Practical presumptions and mathematical problems in estimating the number and size of tumor metastases in experimental oncology are discussed.
The estimations should be based upon microscopic investigation. However, considerable biologic variation necessitates the use of large numbers of experimental animals, which makes the serial sectioning of the organs-applied to other biological materials and thoroughly discussed by earlier workers-impossible in practice.
Therefore, formulae are presented for the calculation of the actual number and total volume of the metastatic corpusclesper unit volume of an organ, from the number and total area of their images in a limited number of sections taken at arbitrary levels through the organ. The influence on the calculations of variations in size and shape of the corpuscles is studied.
The formula for volume was found to hold generally. The estimation for number, which was found to be influenced by the size and the shape of the corpuscles, is further tested on an experimental material of metastases in liver and lungs from a mouse sarcoma. It is concluded that, with the techniques used, the error of the mathematical estimation of the number of metastases is less than 16%. By double determinations it isshown that the statistical error for individual determinations is considerably larger than the maximum error incurred by mathematical estimations.