Relation between zero-stress state and branching order of porcine left coronary arterial tree

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Abstract
The left common coronary arterial trees of eight pig hearts were dissected. The zero-stress state (the state of the organ when the external loads are removed) of the coronary arteries was determined by first cutting the arteries into short, ring-shaped segments perpendicular to the longitudinal axis of the blood vessel and then making a radial cut. This procedure caused the ring to open into a sector whose opening angle (θ), internal and external lengths (circumferences), and wall thickness were measured. Morphometric and θ data were organized in the framework of a diameter-defined Strahler system. We investigated 4 rings from the left common coronary artery (LCCA), 185 from the left anterior descending artery (LAD) and its branches, and 159 from the left circumflex artery (LCX) and its branches. The inner circumferences of the rings ranged over six orders for the LAD arterial tree and five orders for the LCX arterial tree, corresponding to a diameter range of about one order of magnitude for both arteries. θ demonstrates viscoelastic behavior and was measured 30 min after cutting. Our results show that the inner and outer circumference and the wall thickness increase as geometric sequences with the order number. θ is found to decrease linearly toward the smaller orders with a slope of 7.3°/order in the range of the six largest orders. Strain calculations showed that the inner part of the arterial wall is in compression, whereas the outer part of the wall is in tension in the no-load (zero transmural pressure) state. This study provides basic data on the zero-stress state that are necessary for understanding the mechanics of the coronary artery.