A model of insulin distribution and uptake in the perfused rat liver

Indicator dilution curves of 51Cr-EDTA and 125I-insulin injected into perfusate entering the rat liver in vivo are used as a basis for developing a mathematical model of insulin distribution and uptake within the organ. EDTA is not taken up by liver cells and therefore serves as a "volume marker" whose dilution curve reflects the characteristics of perfusate flow through the organ and through the cannulae. These two components are modelled separately but the same approach is used in each case, that is, the minimum number of delayed exponential terms sufficient to reproduce the dilution curves is determined and used as the basis for modelling. This allows the cannula, vascular and sinusoidal volumes to be identified and described as corresponding compartmental configurations. The shape of the insulin dilution curve is additionally influenced by binding to, and uptake by, liver cells. Binding of insulin to receptors on hepatocyte plasma membranes and subsequent internalization of the insulin-receptor complex is modelled by the introduction of additional compartments but this is found to be insufficient unless non-specific binding is also taken into account. The accuracy of determination of the rate constants for insulin-receptor dissociation and for endocytosis is improved by a sudden reduction in the pH of the perfusate about 100 sec after injection of the insulin bolus. This releases any residual receptor bound insulin and is modelled by a sudden shift in the insulin-receptor dissociation rate constant. Matching of the complete model to individual pairs of 51Cr-EDTA and 125I-insulin dilution curves allows vascular and sinusoidal volumes to be determined together with the binding and endocytic rate constants. Use of the model to investigate the effect of substances that modify these rate constants is briefly illustrated in the case where the liver is preperfused with 5 mM indomethacin. The model can also be used to simulate the internal distribution and uptake of insulin with any nominated input function and any set of parameters; this is illustrated by comparing the impulse response in the normal case and that in which indomethacin has been preperfused. Although the present study is confined to insulin, the model and methodology that is developed should be applicable to other ligands for which the hepatocyte carries specific receptors.