Mathematical Modelling of the Blood Circulatory System

Red blood cell.
Red blood cell.

Blood vessels form one of the most complicated and important systems in the human body, the circulatory system. It is exposed to various risks and is poorly amenable to medical treatment. The mathematical modelling of blood transport in arteries, veins, capillaries and other blood vessels is a classical problem which is still very relevant today.

We are interested in modelling the whole circulatory system, taking into account not just the blood vessels themselves, whose walls consist of several layers of anisotropic material, but also the interaction of the vessels with both the surrounding muscle material and the blood flow within. 

One-dimension model for the whole circulatory system

During the past 30 years, considerable progress has been made in developing various asymptotic methods for problems in elasticity theory and hydrodynamics. These include the method of dimension-reduction, which replaces a higher-dimensional model by another one of lower dimension. Another group of methods concerns so-called singular perturbed domains, which often involve the interaction of models of different limit dimensions in applications.

One of the main goals of our project is to bring these modern asymptotic methods to bear on the modelling of the circulatory system with the aim of proposing a one-dimension model for the whole circulatory system which takes into account elastic properties of vessels and their interaction with surrounding muscle material.

This project is a collaboration between the division of Mathematics and Applied Mathematics (MTM) at the Department of Mathematics (MAI), and the division of Applied Thermodynamics and Fluid Mechanics (MVS) at the Department of Management and Engineering (IEI).


List of publications



Departments involved in this project