Beyin Damar Akışında Gaz Halde Emboli Davranışının Matematiksel Modellemesi

Abstract

Gaseous emboli joined to the bloodstream can cause paralysis or death if they reach the middle cerebral artery by causing vascular occlusion impeding the transportation of oxygen to the tissues. Middle cerebral artery is divided into smaller diameter vessels to feed the brain tissue. The diameter of the gaseous emboli that reach this artery can vary from 5 microns to the diameter of the artery. Tracing and examination of the behavior of emboli are of vital importance; but there are no certain results about their formation and the paths they follow in the body despite ongoing applied research. Transcranial Doppler Ultrasound (TCDU) is the most useful preferred method in determining the type, volume and velocity of the embolus in the middle cerebral artery. With the TCDU device, properties of the embolus can be estimated with instantaneous signal measurements at a single point, but its behavior in the veins is unknown. In this study, a mathematical model including mass transport dependent volumetric changes between phases and flow dynamics at three different blood flow rates (32, 50, and 78 cm∙s-1) has been developed to understand the behavior of gaseous nitrogen and oxygen emboli in the middle cerebral artery. Two-dimensional flow simulations were performed for unsteady-state conditions using COMSOL Multiphysics® software for different sizes (50, 250, 500, and 1000 μm in radius) of spherical emboli in a middle cerebral artery of 25 mm length and 2.5 mm diameter. The embolus was positioned at a distance of 5 mm from the entrance of the vessel and its behavior along the 20 mm progression was investigated. It has been shown that the increase in blood flow rate causes the emboli to shrink more rapidly by increasing the amount of gas diffusing into blood. It has been determined that gaseous emboli of 1000 microns and larger in the middle cerebral artery with blood flow rates of 32 cm∙s-1 and lower can clog smaller arteries at the vein outlet and the smallest temporopolar vessels of 1.1 mm diameter.