The Vascular Geometry of Human Arterial Bifurcations

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Abstract
We used angiography to evaluate the branching characteristics of 69 morphologically normal human arterial bifurcations. Each angiographic picture was enlarged photographically and traced on paper. The diameter of the parent vessel (d0), the diameters of the two daughter vessels (d1 and d2-d1 denote the larger vessel), and the angles at which the two branches arise from the parent vessel (teta1 and teta2) were measured on each bifurcation. Because theoretically there are optimal values for angles and diameters that render an arterial bifurcation more efficient physiologically, the measured data were compared with predicted values. Branch diameters correlated better with predicted values than did branching angles. Twenty-six percent of teta1 and only 7.2% of teta2 angles were within the optimal range; 68.2% of teta1 and 79.7% of testa2 were within 2% of optimal values in temrs of physiologic efficiency. On the average, teta1 angles were smaller than teta2 angles (17.0.degree. vs. 29.5.degree.). Morphologic and hemodynamic peculiarities of vessels and errors in the measuring technique must be considered in analyzing the data obtained. Moreover, branching angle measurements changed slightly with age: teta1 became larger and teta2 narrower. In the cardiovascular system branching angles and branch diameters follow, to some degree, the principles predicted by theory. Brancing angles diverging considerably from those principles may indicate the presence of vasculare disease although a direct connection has not been established.