The Mathematical Basis of Fiber-Length Analysis from Fibrogram Data

Abstract

Theoretical equations are developed which give the average length and the length distribution of the whole fiber popula tion from the scan of a fibrogram type specimen. The average fiber length is shown to be equal to twice the area under the fibrogram curve plus an offset which is dictated by the amount of fiber loss in the clamp. The length distribution, in terms of coefficient of variation, is shown to be the square root of three times the length at which the centroid of the fibrogram is located divided by the mean length minus 1. Data are presented for comparison of array data mean length and length distribution with mean length and length distribution by instrument using the derived equations. Linear correlation coefficients between the methods were 0.95 for length and 0.86 for distribution.