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

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Abstract

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 involved processes, we propose a suitable numerical strategy based on the splitting and sequential solution of the coupled problem. We present some preliminary numerical results and investigate the effects of geometry, model parameters and coupling strategy on plaque growth.

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Notes

  1. According to the following definition of TAWSS, this average is intended with respect to the fast time variable t, i.e. along a heartbeat, see Sect. 2.4 for its definition

  2. To further simplify the notation, we omit symbol \(\,\,\widehat{}\,\,\) for the Lagrangian variables when they are arguments.

  3. Here we are using a local-in-time interval [0, T].

  4. Note that TAWSS depends also on space, i.e., \(TAWSS=TAWSS(\tau ,{\varvec{x}}).\)

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Authors and Affiliations

  1. MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milan, MI, Italy

    Silvia Pozzi & Paolo Zunino

  2. Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milan, MI, Italy

    Alberto Redaelli & Emiliano Votta

  3. LaBS, Dipartimento di Chimica, Materiali e Ingegneria Chimica “Giulio Natta”, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milan, MI, Italy

    Christian Vergara

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  1. Silvia Pozzi
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  2. Alberto Redaelli
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Correspondence to Christian Vergara.

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Pozzi, S., Redaelli, A., Vergara, C. et al. Mathematical Modeling and Numerical Simulation of Atherosclerotic Plaque Progression Based on Fluid-Structure Interaction. J. Math. Fluid Mech. 23, 74 (2021). https://doi.org/10.1007/s00021-021-00598-8

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