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Atherosclerosis: The Risk of High Cholesterol

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Introduction to Mathematical Biology

Abstract

Arteries are blood vessels that carry oxygen-rich blood to the heart, brain, and other parts of the body. Atherosclerosis is a disease in which a plaque, a thick hard deposit of fatty material, builds up inside arteries. The plaque contains cholesterol, calcium, cells from the blood, and cells from the arterial wall. Over time the plaque grows, hardens, and narrows the artery. This reduces the flow of oxygen-rich blood, and also make it more likely to cause a blood clot, or thrombus, that will block the blood flow. A blockage formed in the coronary arteries may trigger a heart attack. A blockage formed in the carotid artery (located on each side of the neck, feeding oxygen to the brain) may cause a stroke. Atherosclerosis is the leading cause of death in the United States and worldwide, with annual deaths of 900,000 in the United States and 13 millions worldwide.

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References

  1. Coddington, E.A.: An Introduction to Ordinary Differential Equations. Dover, New York (1989)

    MATH  Google Scholar 

  2. Butcher, J.C.: Numerical Methods for Ordinary Differential Equation. Wiley, New York (2008)

    Book  MATH  Google Scholar 

  3. Strang, G.: Linear Algebra and Its Applications, 4th edn. Brooks/Cole, Belmont (2005)

    MATH  Google Scholar 

  4. Gantmacher, F.R.: The Theory of Matrices, vol. 2. Chelsea, New York (1959)

    MATH  Google Scholar 

  5. van den Driessche, P., Watmough, J.: Further notes on the basic reproduction number. In: Mathematical Epidemiology, pp. 159–178. Springer, Berlin/Heidelberg (2008)

    Google Scholar 

  6. Hale, J.K., Kocak, H.: Dynamics and Bifurcations. Springer, New York (1991)

    Book  MATH  Google Scholar 

  7. Friedman, A., Hao, W., Hu, B.: A free boundary problem for steady small plaques in the artery and their stability. J. Diff. Eqs. 259, 1227–1255 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. Louzoun, Y., Xue, C., Lesinski, G.B., Friedman, A.: A mathematical model for pancreatic cancer growth and treatment. J. Theor. Biol. 351, 74–82 (2014)

    Article  MathSciNet  Google Scholar 

  9. Friedman, A., Tian, J.P., Fulci, G., Chiocca, E.A., Wang, J.: Glioma virotherapy: the effects of innate immune suppression and increased viral replication capacity. Cancer Res. 66, 2314–2319 (2006)

    Article  Google Scholar 

  10. Day, J., Friedman, A., Schlesinger, L.S.: Modeling the immune rheostat of macrophages in the lung in response to infection. Proc. Natl. Acad. Sci. USA 106, 11246–11251 (2009)

    Article  Google Scholar 

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Chou, CS., Friedman, A. (2016). Atherosclerosis: The Risk of High Cholesterol. In: Introduction to Mathematical Biology. Springer Undergraduate Texts in Mathematics and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-29638-8_12

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