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Computational and Mathematical Methods in Medicine
An Interdisciplinary Journal of Mathematical, Theoretical and Clinical Aspects of Medicine
Volume 9, 2008 - Issue 2
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Original Articles

Stability analysis of a model of atherogenesis: An energy estimate approach

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Pages 121-142 | Received 29 Aug 2007, Accepted 12 Dec 2007, Published online: 15 Apr 2008

References

  • Acosta , G. and Durán , R.G. 2003 . An optimal Poincaré inequality in L1 for convex domains . Proc. Am. Math. Soc. , 132 ( 1 ) : 195 – 202 .
  • Caro , C.G. , Fitz-Gerald , J.M. and Schroter , M.F. 1971 . Atheroma and arterial wall shear: Observation, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis . Proc. R. Soc. Lond. B , 177 : 109 – 133 .
  • Chait , A. 2005 . Lipoprotein-associated inflammatory proteins: Markers or mediators of cardiovascular disease? . J. Lipid Res. , 46 : 389 – 403 .
  • Cobbold , C.A. , Sherratt , J.A. and Maxwell , S.J.R. 2002 . Lipoprotein oxidation and its significance for atherosclerosis: A mathematical approach . Bull. Math. Biol. , 64 : 65 – 95 .
  • Cui , D. 2007 . Pivital advance: Macrophages become resistant to cholesterol-induced death after phagocytosis of apoptotic cells . J. Leukoc. Biol. , 82 : 1040 – 1050 .
  • Gantmacher , F.R. and Hirsch , Translated from Russian by K.A. 1959 . The Theory of Matrices , vol. I , 10+374 New York : Chelsea .
  • Goldstein , J.L. 1977 . Binding site on macrophages that mediates uptake and degradation of acetylated low density lipoproteins, producing massive cholesterol deposition . Proc. Natl. Acad. Sci. USA , 76 : 333 – 337 .
  • Hajjar , D.P. and Haberland , M.E. 1997 . Lipoprotein trafficking in vascular cells; molecular trojan horses and cellular saboteurs . J. Biol. Chem. , 272 : 22975 – 22978 .
  • Holzapfel , G.A. , Gasser , T.C. and Ogden , R.W. 2000 . A new constitutive framework for arterial wall mechanics and a comparative study of material models . J. Elasticity , 61 : 1 – 48 .
  • Horstmann , D. 2003 . From 1970 until present: The Keller–Segel model in chemotaxis and its consequences . Jahresber. Deutsch. Math. Verein. , 105 ( 3 ) : 103 – 165 .
  • Ibragimov , A.I. 2005 . A mathematical model of atherogenesis as an inflammatory response . Math. Med. Biol. , 22 : 305 – 333 .
  • Ibragimov , A.I. 2007 . A dynamic model of atherogenesis as an inflammatory response . Dyn. Contin. Discrete Impuls. Syst. , 14 ( 52 ) : 185 – 189 . A Supplement, Advances in Dynamical Systems
  • Keller , E.F. and Segel , L.A. 1971 . Model for chemotaxis . J. Theor. Biol. , 30 : 235 – 248 .
  • Kinscherf , R. 1999 . Characterization of apoptotic macrophages in atheromatous tissue of humans and heritable hyperlipidemic rabbits . Atherosclerosis , 144 ( 1 ) : 33 – 39 .
  • Mantzaris , N. , Webb , S. and Othmer , H.G. 2004 . Mathematical modeling of tumor-induced angiogenesis . J. Math. Biol. , 49 ( 2 ) : 111 – 187 .
  • Podrez , E.A. 2002 . Identification of a novel family of oxidized phospholipids that serve as ligands for the macrophage scavenger receptor CD36 . J. Biol. Chem. , 277 ( 41 ) : 38503 – 38516 .
  • Ross , R. 1995 . Cell biology of atherosclerosis . Annu. Rev. Physiol. , 57 : 791 – 804 .
  • Ross , R. 1999 . Atherosclerosis – an inflammatory disease . N. Engl. J. Med. , 340 ( 2 ) : 115 – 126 .
  • Steinberg , D. 1997 . Low density lipoprotein oxidation and its pathobiological significance . J. Biol. Chem. , 272 : 20963 – 20966 .
  • Stocker , R. and Keaney , J. 2004 . Role of oxidative modifications in atherosclerosis . Physiol. Rev. , 84 : 1381 – 1478 .
  • Tabas , I. 2004 . Apoptosis and plaque destabilization in atherosclerosis: The role of macrophage apoptosis induced by cholesterol . Cell Death Differ. , 11 : S12 – S16 .

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