Study on the methods to test average diameter of tube-like structure in 3D status based on the 2D random section and principle of stereology

If 3-dimensional (3D) tube-like structures being cut randomly, it becomes 2D random profiles, and the diameter from these random profile is not the diameter of the tube-like structure in 3D. So, how to test the average diameter of tube-like structures in 3D status (D-3t) based on 2D random section is what we studied in this paper. The test method was set LIP and the deduced formulas are as following: (1) (D3t) = (root 2 pi .Sigma Lambda t/Sigma Qt) ; (2) (D3t) = (root 2 pi . a . Sigma Pt/Sigma Qt) . In the formulas, A(t), Q(t), and P-t denoted separately the area of profiles, the number of the profiles and the number of test points that hit the profiles in 2D random section, a denoted area for one test point. The methods in this paper could be used to test D3(t) of blood vessels, lymph vessels and cylinder like structure from sections.