Abstract
The mathematical modeling of blood flow in the cardiovascular system has long history. Zero-dimensional (0D) and one-dimensional (1D) models contribute actively to the study of the human cardiovascular system. Usually, low-dimensional models consist of a system of time dependent equations that do not involve spatial derivatives, thus reducing the computational complexity compared to multi-dimensional models. Despite that more complex 3D cardiovascular models are available, there is a tendency of reintroducing the simpler 1D models, due to their capability of involving extensive segments of the cardiovascular system and providing boundary conditions for the advanced 3D models. The low-dimensional models can provide useful information to clinicians about the characteristics of blood flow at the level of individual incidents, patient-specific treatment, and can describe the general phenomena of circulatory physiology. The purpose of the current review is to discuss the advances and evolution of 0D and 1D models of human cardiovascular system.