Estimating length density and quantifying anisotropy in skeletal muscle capillaries

The accurate estimation of stereological parameters defined on anisotropic structures is a long-standing problem. In this paper we seek to estimate the capillary length density JV in skeletal muscle tissue. A well-known model for directional anisotropy in space, namely the 'spherical normal' or 'Fisher axial distribution' model, is found to fit the relevant data satisfactorily. Based on this model, a short-cut estimation method is proposed and illustrated with a numerical example. This method essentially consists in taking the ratio of mean capillary profile counts, as obtained from transversal and longitudinal sections of the muscle tissue, and making use of a table or a graph given in the paper to estimate JV. The conditions under which the methods are applicable and practicable are discussed in detail. Apart from an accurate estimation of JV, an important feature of our method is the possibility of quantifying the degree of anisotropy by a coefficient K (called the concentration parameter of the Fisher axial distribution), which enjoys both a biological significance and a sound statistical basis.