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Medical and Biological Engineering and Computing

, Volume 44, Issue 11, pp 971–982 | Cite as

Theoretical modeling of micro-scale biological phenomena in human coronary arteries

  • Kelvin WongEmail author
  • Jagannath Mazumdar
  • Brandon Pincombe
  • Stephen G. Worthley
  • Prashanthan Sanders
  • Derek Abbott
Original Article

Abstract

This paper presents a mathematical model of biological structures in relation to coronary arteries with atherosclerosis. A set of equations has been derived to compute blood flow through these transport vessels with variable axial and radial geometries. Three-dimensional reconstructions of diseased arteries from cadavers have shown that atherosclerotic lesions spiral through the artery. The theoretical framework is able to explain the phenomenon of lesion distribution in a helical pattern by examining the structural parameters that affect the flow resistance and wall shear stress. The study is useful for connecting the relationship between the arterial wall geometries and hemodynamics of blood. It provides a simple, elegant and non-invasive method to predict flow properties for geometrically complex pathology at micro-scale levels and with low computational cost.

Keywords

Atherosclerosis Axial and radial asymmetry Spiraling lesion Resistance to flow ratio Wall shear stress 

References

  1. 1.
    Ang KC, Mazumdar JN (1995) Mathematical modelling of triple arterial stenoses. Aust Phys Eng Sci Med 18:89–94Google Scholar
  2. 2.
    Aroesty J, Gross JF (1972) Pulsatile flow in small blood vessels—I, Casson Theory. Biorheology 9:33–43Google Scholar
  3. 3.
    Baaijens JP, van Steenhoven AA, Janssen JD (1993) Numerical analysis of steady generalized newtonian blood flow in a 2d model of the carotid artery bifurcation. Biorheology 30(1):63–74Google Scholar
  4. 4.
    Banerjee RK, Back LH, Back MR, Cho YI (2000) Physiological flow simulation in residual human stenoses after coronary angioplasty. J Biomech Eng 122(4):310–320CrossRefGoogle Scholar
  5. 5.
    Berger SA., Jou LD (2000) Flows in stenotic vessels. Ann Rev Fluid Mech 32:347–382zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Bingham E (1922) Fluidity and plasticity. MacGraw Hill, New YorkGoogle Scholar
  7. 7.
    Casson N (1959) A flow equation for pigment oil suspensions of the printing ink type, rheology of dispersive systems. In: Mills CC (ed) Pergamon pressGoogle Scholar
  8. 8.
    Chakravarty S, Datta A (1992) Dynamic response of stenotic blood flow in vivo. Math Comput Model 16:3–20zbMATHCrossRefGoogle Scholar
  9. 9.
    Cokelet GR (1972) Biomechanics, its foundations and objectives, chap. The rheology of human blood. Prentice-Hall, pp 63–87Google Scholar
  10. 10.
    Davies, MJ (1996) Stability and instability: two faces of coronary atherosclerosis. Circulation 94:2013–2020Google Scholar
  11. 11.
    Davies, MJ, Thomas AC (1985) Plaque fissuring-the cause of acute myocardial infarction, sudden ischaemic death, and crescendo angina. Br Heart J 53(4):363–373Google Scholar
  12. 12.
    Falk E, Shah PK, Fuster V (1995) Coronary plaque disruption. Circulation 92:657–671Google Scholar
  13. 13.
    Forrester J, Young D (1970) Flow through a converging diverging tube and its implications in occulsive vascular disease– I. J Biomech 3:297–305CrossRefGoogle Scholar
  14. 14.
    Fox B, James K, Morgan B, Seed A (1982) Distribution of fatty and fibrous plaques in young human coronary arteries. Atherosclerosis 4:337–347CrossRefGoogle Scholar
  15. 15.
    Gertz S, Roberts WC (1990) Hemodynamic shear force in rupture of coronary arterial atherosclerotic plaques. Am J Cardiol 66:1368–1372CrossRefGoogle Scholar
  16. 16.
    Gertz SD, Uretzky G, Wajnberg RS, Navot N, Gotsman MS (1981) Endothelial cell damage and thrombus formation after partial arterial constriction: relevance to the role of coronary artery spasm in the pathogenesis of myocardial infarction. Circulation 63:476–486Google Scholar
  17. 17.
    Glagov S, Weisenberd E, Zarins C, Kolettis RG (1987) Compensatory enlargement of human atherosclerotic coronary arteries. N Engl J Med 316:1371–1375CrossRefGoogle Scholar
  18. 18.
    Herschel H, Bulkey R (1926) Konsistenzmessungen von gummi-benzollosungen. Koll Zeitschr 23:291–300CrossRefGoogle Scholar
  19. 19.
    Kaazempur-Mofrad MR, Isasi AG, Younis HF, Chan RC, Hinton DP, Sukhova G, LaMuraglia GM, Lee RT, Kamm RD (2004) Characterization of the atherosclerotic carotid bifurcation using mri, finite element modeling, and histology. Ann Biomed Eng 32(7):932–946CrossRefGoogle Scholar
  20. 20.
    Kirkeeide RL, Gould KL, Parsel L (1986) Assessment of coronary stenoses by myocardial perfusion imaging during pharmocologic coronary vascodilation. J Am Coll Cardiol 7:103–113Google Scholar
  21. 21.
    MacDonald D (1979) On steady flow through modelled vascular stenoses. J Biomech 12:13–20CrossRefGoogle Scholar
  22. 22.
    MacIsaac AI, Thomas JD, Topol EJ (1993) Toward the quiescent coronary plaque. J Am Coll Cardiol 22:1228–1241CrossRefGoogle Scholar
  23. 23.
    Mann JM, Davies MJ (1996) Vulnerable plaque—relation of characteristics to degree of stenosis in human coronary arteries. Circulation 94:928–931Google Scholar
  24. 24.
    Mazumdar JN (1992) Biofluid mechanics. World Scientific N. J. USAGoogle Scholar
  25. 25.
    Mernone AV, Mazumdar JN (2000) Biomathematical modelling of physiological fluids using a casson fluid with emphasis to peristalsis. Aust Phys Eng Sci Med. 23(3):94–100Google Scholar
  26. 26.
    Morris C, Smith C, Blackshear P (1987) A new method for measuring the yield stress in thin layers of sedimenting blood. Biophys J 52:229–240CrossRefGoogle Scholar
  27. 27.
    Pincombe B (1998) A study of non-newtonian behaviour of blood flow through stenosed arteries. Ph.D. thesis, University of AdelaideGoogle Scholar
  28. 28.
    Pincombe B, Mazumdar JN (1995) A mathematical study of blood flow through viscoelastic walled stenosed arteries. Aust Phys Eng Sci Med 18:81–88Google Scholar
  29. 29.
    Pincombe, B, Mazumdar JN (1997) The effects of post-stenotic dilatations on the flow of a blood analogue through stenosed coronary arteries. Math Comput Model 25:57–70zbMATHMathSciNetCrossRefGoogle Scholar
  30. 30.
    Pincombe B, Mazumdar JN (1998) Herschel-bulkley and casson flow through viscoelastic walled stenosed arteries. In: Tuck EO, Stott JAK (eds) EMAC’98, The Institute of Engineers, Australia, pp 399–402Google Scholar
  31. 31.
    Pincombe B, Mazumdar JN (1998) Numerical model of power law flow through an atherosclerotic artery. In: Noye BJ, Teubner MD (eds) CTAC’97, World Scientific Press, pp 563–570Google Scholar
  32. 32.
    Pincombe B, Mazumdar JN (2002) Techniques for the study of blood flow through both constrictions and post-stenotic dilatations in arteries. Handbook of computational methods in biomaterials, biotechnology and biomedical systems. Kluwer, DorchetGoogle Scholar
  33. 33.
    Poiseuille J (1836) Observations of blood flow. Ann Sci Nat STrie 5, 2Google Scholar
  34. 34.
    Reiber JHC, van der Zwet PMJ, von Land CD, Koning G, Loois G, Zorn I, van den Brand M, Gerbrands JJ (1989) On-line quantification of coronary angiograms with the dci system. Medicamundi 34:89–98Google Scholar
  35. 35.
    Rodbard S, Ikeeda K, Montes M (1967) An analysis of mechanisms of post stenotic dilation. Angiology 18:349–367Google Scholar
  36. 36.
    Seo HS, Lombardi DM, Polinsky P, Powell-Braxton L, Bunting S, Schwartz SM, Rosenfeld ME (1997) Peripheral vascular stenosis in apolipoprotein e-deficient mice: potential roles of lipid deposition. Medial atrophy, and adventitial inflammation. Arterioscler Thromb Vasc Biol 17:3593–3601Google Scholar
  37. 37.
    Shukla JB, Parihar RS, Rao BRP (1980) Effects of stenosis on non-newtonian flow in an artery. Bull Math Biol 42:283–294zbMATHGoogle Scholar
  38. 38.
    Tang D, Yang C, Zheng J, Woodard PK, Sicard GA, Saffitz JE, Yuan C (2004) 3d mri-based multicomponent fsi models for atherosclerotic plaques. Ann Biomed Eng 32(7):947–960CrossRefGoogle Scholar
  39. 39.
    Wensing JW, Meiss L, Mali PTM, Hillen B (1998) Early atherosclerotic lesions spiraling through the femoral artery. Arterioscler Thromb Vasc Biol 18:1554–1558Google Scholar
  40. 40.
    Wong KKL, Mazumdar JN, Abbott D (2005) A study of relationship between geometrical variation of atherosclerotic arteries and flow resistance. In: 12th International conference on biomedical engineering. CD onlyGoogle Scholar
  41. 41.
    Worthley SG, Helft G, Fuster V, Fayad ZA, Fallon JT, Osende JI, Roque M, Shinnar M, Zaman AG, Rodriguez OJ (2000) High resolution ex vivo magnetic resonance imaging of in situ coronary and aortic atherosclerotic plaque in a porcine model. Atherosclerosis 150(2):321–329CrossRefGoogle Scholar
  42. 42.
    Worthley SG, Helft G, Fuster V, Zaman AG, Fayad ZA, Fallon JT, Badimon JJ (2000) Serial in vivo mri documents arterial remodeling in experimental atherosclerosis. Circulation 101(6):586–589Google Scholar
  43. 43.
    Worthley SG, Omar-Farouque HM, Helft G, Meredith IT (2002) Coronary artery imaging in the new millennium. Heart Lung Circ 11(1):19–25CrossRefGoogle Scholar
  44. 44.
    Young D (1968) Effect of a time dependent stenosis on flow through a tube. J Eng Ind Trans Am Soc Mech Eng 90:248–254Google Scholar
  45. 45.
    Zohdi TI (2005) A simple model for shear stress mediated lumen reduction in blood vessels. Biomech Model Mechanobiol 4(1):57–61CrossRefGoogle Scholar

Copyright information

© International Federation for Medical and Biological Engineering 2006

Authors and Affiliations

  • Kelvin Wong
    • 1
    Email author
  • Jagannath Mazumdar
    • 1
  • Brandon Pincombe
    • 3
  • Stephen G. Worthley
    • 2
  • Prashanthan Sanders
    • 2
  • Derek Abbott
    • 1
  1. 1.Centre for Biomedical Engineering (CBME) and School of Electrical & Electronic EngineeringThe University of AdelaideAdelaideAustralia
  2. 2.Cardiovascular Research Centre, Department of Cardiology, Royal Adelaide Hospital and the Discipline of MedicineUniversity of AdelaideAdelaideAustralia
  3. 3.Land Operations DivisionDefence Science and Technology OrganisationEdinburghAustralia

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