ACCURACY OF NUMERICAL INVERSION OF LAPLACE TRANSFORMS FOR PHARMACOKINETIC PARAMETER-ESTIMATION

Numerical inversion of the Laplace transform is a useful technique for pharmacokinetic modeling and parameter estimation when the model equa tions can be solved in the Laplace domain but the solutions cannot be inverted back to the time domain. The accuracy of numerical inversion of the Laplace transform using an infinite series approximation due to Hosono was systematically studied by reference to 17 widely differing functions having known inverse transforms. The error of inversion was found to be very sensitive to the details of the computer implementat ion of the method; for example, double-precision arithmetic is essenti al. The method used to sum the series in the least-squares program MUL TI(FILT) was often unable to achieve a relative error of less than 10( -4), and a Monte Carlo simulation showed that this method is insuffici ently accurate for reliable least-squares parameter estimation. Improv ements to the algorithm are described whereby a better method of apply ing Euler's transformation is used and the number of terms summed is d etermined automatically by the rate of convergence of the series. The improved algorithm is more efficient in inverting easy functions and m ore reliable in inverting difficult functions, especially those involv ing a time lag. With its use, pharmacokinetic parameter estimation can be performed with essentially the same accuracy as when the function is defined in the time domain.