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Dynamic response of stenotic blood flow in vivo. (English) Zbl 0756.92012

The authors deal with a theoretical study of the blood flow in arterial segments in the presence of stenosis. They consider the blood to be composed of two different layers of two different non-Newtonian fluids, characterized by Herschel-Bulkley and power law models. It is inferred that the time variant geometry of the stenosis plays an important role. The effects of surrounding connective tissues are also incorporated. Making use of the quantitative analysis through numerical computation of the interesting variables, the applicability of the model is shown. The present investigations based on realistic considerations may be of some interest to bioengineers engaged in the design and construction of artificial organs.

MSC:

92C35 Physiological flow
76Z05 Physiological flows
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References:

[1] Young, D. F., Effect of a time-dependent stenosis on flow through a tube, J. Engng. Ind., Trans. ASME, 90, 248-254 (1968)
[2] Young, D. F., Fluid mechanics of arterial stenosis, J. Biomech. Engng. Trans. ASME, 101, 157-175 (1979)
[3] Forrester, J. H.; Young, D. F., Flow through a converging-diverging tube and its implications in occlusive vascular disease, J. Biomech., 3, 297-316 (1970)
[4] Hershey, D.; Byrnes, R. E.; Deddens, R. L.; Rao, A. M., Blood rheology: Temperature dependence of the Power law model, A.I.Ch.E. Meeting (December 1964), Boston
[5] Huckaba, C. E.; Hahn, A. N., A generalised approach to the modeling of arterial blood flow, Bull. Math. Biophys., 30, 645-662 (1968)
[6] Charm, S. E.; Kurland, G., Viscometry of human blood for shear rates of \(0-100,000 sec^{−1}\), Nature, 206, 617-618 (1965)
[7] Whitmore, R. L., Rheology of the Circulation (1968), Pergamon Press: Pergamon Press New York
[8] Han, C. D.; Barnett, B., Measurement of the rheological properties of biological fluids, (Gabelnick, H. L.; Litt, M., Rheology of Biological Systems (1973), Charles C. Thomas: Charles C. Thomas Illinois), 195
[9] Krough, A., The Anatomy and Physiology of Capillaries (1929), Hafner Publishing Company: Hafner Publishing Company New York
[10] Copley, A. L.; Stainsby, G., Flow Properties of Blood and other Biological Systems (1960), Pergamon Press: Pergamon Press London
[11] Copley, A. L.; Staple, P. H., Hemorheological studies on the plasmatic zone in the microcirculation of the cheek pouch of Chinese and Syrian hamster, Biorheology, 1, 3-14 (1962)
[12] Block, E. H., A quantitative study of the hemodynamics in the living microvascular system, Am. J. Anatomy, 110, 125-153 (1962)
[13] Block, E. H., Analysis of blood flow with high speed cinephotography, Proc. 4th European Conf. Microcirculation (1966), Cambridge University Press: Cambridge University Press New York, NY
[14] Shukla, J. B.; Parihar, R. S.; Rao, B. R.P., Effects of stenosis on non-Newtonian flow of the blood in an artery, Bull. Math. Biol., 42, 283-294 (1980) · Zbl 0428.92009
[15] Chakravarty, S., Effects of stenosis on the flow behaviour of blood in an artery, Int. J. Engng. Sci., 25, 1003-1016 (1987) · Zbl 0618.76139
[16] Chakravarty, S.; Datta, A., Effects of stenosis on arterial rheology through a mathematical model, Math. Comp. Modelling, 12, 12, 1601-1612 (1989) · Zbl 0703.76109
[17] Kapur, J. N., Mathematical Models in Biology and Medicine (1985), Affiliated East-West Press Pvt. Ltd: Affiliated East-West Press Pvt. Ltd India · Zbl 0574.92001
[18] Patel, D. J.; Fry, D. L., Longitudinal tethering of arteries in dogs, Circulation Research, 19, 1011-1021 (1966)
[19] Atabek, H. B., Wave propagation through a viscous tethered, initially stressed, orthotropic elastic tube, Biophys. J., 8, 626-649 (1968)
[20] Von Rosenberg, D. U., Methods for the Numerical Solution of Partial Differential Equations (1969), Elsevier: Elsevier New York · Zbl 0194.18904
[21] Krylov, V. I.; Skoblya, N. S., A Handbook of Methods of Approximate Fourier Transformation and Inversion of Laplace Transformation (1977), Mir publisher: Mir publisher Moscow · Zbl 0389.65051
[22] Mirsky, I., Wave propagation in a viscous fluid contained in an orthotropic elastic tube, Biophys. J., 7, 165-186 (1967)
[23] Young, J. T.; Vaishnav, R. N.; Patel, D. J., Nonlinear anisotropic viscoelastic properties of canine arterial segments, J. Biomech., 10, 549-559 (1977)
[24] Bertram, C. D., Energy dissipation and pulse wave attenuation in canine carotid artery, J. Biomech., 13, 1061 (1980)
[25] Fry, D. L., Acute vascular endothelial changes associated with increased blood velocity gradients, Circulation Res., 22, 165-197 (1968)
[26] Srivastava, L. M., Flow of couple stress fluid through stenotic blood vessels, J. Biomech., 18, 479-485 (1985)
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