Nonlinear analysis of oscillatory flow in the annulus of an elastic tube: Application to catheterized artery

The changed flow pattern of pulsatile blood flow in an annulus with elastic outer wall has been studied through a mathematical model. The main objecti ve is to apply the model to study the combined effect of introduction of th e catheter and elastic properties of the arterial wall on the pulsatile nat ure of the blood flow. The diameter variation of the wall is considered sma ll for the perturbation analysis to be valid. The steady streaming effect b rings into focus the existence of a nonzero mean pressure gradient in addit ion to the one predicted by the linear theory-a fact overlooked by previous authors. Thus, our results are intended to provide a correction to the "me an pressure gradient-flow rate relationship" usually calculated by neglecti ng the nonlinear inertia terms. This correction depends on the amplitude of the diameter variation, flow rate wave forms, and the phase difference bet ween them. The calculations based on the geometry and the flow conditions r epresenting a real physiological situation as closely as possible suggest t hat mean pressure gradient changes with catheter size for any frequency par ameter. The results obtained for arbritrary frequency parameter and for sma ll steady streaming Reynolds number, Rst, show that the geometry of the wal l plays an important role in the dynamics of the flow even for small cathet er radius. The interaction of the amplitude of catheter oscillation and the amplitude of the wall movement is first manifested through the induced mea n pressure gradient and induced mean velocity. Further, the results are sen sitive to the elastic nature of the wall reflected by the phase difference between the diameter variation and the flow rate. Interesting streamline pa tterns depict distinct boundary layer characteristics both at artery wall a nd catheter wall, Depending upon the material properties, a thin catheter e xperiencing small oscillations due to the flow conditions is likely to have a similar influence to a thicker catheter which remains fairly stationary inside the artery. Finally, the effect of catheterization on various physio logically important flow rate characteristics-mean velocity, mean pressure gradient, wall shear stress-is studied for a range of different catheter si zes and frequency parameters. (C) 2001 American Institute of Physics.