Cubic spline functions and polynomials for calculation of absorption rate

Abstract

A model-independent method for calculation of the absorption rate based on an exact mathematical solution to the deconvolution problem of systems with linear pharmacokinetics and a polyexponential impulse responses has been examined. Theoretical analysis shows how a noninteracting primary input can be precisely evaluated when data on blood levels from a known source such as an i.v, bolus or zero-order infusion are available. This work compares the use of a Lagrange 3rd degree polynomial with that of a cubic spline function (special 3rd degree polynomial) for calculation of the absorption rate. The method is compared to another using simulated data (12 data points) containing various degrees of random noise. The accuracy of the methods is determined by how well the estimates represent the true values. It was found that the accuracy of the two methods was not significantly different, and that it was of the same order of magnitude as the noise level of the data.