The vascular geometry of human arterial bifurcations

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 (teta 1 and teta 2) 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 per cent of teta 1 and only 7.2% of teta 2 angles were within the optimal range; 68.2% of teta 1 and 79.7% of teta 2 were within 2% of optimal values in terms of physiologic efficiency. On the average, teta 1 angles were smaller than teta 2 angles (17.0 degrees vs. 29.5 degrees). Morphologic and hemodynamic pecularities of vessels and errors in the measuring technique must be considered in analyzing the data obtained. Moreover, branching angle measurements changed slightly with age: teta 1 became larger and teta 2 narrower. In the cardiovascular system branching angles and branch diameters follow, to some degree, the principles predicted by theory. Branching angles diverging considerably from those principles may indicate the presence of vascular disease although a direct connection has not been established.