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2002 - 20096
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Yazar: Demiray, Hilmi × Konu: Blood ×

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Listeleniyor 1 - 6 / 6
  • Küçük Resim
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    Waves in an elastic tube filled with a heterogeneous fluid of variable viscosity
    (Pergamon-Elsevier Science Ltd, 2009-07) Demiray, Hilmi
    By treating the artery as a prestressed thin elastic tube and the blood as an incompressible heterogeneous fluid with variable viscosity. we studied the propagation of weakly non-linear waves in such a composite medium through the use of reductive perturbation method. By assuming a variable density and a variable viscosity for blood in the radial direction we obtained the perturbed Korteweg-deVries equation as the evolution equation when the viscosity is of order of epsilon(3/2). We observed that the perturbed character is the combined result of the viscosity and the heterogeneity of the blood. A progressive wave type of solution is presented for the evolution equation and the result is discussed. The numerical results indicate that for a certain value of the density parameter sigma, the wave equation loses its dispersive character and the evolution equation degenerates. It is further shown that, for the perturbed KdV equation both the amplitude and the wave speed decay in the time parameter tau.
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    Reflection and transmission of nonlinear waves from arterial branching
    (Elsevier Ltd, 2006-10) Demiray, Hilmi
    In this work, treating the arteries as a prestressed thin walled elastic tube and the blood as an inviscid fluid, we have studied the reflection and transmission of nonlinear waves from arterial branching, through the use of reductive perturbation method. The reflected and the transmitted waves at the bifurcation point are calculated in terms of the incident wave. The numerical results indicate that the reflected wave is comparatively small whereas the transmitted waves in branches are comparable with the incident wave. This result is quite consistent with the experimental measurements [N. Sergiopulos, M. Spiridon, F. Pythoud, J.J. Meister, On wave transmission and reflection properties of stenosis, J. Biomechanics 26 (1996) 31-38].
  • Küçük Resim
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    Propagation of weakly nonlinear waves in fluid-filled thin elastic tubes
    (Elsevier Science, 2002-11-25) Demiray, Hilmi
    In the present work, we study the propagation of nonlinear waves in a prestressed thin elastic tube filled with an incompressible inviscid fluid. Considering the physiological conditions under which the arteries function, in the analysis the tube is assumed to be subjected to a uniform inner pressure P-0 and the axial stretch ratio lambda(z). In the course of blood flow, a dynamical displacement field is superimposed on this static deformation. Treating the blood as an incompressible inviscid fluid, the nonlinear equations of motion of both the tube and the fluid are obtained. Employing the reductive perturbation method, the propagation of weakly nonlinear waves in the longwave approximation is investigated and the Korteweg-de Vries equations are obtained as the governing equation. It is observed that the present formulation gives two solitary waves associated with dilatational and shear motions of the tube. The results are also discussed for some elastic materials existing in the current literature.
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    Head-on collision of solitary waves in fluid-filled elastic tubes
    (Pergamon-Elsevier Science Ltd, 2005-08) Demiray, Hilmi
    In this work, treating the arteries as a thin walled, prestressed thin elastic tube and the blood as an inviscid fluid, we have studied the propagation of nonlinear waves, in the longwave approximation, through the use of extended PLK perturbation method. The results show that, up to O(epsilon(2)), the head-on collision of two solitary waves is elastic and the solitary waves preserve their original properties after the collision. The leading-order analytical phase shifts and the trajectories of two solitons after the collision are derived explicitly.
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    Non-linear waves in a viscous fluid contained in an elastic tube with variable cross-section
    (Elsevier Ltd, 2006-04) Demiray, Hilmi
    In the present work, treating the large arteries as a thin-walled, long and circularly cylindrical, prestressed elastic tube with variable cross-section and using the reductive perturbation method, we have studied the amplitude modulation of non-linear waves in such a fluid-filled elastic tube. By considering the blood as an incompressible viscous fluid, the evolution equation is obtained as the dissipative non-linear Schrodinger equation with variable coefficients. It is shown that this type of equations admit a solitary wave solution with a variable wave speed. It is observed that, the wave speed increases with distance for narrowing tubes while it decreases for expanding tubes.
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    Waves in fluid-filled elastic tubes with a stenosis: Variable coefficients KdV equations
    (Elsevier B.V., 2007-05-15) Demiray, Hilmi
    In the present work, by treating the arteries as thin-walled prestressed elastic tubes with a stenosis and the blood as an inviscid fluid we have studied the propagation of weakly nonlinear waves in such a medium, in the longwave approximation, by employing the reductive perturbation method. The variable coefficients KdV and modified KdV equations are obtained depending on the balance between the nonlinearity and the dispersion. By seeking a localized progressive wave type of solution to these evolution equations, we observed that the wave speeds takes their maximum values at the center of stenosis and gets smaller and smaller as one goes away from the stenosis. Such a result seems to reasonable from the physical point of view.