A medical device is provided in which one or both ends of the device encourage the formation of tissue across substantially the entire area of the respective end that is exposed to the blood flow for reducing the risk of a thrombotic embolism. The medical device includes a tubular structure having at least one expanded volume portion and a tapered transition portion. The tubular structure may be made through the braiding of a number of strands, and a first end feature may be used to secure the proximal strand ends. The proximal strand ends may be secured via the proximal end of the first end feature, such that the tapered transition portion is formed over the circumferential surface of the first end feature, and only a proximal end surface (or a portion of the proximal end surface) of the first end feature is exposed to the path of flowing blood.