Analyzing attributes of vessel populations.

Almost all diseases affect blood vessel attributes (vessel number, radius, tortuosity, and branching pattern). Quantitative measurement of vessel attributes over relevant vessel populations could thus provide an important means of diagnosing and staging disease. Unfortunately, little is known about the statistical properties of vessel attributes. In particular, it is unclear whether vessel attributes fit a Gaussian distribution, how dependent these values are upon anatomical location, and how best to represent the attribute values of the multiple vessels comprising a population of interest in a single patient. The purpose of this report is to explore the distributions of several vessel attributes over vessel populations located in different parts of the head. In 13 healthy subjects, we extract vessels from MRA data, define vessel trees comprising the anterior cerebral, right and left middle cerebral, and posterior cerebral circulations, and, for each of these four populations, analyze the vessel number, average radius, branching frequency, and tortuosity. For the parameters analyzed, we conclude that statistical methods employing summary measures for each attribute within each region of interest for each patient are preferable to methods that deal with individual vessels, that the distributions of the summary measures are indeed Gaussian, and that attribute values may differ by anatomical location. These results should be useful in designing studies that compare patients with suspected disease to a database of healthy subjects and are relevant to groups interested in atlas formation and in the statistics of tubular objects.