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A MULTISTAGE BIOLOGICALLY BASED MATHEMATICAL MODEL FOR MOUSE LIVER TUMORS INDUCED BY DICHLOROACETIC ACID (DCA) - EXPLORATION OF THE MODEL
Citation:
Rabinowitz, J. R., A B. DeAngelo, M J. Mass, J A. Ross, S Nesnow, M. Schonwalder, J. H. Carter, H. W. Carter, AND R. Richmond. A MULTISTAGE BIOLOGICALLY BASED MATHEMATICAL MODEL FOR MOUSE LIVER TUMORS INDUCED BY DICHLOROACETIC ACID (DCA) - EXPLORATION OF THE MODEL. Presented at AACR, New Orleans, LA, March 26, 2001.
Description:
A biologically based mathematical model for the induction of liver tumors in mice by dichloroacetic acid (DCA) has been developed from histopathologic analysis of the livers of exposed mice. This analysis suggests that following chronic exposure to DCA, carcinomas can arise directly from single initiated cells in the liver as well as within hyperplastic nodules and adenomas. Based on these studies the model for DCA carcinogenesis contains at least 3 precancerous stages and 6 transitions between stages. For each precancerous stage there is a birth rate and a death rate and for each transition there is a transition rate. The PCNA and TUNEL assays were used to obtain birth and death rates for cells in each precancerous stage. A DCA induced transition rate was obtained from experiments determining the mutation frequency induced in the livers of lacI B6C3F1 transgenic mice by DCA. Using these experimentally obtained model parameters and the Kolmogorov backwards equations (with no adjustable parameters) agreement was obtained between the model and the time-to-tumor data for mice exposed to DCA, in their drinking water, for two years. The effect of using a single DCA induced mutation rate for all transitions in the model is examined and the interaction of DCA with other possible perturbations to the individual model parameters is explored. The model has both a two-stage path and a multistage path. Where the DCA induced transition rate is used for all transitions, there is good agreement with the experimental time-to-tumor data, particularly near the conclusion of the experiment. If that transition rate is used for only single transitions while the background mutation rate is used for all other transitions, results are obtained that are 50 -80 % of the experimental values after two years. These results show that increases in the early transition rates are most important. Using the DCA induced transition rate for both transitions in the two-stage path yields a result similar to that seen when only a single transition rate is used. Using the DCA induced transition rate for early transitions in the multistage path yields better results at short times. Using the experimentally determined parameters it is more difficult to obtain agreement with the experimental determination of the number of tumors/animal as a function of time.
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