Wensheng Shen

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A novel convection-diffusion-reaction model is developed to simulate fibroblast growth factor (FGF-2) binding to cell surface receptors (FGFRs) and heparan sulfate proteoglycans (HSPGs) under flow conditions within a cylindrical-shaped vessel or capillary. The model consists of a set of coupled nonlinear partial differential equations (PDEs) and a set of(More)
A mathematical model describing the thermomechanical interactions in biological bodies at high temperature is proposed by treating the soft tissue in biological bodies as a thermoporoelas-tic media. The heat transfer and elastic deformation in soft tissues are examined based on the Pennes bioheat transfer equation and the modified Duhamel-Neuman equations.(More)
—This paper presents a numerical solution to describe growth factor-receptor binding under flow through hollow fibers of a bioreactor. The multi-physics of fluid flow, the kinetics of fibroblast growth factor (FGF-2) binding to its receptor (FGFR) and heparan sulfate proteoglycan (HSPG) and FGF-2 mass transport is modeled by a set of coupled nonlinear(More)
This paper presents a parallel numerical solution to investigate multiple growth factors competitive binding within a bioreactor, an <i>in vitro</i> flow cell culture system. Since we assume all the species have the same flow, thus the multi-physics of fluid flow is modeled by the same incompressible Navier-Stokes equations. The kinetics of biochemical(More)
This paper presents a nonlinear solver based on the Newton-Krylov methods , where the Newton equations are solved by Krylov-subspace type approaches. We focus on the solution of unsteady systems, in which the temporal terms are discretized by the backward Euler method using finite difference. To save computational cost, an adaptive time stepping is used to(More)
We introduce a multiscale mathematical model for simulating ligand-receptor binding, dissociation and transport in blood circulation using a group of nonlinear differential equations. It is assumed that the biological interactions take place in capillaries, ligands bind and dissociate with receptors on the wall of capillary, and ligands are transported by(More)
This paper describes the application of Newton's method to low Mach number steady and unsteady laminar diffusion flames, which are characterized by low flow speed and highly variable density. The newly-emerged vorticity-velocity formulation of the Navier-Stokes equations is used for both steady and unsteady compressible flows to avoid staggered mesh(More)
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