Assessment of glomerular filtration rate by means of the four-, and more compartmental closed models after a single intravenous injection.

This is the continuation of our study on the estimation of glomerular filtration rate (GFR) after a single intravenous injection using the closed compartmental model. In our previous study, a three-compartment closed model including blood, periphery and urine was developed to estimate GFR. Although the model developed in our previous study is an improvement of the two-compartment open model currently used in the assessment of GFR, there is a limitation in our previous model and the current two-compartment open model, i.e. these models are suitable for the tracers whose elimination is solely via the renal pathway. However, several tracers used to assess GFR are eliminated via both renal and non-renal pathways, therefore it is also important to develop the models to include the non-renal elimination pathways for these tracers. In the present study, all the possible non-renal elimination pathways were modelled by means of four-, five-, and n-compartment closed models after a single intravenous injection. Although more compartments were included into the modelling, the results show that the inclusion of more non-renal elimination compartments only leads to the increase in the similar analytical solutions for these compartments. Therefore, the equation in our previous study can be used to estimate GFR for the tracers whose elimination is not only via the renal pathway, but also via the non-renal pathway, even via an arbitrary number of the non-renal pathways.