# Mathematical and Numerical Models of Atherosclerotic Plaque Progression in Carotid Arteries

Published on Jan 1, 2019

· DOI :10.1007/978-3-030-55874-1_109

Silvia Pozzi1 , Christian Vergara24

Estimated H-index: 1

Estimated H-index: 24

Abstract

Published on Jan 1, 2019

· DOI :10.1007/978-3-030-55874-1_109

Silvia Pozzi1 , Christian Vergara24

Estimated H-index: 1

Estimated H-index: 24

Abstract

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2004

8 Authors (Dalin Tang, ..., Chun Yuan)

References17

#1Moritz P. Thon (TUM: Technische Universität München)H-Index: 3

#2André Hemmler (TUM: Technische Universität München)H-Index: 3

Last. Michael W. Gee (TUM: Technische Universität München)H-Index: 22

view all 7 authors...

This work is devoted to the development of a mathematical model of the early stages of atherosclerosis incorporating processes of all time scales of the disease and to show their interactions. The cardiovascular mechanics is modeled by a fluid–structure interaction approach coupling a non-Newtonian fluid to a hyperelastic solid undergoing anisotropic growth and a change of its constitutive equation. Additionally, the transport of low-density lipoproteins and its penetration through the endotheli...

#1Simone Deparis (EPFL: École Polytechnique Fédérale de Lausanne)H-Index: 20

#2Davide Forti (EPFL: École Polytechnique Fédérale de Lausanne)H-Index: 10

Last. Alfio Quarteroni (EPFL: École Polytechnique Fédérale de Lausanne)H-Index: 83

view all 4 authors...

Modeling Fluid-Structure Interaction (FSI) in the vascular system is mandatory to reliably compute mechanical indicators in vessels undergoing large deformations. In order to cope with the computational complexity of the coupled 3D FSI problem after discretizations in space and time, a parallel solution is often mandatory. In this paper we propose a new block parallel preconditioner for the coupled linearized FSI system obtained after space and time discretization. We name it FaCSI to indicate t...

#1Yifan Yang (Interdisciplinary Center for Scientific Computing)H-Index: 2

#2Willi Jäger (Interdisciplinary Center for Scientific Computing)H-Index: 7

Last. Thomas Richter (Heidelberg University)H-Index: 23

view all 4 authors...

In this paper, a model is developed for the evolution of plaques in arteries, which is one of the main causes for the blockage of blood flow. Plaque rupture and spread of torn-off material may cause closures in the down-stream vessel system and lead to ischemic brain or myocardial infarctions. The model covers the flow of blood and its interaction with the vessel wall. It is based on the assumption that the penetration of monocytes from the blood flow into the vessel wall, and the accumulation o...

#1Bruno Guerciotti (Polytechnic University of Milan)H-Index: 5

#2Christian Vergara (Polytechnic University of Milan)H-Index: 24

Last. Maurizio Domanin (University of Milan)H-Index: 9

view all 7 authors...

In this work, we provide a computational study of the effects of carotid endarterectomy (CEA) on the fluid-dynamics at internal carotid bifurcations. We perform numerical simulations in real geometries of the same patients before and after CEA, using patient-specific boundary data obtained by Echo-Color Doppler measurements. We analyze four patients with a primary closure and other four where a patch was used to close arteriotomies. The results show that (i) CEA is able to restore physiological ...

Inexact accurate partitioned algorithms for fluid-structure interaction problems with finite elasticity in haemodynamics

#1Fabio NobileH-Index: 40

#2Matteo Pozzoli (AgustaWestland)H-Index: 3

Last. Christian VergaraH-Index: 24

view all 3 authors...

In this paper we consider the numerical solution of the three-dimensional fluid-structure interaction problem in haemodynamics, in the case of real geometries, physiological data and finite elasticity vessel deformations. We study some new inexact schemes, obtained from semi-implicit approximations, which treat exactly the physical interface conditions while performing just one or few iterations for the management of the interface position and of the fluid and structure non-linearities. We show ...

#1Myriam Cilla (Ciber)H-Index: 10

#2Estefanía Peña (Ciber)H-Index: 37

Last. Miguel Ángel Martínez (Ciber)H-Index: 38

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Atherosclerosis is a vascular disease caused by inflammation of the arterial wall, which results in the accumulation of low-density lipoprotein (LDL) cholesterol, monocytes, macrophages and fat-laden foam cells at the place of the inflammation. This process is commonly referred to as plaque formation. The evolution of the atherosclerosis disease, and in particular the influence of wall shear stress on the growth of atherosclerotic plaques, is still a poorly understood phenomenon. This work prese...

Time accurate partitioned algorithms for the solution of fluid–structure interaction problems in haemodynamics

#1Fabio Nobile (EPFL: École Polytechnique Fédérale de Lausanne)H-Index: 40

#2Matteo PozzoliH-Index: 3

Last. Christian VergaraH-Index: 24

view all 3 authors...

In this work we deal with the numerical solution of the fluid-structure interaction problem arising in the haemodynamic environment. In particular, we consider BDF and Newmark time discretization schemes, and we study different methods for the treatment of the fluid-structure interface position, focusing on partitioned algorithms for the prescription of the continuity conditions at the fluid-structure interface. We consider explicit and implicit algorithms, and new hybrid methods. We study numer...

#1G. Di Tomaso (UCL: University College London)H-Index: 1

#2Vanessa Díaz-Zuccarini (UCL: University College London)H-Index: 13

Last. Cesar Pichardo-Almarza (Pfizer)H-Index: 7

view all 3 authors...

A multiscale model of atherosclerotic plaque formation at its early stage has been developed in order to integrate the various phenomena leading to fatty streak formation. The different scales considered in this model are in both the spatial domain (from cellular to organism level) and the time domain (from seconds to months). The cellular level was considered by modeling the transport and chemical interactions of low-density lipoproteins (LDL) and other agents in a stenosed artery. This was lin...

#1Paolo Crosetto (EPFL: École Polytechnique Fédérale de Lausanne)H-Index: 5

#2Simone DeparisH-Index: 20

Last. Alfio Quarteroni (EPFL: École Polytechnique Fédérale de Lausanne)H-Index: 83

view all 4 authors...

The increasing computational load required by most applications and the limits in hardware performances affecting scientific computing contributed in the last decades to the development of parallel software and architectures. In fluid-structure interaction (FSI) for haemodynamic applications, parallelization and scalability are key issues (see [L. Formaggia, A. Quarteroni, and A. Veneziani, eds., Cardiovascular Mathematics: Modeling and Simulation of the Circulatory System, Modeling, Simulation ...

#1Vincent Calvez (École normale supérieure de Lyon)H-Index: 62

#2Jean Gabriel Houot (Paris V: Paris Descartes University)H-Index: 1

Last. Gabriela Rusnakova (TUHH: Hamburg University of Technology)H-Index: 1

view all 5 authors...

This article is devoted to the construction of a mathematical model describing the early formation of atherosclerotic lesions. The early stage of atherosclerosis is an inflammatory process that starts with the penetration of low density lipoproteins in the intima and with their oxidation. This phenomenon is closely linked to the local blood flow dynamics. Extending a previous work \cite{CEMR} that was mainly restricted to a one-dimensional setting, we couple a simple lesion growth model relying ...

Cited By2

Error analysis of finite difference/collocation method for the nonlinear coupled parabolic free boundary problem modeling plaque growth in the artery

#1Farzaneh Nasresfahani (TMU: Tarbiat Modares University)H-Index: 1

#2Mohammad Reza Eslahchi (TMU: Tarbiat Modares University)H-Index: 14

Abstract The main target of this paper is to present a new and efficient method to solve a nonlinear free boundary mathematical model of atherosclerosis. This model consists of three parabolic, one elliptic and one ordinary differential equations that are coupled together and describes the growth of a plaque in the artery. We start our discussion by using the front fixing method to fix the free domain and simplify the model by changing the mixed boundary condition to a Neumann one by applying su...

Mathematical Modeling and Numerical Simulation of Atherosclerotic Plaque Progression Based on Fluid-Structure Interaction

#1Silvia Pozzi (Polytechnic University of Milan)H-Index: 1

#2Alberto Redaelli (Polytechnic University of Milan)H-Index: 49

Last. Paolo Zunino (Polytechnic University of Milan)H-Index: 28

view all 5 authors...

In this work we propose a mathematical and numerical model to describe the early stages of atherosclerotic plaque formation, which is based on the interaction of processes with different spatial and temporal scales. A fluid–structure interaction problem, used to describe the cardiovascular mechanics arising between blood and the artery wall, is coupled to a set of differential problems describing the evolution of solute concentrations. In order to manage the multiscale-in-space nature of the inv...