Fractal geometry of arterial coronary bifurcations: a quantitative coronary angiography and intravascular ultrasound analysis

Abstract

Coronary artery bifurcations present a harmonious asymmetric geometry that is fractal in nature. Interventional treatment of bifurcation lesions is a major technical issue. The present study is aimed at a precise quantification of this geometry in the hope of deriving a formulation that would be simple to calculate. Forty seven patients with strictly normal coronarographic results obtained ahead of valve replacement were enrolled, and 27 of these underwent IVUS examination to confirm that their arteries were indeed normal. Three reference diameters were measured: those of the mother vessel (Dm) and of either daughter vessel (Dd1, Dd2). One hundred and seventy-three bifurcations were thus subjected to quantitative analysis. The mean diameter of the mother vessels was 3.33+/-0.94 mm, of the major daughter vessels 2.70+/-0.77 mm, and of the minor daughter vessels 2.23+/-0.68 mm. The ratio R=Dm/(Dd1+Dd2) of mother-vessel diameter to the sum of the two daughter-vessel diameters was 3.39/(2.708+2.236)=0.678. This ratio held at all levels of bifurcation: i.e., whatever diameter the mother vessel. The study confirmed the fractal nature of the geometry of the epicardial coronary artery tree, and gave a simple and accurate fractal ratio between the diameters of the mother and two daughter vessels such that Dm=0.678 (Dd1+Dd2). This makes it easy to calculate the precise diameter of any of the three vessels when those of the other two are known.