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Mathematical modeling and numerical simulation of atherosclerotic plaque progression based on fluid-structure interaction. (English) Zbl 1476.65249

The authors present a mathematical model of atherosclerotic plaque growth, which involves both macroscopic cardiovascular processes and molecular and cellular events. To deal with the multiscale-in-space nature of the process of plaque growth, a fluid-structure interaction problem, arising between blood and the artery wall, was coupled to a set of PDEs (Partial Differential Equations) and an ODE (Ordinary Differential Equation) describing the evolution of solute concentrations. To manage the multiscale-in-space nature of the involved processes, the authors propose a suitable numerical strategy based on the splitting and sequential solution of the coupled problem. Some numerical results are presented to show the effects of geometry, model parameters and coupling strategy on plaque growth.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
92C50 Medical applications (general)
92C35 Physiological flow
76Z05 Physiological flows
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
35B32 Bifurcations in context of PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences

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[1] Arzani, A., Coronary artery plaque growth: a two-way coupled shear stress-driven model, Int. J. Numer. Methods Biomed. Eng., 36, e3293 (2019)
[2] Avgerinos, N.; Neofytou, P., Mathematical modelling and simulation of atherosclerosis formation and progress: a review, Ann. Biomed. Eng., 47, 1764-1785 (2019) · doi:10.1007/s10439-019-02268-3
[3] Brown, A.; Teng, Z.; Evans, P.; Gillard, J.; Samady, H.; Bennett, M., Role of biomechanical forces in the natural history of coronary atherosclerosis, Nat. Rev. Cardiol., 13, 210-220 (2016) · doi:10.1038/nrcardio.2015.203
[4] Calvez, V.; Houot, J.; Meunier, N.; Raoult, A.; Rusnakova, G., Mathematical and numerical modeling of early atherosclerotic lesions, ESAIM: Proc., 30, 1-14 (2010) · Zbl 1203.92035 · doi:10.1051/proc/2010002
[5] Caro, C.; Fitz-Gerald, J.; Schroter, R., Arterial wall shear and distribution of early atheroma in man, Nature, 223, 1159-1160 (1969) · doi:10.1038/2231159a0
[6] Chalmers, A.; Cohen, A.; Bursill, C.; Myerscough, M., Bifurcation and dynamics in a mathematical model of early atherosclerosis: how acute inflammation drives lesion development, J. Math. Biol., 71, 1451-1480 (2015) · Zbl 1350.92024 · doi:10.1007/s00285-015-0864-5
[7] Chappell, D.; Varner, S.; Nerem, R.; Medford, R.; Alexander, R., Oscillatory shear stress stimulates adhesion molecule expression in cultured human endothelium, Circ. Res., 82, 532-539 (1998) · doi:10.1161/01.RES.82.5.532
[8] Chatzizisis, Y.; Coşkun, A.; Jonas, M.; Edelman, E.; Feldman, C.; Stone, P., Role of endothelial shear stress in the natural history of coronary atherosclerosis and vascular remodeling: molecular, cellular, and vascular behavior, J. Am. Coll. Cardiol., 49, 2379-2393 (2007) · doi:10.1016/j.jacc.2007.02.059
[9] Chiu, J-J; Usami, S.; Chien, S., Vascular endothelial responses to altered shear stress: pathologic implications for atherosclerosis, Ann. Med., 41, 19-28 (2008) · doi:10.1080/07853890802186921
[10] Cicha, I.; Goppelt-Struebe, M.; Yilmaz, A.; Daniel, W.; Garlichs, C., Endothelial dysfunction and monocyte recruitment in cells exposed to non-uniform shear stress, Clin. Hemorheol. Microcirc., 39, 113-119 (2008) · doi:10.3233/CH-2008-1074
[11] Cilla, M.; Peña, E.; Martínez, M., Mathematical modelling of atheroma plaque formation and development in coronary arteries, J. R. Soc. Interface R. Soc., 11, 20130866 (2014) · doi:10.1098/rsif.2013.0866
[12] Corti, A.; Chiastra, C.; Colombo, M.; Garbey, M.; Migliavacca, F.; Casarin, S., A fully coupled computational fluid dynamics-agent-based model of atherosclerotic plaque development: multiscale modeling framework and parameter sensitivity analysis, Comput. Biol. Med., 118, 103623 (2020) · doi:10.1016/j.compbiomed.2020.103623
[13] Crosetto, P.; Deparis, S.; Fourestey, G.; Quarteroni, A., Parallel algorithms for fluid-structure interaction problems in haemodynamics, SIAM J. Sci. Comput., 33, 1598-1622 (2011) · Zbl 1417.92008 · doi:10.1137/090772836
[14] Cunningham, K.; Gotlieb, A., The role of shear stress in the pathogenesis of atherosclerosis, Lab. Investig. J. Tech. Methods Pathol., 85, 9-23 (2005) · doi:10.1038/labinvest.3700215
[15] Deparis, S.; Forti, D.; Grandperrin, G.; Quarteroni, A., Facsi: A block parallel preconditioner for fluid-structure interaction in hemodynamics, J. Comput. Phys., 327, 700-718 (2016) · Zbl 1373.74036 · doi:10.1016/j.jcp.2016.10.005
[16] Di Tomaso, G.; Diaz-Zuccarini, V.; Pichardo-Almarza, C., A multiscale model of atherosclerotic plaque formation at its early stage, IEEE Trans. Bio-med. Eng., 58, 3460-3463 (2011) · doi:10.1109/TBME.2011.2165066
[17] Donea, J.; Giuliani, S.; Halleux, J., An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions, Comput. Methods Appl. Mech. Eng., 33, 689-723 (1982) · Zbl 0508.73063 · doi:10.1016/0045-7825(82)90128-1
[18] Faxon, D.; Fuster, V.; Libby, P.; Beckman, J.; Hiatt, W.; Thompson, R.; Topper, J.; Annex, B.; Rundback, J.; Fabunmi, R.; Robertson, R.; Loscalzo, J., Atherosclerotic vascular disease conference: writing group III: pathophysiology, Circulation, 109, 2617-2625 (2004) · doi:10.1161/01.CIR.0000128520.37674.EF
[19] Fernández, M.; Gerbeau, J.; Grandmont, C., A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid, Int. J. Numer. Methods Eng., 69, 4, 794-821 (2007) · Zbl 1194.74393 · doi:10.1002/nme.1792
[20] Figueroa, C.; Baek, S.; Taylor, C.; Humphrey, J., A computational framework for fluid-solid-growth modeling in cardiovascular simulations, Comput. Methods Appl. Mech. Eng., 198, 3583-3602 (2009) · Zbl 1229.74097 · doi:10.1016/j.cma.2008.09.013
[21] González Montero, J.; Valls, N.; Brito, R.; Rodrigo, R., Essential hypertension and oxidative stress: new insights, World J. Cardiol., 6, 353-366 (2014) · doi:10.4330/wjc.v6.i6.353
[22] Grundy, SM; Stone, NJ; Bailey, AL; Beam, C.; Birtcher, KK; Blumenthal, RS; Braun, LT; de Ferranti, S.; Faiella-Tommasino, J.; Forman, DE; Goldberg, R.; Heidenreich, PA; Hlatky, MA; Jones, DW; Lloyd-Jones, D.; Lopez-Pajares, N.; Ndumele, CE; Orringer, CE; Peralta, CA; Saseen, JJ; Smith, SC; Sperling, L.; Virani, SS; Yeboah, J., 2018 aha/acc/aacvpr/aapa/abc/acpm/ada/ags/apha/aspc/nla/pcna guideline on the management of blood cholesterol: Executive summary: A report of the american college of cardiology/american heart association task force on clinical practice guidelines, J. Am. Coll. Cardiol., 73, 24, 3168-3209 (2019) · doi:10.1016/j.jacc.2018.11.002
[23] Hao, W.; Friedman, A., The LDL-HDL profile determines the risk of atherosclerosis: a mathematical model, PLoS ONE, 9, e90497 (2014) · doi:10.1371/journal.pone.0090497
[24] Herrmann, R.; Malinauskas, R.; Truskey, G., Characterization of sites with elevated LDL permeability at intercostal, celiac, and iliac branches of the normal rabbit aorta, Arterioscler. Thromb. J. Vasc. Biol. Am. Heart Assoc., 14, 313-323 (1994)
[25] Hirt, C.; Amsden, A.; Cook, J., An arbitrary Lagrangian-Eulerian computing method for all flow speeds, J. Comput. Phys., 14, 227-253 (1974) · Zbl 0292.76018 · doi:10.1016/0021-9991(74)90051-5
[26] Hwang, J.; Saha, A.; Boo, YC; Sorescu, G.; Mcnally, J.; Holland, S.; Dikalov, S.; Giddens, D.; Griendling, K.; Harrison, D.; Jo, H., Oscillatory shear stress stimulates endothelial production of o 2- from p47phox-dependent NAD(P)H oxidases, leading to monocyte adhesion, J. Biol. Chem., 278, 47291-47298 (2003) · doi:10.1074/jbc.M305150200
[27] Kiechl, S.; Willeit, J., The natural course of atherosclerosis: part I: incidence and progression, Arterioscler. Thromb. Vasc. Biol., 19, 1484-1490 (1999) · doi:10.1161/01.ATV.19.6.1484
[28] Ku, D.; Giddens, D.; Zarins, C.; Glagov, S., Pulsatile flow and atherosclerosis in the human carotid bifurcation—positive correlation between plaque location and low and oscillating shear-stress, Arteriosclerosis (Dallas, Tex.), 5, 293-302 (1985)
[29] Kwak, B.; Bäck, M.; Bochaton-Piallat, M-L; Caligiuri, G.; Daemen, M.; Davies, P.; Hoefer, I.; Holvoet, P.; Jo, H.; Krams, R.; Lehoux, S.; Monaco, C.; Steffens, S.; Virmani, R.; Weber, C.; Wentzel, J.; Evans, P., Biomechanical factors in atherosclerosis: mechanisms and clinical implications, Eur. Heart J., 35, 3013-3020 (2014) · doi:10.1093/eurheartj/ehu353
[30] Libby, P., Inflammation in atherosclerosis, Arterioscler. Thromb. Vasc. Biol., 32, 2045-2051 (2012) · doi:10.1161/ATVBAHA.108.179705
[31] Liu, B.; Tang, D., Computer simulations of atherosclerotic plaque growth in coronary arteries, Mol. Cell. Biomech. MCB, 7, 193-202 (2010)
[32] Nichols, W., O’Rourke, M., Vlachopoulos, C. (eds.): McDonald’s Blood Flow in Arteries. Hodder Arnold (2011)
[33] Nixon, A.; Gunel, M.; Sumpio, B., The critical role of hemodynamics in the development of cerebral vascular disease: a review, J. Neurosurg., 112, 1240-1253 (2009) · doi:10.3171/2009.10.JNS09759
[34] Nobile, F.; Pozzoli, M.; Vergara, C., Time accurate partitioned algorithms for the solution of fluid-structure interaction problems in haemodynamics, Comput. Fluids, 86, 470-482 (2013) · Zbl 1290.76166 · doi:10.1016/j.compfluid.2013.07.031
[35] Nobile, F.; Pozzoli, M.; Vergara, C., Inexact accurate partitioned algorithms for fluid-structure interaction problems with finite elasticity in haemodynamics, J. Comput. Phys., 273, 598-617 (2014) · Zbl 1351.76324 · doi:10.1016/j.jcp.2014.05.020
[36] Nobile, F.; Vergara, C., An effective fluid-structure interaction formulation for vascular dynamics by generalized robin conditions, SIAM J. Sci. Comput., 30, 731-763 (2008) · Zbl 1168.74038 · doi:10.1137/060678439
[37] Parton, A.; Mcgilligan, V.; O’Kane, M.; Baldrick, F.; Watterson, S., Computational modelling of atherosclerosis, Brief. Bioinform., 17, 562-575 (2015) · doi:10.1093/bib/bbv081
[38] Pozzi, S.; Vergara, C.; Vermolen, FJ; Vuik, C., Mathematical and numerical models of atherosclerotic plaque progression in carotid arteries, Numerical Mathematics and Advanced Applications ENMATH 2019 (2021), Berlin: Springer, Berlin · Zbl 1475.92010
[39] Ross, R., Atherosclerosis-an inflammatory disease, Am. Heart J., 138, S419-S420 (1999) · doi:10.1016/S0002-8703(99)70266-8
[40] Silva, T.; Jäger, W.; Neuss-Radu, M.; Sequeira, A., Modeling of the early stage of atherosclerosis with emphasis on the regulation of the endothelial permeability, J. Theor. Biol., 496, 110229 (2020) · doi:10.1016/j.jtbi.2020.110229
[41] Swim, E.; Seshaiyer, P., A nonconforming finite element method for fluid-structure interaction problems, Comput. Methods Appl. Mech. Eng., 195, 17-18, 2088-2099 (2006) · Zbl 1119.74049 · doi:10.1016/j.cma.2005.01.017
[42] Tarbell, J., Mass transport in arteries and the localization of atherosclerosis, Annu. Rev. Biomed. Eng., 5, 79-118 (2003) · doi:10.1146/annurev.bioeng.5.040202.121529
[43] Thon, M.; Hemmler, A.; Glinzer, A.; Mayr, M.; Wildgruber, M.; Zernecke-Madsen, A.; Gee, M., A multiphysics approach for modeling early atherosclerosis, Biomech. Model. Mechanobiol., 17, 617-644 (2017) · doi:10.1007/s10237-017-0982-7
[44] Traub, O.; Berk, B., Laminar shear stress: mechanisms by which endothelial cells transduce an atheroprotective force, Arterioscler. Thromb. Vasc. Biol., 18, 677-685 (1998) · doi:10.1161/01.ATV.18.5.677
[45] Yang, Y.; Jager, M.; Neuss-Radu, W.; Richter, T., Mathematical modeling and simulation of the evolution of plaques in blood vessels, J. Math. Biol., 72, 973-996 (2015) · Zbl 1343.35190 · doi:10.1007/s00285-015-0934-8
[46] Zarins, C.; Giddens, D.; Bharadvaj, B.; Sottiurai, V.; Mabon, R.; Glagov, S., Carotid bifurcation atherosclerosis. Quantitative correlation of plaque localization with flow velocity profiles and wall shear stress, Circ. Res., 53, 502-514 (1981) · doi:10.1161/01.RES.53.4.502
[47] Zohdi, T.; Holzapfel, G.; Berger, S., A phenomenological model for atherosclerotic plaque growth and rupture, J. Theor. Biol., 227, 437-443 (2004) · Zbl 1439.92072 · doi:10.1016/j.jtbi.2003.11.025
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