Particle Simulations of Morphogenesis
Koumousakos P., Bayati B., Milde F. and Tauriello G., Mathematical Models and Methods in Applied Sciences
The simulation of the creation and evolution of biological forms requires the development of computational methods that are capable of resolving their hierarchical, spatial and temporal complexity. Computations based on interacting particles, provide a unique computational tool for discrete and continuous descriptions of morphogenesis of systems ranging from the molecular to the organismal level. The capabilities of particle methods hinge on the simplicity of their formulation which enables the formulation of a unifying computational framework encom- passing deterministic and stochastic models. In this paper, we discuss recent advances in particle methods for the simulation of biological systems at the mesoscopic and the macroscale level. We present results from applications of particle methods including reaction-diffusion on deforming surfaces, deterministic and stochastic descriptions of tumor growth and angiogenesis and discuss successes and challenges of this approach.
doi: 10.1142/S021820251100543X (pdf)