Numerical simulation of solitary blood waves in an elastic tube subjected to a localised deformation

Disturbance and repair of solitary waves in blood vessels with aneurysm

“…However, those resulting equations are not able to cover some main aspects such as reflection. The second category applies numerical methods directly on the set of basic equations [3]. In this work, we propose a mathematical model with less assumptions on which the solution can be obtained by analytical studies or numerical methods needing less computational resources.…”

“…The study of solitary waves propagation in elastic cylindrical tube filled with fluid has been a great exploration during this last decade because of its direct applications to the dynamics of blood waves in arteries [1][2][3][4][5][6][7][8]. In fact, the increase in the number of death owing to vascular diseases has brought many researchers to pay attention in this field.…”

The design of a reflectionless arterial prosthesis

“…σ ti is the approximated exponential function for the stress-strain relationship given in [15,16]. This approximated relation is widely known as [3,4,6,7] …”

“…For numerical calculation, we have used the characteristic parameters for the femoral artery of a dog [6]: L v = 4.5 cm, E 01 = 14.1 × 10 6 dyn/cm 2 , n 1 = 0.067 cm −1 , m 1 = 0.080 cm −1 and the thickness of the vessel is 0.018 cm. We consider the prosthesis parameters to be L p = 4.0 cm, n 2 = 0.069 cm −1 and m 2 = 0.089 cm −1 .…”

“…The nonlinear studies that came after brought out the importance of the fluid convective term and particularly took into account the dynamical properties of the tube wall where the nonlinear stress-strain relationship is considered [3][4][5][6]. Most of the works that followed contributed to improve the modeling, in a more realistic way, of elastic tubes [7][8][9] and took into account viscosity, tapering aspect of the tubes [5,10], pathological cases of vessels and prostheses [11].…”