A global solution to a hyperbolic problem for blood flow modelling

Abstract

The paper aims to examine the hyperbolic system of equations governing one-dimensional haemodynamics and its relevance in analysing blood flow under mechanical influences, with particular emphasis on the impact of altering the angle of the leg axis. Methods and approaches for solving hyperbolic equations have been developed in light of their properties and characteristics. The primary objective of this study was to investigate the interplay between vein pressure, pulse wave velocity, and vascular distension. The study revealed an inverse relationship between vein pressure and pulse wave velocity. A decrease in pulse wave velocity occurs when vein pressure rises, and vice versa. Both real measurements and modelling results confirmed this dependence. The pressure in the veins is between 10.8 and 13.6 kPa, and the speed of the pulse wave is between 0.061 and 0.27 kPa. The agreement between real and model data was high. The modelled venous pressure and pulse wave velocity values are close to the actual values. However, it is essential to acknowledge the limitations of this paper. These limitations include the utilisation of one-dimensional haemodynamic models, which fail to consider the three-dimensional structure of the circulatory system. Additionally, the analysis is restricted to examining changes solely in the leg axis angle. The research helps to clarify the relationship between mechanical actions and haemodynamic parameters. The findings may help research and develop new methods for identifying and treating conditions associated with the cardiovascular system.