Histometrical Studies of Liver Cirrhosis by Mathematical Treatments of Linear Intercepts on a Small Number of Random Histological Sections.

Cirrhotic nodules were assumed to be a mixture of ellipsoids of different sizes and eccentricities, and mathematical derivations were discussed to estimate the distribution, the mean and the standard deviation of their sizes with only a small number of random histological sections. Logarithms of the largest axes of nodules approximately formed a normal distribution. With intermediate results, the total nodule volume in an unit volume of the liver and the mean thickness of internodular septa could be estimated. None of the above estimates from 87 autopsy cases of Laennec's cirrhosis of various types revealed discon tinuity in its frequency distribution. Consequently, a classification of liver cirrhosis based on the difference of the above quantities was regarded to be an unsuccessful attempt. Characterization of individual cirrhotic livers with the above estimates was proposed instead of "classification", to ensure unbiased correlations of anatomical properties to other quantities of clinical, functional and etiological implications.