Basic Structure–Function Relations of the Epicardial Coronary Vascular Tree: Basis of Quantitative Coronary Arteriography for Diffuse Coronary Artery Disease

BackgroundQuantitative coronary arteriography has been validated for stenotic segments of coronary arteries. However, it does not currently account for diffuse coronary artery disease, because the normal size of the coronary artery for its distal myocardial bed size is not known and cannot be measured directly with diffuse involvement of the artery. Methods and ResultsFrom clinical coronary arteriograms of 12 patients without coronary artery disease (group 1) and in 17 patients with coronary artery disease (group 2), we determined by quantitative coronary arteriography 1) the relations among measured coronary artery cross-sectional lumen area, summed distal branch lengths, and regional myocardial mass distal to each point in each coronary artery; 2) the ratio of coronary artery lumen area between parent and daughter vessels at 50 bifurcations; and 3) which of three different theoretical physical principles could underlie the tree structure of the human coronary artery system, by comparing the coronary artery size, branch lengths, regional mass, and relations between parent-to-daughter lumen area ratios with those for the different theoretical physical principles to test which principle best fit the observed data and therefore which principle most probably characterizes the human coronary artery tree structure. The results showed that 1) there is a close correlation between the lumen area of a coronary artery at each point along its length and the corresponding summed distal branch lengths and regional myocardial mass in patients without and with coronary artery disease; 2) measured coronary artery lumen area in patients with coronary artery disease is diffusely 30-50% too small for distal myocardial bed size compared with normal subjects; and 3) the observed relations among coronary artery size, distal summed lengths, myocardial bed size, and parent-to-daughter size ratios are not consistent with the theoretical principle of constant mean blood flow velocity in the coronary circulation but are consistent with the principles of minimum viscous energy loss and of limited/adaptive vascular wall shear stress characterized by a 2/3 power law relating coronary artery lumen area to distal summed branch lengths and regional mass or parent-to-daughter branching ratios. ConclusionsThese observations provide a basis for quantifying diffuse coronary artery disease on clinical arteriograms.