Measurements were made of parent and branch vessel diameters and of the included angles of branch-points from postmortem human coronary arteriograms to determine the usefulness of theoretical equations predicting the relationships between parent and branch vessel caliber and between arterial caliber and branch-angle. The formulas were based on the concept that blood vessel size and arrangement provided for blood flow with minimum energy loss. Size relationships between parent vessel and its branches were determined for 42 left main and 53 other epicardial coronary artery branch-points in hearts with angiographically normal arteries. Left main coronary artery branch-points were studied in 68 hearts with various degrees of angiographically defined coronary artery disease. Measured diameters (D) of parent and branch vessels corresponded well to the theoretical formula: (DParent)3 = (DBranch1)3 + (DBranch2)3....,in angiographically normal coronary arteries. The exponent, on the average, is less with increasing grades of vascular disease for left main coronary artery branch-points. Mean area ratio, the sum of the cross-sectional area of the branches divided by the area of parent vessel, decreased with greater arteriographic disease. Area ratio varies with changes in the relative calibers of branch vessels. Fifty-seven branch-angles were determined by graphic analysis of postmortem biplane coronary arteriograms. No relationship could be found between branch-angle and vessel caliber. The included angle between branches varied from 32 degrees to 124 degrees without respect to relative or absolute vessel calibers. The results of these postmortem measurements on human coronary arteriogram suggest that coronary artery caliber may adjust to minimize energy loss at the branch-point but that branch-angle is determined by other factors. Restudy of arteriograms suggests that branch-angle may be determined by branch vessel destination.
