Geodesic
A simple one-dimensional model of a false aneurysm in the femoral artery
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 44, Tome 426 (2014), pp. 64-86 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using the dimension reduction procedure, one-dimensional model of the periodic blood flow in the artery, which flows out through a small hole in the thin elastic artery wall connected to a spindle-shaped hematoma, is constructed. This model is described by a system of two parabolic and one hyperbolic equations provided with mixed boundary and periodicity conditions. The blood exchange between the artery and the hematoma is expressed by the Kirchhoff matching conditions. Despite the simplicity, the constructed model allows us to describe a damping of pulsating blood flow by the hematoma and determine the conditions of its growth. In medicine, considered biological object is called a false aneurysm. 
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V. A. Kozlov; S. A. Nazarov. A simple one-dimensional model of a false aneurysm in the femoral artery. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 44, Tome 426 (2014), pp. 64-86. http://geodesic.mathdoc.fr/item/ZNSL_2014_426_a6/

[1] V. A. Kozlov, S. A. Nazarov, “Poverkhnostnaya entalpiya i uprugie svoistva krovenosnykh sosudov”, Doklady RAN, 441:1 (2011), 38–43 | MR

[2] V. A. Kozlov, S. A. Nazarov, “Asymptotic models of anisotropic elastic walls of blood vessels”, Mathematical Methods in the Applied Sciences, (submitted)

[3] V. A. Kozlov, S. A. Nazarov, “Asimptoticheskaya model vzaimodeistviya potoka krovi so stenkami veny i okruzhayuschei myshechnoi tkanyu”, Doklady RAN, 446:6 (2012), 631–636 | MR

[4] V. A. Kozlov, S. A. Nazarov, “Asimptoticheskie modeli techeniya krovi v arteriyakh i venakh”, Zap. nauchn. semin. POMI, 409, 2012, 80–106 | MR

[5] V. A. Kozlov, S. A. Nazarov, “Odnomernaya model vyazkouprugogo techeniya krovi v tonkom uprugom sosude”, Problemy matem. analiza, Novosibirsk, 2014, (submitted)

[6] G. A. Holzafel, “Collagen in Arterial walls: Biomechanical aspets”, Collagen: Structure and Mechanics, ed. Fratzl P., Springer Science+Businss Media, New York–Berlin, 2008, 285–324

[7] Y. C. Fung, Biomechanics. Mechanical Properties of Living Tissues, Springer, New York–Berlin, 1993

[8] Y. C. Fung, Biomechanics. Circulation, Second edition, Springer, New York–Berlin, 2011

[9] S. A. Nazarov, G. Kh. Svirs, A. S. Slutskii, “Izgibnaya zhestkost tonkoi plastiny, armirovannoi periodicheskimi sistemami raz'edinennykh sterzhnei”, Prikladnaya matem. i mekhanika, 74:3 (2010), 441–454 | MR | Zbl

[10] S. A. Nazarov, G. Kh. Svirs, A. S. Slutskii, “Osrednenie tonkoi plastiny, usilennoi periodicheskimi semeistvami zhestkikh sterzhnei”, Matem. sbornik, 202:8 (2011), 41–80 | DOI | MR | Zbl

[11] L. I. Sedov, Mekhanika sploshnoi sredy, v. 2, Nauka, M., 1984

[12] S. A. Nazarov, K. I. Piletskas, “Reinoldsovo techenie zhidkosti v tonkom trekhmernom kanale”, Litovskii matem. sbornik, 30:4 (1990), 772–783 | MR | Zbl

[13] W. J. Zwiebel, J. S. Pellerito, Introduction to vascular ultrasonography, 5th edition, Elsevier, Philadelphia, 2005

[14] S. G. Mikhlin, Variatsionnye metody v matematicheskoi fizike, Nauka, M., 1970 | MR | Zbl

[15] S. A. Nazarov, Ya. Taskinen, “Asimptotika resheniya zadachi Neimana v tonkoi oblasti s zaostrennoi kromkoi”, Zap. nauchn. semin. POMI, 332, 2005, 193–219 | MR | Zbl