×

Modeling of pressure pulse waves in bypass grafting. (English. Russian original) Zbl 1366.93036

Cybern. Syst. Anal. 53, No. 1, 12-20 (2017); translation from Kibern. Sist. Anal. 2017, No. 1, 16-25 (2017).
Summary: We investigate the dynamics of a bypass in terms of determining the optimal parameters of shunt operation. The equations that describe the propagation of pressure pulse waves in blood vessels are presented in differential form and in approximate form for the averaged values based on the conservation laws. The correspondence of these forms is shown from the solution of the initial-boundary-value problem for vascular junction. The influence of the parameters such as various diameters, wall thicknesses, and elastic properties of blood vessels on the shunt effectiveness is investigated. In particular, we investigate the influence of the shunt form and junction area, as well as the angle of the shunt connection with the vessel, on the passage of the coronary vessels and blood coagulation. On the basis of the calculations, conclusions about the influence of various parameters on the dynamics of bypass are made.

MSC:

93A30 Mathematical modelling of systems (MSC2010)
93C20 Control/observation systems governed by partial differential equations
92C50 Medical applications (general)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] J. Jung, R. W. Lyczkowski, Ch. B. Panchal, and A. Hassanein, “Multiphase hemodynamic simulation of pulsatile flow in a coronary artery,” J. Biomech., Vol. 39, No. 11, 2064-2073 (2006). · doi:10.1016/j.jbiomech.2005.06.023
[2] A. Setchi, A. J. Mestel, K. H. Parker, and J. H. Siggers, “Low-Reynolds-number flow through two-dimensional shunts,” J. Fluid Mech., Vol. 723, 21-39 (2013). · Zbl 1287.76251 · doi:10.1017/jfm.2013.99
[3] M. Cachile, L. Talon, J. M. Gomba, J. P. Hulin, and H. Auradou, “Stokes flow paths separation and recirculation cells in X-junctions of varying angle,” Phys. Fluids, Vol. 24, No. 2 (021704), 1-7 (2012).
[4] R. C. McLean, S. M. Nazarian, T. J. Gluckman, et al. “Relative importance of patient, procedural and anatomic risk factors for early vein graft thrombosis after coronary artery bypass graft surgery,” J. Cardiovascular Surgery, Vol. 52, No. 6, 877-885 (2011).
[5] F. Kabinejadian, L. P. Chua, D. N. Ghista, M. Sankaranarayanan, and Y. S. Tan, “A new coronary artery bypass graft (CABG) sequential anastomosis design,” Annals of Biomedical Engineering, Vol. 38, 3135-3150 (2010). · doi:10.1007/s10439-010-0068-5
[6] D. N. Ghista and T. Moskal, “Biomechanical estimate for optimal coronary bypass graft diameter for maximal coronary perfusion,” in: Biomechanics Symposium, ASME Publications (1983).
[7] I. T. Selezov and Yu. G. Krivonos, Wave Problems in Biohydrodynamics and Biophysics [in Russian], Naukova Dumka, Kyiv (2013).
[8] C. G. Caro, T. J. Pedley, R. C. Schroter, and W. A. Seed, The Mechanics of the Circulation, University Press, Oxford (1978). · Zbl 1234.93001
[9] S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, McGraw-Hill Book Company, New York (1959). · Zbl 0114.40801
[10] E. B. Moodie, D. W. Barday, and R. T. Tait, “A boundary value problem for fluid-filled viscoelastic tubes,” Mathematical Model., Vol. 4, 195-207 (1983). · Zbl 0536.76027 · doi:10.1016/0270-0255(83)90036-2
[11] S. S. Galich and L. S. Fedorova, “Influence of vascular anastomosis technique on the blood flow through it,” A Yearbook of Scientific Papers of the Association of cardiovascular surgeons of Ukraine, Sertsevo-Sudynna Khirurgiya, Issue 21, 71-75 (2013).
[12] A. V. Rudenko, S. S. Galich, and S. A. Mukhasheva, “Total arterial revascularization in coronary heart disease surgery: The state of the art,” A Yearbook of Scientific Papers of the Association of cardiovascular surgeons of Ukraine, Sertsevo-Sudynna Khirurgiya, Issue 21, 439-444 (2013).
[13] S. Goto and S. Handa, “Coronary thrombosis effects of blood flow on the mechanism of thrombus formation,” Japan Heart J., Ser. Vol. 39, 579-596 (1998).
[14] J. J. Hathcock, “Flow effects on coagulation and thrombosis,” Arteriosclerosis, Thrombosis, and Vascular Biology, Vol. 26, 456-461 (2006). · doi:10.1161/01.ATV.0000229658.76797.30
[15] T. J. Pedley, The Fluid Mechanics of Large Blood Vessels, Cambridge Univ. Press, Cambridge (1980). · Zbl 0449.76100 · doi:10.1017/CBO9780511896996
[16] A. Quarteroni, M. Tuveri, and A. Veneziani, “Computational vascular fluid dynamics: Problems, models and methods,” Computing and Visualisation in Science, Vol. 2, 163-197 (2000). · Zbl 1096.76042 · doi:10.1007/s007910050039
[17] I. Selezov, O. Avramenko, G. Fratamico, G. Pallotti, and P. Pettazzoni, “Stress concentration due to advancing heart pulse through a blood vessel joint,” J. Mechanics in Medicine and Biology, Vol. 1, No. 2, 79-96 (2001). · doi:10.1142/S0219519401000106
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.