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Numerical Solution for Blood Losses Phenomenon in Narrow Vessels

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Some diseases have blood losses as one of their clinical characteristics. The bleeding patient could die if it is no properly and quickly handled. In this paper, it is constructed a mathematical model to study the velocity and the pressure in the body during blood losses through the vessel wall. Furthermore, the effects of blood losses to the velocity and pressure during the bleeding are shown here. In this work, the blood flow is modeled using Stokes equation, while the blood leaks are captured using Darcy's law as a boundary condition. Darcy's law is used because a damaged vessel wall can be depicted as a porous material. A numerical approach in two-dimensional using the Finite Different Method is used in this paper. Numerical results show a significant decreasing of the mean velocity and the mean pressure in the vessels due to the blood losses.
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Filtration BC; Blood Losses; Two-Dimensional; Stokes; Darcy's Law

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D.J. Gubler, Dengue and Dengue Hemorrhagic Fever, Clin. Microbiol. Rev., Vol. 11 (Issue 3): 480, 1998.

T. Wolf, G. Kann, S. Becker, C. Stephan, H.R. Brodt, P. de Leuw, ... and K. Zacharowski, Severe Ebola virus disease with vascular leakage and multiorgan failure: treatment of a patient in intensive care, The Lancet, Vol. 385 (Issue 9976):1428-1435, 2015.

A. Kumar, C.L. Varshney, and C.G. Sharma, Computational technique for flow in blood vessels with porous effects, Applied Mathematics and Mechanics, Vol. 26 (Issue 1): 63-72, 2005.

A. Kumar, Mathematical Model of Blood Flow in Arteries with Porous Effects, In 6th World Congress of Biomechanics (WCB 2010) August 1-6 Singapore. (Springer - Berlin Heidelberg, 2010).

P.J. Shopov, and Y.I. Iordanov, Numerical solution of Stokes equations with pressure and filtration boundary conditions, Journal of Computational Physics, Vol 112 (Issue 1): 12-23, 1994.

G.A. Truskey, F. Yuan, and D.F Katz, Transport phenomena in biological systems, (Pearson/Prentice Hall Upper Saddle River NJ, 2004).

A. R. Khaled and K. Vafai, The role of porous media in modeling flow and heat transfer in biological tissues, International Journal of Heat and Mass Transfer, Vol 46 (Issue 26): 4989-5003, 2003.

N. Nuraini, Windarto, S. Jayanti, and E. Soewono, A two-dimensional simulation of plasma leakage due to dengue infection, AIP Conference Proceedings, Vol 1589 (Isuue 1): 444-447, 2014.

M. Kallista, N. Nuraini, L. Natalia, and E. Soewono, Models for the Onset of Plasma Leakage in Dengue Haemorrhagic Fever, Applied Mathematical Sciences, Vol 8 (Issue 75): 3709-3719, 2014.

A.J. Chorin and J.E. Marsden, A Mathematical Introduction to Fluid Mechanics 2nd Edition, (Springer-New York, 1984).

J.D. Anderson Jr, Governing equations of fluid dynamics. In Computational fluid dynamics, (Springer,-Berlin Heidelberg, 15-51, 1992).

R.L. Panton, Incompressible Flow 2nd Edition, (Wiley-Interscience, 1995).

K. Vafai, ed. Handbook of porous media. (Crc Press, 2015).

D.B. Ingham., I. Pop, Transport phenomena in porous media. (Elsevier, 1998).

A.J. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comput., Vol 22: 745—762, 1968.

R. Temam, Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires (II), Archive for Rational Mechanics and Analysis, Vol 33 (Issue 5), 377-385, 1969.

B.A. Seibold, Compact and fast Matlab code solving the incompressible Navier-Stokes equations on rectangular domains.

A. Quarteroni, What mathematics can do for the simulation of blood circulation, MOX Report, 2006.


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