A stereological method for estimating length density of the arterial vascular system

We developed a stereological method for quantitating length density (Lv; vessel length per unit reference volume) of the arterial system. Accurate estimation of Lv for a sparse system of blood vessels in a three-dimensional specimen requires information on individual vessel orientation. The method we present extracts the necessary information on vessel orientation from profile geometry. Major and minor diameters of elliptical profiles of sectioned tubular structures are used to calculate Lv. The method does not require special sectioning alignment and does not assume a prior distribution of blood vessels; however, the method does assume that arteries are cylindrical. A physical model consisting of boiled spaghetti mixed with agar in a cylinder was used to test the stereological method. Measurements of over 1,000 elliptical profiles in 5 separate trials have demonstrated that the method can accurately estimate Lv with < 5% error even when tortuosity is high, i.e., when anisotrophy coefficient is 1.55. This method may facilitate a better understanding of the mechanisms of artery growth by making it possible to quantify linear growth of the arterial system.