Mathematical modelling of atherosclerosis

¹ Department of Computer Science and Mathematics, Lebanese American University P.O. Box 36, Byblos, Lebanon.
² CEMAT/IST Instituto Superior Técnico Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal.
³ Departamento de Matemática, Instituto Superior Técnico Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal.
⁴ Moscow Institute of Physics and Technology, 9 Instituskii Lane, 141707 Dolgoprudny, Russia.
⁵ Marchuk Institute of Numerical Mathematics RAS, 7 Gubkina St., 119333 Moscow, Russia.
⁶ Sechenov University, 8-2 Trubetskaya st., 119991 Moscow, Russia.
⁷ Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France.
⁸ INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France.
⁹ Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, Russia.

^* Corresponding author: simakov.ss@mipt.ru

Received: 14 September 2019
Accepted: 5 November 2019

Abstract

The review presents the state of the art in the atherosclerosis modelling. It begins with the biological introduction describing the mechanisms of chronic inflammation of artery walls characterizing the development of atherosclerosis. In particular, we present in more detail models describing this chronic inflammation as a reaction-diffusion wave with regimes of propagation depending on the level of cholesterol (LDL) and models of rolling monocytes initializing the inflammation. Further development of this disease results in the formation of atherosclerotic plaque, vessel remodelling and possible plaque rupture due its interaction with blood flow. We review plaque-flow interaction models as well as reduced models (0D and 1D) of blood flow in atherosclerotic vasculature.