Mathematical Modeling and Simulation of an Occlusion Device in a Blood Vessel

An occlusion device is placed in an abnormal opening of the heart or its surrounding vessels to regain normal blood flow. There are various occlusion devices available for treatment of various congenital heart defects like PDA, ASD, etc. However, they have limitations like residual shunting, erosion of tissue, displacement and breakage of device, thrombus formation and sudden death. To improve efficiency and to reduce failure of occlusion devices, it is important to simulate blood flow through defect before and after placement of device. It is also important to evaluate stresses and forces exerted by blood flow on device and by the device on the vessel wall. Contact friction between device and vessel wall plays a crucial role in anchoring the device. The objective is to develop a framework to determine conditions to restrict dislocation of device in terms of contact friction. Typical occlusion devices are porous initially and later due to thrombogenesis, their porosity reduces until eventually it acts as a natural permanent plug. Thus, a porous sponge is a good model for an occlusion device. The mathematical model developed here is for differential pressure causing incipient movement of device, and minimum value of contact friction for restricting movement of the device for two shapes, cylindrical and conical, in uncompressed as well as pre compressed forms. The model for differential pressure is fitted by conducting physical experiment with sponge. Mathematically, porosity is modeled using viscous resistance and inertial resistance which are calculated by experiment and simulation with ANSYS. We perform computer experiments (simulations) on a cylindrical device in a cylindrical vessel and on a conical device in a tapered vessel to determine the differential pressure across the device and hence contact friction with varied porosity under boundary conditions as in body. The contact friction required to retain device is lesser in case of conical device compared to cylindrical device. As compression of device increases, friction require to retain it decreases. Hence, lesser porosity results in larger differential pressure and lesser compression which will eventually need higher friction values to retain the device.