Estimating the length density of convoluted tubular systems - II: comparative analysis using five different methods.

An artificial convoluted tubular system with precise predefined parameters was created. It was stereologically analyzed in order to preview the potential probability to introduce errors when applied to biological systems like testicular tubes or glomerule like structures. The length of the convoluted tubules more frequently analyzed was estimated by five different methods. The analytical methods were based on both the number of tubule transections, which is related to the transection area and/or organ volume, and the axis length of an ideal cylinder. Tubular systems were analyzed with or without consideration of the transection shape. When shape was considered, two methods were compared: one evaluating the major and minor axes from elliptical profiles, and the other the crosses between parallel lines of a test system superimposed on circular, elliptical, or more complex profiles. Comparison of the five methods revealed different estimations of the length in relation to the pre-determined model, which varied from an 11.8% overestimation to a 39% underestimation. The fractionator method was proposed as alternative to diminish the work overload when counting intersections between lines of test systems and transection profiles. The results with the fractionator are very promising concerning the application of the method in laboratories of pathology.

A simple method for estimating the length density of convoluted tubular systems.

We present a new method for estimating the length density (Lv) of convoluted tubular structures exhibiting an isotropic distribution. Although the traditional equation Lv=2Q/A is used, the parameter Q is obtained by considering the collective perimeters of tubular sections. This measurement is converted to a standard model of the structure, assuming that all cross-sections are approximately circular and have an average perimeter similar to that of actual circular cross-sections observed in the same material. The accuracy of this method was tested in eight experiments using hollow macaroni bent into helical shapes. After measuring the length of the macaroni segments, they were boiled and randomly packed into cylindrical volumes along with an aqueous suspension of gelatin and India ink. The solidified blocks were cut into slices 1.0 cm thick and 33.2 cm2 in area (A). The total perimeter of the macaroni cross-sections so revealed was stereologically estimated using a test system of straight parallel lines. Given Lv and the reference volume, the total length of macaroni in each section could be estimated. Additional corrections were made for the changes induced by boiling, and the off-axis position of the thread used to measure length. No statistical difference was observed between the corrected estimated values and the actual lengths. This technique is useful for estimating the length of capillaries, renal tubules, and seminiferous tubules.