Closed-Form Formulas for Estimation of Kinetic Parameters in One- and Two-Compartment Models

Nowadays the most reliable approach to estimate the kinetic parameters is to minimize an objective function which is essentially the distance between the measured data and the model generated pseudo data. Due to the highly non-linear nature of the model, common optimization algorithms usually fail to find the true minimum. A brute-force search method sometimes must be used to find the true minimum. This paper attempts to use the Laplace transform and Z-transform methods to derive closed-form formulas for kinetic parameter estimation problems, which assume oneor two-compartment models. The proposed method is computationally efficient and its solution is unique. When data sampling interval is small, the proposed method is able to accurately estimate the kinetic parameter; when the interval is larger, the proposed method fails to give a meaningful estimate. The one-compartment method is more robust than the two-compartment method.