Compelling evidence shows the association of inflammation with atherosclerosis diseases, one of the leading cause of mortality and morbidity worldwide. Recent research indicated that the inflammatory process of atherosclerotic lesions is involved in the progression of atherosclerotic plaques in specific regions, such as the carotid bifurcation, which represents a risk for ischemic stroke as a result of the interaction between the blood and the plaque. We start modeling using 3D idealized geometry in order to capture the most important features of such interactions. Then, we proceed to a partly patient-specific computational domain representing an atherosclerotic artery. Understanding such interactions is of paramount importance preventing the risk of the plaque rupture. The numerical results comparisons have shown that, qualitatively, there is an agreement between idealized atherosclerotic artery and patient-specific atherosclerotic carotid artery. The idealized carotid geometry will be useful in future FSI studies of hemodynamic indicators based on medical images.
- Ross R. Atherosclerosis – An inflammatory disease. New England Journal of Medicine. 340, 115–126 (1999).
- Kayashima Y., Maeda-Smithies N. Atherosclerosis in Different Vascular Locations Unbiasedly Approached with Mouse Genetics. Genes. 11 (12), 1427 (2020).
- Chang Y. C., Hou T. Y., Merriman B., Osher S. A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows. Journal of Computational Physics. 124 (2), 449–464 (1996).
- Peskin C. S. Numerical analysis of blood flow in the heart. Journal of Computational Physics. 25 (3), 220–252 (1977).
- Peskin C. S., McQueen D. M. A three-dimensional computational method for blood flow in the heart – I. Immersed elastic fibers in a viscous incompressible fluid. Journal of Computational Physics. 81 (2), 372–405 (1989).
- Glowinski R., Pan T.-W., Periaux J. A fictitious domain method for Dirichlet problem and applications. Computer Methods in Applied Mechanics and Engineering. 111 (3–4), 283–303 (1994).
- Glowinski R., Pan T.-W., Periaux J. A fictitious domain method for external incompressible viscous flow modeled by Navier–Stokes equations. Computer Methods in Applied Mechanics and Engineering. 112 (1–4), 133–148 (1994).
- Frei S., Richter T., Wick T. Eulerian Techniques for Fluid-Structure Interactions: Part II – Applications. In: Abdulle A., Deparis S., Kressner D., Nobile F., Picasso M. (eds) Numerical Mathematics and Advanced Applications – ENUMATH 2013. Lecture Notes in Computational Science and Engineering. 103, 755–762 (2015).
- Wick T. Flapping and contact FSI computations with the fluid-solid interface-tracking/interface-capturing technique and mesh adaptivity. Computational Mechanics. 53, 29–43 (2014).
- Hughes T. J. R., Liu W. K., Zimmermann T. K. Lagrangian–Eulerian finite element formulation for incompressible viscous flows. Computer Methods in Applied Mechanics and Engineering. 29 (3), 329–349 (1994).
- Donea J., Giuliani S., Halleux J. P. An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid–structure interactions. Computer Methods in Applied Mechanics and Engineering. 33 (1–3), 689–723 (1982).
- Nobile F. Numerical Approximation of Fluid-Structure Interaction Problems with Application to Haemodynamics. Ph.D thesis; École Polytechnique Fédérale de Lausanne, Switzerland (2001).
- Boujena S., Kafi O., El Khatib N. A 2D mathematical model of blood flow and its interactions in the atherosclerotic artery. Mathematical Modelling of Natural Phenomena. 9 (6), 46–68 (2014).
- Boujena S., Kafi O., El Khatib N. Generalized Navier–Stokes equations with non-standard conditions for blood flow in atherosclerotic artery. Applicable Analysis. 95 (8), 1645–1670 (2016).
- El Khatib N., Kafi O., Tiago J., Sequeira A. Numerical simulations of a 3D fluid-structure interaction model for blood flow in an atherosclerotic artery. Mathematical Biosciences and Engineering. 14 (1), 179–193 (2017).
- El Khatib N., Génieys S., Volpert V. Atherosclerosis initiation modeled as an inflammatory process. Mathematical Modelling of Natural Phenomena. 2 (2), 126–141 (2007).
- El Khatib N. Modélisation mathématique de l'athérosclérose. Ph.D thesis; Université Claude Bernard–Lyon 1, France (2009).
- Faggiano E., Formaggia L., Antiga L. An open-source tool for patient-specific fluid-structure vessel mesh generation. Fifth International Symposium on Modelling of Physiological Flows, Chia Laguna, Italy (2013).
- Gambaruto A. M., Janela J., Moura A., Sequeira A. Sensitivity of hemodynamics in a patient specific cerebral aneurysm to vascular geometry and blood rheology. Mathematical Biosciences and Engineering. 8 (2), 409–423 (2011).
- Guerra T., Tiago J., Sequeira A. Optimal control in blood flow simulations. International Journal of Non-Linear Mechanics. 64, 57–69 (2014).
- Ciarlet P. G. Mathematical Elasticity. Vol. 1. Three Dimensional Elasticity. North-Holland (1988).
- Janela J., Moura A., Sequeira A. Absorbing boundary conditions for a 3D non-Newtonian fluid-structure interaction model for blood flow in arteries. International Journal of Engineering Science. 48 (11), 1332–1349 (2010).
- Janela J., Moura A., Sequeira A. A 3D non-Newtonian fluid–structure interaction model for blood flow in arteries. Journal of Computational and Applied Mathematics. 234 (9), 2783–2791 (2010).
- Ramalho S., Moura A., Gambaruto A. M., Sequeira A. Sensitivity to outflow boundary conditions and level of geometry description for a cerebral aneurysm. International Journal for Numerical Methods in Biomedical Engineering. 28 (6–7), 697–713 (2012).
- Li Z.-Y., Howarth S., Trivedi R. A., U-King-Im J. M., Graves M. J., Brown A., Wang L., Gillard J. H. Stress analysis of carotid plaque rupture based on in vivo high resolution MRI. Journal of Biomechanics. 39 (14), 2611–2622 (2006).
- Tang D., Yang C., Zheng J., Woodard P. K., Sicard G. A., Saffitz J. E., Yuan C. 3D MRI-based multicomponent FSI models for atherosclerotic plaques. Annals of Biomedical Engineering. 32, 947–960 (2004).