QUANTITATIVE THEORY OF LIVER-REGENERATION IN THE RAT .2. MATCHING AN IMPROVED MITOTIC INHIBITOR MODEL TO THE DATA

A model of liver regeneration is put forward in which the rate of liver growth is controlled both by a liver-produced mitotic inhibitor and by the availability of parenchymal cells to enter the mitotic cycle. The model can be expressed as a pair of coupled differential equations, the 1st describing the dependence of inhibitor concentration on liver size and inhibitor decay and the 2nd specifying the dependence of liver growth on inhibitor concentration and entry of cells into the mitotic cycle. The model is tested by comparing it solutions to the published data on mitotic indices following partial hepatectomy. For such a comparison, it is necessary to specify the cell-cycle time and the inhibitor dose-response function and half-life. If a negative exponential dose-response function, an inhibitor of half-life of 11.4 h, and a cycle time of 18.25 h are postulated, the solutions match the data of Fabrikant who found that there were 2 waves of mitosis with a period of quiescence between them. The data of Grisham characterized by a single peak of mitosis, is matched by the theory using similar inhibitor properties but a shorter cell-cycle time (13.25 h); this causes the 2 peaks to overlap. In both cases, a better fit is obtained if the 2nd cell cycle is longer than the first by 2-3 h. Cells enter a Go period after mitosis. A mechanism for littoral cell division, which occurs some 24 h after parenchymal cell division, is put forward in which the former cells depend on the enlargement of the latter for the stimulus to divide.