Label escape theory revisited: the effects of resting periods and section thickness

A mathematical theory is developed for the effects of section thickness and resting periods on "label escape"--that is, the tendency for some bone formation sites to display only one label when a double fluorochrome marker is given. It is demonstrated that when section thickness is greater than the interlabel distance, many double labels will appear to be fused, so that they will be counted as single labels. Thus, thinner sections allow more accurate measurement of labeled surfaces, but it turns out that thicker sections yield a better estimate of apposition rate. It is also shown that if the refilling of BMU resorption cavities is interrupted by resting periods of arbitrary frequency and duration, the number of single labels will be increased in proportion to the total duration of the interruptions. Equations are derived which allow one to predict the magnitude of these effects, and to calculate the average total duration of resting periods during refilling from the ratio of single to double labeled surfaces. When the theory is applied to existing experimental data, it is found that substantial resting periods must be present to explain the amount of excess single label which is usually observed.