A method of determining the cross sectional area of muscle fibres

A simple and convenient method is presented of measuring the size, and the variation in size, of muscle fibres cut in cross section. The method is based upon two theorems in geometrical probability. The computing formula is A = Ll where A is the mean cross sectional area of the fibres in the particular muscle, L is the mean value of measurements made across the fibres from the most lateral point on one side to the most lateral point on the other, and l is the mean value of measurements made at random across the fibre (i.e. the mean chord). Both measurements are easily made concurrently, by direct microscopy, using a screw micrometer eyepiece having crossed hair lines.

The standard error is calculated from the various values of L. From a provisional estimate of the standard deviation the optimum number of fibres to measure can be estimated. In normal muscle the mean fibre cross sectional area A can be determined with a relative standard error (RSE) of approximately 2.0% by measuring approximately 250 fibres. Greater accuracy is obtainable by measuring more fibres: the error is halved when the number of measurements is quadrupled.

The variability in size from fibre to fibre is conveniently expressed as the coefficient of variation of A.

Two subsidiary techniques are briefly described. One is an abridged version of the principal method, for use where the standard deviation is not required and precision is not essential. It estimates: mean fibre diameter D = 1.3 l, and mean fibre cross sectional area A = 1.3 l² where l has the same meaning as in the principal method. The other technique, based on point-counting, is suggested for cases where, once again, the standard deviation is irrelevant but an accurate measure of fibre cross sectional area is demanded.