Derivation of One-Dimensional Wave Equation in Blood

Ng, Wen Sheng (2018) Derivation of One-Dimensional Wave Equation in Blood. Final Year Project (Bachelor), Tunku Abdul Rahman University College.

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Abstract

The wall of arteries is treated as elastic, isotropic, long, circularly conical, thin walled and tapered (reduced in thickness towards one end). Also, the tube is assumed to be filled with blood. State of the wall, which is deformation, was taken into consideration during derivation of equations. While blood is considered as incompressible inviscid fluid (Newtonian), with negligible viscosity, in large arteries as red blood cells at arterial wall would move to central region, led to low haematocrit ratio and viscosity at arterial wall. Thus, caused increase in shear rate. Boundary conditions, which is the interaction between arterial wall and fluid in terms of motions is determined and derived along with tube and fluid equations. To solve the dimensionalised into non-dimensionalised equations, non-dimensionalised quantities were introduce. Next, the propagation of weakly non-linear waves in fluid was studied in longwave approximation by applying perturbation theory. After series of derivations, the Forced Korteweg-de Vries (FKdV) is obtained and go through some derivation for a function in hyperbolic secant with power of 2.