A Nonlinear Lumped Parameters Model to Analyze the Dynamics of Venous Reflux

The aim of this work is to formulate a lumped parameters model of the venous tree of the lower limbs in order to study the effects and the possible clinical treatments for Chronic Venous Insufficiency (CVI). CVI is a pathology characterized by an important socio-economic impact due to its relevant prevalence, the costs for its diagnosis and treatment being more frequently widespread among the working population. The planning of haemodynamic surgical operations is critical to treat a pathological pattern of venous blood flow; such planning, in turn, depends on the right analysis of the possible consequences of flow modification. To this regard, the blood flow correction allows to solve the most important venous pathologies, in order to guarantee the restoration of normal blood flow by means of proper modifications of the venous tree. The developed model preserves the geometry of the venous network and considers some non linear resistive and capacitive effects. In fact, the study of the variability of some parameters (i.e. vessel radius) is very important to allow a correct diagnosis of vascular diseases. This variability causes a non linear behaviour of resistance and compliance effects. With the aid of the developed model we evaluate the time profile of blood velocity, flow and pressure in the entire venous network, both in physiological and pathological cases. The obtained results are discussed in comparison with available experimental data.