Mathematical modelling in systems biology. Simulation of the desmoplastic stromal reaction as an example

摘要: A mathematical model of collagen fiber mesh formation was created to evaluate the possible role chemotaxis and haptotaxis in histomorphology a desmoplastic stromal reaction (DSR). Fibroblasts were mathematicaly interpreted as mobile discrete objects, characterized by their velocity position, both dependent on time. This resulted cell migration paths, commonly termed "trajectories" which are modulated stochastic process. The implementation chemotactic effects requires knowledge concentration distribution appropriate chemical substance scenario. simplistic assumption allows calculation numerical solution resulting diffusion equation. Adding necessitates simulation extracellular matrix (ECM). is modeled vector field contains information both, density direction. production new fibers based ordinary differential equations coupled with migratory behavior cells. Filters help smooth trajectories. Appropriate visualization direct comparison results histomorphology. Matches between computed data real counterparts indicate that development models describe forecast course DSR. makes systems biology stepping stone improving biomedical research.