Mathematical Modeling of Stress Induced Type 2 Diabetes and Atherosclerosis: Numerical Methods and Stability Analysis
Abstract views: 3
/ 
PDF downloads: 10
Keywords:
Mathematical Modeling, Reaction-Diffusion, Type 2 Diabetes, Atherosclerosis, StressAbstract
Chronic stress can dysregulate the body's adaptive stress responses, influencing immune, vascular, and metabolic functions, which are significant in cardiovascular disease risks. This cumulative effect of stress can heighten vulnerability to cardiovascular events, particularly in individuals with existing conditions like diabetes. Repeated stress responses may lead to inflammation, endothelial dysfunction, and plaque instability, thereby increasing the risk of atherosclerosis [1]. This article highlights the biochemical stressors with a focus on the mechanistic link towards vascular dysfunction associated with diabetes-mediated stress within a proatherogenic context. Type 2 diabetes causes a spectrum of systemic metabolic dysfunctions with the hallmark features of severe hyperglycemia and associated hyperinsulinemia that both augment oxidative stress and inflammatory responses in the vascular system. These effects are compounded by stress, which induces biochemical stress through the upregulation of reactive oxygen species (ROS) [2, 3, 4, 5]. We propose using mathematical modeling to shed light on how stress-induced changes that lead to increased ROS levels and deleterious metabolic pathways further promote plaque formation, contributing to the critical necessity of stress management in attenuating cardiovascular pathologies in diabetic patients. The study highlights the necessity to identify mechanisms of stress-diabetes interactions on atherosclerosis, which may allow new strategies for improving therapeutics.
References
Vaccarino, V., & Bremner, J. D. (2024). Stress and cardiovascular disease: an update. Nature Reviews Cardiology, 21, 603–616.
Luo X, Wu J, Jing S, Yan L-J. Hyperglycemic Stress and Carbon Stress in Diabetic Glucotoxicity. Aging Dis. 2016;7(1):90–110.
Çetiner, Ö., & Rakıcıoğlu, N. (2020). Hyperglycemia, oxidative stress, and identification of oxidative stress parameters in Type 2 diabetes. Turkish Journal of Diabetes and Obesity, 1, 60-68.
Giacco F, Brownlee M. Oxidative stress and diabetic complications. Circ Res. 2010;107(9):1058-1070.
Khaled A, Ahmed Ikram SSM. Type 2 diabetes and vascular complications: A pathophysiologic view. Biomed Res. 2010;21(2):147-115.
Abdul-Ghani, M., DeFronzo, R. A., Del Prato, S., Chilton, R., Singh, R., & Ryder, R. E. J. (2017). Cardiovascular disease and type 2 diabetes: Has the dawn of a new era arrived? Diabetes Care, 40(7), 813–820.
Ménégaut, L., Laubriet, A., Crespy, V., Leleu, D., Pilot, T., Van Dongen, K., ... & Masson, D. (2023). Inflammation and oxidative stress markers in type 2 diabetes patients with advanced carotid atherosclerosis. Cardiovascular Diabetology, 22, Article 248.
Douglas, G., & Channon, K. M. (2014). The pathogenesis of atherosclerosis. Medicine, 42(9), 480-486.
Lusis, A. J. (2000). Atherosclerosis. Nature, 407(6801), 233-241.
Weber, C., & Noels, H. (2011). Atherosclerosis: current pathogenesis and therapeutic options. Nature Medicine, 17(11), 1410-1426.
Dendup, T., Feng, X., Clennin, M. N., Astell-Burt, T., & Gheorghe, A. (2018). Psychosocial stress and risk of type 2 diabetes: a systematic review and meta-analysis. European Journal of Epidemiology, 33(9), 831–845.
Weber, C., & Noels, H. (2011). Atherosclerosis: Current pathogenesis and therapeutic options. Nature Medicine, 17(11), 1410-1422.
Ross, R. (1999). Atherosclerosis—An inflammatory disease. New England Journal of Medicine, 340(2), 115-126.
Libby, P., Ridker, P. M., & Hansson, G. K. (2011). Progress and challenges in translating the biology of atherosclerosis. Nature, 473(7347), 317–325.
Zhang, Y., Li, J., Dong, X., et al. (2023). Oxidative stress and its role in the pathogenesis of atherosclerosis in diabetes mellitus. Journal of Diabetes Research, 2023
Wang, X., Liu, Z., & Huang, W. (2022). Biochemical stress-induced ROS production and endothelial impairment in diabetic atherosclerosis. Atherosclerosis, 347, 28–38.
Chen, Y., Zhao, L., & Li, W. (2023). Hemodynamic stress accelerates atherosclerosis progression via endothelial dysfunction in diabetes. Frontiers in Cardiovascular Medicine.
Garcia, R., & Ramasamy, R. (2022). Reactive oxygen species and diabetic vascular complications: Focus on atherosclerosis. Antioxidants, 11(6), 1120.
Joseph, J. J., & Golden, S. H. (2017). Cortisol dysregulation: The bidirectional link between stress, depression, and type 2 diabetes mellitus. Annals of the New York Academy of Sciences, 1391(1), 20–34.
Hackett, R. A., & Steptoe, A. (2017). Type 2 diabetes mellitus and psychological stress—A modifiable risk factor. Nature Reviews Endocrinology, 13(9), 547–560.
Ceriello, A., & De Nigris, V. (2020). Hyperglycemia, oxidative stress, and inflammation as a complex system. Endocrine, 70(3), 422–426.
Dinh, H., & Hong, K. (2020). The role of oxidative stress in insulin resistance and type 2 diabetes. Progress in Molecular Biology and Translational Science, 171, 31–54.
Surwit, R. S., Schneider, M. S., & Feinglos, M. N. (1992). Stress and diabetes mellitus. Diabetes Care, 15(10), 1413–1422.
van der Aa, N., et al. (2021). Effectiveness of stress reduction techniques on glycemic control and psychological wellbeing in patients with type 2 diabetes: A systematic review and meta-analysis. Journal of Psychosomatic Research.
Li, J., et al. (2022). Stress management and prevention of type 2 diabetes: A systematic review and meta-analysis. Preventive Medicine.
Sattar, N., & Gill, J. M. R. (2014). Type 2 diabetes as a disease of ectopic fat? BMC Medicine.
Black, P. H., & Garbutt, L. D. (2002). Stress, inflammation and cardiovascular disease. Journal of Psychosomatic Research, 52(1), 1–23.
Steptoe, A., & Kivimäki, M. (2012). Stress and cardiovascular disease. Nature Reviews Cardiology, 9(6), 360–370.
Prugger, C., & Wellenius, G. A. (2022). Psychosocial stress and cardiovascular disease: Pathophysiological mechanisms and therapeutic implications. European Heart Journal, 43(18), 1739–1752.
Libby, P. (2002). Inflammation in atherosclerosis. Nature, 420(6917), 868–874.
Kop, W. J. (1999). Chronic and acute psychological risk factors for clinical manifestations of coronary artery disease. Psychosomatic Medicine, 61(4), 476–487.
Al'Absi, M. (2018). Stress and Cardiovascular Disease: Insights on Mechanisms and Prevention. Current Hypertension Reports, 20(7), 59.
Kivimäki, M., & Steptoe, A. (2018). Effects of stress on the development and progression of cardiovascular disease. Nature Reviews Cardiology, 15(4), 215–229.
Esler, M., Lambert, G., & Schlaich, M. (2023). Chronic stress, the sympathetic nervous system, and heart disease. Journal of the American College of Cardiology, 81(4), 402–414.
Zhang, Y., & Liu, L. (2023). The role of the HPA axis in stress-induced insulin resistance and cardiovascular risk. Frontiers in Endocrinology, 14, 112233.
Smith, L., & Thompson, R. (2022). Inflammation, stress, and atherosclerosis: Exploring the connections. Current Atherosclerosis Reports, 24(5), 367–376.
Li, X., & Wang, Y. (2023). Stress, HPA axis dysfunction, and metabolic diseases. Endocrine Reviews, 44(1), 123–140.
American Diabetes Association. (2023). Standards of Medical Care in Diabetes—2023. Diabetes Care, 46(Supplement_1), S1–S291.
Chandola, T., Brunner, E., & Marmot, M. G. (2006). Chronic stress at work and the metabolic syndrome: Prospective study. BMJ, 332(7540), 521–525.
Bailey, K. J., & Hope, S. V. (2023). The psychological impact of type 2 diabetes diagnosis and management. Diabetes Therapy, 14(2), 345–358.
Gonzalez, J. S., Fisher, L., & Polonsky, W. H. (2023). Psychological stress in diabetes management: Current insights and future directions. Clinical Diabetes, 41(1), 12–21.
Murray, J. D. (2002). Mathematical Biology I: An Introduction (3rd ed.). Springer.
Taubes, C. H. (2008). Modeling Differential Equations in Biology. Prentice Hall
Xie, X. (2023). Steady solution and its stability of a mathematical model of diabetic atherosclerosis. Journal of Biological Dynamics
X. Xie, Well-posedness of a mathematical model of diabetic atherosclerosis, J. Math. Anal. Appl. 505(2) (2022), pp. 18. Paper No. 125606.
X. Xie, Well-posedness of a mathematical model of diabetic atherosclerosis with advanced glycation end-products, Appl. Anal. 101(11) (2022), pp. 3989–4013.
de Vries, M. A., & Westerink, J. (2020). Hemostasis and diabetes: A double-edged sword of inflammation. Journal of Diabetes Research, 2020.
B.Topp, K. Promislow, G. Devries, R.M.Miuraa, andT. Diane, Finegood amodel of b-Cell mass, insulin, and glucose kinetics: Pathways to diabetes, J. Theor. Biol. 206 (2000), pp. 605–619.
R.P. Robertson, Chronic oxidative stress as a central mechanism for glucose toxicity in pancreatic islet beta cells in diabetes, J. Biol. Chem. 279 (2004), pp. 42351–42354.
R. Singh, S. Devi, and R. Gollen, Role of free radical in atherosclerosis, diabetes and dyslipidaemia: Larger-than-life, Diabetes Metab. Res. Rev. 31 (2015), pp. 113–126.
M.T. Johnstone, S.J. Creager, K.M. Scales, J.A. Cusco, B.K. Lee, and M.A. Creager, Impaired endothelium-dependent vasodilation in patients with insulin-dependent diabetes mellitus, Circulation 199388, pp. 2510–2516.
S.B. Williams, J.A. Cusco, M.A. Rody, M.T. Johnstone, and M.A. Creager, Impaired nitric oxide-mediated vasodilation in patients with non-insulin-dependent diabetes mellitus, J. AmColl Cardiol. 27 (1996), pp. 567–574.
M.M. Hennes, I.M. O’Shaughnessy, T.M. Kelly, P. LaBelle, B.M. Egan, and A.H. Kissebah, Insulin resistant lypolisis in abdominally obese hypertensive individuals, Hypertension. 28 (1996), pp. 120–126.
T. Inoguchi, P. Li,F.Umeda,H.Y.Yu,M. Kakimoto,M. Imamura,T.Aoki, T. Etoh,T.Hashimoto, M. Naruse, and H. Sano,High glucose level and free fatty acid stimulate reactive oxygen species production through protein kinase C-dependent activation of NAD(P)H oxsidase in cultured vascular cells, Diabetes 49 (2000), pp. 1939–1945.
W. Hao and A. Friedman, The LDL-HDL profile determines the risk of atherosclerosis: A mathematical model, PLoS.ONE. 9 (2014), pp. 1–15.
A. Friedman,W. Hao, and B. Hu, A free boundary problem for steady small plaques in the artery and their stability, J. Differential Equations 259 (2015), pp. 1227–1255.
W. Hao and A. Friedman, The LDL-HDL profile determines the risk of atherosclerosis: A mathematical model, PLoS.ONE. 9 (2014), pp. 1–15.
Giacco, F., & Brownlee, M. (2010). Oxidative Stress and Diabetic Complications. Circulation Research, 107(9), 1058-1070.
Brownlee, M. (2005). The Pathobiology of Diabetic Complications: A Unifying Mechanism. Diabetes, 54(6), 1615-1625.
Boden, G. (1997). Role of fatty acids in the pathogenesis of insulin resistance and NIDDM. Diabetes, 46(1), 3-10.
López-Otín, C., Blasco, M. A., Partridge, L., Serrano, M., & Kroemer, G. (2013). The hallmarks of aging. Cell, 153(6), 1194–1217.
Fitzgibbon, W. B., Hollis, S. L., & Morgan, J. J. Stability and Lyapunov Functions for Reaction-Diffusion Systems. SIAM Journal on Mathematical Analysis, 28(3) (1997), pp. 595-610.
Smoller, J. (1994). Shock Waves and Reaction-Diffusion Equations (2nd ed.). Springer-Verlag.
Khalil, H. K. Nonlinear Systems. Prentice Hall, 2002, pp. 134.
Heidari M., Ghovatmand M., Noori Skandari M.H., Baleanu D., Numerical solution of reaction–diffusion equations with convergence analysis, Journal of Nonlinear Mathematical Physics 30 (2023), pp. 384–399.
LeVeque, R.J., Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2007.
Bornfeldt, K. E., & Tabas, I. (2011). Insulin resistance, hyperglycemia, and atherosclerosis. Cell Metabolism, 14(5), 575–585.
Ganong, W. F. (2016). Review of Medical Physiology (25th ed.). McGraw-Hill Education.
International Diabetes Federation. (2023). IDF Diabetes Atlas, 10th edition. IDF.
Tsigos, C., & Chrousos, G. P. (2023). Stress, Obesity, and Metabolic Syndrome. Endocrinology and Metabolism Clinics of North America, 52(2), 235–245.
Butler, A. E., Janson, J., Bonner-Weir, S., Ritzel, R., Rizza, R. A., & Butler, P. C. (2003). Beta-cell deficit and increased beta-cell apoptosis in humans with type 2 diabetes. Diabetes, 52(1), 102–110.
Weir, G. C., & Bonner-Weir, S. (2004). Five stages of evolving beta-cell dysfunction during progression to diabetes. Diabetes, 53(Supplement 3), S16–S21.
Cnop, M., Welsh, N., Jonas, J. C., Jörns, A., Lenzen, S., & Eizirik, D. L. (2005). Mechanisms of pancreatic beta-cell death in type 1 and type 2 diabetes: many differences, few similarities. Diabetes, 54(Supplement 2), S97–S107.
Li, X., Fang, P., Mai, J., Choi, E. T., Wang, H., & Yang, X. F. (2023). Targeting mitochondrial reactive oxygen species as novel therapy for inflammatory diseases and cancers. Journal of Hematology & Oncology, 16(1), 1–15.
Li, X., Fang, P., Mai, J., Choi, E. T., Wang, H., & Yang, X. F. (2023). Targeting mitochondrial reactive oxygen species as novel therapy for inflammatory diseases and cancers. Journal of Hematology & Oncology, 16(1), 1–15.
Barter, P. J., & Rye, K. A. (2023). HDL cholesterol concentration or HDL function: which matters? European Heart Journal, 44(9), 873–879.
Rohatgi, A., & de Lemos, J. A. (2023). HDL Cholesterol and Cardiovascular Disease: Reexamining a Complex Relationship. Circulation, 147(12), 900–911.
Rysz-Górzynska, M., Banach, M., & Rysz, J. (2023). The Role of HDL Cholesterol in Prevention and Treatment: Myth or Reality? Current Problems in Cardiology, 48(4), 101567.
Lu, Y., An, Y., Guo, J., et al. (2023). Chronic stress enhances LDL oxidation and promotes atherosclerosis progression in mice. Journal of Lipid Research, 64(5), 100181.
Moore, K. J., & Tabas, I. (2011). Macrophages in the Pathogenesis of Atherosclerosis. Cell, 145(3), 341–355.
Libby, P., Hansson, G. K., & Tabas, I. (2019). Immune and Inflammatory Mechanisms in Atherosclerosis. Circulation Research, 124(2), 315–327.
Chistiakov, D. A., Myasoedova, V. A., Revin, V. V., Orekhov, A. N., & Bobryshev, Y. V. (2022). The Role of Mitochondrial Reactive Oxygen Species in Foam Cell Formation.
Yang, M., &Liu, W. (2023). Stress-Related Hormones Enhance Macrophage Transformation into Foam Cells. Cardiovascular Research, 119(2), 345–356.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Results in Nonlinear Analysis
This work is licensed under a Creative Commons Attribution 4.0 International License.
