A Geometrical Determination of the Extracellular Space in Muscle

Abstract

Fenn 1 and his collaborators have demonstrated that 14.5% of the volume of the freshly excised frog skeletal muscle is unique in that it contains all the chloride of the muscle. This part of the muscle has been called the chloride space and the inference has been drawn that it is identical with the extracellular spaces. The purpose of this note is to add to the existing evidence in favor of this inference a purely geometrical demonstration that the extracellular spaces may well comprise some 15% of the muscle volume.

Consider a muscle, such as the sartorius, made up of parallel cylindrical fibers of diameter D, and let us calculate r, the ratio of the volume of the fiber space to that of the total space. In any thin cross-sectional segment of the muscle r will be given by the ratio of the area of all the fiber cross-sections to that of the entire cross-section. Assuming a regular arrangement of the fibers along the whole length of the muscle, it is clear that r for the whole muscle will be known if the ratio of the areas for any cross-section can be determined. And this can be calculated if some assumptions are made as to the nature of the packing of the fibers.

We may assume two ideal limiting types of packing, A and B (Fig 1.) If the packing is the A-type, the number of fibers per cm² = 1/D², and since the cross-sectional area of a fiber = πD² /4 cm², the total area of the fibers in a cm² of muscle cross-section = π/4 cm². Therefore, r = π/4 = 0.785.