Abstract
Arteriosclerosis is a disease in which the artery walls get thicker and harder. Atherosclerosis is a specific form of arteriosclerosis which allows less blood to travel through the artery and increases blood pressure. Low-density lipoproteins (LDLs) and their ability to aggregate are important in atherosclerosis. In the present study we develop a mathematical model that describes the translation of two aggregated LDSs through blood plasma. We model the two aggregated LDLs as an inverted oblate spheroid and the flow as a creeping steady incompressible axisymmetric one. The mathematical tools that we used are the Kelvin inversion and the semi-separation of variables in the spheroidal coordinate systems. The stream function is given as a series expansion of even order terms of combinations of Gegenbauer functions of angular and radial dependence. The analytical solution is expected to give insight into the study of the various chemical precipitation methods used for the precipitation of lipoproteins, as this is the first step for the measurement of their concentration within blood plasma.
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References
Khoo J C, Miller E, McLoughlin P, Steinberg D (1990) Prevention of low density lipoprotein aggregation by high density lipoprotein or apolipoprotein A-I. J Lipid Res 31:645–652
Steinberg D (1978) The rediscovery, of high density lipoprotein: a negative risk factor in atherosclerosis. Eur J Clin Invest 8:107–109
Cromwell W C, Otvos J D (2004) Low-density lipoprotein particle number and risk for cardiovascular disease. Curr Atheroscler Rep 6(5):381–387. doi:10.1007/s11883-004-0050-5, PMID: 15296705
Lu M, Gursky O (2013) Aggregation and fusion of low-density lipoproteins in vivo and in vitro. Biomol Concepts 4(5):501–518
Pentikäinen M O, Lehtonen E M, Kovanen P T (1996) Aggregation and fusion of modified low density lipoprotein. J Lipid Res 37(12):2638–2649
Xu S (1998) Apolipoprotein(a) binds to low-density lipoprotein at two distant sites in lipoprotein(a). Biochemistry 37(26):9284–9294
Hadjinicolaou M (2014) A mathematical model for the blood plasma flow around two aggregated low density lipoproteins. GENEDIS 2014, Advances in Experimental Medicine and Biology_820, DOI 10.1007/978-3-319-09012-2-11
Dassios G, Hadjinicolaou M, Protopapas E (2012) Blood plasma flow past a red blood cell: mathematical modeling and analytical treatment. Math Methods Appl Sci 35(13):1489–1612
Hadjinicolaou M, Kamvyssas G, Protopapas E (2014) Stokes flow applied to the sedimentation of a red blood cell. Q Appl Math (to appear)
Baganis G, Dassios G, Hadjinicolaou M, Protopapas E (2013) The Kelvin transformation as a tool for analyzing problems in medicine and technology. Math Methods Appl Sci. doi:10.1002/mma.2903
Dassios G (2009) The Kelvin transformation in potential theory and Stokes flow. IMA J Appl Math 74:427–438
Baganis G, Hadjinicolaou M (2009) Analytic solution of an exterior Dirichlet problem in a non-convex domain. IMA J Appl Math 74(5):668–684
Baganis G, Hadjinicolaou M (2010) Analytic solution of an exterior Neumann problem in a non-convex domain. Math Methods Appl Sci 33(17):2067–2075
Dassios G, Kleinman R (1989) On the capacity and Rayleigh scattering for a class of non-convex bodies. Q J Mech Appl Math 42(3):467–475
Dassios G, Hadjinicolaou M, Payatakes AC (1994) Generalized eigenfunctions and complete semiseparable solutions for Stokes flow in spheroidal coordinates. Q Appl Math LII(I):157–191
Hadjinicolaou M, Protopapas E (2013) On the R-semiseparation of the Stokes bi-stream operator in the inverted prolate spheroidal coordinates. Math Methods Appl Sci. doi:10.1002/mma.2841
Happel J, Brenner H (1991) Low Reynolds number hydrodynamics. Kluwer Academic Publishers, London
Lebedev N N (1972) Special functions and their applications. Dover Publications, New York
Acknowledgments
This research has been co-financed by the European Union (European Social Fund—ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)—Research Funding Program: ARCHIMEDES III. Investing in knowledge society through the European Social Fund.
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Hadjinicolaou, M., Protopapas, E. (2015). Translation of Two Aggregated Low-Density Lipoproteins Within Blood Plasma: A Mathematical Model. In: Vlamos, P., Alexiou, A. (eds) GeNeDis 2014. Advances in Experimental Medicine and Biology, vol 820. Springer, Cham. https://doi.org/10.1007/978-3-319-09012-2_12
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DOI: https://doi.org/10.1007/978-3-319-09012-2_12
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