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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