### NEW CONCEPTS AND TEST METHODS OF CURVE PROFILE AREA DENSITY IN SURFACE: ESTIMATION OF AREAL DENSITY ON CURVED SPATIAL SURFACE

#### Abstract

The concepts of curve profile, curve intercept, curve intercept density, curve profile area density, intersection density in containing intersection (or intersection density relied on intersection reference), curve profile intersection density in surface (or curve intercept intersection density relied on intersection of containing curve), and curve profile area density in surface (AS) were defined. AS expressed the amount of curve profile area of Y phase in the unit containing surface area, S(X). The test methods and formulas were deduced, e.g.: AS=ICI /IC=LCI /BC. In the formula, ICI and IC indicated the intersection numbers of test line with curve intercepts (or profiles in 2D) and with the containing curve respectively. BC denoted the length of containing curve, LCI being the length of curve intercepts. The formula means that AS are equal to the curve intercept density and equal to the curve profile intersection density in surface. Issues about AS application and its correction for shrinking tissues were discussed. Example for testing AS was given.

##### Keywords

curve profile area density in surface; curve intercept density; stereology; intersection density relied on intersection reference

DOI: 10.5566/ias.v20.p59-64