A06 – Mathematical modelling and analysis of parameter dependent behaviour of multiscale systems
Summary of the work programme
The aim is to provide mathematical modelling, methods and analysis for electrically active implants. Understanding transitions between qualitatively different macroscopic dynamical behaviour due to changes of design parameters, so-called bifurcations, is important for engineering purposes and optimised medical treatment. The method of equation-free analysis allows us to systematically extract information about the macroscopic behaviour of microscopically defined systems. Applications range from parameter-dependent atomic force microscopy over bone remodelling to neural models of the basal ganglia network dynamics under deep brain stimulation to obtain novel medical treatment strategies.