Modification of Poiseuille Flow to a Pulsating Flow Using a Periodically Expanding-Contracting Balloon

Abstract

Balloon pumps are employed to assist cardiac function in cases of acute myocardial infarction, ventricular arrhythmias, cardiogenic shock, unstable angina, refractory ventricular failure, or cardiac surgery. Counterpulsation, through increasing the diastolic pressure and reducing the systolic pressure, increases coronary perfusion and assists the heart to pump more blood at each contraction. An expanding-contracting balloon, modifying the Poiseuille flow in a straight circular duct, is examined in this study. The balloon is spheroid-shaped, with the length of its minor axis, which is perpendicular to the flow direction, changing in time following a sinusoidal law. The inlet flow volume rate is steady while the rate that the fluid volume leaves the duct varies in time due to the presence of the balloon. For a pulsation frequency of 60 pulses/min, the pressure difference across the pulsating balloon exhibits significant phase lagging behind the outflow volume waveform. The outlet pressure depends on the balloon radius oscillation amplitude and is computed for a range of such. The flow field around the spheroid, periodically expanding-contracting balloon in the steady flow stream is presented, in which the exact pattern of the gradual downstream intensification of the flow pulsation alongside the spheroid body is also identified.

Keywords

• Poiseuille flow
• pulsatile flow
• Womersley flow
• expanding-contracting balloon
• intra-aortic balloon pump
• counterpulsation