A hybrid discrete-continuum technique for individual-based migration models

In this chapter we present a modeling technique that is used to simulate individual-based migration models that are very appropriate for the modeling of cell responses to external signaling cues. The technique, referred to here as the hybrid discrete-continuum (HDC) technique, initially formulates a general problem of cell migration in response to external signaling cues in terms of system partial differential equations (PDEs) describing the evolution of mean-field quantities such as cell density and chemical concentrations. Using a discretized form of the PDEs, it is shown that one can generate a (discrete, stochastic) biased random walk model that enables one to track the migration paths of individual cells. The technique provides a simple but effective way of linking macro- and microscale events.