Complex systems in biomedicine

encompasses the modeling of most diverse compartments such as the cardiovascular, respiratory, skeletal and nervous systems, as well as the mechanical and biochemical interaction between blood flow and arterial walls, or electrocardiac processes and the electric conduction into biological tissues. Mathematical models can be set up to simulate both vasculogenesis (the aggregation and organisation of endothelial cells dispersed in a given environment) and angiogenesis (the formation of new vessels sprouting from an existing vessel) that are relevant to the formation of vascular networks, and in particular to the description of tumor growth. The integration of models aimed at simulating the cooperation and interrelation of different systems is an even more difficult task. It calls for the set up of, for instance, interaction models for the integrated cardio-vascular system and the interplay between central circulation and peripheral compartments, models for the mid-long range cardiovascular adjustments to pathological conditions (e.g. to account for surgical interventions, congenital malformations, or tumor growth), models for the integration among circulation, tissue perfusion, biochemical and thermal regulation, models for parameter identification and sensitivity analysis to parameter changes or data uncertainty – and many others.