# Mathematical and Computational Modelling of Blood Pressure and Flow

• Carole Leguy
Chapter
Part of the Series in BioEngineering book series (SERBIOENG)

## Abstract

Since William Harvey discovered in 1628 that blood circulates in a closed loop in the body, and that the contraction of the heart delivered the driving force to move the blood [1], cardiovascular mechanics has gained a lot of attention and is still subject to research. During the last decades, mathematical models have been developed to grasp the diversity of blood flow patterns and pressure propagation phenomena within the cardiovascular system [2]. The geometry of the arterial and venous system is difficult to describe; blood, a complex non-Newtonian fluid, circulates in vessels with non-linear viscoelastic walls. It is therefore very difficult to take into account the complexity of the cardiovascular system within mathematical or numerical models in a comprehensive manner. Thus, mathematical and numerical models generally focus on particular aspects of the cardiovascular circulation. Two approaches can be used to simulate blood flow: either a phenomenon is simulated locally (and in detail) using 3D Computational Fluid Dynamics (CFD) or fluid structure interaction (FSI) models, or with lumped or wave propagation models to simulate the entire systemic circulation considering a simplified geometry. These models have proven their value to understand normal physiology better [3], to simulate the effects of pathophysiological symptoms, or to predict the effect of medical interventions [4]. In the following sections, physiological considerations will be reviewed and the basic equations that govern blood flow and pressure dynamics within arteries and veins will be presented. Later, lumped, 1D and 3D models will be introduced and finally, clinical relevance and applications will be introduced

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