (z = +L), VEGF transport F degradation” within the domain is governed by the mass balance PDEs equation shown; similar equations for other isoEGF degrada- (VEGF165 to estimate concentrations in space and time with appropriate boundary conditions F is protected forms): -independent ∂ [V165 ] -bound VEGF = D165 2 [V165 ] − kV [V165 ] − kV [V165 ] P deg ∂t onger isoforms (1) kV,H the same rate − on [V165 ][H] + kV,H [V165 H] off KECM Computational model of guiding sprout formation - - Solve to estimate VEGF transport and dynamics 25 Computational model of guiding sprout formation 26 Computational model of guiding sprout formation 27 Computational model of guiding sprout formation 28 Angiogenesis steps: Elongation and branching As the endothelial cells migrate towards the source of angiogenic stimulus, several decisions must be made • • • Will the sprout have branches? How frequently will the sprout branch? How many sprouts can meet the needs for tissue oxygenation? Computational modeling can aid in investigating the conditions necessary for sprout elongation and branching 29 Angiogenesis steps: Elongation and branching Several factors contribute to elongation and branching • Cell migration, mediated by signaling through • • Fibroblast growth factor (FGF Cadherins (junction proteins that link ECs) VEGF Matrix stiffness and composition Chemokines signaling 30 Computational model of elongation and branching Computational methods: cell-based model - Discrete, lattice-based stochastic agent-based model + continuous model of VEGF concentration gradient - Cells have finite volume, deformable shape and compete for space - Different “agents” (cells) move based on pre-defined rules according to some probability, in order to reduce the energy of the system Bauer, Jackson, and Jiang. Biophys J. 2007 31 assumed to be homogeneous throughout the sim main. The rate VEGF decays, l . 0, is also ass constant, and B(x, y, V) is a function describing cell binding and uptake of VEGF. The maximum amount of VEGF that can be internalized by an endothelial cell per unit of time by b. To compute b, we consider the numbe receptors per endothelial cell and the rate at wh receptor complexes can be internalized and surfac recycled. Vascular endothelial cells express bot and VEGFR2. While VEGFR2 is VEGF-specific is not and can bind adhesion molecules and ot factors (49). However, in this model, we do n multiple VEGF isoforms or growth factors, or binding of adhesion molecules, both of which c Cellular Model of Angiogenesis available binding sites. Thus, in our calculation o the total number of VEGFR1 and VEGFR2 recep (3...
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This note was uploaded on 01/20/2014 for the course BME 410 taught by Professor Han during the Spring '08 term at USC.

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