Blood Flow under External Strains: Phenomenological Approach, Theoretical Developments and Numerical Analysis

Abstract

In the medical field, the measurement of blood flow characteristics is often necessary. more specifically, blood pressure is an essential measure when it comes to assessing health. all over the world, many people suffer from hyper- or hypotension, and as it is known that these diseases can lead to serious complications, it is of great interest to determine the blood pressure with high accuracy. Nowadays, such information requires the use of specific materials; the present method for the measurement of the arterial pressure, by applying pressure using an armband (with a control device called sphygmomanometer), is known to introduce significant errors due to the inadequacy of the band dimensions (both the length and the circumference). The objective of the present research is to study and simulate the discharge of the blood in an artery subjected to external strains using theoretical developments and a numerical approach. Based on these modelling results, the response of the fluid to the external pressure of the band can be studied, and finally appropriate corrective factors for the true pressure and the measured pressure could be assessed. This research has been carried out with the aim of sharing medical and engineering views on the subject. The artery can be modelled as a deformable pipe, where the blood flowing in it is a fluid with specific properties. Thus, two complementary and interconnected domains are covered, solid mechanics (to obtain analytic relations between the strains and the deformations, using either linear or non-linear theories) and fluid mechanics (to study the discharge of blood in a deformable pipe, using finite volume methods), therefore considering the problem as a loose fluid–structure interaction (fSI). These two domains, which are well studied for common materials in civil engineering applications, are applied here not only to specific materials but especially to uncommon structures that, besides the somehow common fSI developments, lead to the investigation and research of very specific boundary conditions, giving them a physi cally based behaviour. at present, the research has reached the penultimate step, with the two main mentioned axes being fully developed and tested on their own. In particular, the boundary conditions developed for the models have been investigated and modelled in depth.