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Geometrical Features of the Vascular System

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Computational Cardiovascular Mechanics
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Abstract

Biomechanics relates the function of a physiological system to its structure. The objective of biomechanics is to deduce the function of a system from its geometry, material properties, and boundary conditions based on the balance laws of mechanics. Geometry clearly plays a major role in formulation of boundary value problems in biomechanics and is intimately related to function and physiology. Here, we shall provide an overview of the geometric features of the vascular system with special emphasis on the vascular system of the heart (coronary circulation).

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References

  1. Guo X, Kassab GS. The variation of mechanical properties along the length of the aorta in the C57BL/6 mouse. Am J Physiol. 2003;285(6):H2614–22.

    Google Scholar 

  2. Kaimovitz B, Huo Y, Lanir Y, Kassab GS. Diameter asymmetry of porcine coronary vasculature: structural and functional implications. Am J Physiol. 2008;294(2):H714–23.

    Google Scholar 

  3. Kassab GS. The coronary vasculature and its reconstruction. Ann Biomed Eng. 2000;28: 903–15.

    Article  Google Scholar 

  4. Kassab GS, Rider CA, Tang NJ, Fung YC. Morphometry of pig coronary arterial trees. Am J Physiol (Heart Circ Physiol 34). 1993a;265: H350–65.

    Google Scholar 

  5. Kassab, GS, Fung YC. Topology and dimensions of the pig coronary capillary network. Am J Physiol (Heart Circ Physiol). 1994b;36:H319–25.

    Google Scholar 

  6. Kassab GS, Lin D, Fung YC. Morphometry of the pig coronary venous system. Am J Physiol (Heart Circ Physiol 36). 1994a;267:H2100–13.

    Google Scholar 

  7. Kassab GS, Imoto K, White FC, Rider CA, Fung YC, Bloor CM. Coronary arterial tree remodeling in right ventricular hypertrophy. Am J Physiol (Heart Circ Physiol 34). 1993;265:H366–75.

    Google Scholar 

  8. Kassab GS, Pallencaoe E, Schatz A, Fung YC. The longitudinal position matrix of the pig coronary vasculature and its hemodynamic implications. Am J Physiol (Heart Circ Physiol). 1997a;42:H2832–42.

    Google Scholar 

  9. Kassab GS, Fung YC. The pattern of coronary arteriolar bifurcations and the uniform shear hypothesis. Ann Biomed Eng. 1995;23:13–20.

    Article  Google Scholar 

  10. Kassab GS, Berkley J, Fung YC. Analysis of pig’s coronary arterial blood flow with detailed anatomical data. Ann Biomed Eng. 1997b;25:204–17.

    Article  Google Scholar 

  11. Kassab GS, Lee KN, Fung YC. A hemodynamic analysis of coronary capillary blood flow based on detailed anatomical and distensibility data. Am J Physiol (Heart Circ Physiol). 1999;277(6):H2158–66.

    Google Scholar 

  12. Kassab GS, Schatz A, Imoto K, Fung YC. Remodeling of the bifurcation asymmetry of right ventricular branches in hypertrophy. Ann Biomed Eng. 2000;28:424–30.

    Article  Google Scholar 

  13. Smith NP, Kassab GS. Analysis of coronary blood flow interaction with myocardial mechanics based on anatomical models. Phil Trans R Soc Lond A. 2001;359:1251–63.

    Article  Google Scholar 

  14. Mittal N, Zhou Y, Linares C, Ung S, Kaimovitz, B, Molloi S, Kassab GS. Analysis of blood flow in the entire coronary arterial tree. Am J Physiol (Heart Circ Physiol). 2005a;289: H439–46.

    Google Scholar 

  15. Mittal N, Zhou Y, Ung S, Linares C, Molloi S, Kassab GS. A computer reconstruction of the entire coronary arterial tree based on detailed morphometric data. Ann Biomed Eng. 2005b;33(8):1015–26.

    Article  Google Scholar 

  16. Kaimovitz B, Lanir Y, Kassab GS. Large-scale reconstruction of the porcine coronary arterial vasculature based on detailed anatomical data. Ann Biomed Eng. 2005;33(11):1517–35.

    Article  Google Scholar 

  17. Kassab GS. A functional hierarchy of coronary circulation: Direct evidence of a structure–function relation. Am J Physiol. 2005;289:H2559–65.

    Google Scholar 

  18. Kassab GS. Scaling laws of vascular trees: of form and function. Am J Physiol. 2006;290:H894–903.

    Google Scholar 

  19. Kassa GS. Design of coronary circulation: The minimum energy hypothesis. Compt Methods Appl Mech Eng. 2007;196:3033–42.

    Article  MathSciNet  MATH  Google Scholar 

  20. Huo Y, Kassab GS. Pulsatile blood flow in the entire coronary arterial tree: theory and experiment. Am J Physiol. 2006;291(3):H1074–87.

    Google Scholar 

  21. Huo Y, Kassab GS. A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree. Am J Physiol Heart Circ Physiol. 2007;292(6): H2623–33.

    Article  Google Scholar 

  22. Huo Y, Linares CO, Kassab GS. Capillary perfusion and wall shear stress are restored in the coronary circulation of hypertrophic right ventricle. Circ Res. 2007;100(2):273–83.

    Article  Google Scholar 

  23. Huo Y, Kassab GS. Scaling of flow resistance: from single branch to entire distal tree. Biophys J. 2009a;96:339–46.

    Article  Google Scholar 

  24. Huo Y, Kassab GS. A scaling law of vascular volume. Biophys J. 2009b;96:347–53.

    Article  Google Scholar 

  25. Liu, Y, Kassab GS. Metabolic dissipation in vascular trees. Am J Physiol. 2007;292(3):H1336–9.

    Google Scholar 

  26. Wischgoll T, Meyer J, Kaimovitz B, Lanir Y, Kassab GS. A novel method for visualization of entire coronary arterial tree. Ann Biomed Eng. 2007a;35(5):694–710.

    Article  Google Scholar 

  27. Wischgoll T, Choy JS, Ritman EL, Kassab GS. Validation of image-based extraction method for morphometry of coronary arteries. Ann Biomed Eng. 2007b;35(5):694–710.

    Article  Google Scholar 

  28. Murray CD. The physiological principle of minimum work. I. The vascular system and the cost of blood volume. Proc Nat Acad Sci USA. 1926;12:207–14.

    Article  Google Scholar 

  29. Uylings HBM. Optimization of diameter and bifurcation angles in lung and vascular tree structures. Bull Math Biol. 1977;39:509–19.

    MATH  Google Scholar 

  30. Sherman TF. On connecting large vessels to small: the meaning of Murray’s Law. J Gen Physiol. 1981;78:431–53.

    Article  Google Scholar 

  31. Zhou Y, Kassab GS, Molloi S. On the design of the coronary arterial tree: A generalization of Murray’s law. Phys Med Bio. 1999;44:2929–45.

    Article  Google Scholar 

  32. Wahle A, Wellnhofer E, Mugaragu I, Sauer HU, Oswald H, Fleck E. Quantitative volume analysis of coronary vessel systems by 3-D reconstruction from biplane angiograms. IEEE Med Imaging Conf. 1993;2, 1217–21.

    Google Scholar 

  33. Zhou Y, Kassab GS, Molloi S. In vivo validation of the design rules of the coronary arteries and their application in the assessment of diffuse disease. Phys Med Bio. 2002;47:977–93.

    Google Scholar 

  34. Clark ER. Studies on growth of blood vessels in the tail of the frog larvae, by observation and experiment on the living animal. Am J Anat. 1918;23:37–88

    Article  Google Scholar 

  35. Hudlicka O, Tyler KR. Angiogenesis: the growth of the vascular system. London: Academic Press, 1986, 221.

    Google Scholar 

  36. Zweifach BW. The microcirculation in experimental hypertension: State-of-the-art review. Hypertension. 1983;5:I10–6.

    Google Scholar 

  37. Beighley PE, Thomas PJ, Jorgensen SM, Ritman EL. Maturation of arterial branching geometry – A micro-CT-based analysis. Ann Biomed Eng. 1996;24 (Supl 1):S37.

    Google Scholar 

  38. Beighley PE, Britton SL, Gerard-Koch L, Ritman EL. LV myocardial microcirculation in rats selectively bred for running endurance. FASEB J. 2004;18(4):A257.

    Google Scholar 

  39. Zamir M, Silver MD. Morpho-functional anatomy of the human coronary arteries with reference to myocardial ischemia. Can J Cardiol. 1985;1:363–72.

    Google Scholar 

  40. Zamir M. Distributing and delivering vessels of the human heart. J Gen Physiol. 1988;91: 725–35.

    Article  Google Scholar 

  41. Zamir M. Flow strategy and functional design of the coronary network. In Kajiya, F, Klassen GA, Spaan JAE and Hoffman JIE (Eds.) Coronary Circulation: Basic Mechanism and Clinical Relevance, 1990.

    Google Scholar 

  42. Tanaka A, Mori H, Tanaka E, Mohammed MU, Tanaka Y, Sekka T, Ito K, Shinozaki Y, Hyodo K, Ando M, Umetani K, Tanioka K, Kubota M, Abe S, Handa S, Nakazawa H. Branching patterns of intramural coronary vessels determined by microangiography using synchrotron radiation. Am J Physiol (Heart Circ Physiol 45). 1999;276:H2262–7.

    Google Scholar 

  43. Metzger RJ, Kasnow MA. Genetic control of branching morphogenesis. Science. 1999;284:1635–39.

    Article  Google Scholar 

  44. Baldwin HS. Early embryonic vascular development. Cardiovasc Res. 1996;31:E34–5.

    Article  Google Scholar 

  45. Kassab GS, Gregersen H, Nielsen SL, Liu X, Tanko L, Falk E. Remodeling of the coronary arteries in supra-valvular aortic stenosis. J. Hypertension. 2002;20(12):2429–37.

    Article  Google Scholar 

  46. Mayrovitz HN, Tuma RF, Wiedeman MP. Relationship between microvascular blood velocity and pressure distribution. Am J Physiol. 1977;232(4):H400–05.

    Google Scholar 

  47. Rakusan K, Turek Z. Protamine inhibits capillary formation in growing rat hearts. Circ Res. 1985;57:393–8.

    Article  Google Scholar 

  48. Tomanek RJ. Formation of the coronary vasculature: a brief review. Cardiovasc Res. 1996;31:E46–51.

    Google Scholar 

  49. Huo Y, Choy JS, Svendsen M, Sinha A, Kassab GS. Effects of vessel compliance on flow pattern in the porcine epicardial right coronary arterial tree. J Biomech. 2009c;26;42(5): 594–602.

    Article  Google Scholar 

  50. Bassingthwaighte JB. Design and strategy for the Cardionome Project. Adv Exp Med Biol. 1997;430:325–39.

    Article  Google Scholar 

  51. Huo Y, Kassab GS. Scaling of flow resistance: from single branch to entire distal tree. Biophysical J. 2009;96:339–346.

    Article  Google Scholar 

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Acknowledgments

This research was funded in part by NIH HL055554-11, HL-084529, and HL087235.

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Correspondence to Ghassan S. Kassab .

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Kassab, G.S. (2010). Geometrical Features of the Vascular System. In: Guccione, J., Kassab, G., Ratcliffe, M. (eds) Computational Cardiovascular Mechanics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-0730-1_6

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  • DOI: https://doi.org/10.1007/978-1-4419-0730-1_6

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