Embolic protective devices (EPD) are used in carotid angioplasty to reduce or prevent embolic debris from entering the brain and causing procedure-related strokes. In this chapter we analyze a proximal protection mechanism of EPD that performs cerebral protection by external and common carotid artery occlusion. The mathematical model we use is a one-dimensional (1D) equation system governing blood flow. This system is applied to a patient-specific arterial tree constructed from a 3D computed tomography angiography (CTA) image. We simulate the blood flow in both normal and procedural conditions. Wherever possible we compare our computation results with laboratory or previously published measurements and our model agrees with these data.