MODELING OF SANGUINE FLOW IN DIFFERENT VASCULAR DISEASES
MODELING OF SANGUINE FLOW IN DIFFERENT VASCULAR DISEASES

Summary/Abstract: Modelling and simulation of vascular architecture aims at locating potential vascular pathologies which cannot be observed by direct visualization of the angiography. Arteriovenous vascularization has two basic functions: the first one is the distributive function and the other one consists in the hemodynamic concepts. This paper approaches the study of fractal properties based on hemodynamic function. Arterial and venous vascular tree is designed to perform both functions, but it is very important to make the distinction between them, because they are carried out by different parts of the vascular pressure and venous structures. While the distributive function is linked to the geometric appearance of the vascular tree, the hemodynamic one is related to the dynamics of the blood flow. Previous studies of fractal character of the vascular tree have focused in particular on the distributive function. This paper approaches the study of fractal properties based on hemodynamic function. The simulation of blood flow and pressure in compliant vessels requires the definition of three differential equations. In order to build a structural tree at the level of large arteries terminals, the characters of small vessels must be modeled. The relevant parameters are the radius, bifurcation, asymmetry and area ratio, length and compliance. The mathematical model of uncontrolled circulation can be used in multiple cases: (a) to study the properties of flow self-regulation, irrespective of external control mechanisms; (b) to explain the need for external control mechanisms; (c) to serve as foundation for the construction of a simple model to control the flow. With the help of MatLab software, it was possible to build a graphical user interface to display and process ultrasound images and to simulate the mathematical calculation of the blood flow. This interface is based on two modules: one for acquisition and image processing and the second one for measurement and analysis registration. The modules highlight the modification of the parameters when the patient has cardio vascular diseases and teach the user to make the difference between a normal and a pathological disposition.

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