The sectioning of randomly branched filamentous structures

A theorectical analysis is given of the two-dimensional picture observed when a three-dimensional randomly branched fibrous structure is sectioned. The model adopted consists of randomly oriented, interconnected straight rods having either the same length or a defined distribution of lengths. Expressions are derived for the total number of fragments observed and their total apparant length per unit area projected in the plane of the section, together with the distribution function of the projectd lengths. However, the expression derived for the total projected length per unit area, one-fourth πtρl, where t is the section thickness and ρl the fiber length per unit volume in the three-dimensional stucture, is, however, independent of the above model. The theory is discussed in terms of electron microscopy which has been carried out by other workers on agarose gels.