The purpose of this study is to determine if external counterpulsation (ECP) is feasible to perform, tolerable, and safe as a treatment for patients with acute ischemic stroke (i.e., a blockage of one of the arteries supplying a part of the brain), and to assess what type of effect it might have on 1) the velocity of blood flow in the arteries supplying the brain and 2) stroke symptoms. The hypothesis of the study is that ECP will be feasible and safe to perform, and will be tolerable for patients with acute ischemic stroke at pressures that increase the velocity of arterial blood flow to the brain.