Mathematical Modelling of the Cardiovascular System

The arterial windkessel model and its modifications are discussed extensively in view of the significant role played in lumped parameter modelling of the cardiovascular system. Electric circuit analysis is used to derive and explain the fundamental equations. The reservoir-wave theory is also presented in view of its appealing but controversial approach to arterial haemodynamics. One- and three-dimensional modelling is also discussed in the context of recent developments with emphasis on some of the fundamental equations. The geometrical multiscale approach is presented in relation to its ability to couple dimensionally heterogeneous models for more realistic haemodynamic simulations.