Determination of membrane thickness distribution from orthogonal intercepts

This report deals with the reconstruction of the distribution of membrane thickness T from that of orthogonal intercept length L0, measured in random section planes. In such planes the membrane appears as a band and the linear distance from one of its boundaries perpendicular to the opposite one is the length of the orthogonal intercept. Using a membrane model, an integral equation relating the probability density functions of orthogonal intercept length f(l0) and membrane thickness g(τ) is derived. Relations between moments are derived and the analytic solution to the problem of reconstructing g(τ) from f(l0) is given. The parametric approach by which it is assumed that g(τ) has some known analytic form with unknown parameters is considered, and the use of a suggested analytic form for describing the thickness distribution of the human glomerular basement membrane is discussed.