On solving an isotope dilution model for the partition of phenylalanine and tyrosine uptake by the liver of lactating dairy cows

An isotope dilution model for partitioning phenylalanine and tyrosine uptake by the liver of the lactating dairy cow is constructed and solved in the steady state. An original ten-pool model is adopted and solved by cleaving it into two five-pool sub-models, one representing phenylalanine and the other tyrosine. If assumptions are made, model solution permits calculation of the rate of phenylalanine and tyrosine uptake from portal vein and hepatic arterial blood supply, hydroxylation, and synthesis and degradation of constitutive protein. The model requires the measurement of plasma flow rate through the liver in combination with amino acid concentrations and plateau isotopic enrichments in arterial and portal and hepatic vein plasma during a constant infusion of [1-13C]phenylalanine and [2,3,5,6-2H]tyrosine tracers. It also requires estimates of the rate of oxidation and protein export secretion. Analysis of measurement errors in experimental enrichments and infusion rates on model solutions indicated that accurate values of the intracellular and extracellular enrichments are central to minimising errors in the calculated flows. Solving the model by cleaving into two five-pool schemes rather than solving the ten-pool scheme directly is preferred as there appears to be less compounding of errors and the results consistently appear to be more biologically feasible. The model provides a means for assessing the impact of hepatic metabolism on amino acid availability to peripheral tissues such as the mammary gland.