title: A Novel Analytical Approach to Pulsatile Blood Flow in the Arterial Network.
abstract: Haemodynamic simulations using one-dimensional (1-D) computational models exhibit many of the features of the systemic circulation under normal and diseased conditions. We propose a novel linear 1-D dynamical theory of blood flow in networks of flexible vessels that is based on a generalized Darcy's model and for which a full analytical solution exists in frequency domain. We assess the accuracy of this formulation in a series of benchmark test cases for which computational 1-D and 3-D solutions are available. Accordingly, we calculate blood flow and pressure waves, and velocity profiles in the human common carotid artery, upper thoracic aorta, aortic bifurcation, and a 20-artery model of the aorta and its larger branches. Our analytical solution is in good agreement with the available solutions and reproduces the main features of pulse waveforms in networks of large arteries under normal physiological conditions. Our model reduces computational time and provides a new approach for studying arterial pulse wave mechanics; e.g.,  the analyticity of our model allows for a direct identification of the role played by physical properties of the cardiovascular system on the pressure waves.
authors.affiliation: Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510, Mexico, D.F., Mexico.
authors.forename: Joaquín
authors.identifier: 0000-0002-8425-4520
authors.initials: J
authors.lastname: Flores
authors.affiliation: Division of Imaging Sciences and Biomedical Engineering, St. Thomas' Hospital, King's College London, London, SE1 7EH, UK.
authors.forename: Jordi
authors.initials: J
authors.lastname: Alastruey
authors.affiliation: Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510, Mexico, D.F., Mexico. eugenia.corvera@gmail.com.|Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028, Barcelona, Spain. eugenia.corvera@gmail.com.
authors.forename: Eugenia
authors.initials: E
authors.lastname: Corvera Poiré
mesh_terms: D001013:Aorta, Thoracic / Q000502:physiology*; D001783:Blood Flow Velocity; D002339:Carotid Arteries / Q000502:physiology*; D006801:Humans; D008955:Models, Cardiovascular
keywords: 1-D arterial haemodynamics; 1-D blood flow modelling; Benchmark test cases; Generalized Darcy’s model; Pulse wave propagation