Geodesic
Mathematical modelling of the effects of statins on the growth of necrotic core in atherosclerotic plaque
Weirui Lei1 ; Jiwen Hu1 ; Yaqian Xie1 ; Can Liu1 ; Xuekun Chen1
1 College of Mathematics and Physics, University of South China, Hengyang 421001, China
Mathematical modelling of natural phenomena, Tome 18 (2023), article no. 11.

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A large necrotic core increases the risk of atherosclerotic plaque instability. Statins can delay the growth of necrotic core in plaques, but the kinetic mechanism of statins in slowing down the necrotic core has not yet been addressed in detail. In this paper, a mathematical model is governed by a system of advection-diffusion-reaction equations coupling of the porous nature of vessel wall is established and applied to illustrate the plaque growth with lipid-rich necrotic core (LRNC) with and without statins using finite element method. We study the influence of LRNC plaque growth for different drug concentrations at different time intervals. The results showed that the drug use at different time points has a significant impact on the treatment efficacy. Compared with short-term, low-dose treatment, early statin treatment with high dose showed more pronounced effects on reducing the low-density lipoprotein (LDL) cholesterol, decreasing the volume of necrotic core, changing the characteristics of plaques, and improving the plaque stability. The model is validated by comparing with the clinical data, and may be used to predict the progression of LRNC plaque and the effects of statin therapy.
DOI : 10.1051/mmnp/2023005

Weirui Lei 1 ; Jiwen Hu 1 ; Yaqian Xie 1 ; Can Liu 1 ; Xuekun Chen 1

1 College of Mathematics and Physics, University of South China, Hengyang 421001, China 
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Weirui Lei; Jiwen Hu; Yaqian Xie; Can Liu; Xuekun Chen. Mathematical modelling of the effects of statins on the growth of necrotic core in atherosclerotic plaque. Mathematical modelling of natural phenomena, Tome 18 (2023), article  no. 11. doi : 10.1051/mmnp/2023005. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2023005/

[1] G. Abi Younes, N. El Khatib Mathematical modeling of inflammatory processes of atherosclerosis 2022 5 43

[2] L. Ai, K. Vafai A coupling model for macromolecule transport in a stenosed arterial wall 2006 1568 1591

[3] J. Auer, R. Berent Alirocumab as add-on therapy to statins: current evidence and clinical potential 2018 191 202

[4] L. Badimon, T. Padró, G. Vilahur Atherosclerosis, platelets and thrombosis in acute ischaemic heart disease 2012 60 74

[5] R.Y. Ball, E.C. Stowers, J.H. Burton, N.R.B. Cary, J.N. Skepper, M.J. Mitchinson Evidence that the death of macrophage foam cells contributes to the necrotic core of atheroma 1995 45 54

[6] M. Banach, C. Serban, A. Sahebkar, D.P. Mikhailidis, S. Ursoniu, K.K. Ray, P.W. Serruys Impact of statin therapy on coronary plaque composition: a systematic review and meta-analysis of virtual histology intravascular ultrasound studies 2015 1 21

[7] S. Bellosta, A. Corsini Statin drug interactions and related adverse reactions: an update 2018 25 37

[8] M.A.K. Bulelzai, J.L.A. Dubbeldam Long time evolution of atherosclerotic plaques 2012 1 10

[9] V. Calvez, A. Ebde, N. Meunier, A. Raoult Mathematical modelling of the atherosclerotic plaque formation 2009

[10] A. Causevic-Ramosevac, S. Semiz Drug interactions with statins 2013 277 293

[11] A.D. Chalmers, A. Cohen, C.A. Bursill, M.R. Myerscough Bifurcation and dynamics in a mathematical model of early atherosclerosis 2015 1451 1480

[12] A.D. Chalmers, C.A. Bursill, M.R. Myerscough Nonlinear dynamics of early atherosclerotic plaque formation may determine the efficacy of high density lipoproteins (HDL) in plaque regression 2017 e0187674

[13] K.L. Chambers, M.G. Watson and M.R. Myerscough. A lipid-structured model of atherosclerosis with macrophage proliferation. Preprint https://arxiv.org/abs/2205.04715 (2022).

[14] C. Chen, Y. Gu, J. Tu, X. Guo, D. Zhang Microbubble oscillating in a microvessel filled with viscous fluid: A finite element modeling study 2016 54 64

[15] S. Chung, K. Vafai Effect of the fluid-structure interactions on low-density lipoprotein transport within a multi-layered arterial wall 2012 371 381

[16] M. Cilla, E. Pena, M.A. Martinez Mathematical modelling of atheroma plaque formation and development in coronary arteries 2014 20130866

[17] M. Dabagh, P. Jalali, J.M. Tarbell The transport of LDL across the deformable arterial wall: the effect of endothelial cell turnover and intimal deformation under hypertension 2009 H983 H996

[18] J.T. Davies, S.F. Delfine, C.E. Feinberg, M.F. Johnson, V.L. Nappi, J.T. Olinger, A.P. Schwab, H.I. Swanson Current and emerging uses of statins in clinical therapeutics: a review 2016 13 29

[19] H.S. El-Sawy, A.M. Al-Abd, T.A. Ahmed Stimuli-responsive nano-architecture drug-delivery systems to solid tumor micromilieu: past, present, and future perspectives 2018 10636 10664

[20] N. El Khatib, O. Kafi, A. Sequeira, S. Simakov, Y. Vassilevski, V. Volpert Mathematical modelling of atherosclerosis 2019 603

[21] H. Esterbauer, G. Striegl, H. Puhl, M. Rotheneder Continuous monitoring of in vitro oxidation of human low density lipoprotein 1989 67 75

[22] D.W. Faltaos, S. Urien, V. Carreau, M. Chauvenet, J.S. Hulot, P. Giral, E. Bruckert, P. Lechat Use of an indirect effect model to describe the LDL cholesterol-lowering effect by statins in hypercholesterolaemic patients 2006 321 330

[23] S. Fazli, E. Shirani, M.R. Sadeghi Numerical simulation of LDL mass transfer in a common carotid artery under pulsatile flows 2011 68 76

[24] W.J. Fu, M.T. Chen, L.J. Ou, T. Li, X. Chang, R.L. Huang, J. Zhang, Z. Zhang Xiaoyaosan prevents atherosclerotic vulnerable plaque formation through heat shock protein/glucocorticoid receptor axis-mediated mechanism 2019 5531 5545

[25] R.G. Gerrity The role of the monocyte in atherogenesis: II. Migration of foam cells from atherosclerotic lesions 1981 191 200

[26] L. Gonzalez, B.L. Trigatti Macrophage apoptosis and necrotic core development in atherosclerosis: a rapidly advancing field with clinical relevance to imaging and therapy 2017 303 312

[27] W. Hao, A. Friedman The LDL-HDL profile determines the risk of atherosclerosis: a mathematical model 2014 e90497

[28] W. Hai-Liang, W. Shou-Tao, D.O. Pharmacy Effects of rosuvastatin on macrophage polarization in atherosclerosis 2018 42 44

[29] H.A. Himburg, D.M. Grzybowski, A.L. Hazel, J.A. Lamack, X.M. Li Spatial comparison between wall shear stress measures and porcine arterial endothelial permeability 2004 H1916 H1922

[30] M. Hu, B. Tomlinson Evaluation of the pharmacokinetics and drug interactions of the two recently developed statins, rosuvastatin and pitavastatin 2014 51 65

[31] D.S. Hwang, E.S. Shin, S.J. Kim, J.H. Lee, J.M. Kim, S.G. Lee Early differential changes in coronary plaque composition according to plaque stability following statin initiation in acute coronary syndrome: classification and analysis by intravascular ultrasound-virtual histology 2013 336 344

[32] W.J. Jusko, H.C. Ko Physiologic indirect response models characterize diverse types of pharmacodynamic effects 1994 406 419

[33] M. Kawasaki, K. Sano, M. Okubo, H. Yokoyama, Y. Ito, I. Murata, K. Tsuchiya, S. Minatoguchi, X. Zhou, H. Fujita, H. Fujiwara Volumetric quantitative analysis of tissue characteristics of coronary plaques after statin therapy using threedimensional integrated backscatter intravascular ultrasound 2005 1946 1953

[34] I.V. Kirillova, E.L. Kossovich, R.A. Safonov, N.O. Chelnokova, A.A. Golyadkina and M.S. Shevtsova, Finite element modeling of atherosclerotic plaque evolution. 2016 3rd International Conference on Information Science and Control Engineering (ICISCE). IEEE (2016) 973–977.

[35] H.S. Kruth, W. Huang, I. Ishii, W.Y. Zhang Macrophage foam cell formation with native low density lipoprotein 2002 34573 34580

[36] W. Lei, J. Hu, Y. Liu, W. Liu, X. Chen Numerical evaluation of high-intensity focused ultrasound-induced thermal lesions in atherosclerotic plaques 2021 1154 1168

[37] K. Ley, Y.I. Miller, C.C. Hedrick Monocyte and macrophage dynamics during atherogenesis 2011 1506 1516

[38] J. Li, D. Li, D. Yang, H.L. Hang, Y.W. Wu, R. Yao, X.Y. Chen, Y.L. Xu, W. Dai, D. Zhou, X.H. Zhao Irregularity of carotid plaque surface predicts subsequent vascular event: a MRI study 2020 185 194

[39] P. Libby Inflammation in atherosclerosis 2002 868 874

[40] P. Linsel-Nitschke, A.R. Tall HDL as a target in the treatment of atherosclerotic cardio vascular disease 2005 193 205

[41] B. Martyn Jean Butler Anti-inflammatory drugs in experimental atherosclerosis Part 1. Relative potencies for inhibiting plaque formation 1973 515 522

[42] R.Q. Migrino, M. Bowers, L. Harmann, R. Prost, J.F. Ladisa Carotid plaque regression following 6-month statin therapy assessed by 3T cardiovascular magnetic resonance: comparison with ultrasound intima media thickness 2011 1 10

[43] A.C. Newby, S.J. George, Y. Ismail, J.L. Johnson, G.B. Sala-Newby, A.C. Thomas Vulnerable atherosclerotic plaque metalloproteinases and foam cell phenotypes 2009 1006 1011

[44] A. Nishizawa, C.K. Suemoto, D.S. Farias-Itao, F.M. Campos, K.C. Silva, M.S. Bittencourt, C.A. Pasqualucci Morphometric measurements of systemic atherosclerosis and visceral fat: Evidence from an autopsy study 2017 e0186630

[45] C. Pichardo-Almarza, V. Diaz-Zuccarini From PK/PD to QSP: understanding the dynamic effect of cholesterol-lowering drugs on atherosclerosis progression and stratified medicine 2016 6903 6910

[46] M.F. Piepoli, A.W. Hoes, S. Agewall, C. Albus, C. Brotons, A.L. Catapano, S. Binno European Guidelines on cardiovascular disease prevention in clinical practice: the Sixth Joint Task Force of the European Society of Cardiology and Other Societies on Cardiovascular Disease Prevention in Clinical Practice (constituted by representatives of 10 societies and by invited experts): developed with the special contribution of the European Association for Cardiovascular Prevention Rehabilitation (EACPR) 2016 2315 2381

[47] D.S. Pleouras, A.I. Sakellarios, P. Tsompou, V. Kigka, S. Kyriakidis, S. Rocchiccioli, D. Neglia, J. Knuuti, G. Pelosi, L.K. Michalis, D.I. Fotiadis Simulation of atherosclerotic plaque growth using computational biomechanics and patient-specific data 2020 1 14

[48] M. Prosi, P. Zunino, K. Perktold, A. Quarteroni Mathematical and numerical models for transfer of low-density lipoproteins through the arterial walls: a new methodology for the model set up with applications to the study of disturbed lumenal flow 2005 903 917

[49] A. Roohi, Mathematical Approach of MSE in Thermo-poro-elastic Conditions Improves Decision Making to Use Bore Hole Enlargement (BHE). University of Leoben (2017).

[50] A.A. Rostam-Alilou, H.R. Jarrah, A. Zolfagharian Fluid-structure interaction (FSI) simulation for studying the impact of atherosclerosis on hemodynamics, arterial tissue remodeling, and initiation risk of intracranial aneurysms 2022 1393 1406

[51] A. Sakellarios, C.V. Bourantas, S.L. Papadopoulou, Z. Tsirka, T.D. Vries, P.H. Kitslaar, H.M. Garcia-Garcia Prediction of atherosclerotic disease progression using LDL transport modelling: a serial computed tomographic coronary angiographic study 2016 11 18

[52] W.E. Schiesser PDE models for atherosclerosis computer implementation in R.J. synthesis lectures on biomedical engineering 2018 1 141

[53] M.A. Schwartz, D. Vestweber, M. Simons A unifying concept in vascular health and disease 2018 270 271

[54] T. Silva, W. Jäger, M. Neuss-Radu, A. Sequeira Modeling of the early stage of atherosclerosis with emphasis on the regulation of the endothelial permeability 2020 496 515

[55] N.J. Stone, J.G. Robinson, A.H. Lichtenstein, C.N.B. Merz, C.B. Blum, R.H. Eckel, A.C. Goldberg, D. Gordon, D. Levy, D.M. Lloyd-Jones, P. Mcbride, J.S. Schwartz, S.T. Shero, S.C. Smith, K. Watson, P.W.F. Wilson 2013 ACC/AHA guideline on the treatment of blood cholesterol to reduce atherosclerotic cardiovascular risk in adults: a report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines 2014 2889 2934

[56] S. Sugiyama, K. Niizuma, T. Nakayama Relative residence time prolongation in intracranial aneurysms: a possible association with atherosclerosis 2013 767 776

[57] B.A. Taylor, G. Panza, L.S. Pescatello, S. Chipkin, D. Gipe, W.P. Shao, C.M. White, P.D. Thompson Serum PCSK9 levels distinguish individuals who do not respond to high-dose statin therapy with the expected reduction in LDL-C 2014

[58] D. Velican, C. Velican Coronary anatomy and microarchitecture as related to coronary atherosclerotic involvement 1989 257 262

[59] N. Yang, K. Vafai Modeling of low-density lipoprotein (LDL) transport in the artery-effects of hypertension 2006 850 867

[60] Y. Yuan, P. Li, J. Ye Lipid homeostasis and the formation of macrophage-derived foam cells in atherosclerosis 2012 173 181

[61] B. Zhao, Y. Li, C. Buono, S.W. Waldo, N.L. Jones, M. Mori, H.S. Kruth Constitutive receptor independent low density lipoprotein uptake and cholesteol accumulation by macrophages differentiated from human monocytes with macrophage-colonystimulating factor (M-CSF) 2006 15757 15762

[62] D. Zhou, J. Li, D. Liu, L.Y. Ji, N.Q. Wang, D. Jie, J.C. Wang, M. Ye, X.H. Zhao Irregular surface of carotid atherosclerotic plaque is associated with ischemic stroke: a magnetic resonance imaging study 2019 872 879

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