Analytical Tow-Dimensional Modeling of Blood Flow in a Balloon with Periodic Inflation and Deflation; Application in Intra- and Extra-Aortic Cardiac Assist Devices

The aim of this study is to investigate hemodynamic parameters such as radial and longitudinal velocities, pressure gradients, and wall shear stress of blood flow through a time-varying radius tube with one end closed. Application of this research is in the intra (as AVICENA) and extra cardiac assist devices, in which their balloons can increase the blood’s energy by its periodic inflation and deflation and it makes the blood to be pumped strongly into the aorta. The equation is considered as a two-dimensional model with axial symmetry and analyzed as an analytical solution for aorta. This research shows the continuation of the numerical analysis of the intra- and extra-aortic cardiac assist device in the past papers of the authors in an analytical and two-dimensional model. Results show that the longitudinal velocity is increased as we move from balloon inlet to the balloon outlet along the length of balloon. At a specific time as we move from the balloon walls towards to the centerline of the balloon, the radial velocity of blood flow decreases. It means that the blood flow radial velocity at the centerline of the balloon is close to zero. Pressure is decreased as we move from the end closed to the balloon outlet. Although the wall shear stress increases during contracting of balloon, its value is less than that of existing in aorta, thereby concluding that the chosen-balloon properties may be appropriate to be used for the balloon implanted in the aorta.