A mathematical model of the vascular architecture and of the distribution of resistances in the coronary tree

The architecture and resistance distribution of the coronary arteriolar tree downstream 100 mu diameter vessels are still largely unknown, due to technical difficulties in direct visualization. In this study we propose a mathematical model of the architecture and the single vessel resistance distribution of terminal arteriolar vasculature in the beating dog heart, based on the analysis of embolization-induced changes of total coronary resistance. Coronary embolization was performed by injecting several boluses of 15 mu (6 cases) and 25 mu (6 cases) plastic microspheres into the maximally vasodilated (adenosine infusion) left circumflex artery of the open chest dog. The relation between the number of plastic beads progressively injected to embolize 15 mu and 25 mu vessels and the resulting increase in total coronary resistance (occlusion function) was obtained in each experiment. If we consider a binary symmetric vascular tree with i) equal resistance for vessels of the same branching order and ii) optimal ratio between resistance of parent and daughter vessels at all branching sites, the simulation of embolization in such a system shows that the occlusion function of the terminal vessels N in the linear portion between 0 and N/2 occluded vessels has a slope S' which is 5.6 times lower than the slope S" between N/2 and 3/4 N occluded vessels and 3.6 times lower than the S' of the occlusion function of the preterminal vessels. The occlusion function in our experiments has a ratio S"/S' close to that predicted by the model and a ratio between the S' of the 25 mu and that of 15 mu experiments equal to 4.(ABSTRACT TRUNCATED AT 250 WORDS)