Compartmental model of the renal function using parameter identification techniques



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A method which uses compartmental modeling and parameter identification to measure the dysfunction of the renal system indirectly and simply is presented. The method involves the single injection of a labeled tracer into the blood plasma. Blood plasma samples are taken at intervals following the injection and used with a compartmental model of the renal function. The compartmental model is presented for use with a digital computer to permit the routine fitting of data in a least squares sense in order to determine unknown parameters of the model. The unknown parameters are the constants of interchange between the two compartments and the constant of renal excretion. Identifiability of the unknown parameters using data from only one compartment is shown using the transfer function and using the concepts of observability and controllability. A review of parameter estimation techniques is presented, and three parameter identification algorithms are investigated. The three algorithms are: (1) Herbold algorithm for estimating parameters in systems of differential equations; (2) Quasilinearization algorithm for estimating parameters in systems of differential equations; and (3) Powell algorithm for estimating parameters in a multivariable nonlinear regression equation. Total central processing time for parameter identification using any one of the three algorithms is less than three seconds on a CDC 7600.