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A model for Rose Bengal transport through the hepatobiliary system has been developed, and non-linear programming techniques have been used to derive the model's parameters according to actual patient data. The model is then further analyzed as a Markov chain. A system of checks and balances, and measure of error, is discussed. The particular advantages of this system of liver model compartmentalization include access to 1) analysis of far less data than needed in classic compartmental analysis techniques, 2) utilization of kinetic parameters of appearance of radioactivity in urine and stool in addition to plasma decay curves, and 3) subclassification of disease status within the category of neonatal obstructive liver disease which has not been heretofore available. The final stochastic model provided results which agreed with physiologic interpretation and actual clinical status from prospective study patients and test data derived from various sources.