Because of the critical nature of its function, distributing oxygenated blood from the heart to all the organs of the body, the arterial vascular system has been the object of extensive study in medicine. Since a significant portion of human morbidity and mortality is associated with vascular diseases, diagnostic imaging methods for blood vessels, especially arteries, have received a great deal of attention in the research arena. New imaging and image processing methods produced by the research are often rapidly and routinely applied in the clinic.

Planar X-ray films were the only viable diagnostic imaging method available for many decades after Roentgen's discovery of the new light. Methods to enhance the quality of X-ray images of the vasculature were investigated before the turn of the century, for instance, the injection of mercury into the vessels of cadaver limbs and organs [1]. Much later, with the improvements in nuclear medicine imaging methods and ultrasound in the 1950s and '60s, these techniques were applied to advantage to the vascular system, the former for visualizing and quantifying perfusion defects, and the latter for estimating parameters such as blood velocity and ventricular ejection fraction. Even more recently, computed tomography (CT) and magnetic resonance imaging (MRI) have provided the possibility of true three-dimensional imaging and characterization of vascular structures and arterial tree morphology. For static vessels CT and MR angiography (CTA and MRA) are already capable of producing useful volumetric data sets in which stenoses, aneurysms, and other pathological features can often be appreciated and measured with greater clarity and confidence than is possible with planar projection images.

Unfortunately, the rapid and significant movement of the heart, whose vessels are of paramount interest, makes the coronary vasculature challenging to image even with planar, but especially with (generally slower) 3D imaging modalities. Electron beam CT (EBCT) and fast MRA methods show promise of being capable of freezing heart motion by virtue of data collection times on the order of tens of milliseconds. During the next several years, improvements in MR gradients and other relevant technologies promise to move 3D MRA into the clinical arena. Fast, multi-detector-bank, spiral CT may also make CTA a contender for truly three-dimensional clinical imaging of moving vascular structures.

In the biological context, morphology might be defined as the study of the structure, configuration, shape, or form of animals or organs. Morphometry, then, relates to the process and methods by which measurements of form or structure are made. Arterial tree morphometry is important because the structure, especially lumen diameters and branching patterns, of a space-filling network of pipes has a profound impact on its function of distributing and delivering fluid into a three-dimensional space. For example, flow is proportional to the fourth power of diameter, so the absolute patent diameter of vessels is possibly the most fundamentally sought-after quantity obtainable from diagnostic vascular images. The rate at which arterial branches taper to ever smaller diameters determines the level (that is to say, the vessel size range) in the tree hierarchy that contains the resistance vessels: the primary site of resistance to flow. It is widely accepted that endothelial cells lining the arteries are responsive to shear stress. For example, they may produce factors that signal smooth muscle cells in the vessel media to proliferate, a phenomenon at the root of a number of serious diseases, including systemic and

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pulmonary hypertension. Since the total flow through the tree is knowable, characterization of the tree morphometry may make possible the identification of sites of increased shear stress that may become sites of elevated resistance or plaque formation in pathological conditions. The manner in which the arterial tree branches from the aorta to the periphery of the body, as well as the branching pattern of the subtrees within each organ, has a profound effect on the energy required to pump the blood through the vascular circuit. This directly determines the workload required of the heart. Branching characteristics that are optimal in terms of minimizing energy expenditure have therefore been the subject of a great deal of study.

The purpose of this chapter is to briefly review the field of research involved with exploiting imaging and image processing methods for the morphometric characterization of vascular structures, arterial trees in particular. Some of the basic research methods for arterial tree imaging and morpho-metry employed in our laboratory and others are summarized in somewhat greater detail. The field of vascular imaging, and image processing methods applied to images of the vasculature, is vast and precludes an exhaustive review. I attempt to familiarize the reader with some of the highlights of research in the field, including methods that have found clinical utility, particularly methods based on x-ray images. But most of the images and detail necessarily draws on our work in the basic physiological research setting where, working with static, excised organ preparations, we attempt to morphometrically characterize arterial trees from the largest to the smallest resolvable vessels.

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