Simulations of Chemotaxis and Random Motility in Finite Domains
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Simulations of Chemotaxis and Random Motility in Finite Domains Ehsan Jabbarzadeh and Cameron F. Abrams Department of Chemical Engineering Drexel University 3141 Chestnut St. Philadelphia, PA 19104 ABSTRACT Rational design and selection of candidate porous biomaterials to serve as tissue engineering constructs rests on our ability to understand the influence of the porous microarchitecture on the transport of chemical species (e.g., nutrients and signaling compounds), fluid flow, and cellular locomotion and growth. We have begun to study the behavior of chemotactically mobile cells in response to unsteady signaling molecule concentration fields using a computational simulation-based model. The model couples fully time-dependent finite-difference solution of a reaction-diffusion equation for the concentration field of a generic chemoattractant to biased random walks representing individual moving cells. This model is a first step in building a quantitative, pore-level model of mass and cellular transport in porous tissue-engineered constructs. In these proceedings, we focus on our recent findings regarding the influence of flux-reactive boundary conditions in heterogeneous 2D domains on the chemotactic response of otherwise randomly moving cells. In particular, we find that, when cells are forced to “crawl” around obstacles in order to approach a point source of chemoattractant, the reactivity of the obstacle surface with respect to the chemoattractant strongly determines the morphology of the cells’ paths of locomotion. Cells crawl along non-reactive surfaces and strongly avoid reactive surfaces, due to the nature of the chemoattractant concentration gradients near the surface. We show further that tuning the reactivity of the surfaces of two obstacles defining a gap can control the passage of cells through the gap. From our work, we infer the importance of a proper treatment of boundary conditions in any future pore-level quantitatve modeling of mass transport and cellular response in porous media. INTRODUCTION Current technology gives us the ability to construct a wide variety of porous biomaterials for therapeutic applications, including tissue engineering and immuno-isolated implants. In fact, this ability far outpaces our understanding, at a fundamental level, of why one porous material performs better than another in any given application. In many applications, one of the most important performance requirements is that the material allow for easy development of healthy, internal capillary networks [1]. This neovascularization within an implant greatly reduces the impediment to biochemical transport relative to diffusion through the otherwise present fibrous capsule characteristic of the classical foreign body response (FBR) [2]. Mitigating the FBR in this way allows for optimal nutrient/waste transport for engineered tissues grown on porous scaffolds [3] and has the potential to guarantee rapid, controllable dosing in drug delivery and
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