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Mathematical models and numerical simulations are widely used in the field of hemodynamics, representing a valuable resource to better understand physiological and pathological processes. The theory behind the phenomenon is closely related…

Fluid Dynamics · Physics 2021-06-15 Giulia Bertaglia , Valerio Caleffi , Alessandro Valiani

Analysing the haemodynamics of flow in carotid artery disease serves as a means to better understand the development and progression of associated complex diseases. Carotid artery disease can predispose people to major adverse…

Changes in cardiovascular hemodynamics are closely related to the development of aortic regurgitation, a type of valvular heart disease. Metrics derived from blood flows are used to indicate aortic regurgitation onset and evaluate its…

Computer Vision and Pattern Recognition · Computer Science 2022-04-07 Derek Long , Cameron McMurdo , Edward Ferdian , Charlene A. Mauger , David Marlevi , Alistair A. Young , Martyn P. Nash

Investigating blood flow in the cardiovascular system is crucial for assessing cardiovascular health. Computational approaches offer some non-invasive alternatives to measure blood flow dynamics. Numerical simulations based on traditional…

Numerical Analysis · Mathematics 2024-06-07 Han Zhang , Raymond Chan , Xue-Cheng Tai

We propose and analyze a family of models describing blood perfusion through a tissue surrounding a thin blood vessel. Our goal is to rigorously establish convergence results among 3D-3D Darcy--Stokes, 3D-1D Darcy--Poiseuille, and 1D…

Analysis of PDEs · Mathematics 2025-07-18 Laurel Ohm , Sarah Strikwerda

One-dimensional blood flow model accuracy has been verified in many studies. This work is about introducing gravity into a one-dimensional model. For this purpose, gravitational force was introduced into the existing model. The boundary…

Fluid Dynamics · Physics 2023-06-27 Oleg Shramko , Andrey Svitenkov , Pavel Zun

We perform various numerical tests to study the effect of (boundary) stenosis on blood flow stability, employing a detailed and accurate, second-order finite-volume scheme for numerically implementing a partial differential equation (PDE)…

Numerical Analysis · Mathematics 2024-08-05 Shantanu Singh , Nikolaos Bekiaris-Liberis

Accurate simulation of blood flow in deformable vessels is critical in cardiovascular research for understanding disease progression and informing clinical decision-making. However, due to the thin-walled nature of arteries, traditional…

Computational Engineering, Finance, and Science · Computer Science 2026-01-05 Chenxi Zhao , Dong Wu , Weiyi Kong , Oskar J. Haidn , Xiangyu Hu

We numerically investigate the influence of flow development on secondary flow patterns and subsequent wall shear stress distributions in a curved artery model, and we compute vascular metrics commonly used to assess variations in blood…

Fluid Dynamics · Physics 2022-09-20 Christopher Cox , Michael W. Plesniak

Advances in computational science offer a principled pipeline for predictive modeling of cardiovascular flows and aspire to provide a valuable tool for monitoring, diagnostics and surgical planning. Such models can be nowadays deployed on…

Machine Learning · Computer Science 2019-09-19 Georgios Kissas , Yibo Yang , Eileen Hwuang , Walter R. Witschey , John A. Detre , Paris Perdikaris

The emergence of computational fluid dynamics (CFD) enabled the simulation of intricate transport processes, including flow in physiological structures, such as blood vessels. While these so-called hemodynamic simulations offer…

The impact of increased stiffness and pulsatile load on the circulation and their influence on heart performance have been documented not only for cardiovascular events but also for ventricular dysfunctions. For this reason, computer models…

Numerical Analysis · Mathematics 2021-11-11 Federica Caforio , Christoph M. Augustin , Jordi Alastruey , Matthias A. F. Gsell , Gernot Plank

Morphology of cardiovascular tissue is influenced by the unsteady behavior of the blood flow and vice versa. Therefore, the pathogenesis of several cardiovascular diseases is directly affected by the blood-flow dynamics. Understanding flow…

Blood flow imaging provides important information for hemodynamic behavior within the vascular system and plays an essential role in medical diagnosis and treatment planning. However, obtaining high-quality flow images remains a significant…

Numerical Analysis · Mathematics 2026-04-02 Han Zhang , Xue-Cheng Tai , Jean-Michel Morel , Raymond H. Chan

In this paper, a pore-scale network modeling method, based on the flow continuity residual in conjunction with a Newton-Raphson non-linear iterative solving technique, is proposed and used to obtain the pressure and flow fields in a network…

Fluid Dynamics · Physics 2014-12-02 Taha Sochi

An improved one-dimensional mathematical model based on Pulsed Flow Equations (PFE) is derived by integrating the axial component of the momentum equation over the transient Womersley velocity profile, providing a dynamic momentum equation…

Fluid Dynamics · Physics 2012-12-04 Omer San , Anne E. Staples

It is known that the maximum diameter for the rupture-risk assessment of the abdominal aortic aneurysm is a generally good method, but not sufficient. Alternative features obtained with computational modeling may provide additional useful…

Computational Engineering, Finance, and Science · Computer Science 2020-03-16 Shanlin Qin , Rongliang Chen , Bokai Wu , Jia Liu , Wen-Shin Shiu , Zhengzheng Yan , Xiao-Chuan Cai

We are interested in simulating blood flow in arteries with a one dimensional model. Thanks to recent developments in the analysis of hyperbolic system of conservation laws (in the Saint-Venant/ shallow water equations context) we will…

Numerical Analysis · Mathematics 2013-04-24 Olivier Delestre , Pierre-Yves Lagrée

Computational fluid dynamics (CFD) models are emerging as tools for assisting in diagnostic assessment of cardiovascular disease. Recent advances in image segmentation has made subject-specific modelling of the cardiovascular system a…

Quantitative Methods · Quantitative Biology 2021-01-18 Mitchel J. Colebank , L. Mihaela Paun , M. Umar Qureshi , Naomi Chesler , Dirk Husmeier , Mette S. Olufsen , Laura Ellwein Fix

In fluid physics, data-driven models to enhance or accelerate solution methods are becoming increasingly popular for many application domains, such as alternatives to turbulence closures, system surrogates, or for new physics discovery. In…