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Hemodynamics

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Vascular Biomechanics

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Abstract

This chapter addresses the flow of blood in conduit vessels. We review the composition of blood, a suspension of different-sized particles in plasma, and investigate the forces that act upon said particles. It results in the description of the rheological properties of blood, where single-phasic and bi-phasic models are covered. We then explore blood damage mechanisms with focus on hemolysis and abnormal thrombocyte activation. A key section of this chapter concerns the description of incompressible flows by solving the Navier-Stokes equations for a number of 1D flows. It results in the description of steady-state and steady-periodic flows through circular tubes —the Poiseuille and respective Womersley flows. The exploration of the flow in elastic tubes reveals the expression of the wave speed, an important biomechanical property linked to the condition of the vascular system. Multidimensional flow phenomena, the characteristics of boundary layer flow and the difference between laminar, transitional and turbulent flow are then specified. Wall Shear Stress-related (WSS-related) and transport-related flow parameters, values used in the quantitative description of blood flows, are then addressed. A case study uses the Finite Element Method (FEM) to predict the blood flow in the aneurysmatic aorta, and concluding remarks summarize the chapter.

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Notes

  1. 1.

    Erik Adolf von Willebrand, Finish internist, 1870–1949.

  2. 2.

    Sir George Gabriel Stokes, Irish physicist and mathematician, 1819–1903.

  3. 3.

    Robert Brown, Scottish botanist and palaeobotanist, 1773–1858.

  4. 4.

    Robert Fåhræus, Swedish clinical professor and pathologist, 1888–1968.

  5. 5.

    Maurice Marie Alfred Couette, French physicist, 1858–1943.

  6. 6.

    Henry Eyring, Mexican-born American theoretical chemist, 1901–1981.

  7. 7.

    Daniel Bernoulli, Swiss mathematician and physicist, 1700–1782.

  8. 8.

    Friedrich Wilhelm Bessel, German astronomer, mathematician, physicist, and geodesist, 1784–1846.

  9. 9.

    John Ronald Womersley, British mathematician and computer scientist, 1907–1958.

  10. 10.

    John Crighton Bramwell, British cardiologist, 1889–1976.

  11. 11.

    Archibald Vivian Hill, British physiologist, 1886–1977.

  12. 12.

    Adriaan Isebree Moens, Dutch physiologist, 1846–1891.

  13. 13.

    Diederik Johannes Korteweg, Dutch mathematician, 1848–1941.

  14. 14.

    Andrey Nikolaevich Kolmogorov, Russian mathematician, 1903–1987.

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  1. KTH Solid Mechanics, Department of Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden

    T. Christian Gasser

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Gasser, T.C. (2021). Hemodynamics. In: Vascular Biomechanics. Springer, Cham. https://doi.org/10.1007/978-3-030-70966-2_6

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