Computational phlebology: reviewing computer models of the venous system

Relatively little attention has been paid to the venous system and valves from a cardiovascular engineering perspective up to now. Given the involvement of venous valve haemodynamics in the development of deep vein thrombosis this is an area that needs more detailed investigation and close collaboration between clinicians and cardiovascular engineers. The purpose of this review article is to provide an indication of the physiological conditions that need to be included in any computational model of the venous system, based on recommendations from clinicians, and to summarize published computational models of the venous system by trying to explore their limitations and application range. A MEDLINE search was carried out on the relevant literature from 1940 until today. Several models have been developed with a specific purpose in mind to coincide with the aim of each individual study. The model complexity and laws used in each model vary significantly. There are more simplistic computational models based on electric circuit analogies, termed as lumped parameter models, which can be used to provide boundary conditions to one-dimensional (1D) and three-dimensional (3D) domain models, followed by 1D continuous models based on analytical equations, which allow the description of pressure wave and can be non-linear in nature. Finally, there are the more advanced 3D models, which are based on the principles of haemodynamics, and consider the compliance of the venous system and the effect that venous valves have on the cardiovascular system. In conclusion, it appears that computer modelling of the venous system can contribute greatly to our understanding of venous physiology and allow us to evaluate the haemodynamic interactions that occur in the venous system under different physiological conditions.